Exploring the effects of microphysical complexity in ...

E XPLORING THE EFFECTS OF MICROPHYSICAL COMPLEXITY IN NUMERICAL SIMULATIONS OF LIQUID AND MIXED - PHASE CLOUDS

A THESIS SUBMITTED TO T HE U NIVERSITY OF M ANCHESTER FOR THE DEGREE OF

(P H D) IN THE FACULTY OF E NGINEERING AND P HYSICAL S CIENCES DOCTOR OF PHILOSOPHY

2011

C HRISTOPHER D EARDEN

S CHOOL OF E ARTH , ATMOSPHERIC AND E NVIRONMENTAL S CIENCE

2

CONTENTS

List of Figures

7

List of Tables

15

Abstract

17

Lay Abstract

19

Declaration

21

Copyright

23

The Author

25

Acknowledgements

27

1

Introduction

29

1.1

Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

1.2

The importance of the atmospheric aerosol . . . . . . . . . . . . . . . . .

31

1.2.1

Natural sources . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

1.2.2

Anthropogenic sources . . . . . . . . . . . . . . . . . . . . . . .

32

1.2.3

The implications of aerosols for weather and climate . . . . . . .

32

1.3

Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

1.4

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

2

Literature Review

39

2.1

39

Aerosol indirect effects . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

CONTENTS

2.1.1

Liquid clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

2.1.2

Mixed-phase and ice clouds . . . . . . . . . . . . . . . . . . . .

44

Treatments of cloud microphysics in numerical models . . . . . . . . . .

51

2.2.1

Bin versus bulk microphysics . . . . . . . . . . . . . . . . . . .

52

2.2.2

Cloud droplet activation . . . . . . . . . . . . . . . . . . . . . .

53

2.2.3

Ice crystal formation . . . . . . . . . . . . . . . . . . . . . . . .

59

2.3

Summary and recommendations for further study . . . . . . . . . . . . .

65

2.4

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

2.2

3

Methods and Tools

75

3.1

Introducing the Factorial Method . . . . . . . . . . . . . . . . . . . . . .

75

3.2

Modelling capability . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

3.2.1

The ACPIM . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

3.3 4

5

Investigating the simulation of cloud microphysical processes using a 1-D framework

85

4.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85

4.2

Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

4.3

Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

4.3.1

The bulk schemes . . . . . . . . . . . . . . . . . . . . . . . . . .

91

4.3.2

The bin scheme . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

4.3.3

The 1-D driver model . . . . . . . . . . . . . . . . . . . . . . . .

96

4.4

Initial parcel model results . . . . . . . . . . . . . . . . . . . . . . . . .

97

4.5

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

4.6

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Evaluating effects of microphysical complexity with the Factorial Method

105

5.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

5.2

Model configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.2.1

Bin microphysics . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.2.2

Bulk microphysics . . . . . . . . . . . . . . . . . . . . . . . . . 110 4

CONTENTS

5.2.3 5.3

5.4

Driver model configuration . . . . . . . . . . . . . . . . . . . . . 114

Experimental design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 5.3.1

Initial conditions and idealised forcing . . . . . . . . . . . . . . . 115

5.3.2

Experimental design for the Factorial Method . . . . . . . . . . . 117

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 5.4.1

Initial analysis of cloud fields . . . . . . . . . . . . . . . . . . . 120

5.4.2

Comparison of total precipitation . . . . . . . . . . . . . . . . . 124

5.4.3

Factorial analysis: quantifying the effects of CCN, w1 and T (23 design) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

5.4.4

Factorial analysis: the effect of increasing vertical velocity for a fixed temperature (22 design) . . . . . . . . . . . . . . . . . . . . 131

6

5.5

Summary and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 134

5.6

Appendix A: Method of moment-conserving fits . . . . . . . . . . . . . . 137

5.7

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

Ice formation and growth in simulations of a mixed-phase wave cloud

145

6.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

6.2

Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 6.2.1

Microphysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

6.2.2

Representation of bin structure . . . . . . . . . . . . . . . . . . . 152

6.3

Initialisation of the model . . . . . . . . . . . . . . . . . . . . . . . . . . 153

6.4

RF03: Flight details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

6.5

Model results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 6.5.1

Control simulations: The effect of homogeneous freezing . . . . . 158

6.5.2

Comparison of control simulations with observations . . . . . . . 161

6.5.3

The effect of ice crystal density . . . . . . . . . . . . . . . . . . 166

6.5.4

The effect of riming . . . . . . . . . . . . . . . . . . . . . . . . 168

6.5.5

Additional sensitivity tests with the Factorial Method . . . . . . . 171

6.6

Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 176

6.7

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 5

CONTENTS

7

8

Modelling the evolution of wintertime cumulus over the UK

183

7.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

7.2

Model configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

7.3

Meteorological evaluation of the model simulation . . . . . . . . . . . . 185

7.4

Sensitivity to Hallet-Mossop process . . . . . . . . . . . . . . . . . . . . 190

7.5

Treatment of primary ice in the Morrison scheme . . . . . . . . . . . . . 191

7.6

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

7.7

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

Discussion 8.1

199

A summary of the work completed for this thesis . . . . . . . . . . . . . 199 8.1.1

Paper 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

8.1.2

Paper 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

8.1.3

Paper 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

8.1.4

Paper 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

8.2

Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

8.3

Final thoughts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

8.4

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

A Reprint: Investigating the simulation of cloud microphysical processes in numerical models using a 1-D dynamical framework

209

B Reprint: Evaluating the effects of microphysical complexity in idealised simulations of trade wind cumulus using the Factorial Method

Final word count: 45533

6

211

LIST OF FIGURES

2.1

Schematic of the Twomey effect and Albrecht effect, adapted from the IPCC 4th assessment report . . . . . . . . . . . . . . . . . . . . . . . . .

2.2

41

Global mean radiative forcings of climate between 1750 and 2005 as estimated by the current IPCC report [20], grouped into both natural and anthropogenic mechanisms.

2.3

. . . . . . . . . . . . . . . . . . . . . . . .

43

Schematic cross-section of one branch of the Hadley circulation, illustrating the role of trade wind cumuli in the supply of moisture to the ITCZ (adapted from Siebesma [21]). . . . . . . . . . . . . . . . . . . . . . . .

2.4

45

Schematic of the glaciation effect and thermodynamic effect, adapted from the IPCC 4th assessment report . . . . . . . . . . . . . . . . . . . .

48

2.5

Schematic of an orographically induced wave cloud from ICE-L . . . . .

51

2.6

Köhler curve for an ammonium sulphate particle of dry diameter 200 nm, showing the dependency of the equilibrium supersaturation on the wet particle size, and the competition between the Kelvin term and the Raoult term. Adapted from McFiggans et al. [60] . . . . . . . . . . . . . . . . .

3.1

A geometric representation of the Factorial Method based on a

56

23 ex-

perimental design, where the eight simulations placed at the corners of a cube, with each dimension of the cube representing the average effect of a specific factor. Adapted from Montgomery [3]. . . . . . . . . . . . . . 3.2

77

Graphical representation of the main effects A, B and C in the 23 factorial design, along with the corresponding interaction terms AB , AC , BC and

ABC . Adapted from Mongomery [3]. . . . . . . . . . . . . . . . . . . . 78 7

LIST OF FIGURES

3.3

Perspective views of prolate and oblate spheroids that resemble columnar and planar ice crystals, respectively. Adapted from Chen and Lamb [11].

4.1

80

Flowchart illustrating the application of the Factorial Method to assess the importance of cloud-aerosol interactions in the context of a changing meteoroligy with reference to an explicit bin scheme. . . . . . . . . . . .

4.2

A parcel expansion from the ACPIM model, showing aerosol number concentration versus temperature. . . . . . . . . . . . . . . . . . . . . .

4.3

92

98

Parcel expansion with bulk microphysics, showing droplet number concentration versus temperature. The red line corresponds to a resolved treatment of supersaturation for droplet activation; the blue line represents the predicted droplet number when the Twomey approximation is used (i.e. based solely on updraft speed).

4.4

. . . . . . . . . . . . . . . . .

99

Plots from the bulk parcel model with resolved supersaturation. Top: The first moment of the liquid droplet size distribution ( where

= Nc (c + 1)=c ,

Nc is the droplet number concentration), plotted as a function of

temperature of the rising parcel. The first moment is proportional to the sink of water vapour. Bottom: Saturation ratio versus temperature. . . . . 100 4.5

Parcel model output comparing predicted droplet number with resolved treatment of supersaturation for droplet activation (red) with the diagnosed equilibrium supersaturation method for activation (blue).

5.1

. . . . . 102

Vertical velocity fields as a function of time, as applied to the 1-D column equally at every vertical level. . . . . . . . . . . . . . . . . . . . . . . . 116

5.2

Temperature (solid) and dew-point temperature (dashed) profiles in C taken from the RICO model intercomparison, and used to initialise the models. The additional profiles, “RICO-2” and “RICO-5”, are obtained by cooling the RICO profile uniformly in height by 2 C and 5 C respectively under a fixed relative humidity. 8

. . . . . . . . . . . . . . . . . . . 117

LIST OF FIGURES

5.3

Timeseries of liquid water path from the 1-m, 2-m A-R and bin schemes in the absence of precipitation and sedimentation, such that all condensed water stays in the cloud. The results shown were obtained with the following settings:

5.4

w1 =2 ms 1 , T = RICO and CCN = 100/cc. . . . . . . . . 121

Comparison of cloud droplet number concentration (m 3 ), cloud mass mixing ratio (kg kg 1 ) and rain mixing ratio (kg kg 1 ) from the 2-m AR scheme (left) and the bin scheme (right). The results shown are taken from simulations with w1 = 2 ms 1 , T = RICO and CCN = 100/cc. . . . . . 122

5.5

Comparison of cloud liquid water path (left) and rain water path (right) in kgm

2

from the 2-m A-R scheme (dashed) and bin scheme (solid), for

those simulations shown in Fig. 5.4. . . . . . . . . . . . . . . . . . . . . 122 5.6

Time-height plot of the diagnosed shape parameter for rain from the bin scheme, obtained through the method of moment-conserving fits (see Appendix A). The plot shown is from the CCN=50/cc case, with w1 =0.5 ms

1

and T = RICO profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.7

Timeseries of surface precipitation rates (mm/hr) from each scheme. Clockwise from top left: 1-m, 2-m Twomey, bin, 2-m A-R. Results are shown with CCN = 100/cc and T = RICO, for four different values of w1 . . . . . 125

5.8

Timeseries of accumulated surface precipitation (mm) from each scheme. Clockwise from top left: 1-m, 2-m Twomey, bin, 2-m A-R. Results are shown with CCN = 100/cc and T = RICO, for four different values of w1 .

5.9

125

Relative contribution (%) timeseries plots for each scheme, considering the effects of changes in CCN,

w1 and T , plus their combined interac-

tion effects. The relative contribution is calculated as a percentage of the total variance associated with the change in precipitation at the surface. The contributions shown are based on the following changes: 0.5 ms

1

to 2 ms 1 ; CCN from 50/cc to 100/cc, and

w1 from

T from RICO to

RICO-2. Clockwise from top left: 1-m, 2-m Twomey, bin, 2-m A-R. . . . 129 5.10 As for Fig. 5.9 but for an increase in w1 from 2 ms 9

1

to 4 ms 1 .

. . . . . 130

LIST OF FIGURES

5.11 As Figure 5.9 but for the 2-m A-R scheme with modified fallspeed parameter for rain, such that br is increased from the default value of 0.8 to 0.825. All other fallspeed parameters are unchanged. . . . . . . . . . . . 132 5.12 Total effect on suppression of precipitation (in mm) from each scheme as a function of changes in w1 and CCN, under a fixed temperature (T = RICO). Changes in w1 are considered from 0.5 ms

1

up to 4 ms 1 , and the change

in CCN is from 50/cc to 100/cc. . . . . . . . . . . . . . . . . . . . . . . 133 5.13 As Fig. 5.12 but for changes in w1 starting from 2 ms 1 . 6.1

. . . . . . . . . 134

Time-mean UHSAS aerosol size distribution for RF03 (red); the fits to the UHSAS data used to initialise the model (black), and the summation of the two fitted modes (blue). Log-normal parameters for the first fitted mode (black dashed line) are: number concentration = 100 cm 3 ; geometric mean diameter = 0.0911 m; geometric standard deviation = 1.532. For the second mode (black dot-dashed line): number concentration = 1.125 cm 3 ; geometric mean diameter = 0.26 m; geometric standard deviation = 1.768.

6.2

. . . . . . . . . . . . . . . . . . . . . . . . 155

Timeseries of the straight and level runs (based on aircraft time) made by the research aircraft for RF03, corresponding to different heights above sea level through the evolution of the cloud. In-situ observations were taken along each run for the indicated duration. The average temperatures along each straight and level run are also indicated. The labelling system for the straight and level runs is of the form flight number-cloud numberpenetration number, e.g. 3-2-1 corresponds to the first penetration of the second cloud sampled on RF03. . . . . . . . . . . . . . . . . . . . . . . 156

6.3

Vertical velocity fields used to initialise the model relative to the in-situ observations. The vertical velocity is constant with height in the model domain, i.e. applied equally at each model level. Any offsets from the measured values were necessary to avoid discontinuities in parcel streamlines in the model initialisation process. . . . . . . . . . . . . . . . . . . 157 10

LIST OF FIGURES

6.4

Time-height contour plots from 3-2-5, showing on the top row: liquid mass in kg kg

1

(colours) and ice mass in kg kg

1

(contours) for cases

with homogeneous freezing both off and on (heterogeneous freezing is enabled in both cases). Bottom row: the corresponding temperature in degrees celcius (colours), with ice mass contours overlaid. The dashed black line in the plots denotes the closest model level to the aircraft flight track. The same number of ice contours are used (ten) for both sets of model runs, thus they are an indicator of where the majority of the ice mass is contained in each run and does not necessarily represent the same amount of ice in each case. . . . . . . . . . . . . . . . . . . . . . . . . . 159

6.5

As figure 6.4 but for simulations of 3-2-1 (top) and 3-2-7 (bottom)

. . . 160

6.6

Observed ice crystal concentrations (m 3 ) for sizes larger than 125 m compared against those predicted by the model control simulations for the 3-2-5 flight track. The observed concentrations in all cases are taken from measurements using the fast 2D-C probe as discussed in Field et al [8].

6.7

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

Addtional flight level diagnostics for 3-2-5, comparing predicted values from the model with the observations where possible. The observations are in black whilst the model results are in blue (with homogeneous freezing) and red (without homogeneous freezing). From top downwards: ice water content in g m 3 , with observations derived from integrated 2D-C data assuming spherical ice and constant density of 100 kg m 3 ; liquid water content in g m 3 , with observed values from the King liquid water content probe; relative humidity with respect to ice; predicted average aspect ratio of ice crystals from the model; predicted average density of ice crystals from the model (kg m 3 ). . . . . . . . . . . . . . . . . . . . . . 162

6.8

As figure 6.6 but for penetrations 3-2-1 (top) and 3-2-7 (bottom). . . . . 164 11

LIST OF FIGURES

6.9

Comparison of the observed and predicted ice crystal concentrations for penetration 3-2-5, where the predicted concentrations are shown along a trajectory approximately 100 m above the position of the aircraft altitude level. Simulations use prognostic ice density, with both homogeneous freezing off (red) and on (blue).

. . . . . . . . . . . . . . . . . . . . . . 165

6.10 As figure 6.9, but for model simulations with (top): spherical ice crystals and constant bulk ice density of 100 kg m 3 ; (bottom): prognostic ice density but with the deposition density reduced by a factor of two. Both model simulations have homogeneous and heterogeneous freezing enabled. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

6.11 Example images of ice crystals from the CPI probe observed along penetration 3-2-5. a) A sample of ice crystals detected in the liquid cloud region, around 700-900 seconds (air parcel time), showing a few heavily rimed crystals. b) A sample of ice crystals detected in the ice tail region of the cloud (between 1100-1180 seconds) which are less or not affected by riming. Analysis of CPI data for penetrations 3-2-1 and 3-2-3 revealed similar evidence of rimed ice crystals in the liquid cloud region only.

. . 168

6.12 Plots of average rimed mass per ice crystal (kg kg 1 ) from simulations of (a) 3-2-1 and (b) 3-2-5. In each case, the top plot corresponds to simulations with both heterogeneous and homogeneous freezing enabled; the bottom plot shows results from simulations with just heterogeneous nucleation of ice permitted. The black dashed line indicates the position of nearest model level to the flight track. . . . . . . . . . . . . . . . . . . . 170

6.13 Cumulative number concentration of aerosols above a given size threshold, from UHSAS measurements of RF03. The cumulative concentration is plotted in cm

3

for diameters between 0.1 and 1.0 m. . . . . . . . . . 173 12

LIST OF FIGURES

6.14 Timeseries plots from the Factorial Method analysis, showing the average effects of each factor (top) and the effects of interactions between factors (bottom) in terms of the induced change in predicted ice crystal concentration above 125 m along the flight track. The two-factor interactions represent the competition between: homogeneous freezing and the deposition coefficient (AB ), homogeneous freezing and the IN concentration (AC ) and finally the deposition coefficient and IN concentration (BC ). The remaining three-factor interaction (ABC ) represents the dependency of the AB interaction on the value of C . . . . . . . . . . . . . . . . . . . 174 7.1

The domain configuration used for the simulation of the shallow convective cloud on 22nd January 2009 with the WRF model. . . . . . . . . . . 185

7.2

Reflectivity from the Chilbolton radar versus that simulated by the WRF integration for 22nd January 2009. . . . . . . . . . . . . . . . . . . . . . 186

7.3

Simulated reflectivity between 12z and 18z, 22nd January 2009, as calculated at 5 minute intervals. This simulation differs to that shown in figure 7.2 as it uses a fixed droplet number concentration of 150 cm the in-situ measurements.

7.4

3

based on

. . . . . . . . . . . . . . . . . . . . . . . . . 186

Temperature profiles from the WRF model simulation (red) and those from radiosonde data (black) at selected locations. All profiles are taken at 12z on 22nd January 2009.

7.5

. . . . . . . . . . . . . . . . . . . . . . . 188

Meridional cross-sections from model output at 51 N at time 12z. Top: liquid mixing ratios (rain and droplet categories); bottom: ice mixing ratios (snow and graupel categories). Plots are in units of g kg 1 .

7.6

. . . . . 189

WRF modelling results; Top panel: Snow mixing ratio (kg kg 1 ) at 12z and model level 11 (1.42 km) for the simulation with H-M (left) and without (right). Chilbolton location is 51.15 N, 1.45 W. Middle panel: same as top but for snow number concentration (kg 1 ). Bottom: Same as middle but for graupel number concentration (kg 1 ). . . . . . . . . . . . . . 192

7.7

Surface precipitation accumulated between 14:25z and 14:30z for: WRF with H-M (top); WRF without H-M (bottom). . . . . . . . . . . . . . . . 193 13

LIST OF FIGURES

7.8

Instantaneous ice number concentration tendencies (kg

1

timestep 1 ) taken

at model level 17 (2.8 km) at 14z. Top: Tendency from Cooper parameterization when the Cooper scheme is the sole source of primary ice. Middle: Tendency from the droplet freezing parameterization when droplet freezing is the sole source of primary ice. Bottom: Tendency from Cooper parameterization when both the Cooper and droplet freezing schemes are permitted to act together. In all these simulations, the H-M process was disabled. 7.9

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

Cloud top temperature field in C at 13:30z (top) and 14:00z (bottom) from the simulation with just the droplet freezing mechanism active, and H-M off.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

14

LIST OF TABLES

3.1

Design matrix for the general

23 factorial design, illustrating the use of

both the geometric and standard notation systems to distinguish between treatment combinations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1

76

Cloud base droplet number concentration (Nc; /cc), as a function of updraught speed for (top): maritime conditions (c

= 120=cc and k = 0:4),

and (bottom): continental conditions (c = 1000=cc and k

= 0:5). . . . . . 97

5.1

Design matrix for the general 23 factorial design. . . . . . . . . . . . . . 118

5.2

Summary of the factorial design for the bin microphysics. . . . . . . . . . 120

5.3

Summary of the factorial design for the bulk microphysics. . . . . . . . . 120

5.4

Surface precipitation totals (mm) for each scheme as a function of CCN and w1 for three different temperature profiles, namely RICO (top); RICO2 (middle); and RICO-5 (bottom). Those results highlighted in bold type are plotted in Figure 5.7 and Figure 5.8 as timeseries of surface precipitation rate and accumulated surface precipitation respectively. . . . . . . . 126

5.5

Rain evaporation (kgm 2 ; top), accretion (kgm 2 ; middle) and surface precipitation (mm; bottom) accumulated over 2 h from the 2-m A-R scheme, as a function of CCN, w1 and T , and also from the 2-m A-R scheme with increased fallspeed parameter for rain, such that br

= 0:825. The evapo-

ration and accretion terms are calculated by integrating the process rates with height at each timestep, and then integrating these values in time over a 2 h period. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 15

LIST OF TABLES

6.1

Chosen factors and the values assigned to them based on a design.

6.2

23 factorial

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

The experimental design matrix for the 23 design used in this study. The run labels follow the convention of ’standard notation’, whereby the presence of a lower case letter denotes the high value of that factor, and the absence of a lowercase letter indicates the low value of that factor. For example, run ab corresponds to the model simulation where factors A and

B are at the ’high’ level, and C is at the ’low’ level. The label (one) is reserved for the simulation when all three factors are at the low level.

16

. . 172

ABSTRACT

Thesis title: Exploring the effects of microphysical complexity in numerical simulations of liquid and mixed-phase clouds. Submitted by Christopher Dearden to The University of Manchester for the degree of doctor of philosophy (PhD). November 23, 2011 This thesis forms a NERC funded CASE studentship with the Met Office, whose aim is to investigate the treatment of cloud microphysical processes in numerical models, with a particular focus on exploring the impacts and possible benefits of microphysical complexity for the purpose of simulating clouds and precipitation. The issue of complexity is an important one in numerical modelling in order to maintain computational efficiency, particularly in the case of operational models. The latest numerical modelling tools are utilised to perform simulations of cloud types including idealised trade wind cumulus, orographic wave cloud and wintertime shallow convective cloud. Where appropriate, the modelling results are also validated against observations from recent field campaigns. The Factorial Method is employed as the main analysis tool to quantify the effect of microphysical variables in terms of their impact on a chosen metric. Ultimately it is expected that the techniques and results from this thesis will be used to help inform the future development of cloud microphysics schemes for use in both cloud resolving and operational models. This is timely given the current plans to upgrade the microphysics options available for use within the Met Office Unified Model. For an idealised warm cloud, it is shown that different bin microphysics schemes can produce different results, and therefore additional microphysical complexity does not necessarily ensure a more consistent simulation. An intercomparison of bin microphysics schemes in a 1-D column framework is recommended to isolate the origin of the discrepancies. In relation to the mixed-phase wave cloud, model simulations based on an adaptive treatment of ice density and habit struggled to reproduce the observed ice crystal growth rates, highlighting the need for further laboratory work to improve the parameterization of ice growth by diffusion within the sampled temperature regime. The simulations were also found to be largely insensitive to values of the deposition coefficient within the range of 0.1 to 1.0. Results from a mesoscale modelling study of shallow wintertime convection demonstrate the importance of the representation of dynamical factors that control cloud macrostructure, and how this has the potential to overshadow any concerns of microphysical complexity. Collectively, the results of this thesis place emphasis on the need to encourage more synergy between the dynamics and microphysics research communities in order to improve the future performance of numerical models, and to help optimise the balance between model complexity and computational efficiency.

17

18

LAY ABSTRACT

Thesis title: Exploring the effects of microphysical complexity in numerical simulations of liquid and mixed-phase clouds. Submitted by Christopher Dearden to The University of Manchester for the degree of doctor of philosophy (PhD). November 23, 2011 The problem of the Earth’s average surface temperature increasing due to the release of greenhouse gases from fossil fuel burning has been well established over the past few decades. However it is perhaps less well known generally that human activities also lead to an increase in microscopic liquid and solid particles within the atmosphere, that individually are too small to be seen with the naked eye. Such particles, known within the atmospheric science community as atmospheric aerosols, are very important for several reasons including their effects on air quality (and thus human health), visibility, and also their ability to absorb and reflect radiation of different wavelengths. This latter effect can occur through the direct presence of aerosols in the atmosphere, causing a warming or cooling effect, but also indirectly through the ability of aerosols to act as tiny surfaces upon which water vapour can condense to form clouds. Clouds are important in weather and climate not just as a source of precipitation but also, for example, their role in reducing the amount of sunlight that reaches the Earth’s surface, and for trapping heat released from the ground. Changes in the number of aerosols released into the atmosphere due to human activities (e.g. from fossil fuel burning and the burning of vegetation during land clearance) can impact on cloud properties and precipitation in ways that are not yet fully understood. Current estimates from computer simulations of the Earth’s climate suggest that to date, the increase in aerosol numbers due to human activity is likely to have enhanced the ability of clouds to reflect incoming sunlight back out to space. It is believed that this cooling effect has helped to mask the effects of global warming to some degree, although the exact extent remains very poorly quantified. This PhD thesis seeks to increase our understanding of the influence of atmospheric aerosols on clouds by utilising the very latest computer models. We show that even the most detailed simulations representing the effects of aerosols on clouds do not necessarily produce consistent results when compared against each other. For clouds containing both liquid droplets and ice crystals together, the results of our computer simulations show that the ability to represent the number of aerosols above a certain size is important for determining how many ice crystals are formed and the overall structure of the cloud as a whole. Also the ability of the computer model to account for changes in the shape and size of ice crystals as they grow was found to be important too. These results show that in some cases, it is beneficial to be able to represent the effects of aerosols on clouds, although future work is needed to understand why even the most sophisticated simulations can disagree with each other.

19

20

DECLARATION

The University of Manchester PhD by published work Candidate Declaration

Candidate Name: Christopher Dearden

Faculty: Engineering and Physical Sciences

Thesis Title: Exploring the effects of microphysical complexity in numerical simulations of liquid and mixed-phase clouds

Declaration to be completed by the candidate:

I declare that no portion of this work referred to in this thesis has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning.

Signed:

Date: November 23, 2011

21

22

COPYRIGHT

The author of this thesis (including any appendices and/or schedules to this thesis) owns any copyright in it (the "Copyright")1 and s/he has given The University of Manchester the right to use such Copyright for any administrative, promotional, educational and/or teaching purposes. Copies of this thesis, either in full or in extracts, may be made only in accordance with the regulations of the John Rylands University Library of Manchester. Details of these regulations may be obtained from the Librarian. This page must form part of any such copies made. The ownership of any patents, designs, trade marks and any and all other intellectual property rights except for the Copyright (the "Intellectual Property Rights") and any reproductions of copyright works, for example graphs and tables ("Reproductions"), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such Intellectual Property Rights and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property Rights and/or Reproductions. Further information on the conditions under which disclosure, publication and exploitation of this thesis, the Copyright and any Intellectual Property Rights and/or Reproductions described in it may take place is available from the Head of School of Earth, Atmospheric and Environmental Science(or the Vice-President) and the Dean of the Faculty of Engineering and Physical Sciences, for Faculty of Engineering and Physical Sciences candidates. 1 This excludes material already printed in academic journals, for which the copyright belongs to said journal and publisher. Pages for which the author does not own the copyright are numbered differently from the rest of the thesis.

23

24

THE AUTHOR

After graduating from Lancaster University in 2002 with an MPhys degree in Physics, Chris began his career in atmospheric science in January 2003 when he joined the Met Office Hadley Centre for Climate Prediction and Research (now the Hadley Centre for Climate Change). He became a member of the Climate Model Development and Evaluation group, and amongst other responsibilities he became heavily involved in the development of the HadGEM2-AO climate model, the physical model upon which interactive earth system modules would later be coupled as part of the HadGEM2-ES model. The main aim of the HadGEM2-AO project was to substantially reduce model biases inherited from its predecessor HadGEM1. Specifically the biases were associated with mean state tropical sea surface temperatures, as well as the representation of major modes of variability such as the El-Nino Southern Oscillation (ENSO) and the Indian Monsoon. Consequently Chris developed his knowledge of tropical meteorology and became an active member of the ENSO and Monsoon working groups. Following completion of the Met Office Foundation Meteorology programme in the summer of 2003, Chris chose to study part-time for an MSc in Weather, Climate and Modelling through the University of Reading, which he completed in 2006. For his MSc dissertation, Chris conducted an idealised modelling study exploring the relationship between the diabatic heating associated with mesoscale convective systems and their impact on the local atmospheric circulation. The main result of this study identified that errors in the vertical distribution of latent heat release associated with the parameterisation of deep convection could be a contributor to the poor simulation of the ENSO in the HadGEM1 model. It was this work that inspired Chris to learn more about the importance of cloud microphysical processes, resulting in him taking up a PhD studentship at the University of Manchester in 2007.

25

26

ACKNOWLEDGEMENTS

There are a number of people I wish to thank for their help and input during the course of my PhD. Firstly I’d like to say a huge thankyou to Dr. Paul Connolly for being a great supervisor, and for always having the time to provide advice and guidance when I’ve needed it. It’s been a privilege to work with you. Thanks also go to Prof. Tom Choularton and Dr. Paul Field for being invaluable sources of knowledge. To Dr. Ben Shipway and Dr. Adrian Hill of the Met Office - many thanks for countless fruitful discussions on various cloud microphysics related modelling issues over the past few years. I’d also like to acknowledge my fellow scientists, both past and present, in room 3.16 (aka ’The Coal Face’) for making it such an enjoyable place to work. Tea, anyone? There are several members of my family I would like to thank including my Mum and Dad for all their encouragement and support, and specifically my wife Claire for having endless amounts of patience and understanding, particularly during this final year when I have been at my most busiest. Finally, I would like to dedicate this thesis to both Claire and my son Harry, who was born during the early part of my 3rd year.

27

28

CHAPTER

ONE INTRODUCTION “I stood unwound beneath the skies And clouds unbound by laws. The cryin’ rain like a trumpet sang And asked for no applause.” Excerpt from Lay Down Your Weary Tune by Bob Dylan, 1963.

1.1

Motivation

Numerical models designed to simulate the evolution of the Earth’s atmopshere encompass a range of spatial and temporal scales. Collectively, they are the platform from which all forecasts and predictions of future weather and climate are made, from sitespecific ‘nowcasts’ up to several hours ahead, to predictions of global circulation changes over decadal and centennial scales. Of common importance to all such models is the representation of cloud. For instance, the ability of a Numerical Weather Prediction (NWP) model to capture the conditions conducive to cloud formation and its subsequent evolution is key to determining the accuracy of precipitation forecasts and, in particular, extreme weather events [1]. However clouds also have a fundamental effect on the climate of the Earth system, where they play a crucial role in the Earth’s radiation budget: cloud cover, height and reflectivity are all factors that determine the sign and magnitude of the cloud radiative forcing. Formally, cloud radiative forcing is defined by Chen et al [2] as the change in radiative flux at the tropopause in the presence of a cloud relative to clear sky conditions. In general, the associated change in equilibrium surface temperature associated with a given radiative forcing term is specified as: 29

CHAPTER 1. INTRODUCTION

Ts = F where

(1.1.1)

Ts is the change in global mean surface temperature in K, F is the mag-

nitude of the radiative forcing in W m 2 , and

is the climate sensitivity. The climate

sensitivity determines the temperature response of the climate system to a change in radiative forcing. The equilibrium climate sensitivity is defined as the change in global mean annual surface temperature arising from a doubling of CO2 once the system has reached a new equilibrium state. Coupled atmosphere-ocean climate models are used to estimate this quantity; however the models do not produce a consistent answer. The IPCC Intergovernmental Panel on Climate Change [3] states that estimates of the equilibrium climate sensitivity from the current generation of climate models lies in the range from 2.1 K to 4.4 K, with a mean value of 3.2 K. At the heart of this uncertainty is the representation of clouds in current climate models. The low clouds, such as stratocumulus, primarily reflect incoming solar radiation back out to space and thus exert a negative radiative forcing. In contrast, the high clouds e.g. cirrus are primarily transparent to incoming solar radiation yet are able to trap outgoing longwave radiation and so exert a warming effect. Estimates of the net global cloud radiative forcing from satellite data indicate a value of -13 W m

2

[4], and so the overall global

effect of clouds in the present climate is to cool the Earth’s surface. However the response of clouds to increasingly rising temperatures associated with anthropogenic greenhouse gas emission could potentially lead to a change in the global cloud radiative forcing, acting to either amplify or reduce the effects of global warming; this is referred to as the cloud feedback. Thus clouds can be considered to have a pivotal role in determining the extent of future climate change. Indeed the IPCC [3, p. 636] identifies inter-model differences in cloud feedbacks as the primary contributor to the uncertainty surrounding estimates of the climate sensitivity. The ongoing challenge for the weather and climate modelling communities is therefore to identify the minimum level of complexity required for the successful simulation of clouds and precipitation, and to construct appropriate parameterizations to increase model forecast skill and to minimise the uncertainty in climate predictions respectively. To identify the key processes involved, it is necessary to explore the links 30

1.2. THE IMPORTANCE OF THE ATMOSPHERIC AEROSOL

between the cloud microphysics and the resulting cloud macrostructure, and the extent to which the former influences the evolution of the latter. This is a particular challenge, as it involves analysis of data obtained from a combination of in-situ and remote sensing measurements, laboratory experiments and cloud-resolving modelling studies. Essential to each of these approaches is a consideration of the role of the atmospheric aerosol.

1.2

The importance of the atmospheric aerosol

The general definition of the term ’aerosol’ refers to the suspension of particulate matter, either solid or liquid, within a gas. In the atmospheric science community, widespread usage of the term relates specifically to the particulate matter present within the atmosphere and this definition is the one adopted for the purpose of this study. The size range of atmospheric aerosols covers several orders of magnitude, from the nanometre scale to giant aerosol with diameters around 100 m. The existence of atmospheric aerosols can be explained as a consequence of both natural and anthropogenic activity, and can be both organic and inorganic in nature. They are grouped into one of three categories, or modes, according to their size. The nucleation mode describes the smallest aerosols that are produced by gas-to-particle conversion, covering a diameter range between 0.001 - 0.1 m. The nucleation mode is also referred to as the Aitken mode. Such aerosols contribute a very small fraction of the total aerosol mass, in contrast to their number concentration which is relatively high. The accumulation mode refers to those particles between 0.1 1 m diameter that form via coagulation of smaller nucleation mode particles, or those particles that have grown over time into the accumulation mode by condensation. Finally the coarse particle mode refers to the largest aerosols with diameters greater than 1 m. Examples of coarse mode aerosols include mineral dust and volcanic ash.

1.2.1

Natural sources

Examples of naturally occurring inorganic aerosols in the atmosphere include sulphates resulting from the oxidation of sulphur dioxide in the gas phase or in solution. Natural sources of sulphur dioxide include volcanic eruptions, and also marine phyto31


plankton via oxidation of dimethyl sulphide (DMS) [5]. Other natural sources of inorganic aerosols include the oceans, which produce sea-salt aerosol through the bubble-bursting mechanism [6], and also desert regions such as the Sahara where weather systems are responsible for the large-scale lifting and transportation of desert dust into the atmosphere. Organic aerosols form naturally in the atmosphere from biogenic emissions from plants and trees; such gaseous pre-cursors undergo nucleation in the atmosphere to form secondary organic aerosol (SOA) [7].

1.2.2

Anthropogenic sources

The main source of anthropognenic aerosols is from fossil fuel burning, which is responsible for the production of organic compounds emitted as either primary aerosols, or as volatile organic compounds (VOCs) which form SOA particles when they condense in the atmosphere. Fossil fuel burning also contributes around 72% of all sulphur dioxide in the atmosphere [8, p. 153], which then undergoes oxidation to form sulphuric acid and other sulphate aerosol. Biomass burning also contributes to the presence of organic compounds, including black carbon from incomplete combustion, and some inorganics including nitrates and sulphates. Agricultural activities such as harvesting and ploughing are an anthropogenic source of mineral dust, as are industrial practices such as the production and transportation of cement.

1.2.3

The implications of aerosols for weather and climate

The presence of aerosols in the atmosphere is significant for two main reasons. The first relates to the interaction of aerosol with incoming solar radiation, thus exerting a radiative forcing known as the aerosol direct effect which can produce a warming or cooling of the atmosphere depending on the composition and size of the aerosol particle in question [9]. Accumulation mode aerosols have a size range comparable to the wavelength of incoming solar radiation (400 nm - 1 m) and thus typically reflect short wave radiation back out to space via Mie scattering. The net global aerosol direct effect as estimated by the IPCC is -0.50

0.40 W m

2

[8, p. 171]. However not all types of aerosol exert a

negative direct effect. For example, black carbon strongly absorbs incoming solar radia32

1.2. THE IMPORTANCE OF THE ATMOSPHERIC AEROSOL

tion and therefore acts to warm the atmosphere; the direct effect due to black carbon from fossil fuel burning alone is estimated to be +0.2 0.15 W m

2

[8, p. 165].

The second mechanism by which aerosols play a key role in the atmosphere, and of principal importance to this study, is through their ability to lower the energy required for phase transition of water. Water soluble aerosols act as nucleation sites more commonly referred to as condensation nuclei (CN), which provide suitable surfaces upon which water vapour can condense. Those aerosol which readily activate to form cloud droplets in the atmosphere are known as Cloud Condensation Nuclei (CCN). Such activation occurs in conditions when the atmosphere is supersaturated with respect to water, i.e. when the amount of water vapour present in air is above the level of water saturation for a given temperature (above 100% relative humidity with respect to water). The ability of aerosol to initiate the formation of a cloud particle, whether in the liquid or ice phase, is an example of heterogeneous nucleation. Due to the ubiquity of CCN in the atmosphere and the short timescales upon which condensation occurs, atmospheric supersaturations with respect to water rarely exceed 1% [6], the exception being inside the updraught cores of convective clouds. Indeed, supersaturations of several hundred percent are required for water vapour molecules to nucleate homogeneously [6] and so liquid cloud droplets in the atmosphere must form exclusively via heterogeneous nucleation. Supersaturations with respect to ice, typically characterised by the existence of droplets in the liquid phase below 0 C, are much more common in the atmosphere. At temperatures below 0 C, the saturation vapour pressure over ice is lower than that over liquid water [6]; however the effects of surface tension of the liquid droplets must first be overcome in order for the phase transition from the metastable state to the stable state to occur. Homogeneous freezing of liquid water occurs around -35 C and below, and this mechanism can be an important source of ice in cirrus clouds [10]. However clouds are also found to glaciate at temperatures greater than the homogeneous freezing threshold, and for this to happen a proportion of the aerosol population must act as ice-forming nuclei (IN). Insoluble aerosols, which tend to make poor CCN, have the ability to initiate the onset of the ice phase heterogeneously. Number concentrations of IN are much less than those of CCN in the atmosphere (typically 1 in 105 ) [6] and are typically measured in 33


terms of number per litre as opposed to per cubic centimetre, although the concentration of active IN is generally found to increase with decreasing temperature [6]. Thus aerosol indirect effects are not solely confined to the liquid phase. The role of the atmospheric aerosol in modulating the number and size of cloud particles is believed to be important in determining the way clouds interact with radiation [11], and there are also suggestions that aerosols may affect cloud lifetime by modifying the efficiency of precipiation development [12, 13]. The potential for aerosols to interact with and therefore modulate the properties of clouds and precipitation are commonly known as aerosol indirect effects. Such effects could have significant implications both on the local and global scales; however considerable uncertainty exists in terms of quantifying the magnitude of the indirect effect [8]. It should be noted that aerosols can also impact upon clouds via another mechanism that is distinct from the indirect effect, namely the semi-direct effect [14]. This arises as a consequence of those aerosols such as black carbon which are effective at absorbing short-wave radiation. The resulting localised warming effect acts to reduce the ambient relative humidity and increase evaporation of cloud. While the potential significance of the semi-direct effect is recognised, it will not be considered any further in this study.

1.3

Thesis Overview

The importance of aerosol effects on cloud from both a weather and climate perspective are poorly quantified and consequently the level to which aerosol-cloud interactions should be represented in numerical models remains unidentified. The general aim of this thesis is therfore to explore the extent to which the simulation of cloud macrophysical properties in numerical models is influenced by the choices and assumptions that govern the treatment of cloud microphysical processes. It is the intention that the outcomes of this study will ultimately help contribute to an improved representation of aerosol-cloud interactions in numerical models. This thesis is presented in the alternate format as permitted by and consistent with The University of Manchester thesis submission guidelines, and is organised as follows. Chapter 2 forms the basis of a literature review concerning the level of current understanding regarding aerosol effects on cloud, with a particular focus on developments within the 34

1.4. REFERENCES

past decade. The review begins by adopting a regime-based approach to identify specific cloud types upon which the remainder of the thesis should focus. The literature review also summarises our present knowledge concerning the representation of cloud microphysical processes across the spectrum of numerical models, and concludes with specific recommendations for further study. Chapter 3 then introduces the modelling tools and techniques that are to be utilised in the remainder of the work in order to address the open issues identified at the end of the literature review. Chapter 4 marks the first of three lead-author papers presented in this thesis and describes the methodology for isolating and quantifying the effects of microphysical complexity on different cloud types using the tools introduced in chapter 3. This paper also includes some results from parcel model simulations which compare the behaviour of different numerical treatments of droplet number concentration in microphysics schemes. The second paper, forming chapter 5, contains the main set of results from the application of the method presented in the previous paper to the case of an idealised warm cloud within a one dimensional kinemtic framework. The same techniques and methods are extended to a consideration of the mixed-phase in chapter 6, by performing simulations of orographic wave clouds from a recent field campaign where the model results are also validated against the available in-situ measurements. The final piece of original work is presented in chapter 7, written as a co-authorship contribution to a paper prepared with colleagues at the University of Manchester and shows results from a mesoscale modelling study designed to identify the key factors influencing the simulation of a wintertime mixed-phase shallow convective cloud. The thesis concludes in chapter 8, which discusses and summarises the key findings from the work as a whole whilst highlighting those results that are worthy of future investigation.

1.4

References

[1] B. W. Golding, P. Clark, and B. May, “The Boscastle flood: Meteorological analysis of the conditions leading to flooding on 16th August 2004”, Weather. 60, 230– 235. (2005).

35


[2] T. Chen, W. B. Rossow, and Y. C. Zhang, “Radiative effects of cloud-type variations”, Journal of Climate. 13, 264–286. (2000). [3] D.A. Randall et al. “Climate Models and Their Evaluation.” In: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Ed. by S. Solomon et al. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA., 2007. [4] V. Ramanathan et al., “Cloud-radiative forcing and climate - results from the Earth Radiation Budget Experiment”, Science. 243, 57–63. (1989). [5] M. O. Andreae, “Ocean-atmosphere interactions in the global biogeochemical sulfur cycle.”, Marine Chemistry. 30. (1990). [6] H. R. Pruppacher and J. D. Klett. Microphysics of Clouds and Precipitation. Kluwer Academic Publishers., 1997. [7] F. Fehsenfeld et al., “Emissions of volatile organic compounds from vegetation and the implications for atmospheric chemistry”, Global Biogeochemical Cycles. 6, 389–430. (1992). [8] P. Forster et al. “Changes in Atmospheric Constituents and in Radiative Forcing.” In: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Ed. by S. Solomon et al. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA., 2007. [9] J. Haywood and O. Boucher, “Estimates of the direct and indirect radiative forcing due to tropospheric aerosols: A review”, Reviews of Geophysics. 38, 513–543. (2000). [10] K. Sassen and G. C. Dodd, “Homogeneous nucleation rate for highly supercooled cirrus cloud droplets”, Journal of the Atmospheric Sciences. 45, 1357–1369. (1988). [11] S. A. Twomey, “The influence of pollution on shortwave albedo of clouds”, Journal of the Atmospheric Sciences. 34, 1149–1152. (1977).

36

1.4. REFERENCES

[12] B. A. Albrecht, “Aerosols, cloud microphysics, and fractional cloudiness”, Science. 245, 1227–1230. (1989). [13] U. Lohmann, “A glaciation indirect aerosol effect caused by soot aerosols”, Geophysical Research Letters. 29, 4. (2002). [14] H. Grassl. “Possible changes of planetary albedo due to aerosol particles.” In: Man’s Impact on Climate. Elsevier: New York, 1979.

37

38

CHAPTER

TWO LITERATURE REVIEW

2.1

Aerosol indirect effects

The first section of this chapter is concerned with establishing the extent of current knowledge surrounding aerosol effects on cloud (also known as ’aerosol indirect effects’, or ’aerosol-cloud interactions’) from both an observational and modelling perspective, with the aim of exposing those specific cloud regimes that would benefit from further study. Stevens and Feingold [1] argue that in order to further our understanding of aerosolcloud interactions within the Earth’s atmopshere, it is necessary to adopt a systematic regime-based method such that indirect effects are considered as a function of cloud type. Such a philosophy is adopted in the review presented here, beginning with the liquid phase.

2.1.1

Liquid clouds

The 1st indirect effect, also known as the cloud albedo or Twomey effect [2], manifests itself as an increase in the cloud albedo caused by an increase in CCN concentration, whilst the cloud liquid water content is held constant. The increase in CCN acts to increase the overall number of cloud droplets, but reduce mean cloud droplet size. This leads to an increase in surface area of the water droplets in the cloud, thus allowing more incoming solar radiation to be reflected back out to space for all but the thickest clouds. Such increases in droplet number due to anthropogenic emissions of aerosol are supported by observational studies of Warner and Twomey [3], who noted that biomass burning 39

CHAPTER 2. LITERATURE REVIEW

aerosols from sugar cane fires in Queensland, Australia, increased droplet number concentrations downwind of the fire. A similar result was obtained in the study of Rosenfeld [4], who observed that smoke rich in CCN from forest fires reduced overall cloud droplet sizes. A study of marine boundary layer clouds by Coakley et al [5] based on satellite data provided observational evidence for the increase in reflectivity of such clouds due to pollution from ship stack exhausts. A hypothesis proposed by Charlson, Lovelock, Andreae and Warren (more commonly known as the CLAW hypothesis, [6]) built on the idea of the Twomey effect by proposing a natural biological mechanism by which DMS emissions from marine phytoplankton may have a negative feedback on global temperature, whereby DMS is oxidized to sulphate aerosols thus increasing the CCN concentration over the oceans. As a consequence of the Twomey effect, a 2nd indirect effect was later put forward by Albrecht [7], also occasionally referred to as the cloud lifetime effect or Albrecht effect. In this paper, it was hypothesised that the more numerous but smaller cloud droplets arising from the Twomey effect could act to reduce the efficiency of coalescence, suppressing the rate of growth of cloud droplets to raindrop size and leading to a reduction in precipitation efficiency. As a result the cloud liquid water path would increase and the cloud could persist for longer. The schematic in Figure 2.1 illustrates the current conceptual understanding of both the cloud albedo effect and the cloud lifetime effect. It is worthy of note that the 2nd indirect effect was originally proposed in the context of one particular regime, specifically sub-tropical marine boundary layer clouds.

The realisation that increasing CCN concentrations within maritime boundary layer clouds can modulate cloud albedo (and possibly cloud lifetime and/or precipitation efficiency) has led to the idea of a potential geoengineering solution to the problem of anthropogenic climate change. A number of geoengineering projects based around the deliberate injection of aerosols into the atmosphere have been proposed in recent years with the intention of manipulating the Earth’s climate on a global scale [8–10]. One idea in particular relates specifically to liquid-only clouds [10], with the premise that the 1st indirect effect, and possibly the 2nd indirect effect as well, could be exploited to regulate the earth’s temperature via anthropogenic modification of the droplet size distribution in marine stratiform clouds. This would be achieved by spraying seawater into the atmo40

2.1. AEROSOL INDIRECT EFFECTS

Figure 2.1: Schematic of the Twomey effect and Albrecht effect, adapted from the IPCC 4th assessment report

sphere to create extra sea-salt aerosol. However as with the other geoengineering ideas, our understanding of the potential global consequences of such a deliberate intervention is far from complete, and it is clear that more research is needed before any such approach can become a viable option. For instance, it is known that existing observations are not always consistent with the conceptual understanding of warm cloud indirect effects, particularly in relation to the Albrecht effect. Although the suppression of drizzle due to anthropogenic aerosol emission has been observed in the influence of ship tracks on marine stratus cloud off the Washington coast [11] and also from analysis of polluted clouds versus clean clouds off the west coast of Canada [12], observational evidence for the increase in cloud liquid water is less conclusive. Radke et al [13] used aircraft observations to compare ship track clouds with surrounding clouds and found higher liquid water contents in the ship tracks relative to surrounding clouds, upholding Albrecht’s hypothesis. However more recent studies of ship tracks reveal a decrease in liquid water content of such clouds relative to clean clouds [14, 15]. A possible explanation for the reduced cloud liquid water in these cases is that evaporation of smaller droplets increases entrainment rates of environmental air into the cloud. Modelling studies of shallow cumulus [16] have identified such an evaporation-entrainment feedback mechanism which acts to dilute polluted cumulus clouds, with the consequence that overall cloud lifetimes are not statistically different from clean clouds and in some cases the lifetime of individual 41


polluted clouds may even be less than those of clean clouds. This highlights the complex nature of aerosol interactions with warm clouds, and how the specifics of the local environmental conditions may also play an important role.

To date, only indirect effects pertaining to liquid clouds have typically been included in climate models. The first climate models (also known as General Circulation Models, or GCMs) to consider aerosol-cloud interactions did so by using sulphate aerosols as a surrogate for all anthropogenic aerosols, allowing for an estimate of the Twomey effect. This was typically achieved via schemes based on an empirical diagnostic relationship expressing cloud droplet number as a function of the aerosol mass or concentration [17, 18]; such relationships were not necessarily limited to a consideration of sub-tropical marine boundary layer clouds. A weakness of such schemes is that the droplet number concentration is independent of the magnitude of the vertical velocity, a quantity which is important in determining the number of aerosols that activate to form cloud droplets. Later schemes would take the variation in vertical velocity into account when diagnosing the concentration of cloud droplets [19], although the magnitudes of the grid-scale vertical velocity as resolved by the relatively coarse model grid (typically 100km in GCMs) are too small compared to those associated with cloudy updraughts. Models with horizontal resolutions greater than a few kilometres also require an additional cumulus parameterization, as such models do not have sufficient resolution to explicitly resolve the convective motions through the dynamics. In the case of climate models, convection needs to be parameterized since convective activity occurs on scales smaller than the model grid can support. Convection schemes have historically contained little in the way of microphysical detail, as they were designed originally to represent the dynamics of convection as a means of transporting heat and moisture vertically through the atmosphere. In addition, current GCMs also do not adopt a consistent treatment of aerosols, with some models including more aerosol species than others, while some models represent aerosols as internal mixtures and others externally [20, p. 174]. With these issues and limitations in mind, the IPCC 4th assessment report [20] presents a median value for the Twomey effect of -0.7 W m 2 , with an uncertainty range of -0.3 W m confidence level (see Figure. 2.2). 42

2

to -1.8 W m

2

at the 90%


Figure 2.2: Global mean radiative forcings of climate between 1750 and 2005 as estimated by the current IPCC report [20], grouped into both natural and anthropogenic mechanisms.

The enforced reliance on convection schemes in GCMs is a barrier to capturing aerosol effects on convective cloud. Warm convective cloud is ubiquitous in the sub-tropical oceans and is more commonly referred to as trade wind cumulus. These clouds play a crucial role in mixing moisture away from the surface where it is subsequently detrained into the cloud layer and transported to the deep tropics by the trade winds to the Inter Tropical Convegence Zone (ITCZ) to fuel deep convection ([21]; see Figure 2.3). Their role in the hydrological cycle means that potential modification of the precipitation efficiency of trade wind cumulus through changing aerosol concentrations (and therefore modification of the influx of moisture to the deep tropics) could have significant climatological consequences [22]. Thus there is a need to explore the susceptibility of the microphysics of warm shallow convection to changes in aerosol loadings. Likewise coastal stratocumulus clouds are also poorly represented in GCMs, where errors often manifest themselves in the form of a sea-surface temperature (SST) bias in the South East Pacific region [23, 43


24], which in turn can contribute to deficiencies in the simulation of the El-Nino Southern Oscillation (ENSO). The poor representation of these expansive cloud decks arises due to a lack of understanding of the coupling mechanisms between the ocean, atmosphere and particularly the cloud microphysical processes that are believed to sustain them. It is also worthy of note that marine boundary layer clouds have recently been identified as the key contributor to the large uncertainties in estimates of cloud feedbacks in climate models [25]. While such uncertainties exist it is difficult to justify the use of climate models as a tool to conduct detailed studies of the susceptibility of these cloud types to the effects of changes in aerosol properties. Thus there is a need to improve our understanding of these warm cloud regimes such that ultimately their representation in NWP and global climate models can be improved. This can be achieved through dedicated cloud modelling studies combined with observations from field campagins. Examples of recent field projects include RICO (Rain In shallow Cumulus over the Ocean; [26] and VOCALS-REx (VAMOS-Ocean-Cloud-Atmosphere-Land-Study - Regional Experiment; [27]) which have strived to improve our understanding of the microphysical processes that control the macrostructure of marine boundary layer clouds and their role in regional and global climate. The data collected from these campaigns provides a useful constraint for cloud models, the results from which can be used to conduct more detailed studies of the relevant microphysical processes [22, 28, 29].

2.1.2

Mixed-phase and ice clouds

Indirect effects for clouds involving the ice phase are even more uncertain than those involving liquid-only clouds. One of the main difficulties in evaluating indirect effects on cold clouds is that ice crystal concentrations are not always a good indicator of active IN concentrations, and consequently the effects of IN on cold clouds are generally not yet represented in GCMs. Indeed, it is not uncommon for observations of ice crystal concentrations to far exceed the concentration of IN [30]. There are several possible reasons for this, which are now discussed. The first is that heterogeneous ice nucleation is not the only process which can lead to an increase in ice number concentrations. For example at relatively high temperatures (between -3 C and -8 C to be precise), Hallett & Mossop [31] 44


Figure 2.3: Schematic cross-section of one branch of the Hadley circulation, illustrating the role of trade wind cumuli in the supply of moisture to the ITCZ (adapted from Siebesma [21]).

identified that secondary ice production can occur during the riming process (the accretion of liquid drops onto existing ice crystals). Different mechanisms have been proposed to explain this phenomenon. Experiments by Choularton et al [32] suggested that at this temperature the freezing of supercooled droplets upon contact with the ice surface occurs from the oustide-in, resulting initially in the formation of an ice shell around the surface of the droplet which can shatter when the liquid within freezes and expands. Griggs and Choularton [33] later observed that liquid from within the freezing droplet can be ejected at the point of fracture, freezing rapidly to form a ’spicule’ of ice. It was hypothesised that the formation of the spicule is likely to result in small fragments of ice being ejected from the edges of the fractured shell. An alternative mechanism was later proposed by Dong and Hallett [34], who suggested that shattering and hence fragmentation of ice can also occur as a result of thermal stress arising from temperature gradients within the droplet during the freezing process. At temperatures below -35 C, homogeneous freezing (that is, the freezing of liquid droplets in the absence of IN) can also be an important source of ice crystals. Secondly, and perhaps most importantly, in-situ measurements of ice crystal concentrations have been known to suffer from the issue of shattering, whereby the inlets and/or tips of instrument probes act as a physical barrier upon which ice crystals can 45


collide and break into numerous smaller particles, which then enter the sampling region leading to overestimates of the true ice crystal concentration by as much as an order of magnitude or more [35, 36]. To tackle the problem, techniques have been devised which attempt to correct in-situ data contaminated by shattering artefacts (e.g. based on filtering of particle interarrival times as described in Field et al [37]). The recent study by Korolev et al [38] has also shown that it is possible to modify the design of probe inlets and tips on aircraft instruments in order to vastly reduce fragmentation of ice crystals. It is worthy of note that in-situ measurements are less susceptible to contamination by shattering effects in clouds that have a narrow size distribution of ice crystals (for example lee wave clouds; see [39]), and consequently such clouds make particularly useful subjects for studying the relationship between IN and ice crystal concentrations.

Despite the difficulties in quantifying concentrations of active IN, a consideration of deep convection has led to the identification of some potentially important mechanisms by which aerosols could influence the microphysics of such clouds. In-situ measurements documented by Rosenfeld [4] and Rosenfeld & Woodley [40] suggest that the effect of anthropogenic aerosols on cloud droplet size acts to suppress precipitation in deep convective clouds, and delay the onset of freezing. This observational result was supported by a cloud-resolving modelling study [41] which showed that supercooled droplets could be simulated at -37.5 C, but only if the cloud droplets were small and numerous. When the droplets reach a temperature of -37.5 C and freeze homogeneously, the associated latent heat release would result in a thermodynamic effect, providing the convective updraught with more energy and allowing for greater cloud top heights than in a clean cloud [42]. More recently, cloud-resolving model studies have suggested the possible existence of an optimal number of cloud droplets, responsible for the greatest cloud top heights in deep convective storms [43]. The optimal number ensures a peak in supercooled liquid water content, which maximises the amount of latent heat released upon freezing. Lohmann and Feichter [44] comment that the thermodynamic effect manifests itself as a delay in the onset of freezing caused by smaller but more numerous cloud droplets. However, as discussed by Connolly [45], it is perhaps more accurate to describe the thermodynamic effect in terms of the rate of change of glaciation induced by the change in droplet size. 46


For a fixed number of freezing nuclei, the Twomey effect would result in a reduction in the number of freezing nuclei per drop, meaning less water mass would freeze per second. Thus the onset of freezing is not affected; however the rate of glaciation is. Another indirect effect in relation to mixed-phase clouds is the glaciation effect [44], whereby an increase in IN concentration is believed to produce an increase in precipitation efficiency. The glaciation effect was first proposed based on the results of a GCM study [46], which parameterised the effects of hydrophillic soot aerosols acting as IN based on laboratory measurements [47]. The parameterization represents heterogeneous freezing of supercooled cloud droplets upon contact with soot particles in the temperature range 0 C to -35 C. Via this mechanism, the increase in available IN from pre-industrial times to the present day was found to produce a positive radiative forcing and an increase in precipitation via the ice phase. This is thought to be made possible via the WegenerBergeron-Findeisen (WBF) process, which allows ice particles to grow at the expense of cloud droplets by virtue of the saturation vapour pressure over ice being less than that over water. The result is a reduction in cloud cover and cloud optical depth, meaning an increase in solar radiation flux at the top of the atmosphere. Through this mechanism, the glaciation effect has the potential to at least partly offset the cloud lifetime effect. Both the glaciation and thermodynamic effects are illustrated schematically in Figure. 2.4. It is important to recognise that the extent to which precipitation is modified in a mixed-phase cloud due to an increase in IN concentration is likely to depend strongly on cloud type. For instance, a study of Arctic boundary layer clouds [48] showed that the effect of an increase in IN concentration via entrainment of polluted air from above the inversion can lead to complete glaciation of the cloud, resulting in high concentrations of ice crystals which are individually too small for sedimentation and collision processes to be effective. In such cases the result is an increase in both the residence time of ice particles and the total cloud water path, in contrast to the general conceptual understanding of the glaciation effect presented in the majority of the literature. Also recent simulations of deep mixed-phase frontal cloud over the UK suggest that while ice crystal concentrations are sensitive to IN concentration in such clouds, the effect on precipitation is much more subtle such that the amount of precipitation produced only has a weak dependence on 47


Figure 2.4: Schematic of the glaciation effect and thermodynamic effect, adapted from the IPCC 4th assessment report

IN concentration, the main impact being on the spatial distribution of precipitation [49]. Similarly in the case of cirrus clouds, where homogeneous freezing must also be taken into account, the effect of an increase in IN concentration is again non-trivial. It has been suggested that an increase in IN concentration could potentially lead to fewer and larger ice crystals in cirrus clouds due to competition between homogeneous and heterogeneous ice nucleation mechanisms1 , thus increasing sedimentation and potentially resulting in a shorter cloud lifetime [50]. Since cirrus are believed to warm the Earth, any mechanism which acts to reduce the lifetime of cirrus would therefore reduce their net warming effect. These results serve as a good example of how the effects of changes in IN concentrations can potentially manifest themselves in different ways according to the type of cloud in question. Lohmann and Feichter [44] suggest an additional potential indirect effect on mixedphase clouds, referred to as the riming effect. For a given supercooled liquid water content, both riming and precipitation rates may be reduced due to the effect of an increase in CCN concentration. This has been observed in mid-latitude orographic wave clouds [51]. The reduction in mean droplet diameter due to the increased CCN concentration is believed to reduce the efficiency of droplet accretion onto existing ice crystals. The 1 Both homogeneous and heterogeneous nucleation of ice crystals are discussed in more detail later in this chapter in section 2.2.3. The idea of competition between homogeneous and heterogeneous nucleation mechanisms is explored further in chapter 6 in the context of a mixed-phase orographic wave cloud.

48


idea that cloud droplet size may impact on riming rates is explored in chapter 6 using a detailed cloud resolving model to simulate the growth of ice crystals in an orographic wave cloud. It is interesting to note that GCM simulations examining the climatic effect of smaller cloud droplets on the riming process in stratiform mixed-phase clouds [52] do not support a reduction in snowfall rate, but actually suggest the opposite. This is because of feedbacks in the climate system such that the effect of the anthropogenic aerosols acts to increase cloud optical depth, which reduces the amount of solar radiation reaching the surface, thus cooling the atmosphere below cloud base and producing conditions preferable for the growth of ice-phase precipitation. Given that this is a single GCM study, where feedbacks in the climate system are known to be particularly uncertain, the realism of this result is open to debate and thus the potential global significance of a riming effect remain unknown. It is important to clarify that of all the potential indirect effects discussed in the current chapter, the IPCC only recognises the cloud albedo effect as a true radiative forcing. The IPCC AR4 defines radiative forcing as: ’The change in net (down minus up) irradiance (solar plus longwave; in W m 2 ) at the tropopause after allowing stratospheric temperatures to readjust to radiative equilibrium, but with surface and tropospheric temperatures and state held fixed at the unperturbed values’. With the exception of the cloud albedo effect, the indirect effects presented in this review act to modify liquid and/or ice water content, and so exert a feedback on the hydrological cycle which acts to perturb the original state of the climate sytem. Consequently, by definition the IPCC only includes the cloud albedo effect when considering the contribution of the indirect effect to the global mean radiative forcing of climate (see Figure. 2.2). However the importance of other aerosol effects on cloud is recognised in the statement that ’feedbacks due to cloud lifetime, semi-direct or aerosol-ice cloud effects can either enhance or reduce the Twomey effect’ [20]. To improve our understanding of the effects of aerosols across the range of different mixed-phase cloud types, in recent years field projects such as APPRAISE (Aerosol Propertes, PRocesses And InfluenceS on the Earth’s climate) and ICE-L (Ice in Clouds Experiment - Layer clouds) have strived to increase our knowledge through a combination 49


of in-situ measurements, laboratory studies and cloud modelling. The ICE-L project in particular focussed on measurements of lenticular wave clouds, with the specific aim of understanding ice particle number concentrations in relation to the physical and chemical properties of the aerosol entering the cloud. Such wave clouds can occur under stable conditions in regions of steep orography, for example when air is advected over a mountain range (see Figure 2.5); as air parcels are forced to rise, the vertical displacement produces an oscillation with a frequency that is dependent upon the stability of the environmental air. The wave clouds form at the crest of the waves as a result of adiabatic cooling, and appear stationary with reference to the obstruction that leads to their formation. Such clouds can generally be treated in isolation due to their relatively small physical dimensions; they are typically associated with laminar flows and minimal turbulent mixing, allowing them to persist beyond an hour in an approximate steady state. Such characteristics mean that wave clouds act as natural laboratories for investigating ice nucleation mechanisms; furthermore as noted earlier, in-situ measurements of ice crystal concentrations in lee wave clouds are much less prone to shattering effects. A consideration of wave clouds across a range of temperatures, humidities, and vertical wind speeds therefore provides an excellent constraint for cloud modelling studies whose aim is to explore the effects of heterogeneous ice nucleation. It is for these reasons that ICE-L wave clouds are chosen as the subject of the numerical modelling study presented in chapter 6 of this thesis. The APPRAISE-CLOUDS project had a wider scope and considered a variety of mixed-phase clouds over the UK, including cumulus, altocumulus and nimbostratus, providing in-situ observations of aerosol and cloud particle size distributions which can be used to understand the dominant mechanisms of ice formation and growth within the cloud. Such in-situ measurements can then be combined with modelling case studies to isolate the potential importance of specific microphysical processes in terms of the evolution of the cloud and the potential impacts on precipitation. Indeed an APPRAISE case study is simulated in chapter 7 using a mesoscale model to explore the role of both primary and secondary ice formation in the evolution of a wintertime cumulus cloud, the in-situ measurements from which show ice crystal concentrations consistent with the Hallet-Mossop process.

50

2.2. TREATMENTS OF CLOUD MICROPHYSICS IN NUMERICAL MODELS

Figure 2.5: Schematic of an orographically induced wave cloud from ICE-L

2.2

Treatments of cloud microphysics in numerical models

Having highlighted specific cloud regimes where our understanding is limited and would benefit from further modelling studies, it is now prudent to undertake a detailed review of the different representations of microphysical processes available for use. It is important to recognise that the complexity of a microphysics scheme can vary widely and depends on the exact nature of the model being used. As the resolution of a numerical model increases, it becomes more expensive to run and so must rely on computationally efficient physics schemes to ensure the model runs at an acceptable speed. The resulting balance between minimising computational cost and the natural desire to maintain model complexity imposes a restraint on the level of sophistication of microphysics schemes, and begs the following question - what are the key aerosol-cloud interactions that need to be represented in numerical models, and what level of complexity is sufficient to represent them? 51


2.2.1

Bin versus bulk microphysics

Dedicated cloud models for off-line research can typically afford to employ relatively sophisticated microphysics schemes, which are based on either bin or bulk microphysics schemes. In the case of bin microphysics, the particle size distribution is resolved by discretizing the distribution into multpile size categories, or size bins, and have the ability to capture the evolution of a particle size distribution explicitly. The computational demands of such schemes currently prohibits their use in operational models. The alternative to bin schemes is to use bulk microphysical parameterizations, also referred to as "bulk schemes". Bulk schemes work by assuming some functional form of the hydormeteor size distribution a priori, which is typically inferred from aircraft measurements, and the moments of which can be expressed analytically. The bulk scheme then calculates the moments of the assumed size distribution in order to return useful bulk quantities such as mixing ratio and number concentration. By assuming a functional form of the size distribution whose integral can be solved analytically, the number of prognostic equations the scheme needs to hold is vastly reduced compared to the bin approach. In the case of single moment bulk schemes, the scheme simply holds a single moment (the hydrometeor mixing ratio) as a prognostic variable; the hydrometeor number concentration is then either specified simply as a constant, or it can be diagnosed from some other quantity (such as the resolved updraught speed in the case of droplet number concentration). This value is then used in determining microphysical process rates such as autoconversion and accretion. Dual-moment schemes predict two moments - the mixing ratio and the number concentration. Consequently dual moment bulk schemes are seen as a useful compromise between the costly bin approach and the limitations of the single moment approach. Theoretically, a predicted or diagnostic droplet number as opposed to a fixed value could give more accurate estimates of process rates and hence aerosol indirect effects, although there are a wide range of different schemes and methods for parameterizing droplet activation and a consensus does not exist in terms of an overall general form. In terms of the ice phase, the lack of an explicit theory for primary ice nucleation means that the representation of heterogeneous ice formation in bin schemes is parameterized in much the same way as it is in bulk schemes. Potentially, the main advantage of the bin approach when 52


modelling the ice phase lies in the ability to capture the evolution of the ice size distribution and possibly more accurate representations of size sorting, although at the time of writing the vast majority of mixed-phase bin microphysical modelling studies have been based on deep convection [53–55], and there are comparitively few bin simulations of mixed-phase layer clouds. In this regime the benefits of the explicit bin approach remain largely unquantified.

2.2.2

Cloud droplet activation

Our understanding of the mechanisms of cloud droplet formation are currently ahead of our ability to implement this knowledge in most numerical models, due to the need to maintain computational efficiency. The challenge for the modelling cummunity is therefore how to transfer the key aspects of this theoretical understanding to such models by means of appropriate parameterizations. Droplet activation in bin microphysical models is typically based on a simplified version of Köhler theory, which can be derived from a consideration of the diffusional growth equation, shown below in the radius flux form for a single, homogeneous, spherical droplet:

r

dr = dt

Dv (ev es;v (T)) Dv Le L es;v (T ) Le 1 + L Rv T T Rv T

(2.2.1)

r = droplet radius (cm); Dv = molecular diffusion coefficient of water vapour in air (cm2 s 1 ); ev = ambient vapour pressure at the surface of the droplet (Pa); es;v (T ) = saturation vapour pressure at temperature T (Pa); Le = latent heat of evaporation of water (J g 1 ); L = droplet density (g cm 3 ); = thermal conductivity of moist air (J cm 1 s 1 K 1 ); Rv = specific gas constant for water vapour; (J g 1 K 1 ); T = temperature (K); The reader is directed to Pruppacher & Klett [56] and Rogers & Yau [57] for the full derivation of the above equation. By dividing the right hand side of equation 2.2.1 by Dv and es;v (T ), the equation can also be written thus: 53


r

where

dr = dt

Le L T

S 1 L 1 + D eR (TT ) R T L

e

v

v

(2.2.2)

v

s;v

S is the ambient saturation ratio, given by ev =es;v (T ). The complete form of

the diffusional growth equation requires corrections to the diffusion coefficient, thermal conducitivity and saturation vapour pressure terms. Full details of the correction terms are given in Jacobson [58]. In the case of the diffusion coefficent, a correction is necessary to take account of the sticking probability of water molecules near the particle surface. This is reflected mathematically via the mass accommodation coefficient, also known as the condensation coefficient, which is the fractional number of collisions of gas molecules with the particle surface that results in the gas molecules succesfully sticking. Corrections are also necessary to the thermal conductivity to take account of the thermal accommodation coefficient, which determines the fractional number of molecules that bounce off the particle surface that have acquired the temperature of the droplet. In the case of water-vapour growth, the thermal accomodation coefficient is close to unity, with a typical value of 0.96 [56]. The mass accommodation coefficient is the source of more uncertainty; Pruppacher and Klett suggest it can be as low as 0.04, although more recent studies [59] support a value of unity. In terms of the saturation vapour pressure, the effects of curvature and solutes both need to be accounted for when considering condensation growth of aerosol particles. Equation 2.2.2 ignores the effects of curvature and the presence of a solute on the droplet equilibrium vapour pressure; when such effects are included, the equation becomes:

r

dr = dt

Le L T

S

1

Le Rv T

A

+ rB3 ; 1 + D eR (TT ) r

L

v

(2.2.3)

v

s;v

where

A=

2 L Rv T

with = the surface tension of the droplet in units of J cm 2 , and 54

(2.2.4)


B=

3ims Mw ; 4Ms L

(2.2.5)

where i is the van’t Hoff factor (the number of ions per solute molecule), mass of the solute (g),

ms is the

Mw is the molar mass of water in the droplet (g mol 1 ) and Ms

is the molar mass of solute in the droplet (g mol 1 ). In deriving equations 2.2.4 and 2.2.5, the assumption of a dilute solution is made such that the surface tension and droplet density are equal to those of water. By taking the aerosol particle to be in equilibrium with its environment (i.e. setting the

dr=dt term in equation 2.2.3 to equal zero), the simplified version of the Köhler equation is obtained:

S = Seq = 1 +

A r

B ; r3

(2.2.6)

where Seq is the saturation ratio at equilibrium, i.e. where the ambient vapour pressure is equal to the equilibrium vapour pressure over the surface of the droplet. The term including A is more commonly known as the Kelvin term, or the curvature term. Essentially, it says that for a decrease in droplet size, the vapour pressure over the surface of the droplet must increase for it to stay in equilibrium. This is because as droplet radius decreases, the net force of hydrogen bonds that hold the water droplet together becomes weaker, and water molecules are lost more easily compared to droplets with larger radii. Thus the supersaturation must increase to maintain equlibrium. The effect of surface tension of a particle, , is included in the Kelvin term. Surface tension can be defined as the work per unit area required to extend the surface of the droplet; it is temperature dependent and is found to decrease with increasing temperature. The higher the surface tension, the more rapidly evaporation tends to occur. Values of surface tension for different solutes are given in Pruppacher and Klett [56, p. 133]. The last term on the right hand side of equation 2.2.6 involving

B corresponds to

the Solute term (also known as the Raoult term), which accounts for the reduction in equilibrium vapour pressure due to the presence of a solute. Solutes can break up into ionic components in a process known as dissociation, and the molecules of the solute replace water molecules at the surface of the drop. The more a solution dissociates, the 55


Figure 2.6: Köhler curve for an ammonium sulphate particle of dry diameter 200 nm, showing the dependency of the equilibrium supersaturation on the wet particle size, and the competition between the Kelvin term and the Raoult term. Adapted from McFiggans et al. [60]

lower the equilibrium vapour pressure for a given droplet size. The Raoult term explains why very small solution droplets can exist in equilibrium below 100% relative humidity. Köhler curves can be constructed using equation 2.2.6 to determine the equilibrium saturation for a given droplet radius. Figure 2.6 shows the Kohler curve for a 200 nm dry diameter ammonium sulphate particle; different Köhler curves can be constructed provided that the quantities T; ms and Ms are known. If the supersaturation in the rising air parcel is greater than the equilibrium saturation for a given particle radius, then the particle will grow in size until it reaches a new equilibrium. By the same token, if the resolved saturation drops sufficiently, then the droplet would reduce in size by evaporation in order to reach a new equilibrium with its environment. The critical radius rc required for droplet activation can be obtained by finding the maxima of equation 2.2.6 obtained by differentation with respect to r, and then setting the result equal to zero. Re-arranging in terms of r then gives: 56


rc =

r

3B A

(2.2.7)

Substituting equation 2.2.7 into 2.2.6 leads to an expression for the critical supersaturation, Sc :

r

Sc = 1 +

4A3 27B

(2.2.8)

Upon reaching the critical radius, any further increase in wet particle size will lead to runaway growth and the result is cloud droplet activation. It has been shown how the critical radius is dependent on both the Kelvin and Raoult terms, which in turn are dependent on the composition of the aerosol particle in question. The mixing state of an aerosol population is important; ambient aerosols consist mostly of internal mixtures, e.g. single particles that consist of different chemical components [60]. The organic content of internal mixtures can affect the water uptake and the resulting optical properties compared to a pure inorganic particle. The varying contents of water-soluble and insoluble substances in internally mixed particles makes the situation particularly complex, as does the vast array of organic compounds that are known to exist in the atmosphere [61]. This makes the numerical modelling of the effects of organic compounds in itself a complex and challenging task. The effect of CCN composition on the resulting size distribution of cloud droplets is important not only from a cloud albedo perspective, but also because it can potentially impact upon the precipitation efficiency. Warm rain formation occurs due to collision and coalescence of cloud droplets, which allows cloud droplets to reach raindrop size (typically of the order of 1mm). For collision between droplets, a broad size distribution of cloud droplets is favoured, whereby the larger droplets fall faster relative to the smaller droplets through the depth of the cloud, sweeping out large cross-sectional areas as they fall, collecting the smaller droplets and growing by accretion. It should be noted that a collision between two cloud droplets does not necessarily result in sticking; the efficiency of two droplets successfully coalescing upon contact is dependent upon the impact speed, which in turn is dependent on the sizes of the collector drop and the drops being collected. Larger speeds are necessary to overcome the surface tension of droplets and increase the probability of a successful 57


collision (but too large and the drops can break up and fragment into smaller droplets upon collision [62, 63]). If a cloud consists of lots of relatively small droplets, all of a similar size, the differential velocities between falling droplets is low and hence the efficiency of collision and coalescence will also be small, and hence rain is unlikely to form. From this, it is possible to conclude that changes in CCN concentration, composition and size all play a role in determining the resulting cloud droplet size distribution, which under certain regimes could possibly affect the cloud liquid water path and cloud lifetime. The alternative to Köhler theory in bin schemes is simply to parameterise the effect of aerosols on droplet activation, for example using the power-law relation of Twomey [64]:

NCCN = csk ;

(2.2.9)

where s is the supersaturation (%), NCCN is the number of activated CCN at a given supersaturation, c is the number concentration of CCN active at 1% supersaturation and k is a constant whose value depends on the airmass type. For dual-moment bulk schemes which do not resolve supersaturation explicitly and instead use the method of saturation adjustment [65], the Twomey power-law relationship can still be utilised by approximating the supersaturation

s in equation 2.2.9 based on

the resolved grid-scale updraught velocity [57]. It is fair to say that although the issue of microphysical complexity in the context of sub-tropical boundary layer clouds has been explored to some extent already in recent years [54, 66, 67], it has been done so mainly according to the complexity of the treatment of rain. Currently a consensus does not exist concerning the extent to which aerosols need to be represented in cloud models for the purpose of droplet activation. In the context of sub-tropical marine boundary layer clouds at least, the answer is likely to depend on thermodynamic conditions such as updraught speed, which determines the maximum supersaturation at cloud base, and also the composition and size of the aerosol particles in question. There is also increasing evidence for the need to consider changes in environmental conditions too, which in some cases can overshadow the effects of aerosol on cloud properties [68]. 58


2.2.3

Ice crystal formation

Unlike liquid drops, ice crystals are observed to form both homogeneously and heterogeneously in the atmosphere, and consequently it is important to distinguish between the two pathways of ice formation. An appreciation of homogeneous nucleation theory is also a useful precursor to understanding existing parameterizations of heterogeneous ice nucleation.

Homogeneous nucleation Strictly, homogeneous nucleation refers to the process by which liquid water droplets freeze in the absence of aerosol acting as ice nuclei. With no IN present, supercooled cloud droplets can only freeze when the temperature is cold enough (around -35 C and below). It is typically associated with ice initiation in cirrus clouds, and has also been observed to take place in convective updraughts [40]. The classical stochastic theory of homogeneous nucleation is described in detail by Pruppacher and Klett [56]; to minimise repetition this section is intended only as a summary of the key points of the theory. It is believed that homogeneous freezing occurs as the result of stochastic growth of ice embryos within a supercooled droplet, and upon reaching a critical size they can initiate freezing of the whole droplet. The homogeneous freezing rate can then be determined from the nucleation rate of ice in supercooled water, which gives the number of liquid-tosolid nucleation events ("germs") per unit time per unit volume. For pure water droplets, the nucleation rate depends only on temperature. The formation of ice from homogenous freezing is given by the following equation:

1 dNu = Vd J ( T ) Nu dt

(2.2.10)

where Nu is the number concentration of unfrozen drops; Vd is the drop volume (assuming a constant value for all drops) and J (T ) is the nucleation rate of ice-germ formation in supercooled liquid drops (cm

3

s 1 ) [56].

Equation 2.2.10 can be integrated to the give the number concentration of unfrozen drops as a function of time t, provided the initial number of droplets N0 , the drop volume and the nucleation rate are known: 59


Nu = N0 exp( Vd J (T )t)

(2.2.11)

Equation 2.2.11 holds true for a pure water droplet. However as discussed in the previous section, droplets can form upon soluble aerosol particles, and then later freeze homogeneously. The presence of the solute acts to depress the freezing point of the droplet, as well as depressing the melting point of ice. Although an analytical solution for homogeneous freezing of solution droplets is not known to exist, the parameterization of Koop et al [69] suggested that the nucleation rate in solution drops depends only on the water activity. Results from the laboratory seem to support the approach, e.g. good agreement was obtained with the AIDA chamber results of measured freezing rates of sulphuric acid solution droplets [70]. The scheme of Koop et al has since been used as the basis for numerical parameterizations of homogeneous freezing in GCMs [71, 72], which has enabled the first predictions of ice crystal concentrations from homogeneous freezing in cirrus clouds. It is also used to parameterize homogeneous freezing in the mixed-phase modelling study in chapter 6.

Heterogeneous nucleation Having considered the parameterization of ice crystal formation in the absence of IN, the ability of aerosols to initiate the formation of ice at temperatures greater than the homogeneous freezing threshold are now discussed. Relative to the liquid phase, there is much more to learn about the effects of aerosols on initiating the ice phase. No theory exists to describe ice activation for a given type of ice nuclei [30]; consequently treatment of heterogeneous ice nucleation is as much of an issue in high resolution cloud resolving models as it is in global climate models. The situation is further complicated by the identification of several possible primary ice nucleation modes by which IN can initiate the ice phase, namely condensation freezing, immersion freezing, contact freezing and deposition nucleation. The representation of these nucleation modes in cloud models are discussed in detail in the review paper by Khain et al [73]; in the interests of brevity a brief description of the nucleation modes is now given. The immersion and condensation nucleation modes are both examples of heteroge60


neous freezing mechanisms. The modes are similar in that an IN contained within a haze particle initiates the freezing process at a certain temperature greater than the homogeneous freezing threshold. As noted in de Boer et al [74], the difference between the two modes is not always clearly defined, but it is important to distinguish clearly between the two mechanisms. The immersion mode is distinguished from the condensation mode if freezing occurs after a deliquesced aerosol particle reaches its critical radius, i.e. after cloud droplet formation, and thus requires existing droplets to be present. In the case of condensation nucleation, the freezing occurs during the deliquescence process before droplet activation has occurred. The immersion freezing process has been identified in Kärcher and Lohmann [50] as being the most likely heterogeneous nucleation mode associated with cirrus clouds. The modelling study of Field et al [39] also showed that condensation freezing is the most likely candidate in explaining the early onset of ice formation in observations of mixed-phase wave clouds from the ICE-L campaign. A third freezing mode also exists, namely the contact mode, which describes the mechanism by which interstitial IN collide with a supercooled water droplet, causing freezing upon contact. In wave clouds, vertical velocities are often large enough to activate all the available aerosols as cloud droplets, leaving no interstitial aerosol behind. This, coupled with the fact that turbulent mixing does not play a significant role in orographic wave clouds, suggests that contact freezing is an unlikely freezing mechanism in such clouds. However this does not rule out the possibility of contact freezing being potentially important in more weakly forced supercooled layers, where turbulent mixing could entrain aerosols into the cloud thus acting as a potential source of contact IN. Finally the deposition mode occurs when the environment is supersaturated with respect to ice. When this condition is met, vapour can be deposited directly onto the surface of the IN to form ice if the temperature is low enough. IN that initiate ice particles by this mechanism are known as deposition nuclei. The deposition mode shares some similarities with the condensation mode, in that the presence of cloud droplets is not a prerequesite for either of these modes to occur. Furthermore, at water saturation it can be very difficult to experimentally distinguish between the deposition mode and the condensation freezing mode and so consequently the combined modes are sometimes treated together and referred to as ’deposition/condensation’

61


nucleation. One of the biggest issues within the topic of ice nucleation has been the ’stochastic vs singular’ debate, which has been ongoing since the 1950s. One of the first studies of immersion freezing of supercooled liquid droplets was conducted in the laboratory by Bigg [75, 76]. Based on his experiments, Bigg developed an empirical relationship to describe the probability of droplet freezing, Pfrz in terms of the droplet volume Vd (cm3 ), the degree of supercooling Ts = (273.15 -

T (K)) C and the length of time in seconds t

that the supercooling is maintained:

ln(1 Pfrz ) = Vd tK (exp[aTs ] 1); where

(2.2.12)

a and K are constants determined from empirical fits to laboratory data, and

have values of 0.82 and 2.90e-8 respectively. Thus the Bigg scheme predicts that all droplets would eventually freeze given enough time, in line with stochastic theory. Indeed the stochastic nature of the Bigg scheme is equivalent to that used for homogeneous freezing, where instead of using the nucleation rate of pure water, the nucleation rate J (T ) is instead specified from Bigg [76], such that:

J (Ts ) = K (exp[aTs ] 1);

(2.2.13)

In the case where Ts is greater than 5 C, combining equation 2.2.10 with the equation 2.2.13 gives the approximate result that:

dNu = Vd K (exp[aTs ])dt; Nu

(2.2.14)

Integrating from Nu at time t = 0 to Nu at time t then gives:

ln where

N0 = Vd K (exp[aTs ])t Nu (t)

(2.2.15)

N0 = Nu (t = 0). As indicated in Khain et al [73], most cloud models use

the stochastic Bigg scheme for modelling the immersion freezing process. Indeed the mesoscale modelling study in chapter 7 uses the Bigg scheme for this purpose. However the stochastic hypothesis is not the only theory with regards heterogeneous freezing. An 62


alternative theory was proposed by Langham and Mason [77] from which the singular hypothesis was born. The philosophy of the singular hypothesis is based around the idea that the number concentration of ice crystals formed via heterogeneous freezing of droplets is dependent only on the minimum temperature reached, thus implying that ice nuclei operating in the immersion or condensation freezing modes have a set temperature at which they nucleate. Homogeneity of the freezing nuclei distribution amongst the cloud liquid water is assumed, with the implication that larger supercooled drops have a higher probability of containing a freezing nucleus. Thus the equivalent of equation 2.2.15 for the singular hypothesis is:

ln

N0 = Vd np (Ts ); Nu

(2.2.16)

where np (Ts ) is the number of particles inside a drop which become active as IN at supercooled temperature Ts , equal to

Rt 0

J (Ts )dt.

Since the review by Khain et al [73], there have been some advancements in parameterizations of ice crystal formation designed for use in cloud models which favour the singular explanation of ice nucleation. For immersion freezing, examples include the work of Diehl and Wurzler [78], who developed a parameterization accounting for the different freezing characteristics of both soluble and insoluble particles, whilst other studies have considered the heterogeneous freezing (immersion and condensation modes together) of different desert dust samples [79]. In terms of deposition nucleation, efforts have also been made to parameterize the ice nucleating ability of specific types of dust aerosol using the AIDA chamber [80]. Whilst these are clear indications of progress, these parameterizations are specific to a given type of IN, and a complete theory of heterogeneous ice nucleation remains elusive. One of the first parameterizations of heterogeneous ice formation to be widely adopted in numerical models [81] did not distinguish between the different nucleation modes, and simply related ice number concentration as a function of temperature thus:

NIN = A exp( T ) where NIN is the number of IN per litre active above temperature T (K); 63

(2.2.17)

A =10 5 L 1 ;


=0.6 C

1

and

T = T0

T , where T0 =273.15 K. The exponential relation was

obtained through the combination of data from a dozen sets of measurements by various instruments, over a temperature range of -15 C to -30 C. Other parameterizations of active IN concentrations still widely used today due to their simplicity include that of Cooper [82] and Meyers et al. [83]. However when compared against each other across a range of temperatures, these schemes predict quite different active IN concentrations, particularly at temperatures above -15 C. The origin of the discrepancy comes from the fact that observations for a given temperature are poorly constrained and can cover several orders of magnitude [84]. For instance, the Meyers et al. parameterization of depositioncondensation freezing is based on a limited number of datasets from surface-based continuous flow chamber measurements over specific temperatures and supersaturations (specifically between -7 C and -20 C, for ice supersaturations between 2% and 25%, and for water supersaturations between -5% and +4.5%). Consequently the Meyers et al scheme does not wholly reflect the full extent of spatial and temporal variations of IN observed in the real atmosphere. However the simplicity of the scheme has led to its widespread use in GCMs, although its application is not always constrained to the clearly defined temperature and supersaturation regimes over which it is defined. To address these issues, DeMott et al [84] recently proposed a new parameterization of active IN concentration as a function of temperature and the concentration of aerosols greater than 500 nm. This parameterization has the advantage in that the observations used to construct the parameterization are taken from 9 independent field campaigns covering different locations over land spanning a 14 year period, and thus reflects the spatial and temporal variations of IN measurements in the atmosphere. The correlation between observations of active IN concentrations and the number of aerosol particles larger than 500 nm helps to reduce the uncertainty from a factor of 1000 to less than 10. It is speculated that the remaining uncertainty is due to differences in aerosol composition and possibly other as yet unidentified factors. The extra degree of freedom offered by the Demott scheme compared to the more traditional nucleation parameterisations makes it a more desirable choice for use in cloud resolving models. Consequently the DeMott scheme is used in the ICE-L modelling study in chapter 6.

64

2.3. SUMMARY AND RECOMMENDATIONS FOR FURTHER STUDY

2.3

Summary and recommendations for further study

The first section of this review highlighted those specific cloud regimes where the need to develop our understanding of aerosol-cloud interactions is urgent. The first regime to be considered was that of the sub-tropical marine boundary layer, where changes in aerosol properties could affect the global radiation budget and the hydrological cycle, thus having potentially significant consequences for global climate. It has been argued that GCMs do not yet provide a suitable basis for conducting studies of aerosol indirect effects in this regime, since considerable uncertainty is associated with the macrophysical representation of marine boundary clouds across the spectrum of available models. It is thus apparent that a combination of cloud-resolving modelling, observational measurements and laboratory studies are all required to further our understanding. The point has also been made that whilst dedicated cloud models have the capacity to provide insight into the effects of aerosol on different cloud types, a consensus does not exist concerning the level of microphysical complexity required to capture the key aerosol-cloud interactions. The review of the existing literature has also revealed that meteorological conditions must also be accounted for when considering the effect of aerosols on marine boundary layer clouds. Thus it is recommended that one of the specific aims of this thesis should be to devise an objective method capable of quantifying the importance of increasing the level of microphysical sophistication in cloud models against a backdrop of changing environmental conditions. A simulation based on bin microphysics with explicit treatment of aerosol should be used to evaluate the performance of simpler bulk microphysical parameterizations. This would ultimately help to identify those meteorological regimes where the additional complexity (and therefore computational expense) is warranted, such that the results can be used to inform the necessary level of complexity required to simulate liquid clouds in operational models. In terms of clouds involving the ice phase, the vast majority of GCMs do not consider aerosol-ice cloud interactions at all due to the difficulties in quantifying the relationship between IN and ice crystal concentrations, and it is clear that there is still much to learn with regards the factors that control ice nucleation processes. In particular a complete theory of heterogeneous nucleation that can account for the varying degrees of nucleation 65


ability among ice nuclei is lacking. However a new generation of ice nucleation parameterization is currently emerging, which is based on aerosol properties as well as temperature, and there is a need to test such parameterizations within cloud models against the latest in-situ observations. Korolev and Field [85] showed that accurate prediction of ice nucleation rates in numerical models is essential in order to maintain mixed-phase layers, since the number density of ice was found to control the balance between the liquid phase and the ice phase. The recent ICE-L project focused on ice nucleation in orographic wave clouds, which make excellent subjects for numerical modelling studies due to their relatively simple dynamics and long lifetime. Therefore it is recommended that simulations of mixed-phase clouds from the recent ICE-L field campaign be conducted to challenge the ability of the latest numerical models to reproduce the observed ice crystal concentrations and growth rates, with the intention that the results of the study will inform future model developments in this area. Similarly, simulation of an APPRAISE-CLOUDS case study is also recommended to complement the existing in-situ observations. One particular APPRAISE case study, from 22nd Jaunary 2009, focuses on a line of precipitating wintertime shallow cumuli, where the observed cloud tops were no less than -8 C. By considering two quite different examples of mixed-phase clouds, one at relatively high temperatures (the APPRAISE case) and the other at temperatures more consistent with the mid to upper troposphere (ICE-L wave cloud), it is possible to explore not only the role of primary ice nucleation but also the potential influence of secondary ice formation and homogeneous nucleation as well, and how these additional sources of ice contribute to the cloud macrostructure and general evolution. The next chapter introduces the key tools and methods that are to be used in the remainder of this thesis to address these recommendations.

2.4

References

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69


[35] P. R. Field et al., “Ice particle interarrival times measured with a fast FSSP”, Journal of Atmospheric and Oceanic Technology. 20, 249–261. (2003). [36] G. M. McFarquhar et al., “Importance of small ice crystals to cirrus properties: Observations from the Tropical Warm Pool International Cloud Experiment (TWPICE)”, Geophysical Research Letters. 34. (2007). [37] P. R. Field, A. J. Heymsfield, and A. Bansemer, “Shattering and particle interarrival times measured by optical array probes in ice cloud”, Journal of Atmospheric and Oceanic Technology. 23, 1357–1371. (2006). [38] A. V. Korolev et al., “Small ice particles in tropospheric clouds: fact or artifact? Airborne Icing Instrumentation Evaluation Experiment”, Bulletin of the American Meteoroligcal Society, in press. (2010). [39] P. R. Field et al., “Ice in Clouds Experiment - Layer Clouds. Part II: Testing freezing mechanisms in lee wave clouds”, In preparation. (2011). [40] D. Rosenfeld and W. L. Woodley, “Deep convective clouds with sustained supercooled liquid water down to-37.5 degrees C”, Nature. 405, 440–442. (2000). [41] A. P. Khain, D. Rosenfeld, and A. Pokrovsky, “Simulating convective clouds with sustained supercooled liquid water down to -37.5 degrees C using a spectral microphysics model”, Geophysical Research Letters. 28, 3887–3890. (2001). [42] A. Khain, D. Rosenfeld, and A. Pokrovsky, “Aerosol impact on the dynamics and microphysics of deep convective clouds”, Quarterly Journal of the Royal Meteorological Society. 131, 2639–2663. (2005). [43] P. J. Connolly et al., “Cloud-resolving simulations of intense tropical Hector thunderstorms: Implications for aerosol-cloud interactions”, Quarterly Journal of the Royal Meteorological Society. 132, 3079–3106. (2006). [44] U. Lohmann and J. Feichter, “Global indirect aerosol effects: a review”, Atmospheric Chemistry and Physics. 5, 715–737. (2005). [45] P. Connolly. “An investigation into the microphysics of deep convection”. PhD thesis. University of Manchester, 2005.

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[58] M. K. Jacobson. Fundementals of Atmospheric Modeling, 2nd edition. Cambridge University Press, 2005. [59] A. Laaksonen et al., “Commentary on cloud modelling and the mass accommodation coefficient of water”, Atmospheric Chemistry and Physics. 5, 461–464. (2005). [60] G. McFiggans et al., “The effect of physical and chemical aerosol properties on warm cloud droplet activation”, Atmospheric Chemistry and Physics. 6, 2593– 2649. (2006). [61] D. M. Murphy, “Something in the air”, Science. 307, 1888–1890. (2005). [62] T.B. Low and R. List, “Collision, coalescence and breakup of raindrops .1. Experimentally established coalescence efficiencies and fragment size distributions in breakup”, Journal of the Atmospheric Sciences. 39, 1591–1606. (1982). [63] T. B. Low and R. List, “Collision, coalescence and breakup of raindrops .2. Parameterization of fragment size distributions”, Journal of the Atmospheric Sciences. 39, 1607–1618. (1982). [64] S. A. Twomey, “The Nuclei of Natural Cloud Formation. Part II: The Supersaturation in Natural Clouds and the Variation of Cloud Droplet Concentrations”, Geofisica pura e applicata. 43, 227–242. (1959). [65] J. M. Straka. Cloud and Precipitation Microphysics. Cambridge University Press, 2009. [66] H. Morrison and W. W. Grabowski, “Comparison of bulk and bin warm-rain microphysics models using a kinematic framework”, Journal of the Atmospheric Sciences. 64, 2839–2861. (2007). [67] H. Morrison, G. Thompson, and V. Tatarskii, “Impact of Cloud Microphysics on the Development of Trailing Stratiform Precipitation in a Simulated Squall Line: Comparison of One- and Two-Moment Schemes”, Monthly Weather Review. 137, 991–1007. (2009). [68] L. Nuijens, B. Stevens, and A. P. Siebesma, “The Environment of Precipitating Shallow Cumulus Convection”, Journal of the Atmospheric Sciences. 66, 1962– 1979. (2009). 72

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[81] N. H. Fletcher. Physics of Rain Clouds. Cambridge University Press, London, 1962. [82] W. A. Cooper, “Ice initiation in Natural Clouds: Precipitation Enhancement - A Scientific Challenge”, Meteorological Monographs. 21, 29–32. (1986). [83] M. P. Meyers, P. J. Demott, and W. R. Cotton, “New primary ice-nucleation parameterizations in an explicit cloud model”, Journal of Applied Meteorology. 31, 708–721. (1992). [84] P. J. DeMott et al., “Predicting global atmospheric ice nuclei distributions and their impacts on climate”, Proceedings of the National Academy of Sciences of the United States of America. 107, 11217–11222. (2010). [85] A. V. Korolev and P. R. Field, “The effect of dynamics on mixed-phase clouds: Theoretical considerations”, Journal of the Atmospheric Sciences. 65, 66–86. (2008).

74

CHAPTER

THREE METHODS AND TOOLS

This chapter provides an introduction to the modelling and analysis tools that are utilised throughout the remainder of the thesis. The tools and techniques presented here are employed in the subsequent chapters to ensure that the outcomes from the literature review can be properly addressed.

3.1

Introducing the Factorial Method

The previous chapter concluded that, in order to address the issue of exactly how important aerosols are from a cloud microphysics perspective, and therefore the extent to which aerosols need to be represented in numerical models, it is necessary to isolate the effects of meteorology from the effects of aerosol. One such method that has been employed recently in the context of cloud modelling is the Factorial Method (FM), which was used by Teller & Levin [1] to study the factors controlling precipitation formation in a winter time deep convective storm. It is similar in principle to the Factor Separation method used earlier by Stein and Alpert [2], with the advantage that the FM includes the entire range of possible interactions when calculating the relative contributions of each factor, thus allowing them to be compared directly against each other. To illustrate the use of the Factorial Method, consider three variables of interest, labelled A,

B and C (henceforth referred to as ’factors’). If each factor is initialised with

two different starting values, representing a low and a high level, then this satisfies a

23

factorial design. In this case eight model simulations (or ’treatment combinations’) are required to explore the sensitivity of the model to the defined parameter space in terms 75

CHAPTER 3. METHODS AND TOOLS Table 3.1: Design matrix for the general 23 factorial design, illustrating the use of both the geometric and standard notation systems to distinguish between treatment combinations. Run

1 2 3 4 5 6 7 8

A

B

C

+ +

+ +

+ +

+ +

+ + + +

Labels

(1) a b ab c ac bc abc

of a chosen metric. In the case of Teller & Levin, factors including CCN concentration and temperature profile were chosen and their role in influencing the amount of surface precipitation produced was quantified for different initial values of each factor. A standard notation system is used to identify the eight simulations in the

23 design

[3], where lower case letters are used to denote the ’high’ value of a factor, and the absence of a lower case letter denotes the ’low’ value of that factor. The label (1) is reserved for the reference simulation where are all three factors are at their ’low’ level. Thus in standard notation the eight simulations required can be written as (1); a; b; ab; c; ac; bc and abc. For example,

ab refers to the simulation where factors A and B are at the high level, and

factor C is at the low level. A geometric notation system, based on the use of "+" and "-" labels to denote high and low values for each factor, can also be used. The design matrix is tabulated in 3.1. The eight simulations in the

23 experimental configuration can also be visualised

graphically as in Figure 3.1, where a simulation is placed at each corner of a cube such that the x, y and z dimensions represent the main effects of factors A, B and C respectively. Figure 3.1 can be used to help calculate the average sensitivity of the model to a change in each factor, also known as the main effect. For example, the main effect of factor A is simply the average of those runs where A is at the high level minus the average of those runs where

A is at the low level. Based on Figure 3.1, this corresponds to the

difference in averages between the four runs in the right hand face of the cube and the four runs in the left hand face of the cube. Figure 3.2 shows how this can be extended to 76

3.1. INTRODUCING THE FACTORIAL METHOD

Figure 3.1: A geometric representation of the Factorial Method based on a 23 experimental design, where the eight simulations placed at the corners of a cube, with each dimension of the cube representing the average effect of a specific factor. Adapted from Montgomery [3].

the remaining factors to allow calculation of the main effects for

B and C as well. The

interactions between factors, which quantify the extent to which the role of one factor depends on the value of another, can be calculated via consideration of differences in the diagonal planes of the cube, also shown in Figure 3.2.

For the needs of this particular work, the Factorial Method will be extended to act as a tool to help compare and contrast the sensivities and behaviour of different microphysics schemes across a range of complexities under a set of controlled conditions. There is a subjective element to the Factorial Method which arises from the need to pre-select specific variables for study, and more importantly, the range of values to apply to each variable. Thus careful planning is required in the experimental design stage to ensure that the Factorial Method produces meaningful results. 77

CHAPTER 3. METHODS AND TOOLS

Figure 3.2: Graphical representation of the main effects A, B and C in the 23 factorial design, along with the corresponding interaction terms AB , AC , BC and ABC . Adapted from Mongomery [3].

3.2 3.2.1

Modelling capability The ACPIM

With regards to numerical modelling capability, this study exploits the recent advances in process model development at the University of Manchester. Specifically, the AerosolCloud-Precipitation-Interaction-Model (ACPIM) will act as the main modelling tool to satisfy the needs of this work. The ACPIM is a mixed-phase bin microphysics model, with an explicit treatment of both aerosols and water particles (liquid and ice). The ACPIM 78

3.2. MODELLING CAPABILITY

uses a single moment aerosol mass grid such that the aerosol bins are fixed with 154 bins representing the aerosol size distribution. The average mass in each bin is assumed to be given by the mass of the bin centre, and that this average mass does not vary in time. Particle size distributions are represented on a 2-D grid as in the scheme of Bott [4], such that both liquid and ice particle distributions are categorised according to both water mass and aerosol mass. Thus for a given water mass bin, the 2-D grid stores the variation in number concentration across the range of aerosol mass bins, and vice versa. This approach allows changes in the aerosol size distribution to be simulated due to collisions between droplets.

Growth of liquid particles through to activation as cloud droplets, and subsequent growth by condensation, is handled continuously via solving the diffusional growth equation as in equation 2.2.1 (plus corrections to the molecular diffusivity, thermal conductivity and the saturation vapour pressure over a solution droplet as discussed in section 2.2.2.) A noteworthy feature of the ACPIM that is of particular relevance to this study is the ability to treat multi-component aerosols (including both soluble and insoluble material) that can be either externally or internally mixed, based on outputs from the Aerosol Diameter Dependent Equilibrium Model, ADDEM [5, 6]. The ADDEM provides saturation vapour pressures of liquid particles, which is then fed into the droplet growth equation and solved in ACPIM such that the effects of specific aerosol compositions can be explored in both liquid and mixed-phase clouds. Unless stated otherwise in future chapters, advection of water mass up and down the bin grid due to condensation and evaporation is represented by the single moment quasi-stationary scheme [7], where a particle grows/evaporates to some exact size during a timestep, and then is adjusted back onto the stationary grid at the end of each step. Collision-coalescence processes are parameterized using the flux method of Bott [4]. The ICE-L modelling study in chapter 6 takes advantage of some very recent developments to the ACPIM model [8] where the single-moment bin structure is replaced with a double-moment moving centre scheme [7] for the treatment of the water and ice mass grid. In this approach, the bin edges of the mass grids are fixed but the bin centres vary between the low and high bin edges. This permits the average mass within each bin to vary in time, with the advantage that this results in less numerical diffusion 79


Figure 3.3: Perspective views of prolate and oblate spheroids that resemble columnar and planar ice crystals, respectively. Adapted from Chen and Lamb [11]. and therefore less artificial spreading of the size distribution during growth by diffusion and collision-coalescence compared to single-moment solutions. With regards the treatment of the ice phase, a variety of recent ice nucleation parameterizations are included in the model, e.g. the parameterizations of Connolly et al [9] and DeMott et al [10], both of which determine the number of active IN as a function of aerosol properties. In the case of the ICE-L modelling work in chapter 6, the DeMott et al scheme is used to parameterize heterogeneous freezing of cloud droplets, such that:

NIN;T = a1 (273:16 TK )b1 (naer;0:5 )(c1 (273:16 K

TK )+d1 ) ;

(3.2.1)

where a1 = 5.94e-5, b1 = 3.33, c1 = 2.64e-2, d1 = 3.3e-3, TK is the cloud temperature in Kelvin, naer;0:5 is the number concentration of aerosols with diameter larger than 500 nm (in std cm 3 ) and NIN;T is the IN number concentration (std L 1 ) active at temperature K

TK . Both riming and aggregation processes are also represented through consideration of the stochastic collection equation. With regards ice growth rates, the ACPIM adopts the capacitance growth model of Chen & Lamb [11], which is able to represent the evolution of ice crystal habit based on a consideration of the aspect ratio of spheroidal ice crystals, where = c=a, where ’c’ is the c-axis length and ’a’ is the a-axis length (see Figure 3.3). 80

3.2. MODELLING CAPABILITY

This approach allows the model to describe the link between changes in the apparent volume of an ice crystal during depositional growth and the change in aspect ratio, and how this feeds back on the growth rates of ice crystals. The change in mass of an ice crystal with time is given by the following equation describing vapour diffusion growth of ice crystals:

4Cs dm h i = R T + L L dt v

s

ei D v

s

T Ki

T Rv

1

i ;

(3.2.2)

where C is the crystal capacitance, specified in [12] for both oblate and prolate spheroids;

V is the spheroid volume, si is supersaturation with respect to ice, Rv is the vapour gas constant, Ls is the latent heat of sublimation, vapour pressure,

T is temperature, ei is the ice equilibrium

Dv is the effective vapour diffusivity and Ki is the effective thermal

conductivity. Equation 3.2.2 can also be expressed as a change in crystal volume

dV ,

where

dV =

1

dep

dm;

(3.2.3)

and dep is the deposition density (the density of deposited vapour onto an ice crystal), and is expressed as (in g cm 3 ):

dep = 0:91 exp [ 3: max( 0:05; 0)= (T )] ; where is the excess vapour density in g m 3 , and

(3.2.4)

is called the inherent growth

ratio and controls the distribution of mass deposition onto the basal (c-axis) and prism (a-axis) faces of the crystal according to the ratio of the deposition coefficients along the two axes:

(T ) =

c a

(3.2.5)

thus determines the primary habit evolution; it is a function of temperature and was determined by Chen and Lamb from experimental data exploring growth rates of ice crystals and subsequent habits across a range of temperatures between 0 C and -30 C. 81

CHAPTER 3. METHODS AND TOOLS The dependency between the change in aspect ratio and the change in crystal volume

V is given by: d ln() =

1 d ln(V ) +2

Equation 3.2.6 can be obtained from the volume of a spheroid

(3.2.6)

V = 43 a3 and the

assumption of a mass distribution relationship which controls the rate of crystal growth along each axis, such that:

dc = (T ); da

(3.2.7)

where is the ratio of the vapour density gradients along the c-axis and a-axis respectively. Equations 3.2.3 and 3.2.6 are solved in ACPIM to allow for changes in ice crystal habit (the aspect ratio) to feed back on ice crystal growth rates. Due to the complexity of the ACPIM microphysics, the computational expense of the model is considerable and with the presently available resources, its use is currently restricted to relatively simple dynamical frameworks such as lagrangian parcel models and 1-D column models with prescribed forcing. Whilst the use of a kinematic framework does not allow for a complete representation of cloud dynamics, it has the advantage that differences in the behaviour of microphysics schemes can be easily isolated without the added complication of feedback mechanisms, and as such the insight gained through testing schemes in a kinematic framework forms a useful point of reference in advance of more complex 3-D modelling studies. Consequently the 1-D column model is deemed to be suitable for exploring the sensitivity of idealised warm clouds to changes in the representation of the cloud microphysics. For the proposed ICE-L wave cloud modelling work, the 1-D column model is sufficient to represent the dynamics of such clouds due to their laminar nature and minimal turbulent mixing, and therefore allows for a direct comparison with the observational measurements. It is intended that the ACPIM bin microphysics is used to conduct the comparison with the ICE-L in-situ observations, and also as the benchmark against which simpler bulk parameterizations can be compared and validated in the case of the idealised warm cloud modelling. In both instances the statistical technique of the Factorial Method can then be utilised to quantify the response 82

3.3. REFERENCES

of the model microphysics to changes in selected variables in terms of a chosen metric. Because the ACPIM bin microphysics model is currently only available for use within a 1-D column framework, an alternative model must be used to conduct the 3-D simulations necessary for the suggested APPRAISE-CLOUDS case study. Thus the Weather Research and Forecasting (WRF) mesoscale model is used in chapter 7 in an attempt to establish the roles of both primary and secondary ice formation on the evolution of shallow cumulus clouds in the UK winter of 2008/2009. For the needs of this study, the WRF model is configured to run at a convection-permitting resolution of 1km, with the bulk microphysics scheme of Morrison et al ([13], henceforth referred to as the ’Morrison scheme’) to simulate both liquid and mixed-phase cloud. The Morrison scheme has the advantage of being able to select between a single moment or dual moment treatment of liquid water, which may have important implications for riming rates and hence precipitation rates. Because of this in-built flexibility, it is also intended that the Morrison microphysics be used as the bulk scheme of choice when comparing against the ACPIM bin microphysics in the idealised 1-D modelling. More details on this are provided in the next chapter.

3.3

References

[1] A. Teller and Z. Levin, “Factorial method as a tool for estimating the relative contribution to precipitation of cloud microphysical processes and environmental conditions: Method and application”, Journal of Geophysical Research-Atmospheres. 113, 13. (2008). [2] U. Stein and P. Alpert, “Factor Separation in Numerical Simulations”, Journal of the Atmospheric Sciences. 50, 2107–2115. (1993). [3] D. C. Montgomery. Design and Analysis of Experiments. 5th ed. John Wiley, New York, 2005. [4] A. Bott, “A flux method for the numerical solution of the stochastic collection equation: Extension to two-dimensional particle distributions”, Journal of the Atmospheric Sciences. 57, 284–294. (2000).

83


[5] D. O. Topping, G. B. McFiggans, and H. Coe, “A curved multi-component aerosol hygroscopicity model framework: Part 1 - Inorganic compounds”, Atmospheric Chemistry and Physics. 5, 1205–1222. (2005). [6] D. O. Topping, G. B. McFiggans, and H. Coe, “A curved multi-component aerosol hygroscopicity model framework: Part 2 - Including organic compounds”, Atmospheric Chemistry and Physics. 5, 1223–1242. (2005b). [7] M. K. Jacobson. Fundementals of Atmospheric Modeling, 2nd edition. Cambridge University Press, 2005. [8] P. J. Connolly, C. Emersic, and P. R. Field, “A laboratory investigation into the aggregation efficiency of small ice crystals”, Submitted to Atmospheric Chemsitry and Physics Discussions. (2011). [9] P. J. Connolly et al., “Studies of heterogeneous freezing by three different desert dust samples”, Atmospheric Chemistry and Physics. 9, 2805–2824. (2009). [10] P. J. DeMott et al., “Predicting global atmospheric ice nuclei distributions and their impacts on climate”, Proceedings of the National Academy of Sciences of the United States of America. 107, 11217–11222. (2010). [11] J. P. Chen and D. Lamb, “The theoretical basis for the parameterization of ice crystal habits - growth by vapor-deposition”, Journal of the Atmospheric Sciences. 51, 1206–1221. (1994). [12] H. R. Pruppacher and J. D. Klett. Microphysics of Clouds and Precipitation. Kluwer Academic Publishers., 1997. [13] H. Morrison, J. A. Curry, and V. I. Khvorostyanov, “A new double-moment microphysics parameterization for application in cloud and climate models. Part I: Description”, Journal of the Atmospheric Sciences. 62, 1665–1677. (2005).

84

CHAPTER

FOUR INVESTIGATING THE SIMULATION OF CLOUD MICROPHYSICAL PROCESSES USING A 1-D FRAMEWORK The following chapter has been published in Atmospheric Science Letters under the full title of "Investigating the simulation of cloud microphysical processes in numerical models using a 1-D dynamical framework". See appendix A for reprint. Author: C. Dearden

This chapter is solely the work of C. Dearden and presents a strategy for comparing the performance of a suite of microphysics schemes of varying levels of complexity based on the Factorial Method. The purpose is to quantify the impact of microphysical sophistication on the simulation of liquid and mixed-phase clouds in numerical models, paying particular attention to the required level of coupling with aerosols. In this paper the chosen microphysics schemes are implemented and tested within a Lagrangian parcel model in advance of their inclusion within the 1-D framework. The parcel model tests are able to qualitatively demonstrate the importance of the treatment of droplet activation in bulk microphysics schemes. A diagnostic relationship for in-cloud supersaturation is also validated in the parcel model against a resolved treatment of supersaturation, and the benefits of the diagnostic approach are demonstrated for use in bulk parameterizations.

4.1

Introduction

The level of microphysical complexity implemented within a Numerical Weather Prediction (NWP) model or climate model is an important consideration because model complexity has to be balanced alongside cost implications, ultimately determined by compu85

CHAPTER 4. CLOUD MICROPHYSICAL PROCESSES IN A 1-D FRAMEWORK

tational limitations. It is important to capture liquid phase processes accurately not just because they determine the structure of warm clouds, but also because liquid droplets can exist at temperatures below 0 C in the form of supercooled water, which plays a role in ice formation through homogeneous and heterogeneous freezing mechanisms [1]. Consequently an accurate representation of the liquid phase should be achieved first, as a precursor to an eventual improved treatment of the ice phase. Since aerosols in the atmosphere are known to reduce the size of the energy barrier required for the phase transition of water, a study of liquid phase microphysics is incomplete without consideration of the role of cloud condensation nuclei (CCN). The effect of CCN can lead to the modification of cloud properties on the large-scale: the albedo of warm clouds is enhanced in the presence of CCN by virtue of an increase in the surface area of droplets [2]. Such interactions, known as aerosol indirect effects, can have important consequences for the net cloud radiative forcing and hence climate. Aerosol indirect effects may also be important for weather, as they can prolong the lifetime of a cloud by increasing the liquid water content due to a suppression in the drizzle rate [3]. However observational evidence is not always consistent with this [4], suggesting that the specifics of the meteorology may be important. This makes it difficult to isolate the aerosol effects and identify those that may be worthy of parameterization. In recent years, considerable advances in understanding have been made in accounting for CCN properties on droplet activation [5], and detailed process models have been designed to investigate the remaining uncertainty surrounding the role of organic compounds [6, 7]. Such process models can be used to inform and constrain the development of microphysics schemes that describe either the bulk properties of hydrometeors ("bulk schemes") or resolve the hydrometeor size distribution explicitly by breaking it down into discrete size bins ("bin schemes"). However the performance of these schemes still needs to be considered under a range of thermodynamic environments in order to establish whether the additional microphysical complexity can consistently add any skill to the model.

Bulk schemes work by assuming some form of the particle size distribution based on aircraft observations. Typically the distribution is based on a gamma function, which is in turn a function of particle diameter, D: 86

4.2. METHODOLOGY

nx (D) = nx0 D exp( x D); x

(4.1.1)

where the class of hydrometeor is denoted by x, nx is the number distribution, nx0 is the intercept parameter, x is the shape parameter (which when set to zero, reduces Eq. 4.1.1 to an exponential distribution) and x is the slope parameter. The size-mass relationship is specified as:

Mx ( D ) = c x D d ; x

where

(4.1.2)

Mx is the particle mass and cx and dx are constants. The moments M of the

particle size distribution are given by:

Mk =

Z1 1

Dk nx (D)dD;

where k can take any real value and denotes the k The number concentration corresponds to k

(4.1.3)

th moment of the size distribution.

= 0, and mass mixing ratio to k = dx , where

dx for a spherical hydrometeor is equal to three. Thus the moments return useful information regarding bulk cloud properties. Single moment schemes solve for the mixing ratio, related to the third moment, whereas dual moment schemes predict number concentration as well and so are doubly expensive because they must hold twice the number of prognostic variables. By predicting number as well as mass, dual moment treatments of cloud water must include a rate equation describing the activation of droplets and thus have the ability to parameterize the effects of aerosol. This study will attempt to quantify this advantage and decide whether the application of a dual moment bulk scheme can be warranted for the simulation of the liquid phase.

4.2

Methodology

The methodology adopted for this work is based on testing the performance of a suite of microphysics schemes of increasing levels of sophistication within a common 1-D framework. Such a framework enables control over atmospheric thermodynamic vari87


ables, whilst allowing the performance of the schemes to be analysed in isolation from systematic errors that can arise from elsewhere. Since CCN lead to the formation of liquid droplets in the atmosphere, specific consideration will be given to establishing the sensitivity of cloud properties to changes in aerosol properties such as concentration and composition. This will be achieved through the Factorial Method (FM), which involves systematically exploring the phase space of thermodynamic and microphysical variables to assess the impact on precipitation reaching the ground. This will enable an assessment to be made concerning the importance of aerosol effects in the context of changing meteorological conditions, and therefore whether any robust conclusions concerning cloudaerosol interactions can be reached. Equally as importantly, the minimum requirements needed to simulate these aerosol effects in numerical models will also be ascertained. The FM is described in Teller and Levin [8], where its application is demonstrated using the Tel Aviv University 2-D (TAU 2D) cloud resolving model to investigate the relative contributions of a number of factors to changes in surface precipitation from mixed-phase convective cloud. For brevity, the key aspects of the method are now described. Factors are chosen to reflect those variables whose effects require evaluation, e.g. CCN concentration, or initial temperature profile. If k factors are considered at two levels (corresponding to a high value and a low value), this would give a 2k factorial design. In the case of three factors, labelled A, B and C respectively, 8 simulations would be needed. Each simulation is labelled according to the level of the factors used, such that a high value of the factors A, B and C is denoted by a lowercase letter a, b and c respectively, and the low value is denoted by the absence of the corresponding letter. The case when all three factors are considered at their low levels is denoted as

(one). Thus the eight treatment

combinations in standard order can be written as (one), a, b, ab, c, ac, bc and abc. From this it can be seen that three degrees of freedom are associated with the main effects of A,

B and C , and four degrees of freedom are associated with the interactions between AB , AC , BC and ABC . The main effect of A can be obtained from the average of the four treatment combinations where A is at the high level, minus the average of the four treatment combinations where A is at the low level. In standard notation, this can be written as: 88

4.2. METHODOLOGY

((one) + b + c + bc) 4

(4.2.1)

1 A = [a + ab + ac + abc (one) b c bc] 4

(4.2.2)

A=

(a + ab + ac + abc) 4

The effects of B and C are obtained in a similar manner, yielding:

1 B = [b + ab + bc + abc (one) a c ac] 4

(4.2.3)

1 C = [c + ac + bc + abc (one) a b ab] 4

(4.2.4)

The effects of the two-factor interactions (namely thus. The

AB , AC and BC ) are computed

AB interaction can be thought of as one-half of the difference between the

average A effects at the two levels of B :

1 AB = [(average A effect at high B value) (average A effect at low B value)] 2 1 AB = [abc bc + ab b ac + c a + (one)] 4

(4.2.5)

Following similar logic, the AC and BC interactions are given by:

1 AC = [(one) a + b ab c + ac bc + abc] 4

(4.2.6)

1 BC = [(one) + a b ab c ac + bc + abc] 4

(4.2.7)

The remaining effect, the interaction of all three factors

(ABC ), is defined as the

average difference between the AB interaction for the two levels of C :

1 ABC = [abc bc ac + c ab + b + a (one)] 4 89

(4.2.8)


The terms in square brackets in the above equations are known as the contrasts in the treatment combinations. The contrasts are useful to evaluate since they are required to calculate the sums of squares for each of the effects. In general the sum of squares for any effect is calculated by:

SS =

1 (Contrast)2 2k

(4.2.9)

The relative contribution of each effect to the total variance can be quantified in terms of a percentage of the total sum of squares, where the total is given by:

SST = SSA + SSB + SSC + SSAB + SSAC + SSBC + SSABC

(4.2.10)

The reader is referred to Montgomery [9] for the general case where more than three factors need to be evaluated. The factors chosen for this particular study are: 1. Updraught speed (to explore the effects on the number of droplets activated at cloud base); 2. Initial temperature profile (to explore the effect of cloud base temperature on droplet activation); 3. Aerosol composition (to explore the impact of increases in organic material in both internal and external mixing states); 4. Aerosol size (to establish the impact of increasingly larger CCN); 5. Aerosol concentration (to investigate the relationship between increases in aerosol number and the rate of autoconversion) A 1-D column model (described in section 4.3.3) with prescribed forcing and a fixed vertical resolution will be used to drive a suite of microphysics schemes in order to investigate the impact of each of the above factors on surface precipitation. The impact on the cloud albedo will also be considered in terms of the effective radius of droplets, an important quantity for climate models to predict since it determines the cloud radiative forcing. 90

4.3. MODEL DESCRIPTION

The importance of the microphysical factors (aerosol composition, size and concentration) relative to the effects of meteorology (updraught speed and temperature profile) will be judged in terms of their role in explaining the total variance. The FM will be applied to both bin and bulk microphysics schemes in the same 1-D framework, including a dual moment liquid scheme with the option of prognostic aerosol, and a less computationally demanding single moment treatment of liquid. Results from the bulk schemes will be compared in turn with those from the bin scheme, to establish whether they are capable of producing similar sensitivities. As the complexity of the bulk schemes reduces, so does the potential to represent aerosol-cloud interactions. However this may not be a limiting factor if the effects of aerosol are shown from the bin scheme to be insignificant compared to the effects of meteorology. Ultimately the tests will identify the level at which aerosols need to be represented within a bulk microphysics scheme for the purpose of simulating liquid phase processes. Once the comparison of the microphysics schemes has been conducted in the 1-D framework, the bulk schemes will be engineered into a 3-D cloud resolving model and a series of warm and mixed-phase case studies will be performed in a mesoscale framework. This will qualitatively demonstrate whether any improvements in model skill can be had by increasing the complexity of the microphysics. Figure 4.1 shows a flowchart which summarises the methodology through from start to finish.

4.3 4.3.1

Model Description The bulk schemes

The bulk microphysics will be based around the existing scheme of Morrison et al. [10]. It includes a dual-moment representation of cloud liquid droplets, rain, cloud ice, snow and graupel, with assumed size distributions of the form given in Eq. 4.1.1. Within the Morrison scheme, various options are available to specify the treatment of droplet activation, and the representation of aerosol. This built-in flexibility will be exploited to develop a hierarchy of bulk schemes, starting from relatively simple microphysics, with each subsequent scheme benefiting from an incremental increase in complexity. This will allow any improvements in performance between schemes to be easily traceable and 91


Figure 4.1: Flowchart illustrating the application of the Factorial Method to assess the importance of cloud-aerosol interactions in the context of a changing meteoroligy with reference to an explicit bin scheme.

92


attributable. Details of the proposed hierarchy are now presented, along with a discussion of the added functionality each scheme provides relative to its predecessor.

Single moment liquid water and rain As the Morrison scheme uses a dual moment approach for all hydrometeors, a version of the scheme will be developed that simplifies the treatment of liquid water and rain to single moment; consequently droplet number must be prescribed. Typically in single moment schemes it is specified as a constant, e.g. Thompson et al. [11]. Although a single moment scheme cannot account for the effects of aerosol composition or size, the effects of aerosol concentration can be explored by proxy through changes in the prescribed droplet number.

Single moment liquid water, dual moment rain The use of a dual moment scheme for rain will facilitate the simulation of the thermodynamic indirect effect [12], since the predicted number concentration for rain will have an effect on the collection rate of cloud droplets by falling rain drops. This could be significant for cases of deep convection, where the amount of supercooled water that freezes homogeneously leads to the release of latent heat. The degree of latent heating can result in a more vigorous convective updraft, allowing higher cloud top heights to be achieved. Comparison with the single moment rain scheme will help to decide whether a dual-moment treatment of rain is necessary.

Dual momemt liquid water, dual moment rain The transition from prescribed droplet number concentration to a prognostic treatment has consequences for the simulation of the mixed phase, since it provides the opportunity to investigate the possibility of a riming indirect effect, first proposed by Lohmann and Feichter [12]. An explicit treatment of droplet activation is also required. Particular attention will be given to assessing the sensitivity of total precipitation to the handling of cloud droplet activation. The influence of aerosols will initially be accounted for using the activation spectrum relation [13], which relates droplet number N to supersaturation 93

CHAPTER 4. CLOUD MICROPHYSICAL PROCESSES IN A 1-D FRAMEWORK ratio, s:

N = csk ;

(4.3.1)

where c and k are constants that depend on the type of airmass, and s = (qv =qsat x

1)

100%, where qv is the (supersaturated) vapour mixing ratio and qsat is the saturation

mixing ratio. This requires the Morrison scheme to be able to predict supersaturations explicitly. Currently a saturation adjustment method is used, whereby excess water vapour above saturation is instantaneously removed and converted to the liquid phase. Such a method is justified within a mesoscale framework, where model timesteps are typically longer than the growth rate of droplets through condensation of the available water vapour. However this technique never permits a supersaturation to be maintained, thus rendering it incompatible with Eq. 4.3.1. Consequently to study droplet activation based on Eq. 4.3.1 in the 1-D framework, the saturation adjustment method must be replaced with a diffusional growth equation which is specified in Pruppacher and Klett [14]:

dm (qv =qsat 1) 0 = CF ; dt AB

(4.3.2)

where dm=dt is the rate of change of mass due to evaporation/condensation, AB is a function of temperature, C

= D=2 assuming spherical particles and F 0 is the ventilation

coefficient (in this study, ventilation effects are ignored for cloud droplets). To account for changes in aerosol composition in this scheme, N

s relationships for

different aerosol types can be constructed off-line using the bin-resolved microphysics scheme with droplet activation based on Kohler theory. From the N

s relations, N

w parameterizations for different aerosol types can then be developed in the manner of Twomey [15], such that the droplet number will depend on updraft speed

w rather than

the resolved supersaturation.

Dual moment liquid water and rain, with prognostic treatment of aerosol Whilst the previous schemes attempt to account for the effects of aerosols on some level, they do so non-interactively. The use of a prognostic dual moment scheme for aerosols addresses this limitation, such that the effect of aerosol transport on cloud prop94


erties is handled explicitly and so does not need to be parameterized. The dual-moment aerosol scheme would hold mass and number concentration as prognostic variables, and provided that the spread was known, the number size distribution of the aerosols present could be represented by a log-normal function [16]. The effects of aerosol size can then be explored by changing the spread of the log-normal function. A potential problem arises in that after activation of droplets, the aerosol size distribution will adjust back to a lognormal function, which may not be realistic. The issue of whether or not it is sufficient to reduce number and mass of aerosol and recalculate the parameters based on a log-normal relationship will be investigated. As well as internal mixtures, it will be possible to account for external mixtures in this scheme, by simply adding more prognostic variables to reflect different aerosol species.

4.3.2

The bin scheme

The bin scheme used to validate the performance of the bulk schemes is based on the Aerosol-Cloud-Precipitation-Interaction Model (ACPIM), which is in the final stages of development at the University of Manchester. It is a state of the art microphysical process model that accounts for multi-component aerosol thermodynamic properties in different mixing states, with droplet activation from Kohler theory. The microphysics is initialized assuming a log-normal aerosol size distribution, thus requiring inputs for the geometric mean diameter, the spread and the total aerosol number. ACPIM is particularly suited to studying the effects of aerosol composition on cloud because it uses results from the ADDEM model (Aerosol Diameter Dependent Equilibrium Model), described in detail in Topping et al. [6, 7], to obtain the equilibrium behaviour of multi-component aerosols. ADDEM allows for a treatment of the effect of curvature (the Kelvin effect) in determining the hygroscopic properties of mixed inorganic/organic aerosols, and uses the general form of the Kohler equation housed within an iterative loop with a guaranteed convergence scheme to solve for the new equilibrium state. This allows accurate equilibrium vapour pressures to be computed for a wide range of internal and external mixtures, which can then be fed as inputs into ACPIM to study the effects of composition on cloud properties. Although the focus of this paper is on the effects of CCN, the ACPIM also 95


allows the insoluble fraction of aerosol to be specified, thus making it a suitable scheme to study heterogeneous freezing processes [17]. This opens up the possibility of a future study to quantify the importance of ice nuclei (IN) effects on mixed-phase cloud using the FM.

4.3.3

The 1-D driver model

This study employs the Kinematic Driver model, KiD (http://appconv.metoffice. com/microphysics/doc.html) to force the microphysics and initiate cloud formation. The KiD model operates in a 1-D column with a fixed number of vertical levels and provides an ideal test bed for intercomparison of different microphysics schemes, based around a common advection component. The KiD model comes complete with a suite of test cases, the most simple of which consists of a single warm updraft, sinusoidal in time and constant in height, to advect vapour and hydrometeors in the vertical. Instantaneous cloud-related diagnostics, including hydrometeor mass mixing ratios, number concentration and surface precipitation, can be output at selected time intervals for subsequent analysis. The KiD model does not account for the effects of entrainment into the cloudy updraft; its main purpose is to provide a flexible framework that facilitates the testing and comparison of different microphysical treatments given a prescribed vertical velocity. While the importance of accurate atmospheric dynamics is recognized, it is first necessary to gain a fundamental understanding of the pure microphysical behaviour, and this is most easily achieved under relatively simple dynamical forcing. Subsequent work will then build on this understanding by introducing the effects of entrainment, in full 3-D case studies of warm clouds with a cloud resolving model. Prior to inclusion within the KiD model, the microphysics schemes will first be developed and tested within a closed lagrangian parcel model. Such a framework does not allow for the effects of sedimentation to be studied, hence why the KiD model must be used to fulfil the needs of this study. However a parcel model provides a suitable platform for comparing the different treatments of droplet activation, and how this determines the resulting number of droplets activated both at cloud base and within the cloud itself. The ability of the bulk schemes to capture accurate droplet concentrations will be a key factor in how they perform in a 1-D 96

4.4. INITIAL PARCEL MODEL RESULTS Table 4.1: Cloud base droplet number concentration (Nc; /cc), as a function of updraught speed for (top): maritime conditions (c = 120=cc and k = 0:4), and (bottom): continental conditions (c = 1000=cc and k = 0:5). Nc Twomey approximation Resolved supersaturation

10m/s 120 120

3m/s 120 115

1m/s 96 85

0.1m/s 54 47

Twomey approximation Resolved supersaturation

1000 900

719 623

517 429

259 204

column model; on this subject the parcel model can provide very useful insight. Some preliminary results are now discussed.

4.4

Initial parcel model results

The parcel model has been used to compare droplet number as predicted by the bulk scheme to that from the bin scheme. In the bulk microphysics scheme, Eq. 4.3.1 is used for droplet activation. However parcel model tests reveal that the resolved treatment of supersaturation requires a timestep of 0.1 seconds or better for stability. To overcome this problem, activation of droplets can be predicted from the Twomey [15] approximation, which is based solely on updraft speed and thus is not restricted by the choice of model timestep. Table 1 demonstrates the validity of the Twomey approximation for predicting cloud base droplet number concentrations. The predicted droplet number is compared under a range of updraft speeds and for activation parameters corresponding to both maritime and continental conditions. In all cases, the parcel model ascent was initialised with a temperature of 300K, a relative humidity of 95% and a pressure of 1000mb. The values predicted by the Twomey approximation lie within 10-20% of those predicted from the resolved supersaturation approach. The agreement improves at higher updraft speeds, and at lower values of c. However, while the Twomey approximation is sufficient to capture cloud base droplet number, once in-cloud, the processes of condensation and subsequent collision/coalescence become important. This is demonstrated using ACPIM in parcel model mode, as shown in figure 4.2. In this run, aerosols are assumed to consist solely of ammonium sulphate, with a geometric mean diameter of 60nm, a spread 97


Figure 4.2: A parcel expansion from the ACPIM model, showing aerosol number concentration versus temperature.

of 0.1 and a total aerosol number of 100/cc. A fixed updraft speed of 1m/s was prescribed, starting from an initial temperature of 300K, a relative humidity of 95% and a pressure of 1000mb. It can be seen how aerosol number reduces by an amount between 20-25% due to activation of droplets at cloud base, above which no further activation occurs because the supersaturation in the parcel reduces as the existing droplets grow by condensation. A similar parcel ascent was replicated with bulk microphysics, for the same initial thermodynamic conditions, and with the activation parameters c

= 100 and k = 0:4. Figure 4.3

shows how the Twomey approximation applied to in-cloud activation of droplets (blue line) would lead to a considerable overestimate of droplet number. When the supersaturation is resolved explicitly in the bulk scheme (figure 4.3; red line), droplet number above cloud base stays roughly constant initially and then rapidly reduces as the droplets grow big enough for self-collection and accretion processes to become important. However, autoconversion of droplets to rain acts to reduce droplet mass and number, which in turn reduces the sink of water vapour (figure 4.4), allowing the supersaturation within the parcel to slowly increase again (figure 4.4). Since the activity spectrum relation (equation 98

4.4. INITIAL PARCEL MODEL RESULTS

Figure 4.3: Parcel expansion with bulk microphysics, showing droplet number concentration versus temperature. The red line corresponds to a resolved treatment of supersaturation for droplet activation; the blue line represents the predicted droplet number when the Twomey approximation is used (i.e. based solely on updraft speed).

4.3.1) does not account for the depletion of CCN, anomalous new droplets are activated within the supersaturated environment. Figure 4.3 illustrates that the resolved supersaturation approach is clearly more desirable than the Twomey approach for droplet activation, since it accounts for condensation/deposition as a sink of water vapour and thus allows for a more realistic treatment of droplet activation when existing condensate is present (i.e. within cloud). However it requires a very short timestep for stability, rendering it impractical for use in operational models. A compromise can be struck by restricting the use of the Twomey approach to cloud base activation only. When in cloud, it is possible to approximate the result achieved with the resolved supersaturation approach without the restriction of very small timesteps; such an approach involves consideration of the prognostic equation for supersaturation, [10], which in the absence of the ice phase, is given by:

d = dt

1 1 + c r

dqsat dT 99

dT dt

RAD

gw ; cp

(4.4.1)


Figure 4.4: Plots from the bulk parcel model with resolved supersaturation. Top: The first moment of the liquid droplet size distribution ( = Nc (c + 1)=c , where Nc is the droplet number concentration), plotted as a function of temperature of the rising parcel. The first moment is proportional to the sink of water vapour. Bottom: Saturation ratio versus temperature.

100

4.5. SUMMARY where

= qv

qsat , T is temperature, c and r are the phase relaxation timescales

associated with cloud droplets and rain respectively, ( @T @t )RAD is the radiative heating rate (which is zero in the parcel model),

g is the gravitational acceleration, w is the vertical

velocity and cp is the specific heat of air at constant pressure. Solving Eq. 4.4.1 for d dt

= 0 yields a diagnostic relationship for the maximum supersaturation available for

droplet activation within the current timestep, which is given by:

dqsat = dT

dT dt

RAD

gw cp

1 1 + c r

1

Eq. 4.4.2 can be used for in-cloud activation of new droplets, by expressing

(4.4.2)

as a

percentage supersaturation ratio and inserting into Eq. 4.3.1. Then if the potential number of newly activated droplets predicted by Eq. 4.3.1 is less than the number that already exists, no additional droplets are activated within the timestep. To prevent unrealistically large droplet numbers when the phase relaxation timescale is long, the potential number of newly activated droplets is not allowed to exceed that obtained by the Twomey approach. The result is shown in figure 4.5, which compares predicted droplet number with resolved supersaturation in red with the diagnosed equilibrium supersaturation for in-cloud activation given by Eq. 4.4.2 in blue. Qualitatively the agreement is much better than in figure 4.3, with the added advantage that the equilibrium supersaturation method is not limited to small timesteps.

4.5

Summary

The Factorial Method of Teller and Levin [8] is to be employed within the 1-D Kinematic Driver model with state-of-the-art bin microphysics and aerosol. The use of the 1-D model is intended to aid in the identification of the key processes at work, providing isolation from non-linear interactions and systematic bias that may arise from other aspects of a model. The method will seek to separate the significance of aerosol effects on clouds from the effects of meteorology, and thus dictate the minimum level of complexity that needs to be incorporated into a bulk microphysics scheme to successfully simulate liquid clouds. Where possible, the potential for tuning aspects of a single moment liquid 101


Figure 4.5: Parcel model output comparing predicted droplet number with resolved treatment of supersaturation for droplet activation (red) with the diagnosed equilibrium supersaturation method for activation (blue).

scheme to a bin scheme will be explored, as a cost-effective alternative to the more expensive dual moment options. Initial results from a parcel model provides useful insight into the effects of changing the treatment of droplet activation in the bulk scheme, and reveals a potential weakness in schemes that do not include an explicit representation of aerosol. To investigate the impacts on surface precipitation, the microphysics schemes must be engineered into the KiD model where sedimentation between vertical levels is permitted. Thus future work will focus on applying the FM within the KiD framework for a range of updraft speeds and temperatures, to help quantify the benefits of increasing microphysical complexity based on the metrics of surface precipitation and effective radius. Particular attention will be given to establishing the benefits of a prognostic aerosol scheme in bulk schemes. The importance of entrainment will be addressed by performing 3-D case studies of warm clouds, to see if the conclusions from the FM/1-D experiments are upheld given more realistic dynamical forcing. 102

4.6. REFERENCES

Acknowledgements The author would like to thank Dr. Paul Connolly, University of Manchester, for supplying the ACPIM model, and Dr. Ben Shipway, UK Met Office, for supplying the KiD model.

4.6

References

[1] W. Cantrell and A. Heymsfield, “Production of ice in tropospheric clouds - A review”, Bulletin of the American Meteorological Society. 86, 795–+. (2005). [2] S. A. Twomey, “The influence of pollution on shortwave albedo of clouds”, Journal of the Atmospheric Sciences. 34, 1149–1152. (1977). [3] B. A. Albrecht, “Aerosols, cloud microphysics, and fractional cloudiness”, Science. 245, 1227–1230. (1989). [4] J. A. Coakley and C. D. Walsh, “Limits to the aerosol indirect radiative effect derived from observations of ship tracks”, Journal of the Atmospheric Sciences. 59, 668–680. (2002). [5] G. McFiggans et al., “The effect of physical and chemical aerosol properties on warm cloud droplet activation”, Atmospheric Chemistry and Physics. 6, 2593– 2649. (2006). [6] D. O. Topping, G. B. McFiggans, and H. Coe, “A curved multi-component aerosol hygroscopicity model framework: Part 1 - Inorganic compounds”, Atmospheric Chemistry and Physics. 5, 1205–1222. (2005). [7] D. O. Topping, G. B. McFiggans, and H. Coe, “A curved multi-component aerosol hygroscopicity model framework: Part 2 - Including organic compounds”, Atmospheric Chemistry and Physics. 5, 1223–1242. (2005b). [8] A. Teller and Z. Levin, “Factorial method as a tool for estimating the relative contribution to precipitation of cloud microphysical processes and environmental conditions: Method and application”, Journal of Geophysical Research-Atmospheres. 113, 13. (2008). 103


[9] D. C. Montgomery. Design and Analysis of Experiments. 5th ed. John Wiley, New York, 2005. [10] H. Morrison, J. A. Curry, and V. I. Khvorostyanov, “A new double-moment microphysics parameterization for application in cloud and climate models. Part I: Description”, Journal of the Atmospheric Sciences. 62, 1665–1677. (2005). [11] G. Thompson, R. M. Rasmussen, and K. Manning, “Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part I: Description and sensitivity analysis”, Monthly Weather Review. 132, 519–542. (2004). [12] U. Lohmann and J. Feichter, “Global indirect aerosol effects: a review”, Atmospheric Chemistry and Physics. 5, 715–737. (2005). [13] R. R. Rogers and M. K. Yau. A Short Course in Cloud Physics, 3rd edition. Butterworth and Heinemann, 1989. [14] H. R. Pruppacher and J. D. Klett. Microphysics of Clouds and Precipitation. Kluwer Academic Publishers., 1997. [15] S. A. Twomey, “The Nuclei of Natural Cloud Formation. Part II: The Supersaturation in Natural Clouds and the Variation of Cloud Droplet Concentrations”, Geofisica pura e applicata. 43, 227–242. (1959). [16] M. K. Jacobson. Fundementals of Atmospheric Modeling, 2nd edition. Cambridge University Press, 2005. [17] P. J. Connolly et al., “Studies of heterogeneous freezing by three different desert dust samples”, Atmospheric Chemistry and Physics. 9, 2805–2824. (2009).

104

CHAPTER

FIVE

EVALUATING EFFECTS OF MICROPHYSICAL COMPLEXITY WITH THE FACTORIAL METHOD The following chapter has been published in Atmospheric Chemistry and Physics, under the full title of "Evaluating the effects of microphysical complexity in idealised simulations of trade wind cumulus using the Factorial Method". See appendix B for reprint. Authors: C. Dearden, P. J. Connolly, T. W. Choularton and P. R. Field

The aim of this chapter is to explore and quantify the effects of microphysical complexity in simulations of marine boundary layer cloud using surface precipitation as a metric. This paper applies the statistical tool of the Factorial Method as described in the previous chapter to quantify the sensitivity of idealised warm cloud to changes in complexity of the liquid phase. The atmospheric modelling community may find such an approach to be a useful validation and development tool for comparing and contrasting the behaviour of different microphysics schemes under a set of controlled conditions. This chapter is primarily the work of C. Dearden. The ACPIM model used in this study was created by Dr. Paul Connolly; Prof. Choularton and Dr. Field assisted in the proof-reading of the final manuscript. Note that the study by Shipway & Hill (2011) as referenced in this chapter is currently awaiting publication under the revised title of "Diagnosis of systematic differences between multiple parametrizations of warm rain microphysics using a kinematic framework". 105

CHAPTER 5. EVALUATING MICROPHYSICAL COMPLEXITY WITH THE FACTORIAL METHOD

5.1

Introduction

Shallow convective clouds play an important role in the global circulation and the hydrological cycle of the Earth system. Sub-tropical marine shallow cumuli, capped by the trade wind inversion, transport moisture vertically within the cloud layer, where it is subsequently detrained and transported to the tropics by the trade winds to fuel deep convection within the Inter Tropical Convergence Zone (ITCZ). The development of precipitation in trade wind cumuli is believed to be sensitive to cloud condensation nuclei (CCN) concentrations by virtue of aerosol-cloud interactions, and such interactions could potentially have important climatological consequences [1]. Yet the overall magnitude of this sensitivity is poorly understood. Twomey [2] showed that an increase in CCN concentration under a fixed liquid water content can lead to higher cloud droplet number concentrations but a reduction in overall droplet size. Albrecht [3] later suggested that the reduction in size of cloud droplets as a result of the Twomey effect could potentially act to reduce the precipitation efficiency of marine boundary layer clouds. However the extent to which aerosols are able to modify cloud macroscopic properties in a buffered system such as the Earth’s atmosphere is likely to be more subtle than a consideration of microphysical processes alone would suggest [4]. In principle, numerical models are useful tools to help establish and understand the complex nature of the interaction between aerosols, clouds and precipitation in the context of the trade wind regime. However, the macrostructure of shallow maritime convective cloud is poorly represented in the current generation of General Circulation Models (GCMs), and consequently such large-scale models are not a suitable basis upon which to explore such links. This has been shown most recently in a study by Medeiros & Stevens[5], who used a conditional sampling technique to demonstrate that GCMs struggle to produce a satisfactory macrophysical representation of the shallow cumulus cloud regime when validated against reanalysis data. The poor representation of shallow convection in GCMs stems from their reliance upon convective parameterizations, which is also believed to be responsible for the uncertainty surrounding global estimates of the climate sensitivity [6]. Instead it is more appropriate to use Large Eddy Simulations (LES) at convection-permitting resolutions of 100 m or less to investigate the extent to which cloud 106

5.1. INTRODUCTION

microphysical processes influence the cloud macrostructure. Field campaigns such as the Rain In shallow Cumulus over the Ocean project [RICO, 7] and the INDian Ocean EXperiment [INDOEX, 8] play an important role in constraining and validating LES models, [e.g., 1, 9]. In particular, the LES intercomparison study of vanZanten et al [10] based on the RICO field study suggests that differences in the representation of microphysical processes is the main reason for the large variation in the timing and amount of precipitation produced between models.

LES models based on bulk microphysical parameterizations typically operate by assuming a functional form of the hydrometeor size distribution and solve prognostic equations representing the moments of the distribution, namely the mass mixing ratio for single-moment (1-m) schemes and additionally number concentration for dual-moment (2-m). Bulk schemes are cheaper to run than explicit bin schemes, but must make simplifying assumptions in order to ensure computational efficiency. As the reliance on bulk microphysics schemes is likely to continue in the future, it is becoming increasingly necessary to develop objective methods of validating their performance. This has typically been achieved via comparison against explicit bin-resolved microphysics within simple kinematic driver models. For example the study of Morrison & Grabowski [11] used a 2-D kinematic framework to assess the performance of 2-m bulk microphysics in terms of simulating warm clouds using an explicit bin scheme as a benchmark, where both schemes assume a fixed background aerosol size distribution. They considered idealised representations of a shallow cumulus regime and a stratocumulus regime. However such regimes can themselves cover a broad range of environmental conditions, and it is important to assess the sensitivity of the microphysics to variations in the meteorological conditions as well. The observational study of Nuijens et al [12] assessed the sensitivity of precipitation from shallow cumulus during RICO to variations in the meteorological environment, and concluded that subtle variations in the meteorological conditions can have a strong influence on precipitation, even speculating that this may be a stronger control on precipitation than aerosol effects alone. It is fair to say that in general, the need to account for changes in meteorology when using LES models to evaluate microphysical sensitivities has been somewhat overlooked. Recent exceptions include the work of Wang & McFarquhar [1] 107

CHAPTER 5. EVALUATING MICROPHYSICAL COMPLEXITY WITH THE FACTORIAL METHOD and Teller & Levin [13]. In the case of the latter, the Factorial Method (FM) was used to quantify the sensitivity of precipitation in simulations of mixed-phase convective cloud when both meteorological and microphysical factors occur synergistically. The technique of isolating the effects of individual factors in the context of atmospheric modelling was pioneered by Stein & Alpert [14]. Dearden [15] proposed to expand the use of the FM across a hierarchical suite of microphysics schemes within a one dimensional kinematic framework, consisting of a bulk scheme with the choice of both 1-m and 2-m liquid water, and an explicit bin scheme with prognostic treatment of aerosol, capable of accounting for the effects of aerosol composition. Such a method allows the macroscopic forcing conditions to be easily constrained, and is adopted here in relation to quantifying the impact of microphysical complexity on precipitation development in the context of idealised shallow cumulus cloud. The sensitivity of the bulk schemes can be quantified and compared to that of the bin scheme such that it may be possible to isolate those meteorological regimes where the additional microphysical complexity is warranted. It is important to note that the nature of the 1-D kinematic framework is such that it does not permit feedbacks between microphysics and dynamics and thus does not provide a complete representation of cloud dynamics. Whilst the importance of feedback effects are recognised, they also make it difficult to isolate differences that arise purely from the treatment of microphysics and potentially other factors (such as the numerical treatment of advection), and so an idealised study in the absence of feedbacks is beneficial in terms of identifying and understanding the potential limitations of simpler bulk parameterizations. The simplicity of the driver model also allows for a greater number of sensitivity tests to be performed compared to 3-D simulations due to the reduced computational burden. Finally simple 1-D frameworks have very recently been used to develop our understanding of rain formation in shallow cumulus clouds [16], and also to develop improved parameterizations of rain evaporation for use in dual-moment bulk schemes [17], which demonstrates their usefulness as a tool for advancing our understanding in this area.

This paper is organised as follows. A description of the microphysics and the idealised driver model are presented in section 5.2. Section 5.3 considers the details of the experimental design based on the FM. The results from each microphysics scheme are 108

5.2. MODEL CONFIGURATION

analysed and compared in section 5.4, and the potential implications of these findings are addressed in section 5.5, including a discussion of how feedbacks between microphysics and dynamics may potentially modify the sensitivities shown.

5.2

Model configuration

The suite of microphysical schemes considered for testing are embedded within a 1-D column framework, within which the initial temperature and humidity profiles are prescribed, along with the vertical velocity field responsible for producing the supersaturation necessary for cloud formation. The hierarchy of microphysical complexity ranges from a fully explicit treatment of liquid water and aerosol to a bulk parameterization of warm rain processes with the option of both 2-m and 1-m cloud liquid water. A detailed description of each of the schemes considered is now given, starting with the bin microphysics.

5.2.1

Bin microphysics

The bin scheme used in this study is the Aerosol-Cloud-Precipitation-InteractionModel (ACPIM), developed at the University of Manchester. ACPIM is a state-of-the-art process model that has been created primarily to study the effects of aerosol on mixedphase cloud as part of the core modelling suite for the Aerosol Properties Processes And InfluenceS on the Earth’s climate (APPRAISE) project. For the purpose of this study its use is restricted to liquid-only processes. The ACPIM model supports a prognostic treatment of aerosol, allowing the effects of the aerosol size distribution and also composition to be explored; this feature was used in the simulations performed for this study. Activation of droplets in ACPIM is based on Köhler theory. 147 mass bins are used to resolve the liquid drop size distribution, and 154 are used for aerosol. The ambient supersaturation is resolved using a variable sub-step to ensure it is captured to a sufficient level of accuracy, regardless of the choice of the main model timestep. Each aerosol bin solves prognostic equations for the mass and number of aerosols. Condensation occurs continuously via the droplet growth equation [18], where the equilibrium vapour pressure is supplied by Köh109

CHAPTER 5. EVALUATING MICROPHYSICAL COMPLEXITY WITH THE FACTORIAL METHOD ler theory using data from a thermodynamic model [ADDEM, 19]. The growth equation is solved explicitly using the Variable-coefficient Ordinary Differential Equation solver (VODE) available from the netlib repository (www.netlib.org). Initial growth of the cloud droplets is dominated by the diffusional growth equation, and subsequent growth to rain drop size through the collision-coalescence process is handled by explicitly solving the 2-D stochastic collection equation [20], with the collision efficiency based on the look up table by Hall [21]. In the version of ACPIM used for this study, the efficiency of coalescence is taken to be unity, such that the overall collection efficiency is equal to the Hall collision efficiency. In terms of gas kinetic effects, the condensation coefficient in all cases is taken to be unity, based on Laaksonen et al [22]. For this study, a single log-normal aerosol size distribution is used with a geometric standard deviation of 1.28, and a geometric mean diameter of 0.06 microns. These values are based on the bimodal distribution defined in the RICO model intercomparison study [10]; the giant mode was found to have minimal impact on precipitation for the range of CCN concentrations considered. In terms of the aerosol composition, pure sea-salt was assumed in all cases. Tests with ammonium sulphate were also performed, although the effect on precipitation was found to be small, with only a slight increase in rain at lower updraught speeds.

5.2.2

Bulk microphysics

The bulk scheme is based on a liquid-only version of the scheme described in Morrison et al [23], such that the two classes of hydrometeor considered are cloud liquid water and rain. The scheme is a flexible multi-moment scheme, allowing the choice of either a 1-m or 2-m treatment for liquid droplets. The scheme also contains different options for the treatment of droplet activation in the 2-m liquid case. Saturation adjustment is used in the bulk schemes, such that any water vapour present above 100% relative humidity is assumed to instantaneously condense onto existing cloud droplets. Such an assumption is appropriate because the mass of water vapour above saturation is typically much smaller than the mass of cloud water. The autoconversion and accretion schemes used in all cases are those of Khairoutdinov & Kogan [24], henceforth 110

5.2. MODEL CONFIGURATION

referred to as the KK scheme. A radius of 25 microns is used to separate the cloud liquid water and rain categories. The microphysical process rates in the KK scheme are formulated via multiple nonlinear regression of simulated spectra from LES studies of marine boundary layer clouds, and so are considered to be an appropriate choice for this study. Self-collection of rain drops is also accounted for, and is based on the parameterization specified in Seifert & Beheng [25]. Self-collection of rain drops is potentially an important process; indeed the LES study of shallow convection by Stevens & Seifert [26] suggests that bulk schemes which do not include a parameterization of self-collection are more likely to exhibit higher evaporation rates due to having rain drop spectra that contain higher concentrations of smaller rain drops. In all cases, a 2-m scheme is used for rain. Dearden [15] had originally proposed to include a 1-m treatment for rain as well, but this was not included in the final experimental design because it was not possible to identify a single value of the rain intercept parameter that was appropriate for different values of droplet number concentration. The benefits of 2-m rain over 1-m rain have been well documented recently, e.g. in the studies by Morrison et al [27], although Shipway & Hill [28] and references therein suggest that 2-m rain schemes with an invariant shape parameter can suffer from the problem of excessive size-sorting. The particle size distribution for both rain and cloud liquid water is defined by a gamma distribution [29] of the form

n(D) = N0 D e

D

(5.2.1)

where n(D) is the number concentration for a given particle diameter size D; the integral of equation 5.2.1 with respect to the intercept parameter,

D gives the total number concentration, NT . N0 is

is the slope parameter and is the shape parameter. N0 is

determined as a function of the total number concentration

N0 =

NT +1 ( + 1)

(5.2.2)

For rain, is set to zero, which reduces equation 5.2.2 to an exponential distribution [30], 111

CHAPTER 5. EVALUATING MICROPHYSICAL COMPLEXITY WITH THE FACTORIAL METHOD such that N0

= NT .

Terminal fall speeds for rain are given by the following

Vr (D) = (0 =)g ar Db ef D ; r

r

r

(5.2.3)

where 0 is the density of air at sea level, and the constants ar , br , fr and gr are set to 841, 0.8, 0.0 and 0.54 respectively, following Liu & Orville [31]. The different combinations of the bulk scheme are now presented, starting with the simplest level of complexity.

1-m liquid, 2-m rain In the simplest treatment considered here, only one prognostic variable is used to represent cloud liquid water (the mass mixing ratio), and the droplet number concentration is taken as a constant in the calculation of the intercept parameter in equation 5.2.2. The experimental set up of the 1-m scheme is such that the assumed droplet number concentration is taken to be equal to the CCN concentration, with the implicit assumption that all available CCN activate to form cloud droplets.

2-m liquid (Twomey activation), 2-m rain Moving from 1-m to 2-m liquid grants the ability to predict droplet number, thus requiring an explicit term representing activation of cloud droplets. The consequence of this is that in the 2-m scheme, not all available CCN are necessarily activated for a given updraught speed, which may lead to lower droplet number concentrations when compared to the 1-m scheme. The first treatment of droplet activation considered is based on the parameterization of Twomey [32], which in Rogers & Yau [33] is approximated as:

NCCN 0:88c2=(k+2) [7:10 2 w3=2 ]k=(k+2) where w is the grid-scale vertical velocity in cms

1

(5.2.4)

and the number concentration of active

CCN is NCCN , in cm 3 . The variables c and k are activation parameters where c represents the number concentration of CCN active at 1% supersaturation and k represents the ease 112

5.2. MODEL CONFIGURATION with which droplets form. In this study, a value of 0.4 is used for k based on measurements of tropical maritime airmasses [18].

2-m liquid (Abdul-Razzak activation), 2-m rain

The second option for droplet activation is based on the parameterization of AbdulRazzak et al [34], henceforth identified as A-R, which assumes a single log-normal aerosol size distribution for a given chemical composition, requiring knowledge of the geometric mean radius of aerosol particles and the standard deviation. This information is then used to parameterise the maximum supersaturation in the rising air parcel given the vertical velocity, which in turn determines the fraction of aerosols activated to form cloud droplets. The aerosol log-normal parameters used are the same as those employed to initialise the bin model, as is the assumed chemical composition. By repeating the 2-m liquid simulations using the A-R scheme for droplet activation, it will be possible to quantify the benefits of explicitly specifying the aerosol log-normal parameters, albeit assuming a fixed form. Dearden [15] had originally proposed the option of a prognostic treatment of aerosol for the bulk scheme; however this was not considered due to time constraints. The possibility of a 2-m aerosol scheme coupled to the 2-m bulk microphysics will be revisited in future work on the subject. The only difference between the 2-m schemes is in terms of the droplet activation scheme used. For cloud base activation, droplet number in the A-R scheme is determined as a function of both the updraught speed and the aerosol properties. This is different from the Twomey approach, which determines cloud base droplet number based on the updraught speed and the value of the chosen c and k parameters. In both the Twomey and A-R cases, in-cloud activation is also permitted, and is based on a diagnostic calculation of the in-cloud equilibrium supersaturation within the current timestep. This diagnostic relation is a feature of the Morrison scheme, and should a supersaturation be diagnosed, in-cloud activation is allowed to occur via the specified activation scheme. 113


5.2.3

Driver model configuration

The bulk microphysics are driven using the 1-D Kinematic Driver Model, KiD [28] whilst the ACPIM microphysics is currently embedded within its own 1-D column model. To obtain consistency with ACPIM, some changes have been made to the standard KiD model to ensure consistency between driver models, thus ensuring that both bin and bulk microphysics schemes can be compared rigorously. The details of the necessary changes in the KiD model are now presented.

Advection The advection scheme common to both driver models is a 4th order, positive definite, monotonic scheme of Bott [35, 36]. The Bott scheme is used to advect vapour and liquid water. The default advection scheme in the KiD model is the Total Variance Diminishing (TVD) scheme of Leonard [37] known as ULTIMATE, but for the purpose of this study the Bott scheme is used for consistency with ACPIM. There is no advection of potential temperature in the column; indeed the potential temperature and pressure fields are held fixed such that the microphysics is not permitted to influence the evolution of the dynamics. This was deemed necessary such that the pure microphysical behaviour of each scheme could be compared fairly, in the absence of thermodynamic feedbacks. A slight caveat is in the handling of sedimentation. The ACPIM driver model is configured to combine sedimentation with vertical advection due to air motion in a single calculation, which is handled using the 4th order Bott scheme. In KiD, sedimentation of cloud liquid water and rain is handled within the Morrison microphysics scheme itself using a timesplit 1st order upwind method, where a size threshold of 50 microns diameter is used to separate cloud liquid water from rain. The potential implications of these differences are addressed in section 5.4.

Initialisation of thermodynamics Both models accept inputs for potential temperature and vapour mixing ratio at specified height levels; this defines the initial thermodynamic profiles. These points are then linearly interpolated onto the model vertical grid at every level. The model then con114

5.3. EXPERIMENTAL DESIGN

verts from potential temperature to absolute temperature to pass to the microphysics, for which it needs the pressure field. Pressure is obtained by solving the following first-order differential based on the hydrostatic equation and the ideal gas law:

pg dp = dz RT

(5.2.5)

Equation 5.2.5 is solved based on Press et al [38] in both KiD and ACPIM.

5.3 5.3.1

Experimental design Initial conditions and idealised forcing

The forcing for the idealised warm shallow cumulus case is based on the “warm1” configuration as defined in the KiD documentation which can be downloaded from http: //appconv.metoffice.com/microphysics/doc.html. It consists of a single updraught, constant in height and sinusoidal in time:

8 > < w1 sin(t=t2 ) w(z; t) = > : 0:0

if t < t2 ,

(5.3.1)

if t > t2

The timescale t2 is dependent upon the peak updraught speed, w1 , such that t2

= 1200=w1 .

For a peak updraught speed of 0:5 ms 1 , this would result in the vertical velocity field reducing to zero after 2400 s. Thus values of

w1 greater than 0.5 ms

1

would reduce the

timescale over which the updraught is applied. The evolution of the updraught velocity with time for different values of

w1 is plotted in Figure 5.1, as applied equally at every

vertical level. The warm1 case is based on the composite profile used to initialise models for the GCSS RICO intercomparison. However, as noted in Shipway & Hill [28], there is a slight issue with simulations based on the warm1 profile in that the resulting profile of liquid water content decreases with height after reaching a maximum above cloud base, which is not necessarily realistic for a warm shallow convective cloud. This is a consequence of the fact that the whole column is lifted in response to the vertical velocity field, where at 115


5

w =4m/s 1

w =2m/s

4.5

1

w1=1m/s

Magnitude of vertical velocity (m/s)

4

w1=0.5m/s

3.5 3 2.5 2 1.5 1 0.5 0 0

500

1000

1500 2000 Time (seconds)

2500

3000

3500

Figure 5.1: Vertical velocity fields as a function of time, as applied to the 1-D column equally at every vertical level.

a given timestep the applied vertical velocity is the same at every gridpoint. The relative humidity reaches a peak at around 750 m; at grid points above this height, the relative humidity begins to decrease such that the amount of water vapour available for condensation is reduced, leading to a slight reduction in liquid water content with height. Despite this, and given the highly idealised nature of the 1-D framework to begin with, the warm1 profile still acts as a suitable basis upon which to conduct a comparison of different microphysics schemes. The reader is made aware that in the 1-D intercomparison of Shipway & Hill [28], the lowest levels of the warm1 profile were made slightly drier, to produce a liquid water content profile that increased with height and an overall reduction in liquid water path. This produced a reduction in surface precipiation totals relative to the original warm1 profile, given the same peak updraught velocity. Changes in temperature are considered such that the warm1 profile is shifted to cooler temperatures resulting in a constant cooling with height whilst keeping the relative humidity fixed. The result is such that changes in thermodynamics do not affect the cloud height or depth. The temperature profile used in this study is plotted in Figure 5.2. In all cases, the simulations are left to run for long enough until they have finished precipitating (typically two hours) and diagnostic output is available at the end of each timestep (every 116


RICO 3000 T Td 2500

Height (metres)

2000

1500

1000

500

0 −5

0

5

10 15 20 Temperature (Degrees C)

25

30

Figure 5.2: Temperature (solid) and dew-point temperature (dashed) profiles in C taken from the RICO model intercomparison, and used to initialise the models. The additional profiles, “RICO-2” and “RICO-5”, are obtained by cooling the RICO profile uniformly in height by 2 C and 5 C respectively under a fixed relative humidity. 5 s). The vertical grid spacing in both models is set to 30 m, with 100 levels giving a domain height of 3 km.

5.3.2

Experimental design for the Factorial Method

The experimental design based around the FM is now presented. It should be noted that changes in meteorological factors, namely the temperature profile and updraught velocity, are treated consistently in each scheme; however the choice of microphysical factors to explore depends on the level of complexity of the microphysics scheme in question. The factorial design is based around the 2n design, meaning two values, arbitrarilly labelled “low” and “high”, are assigned to n number of factors, and the effect of changing from the “low” to the “high” value is calculated for each factor. Values for each factor are chosen such that the effect of moving from the “low” value to the “high” value acts to reduce the amount of precipitation reaching the surface. Thus each factor can be evaluated in terms of its percentage contribution to precipitation suppression. In some cases, repetitions of the 2n design are considered to allow the effect of more than one “high” value to be explored. 117

CHAPTER 5. EVALUATING MICROPHYSICAL COMPLEXITY WITH THE FACTORIAL METHOD Table 5.1: Design matrix for the general 23 factorial design. Run

1 2 3 4 5 6 7 8

A

B

C

+ +

+ +

+ +

+ +

+ + + +

Labels (one)

a b ab c ac bc abc

General example: 23 design

Consider the following general example based on 3 factors, labelled A, B and C respectively, each at two levels, yielding a

23 design. Thus eight treatment combinations

(experiments) would be necessary to fulfill the requirements of the study. To denote low and high values, the geometric notation system is used such that “ ” indicates low and “+” indicates high, and the eight runs required in the

23 design are given in Table 5.1.

Table 5.1 also writes the treatment combinations based on the labelling system of lowercase letters, which in standard order is written as (one), a, b, ab, c, ac, bc and abc. In this system, the presence of a lowercase letter represents the high value of that factor, and the absence of a letter denotes the low value. The label (one) is reserved for the case when all factors are at their low value. Using the lowercase letter labels, it is possible to write down expressions for the main effects; that is, the average effect of each factor due to the change in value from low to high. Similar expressions for the interactions between main effects can also be derived. For full details on the calculation of the main effects and interaction terms based on a general 23 design, the reader is referred to Dearden [15] and references therein. Once the main effects and interaction terms have been calculated, the relative contribution of each effect or interaction to the total variance can also be quantified in terms of a percentage of the total sum of squares. The calculation of the sum of squares for a given effect or interaction term is also specified in Dearden [15]. 118


Factorial design for bin microphysics Table 5.2 summarises the factorial design for the ACPIM model. A 23 design is used, giving three factors in total, two of which, namely w1 and T , are meteorological in nature and represent vertical velocity and the ambient temperature respectively. The remaining factor, CCN, is a microphysical factor which represents the number concentration of the aerosol present within the column at each vertical level. 36 numerical simulations are required to fulfill the design presented in Table 5.2. The CCN factor is designed to explore the effect of increasing the aerosol number concentration from a starting value of 50/cc, whilst the geometric mean radius and standard deviation as defined in section 5.2 are held constant.

Factorial design for bulk microphysics

Table 5.3 summarises the factorial design for the bulk microphysics, also based around a 23 design and requiring 135 simulations in each case. The reduced computational burden of the bulk parameterizations compared to the bin scheme is exploited to perform a more thorough exploration of the parameter space. The meteorological factors w1 and T are defined to be the same as in the bin scheme, although the w1 factor covers a greater range of values. In the 2-m bulk scheme, the CCN factor relates to the maximum droplet number concentration permitted. For 2-m Twomey, this is equal to the value of c in equation 5.2.4. For 2-m A-R, the CCN factor relates to the aerosol number concentration based on the unimodal log-normal distribution, as in the bin scheme. In the 1-m scheme, the CCN factor is simply the prescribed value of droplet number, which implicitly assumes that all available aerosol have activated to form cloud droplets. It should be noted that no attempt was made to tune the bulk schemes to the bin scheme prior to running the experiments. It should also be recognised that the choice of c and k parameters in the Twomey case implies a different aerosol spectrum compared to that used in the other schemes, which could contribute to differences in droplet number concentration, most notably at low updraught speeds. 119

CHAPTER 5. EVALUATING MICROPHYSICAL COMPLEXITY WITH THE FACTORIAL METHOD Table 5.2: Summary of the factorial design for the bin microphysics. Factor

w1 T

CCN

Description Values 1 Peak vertical velocity (ms ) 0.5, 1, 2, 4 Temperature Profile RICO, RICO-2, RICO-5 Aerosol no. concentration (/cc) 50, 100, 200

Table 5.3: Summary of the factorial design for the bulk microphysics. Factor

w1 T

CCN

5.4 5.4.1

Description Values 1 Peak vertical velocity (ms ) 0.5 to 4 in intervals of 0.25 Temperature Profile RICO, RICO-2, RICO-5 Aerosol number concentration /cc (2-m A-R) 50, 100, 200 No. of droplets active at 1% supersaturation /cc (2-m Twomey) Droplet number concentration /cc (1-m)

Results Initial analysis of cloud fields

To illustrate the equality of the driver models, tests were performed based on both the bulk and bin microphysics with precipitation and sedimentation processes switched off, such that the only microphysical processes permitted are condensation and evaporation. The resulting liquid water paths from each scheme are plotted in Figure 5.3. It can be seen that the curves agree so closely that they appear to be coincident, which confirms the consistency of the forcing conditions between driver models (and also confirms the validity of the saturation adjustment approach used in the bulk schemes). It can also be concluded from this result that, once precipitation and sedimentation are permitted to occur, any subsequent differences in cloud liquid water path can be attributable to the treatment of these processes. Figure 5.4 shows time-height plots from the bin and 2-m A-R schemes with precipitation and sedimentation enabled, for w1

= 2 ms 1 , T = RICO and CCN = 100/cc. In both

cases, the dynamical forcing conditions produce a cloud whose base is around 500 m and a top at 2 km. As the prescribed updraught reduces to zero, and in the absence of any parameterised entrainment effects or negative vertical velocities, a thin residual layer of cloud is allowed to persist in a steady state. Admittedly this is not realistic; indeed Seifert 120

5.4. RESULTS

3 2−m bin

Liquid water path (kg m−2)

2.5

1−m

2

1.5

1

0.5

0

−0.5 0

500

1000

1500 2000 2500 Time (seconds)

3000

3500

Figure 5.3: Timeseries of liquid water path from the 1-m, 2-m A-R and bin schemes in the absence of precipitation and sedimentation, such that all condensed water stays in the cloud. The results shown were obtained with the following settings: w1 =2 ms 1 , T = RICO and CCN = 100/cc. & Stevens [16] showed that the finite lifetime of shallow cumulus cloud is an important timescale in determining precipitation efficiency. However this shortcoming does not impinge upon the ability of the model to reveal interesting differences in the behaviour of the chosen microphysics schemes. Furthermore, the influence of the residual cloud layer on the precipitation rate is minimal because the droplets that remain are too small for effective collision and coalescence to occur, and so there is no real concern of any possible contamination issues arising from this deficiency. To allow comparison of rain mixing ratios, the bin scheme diagnoses rain based on those liquid drops greater than 50 microns in diameter, in accordance with the KK scheme. The results share some similarities with those of Seifert & Stevens [16], who used a similar 1-D model to compare an alternate pair of bin and 2-m bulk microphysics schemes with each other, but some differences as well. For instance, both studies show that the bulk scheme is able to capture the height and time of rain formation reasonably well. However in this particular study, Figures 5.4 and 5.5 show that the bin simulation converts more of the cloud to rain than the bulk scheme. Given that the liquid water paths are essentially the same in the absence of precipitation processes as shown in Figure 5.3, this suggests that 121


Figure 5.4: Comparison of cloud droplet number concentration (m 3 ), cloud mass mixing ratio (kg kg 1 ) and rain mixing ratio (kg kg 1 ) from the 2-m A-R scheme (left) and the bin scheme (right). The results shown are taken from simulations with w1 = 2 ms 1 , T = RICO and CCN = 100/cc.

3

2 2−m bulk (A−R) Bin

1.8

2.5

1.6 Rain water path (kg m−2)

Cloud liquid water path (kg m−2)

2−m bulk (A−R) Bin

2

1.5

1

1.4 1.2 1 0.8 0.6 0.4

0.5

0.2 0 0

10

20

30

40

50

0 0

60

Time (minutes)

10

20

30

40

50

60

Time (minutes)

Figure 5.5: Comparison of cloud liquid water path (left) and rain water path (right) in kgm 2 from the 2-m A-R scheme (dashed) and bin scheme (solid), for those simulations shown in Fig. 5.4.

the collision-coalescence process in the ACPIM bin scheme is more efficient at producing rain compared to the KK autoconversion and accretion schemes. The implications of the larger rain water path in the bin scheme are addressed later in section 5.4.3. It should also be remembered that the bulk scheme uses an exponential size distribu122

5.4. RESULTS

Figure 5.6: Time-height plot of the diagnosed shape parameter for rain from the bin scheme, obtained through the method of moment-conserving fits (see Appendix A). The plot shown is from the CCN=50/cc case, with w1 =0.5 ms 1 and T = RICO profile.

tion for rain, which implicitly assumes a shape parameter of zero. It is possible to test the validity of this assumption using the bin scheme; this is accomplished by fitting a gamma function to the resolved size distribution and diagnosing for rain through consideration of those drops greater than or equal to 50 microns in diameter. This is achieved through the method of moment-conserving fits, the mathematics of which are derived in Appendix A. Figure 5.6 plots the evolution of the diagnosed shape parameter with height and time from the bin scheme. The magnitude of varies considerably through the evolution of the cloud; around the onset of in-cloud rain formation, values of

is close to zero, but

are consistently higher below cloud base. This result is important since a

varying shape parameter has implications for rates of sedimentation [39] and evaporation, which could be significant in full 3-D simulations when feedbacks between microphysics and dynamics can influence the temperature of the sub-cloud layer. The deficiencies of assuming a fixed value of zero are also discussed in Stevens & Seifert [26]. 123


5.4.2

Comparison of total precipitation

Table 5.4 shows the total precipitation amounts (in mm) for a subset of the total number of experiments from all four schemes. The nature of the table allows for comparison of each scheme as a function of changing CCN concentrations, cloud base updraught speeds and temperature profiles. Before a more rigorous analysis of this data is performed using the FM, some broad observations can first be made. With regard the 1-m scheme, the assumption of a fixed droplet number means that the total precipitation is essentially insensitive to vertical velocity; however in the other schemes, an increase in the magnitude of vertical velocity generally produces a reduction in the total amount of precipitation produced, with some minor exceptions to this pattern at low updraught speeds. This is a consequence of the ability of the other three schemes to predict droplet number; not all CCN are necessarily activated as cloud droplets for a given updraught. The reduction of precipitation towards larger updraughts can be attributed to aerosol indirect effects, since stronger vertical velocities activate more CCN which in turn reduces the precipitation efficiency (the reader is reminded that by design, the maximum extent the column is lifted is the same regardless of the updraught speed; this explains why precipitation amounts do not increase with higher vertical velocities). It can also be seen that as vertical velocity is increased in the 2-m schemes, the total precipitation amounts begin to converge on those from the 1-m scheme. It is worthy of note that in some instances, an increase in w1 from 0.5 ms

1

to 1 ms

1

some of the 0.5 ms

actually results in a slight increase in precipitation. This is because 1

simulations are still producing small amounts of drizzle at the end

of the integrations, and so have not quite finished precipitating by the time the simulations are stopped. Thus precipitation totals appear slightly underestimated in these cases. All four schemes agree, at least in a qualitative sense, on a reduction in precipitation amount as a function of cooling temperature. This is because under a fixed relative humidity, the available source of water vapour that is converted to liquid water during condensation is reduced as the temperature profile cools. Figures 5.7 and 5.8 plot the precipitation rate and accumulated precipitation totals respectively as a function of time, for those experiments highlighted in bold in Table 5.4. Figure 5.7 reveals that all four schemes show a delay in the onset of precipitation as a 124

5.4. RESULTS

1−m

2−m (Twomey) 10

w1=4m/s

Surface precip rate (mm per hour)


10

w1=2m/s 8

w1=1m/s w1=0.5m/s

6

4

2

0 0

20

40

60

80

100

w1=2m/s 8

w1=1m/s w1=0.5m/s

6

4

2

0 0

120

w1=4m/s

20

40

Time (minutes) 2−m (A−R) Surface precip rate (mm per hour)


10

w1=4m/s w1=2m/s

8

w1=1m/s w =0.5m/s 1

6

4

2

20

40

60

80

100

120

Bin

10

0 0

60

Time (minutes)

80

100

w1=2m/s 8

w1=1m/s w =0.5m/s 1

6

4

2

0 0

120

w1=4m/s

20

40

Time (minutes)

60

80

100

120

Time (minutes)

Figure 5.7: Timeseries of surface precipitation rates (mm/hr) from each scheme. Clockwise from top left: 1-m, 2-m Twomey, bin, 2-m A-R. Results are shown with CCN = 100/cc and T = RICO, for four different values of w1 . 2−m (Twomey) 1.8

1.6

1.6

Accumulated surface precip (mm)


1−m 1.8

1.4 1.2 1 0.8 0.6

w1=4m/s

0.4

w1=2m/s w1=1m/s

0.2 0 0

w1=0.5m/s 20

40

60

80

100

1.4 1.2 1 0.8 0.6

w1=4m/s

0.4

w1=2m/s

0 0

120

w1=1m/s

0.2

w1=0.5m/s 20

40

Time (minutes)

1.6

1.6

1.4 1.2 1 0.8 0.6

w1=4m/s

0.4

w1=2m/s w1=1m/s

0.2

w1=0.5m/s 20

40

60

80

100

120

Bin 1.8



2−m (A−R) 1.8

0 0

60

Time (minutes)

80

100

1.4 1.2 1 0.8 0.6

w1=4m/s

0.4

w1=2m/s

0 0

120

Time (minutes)

w1=1m/s

0.2

w1=0.5m/s 20

40

60

80

100

120

Time (minutes)

Figure 5.8: Timeseries of accumulated surface precipitation (mm) from each scheme. Clockwise from top left: 1-m, 2-m Twomey, bin, 2-m A-R. Results are shown with CCN = 100/cc and T = RICO, for four different values of w1 . 125

CHAPTER 5. EVALUATING MICROPHYSICAL COMPLEXITY WITH THE FACTORIAL METHOD Table 5.4: Surface precipitation totals (mm) for each scheme as a function of CCN and w1 for three different temperature profiles, namely RICO (top); RICO-2 (middle); and RICO-5 (bottom). Those results highlighted in bold type are plotted in Figure 5.7 and Figure 5.8 as timeseries of surface precipitation rate and accumulated surface precipitation respectively. CCN RICO

w1 = 0:5 ms w1 = 1:0 ms w1 = 2:0 ms w1 = 4:0 ms

1-m 1 1 1 1

50/cc 1.38 1.40 1.40 1.40

RICO-2

w1 = 0:5 ms w1 = 1:0 ms w1 = 2:0 ms w1 = 4:0 ms

1-m 1 1 1 1

50/cc 1.21 1.23 1.23 1.22

RICO-5

w1 = 0:5 ms w1 = 1:0 ms w1 = 2:0 ms w1 = 4:0 ms

100/cc 1.22 1.24 1.24 1.23

100/cc 1.04 1.06 1.06 1.06 1-m

1 1 1 1

50/cc 0.97 0.99 0.98 0.98

100/cc 0.80 0.81 0.81 0.81

2-m (Twomey) 200/cc 50/cc 1.00 1.48 1.02 1.44 1.41 1.02 1.02 1.41

100/cc 1.35 1.30 1.25 1.24

200/cc 50/cc 1.18 1.39 1.13 1.41 1.08 1.41 1.03 1.40

2-m (Twomey) 200/cc 50/cc 0.82 1.32 0.84 1.27 1.25 0.84 0.84 1.24

100/cc 1.18 1.13 1.08 1.07

200/cc 50/cc 1.00 1.24 0.96 1.25 0.90 1.24 0.86 1.24

2-m (Twomey) 200/cc 50/cc 0.58 1.08 0.60 1.04 1.01 0.60 1.01 0.60

100/cc 0.93 0.89 0.84 0.83

200/cc 50/cc 0.76 1.02 0.72 1.01 0.66 1.01 0.62 1.00

2-m (A-R)

Bin

100/cc 1.30 1.26 1.25 1.24

100/cc 1.57 1.54 1.52 1.49

200/cc 50/cc 1.24 1.63 1.09 1.67 1.04 1.67 1.03 1.65

2-m (A-R)

Bin

100/cc 1.14 1.08 1.07 1.07

100/cc 1.38 1.34 1.31 1.29

200/cc 50/cc 1.07 1.47 0.91 1.48 0.86 1.47 0.86 1.46

2-m (A-R)

Bin

100/cc 0.90 0.84 0.83 0.83

100/cc 1.12 1.06 1.03 1.01

200/cc 50/cc 0.82 1.22 0.66 1.21 0.62 1.20 0.61 1.18

200/cc 1.47 1.34 1.27 1.25

200/cc 1.27 1.13 1.06 1.05

200/cc 0.99 0.84 0.78 0.76

function of reducing vertical velocity. The timing of surface precipitation is quite similar between the bulk and bin schemes, with a slight tendency for the bulk scheme to produce fractionally earlier surface precipitation at lower updraught speeds. There is a relatively large jump in the peak precipitation rates between the 2-m bulk schemes and the bin scheme; consequently the bin scheme produces larger precipitation totals than the bulk schemes as confirmed by Figure 5.8. It is interesting to note that in the KiD intercomparison study by Shipway & Hill [28], the 1-m Morrison scheme was found to overestimate precipitation as validated against the explicit TAU bin model [40] in the same idealised framework. This is in contrast to the results shown here when comparing the Morrison bulk scheme with ACPIM, suggesting that differences between bin schemes can be as large as those between bulk schemes. A similar conclusion was also reached in the 3-D LES intercomparison of vanZanten et al [10], where the spread in precipitation amongst the three bin models considered was found to be as large as the variation between the bulk schemes. A possible explanation for the difference in this particular case is that the TAU126

5.4. RESULTS

bin model accounts for the coalescence efficiencies of droplets based on the work of Ochs et al [41], which acts to reduce the number of successful collisions involving collector drops in the size range 0.1 to 0.6 mm, whereas the version of ACPIM used in this study assumes a coalescence efficiency of unity for all drop sizes. A detailed investigation into the impact of collection efficiencies on surface precipitation in bin schemes is beyond the scope of this study; however this should be considered in future work to determine the extent to which the choice of collection kernel can account for differences in behaviour between bin schemes.

5.4.3

Factorial analysis: quantifying the effects of CCN, w1 and T (23 design)

The FM is now used to quantify the sensitivity of the schemes to the choice of microphysical and meteorological factors based on the data provided in Table 5.4. This section explores the relative importance of each factor as a function of time throughout the evolution of the cloud, and compares the sensitivities of each scheme to illustrate differences in behaviour. Calculation of the relative contributions for each factor and their interactions follows the methodology explained in Dearden [15]. Figure 5.9 considers the effect of changes in each factor on the metric of accumulated surface precipitation, and the relative importance of each factor in terms of the enhancement or suppression of surface precipitation is expressed as a percentage of the total variance as a function of time. Specifically, an increase in w1 is considered from 0.5 ms 2 ms 1 , along with a cooling of the temperature profile,

1

to

T , from RICO to RICO-2, and

an increase in CCN from 50/cc to 100/cc. Figure 5.9 shows that, in all four schemes, the change in precipitation is dominated by the change in vertical velocity in the early stages of cloud development. Beyond 40 minutes, the relative importance of the vertical velocity effect reduces and by the end of the simulations, the change in temperature produces the largest effect on the suppression of precipitation. However the schemes disagree on the extent of the relative importance of the CCN and temperature effects. It can be seen in Figure 5.9 that the contribution of the CCN effect is largest in the 1-m scheme; this is a consequence of the experimental setup for the 1-m scheme where an assumption is made 127

CHAPTER 5. EVALUATING MICROPHYSICAL COMPLEXITY WITH THE FACTORIAL METHOD that the change in droplet number is equal to the change in CCN concentration, independent of the change in vertical velocity. For the 2-m bulk schemes, the contribution of the CCN effect is slightly reduced; this can be explained as follows. For slowly increasing updraught speeds such as the 0.5 ms

1

case, the ability to predict droplet number results

in competition for water vapour between growth of existing droplets and activation of new droplets; this is demonstrated by Dearden [15] using a simple lagrangian parcel model. The presence of CCN that activate at relatively low updraught speeds act as a sink of water vapour through growth by condensation, resulting in fewer droplets being activated overall compared to the 1-m scheme where by design the droplet number concentrations are slightly higher. This explains why the 1-m scheme has the largest relative contribution from the effect of CCN according to Figure 5.9. However the 2-m A-R scheme, which includes a parameterization for the maximum supersaturation based on the vertical velocity and the properties of the aerosol size distribution, shows less of a change in droplet number at low updraught speeds and therefore less of an impact on precipitation. Consequently Figure 5.9 shows that the 2-m A-R scheme improves the comparison with the bin scheme. However in more rapidly increasing updraughts, Figure 5.10 shows that the benefit of predicting droplet number concentration is lost and the 2-m A-R scheme produces largely the same sensitivity as the 1-m scheme. This is a consequence of the fact that, towards larger vertical velocities, the droplet number concentrations converge in the bulk schemes, thus producing very similar sensitivities. Some additional simulations with the 1-m scheme were also performed where the assumed droplet concentration at low updraught speeds was set to a value more representative of the predicted values from the 2-m A-R scheme. The results from these tests (not shown) reveal that tuning the droplet number concentration in the 1-m scheme allows the total precipitation values to match those produced by the 2-m A-R scheme, whilst also improving the agreement in terms of the relative contributions. This result suggests that a diagnostic representation of droplet number based on CCN number and updraught velocity would be sufficient to capture aerosol indirect effects for the chosen scenario. This has important implications when considering the balance between model complexity and computational efficiency, as it shows that in the absence of feedbacks at least, a prognostic variable for droplet

128

5.4. RESULTS

1−m

2−m (Twomey)

100

100 CCN Temperature Vertical velocity Interactions

90

80

Relative Contribution (%)


80 70 60 50 40 30

70 60 50 40 30

20

20

10

10

0 0

20

40

60

80

100

CCN Temperature Vertical velocity Interactions

90

0 0

120

20

40

Time (minutes)

2−m (A−R)

100

120


90

80

70 60 50 40 30

70 60 50 40 30

20

20

10

10 20

40

60

80

100


90


80


80

Bin

100

0 0

60

Time (minutes)

0 0

120

Time (minutes)

20

40

60

80

100

120

Time (minutes)

Figure 5.9: Relative contribution (%) timeseries plots for each scheme, considering the effects of changes in CCN, w1 and T , plus their combined interaction effects. The relative contribution is calculated as a percentage of the total variance associated with the change in precipitation at the surface. The contributions shown are based on the following changes: w1 from 0.5 ms 1 to 2 ms 1 ; CCN from 50/cc to 100/cc, and T from RICO to RICO-2. Clockwise from top left: 1-m, 2-m Twomey, bin, 2-m A-R. number may not be necessary, and that a diagnostic treatment of droplet number could help to minimise the cost of the scheme without compromising the ability of the model to capture the effects of aerosol. The remaining difference in sensitivities between the bin and 2-m A-R bulk scheme as shown in Figures 5.9 and 5.10 can be explained by considering the effects of evaporation below cloud base. It has already been shown that the rain mass falling out of the cloud in the bin scheme is greater than in the bulk schemes (Figure 5.4), but also that the bin scheme produces consistently larger amounts of surface precipitation. It is hypothesised that differences in collection efficiencies between the bulk and bin schemes are contributing to the different sensitivities to temperature and CCN, and specifically that larger rain drop sizes in the bin scheme are leading to an overall reduction in rain evaporation. To explore this hypothesis, a sensitivity test was performed with the 2-m A-R scheme where the rain fall speed parameter br is increased from the default value of 0.8 to 0.825 to facilitate 129

CHAPTER 5. EVALUATING MICROPHYSICAL COMPLEXITY WITH THE FACTORIAL METHOD 1−m

2−m (Twomey)

100


90

80



80 70 60 50 40 30

70 60 50 40 30

20

20

10

10

0 0

20

40

60

80

100


90

0 0

120

20

40

Time (minutes)

2−m (A−R)

100

120


90

80

70 60 50 40 30

70 60 50 40 30

20

20

10

10 20

40

60

80

100


90


80


80

Bin

100

0 0

60

Time (minutes)

0 0

120

Time (minutes)

20

40

60

80

100

120

Time (minutes)

Figure 5.10: As for Fig. 5.9 but for an increase in w1 from 2 ms

1

to 4 ms 1 .

larger rain drops, in order to test the impact on evaporation and the amount of rain that reaches the surface. Table 5.5 shows that the modification to the fallspeeds for rain in the bulk scheme leads to an increase in accretion, a reduction in rain evaporation, and in turn an increase in the total surface precipitation. Figure 5.11 shows the effect of this change on the relative contributions in the bulk scheme, and illustrates how the effect of CCN is reduced at the expense of the effect of temperature in accordance with the bin scheme. However it is also recognised that differences in the numerical treatment of sedimentation between the bin and bulk schemes (as discussed in section 5.3) may be contributing to the difference in sensitivities as well. To explore this further, extra tests were performed with the bulk scheme where the existing first-order treatment of sedimentation was circumvented and replaced with increasingly higher order forward-difference approximations as specified in Jacobson [42, p. 180], up to and including a fourth-order scheme for consistency with the bin model. Results from these tests (not shown) reveal that increasing the order of approximation from first to second order leads to a small increase in total surface precipitation (around 5%) over the range of bulk simulations considered. Subsequent increases to third and fourth order accuracy were found to have negligible impact 130

5.4. RESULTS Table 5.5: Rain evaporation (kgm 2 ; top), accretion (kgm 2 ; middle) and surface precipitation (mm; bottom) accumulated over 2 h from the 2-m A-R scheme, as a function of CCN, w1 and T , and also from the 2-m A-R scheme with increased fallspeed parameter for rain, such that br = 0:825. The evaporation and accretion terms are calculated by integrating the process rates with height at each timestep, and then integrating these values in time over a 2 h period. RICO

w1 0.5 ms 1.0 ms 2.0 ms 4.0 ms

1 1 1 1

RICO-2

2-m A-R 2-m A-R (br = 0:825) 2-m A-R 2-m A-R (br = 0:825) 50/cc 100/cc 50/cc 100/cc 50/cc 100/cc 50/cc 100/cc 0.48 0.45 0.41 0.39 0.44 0.41 0.38 0.35 0.43 0.41 0.37 0.35 0.41 0.39 0.35 0.33 0.44 0.42 0.37 0.36 0.42 0.40 0.35 0.34 0.43 0.41 0.36 0.35 0.45 0.43 0.38 0.36 RICO

w1 0.5 ms 1.0 ms 2.0 ms 4.0 ms

1 1 1 1

RICO-2

2-m A-R 2-m A-R (br = 0:825) 2-m A-R 2-m A-R (br = 0:825) 50/cc 100/cc 50/cc 100/cc 50/cc 100/cc 50/cc 100/cc 1.58 1.57 1.64 1.63 1.41 1.40 1.47 1.46 1.60 1.55 1.65 1.62 1.43 1.37 1.48 1.44 1.60 1.55 1.65 1.62 1.43 1.36 1.48 1.43 1.42 1.36 1.47 1.43 1.58 1.54 1.63 1.61 RICO

w1 0.5 ms 1.0 ms 2.0 ms 4.0 ms

1 1 1 1

RICO-2

2-m A-R 2-m A-R (br = 0:825) 2-m A-R 2-m A-R (br = 0:825) 50/cc 100/cc 50/cc 100/cc 50/cc 100/cc 50/cc 100/cc 1.39 1.30 1.49 1.41 1.24 1.14 1.33 1.25 1.41 1.26 1.51 1.38 1.25 1.08 1.34 1.21 1.41 1.25 1.51 1.38 1.24 1.07 1.34 1.20 1.24 1.07 1.34 1.20 1.40 1.24 1.51 1.37

on precipitation. These results suggest that the use of a lower order treatment of sedimentation in the bulk scheme does not contribute significantly to the differences shown when comparing against the bin scheme.

5.4.4

Factorial analysis: the effect of increasing vertical velocity for a fixed temperature (22 design)

It is now prudent to explore the sensitivity of surface precipitation to different levels of change in the vertical velocity field. The sensitivities of each scheme can be compared through consideration of the total effect on precipitation suppression, as described in section 5.3; the sign and magnitude of the result indicates the direction and significance of 131



90


80 70 60 50 40 30 20 10 0 0

20

40

60 Time (minutes)

80

100

120

Figure 5.11: As Figure 5.9 but for the 2-m A-R scheme with modified fallspeed parameter for rain, such that br is increased from the default value of 0.8 to 0.825. All other fallspeed parameters are unchanged.

the induced change. In this case the factors considered are CCN and

w1 , with a fixed

background temperature and humidity based on the RICO profile, yielding a

22 design.

The results from the following FM analysis are based on values of surface precipitation accumulated at the end of the model simulation. Following the logic from section 5.3, the 22 design has three degrees of freedom, such that the total effect is equal to the sum of the effects of the two main factors plus their interaction. Figure 5.12 considers the total effect on precipitation resulting from repeated increases in w1 from a low value of 0.5 ms 1 , plus the additional effect of an increase in CCN from 50/cc to 100/cc. For the 1-m scheme, Figure 5.12 illustrates that the reduction in precipitation is due solely to the change in droplet number and is essentially insensitive to changes in updraught speed, which is clearly a limitation when comparing against the bin scheme (solid black line) under the same conditions. In theory the sensitivity of the 1-m scheme to vertical velocity could be increased by using a diagnostic relationship for droplet number concentration instead of the assumption of a fixed value as used in this study. Both 2-m schemes show an increase in suppression of rainfall as a function of increasing vertical velocity, which in a qualitative sense agrees with the bin scheme. However the 2-m Twomey scheme considerably overestimates the amount by which pre132

5.4. RESULTS

0 Bin 2−m (Twomey) 1−m 2−m (A−R)

−0.05

Total effect (mm)

−0.1

−0.15

−0.2

−0.25

0.5

1

1.5 2 2.5 3 Change in vertical velocity (from 0.5 m/s)

3.5

4

Figure 5.12: Total effect on suppression of precipitation (in mm) from each scheme as a function of changes in w1 and CCN, under a fixed temperature (T = RICO). Changes in w1 are considered from 0.5 ms 1 up to 4 ms 1 , and the change in CCN is from 50/cc to 100/cc.

cipitation is suppressed. This can be understood by considering the total precipitation for the 50/cc case from Table 5.4. The 2-m Twomey scheme produces relatively more precipitation than the other schemes at low updraught speeds, suggesting that it activates fewer droplets at 50/cc. Thus when the value of CCN is increased to 100/cc, the suppression of precipitation appears to be exaggerated. The implications of this are that for this idealised case, a single value of k for different CCN concentrations is not appropriate, and that the value of k should change as a function of the assumed CCN concentration. This problem is alleviated in the 2-m A-R scheme, where knowledge of the aerosol composition and log-normal size distribution is advantageous in obtaining a better agreement with the bin scheme.

For values of

w1 starting from 2 ms

1

(as shown in Figure 5.13), all four schemes

are in much better agreement in terms of the overall amount by which precipitation is suppressed. Thus it is difficult to justify the increased computational expense of a 2-m liquid scheme in this regime when a 1-m scheme performs in such a similar manner. 133


0 Bin 2−m (Twomey) 1−m 2−m (A−R)

−0.05

Total effect (mm)

−0.1

−0.15

−0.2

−0.25

2

2.5 3 3.5 Change in vertical velocity (from 2.0 m/s)

4

Figure 5.13: As Fig. 5.12 but for changes in w1 starting from 2 ms 1 .

5.5

Summary and discussion

The Factorial Method has been used to compare the sensitivities of warm shallow cumulus cloud as simulated by four different microphysics schemes of increasing levels of complexity using an idealised 1-D column framework. The use of a simple driver model is intended to aid the comparison by removing the sensitivity to dynamical feedbacks, thus isolating the pure microphysical behaviour. The chosen factors include the magnitude of the cloud base vertical velocity, the ambient temperature profile, and the assumed number of aerosol available to act as CCN. The sensitivity of each scheme was assessed and quantified in terms of the suppression of precipitation at the surface, with the bin scheme used as a benchmark in order to validate the performance of the bulk schemes. The reader is reminded that all of the results found in this study are specific to the particular test case in question, and future work will be necessary using the tools presented in this paper to determine the generality of our results. For the idealised case considered in this study where feedback effects are neglected, the performance of the bulk schemes for cloud base updraught speeds up to 2 ms

1

was found to depend on the assumptions

made with regards the method of droplet activation. At updraughts larger than 2 ms 1 , all schemes activate most if not all of the available CCN and so essentially reduce to the same droplet number concentrations. In this regime the 2-m bulk schemes were found 134

5.5. SUMMARY AND DISCUSSION

to behave much like the 1-m bulk scheme. This suggests that for models with sufficient resolution, it is theoretically possible to optimise the balance between complexity and cost by allowing the model to choose the appropriate level of microphysical detail based on the magnitude of the cloud base updraught speed and knowledge of microphysical parameters such as aerosol number concentration and size. This stresses the importance of coupling the microphysics to a prognostic aerosol scheme to provide the necessary information. It should also be noted that it was possible to tune the 1-m scheme at low updraught speeds to produce essentially the same precipitation amounts and sensitivities as the 2-m scheme, by fixing the assumed droplet number concentration to match those of the predicted concentrations. This suggests that in the absence of feedbacks, a diagnostic relationship for droplet number may perform just as well as a prognostic treatment. This has obvious advantages in terms of computational efficiency given that one less prognostic variable would need to be advected. Further comparison of the schemes also highlighted some fundamental differences in behaviour worthy of comment. For instance the bin scheme consistently produced larger amounts of precipitation when compared to the bulk schemes, even in scenarios where all schemes produced very similar droplet number concentrations. A cooling of the temperature profile by 2 C under a fixed relative humidity was also found to produce a relatively higher contribution to precipitation suppression in the bin scheme compared to the bulk schemes. It was possible to enhance the dominance of the temperature effect in the bulk scheme and thus improve the agreement with the bin scheme by modifiying the fallspeed parameters for rain, which served to increase accretion, reduce evaporation and thus increase the surface precipitation. Differences in evaporation of rain between schemes may have important consequences in terms of dynamical feedbacks in full 3-D simulations, by modifying the extent of evaporative cooling of the sub-cloud layer. A consideration of such feedbacks is beyond the scope of this paper, but warrants further investigation in future work. It is important to note that separate intercomparison studies comparing bin and bulk schemes using the KiD framework do not necessarily support the conclusion that bin schemes produce more precipiation than bulk schemes. Thus the enhanced sensitivity to 135

CHAPTER 5. EVALUATING MICROPHYSICAL COMPLEXITY WITH THE FACTORIAL METHOD temperature as seen in the ACPIM bin model may not be a general feature of bin schemes. Although it was shown that the bulk scheme could be effectively tuned to produce better agreement with this particular bin scheme, the same tuning may not necessarily improve the agreement relative to other bin schemes. Future work should therefore focus on investigating and understanding the origin of differences between bin schemes to increase confidence in their use as benchmarks against which simpler bulk parameterizations are validated. Suggested variables for investigation include the number of size bins used to resolve the liquid size distribution, the treatment of aerosol (whether a fixed log-normal mode or prognostic), the choice of collection kernel and the numerical treatment of advection. In light of these potential sources of differences, the need to constrain bin schemes with field observations and laboratory experiments is also recognised.

A big caveat in producing these conclusions is the absence of entrainment and feedback effects in the 1-D framework. The 1-D framework does not account for entrainment mixing within the cloud, and in reality, the effect of entrainment mixing could to some extent counteract the change in temperature due to vertical advection. There is a growing suggestion within the available literature that the inclusion of feedback effects is likely to dampen the sensitivity of warm clouds to increases in aerosol loadings. For instance, the study by Jiang et al [43] used a 3-D LES modelling approach to compare the lifetime of polluted cumulus clouds to those of clean cumulus clouds when entrainment is allowed to occur. The results suggest the overall lifetime of both the polluted and clean clouds are statistically similar, and propose an evaporation-entrainment feedback mechanism which acts to dilute polluted clouds (i.e. reduce liquid water content) and therefore reduce the overall sensitivity of warm shallow cumuli to changes in aerosol concentration. Stevens & Feingold [4] also argue that in reality, the sensitivity of clouds and precipitation to changes in aerosol concentration is on average weaker than a purely microphysical consideration alone would suggest, due to the capacity of the system to respond differentially to changes in aerosol, thereby acting to buffer the global system against such changes and reducing the overall effect. Stevens & Sefiert [26] even suggest that the effect of increased aerosol loadings on shallow convection could in some instances lead to an enhancement of precipitation, since the delay in the onset of rain formation may allow the cloud to 136

5.6. APPENDIX A: METHOD OF MOMENT-CONSERVING FITS

achieve a greater depth and therefore a higher liquid water path. Therefore the results of this study should be considered only as a starting point, with the recommendation that the techniques of factor separation be utilised in future work to help quantify the extent to which the sensitivities shown in this paper are modified within a more realistic dynamical framework.

5.6

Appendix A: Method of moment-conserving fits

Diagnosis of the shape parameter for in the ACPIM model is based on the following methodology, which fits the resolved liquid size distribution for drop diameters greater than 50 microns to a gamma function. In general, the k -th moment of a size distribution n(D) is specified as:

Mk = where in this case

Z1 0

Dk n(D)dD

(5.6.1)

n(D) is based on a gamma distribution as in equation 5.2.1. The

k-th moment of a gamma distribution can be expressed analytically, and is given by: Mk = N0

( + k + 1) +k+1

(5.6.2)

Consequently the zeroth, first and second moments of a gamma distribution are written as follows:

( + 1) +1 ( + 2) M1 = N0 +2 ( + 3) M2 = N0 +3

M0 = N0

(5.6.3) The quantity F is now introduced and defined as the square of the first moment divided by the product of the second and zeroth moments: 137


F=

( + 2)2 M12 = M2 M0 ( + 1) ( + 3)

(5.6.4)

Using the following property of gamma functions,

() = ( 1) ( 1)

(5.6.5)

it is possible to re-write the expression for F as follows:

F=

( + 1)2 ( + 1)2 +1 = ( + 1)( + 2)( + 1) ( + 1) + 2

(5.6.6)

Rearranging equation 5.6.6 in terms of gives:

=

1 2F F 1

(5.6.7)

Equation 5.6.7 is used to calculate the shape parameter , where the quantity

F is

obtained from the model microphysics based on explicit calculation of the moments of the resolved size distribution given by Mk

=

Pm

k i=1 Ni Di , where

Ni and Di are the number

concentration and diameter respectively for size category i, and m is the total number of size bins. Rain was diagnosed in the bin scheme using a diameter thresold of 50 microns for consistency with the bulk autoconversion scheme.

Acknowledgements The first author would like to thank Ben Shipway and Adrian Hill of the Met Office for their advice and feedback in setting up the KiD model. Thanks also to Hugh Morrison of NCAR, USA for supplying the latest version of the bulk microphysics code used in this study, and to the three anonymous reviewers whose comments helped to improve the final manuscript.

138

5.7. REFERENCES

5.7

References

[1] H. L. Wang and G. M. McFarquhar, “Modeling aerosol effects on shallow cumulus convection under various meteorological conditions observed over the Indian Ocean and implications for development of mass-flux parameterizations for climate models”, Journal of Geophysical Research-Atmospheres. 113, 20. (2008). [2] S. A. Twomey, “The influence of pollution on shortwave albedo of clouds”, Journal of the Atmospheric Sciences. 34, 1149–1152. (1977). [3] B. A. Albrecht, “Aerosols, cloud microphysics, and fractional cloudiness”, Science. 245, 1227–1230. (1989). [4] B. Stevens and G. Feingold, “Untangling aerosol effects on clouds and precipitation in a buffered system”, Nature. 461, 607–613. (2009). [5] B. Medeiros and B. Stevens, “Revealing differences in GCM representations of low clouds”, Climate Dynamics. 36, 385–399. (2010). [6] S. Bony and J. L. Dufresne, “Marine boundary layer clouds at the heart of tropical cloud feedback uncertainties in climate models”, Geophysical Research Letters. 32, 4. (2005). [7] R. M. Rauber et al., “Rain in shallow cumulus over the ocean - The RICO campaign”, Bulletin of The American Meteorological Society. 88, 1912+. (2007). [8] A.J. Heymsfield and G.M. McFarquhar, “Microphysics of INDOEX clean and polluted trade cumulus clouds”, Journal of Geophysical Research-Atmospheres. 106, 28653–28673. (2001). [9] S. J. Abel and B. J. Shipway, “A comparison of cloud-resolving model simulations of trade wind cumulus with aircraft observations taken during RICO”, Quarterly Journal of the Royal Meteorological Society. 133, 781–794. (2007). [10] M. C. vanZanten et al., “Controls on precipitation and cloudiness in simulations of trade-wind cumulus as observed during RICO”, Journal of Advances in Modelling Earth Systems, in press. (2011).

139

CHAPTER 5. EVALUATING MICROPHYSICAL COMPLEXITY WITH THE FACTORIAL METHOD [11] H. Morrison and W. W. Grabowski, “Comparison of bulk and bin warm-rain microphysics models using a kinematic framework”, Journal of the Atmospheric Sciences. 64, 2839–2861. (2007). [12] L. Nuijens, B. Stevens, and A. P. Siebesma, “The Environment of Precipitating Shallow Cumulus Convection”, Journal of the Atmospheric Sciences. 66, 1962– 1979. (2009). [13] A. Teller and Z. Levin, “Factorial method as a tool for estimating the relative contribution to precipitation of cloud microphysical processes and environmental conditions: Method and application”, Journal of Geophysical Research-Atmospheres. 113, 13. (2008). [14] U. Stein and P. Alpert, “Factor Separation in Numerical Simulations”, Journal of the Atmospheric Sciences. 50, 2107–2115. (1993). [15] C. Dearden, “Investigating the simulation of cloud microphysical processes in numerical models using a one-dimensional dynamical framework”, Atmospheric Science Letters. 10, 207–214. (2009). [16] A. Seifert and B. Stevens, “Microphysical Scaling Relations in a Kinematic Model of Isolated Shallow Cumulus Clouds”, Journal of the Atmospheric Sciences. 67, 1575–1590. (2010). [17] A. Seifert, “On the Parameterization of Evaporation of Raindrops as Simulated by a One-Dimensional Rainshaft Model”, Journal of the Atmospheric Sciences. 65, 3608–3619. (2008). [18] H. R. Pruppacher and J. D. Klett. Microphysics of Clouds and Precipitation. Kluwer Academic Publishers., 1997. [19] D. O. Topping, G. B. McFiggans, and H. Coe, “A curved multi-component aerosol hygroscopicity model framework: Part 1 - Inorganic compounds”, Atmospheric Chemistry and Physics. 5, 1205–1222. (2005). [20] A. Bott, “A flux method for the numerical solution of the stochastic collection equation: Extension to two-dimensional particle distributions”, Journal of the Atmospheric Sciences. 57, 284–294. (2000). 140

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[21] W. D. Hall, “A detailed microphysical model within a two-dimensional dynamic framework - Model description and preliminary-results”, Journal of the Atmospheric Sciences. 37, 2486–2507. (1980). [22] A. Laaksonen et al., “Commentary on cloud modelling and the mass accommodation coefficient of water”, Atmospheric Chemistry and Physics. 5, 461–464. (2005). [23] H. Morrison, J. A. Curry, and V. I. Khvorostyanov, “A new double-moment microphysics parameterization for application in cloud and climate models. Part I: Description”, Journal of the Atmospheric Sciences. 62, 1665–1677. (2005). [24] M. Khairoutdinov and Y. Kogan, “A new cloud physics parameterization in a largeeddy simulation model of marine stratocumulus”, Monthly Weather Review. 128, 229–243. (2000). [25] A. Seifert and K. D. Beheng, “A double-moment parameterization for simulating autoconversion, accretion and selfcollection”, Atmospheric Research. 59, 265–281. (2001). [26] B. Stevens and A. Seifert, “Understanding macrophysical outcomes of microphysical choices in simulations of shallow cumulus convection”, Journal of the Meteorological Society of Japan. 86, 143–162. (2008). [27] H. Morrison, G. Thompson, and V. Tatarskii, “Impact of Cloud Microphysics on the Development of Trailing Stratiform Precipitation in a Simulated Squall Line: Comparison of One- and Two-Moment Schemes”, Monthly Weather Review. 137, 991–1007. (2009). [28] B. J. Shipway and A. A. Hill, “A 1D modelling framework for a microphysics intercomparison study: Part I”, Submitted to the Quarterly Journal of the Royal Meteorological Society. (2011). [29] J. M. Straka. Cloud and Precipitation Microphysics. Cambridge University Press, 2009. [30] J. S. Marshall and M. K. Palmer, “The distribution of raindrops with size”, J. Meteor. 5, 165–166. (1948).

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CHAPTER 5. EVALUATING MICROPHYSICAL COMPLEXITY WITH THE FACTORIAL METHOD [31] J. Y. Liu and H. D. Orville, “Numerical modelling of precipitation and cloud shadow effects on mountain-induced cumuli”, Journal of the Atmospheric Sciences. 26, 1283–&. (1969). [32] S. A. Twomey, “The Nuclei of Natural Cloud Formation. Part II: The Supersaturation in Natural Clouds and the Variation of Cloud Droplet Concentrations”, Geofisica pura e applicata. 43, 227–242. (1959). [33] R. R. Rogers and M. K. Yau. A Short Course in Cloud Physics, 3rd edition. Butterworth and Heinemann, 1989. [34] H. Abdul-Razzak, S. J. Ghan, and C. Rivera-Carpio, “A parameterization of aerosol activation - 1. Single aerosol type”, Journal of Geophysical Research-Atmospheres. 103, 6123–6131. (1998). [35] A. Bott, “A positive definite advection scheme obtained by nonlinear renormalization of the advective fluxes”, Monthly Weather Review. 117, 1006–1015. (1989). [36] A. Bott, “Monotone flux limitation in the area-preserving flux-form advection algorithm”, Monthly Weather Review. 120, 2592–2602. (1992). [37] B. P. Leonard, M. K. MacVean, and A. P. Lock, “Positivity-preserving numerical schemes for multidimensional advection”, NASA Technical Memorandum. (1993). [38] W. H. Press et al. Numerical Recipes 3rd edition: The Art of Scientific Computing. Cambridge University Press., 2007. [39] J. A. Milbrandt and R. McTaggart-Cowan, “Sedimentation-Induced Errors in Bulk Microphysics Schemes”, Journal of the Atmospheric Sciences. 67, 3931–3948. (2011). [40] S. Tzivion, G. Feingold, and Z. Levin, “An efficient numerical-solution to the stochastic collection equation”, Journal of the Atmospheric Sciences. 44, 3139– 3149. (1987). [41] H. T. Ochs, R. R. Czys, and K. V. Beard, “Laboratory measurements of coalescence efficiencies for small precipiating drops”, Journal of the Atmospheric Sciences. 43, 225–232. (1986).

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[42] M. K. Jacobson. Fundementals of Atmospheric Modeling, 2nd edition. Cambridge University Press, 2005. [43] H. Jiang et al., “Aerosol effects on the lifetime of shallow cumulus”, Geophysical Research Letters. 33. (2006).

143

144

CHAPTER

SIX ICE FORMATION AND GROWTH IN SIMULATIONS OF A MIXED-PHASE WAVE CLOUD The following chapter has been prepared for submission to the Journal of Advances in Modelling Earth Systems, under the full title of "Factors influencing ice formation and growth in simulations of a mixed-phase wave cloud". Authors: C. Dearden, P. J. Connolly and P. R. Field

Having considered the effects of aerosols on liquid clouds in the previous chapter, the attention now turns to the mixed-phase. Specifically, simulations of a mixed-phase orographically induced wave cloud sampled in-situ during the ICE-L (Ice in Clouds Experiment - Layer clouds) field campaign are performed and compared directly against the available observations along various straight and level flight paths. The simulations are again based on the ACPIM bin microphysics model embedded within a 1-D column framework, modified here to include ice phase microphysical processes with the latest parameterizations for heterogeneous ice nucleation. Wave clouds are a suitable subject for process studies given their simple dynamics and laminar nature, making them ideal ’natural laboratories’ to investigate ice formation and growth mechanisms. The simulations focus on the second of two clouds sampled during ICE-L case study RF03, the in-situ data from which exhibits some interesting and more complex microphysics than other flights from the campaign, the origins of which are not fully conclusive from a consideration of the measurements alone. The model is used to explore the effects of both heterogeneous and homogeneous nucleation in explaining the ice crystal concentrations observed along the aircraft sampling altitude. Simulations were performed to explore the sensitivity of the model to the assumptions made regarding the treatment of ice crystal density and habit, and the impact this has on the simulated ice growth rates and the agreement with the ob145

CHAPTER 6. SIMULATIONS OF A MIXED-PHASE WAVE CLOUD

servations. Some additional model runs are also performed to address the issue of how hypothetical changes in IN concentration affect the competition between heterogeneous and homogeneous ice formation in the wave cloud, where the Factorial Method is used to isolate and quantify the effect of such non-linear interactions. This chapter is primarily the work of C. Dearden. The role of the co-authors in producing this work is acknowledged; firstly Dr. Paul Connolly for providing the ACPIM model, and secondly Dr. Paul Field for supplying the observational data used for both model validation and initialisation. Modifications to the standard ACPIM code necessary in order to conduct the ICE-L simulations were made by C. Dearden.

6.1

Introduction

The simulation of clouds, particularly those involving the ice phase, remains a major source of uncertainty in numerical models of the Earth’s atmosphere. It is well established that the lack of a standard theory of the factors controlling heterogeneous ice nucleation means that the problem of accurately quantifying ice crystal number concentrations is as much of an issue in cloud resolving modelling studies as it is in global scale modelling [1], and that the parameterizations of active ice nuclei (IN) concentrations typically used in cloud and climate models to date [2–4] can disagree with each other by as much as a factor of 1000 for a specified temperature. It is believed that active IN concentrations need to be predicted to within a factor of 10 at worst in order to avoid significant errors in cloud microphysical processes [5], which in turn can lead to errors in climate model predictions due to the impact on the cloud radiative forcing. Thus projects such as the Ice in Cloud Experiment - Layer clouds (ICE-L) field campaign [6] provide a much needed observational constraint which can be used to help develop and test the latest parameterization schemes describing primary heterogeneous ice formation and growth. The ICE-L campaign focused on mixed-phase lenticular wave clouds over the Rocky mountains, USA in the autumn of 2007. Measurements from ICE-L are particularly useful because the isolation, long lifetime and minimal turbulent mixing of the clouds in question makes them ideal natural laboratories to explore ice nucleation and subsequent growth mechanisms via in-situ measurements. Furthermore, the problem of shattering of large ice crystals 146

6.1. INTRODUCTION

on instrument inlets leading to contamination of previous IN measurements (see [7] and references therein) is largely avoided in ICE-L due to the narrow size distribution of ice particles in orographic wave clouds [8].

In-situ measurements from dedicated field campaigns combined with cloud resolving modelling studies together form a pathway towards increasing our knowledge of mixedphase microphysical processes and thus improving our ability to represent ice clouds in weather and climate models. Indeed several modelling studies based on the ICE-L project have already led to advancements in understanding. For instance, the study by Field et al [8] used a kinematic 1-D column model framework to identify the dominant heterogeneous ice nucleation mechanisms most likely responsible for ice formation across the range of ICE-L wave clouds sampled. This was achieved through a simplified representation of the different nucleation modes combined with a prognostic IN treatment. An ensemble of model integrations were performed for a range of prognostic IN values and the simulations that gave the best agreement with the observations (in terms of the ice number concentration and the timing of the onset of ice formation) were identified. They concluded that condensation/immersion freezing gave the best agreement with the in-situ measurements. This corroborates recent results from several years of remote sensing of mid-level clouds [9] and also laboratory studies of ice nucleation on dust particles [10]. The study by Eidhammer et al [7] focused on one particular ICE-L case study from the 18th November 2007 (RF04), and used a Lagrangian parcel model framework to demonstrate that two of the latest primary nucleation parameterizations were found to predict ice crystal number concentrations within the cloud to within a factor of three of the observations. Whilst these modelling results represent clear progress, there are still aspects of the measurements that are not fully understood and thus warrant further modelling work to investigate, hence the motivation for this paper. For instance, in-situ measurements from the second of two clouds sampled on the 16th November (RF03) showed very different ice crystal concentrations compared to RF04, despite both clouds showing comparable vertical velocities and temperatures along the flight track [11]. Specifically, RF03 exhibited steadily increasing ice crystal concentrations along the flight track in the mixed-phase region of the cloud, followed by a distinct ice tail where the ice concentrations jumped 147


significantly. There are two possible explanations for this behaviour:

* The chemical composition of the aerosol present in the two cases may have been different;

* Homogeneously nucleated ice may have formed at some higher altitude in RF03 and then crossed the flight track level at some later time as the ice followed streamlines along the descending part of the wave.

RF03 was also unique in that a few rimed ice crystals were detected in the earlier mixed-phase part of the cloud, the origin of which is not fully understood. Thus the aim of this paper is to build up a comprehensive understanding of the history of the RF03 case using a 1-D column model that can advect air parcels along multiple trajectories, and to establish the key factors that affect the ability of the model to replicate the observed microphysical characteristics.

6.2

Model description

The model used in this paper is the recently developed University of Manchester Aerosol-Cloud-Precipitation-Interaction-Model (ACPIM), a detailed mixed-phase bin microphysics model that takes advantage of recent developments in the representation of ice phase processes. Whilst the authors are aware of several existing bin microphysical simulations of the mixed-phase [12–14], these are in relation to cases of deep convection, and the authors are not aware of any recent mixed-phase bin modelling studies in the context of layer clouds; this paper provides an opportunity to address this imbalance. The ACPIM bin microphysics can be run either as a Lagrangian parcel model [10], or in a 1-D Eulerian framework with a discrete vertical resolution, as is the case for this study. The ACPIM microphysics has already been run within a 1-D column environment for the case of a precipitating idealised warm cloud [15] although the ACPIM has since been extended to include a treatment of the ice phase as well. 148


6.2.1

Microphysics

With respect to the liquid phase, the ACPIM solves the diffusional growth equation [16] to represent droplet activation and subsequent condensational growth. The Aerosol Diameter Dependent Equilibrium Model, ADDEM [17, 18] provides equilibrium vapour pressures of liquid particles, which are then fed into the droplet growth equation and solved in ACPIM such that the effects of specific aerosol compositions can be explored in both liquid and mixed-phase clouds. Collision and coalescence processes can be represented in ACPIM by solving the stochastic collection equation, although in this instance collisions between droplets are not considered as the sampled clouds were not observed to be drizzling. Similarly no riming or aggregation is permitted in the model simulations by default, although a later section of this paper does consider the effects of riming as an additional sensitivity test. In these cases it is assumed that the rime mass is added as a spherical shell around the exterior of ice crystals, with density equal to that of pure ice. For ice nucleation, the scheme of Koop et al [19] is used to represent homogeneous freezing as a function of water activity of the solution droplets. In terms of heterogeneous nucleation, for this study the ACPIM uses the recent parameterization of DeMott et al [5], which determines ice crystal concentrations as a function of temperature and the number of aerosols greater than 500 nm thus:

NIN;T = a1 (273:16 TK )b1 (naer;0:5 )(c1 (273:16 K

TK )+d1 ) ;

(6.2.1)

where a1 = 5.94e-5, b1 = 3.33, c1 = 2.64e-2, d1 = 3.3e-3, TK is the cloud temperature in Kelvin, naer;0:5 is the number concentration of aerosols with diameter larger than 500 nm (in std cm 3 ) and NIN;T is the IN number concentration (std L 1 ) active at temperature K

TK . The aerosol size distribution is initialised from in-situ measurements described later in section 6.3. The ACPIM supports different levels of complexity regarding the treatment of factors influencing ice growth rates. The representation of depositional growth in the ACPIM is based on the capacitance growth model described in Chen and Lamb [20], which is able to represent the evolution of ice crystal habit based on a consideration of the aspect ratio

of spheroidal ice crystals, where = c=a, where ’c’ is the c-axis length and ’a’ is the a149


axis length. Aspect ratios greater than 1 are prolate spheroids and correspond to columnar crystals, and values less than 1 are oblate spheroids describing plate-like crystals. In the adaptive parameterization of ice crystal habit, the rate of change of mass with time is given by the following equation describing vapour diffusion growth of ice crystals:

4Cs dm h i = R T + L L dt v

s

ei D v

where

s

T Ki

T Rv

1

i ;

(6.2.2)

C is the crystal capacitance, specified in Pruppacher and Klett [16] for both

oblate and prolate spheroids; V is the spheroid volume, si is supersaturation with respect to ice, Rv is the vapour gas constant, Ls is the latent heat of sublimation, T is temperature,

ei is the equilibrium vapour pressure with respect to ice, Dv is the effective vapour diffusivity and Ki is the effective thermal conductivity. Equation 6.2.2 can also be expressed as a change in crystal volume dV , where

dV =

1

dep

dm;

(6.2.3)

and dep is the deposition density (the density of deposited vapour onto an ice crystal), and is expressed as (in g cm 3 ):

dep = 0:91 exp [ 3: max( 0:05; 0)= (T )] ; where is the excess vapour density in g m 3 , and

(6.2.4)

is called the inherent growth

ratio and controls the distribution of mass deposition onto the basal (c-axis) and prism (a-axis) faces of the crystal according to the ratio of the deposition coefficients

along

the two axes:

(T ) =

c a

(6.2.5)

thus determines the primary habit evolution; it is a function of temperature and was determined by Chen and Lamb from experimental data exploring growth rates of ice crystals and subsequent habits across a range of temperatures between 0 C and -30 C. The dependency between the change in aspect ratio and the change in crystal volume 150


V is given by: d ln() =

1 d ln(V ) +2

Equation 6.2.6 can be obtained from the volume of a spheroid

(6.2.6)

V = 43 a3 and the

assumption of a mass distribution relationship which controls the rate of crystal growth along each axis, such that:

dc = (T ); da where

(6.2.7)

is the ratio of the vapour density gradients along the c-axis and a-axis re-

spectively. Equations 6.2.3 and 6.2.6 are solved in ACPIM to allow for changes in ice crystal habit (the aspect ratio) to feed back on ice crystal growth rates. Thus through the Chen and Lamb approach, ACPIM is able to provide an adaptive representation of ice crystal density and aspect ratio, such that the growth and habit of ice crystals can respond to changing thermodynamic conditions whilst also accounting for their prior growth history. As noted recently [21], relatively few numerical simulations of cold clouds have focused on predicting changes in aspect ratios based on the Chen and Lamb scheme, and the effect this has on the evolution of ice crystal size distributions. Indeed, the effect of ice crystal habits in terms of cloud evolution and in particular, precipitation, are known to be profound [22], and so this is a potentially important feature of the model. It is also possible within the ACPIM to specify a simpler treatment of ice crystal growth based on the assumption of spherical ice crystals (i.e. an aspect ratio of unity) with a constant bulk density. The sensitivity of the model simulations to the treatment of depositional growth are explored later in this paper. Fallspeeds are calculated as a function of the area ratio of ice crystals, based on the recent findings of Heymsfield and Westbrook [23]. This was shown to improve computed fallspeeds for particles of different habits relative to laboratory measurements. The area ratio is defined as the ratio of the projected area of the ice crystal to that of a circumscribing circle whose diameter is given by the maximum dimension of the ice crystal. The projected area for monomer ice crystals depends on their aspect ratio. Specifically, for plates (aspect ratios less than 1), the projected area is given by the area of a circle with 151


radius equal to the a-axis length, and for columns (aspect ratios greater than 1) it is equal to that of an ellipse with semi-minor axis equal to the a-axis length and semi-major axis equal to the c-axis length.

6.2.2

Representation of bin structure

The ACPIM uses a constant aerosol mass grid such that the aerosol bins are fixed (consistent with a single-moment representation), with 154 bins representing the aerosol size distribution. Both liquid and ice particle distributions are represented using a 2-D grid as in Bott [24], such that particle number concentrations are categorised according to both water mass and aerosol mass. Thus for a given water mass bin, the 2-D grid stores the variation in number concentration across the range of aerosol mass bins, and vice versa. This allows for changes in the spectrum of aerosol mass to be simulated due to collisions between droplets. It is important to note that in this study, in contrast to the single-moment mass grids used in Bott [24], the ACPIM is configured to use a double-moment ’moving centre’ bin structure to describe the evolution of both liquid and ice size distributions over time [25], such that the centre of the mass bins are allowed to vary between the low and high bin edges. This is based on the latest developments to the ACPIM model described in Connolly et al [26], who showed that numerical diffusion during growth by vapour diffusion and collision-coalescence processes is reduced considerably with double-moment bin structures compared to single-moment solutions. Vertical advection of potential temperature and water vapour is handled using the positive definite, monotonic scheme of Bott [27], where the polynomial interpolation is extended to 8th order [28]. Because a variable mass grid is used to describe the evolution of liquid and ice size distributions, the average mass within a given bin is not necessarily constant with height and so a different advection scheme must be used in this case. Consequently the dual-moment hybrid binning scheme described in Chen and Lamb is used for vertical advection of liquid and ice [29]. All simulations are performed with 320 levels in the vertical, and a fixed vertical resolution of 15m with diagnostic output available every 10 seconds. 152

6.3. INITIALISATION OF THE MODEL

6.3

Initialisation of the model

Due to the one dimensional Eulerian nature of the driver model, vertical profiles of total water and potential temperature constrained from the observations are required to initialise the model and provide the basis of a realistic environment within which to study the formation and evolution of the wave cloud. However at any given time, observations of the wave cloud only exist at a single height level, corresponding to the altitude of the flight track. Thus to obtain the initial profiles, the back trajectory method as employed in Field et al [8] is used, with the assumption that the flow is adiabatic such that total water and potential temperature are conserved along streamlines. By advecting the observations backwards in time along streamlines according to the measured vertical velocity (with all microphysical processes disabled), it is possible to obtain a vertical profile at some earlier time upstream of the wave cloud, from which the model can be run forwards (with microphysics enabled) to provide simulations of the wave cloud for further study. The procedure entails taking the measured timeseries of vertical velocity from the aircraft along a given flight track, and subsequently reversing and inverting it. The reversed vertical velocity field is then applied across all vertical model levels equally, with the implicit assumption that the vertical velocity field as measured by the aircraft is constant with height across the model domain, which covers a height of 4.8 km (although the resultant clouds that form have considerably smaller depths than this, with an average liquid cloud depth of 1 km across the whole range of clouds sampled [6]). The model level closest to the flight level at the end of the aircraft run is initialised with the corresponding observations at that time. Prognostic variables are then advected backwards in time from the end of the run to the start of the run according to the reversed velocity timeseries, and should an advected point recross the flight level at some earlier time, the model is updated with the new observations. This procedure leads to the production of the vertical profiles of potential temperature and moisture used to initialise the model. In practice the method can sometimes lead to discontinuities of streamlines along the flight level, and thus it is necessary to include a small offset to the vertical velocity field when performing the back trajectories to ensure that the fields of potential temperature and water vapour follow continuous streamlines. The addition of an offset to the vertical velocity is justified because 153


of the uncertainty in the absolute measurements from the aircraft. The ACPIM model also requires initialisation in terms of the aerosol composition and size distribution. In terms of hygroscopic growth of the aerosol particles, the equilibrium behaviour for specific aerosol chemical components are parameterized in the ACPIM model as a function of diameter based on results from the Aerosol-Diameter-DependentEquilibrium Model (ADDEM; [17, 18]) thus allowing for the effects of composition on the growth rate of droplets to be accounted for. The study of Pratt et al [30] analysed the residues of both cloud droplets and cloud ice in RF03 and identified the dominant presence of playa (dry lakebed) salts. Further evaluation of the ability of the playa salts to act as CCN was conducted in the same study, with the conclusion that the playa salts have a relatively high hygroscopicity and a CCN efficiency close to that of sea-salt. With this in mind, the ACPIM model runs were configured to use pure sea-salt as the most suitable proxy for playa salts, although the strong dynamical forcing of the wave clouds meant that the model results were not found to be particularly sensitive to this choice. With regards aerosol spectra, the time-mean size distribution from the Ultra-High Sensitivity Aerosol Spectrometer (UHSAS) probe (averaged over periods where the potential temperature range matched that of the sampled cloud) was used to construct two fitted log-normal modes which are in turn used as inputs to the model (see Figure. 6.1). It should be noted that the UHSAS only produced reliable measurements in the range 0.11 m , and so data below 100 nm was ignored when producing the aerosol log-normal fits (although it is assumed that the fitted modes continue to smaller sizes). Since the wave clouds are quite strongly forced, the model was found to activate all the available aerosols as cloud droplets, producing a typical droplet number concentration of 100 cm

3

which

is consistent with the in-situ measurements. The number of aerosols present greater than 500 nm in diameter is particularly important as this controls the predicted ice crystal concentration in the model parameterization of heterogeneous ice nucleation. For the time-mean UHSAS data, the aerosol number greater than 500 nm is 0.116 cm

3

(with an uncertainty range of 0.09-0.14 cm

the poisson sampling error), compared with 0.128 cm

3

3

based on

for the fitted modes combined.

Thus the fitted modes are safely within the uncertainty range of the measurements. 154

6.4. RF03: FLIGHT DETAILS

Figure 6.1: Time-mean UHSAS aerosol size distribution for RF03 (red); the fits to the UHSAS data used to initialise the model (black), and the summation of the two fitted modes (blue). Log-normal parameters for the first fitted mode (black dashed line) are: number concentration = 100 cm 3 ; geometric mean diameter = 0.0911 m; geometric standard deviation = 1.532. For the second mode (black dot-dashed line): number concentration = 1.125 cm 3 ; geometric mean diameter = 0.26 m; geometric standard deviation = 1.768.

6.4

RF03: Flight details

In the field campaign, several straight and level passes were made through the cloud to characterise the evolution of the cloud microphysics as a function of altitude and time (see Figure 6.2). Measurements were first taken near the base of the liquid cloud and subsequent passes were made at higher levels in the cloud, finishing with measurements near cloud top. The typical horizontal wind speed through the wave cloud was 20 ms 1 , with the aicraft flying into the wind. By performing simulations of the wave cloud corresponding to different straight and level runs, it is possible to build up an understanding of the influence of both heterogeneous and homogeneous freezing in this particular case, and how the competition between the two ice nucleation mechanisms affects the ice crystal concentration at varying 155


Figure 6.2: Timeseries of the straight and level runs (based on aircraft time) made by the research aircraft for RF03, corresponding to different heights above sea level through the evolution of the cloud. In-situ observations were taken along each run for the indicated duration. The average temperatures along each straight and level run are also indicated. The labelling system for the straight and level runs is of the form flight number-cloud number-penetration number, e.g. 3-2-1 corresponds to the first penetration of the second cloud sampled on RF03.

altitudes through the cloud depth. When producing the initial vertical profiles in order to initialise the ACPIM model, the simulation of 3-2-3 was found to require a very large vertical velocity offset (+0.8 ms 1 ) in order for eliminate discontinuities in streamlines. With this is mind it was decided to focus on penetrations 3-2-1, 3-2-5 and 3-2-7 for the basis of the modelling work, where the corresponding velocity offsets are considerably lower (+0.2 ms 1 , +0.3 ms

1

and +0.0 ms

1

respectively). Simulations of 3-2-6 are not

considered since parcel trajectories for this particlular penetration were not found to reach low enough temperatures to be influenced by homogeneous freezing. The vertical velocity timeseries used to initialise the model relative to the in-situ measurements are plotted in Figure 6.3 in terms of air parcel time, obtained by multiplying the observation time by the ratio of the aircraft ground speed to the horizontal wind speed. 156

6.4. RF03: FLIGHT DETAILS

Figure 6.3: Vertical velocity fields used to initialise the model relative to the in-situ observations. The vertical velocity is constant with height in the model domain, i.e. applied equally at each model level. Any offsets from the measured values were necessary to avoid discontinuities in parcel streamlines in the model initialisation process.

157


6.5 6.5.1

Model results Control simulations: The effect of homogeneous freezing

This section shows results from model control simulations produced using a deposition coefficient of unity, and a prognostic treatment of ice density based on the Chen & Lamb model assuming an initial density of pure ice (910 kg m 3 ). The time-height plots shown in Figure 6.4 illustrate the onset and formation of both the liquid and ice phases, along with the corresponding temperature field, for the simulation of penetration 3-2-5. The closest model level to the flight track (based on the pressure level of the aircraft transit) is marked with a dashed black line. It can be seen that the model produces a cloud in response to the rising and cooling of air parcels in a manner that is consistent with the dynamical forcing shown in Figure 6.3. In the simulation, no ice is produced prior to the onset of cloud droplet formation, although once liquid droplets are present the cloud very quickly evolves into a mixed-phase regime as the droplets freeze (this is confirmed later in Figure 6.7). With homogeneous freezing disabled, the lowest temperature at which liquid droplets were simulated was -37 C and heterogeneous ice was produced throughout the depth of the cloud, with ice mass steadily increasing with time as the ice grows by deposition in the ice supersaturated environment. It can be seen how the cloud persists in a mixed-phase state up to approximately 1200s into the simulation. At this time the vertical velocities are strongly negative, causing air parcels to descend and warm, leading to evaporation of the remaining liquid droplets. Beyond this time only an ice-tail remains, and parcel trajectories intercept the flight level at multiple points. In the case with both homogeneous and heterogeneous freezing enabled, it can be seen that considerably more ice mass is produced earlier on at cloud top. Soon after the liquid cloud forms, parcel trajectories reach temperatures low enough to initiate the homogeneous freezing process. Analysis of the ice crystal number concentrations in the upper regions of the simulated cloud suggest that at most, 14% of the liquid droplets freeze homogeneously. As the vertical velocities become weaker in the transition from the updraft to the downdraft region of the wave, the in-cloud vapour pressure is no longer sufficient to sustain the remaining liquid droplets in the upper region of the liquid cloud 158

6.5. MODEL RESULTS

Figure 6.4: Time-height contour plots from 3-2-5, showing on the top row: liquid mass in kg kg 1 (colours) and ice mass in kg kg 1 (contours) for cases with homogeneous freezing both off and on (heterogeneous freezing is enabled in both cases). Bottom row: the corresponding temperature in degrees celcius (colours), with ice mass contours overlaid. The dashed black line in the plots denotes the closest model level to the aircraft flight track. The same number of ice contours are used (ten) for both sets of model runs, thus they are an indicator of where the majority of the ice mass is contained in each run and does not necessarily represent the same amount of ice in each case.

and rapid glaciation occurs via the Wegener-Bergeron-Findeisen (WBF) process. Immediately downwind of the liquid cloud the ice contours in Figure 6.4 show a noticeable increase in ice mass crossing the flight level due to the effect of homogeneous freezing. Thus the influence of homogeneous freezing is clearly important in this particular simulation. A consideration of Figure 6.5 reveals that similar conclusions are reached for the simulation of 3-2-7; the influence of homogeneous freezing in the simulation of 3-2-1 is also apparent in Figure 6.5 but appears to be somewhat weaker than the other two cases. This is a consequence of liquid water only reaching -35.3 C in this simulation, and it is not clear from the contours whether enough homogeneously nucleated ice reaches the flight level to significantly influence the predicted ice concentration. To undertake a more rigorous analysis of the model performance, diagnostics along the flight track level must be compared directly to the available in-situ observations. 159


Figure 6.5: As figure 6.4 but for simulations of 3-2-1 (top) and 3-2-7 (bottom)

Figure 6.6: Observed ice crystal concentrations (m 3 ) for sizes larger than 125 m compared against those predicted by the model control simulations for the 3-2-5 flight track. The observed concentrations in all cases are taken from measurements using the fast 2D-C probe as discussed in Field et al [8]. 160

6.5. MODEL RESULTS

6.5.2

Comparison of control simulations with observations

For penetration 3-2-5, Figure 6.6 compares timeseries of the predicted ice concentration in m

3

from the model control simulations with the corresponding in-situ mea-

surements from the NCAR developed 2D-C probe, upgraded with faster photodiodes compared to earlier 2D-C probes to help minimise sampling errors [8]. The predicted concentrations from the model are taken from the closest model level to the flight track, i.e. along the black dashed line in Figure 6.4. The concentrations in both cases are restricted to a consideration of those ice crystals larger than 125 m. Whilst the use of a minimum size threshold is likely to underestimate the total ice crystal concentration, the same threshold is used when counting the predicted concentrations from the model to ensure a meaningful comparison. The results from both simulations (i.e. with and without homogeneous freezing) are shown together on the same plot. Initially the measurements show a steady increase in ice crystal concentration along the flight track; since the temperature along the flight track within the liquid cloud does not change by more than 0.5 C this is unlikely to be explained by temperature-dependent nucleation (although as discussed in Heymsfield et al [6], this does not rule out the possibility that nucleation is time-dependent). However the model maintains a more constant ice crystal concentration along the flight track, where the onset of ice formation is delayed slightly relative to the measurements. Around 900s parcel time there is a much larger jump in the observed ice crystal concentration, which the model simulation without homogeneous freezing is not able to reproduce. Instead in the absence of homogeneous freezing the predicted concentration stays reasonably steady at around 1L 1 ; the ice also persists for too long in the model run, when in the observations there is a distinct drop in ice concentration around 1200s. When homogeneous freezing is permitted to occur in the model (dashed blue line in Figure 6.6), the agreement with the observations improves, at least in a qualitative sense, with the model now able to produce a dinstinct ice tail, although it occurs too late compared to the observations and also overestimates. However the rapid reduction in ice crystal concentration above 125 m that follows is well captured by the model; this can be explained through consideration of the relative humidity plot in Figure 6.7. The effect of homogeneously nucleated ice in the upper regions of the cloud 161


Figure 6.7: Addtional flight level diagnostics for 3-2-5, comparing predicted values from the model with the observations where possible. The observations are in black whilst the model results are in blue (with homogeneous freezing) and red (without homogeneous freezing). From top downwards: ice water content in g m 3 , with observations derived from integrated 2D-C data assuming spherical ice and constant density of 100 kg m 3 ; liquid water content in g m 3 , with observed values from the King liquid water content probe; relative humidity with respect to ice; predicted average aspect ratio of ice crystals from the model; predicted average density of ice crystals from the model (kg m 3 ).

162

6.5. MODEL RESULTS

is to increase the sink of supersaturation such that by the time the air descends and warms in the descending part of the wave, the relative humidity is considerably lower than it otherwise would be. Consequently this reduction in relative humidity leads to sublimation of the heterogeneously nucleated ice in the subsaturated air and hence reduces the number of ice crystals above the 125 m size threshold. Thus treatment of the homogeneous freezing process in the model is necessary not only to explain the peaks in observed ice crystal concentration, but also to explain the reduction in ice concentration above 125 m downstream of the ice tail by virtue of competition for the available water vapour. Figure 6.7 also reveals some interesting features with regards the effect of homogeneous freezing on the predicted aspect ratio and density of the ice crystals in the model. When homogeneous freezing is enabled, the onset of the ice tail coincides with a sudden change in both the aspect ratio and the ice crystal density. The reduction in the aspect ratio signifies a change in the properties of the ice population from a mainly columnar habit to more spherical ice crystals. This is indicative of a regime change from heterogeneously nucleated ice to a population that is dominated by homogeneously nucleated crystals, which individually exhibit less growth (and therefore an overall lower aspect ratio) than their heterogeneously nucleated counterparts. Similar findings can be reached through consideration of the ice density diagnostic, where the model shows an increase in the density of ice crystals due to the influence of homogeneous ice intercepting the flight track. This result is qualitatively consistent with the findings of the laboratory study by Bacon et al [31, their Table 1], who showed that ice crystals produced by the freezing of droplets have lower aspect ratios, higher densities and reduced growth rates relative to seed-initiated ice crystals. This demonstrates that a prognostic treatment of ice density in models can be employed as a useful indicator to track changes in the history of the ice population, which a model assuming a constant bulk density for instance would not be capable of. The predicted ice water content is underestimated relative to the calculated value from the 2D-C measurements, although it must be noted that the observed ice water content is derived assuming spherical ice and a constant bulk density of 100 kg m 3 . This bulk density is based on results from Heymsfield et al [6, their Figure 18b], who showed that an effective ice density of 100 kg m

3

or less is necessary to account for the observed growth rates in

163


Figure 6.8: As figure 6.6 but for penetrations 3-2-1 (top) and 3-2-7 (bottom). ICE-L wave clouds. The study by Heymsfield et al shows that the effective ice density reduces below 100 kg m

3

at larger crystal sizes, and so the assumption of a constant value

may lead to an overestimation of the calculated ice water content in Figure 6.7. Note the sensitivity of the model to changes in the treatment of ice crystal density are explored in more detail in section 6.5.3. The comparison of the predicted ice crystal concentration with the observations for penetrations 3-2-1 and 3-2-7 are shown in Figure 6.8. The influence of homogeneous freezing along the flight track in the simulation of 3-2-1 appears to be very small, and results in no noticeable improvement when compared with the observations. This is a consequence of the fact that liquid droplets are only exposed to a minimum temperature of -35.3 C for this particular simulation, and so the amount of homogeneously nucleated ice produced is much lower than in the other simulated cases. This is most likely a conse164

6.5. MODEL RESULTS

Figure 6.9: Comparison of the observed and predicted ice crystal concentrations for penetration 3-2-5, where the predicted concentrations are shown along a trajectory approximately 100 m above the position of the aircraft altitude level. Simulations use prognostic ice density, with both homogeneous freezing off (red) and on (blue). quence of uncertainty in the absolute measurements of vertical velocity from the aircraft and the shortcomings of the model initialisation method. For 3-2-7, Figure 6.8 shows that homogeneous freezing has more of an influence on the predicted ice crystal concentration along the flight track as suggested by Figure 6.5, but the peaks do not coincide with those seen in the observations. The parcel trajectories in Figure 6.5 suggest that homogeneous freezing takes place too close to the model flight level in the model simulation, producing anomalous peaks in ice crystal concentration associated with homogeneous freezing in the liquid cloud regime and an ice tail that peaks too early. It can be argued that given the uncertainty in the vertical wind measurements and the simplifying assumptions necessary to produce the initial profile, it is justifiable to consider adjacent model levels within the vicinity of the flight track location to see if the agreement between the predicted and observed values can be improved. In the case of 3-2-7 the simulation of ice crystal concentrations relative to the available observations was improved by considering the predicted values 100 m below the flight level (not shown), although it was not possible to do so without compromising other aspects of the simulation (specifically ice water content and relative humidity). In the simulation of penetration 3-2-5 however, this approach is more succesful and highlights a potentially important conclusion that is worthy of further comment. Figure 6.9 plots the predicted ice concentrations from 3-2-5 approximately 100 m above the flight level plotted in Figure 6.4, revealing an increase in ice crystal concentration within 165


the liquid cloud that is more consistent with that seen in the measurements. The improvement in the predicted concentrations around 500 s parcel time can be explained by advection of homogeneously nucleated ice crystals from above in a time period when the vertical velocities are weakly negative. This is a potentially important result since it means that the ice crystal concentrations along certain penetrations of the liquid cloud may have contained non-negligible concentrations of homogeneously nucleated ice, which may have led to slight overestimates of IN concentrations for this particular cloud in the modelling study of Field et al [8]. It is unfortunate that it was not possible to explore this further in the penetration of 3-2-1 due to the apparent uncertainty in the forcing conditions leading to insufficient homogeneous nucleation in this simulation. This at least serves as a reminder of how small discrepancies in thermodynamic factors can have significant consequences for the accuracy of the simulation of the cloud microphysics.

6.5.3

The effect of ice crystal density

All the simulations presented so far have employed a prognostic treatment of ice crystal density based on the Chen and Lamb model. However some additional sensitivity studies were also performed based on the discussion in Heymsfield et al [6], which suggests that the ice growth rates seen in the ICE-L measurements are consistent with very low effective ice densities of 100 kg m 3 . Thus some repeated model simulations for flight track 3-2-5 were performed based on a simpler treatment of ice crystal density, where the assumption of spherical ice crystals is made along with a constant bulk density of 100 kg m 3 . The results of these simulations, shown in Figure 6.10 (top panel) reveal that the assumption of such a low bulk density does allow the heterogeneous ice crystals to reach larger sizes more quickly, however the onset of ice now occurs too early compared to the observations. This has a detrimental effect on the predicted ice number concentrations in the ice tail region of the cloud, where too many ice crystals are large enough to remain above the 125 m size threshold downwind of the observed ice tail despite the effects of sublimation. Given laboratory results concerning the dependency of ice growth rates on the mechanism of nucleation [31], it may not be justifiable to assume a constant bulk density for all ice crystals for clouds where both homogeneous and heterogeneous 166

6.5. MODEL RESULTS

Figure 6.10: As figure 6.9, but for model simulations with (top): spherical ice crystals and constant bulk ice density of 100 kg m 3 ; (bottom): prognostic ice density but with the deposition density reduced by a factor of two. Both model simulations have homogeneous and heterogeneous freezing enabled.

freezing are important. Further tests showed that it was possible to modify the prognostic scheme for ice density to improve the performance of the model relative to the observations. This was achieved by reducing the deposition density (Equation 6.2.4) by a factor of two, the results of which are also shown in Figure 6.10. The effect of this change enables ice crystals to grow faster relative to the control simulations with prognostic ice density, whilst also maintaining the ability to predict changes in aspect ratio and the influence this has on growth rates. However this is not an ideal solution and only serves to highlight the limitations of existing knowledge concerning those factors that influence ice growth rates. In all cases it was noted that the maximum predicted ice crystal concentration in the ice tail 167


exceeded that seen in the observations; it is possible that this is due to an overestimation of homogeneously nucleated ice from the Koop et al parameterization.

6.5.4

The effect of riming

Figure 6.11: Example images of ice crystals from the CPI probe observed along penetration 3-2-5. a) A sample of ice crystals detected in the liquid cloud region, around 700-900 seconds (air parcel time), showing a few heavily rimed crystals. b) A sample of ice crystals detected in the ice tail region of the cloud (between 1100-1180 seconds) which are less or not affected by riming. Analysis of CPI data for penetrations 3-2-1 and 3-2-3 revealed similar evidence of rimed ice crystals in the liquid cloud region only. In an effort to understand the source of the few heavily rimed crystals seen in the observations (see Figure 6.11), additional simulations were performed with the riming process included, thus permitting collisions between liquid and ice particles to act as a sink of liquid and a source of ice mass. Simulations of both 3-2-1 and 3-2-5 with riming enabled were performed for cases both with and without homogeneous freezing; in all cases the riming efficiency (i.e. the probability of a liquid droplet sticking to an ice crystal upon contact) was taken to be unity. For clarification, only collisions between liquid and ice cloud particles were accounted for; collisions between liquid drops only 168

6.5. MODEL RESULTS

(accretion) and ice crystals only (aggregation) were not considered in the simulations. In these simulations, the stochastic collection equation was solved based on the number and mass conserving method of moments. The average rime mass per ice crystal from the simulations of 3-2-1 and 3-2-5 are shown in Figure 6.12. It is clear from Figure 6.12 that in both cases, the average amount of rime mass per ice crystal is reduced considerably in the absence of homogeneous nucleation. Thus the additional source of ice from homogeneous freezing was found to increase the efficiency of the riming process. Additional simulations were also performed for 3-2-1 where the total number of aerosols with diameter less than 500 nm was doubled, whilst the number concentration of aerosols larger than 500 nm (i.e. the potential number of IN) was left unchanged. This resulted in an approximate doubling of the cloud droplet number concentration in the cloud to 200 cm 3 , and the effect of the smaller droplets was to reduce the average rime mass per ice crystal by as much as a factor of five. This result is qualitatively consistent with the observational study of Borys et al [32], who observed that riming rates are reduced in orographic wave clouds due to a reduction in cloud droplet size under a fixed liquid water content. In the simulation of 3-2-5, although the overall amount of rimed ice produced is less than in the simulation of 3-2-1, the rimed ice crystals are closer to the flight track level. In particular, the simulated rimed crystals are closest to the aircraft altitude between 700900 s parcel time, and with the afore-mentioned uncertainty in the initialisation of the model taken into account, it is possible to conceive that rimed ice could intercept the flight level at this time. This would certainly explain the presence of the few heavily rimed ice crystals seen in the in-situ observations within the liquid cloud. It should be remembered when interpreting these results that the concentrations of homogeneously nucleated ice particles are likely to be underestimated in the simulation of 3-2-1, and as such more liquid water is potentially available for riming in the upper regions of the cloud relative to the simulation of 3-2-5. As discussed in section 6.5.1, the weakening updraught speeds during the transition from positive to negative vertical velocities, coupled with the higher concentrations of homogeneous ice in 3-2-5, allow the WBF process to become more effective at removing the remaining droplets in the upper regions of the cloud. Con169


Figure 6.12: Plots of average rimed mass per ice crystal (kg kg 1 ) from simulations of (a) 3-2-1 and (b) 3-2-5. In each case, the top plot corresponds to simulations with both heterogeneous and homogeneous freezing enabled; the bottom plot shows results from simulations with just heterogeneous nucleation of ice permitted. The black dashed line indicates the position of nearest model level to the flight track.

170

6.5. MODEL RESULTS

sequently dynamical factors were found to be important in determining the amount of rimed ice produced in the model simulations through the ability to regulate the role of the WBF mechanism.

6.5.5

Additional sensitivity tests with the Factorial Method

Having considered the performance of the model in the context of the in-situ measurements, the results of some additional sensitivity tests are now presented in relation to exploring the susceptibility of the model simulation to hypothetical changes in IN number concentration. The paper by DeMott et al [5] states that active IN concentrations must be accurate to within a factor of 10 in cloud and climate models in order to prevent significant discrepancies arising in the simulation of cloud properties, from both a microphysical and radiative perspective. Since the DeMott parameterization of active IN concentration is a function of both aerosol number greater than 500 nm and temperature, this scheme in conjunction with the ACPIM model can be used to test the sensitivity of the wave cloud to changes in aerosol number concentration, with the aim of establishing how errors in the representation of aerosol size distributions may manifest themselves in terms of the impact on microphysical processes. To assess the model sensitivity in this regard, the Factorial Method (FM) is employed, which has been used previously in the context of cloud modelling [14, 15] to quantify the relative importance of selected microphysical variables to changes in a chosen metric. The FM is particularly useful as it can isolate and quantify the non-linear dependencies between specific variables, which can be significant for ice phase microphysics. For this particular case, the FM is applied to quantify the extent to which an increase in the number of aerosol available to act as IN affects the overall ice crystal concentration through the competition with homogeneous ice nucleation. It is also worthy of remembrance at this point that all the model simulations thus far have assumed a deposition coefficient of unity, but this quantity is known to be uncertain for ice ([16, pg 165] and [33]). Indeed lower values of the deposition coefficient could slow the growth rate of ice by deposition, thus reducing the sink of supersaturation and potentially maintaining a higher level of supersaturation for longer such that it may have a non-negligible effect on homogeneous freezing rates. Recent laboratory estimates 171

CHAPTER 6. SIMULATIONS OF A MIXED-PHASE WAVE CLOUD Table 6.1: Chosen factors and the values assigned to them based on a 23 factorial design. Factor label Factor description Values A The effect of homogeneous freezing 0ff; On B The value of the deposition coefficient 1.0; 0.1 C The aerosol size threshold representing number of potential IN 500 nm; 300 nm

Table 6.2: The experimental design matrix for the 23 design used in this study. The run labels follow the convention of ’standard notation’, whereby the presence of a lower case letter denotes the high value of that factor, and the absence of a lowercase letter indicates the low value of that factor. For example, run ab corresponds to the model simulation where factors A and B are at the ’high’ level, and C is at the ’low’ level. The label (one) is reserved for the simulation when all three factors are at the low level. Run label Value of A (one) Off a On b Off ab On c Off ac On bc Off abc On

Value of B 1.0 1.0 0.1 0.1 1.0 1.0 0.1 0.1

Value of C 500 nm 500 nm 500 nm 500 nm 300 nm 300 nm 300 nm 300 nm

for the deposition coefficient in cirrus clouds suggest a value between 0.1 and 1.0 [34]. Thus the effect of the uncertainty in the value of the deposition coefficient is also taken into account in the experimental design of the FM. Three factors are chosen for study, with two values assigned to each factor, yielding a

23 factorial design such that eight model simulations are required. Specifically, the factors considered are the role of homogeneous freezing (labelled A), the value of the deposition coefficient (B ), and the number concentration of potential IN (C ). The values assigned to each factor along with the experimental design matrix are tabulated in Tables 6.1 and 6.2 respectively. For each factor, the ’low’ and ’high’ values are designated such that the transition from low to high would be expected to increase the ice crystal concentration at some point along the flight track. The DeMott parameterization represents the potential number of available IN as those aerosol greater than 500 nm in diameter. By reducing this threshold from 500 nm to 300 nm, the number of potential IN increases from a concentration of 0.11 cm

3

to 1.0 cm 3 , approximately a factor of nine increase, as shown in

Figure 6.13. 172

6.5. MODEL RESULTS

Figure 6.13: Cumulative number concentration of aerosols above a given size threshold, from UHSAS measurements of RF03. The cumulative concentration is plotted in cm 3 for diameters between 0.1 and 1.0 m.

The FM analysis was applied to simulations where the influence of homogeneous freezing was appreciable, namely 3-2-5 and 3-2-7, with similar conclusions for each case. Figure 6.14 shows the results of the Factorial Method analysis for simulations of 3-2-7, specifically the average effect of each factor (A, B and C ), with the individual interaction terms (AB , AC , BC , ABC ) that represent the competition between factors on a separate axis. The analysis was performed for simulations with a prognostic treatment of ice density, although the results were not found to be sensitive to this choice. Considering the main effects first, the dominant variable in terms of the effect on the ice crystal concentration along the flight track is the effect of homogeneous freezing, shown in blue. The effect of increasing number of potential IN by a factor of ten leads to an increase in heterogeneous ice of around 2L 1 , which is approximately a factor of three increase from the concentration shown in Figure 6.8. The average effect of the change in deposition coefficient from 1.0 to 0.1 is the least important of the three factors considered. The dominant 173


Figure 6.14: Timeseries plots from the Factorial Method analysis, showing the average effects of each factor (top) and the effects of interactions between factors (bottom) in terms of the induced change in predicted ice crystal concentration above 125 m along the flight track. The two-factor interactions represent the competition between: homogeneous freezing and the deposition coefficient (AB ), homogeneous freezing and the IN concentration (AC ) and finally the deposition coefficient and IN concentration (BC ). The remaining three-factor interaction (ABC ) represents the dependency of the AB interaction on the value of C .

174

6.5. MODEL RESULTS

interaction term is between

AB and AC , representing the susceptibility of the homo-

geneous freezing process to the changes in deposition coefficient and IN concentration respectively. Where the effect of

AB is negative, this shows that the effect of homoge-

neous freezing reduces in response to the lowering of the deposition coefficient from 1.0 to 0.1. Similar conclusions are reached for the interaction AC , the case when the IN concentration is increased. However Figure 6.14 shows that the magnitude of the interaction terms are considerably smaller than the average effects; indeed, in terms of the overall contribution to the change in ice crystal concentration, the interaction terms typically explain no more than 10% of the total variance. This means that the specified changes to the deposition coefficient and the assumed IN concentration have a relatively small impact on the homogeneous freezing process, and that for the range of values tested, the specified microphysical factors do not have a particularly strong dependence on each other. If the cloud were more weakly forced initially such that the magnitude of the updraughts were smaller when ice was first formed, it is possible to conceive that competition between microphysical factors could have a more significant impact on the model predictions of ice crystal concentration. For example, if the vapour pressure in cloud at the time of heterogeneous ice formation was less than the equilibrium vapour pressure over water but greater than that over ice at a given temperature, then heterogeneously nucleated ice would grow at the expense of liquid droplets through the WBF process, therefore reducing the potential number of liquid droplets in the cloud available for homogeneous freezing. However as noted in the study by Korolev [35], the WBF process is more likely to be less important in clouds with stronger updraughts, where the in-cloud vapour pressure can be high enough to sustain growth of both liquid droplets and ice crystals simultaneously. Such conclusions are not dissimilar to those of Karcher and Lohmann [36] in the context of cirrus clouds, who suggested that, depending on the dynamical forcing conditions, increases in IN concentration can lower the overall ice crystal concentration in cirrus through competition with, and possibly even suppression of, the homogeneous freezing process.

175


6.6

Summary and conclusions

This study has sought to explain the measurements of ice crystal concentration from an ICE-L wave cloud using a detailed microphysics model embedded within a 1-D column framework. The study has focused on the role of competition between heterogeneous and homogeneous freezing in accounting for the in-situ observations of ice crystal number, and has also considered more subtle features such as the ability of the model to explain the origin of heavily rimed particles seen in images of ice crystals sampled in-situ. Homogeneously nucleated ice was produced in all the model simulations of the chosen wave cloud, and although it did not always intercept the simulated flight level in the model, the limitations of the model forcing must be taken into account here. The initialisation of the model is based on in-situ data available at a single penetration through the cloud at any one time, coupled with the assumption that the vertical velocity is the same above and below the flight track level for the whole model domain. Whilst this was found to have little impact on the predicted ice concentrations associated with heterogeneous nucleation, this was found to be more of an issue when considering the influence of homogeneous nucleation, which is highly sensitive to the representation of the cloud macrostructure (such as cloud depth and cloud top temperature). The model was also found to be sensitive to the assumptions made regarding the treatment of ice density and habit, and the use of a prognostic treatment of ice density was shown to be advantageous for simulating changes in aspect ratio along the flight track in response to the presence of both heterogeneous and homogeneously nucleated ice. However this approach still struggled to simulate the rapid linear growth seen in the observations; whilst this could be improved to some degree through a consideration of the deposition density, this was somewhat arbitrary, highlighting the need for further work in this area to improve the representation of ice growth rates in numerical models. In cases where the predicted ice crystal concentrations along the flight track were clearly affected by homogeneous freezing, it was possible to conduct additional sensitivity studies based around the Factorial Method (FM) to explore the effect of changes in the deposition coefficient and the potential number of IN in the model. The results of the FM analysis show that the peaks in ice crystal concentration arising from homoge176

6.6. SUMMARY AND CONCLUSIONS

neous nucleation were relatively robust to changes in the chosen microphysical factors. The strong dynamical forcing of the cloud in question should be taken into account when considering this result, as this has the potential to overshadow the competition between homogeneous and heterogeneous ice formation to some extent. Since the vertical velocities measured during RF03 are fairly typical of those encountered during the ICE-L field campaign as a whole, it is possible to suggest that for wave clouds where both homogeneous and heterogeneous freezing processes are active, model errors associated with the number concentration of large aerosols are likely to have less of an effect on the simulation of the cloud microphysical processes compared to more weakly forced clouds, where the competition between the two distinct pathways of primary ice nucleation is likely to be more important through the effects of the WBF process. The dynamical forcing was also found to play a role in determining the amount of liquid water available for riming in the model simulations. After homogeneous nucleation occurs, the in-cloud updraught speeds become weaker in the transition from positive to negative vertical velocities, and this causes the remaining droplets in the upper region of the cloud to evaporate in the presence of the homogeneous ice crystals as a result of the WBF process. This rapid glaciation imposes a limit on the amount of riming possible, although the results from the model simulations suggest that some rimed ice could still intercept the flight level within the liquid cloud regime, which is qualitatively consistent with the detection of a few heavily rimed ice crystals in the in-situ observations. Given the relative microphysical complexity of the RF03 case compared to other ICEL wave clouds, it is encouraging that the modelling results shown in this paper can help to understand and explain particular features of the in-situ observations. However there are certain aspects of the model performance which are not able to reproduce the microphysical measurements and in this regard, the in-situ observations also act as a very useful dataset against which models can be constrained and improved. The discrepancies between the predicted and observed ice crystal concentrations are likely to have arisen from the limitations of the observational constraints used to initialise the model. In conclusion the results of this modelling study show that despite recent improvements in parameterizing ice phase microphysical processes, it is equally as important to consider the repre177


sentation of the dynamical factors that influence the cloud macrostructure, and that subtle variations in such factors can have significant consequences for the simulation of the cloud microphysics. There is also evidence from the Factorial Method analysis to suggest that dynamical considerations should be taken into account when considering the extent to which the effects of aerosol need to be represented in microphysics schemes, and that such an approach may help to optimise the balance between microphysical complexity and computational cost in the future development of ice phase microphysics parameterizations for use in larger scale models.

Acknowledgements The first author would like to thank the ICE-L team for their permission to use the ICE-L dataset. This work was funded by NERC studentship reference NE/F00821X/1.

6.7

References

[1] W. Cantrell and A. Heymsfield, “Production of ice in tropospheric clouds - A review”, Bulletin of the American Meteorological Society. 86, 795–+. (2005). [2] M. P. Meyers, P. J. Demott, and W. R. Cotton, “New primary ice-nucleation parameterizations in an explicit cloud model”, Journal of Applied Meteorology. 31, 708–721. (1992). [3] W. A. Cooper, “Ice initiation in Natural Clouds: Precipitation Enhancement - A Scientific Challenge”, Meteorological Monographs. 21, 29–32. (1986). [4] N. H. Fletcher. Physics of Rain Clouds. Cambridge University Press, London, 1962. [5] P. J. DeMott et al., “Predicting global atmospheric ice nuclei distributions and their impacts on climate”, Proceedings of the National Academy of Sciences of the United States of America. 107, 11217–11222. (2010). [6] A.J. Heymsfield et al., “Ice in Clouds Experiment - Layer CLouds. Part I: Ice Growth Rates Derived from Lenticular Wave Cloud Penetrations”, In preparation. (2011). 178

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[7] T. Eidhammer et al., “Ice Initiation by Aerosol Particles: Measured and Predicted Ice Nuclei Concentrations versus Measured Ice Crystal Concentrations in an Orographic Wave Cloud”, Journal of the Atmospheric Sciences. 67, 2417–2436. (2010). [8] P. R. Field et al., “Ice in Clouds Experiment - Layer Clouds. Part II: Testing freezing mechanisms in lee wave clouds”, In preparation. (2011). [9] C. D. Westbrook and A. J. Illingworth, “Evidence that ice forms primarily in supercooled liquid clouds at temperatures >-27 degrees C”, Geophysical Research Letters. 38. (2011). [10] P. J. Connolly et al., “Studies of heterogeneous freezing by three different desert dust samples”, Atmospheric Chemistry and Physics. 9, 2805–2824. (2009). [11] P.R. Field et al. “Contrasting the ice nucleation in two lee wave clouds observed during the ICE-L campaign”. In: 15th International Conference on Clouds and Precipitation, July 7-11, Cancun, Mexico. 2008. [12] A Khain et al., “Simulation of effects of atmospheric aerosols on deep turbulent convective clouds using a spectral microphysics mixed-phase cumulus cloud model. Part I: Model description and possible applications”, Journal of the Atmospheric Sciences. 61, 2963–2982. (2004). [13] A. Seifert et al., “A comparison of spectral bin and two-moment bulk mixed-phase cloud microphysics”, Atmospheric Research. 80, 46–66. (2006). [14] A. Teller and Z. Levin, “Factorial method as a tool for estimating the relative contribution to precipitation of cloud microphysical processes and environmental conditions: Method and application”, Journal of Geophysical Research-Atmospheres. 113, 13. (2008). [15] C. Dearden et al., “Evaluating the effects of microphysical complexity in idealised simulations of trade wind cumulus using the Factorial Method”, Atmospheric Chemistry and Physics. 11, 2729–2746. (2011). [16] H. R. Pruppacher and J. D. Klett. Microphysics of Clouds and Precipitation. Kluwer Academic Publishers., 1997.

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[17] D. O. Topping, G. B. McFiggans, and H. Coe, “A curved multi-component aerosol hygroscopicity model framework: Part 1 - Inorganic compounds”, Atmospheric Chemistry and Physics. 5, 1205–1222. (2005). [18] D. O. Topping, G. B. McFiggans, and H. Coe, “A curved multi-component aerosol hygroscopicity model framework: Part 2 - Including organic compounds”, Atmospheric Chemistry and Physics. 5, 1223–1242. (2005b). [19] T. Koop et al., “Water activity as the determinant for homogeneous ice nucleation in aqueous solutions”, Nature. 406, 611–614. (2000). [20] J. P. Chen and D. Lamb, “The theoretical basis for the parameterization of ice crystal habits - growth by vapor-deposition”, Journal of the Atmospheric Sciences. 51, 1206–1221. (1994). [21] L. M. Sheridan et al., “Influence of Ice Crystal Aspect Ratio on the Evolution of Ice Size Spectra during Vapor Depositional Growth”, Journal of the Atmospheric Sciences. 66, 3732–3743. (2009). [22] B. J. Mason, “The shapes of snow crystals - fitness for purpose?”, Quarterly Journal of the Royal Meteorological Society. 120, 849–860. (1994). [23] A. J. Heymsfield and C. D. Westbrook, “Advances in the Estimation of Ice Particle Fall Speeds Using Laboratory and Field Measurements”, Journal of the Atmospheric Sciences. 67, 2469–2482. (2010). [24] A. Bott, “A flux method for the numerical solution of the stochastic collection equation: Extension to two-dimensional particle distributions”, Journal of the Atmospheric Sciences. 57, 284–294. (2000). [25] M. K. Jacobson. Fundementals of Atmospheric Modeling, 2nd edition. Cambridge University Press, 2005. [26] P. J. Connolly, C. Emersic, and P. R. Field, “A laboratory investigation into the aggregation efficiency of small ice crystals”, Submitted to Atmospheric Chemsitry and Physics Discussions. (2011). [27] A. Bott, “Monotone flux limitation in the area-preserving flux-form advection algorithm”, Monthly Weather Review. 120, 2592–2602. (1992). 180

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[28] A. A. Costa and A. J. C. Sampaio, “Bott’s area-preserving flux-form advection algorithm: Extension to higher orders and additional tests”, Monthly Weather Review. 125, 1983–1989. (1997). [29] J. P. Chen and D. Lamb, “Simulation of cloud microphysical and chemical processes using a multicomponent framework .1. Description of the microphysical model”, Journal of the Atmospheric Sciences. 51, 2613–2630. (1994). [30] K. A. Pratt et al., “Observation of playa salts as nuclei in orographic wave clouds”, Journal of Geophysical Research-Atmospheres. 115. (2010). [31] N. J. Bacon, M. B. Baker, and B. D. Swanson, “Initial stages in the morphological evolution of vapour-grown ice crystals: A laboratory investigation”, Quarterly Journal of the Royal Meteorological Society. 129, 1903–1927. (2003). [32] R. D. Borys et al., “Mountaintop and radar measurements of anthropogenic aerosol effects on snow growth and snowfall rate”, Geophysical Research Letters. 30, 4. (2003). [33] K.M. Gierens, M. Monier, and J.F. Gayet, “The deposition coefficient and its role for cirrus clouds”, Journal of Geophysical Research-Atmospheres. 108. (2003). [34] J. Strotzki. personal communication. 2010. [35] A. Korolev, “Limitations of the wegener-bergeron-findeisen mechanism in the evolution of mixed-phase clouds”, Journal of the Atmospheric Sciences. 64, 3372– 3375. (2007). [36] B. Karcher and U. Lohmann, “A parameterization of cirrus cloud formation: Heterogeneous freezing”, Journal of Geophysical Research-Atmospheres. 108, 15. (2003).

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182

CHAPTER

SEVEN

MODELLING THE EVOLUTION OF WINTERTIME CUMULUS OVER THE UK

In addition to the 1-D modelling presented in the previous chapters, some 3-D simulations have also been performed through collaborative work with colleagues at the University of Manchester in the context of an APPRAISE-CLOUDS case study. The motivation for this work arose from the need to understand the role of both primary and secondary ice formation in the evolution of a narrow line of shallow convective cloud sampled both remotely and in-situ over the southern half of the UK during the winter of 2008/2009. Model simulations of the case study are performed with the WRF (Weather, Research and Forecasting) model to assess the ability of the Hallet-Mossop process to control precipitation formation under these conditions. The results show that the Hallet-Mossop process has some effect on the distribution of precipitation produced, but much less impact on the precipitation intensity. However this conclusion is subject to an important caveat concerning the simulation of the cloud macrostructure that results in the model cloud top temperature reaching lower values than observed in-situ or obtained from satellite data. This chapter, including the setup, execution and analysis of the model simulations is solely the work of C. Dearden. It is the intention that the findings presented here are to contribute to a paper currently in preparation under the working title of "Ice formation and development in aged, wintertime cumulus over the UK : Observations and Modelling" by I. Crawford et al. 183

CHAPTER 7. MODELLING WINTERTIME CUMULUS OVER THE UK

7.1

Introduction

Numerical modelling studies can provide useful insight in terms of identifying the dominant microphysical processes that occur in clouds. In this instance, results from a mesoscale model are used to address the issue of how important the Hallet-Mossop process is in terms of the evolution of a mixed-phase cumulus cloud over the UK and the associated precipitation. The case in question is from the 22nd January 2009, when a narrow but extensive line (approximately 100 km long) of shallow convective cloud was studied using in-situ aircraft measurements in conjunction with ground based remote sensing observations of radar and lidar as part of the Aerosol Properties, PRocesses And InfluenceS on the Earth’s climate (APPRAISE) project. The shallow convective cloud was observed to pass the Chilbolton area around 15z UTC. Lidar measurements (not shown) indicate cloud base to be around 1 km with a corresponding temperature of -1 C, while in-situ measurements suggest cloud top was around 2.3 km with minimum temperatures no less than -8 C. The in-situ microphysics measurements suggest that the Hallett-Mossop (HM) process [1] was active in this cloud, with ice crystal concentrations reaching peaks of 100L 1 . Thus the purpose of this modelling study is to compliment the in-situ obervations to ascertain the role of the H-M process in determining the precipitation efficiency of the cloud.

7.2

Model configuration

Model simulations of the case study are performed with the Weather, Research and Forecasting (WRF) model version 3.1.1, to investigate the processes influencing precipitation formation. The model domains were set up as shown in Figure 7.1. The outermost domain has a horizontal resolution of 9 km, with an 18 s timestep. The 2nd domain is configured on a 3:1 ratio, giving a 3 km resolution and a 6 s timestep. Finally the innermost domain focuses on the region of interest and is configured with a 1 km resolution and 3 s timestep. The model was initialised at 00z, 22nd January 2009 with NCEP analysis data at 1 degree horizontal resolution. The boundary conditions for the outer domain are also constrained by the NCEP analyses and are updated every 6 hours from 00z up to 184

7.3. METEOROLOGICAL EVALUATION OF THE MODEL SIMULATION

Figure 7.1: The domain configuration used for the simulation of the shallow convective cloud on 22nd January 2009 with the WRF model. and including 18z; boundary conditions for the inner domains are provided by the parent domain. The analysis data are interpolated onto 80 vertical levels, with a model top at 20 km. The model was configured for one-way nesting such that the inner domains do not feedback onto the parent domains. In terms of the microphysics, the Morrison et al bulk scheme [2] was used. This contains dual-moment representations of rain, cloud ice, snow and graupel, with the option of either single or dual moment liquid cloud. A gamma distribution is used to describe the cloud droplet size distribution, with a diagnostic relation for the shape parameter; for all other hydrometeors the Marshall-Palmer distribution [3] is used, which implicitly assumes a shape parameter equal to zero.

7.3

Meteorological evaluation of the model simulation

An initial 24 hour simulation was performed with WRF, starting from 00z, with droplet activation based on the approximation of Twomey [4], where the number of CCN activated to form cloud droplets is a function of vertical velocity and the activation parameters

c and k, which initially were set to 1000 and 0.5 respectively. The model de-

rived reflectivity was calculated at the gridpoint closest to Chilbolton (51.15 N, 1.45 W) within the innermost domain, to allow for comparison with the reflectivity timeseries as 185


Figure 7.2: Reflectivity from the Chilbolton radar versus that simulated by the WRF integration for 22nd January 2009.

Figure 7.3: Simulated reflectivity between 12z and 18z, 22nd January 2009, as calculated at 5 minute intervals. This simulation differs to that shown in figure 7.2 as it uses a fixed droplet number concentration of 150 cm 3 based on the in-situ measurements.

186


measured using the vertically pointing Chilbolton radar. The model reflectivity is diagnosed from the 6th moment of the size distribution for precipitation-sized particles (i.e. rain, snow and graupel), and it is calculated from model output which is available at 30 minute intervals. Figure 7.2 reveals that the model provides an acceptable simulation in terms of the cloud structure and the general synoptic conditions. The large-scale frontal systems that are present overnight and throughout the morning are well simulated. The most interesting aspect of the simulation appears to be the presence of a reflectivity signature around 14:30z, which is consistent with the onset of convection over Chilbolton as seen in the radar. The concentration of droplets in this simulated shallow convective cloud is 350-400 cm

3

(not shown), whereas the in-situ observations of the cloud indicate that

the peak concentration of droplets was around 150 cm 3 . Thus a repeat simulation was performed using the same Morrison microphysics, but instead of using a dual-moment representation for liquid droplets, a single-moment treatment with a fixed droplet number concentration of 150 cm

3

was used instead. It should be noted that the sensitivity

of the simulated cloud to the treatment of the liquid phase was found to be small, and did not alter the fundamental conclusions of the work. From 12z onwards the temporal resolution of the model output was also increased from 30 minutes to 5 minutes in order to facilitate a more rigorous comparison with the Chilbolton radar. Figure 7.3 confirms that the timing of convection is well captured by the model, although the simulated cloud top is slightly too high. This can be explained through analysis of model temperature profiles vs radisonde data for selected locations at 12z (Figure 7.4), which shows that the model is not able to capture the sharp inversion around 2 km which is clearly present in the radiosonde profiles. Whilst the comparison of the reflectivity alone suggests the timing of convection is well captured, a consideration of the history of the convective cloud and its evolution reveals some additional differences between the model and the observations that are worthy of comment. In the model, the cloud is fully developed over the Devon & Cornwall peninsula by 12z and proceeds to be advected due eastwards where it finally reaches the Chilbolton region around 14:30z. This is in contrast to the rainfall radar observations, which suggest the cloud follows a more north westerly approach to Chilbolton with a later spin-up. Thus the model manages to initiate convective activity

187


Figure 7.4: Temperature profiles from the WRF model simulation (red) and those from radiosonde data (black) at selected locations. All profiles are taken at 12z on 22nd January 2009.

too soon and then sustain it for too long, such that the cloud is continually replenished as it advects eastwards over the UK, enabling precipitation to be maintained. Meridional cross-sections through the simulated cloud taken at a latitude of 51 N at 12z (shown in Figure 7.5) confirm the mixed-phase nature of the cloud and the fact that it is producing precipitation at this time, which appears to originate from the ice-phase and then melts to form rain below cloud base (approximately 1 km). 188


Figure 7.5: Meridional cross-sections from model output at 51 N at time 12z. Top: liquid mixing ratios (rain and droplet categories); bottom: ice mixing ratios (snow and graupel categories). Plots are in units of g kg 1 .

189


7.4

Sensitivity to Hallet-Mossop process

In the Morrison scheme, the H-M process is allowed to occur in the temperature range between -3 C and -8 C, and also depends on the mass of supercooled liquid (both cloud liquid water and rain) available for riming. Rime splintering acts to increase both the mass and number of the cloud ice category, and can act on both snow and graupel depending on which categories are present. Growth of snow through riming of cloud water is converted to graupel, independent of the H-M process. An additional simulation was performed where the H-M process is switched off in the Morrison scheme from the start of the run (midnight 22/01/09) and the results are compared directly to the simulation where H-M is included. Figure 7.6 shows that, by 12z, a considerable reduction is noticeable in both snow mass and number due to the effect of switching off the H-M process. In particular, the snow number concentration reduces from peak values of around 15000 kg

1

to less

than 1000 kg 1 . Figure 7.6 also shows the effect on the graupel number concentration, where the impact of H-M is revealed to be weaker. The graupel number concentrations even in the absence of H-M still reach up to 5000 kg

1

(around several per litre) at 12z.

The impact on precipitation at 14:30z is shown in Figure 7.7. The effect of switching off H-M leads to a reduction in the spatial extent of the precipitation produced, however there is no significant reduction in the maximum intensity and therefore the H-M process does not appear to be critical to the production of precipitation in this particular simulation. This suggests that the graupel number concentrations in the absence of H-M are enough to sustain precipitation, where graupel is formed through the growth of snow by riming. Additional simulations (not shown) reveal that disabling the graupel category, such that the solid phase is represented by simply cloud ice and snow, results in an increase in snow mass due to conservation of total water; however there is a shift in the size distribution towards larger, fewer snow flakes ( 1L 1 ) due to aggregation (the lack of a self-collection term for graupel explains the higher number concentrations when graupel is enabled). The impact of this change in size and habit of ice crystal was found to have little impact on surface precipitation, suggesting that the simulated shallow convective cloud is largely insensitive to the categorisation of ice. A further test with ice processes switched off completely reveal considerably reduced precipitation, and most notably a distinct lack 190

7.5. TREATMENT OF PRIMARY ICE IN THE MORRISON SCHEME

of precipitation over the Chilbolton area by 14:30z. Thus it can be concluded that for this particular case, the model is apparently able to sustain precipitation solely via the parameterized mechanisms of primary ice nucleation, and that this result does not depend strongly on the subsequent ice growth mechanisms. This naturally poses a new question where does the predicted primary ice at a concentration of several per litre come from?

7.5

Treatment of primary ice in the Morrison scheme

Primary ice nucleation in the version of the Morrison scheme used in this study can be divided into two mechanisms. The first of these is based on the parameterization of Cooper [5], and is permitted to occur at all temperatures less than -8 C or if the supersaturation with respect to ice exceeds 8%. The concentration of ice crystals predicted by the Cooper parameterization is limited to a maximum value of 500L

1

to prevent un-

realistically high concentrations at low temperatures. If the predicted concentration of new ice crystals from the Cooper scheme is less than the concentration of ice particles already present, no additional ice particles are allowed to form via this scheme. Based on the coldest cloud top temperature in the model simulation (-14 C), the ice crystal concentration predicted by the Cooper parameterization is 0.35L 1 . This is approximately six times larger than the parameterized concentration predicted by the Cooper scheme for the coldest observed cloud top temperature (-8 C). The second mechanism by which primary ice can form is based on the freezing of supercooled liquid, with separate treatments for cloud liquid droplets and rain. The freezing parameterizations are allowed to occur if the temperature is below -4 C and if there is liquid water and/or rain present. The mass and number of raindrops that freeze is then determined from the parameterization of immersion freezing by Bigg [6, 7]. In the case of cloud droplets, feezing can also occur due to contact freezing (where the number of contact IN is obtained from Meyers et al [8]), in addition to immersion freezing, also parameterized by the Bigg scheme. Due to the stochastic nature of both the contact and immersion freezing parameterizations, drop freezing in the model operates independently of the existing total ice crystal concentration, and is limited only by the number concentration of liquid drops available. Thus new ice crystals can continue to be produced by drop freezing so long as there is supercooled 191


Figure 7.6: WRF modelling results; Top panel: Snow mixing ratio (kg kg 1 ) at 12z and model level 11 (1.42 km) for the simulation with H-M (left) and without (right). Chilbolton location is 51.15 N, 1.45 W. Middle panel: same as top but for snow number concentration (kg 1 ). Bottom: Same as middle but for graupel number concentration (kg 1 ).

192

7.5. TREATMENT OF PRIMARY ICE IN THE MORRISON SCHEME

Figure 7.7: Surface precipitation accumulated between 14:25z and 14:30z for: WRF with H-M (top); WRF without H-M (bottom).

liquid present and the temperature is low enough. Repeated simulations were performed with the model to isolate the contribution from each primary ice nucleation scheme to the total ice crystal concentration and the subsequent impact on precipitation. This was done by switching off each nucleation scheme in turn to isolate the effect of the other (NB - freezing of droplets is treated as a single mechanism from the combined effect of both contact freezing and immersion freezing schemes together). The H-M process was left switched off for these simulations to focus purely 193


Figure 7.8: Instantaneous ice number concentration tendencies (kg 1 timestep 1 ) taken at model level 17 (2.8 km) at 14z. Top: Tendency from Cooper parameterization when the Cooper scheme is the sole source of primary ice. Middle: Tendency from the droplet freezing parameterization when droplet freezing is the sole source of primary ice. Bottom: Tendency from Cooper parameterization when both the Cooper and droplet freezing schemes are permitted to act together. In all these simulations, the H-M process was disabled. 194

7.6. CONCLUSIONS

on primary ice. The model tended to produce most of the ice near the top of the cloud which quickly grows to form snow (and subsequently graupel), which then sedimentated out. This removal of ice at cloud top allows for fresh ice to form at subsequent timesteps. Additional diagnostics were also added to the model to quantify the instantaneous change in ice crystal concentration within a timestep due to both the Cooper scheme and the droplet freezing scheme separately. Specifically, tendencies for ice, snow and graupel number concentration were output directly at each timestep. Here, tendency is defined as the ability of a particular process to influence model evolution. Figure 7.8 shows results from model level 17 (approximate height 2.8 km) at 14:00z comparing the tendency of the Cooper parameterization (units: kg

1

timestep 1 ) with that produced from the param-

eterization of droplet freezing, from simulations when both mechanisms are operating in isolation from each other and also when they operate together. Through analysis of these diagnostics, evidence was found for competition between the two pathways of ice formation, such that switching off one nucleation mechanism was compensated for by an increase in the other. Cloud top temperature (ignoring any cloud above 4 km to focus on shallow cloud) was not found to change significantly from run to run. Figure 7.9 shows that a significant fraction of the simulated shallow convective cloud exhibits a temperature below -10 C at cloud top, with some localised turrets approaching -14 C, which is lower than that inferred from both the satellite and in-situ data. Given that cloud top temperature is lower in the model than in reality, in any given configuration the model produces too much primary ice, a problem which is exacerbated by the ability of the model to regenerate small amounts of fresh ice at later timesteps.

7.6

Conclusions

A mesoscale modelling framework has been used to investigate the role of the HalletMossop secondary ice production process in terms of its influence on preciptation from a wintertime shallow convective cloud region over the southern part of the UK. Whilst the model results showed some increase in the spatial extent of precipitation occurance due to inclusion of the Hallet-Mossop process, the ice crystal concentration from primary ice nucleation was found to have the most significant control on precipitation, at least in 195


Figure 7.9: Cloud top temperature field in C at 13:30z (top) and 14:00z (bottom) from the simulation with just the droplet freezing mechanism active, and H-M off.

196

7.7. REFERENCES

this particular case. The WRF model was able to reproduce total ice number concentrations of several per litre even in the absence of the Hallet-Mossop process, which was sufficient to sustain precipitation as the convective cells were advected eastwards towards the Chilbolton region. However, the model was only able to produce such relatively high concentrations due to the fact that cloud tops in the model were able to achieve lower temperatures than actually observed. This was due to the inability of the model to capture the temperature inversion observed at 2 km. This result serves as a useful illustration of the outstanding issues and challenges that exist when representing shallow convection in current mesoscale models, particularly in terms of the importance of cloud macrostructure and how errors in the meteorological conditions in the model can dominate over microphysical considerations.

7.7

References

[1] J. Hallett and S. C. Mossop, “Production of secondary ice crystals during the riming process”, Nature. 249, 26–28. (1974). [2] H. Morrison, J. A. Curry, and V. I. Khvorostyanov, “A new double-moment microphysics parameterization for application in cloud and climate models. Part I: Description”, Journal of the Atmospheric Sciences. 62, 1665–1677. (2005). [3] J. S. Marshall and M. K. Palmer, “The distribution of raindrops with size”, J. Meteor. 5, 165–166. (1948). [4] R. R. Rogers and M. K. Yau. A Short Course in Cloud Physics, 3rd edition. Butterworth and Heinemann, 1989. [5] W. A. Cooper, “Ice initiation in Natural Clouds: Precipitation Enhancement - A Scientific Challenge”, Meteorological Monographs. 21, 29–32. (1986). [6] E. K. Bigg, “The supercooling of water”, Proceedings of the Physical Society of London Section B. 66, 688–694. (1953a). [7] E. K. Bigg, “The formation of atmospheric ice crystals by the freezing of droplets”, Quarterly Journal of the Royal Meteorological Society. 79, 510–519. (1953b).

197


[8] M. P. Meyers, P. J. Demott, and W. R. Cotton, “New primary ice-nucleation parameterizations in an explicit cloud model”, Journal of Applied Meteorology. 31, 708–721. (1992).

198

CHAPTER

EIGHT

DISCUSSION

8.1

A summary of the work completed for this thesis

This thesis has explored the sensitivity of different microphysics schemes to changes in both microphysical and dynamical factors for the purpose of simulating aerosol-cloud interactions in numerical models. The main motivation for the work was to address the urgent issue concerning the level of sophistication required from a microphysics scheme in order to simulate the effects of aerosols on cloud, such that the balance between complexity and computational cost can be optimised. Selected microphysics scheme of varying levels of complexity have been tested and implemented within a range of dynamical frameworks, including a Lagrangian parcel model, a 1-D column model and a 3-D mesoscale model. Whilst the 1-D kinematic model used in this study is simplistic and does not permit a complete representation of cloud dynamics due to the inability to capture dynamical-microphysical-radiative feedbacks, it has served as a very useful testbed for isolating the pure microphysical behaviour of different schemes, and has demonstrated the potential to help understand the origin of differences in the representation of cloud and precipitation in more realistic dynamical frameworks. The 3-D model was necessary to perform studies of the evolution of mixed-phase convective cloud as part of the APPRAISE project. A summary of the main aims and outcomes from each of the papers presented in this thesis is now given. 199

CHAPTER 8. DISCUSSION

8.1.1

Paper 1

The first paper (chapter 4) laid out the formal methodology that was to form the foundation of the work done for the rest of the thesis. Central to this methodology is the application of the Factorial Method as a tool to help contrast and compare the sensitivities of different microphysics schemes under controlled conditions. In this paper, specific bin and bulk microphysics schemes were identified for use, and in advance of their inclusion within a 1-D Eulerian grid model with prescribed dynamics, they were tested within a Lagrangian parcel model framework. The results of these tests demonstrate the importance of the assumptions made with regards the treatment of droplet activation within bulk microphysics schemes. A version of the bulk microphysics scheme was developed with a resolved treatment of supersaturation, and this was used to verify a diagnostic treatment of supersaturation that lead to more realistic behaviour of in-cloud activation relative to a parameterization of droplet number based solely on updraught speed. The outcomes of the parcel model tests therefore helped to identify the most appropriate settings to use in the bulk scheme prior to being integrated into the 1-D column framework.

8.1.2

Paper 2

In chapter 5, the second paper presented results from application of the microphysics schemes tested in the first paper to the case of an idealised precipitating liquid cloud in the trade wind regime, where the schemes were driven by the 1-D kinematic framework and the Factorial Method was used to quantify and compare the sensitivities to both microphysical and dynamical changes. It was found that a uniform reduction of the temperature profile within the boundary layer by 2 C under a fixed relative humidity produced a suppression of precipitation at the surface greater than that produced by an increase in CCN concentration from 50 cm

3

to 100 cm 3 , although the extent to which the change in tem-

perature dominated the response was found to vary from scheme to scheme. In particular, the bin scheme was found to have a weaker sensitivity to changes in CCN concentration because it was able to produce raindrops more efficiently than the bulk scheme and therefore was less dependent on the initial number of available CCN. Comparison of these findings with those from other independent studies using the same 1-D dynamical frame200

8.1. A SUMMARY OF THE WORK COMPLETED FOR THIS THESIS

work also suggested that differences in precipitation between bin schemes can be just as large as those between bulk schemes, implying that the addition of extra microphysical complexity associated with the spectral bin approach does not necesarily guarantee a more accurate representation of reality. This is a crucial point to address if bin schemes are to be used as benchmarks against which simpler bulk parameterizations are validated and constrained. The results of this study suggest that in this case, the difference in sensitivities is at least in part controlled by the assumptions made with regards the efficiency of the collision and coalescence process, although differences in the numerical treatment of sedimentation and advection could not be ruled out and should also be considered as a possible contributing factor. In any case, more laboratory work and field studies are needed to constrain bin microphysics schemes in this regard. There is also a suggestion from the Factorial Method results that in bulk microphysics schemes, a single-moment treatment of liquid water may be sufficient in cases where updraught speeds are high, since equivalent runs with prognostic droplet number were found to exhibit very similar sensitivities and precipitation amounts under such conditions.

8.1.3

Paper 3

The 1-D column framework was also used in a consideration of the mixed-phase in the third paper (chapter 6), specifically for a wave cloud sampled as part of the ICE-L field campaign. Given the relative dynamical simplicity of such orographically induced clouds, in this case it was possible to conduct a comparison of the 1-D modelling results with the availale in-situ measurements. The model used was the same bin microphysics model as in the idealised liquid cloud case of the second paper, but extended here to include a relatively detailed representation of ice microphysical processes. The results of the wave cloud modelling confirm that a consideration of homogeneous freezing in addition to heterogeneous freezing is required in order to explain the measured concentrations of ice above the 125 m size threshold. The prognostic treatment of ice density used in the model was shown to be capable of representing adaptive growth of ice crystals such that realistic changes in ice crystal habit and density were captured, providing useful information as to the history of the cloud in terms of ice nucleation and growth. However 201


there is still room for improvement as the adaptive scheme for ice crystal growth was not quite able to capture the rapid growth rates of ice seen in the observations. The bin model was also used to help understand the origin of the few heavily rimed ice crystals seen in the observations. Besides the treatment of depositional growth in the model, dynamical factors were also found to play a significant role in the simulation of the cloud. Indeed the Factorial Method was used to demonstrate that if homogeneous nucleation is important in these clouds, then it tends to dominate over other microphysical subtleties and only the dynamic forcing is relevant as a major factor. The point is also made that this may not be the case in clouds with less strong updraughts. The sensitivity to aerosol is also likely to be higher if the wave cloud temperatures are greater than -35 C so that homogenous nucleation is negligible. Thus in terms of addressing the issue of microphysical complexity, the use of more complex schemes to predict active IN number concentrations is likely to benefit the simulation of weakly forced ice clouds more so than strongly driven cases. The results from the Factorial Method also revealed that the value of the deposition coefficient did not have a significant impact on the model results within the current uncertainty range of 0.1 - 1.0.

8.1.4

Paper 4

The focus on the mixed-phase continued in the fourth and final paper (chapter 7), although the type of cloud considered was quite different to that studied in the previous paper. The attention turned to the case of a shallow convective cloud over the UK from the winter of 2008/2009 that was sampled both in-situ and remotely as part of the APPRAISE project. In order to compliment the available aircraft and ground-based measurements, the WRF model was used in an attempt to understand the key microphysical processes that controlled the evolution of the cloud and the associated precipitation. A specific aim was to establish the role of the Hallet-Mossop process on precipitation efficiency. However it was shown that in this particular case, the simulation of the cloud was largely controlled by discrepancies in the meteorological conditions between the model and the observations. Specifically, the inability of the model to simulate the sharp inversion observed around 2km allowed the simulated cloud to achieve colder temperatures 202

8.2. FUTURE WORK

than those seen in the satellite and in-situ data. Consequently the number concentration of primary ice produced by the model was found to be large enough to sustain precipitation even in the absence of the Hallet-Mossop process, whilst secondary ice production was found to only impact on the pattern of precipitation and less so the intensity. Tests with both single and dual moment treatment of liquid water showed little sensitivity, and did not change the fundamental conclusions of the modelling work. Therefore in this instance any further increases in the complexity of the microphysics would be unlikely to make a significant impact on the simulation given the deficiencies in the representation of the cloud macrostructure. There are some parallels here with the results from the ICE-L wave cloud modelling study, which revealed that the discrepancies between the observed and predicted ice crystal concentrations were in some instances determined by errors in dynamical factors that controlled the homogeneous freezing process.

8.2

Future work

It is fair to say that the outstanding issues concerning the treatment of aerosol-cloud interactions in numerical models are so vast that the results of this study have only begun to scratch the surface of the problem. However the tools and techniques developed here could easily be extended in future work to cover additional cloud regimes which it was not possible to address within the timeframe of this thesis. For instance, further investigation of the effects of microphysical complexity on deep convection is warranted, since the idea of optimum CCN concentrations [1] to maximise storm intensity was postulated based on cloud resolving model studies using single-moment liquid with a fixed droplet number. It would be of interest to determine the sensitivity of this result to different levels of complexity of the liquid phase, e.g. extended to two-moment liquid, where the ability to predict changes in droplet number concentration may have consequences for rates of riming and hence precipitation. It is also recognised that the regimes considered in this thesis (namely idealised trade wind cumulus, orographic wave clouds and shallow wintertime convective cloud) are all examples of relatively strongly forced clouds dynamically speaking. Thus it would also be of benefit in future work to consider clouds where updraught speeds are weaker, i.e. layer clouds such as marine stratocumulus whose climatic 203


importance was noted earlier in chapter 2. Indeed these issues have already started to be addressed through collaborative work to investigate the impact of the representation of the liquid phase microphysics for different VOCALS-REx case studies using the Met Office Large Eddy Model (LEM, [2]).

1

The LEM work tests the ability of both the standard LEM bulk microphysics scheme (single-moment liquid, dual-moment rain) and the dual-moment Morrison scheme (the same version used in chapter 5 [3]) to reproduce the observed bulk characteristics of two distinct stratocumulus layers at 20 S, 72 W and 20 S, 76 W, both sampled in-situ on 13th November 2008 during VOCALS-REx. The cloud layer at 72 W is a relatively thin, non-precipitating layer, whereas the other at 76 W is deeper and drizzling. The droplet number concentration in the standard LEM microphysics is determined directly from the CCN concentration (implicitly assuming that all CCN activate to form cloud droplets), whereas in the Morrison scheme the droplet number concentration is predicted from the Twomey power-law relationship [4]. Thus in theory the Morrison microphysics does not necessarily activate all the available CCN and can therefore produce fewer and larger droplets relative to the standard LEM microphysics scheme. It is important to note that both schemes employ different autoconversion schemes, with the standard LEM case using the Kessler scheme [5] and the Morrison microphysics configured to use the scheme of Seifert & Beheng [6]. Preliminary results suggest that for the thinner layer, both schemes produce either very little or no precipitation and the simulated mean liquid water path and albedo are very similar. In the scheme with prognostic droplet number (the Morrison mirophysics), the turbulent motions within the cloud are strong enough to activate virtually all the CCN, and so droplet number concentrations are quite similar in both simulations. This suggests that for this particular case, the addition of the extra prognostic variable for droplet number in the Morrison scheme appears to be largely redundant as the simulation using the 1-m standard LEM case produces very similar results. Work is currently ongoing to conduct additional simulations for the deeper cloud layer at 76 W. Ultimately the results will reveal whether the added complexity of a prognostic droplet number variable can be justified for the cases considered. 1 This work is currently in progress by the author and is intended for future publication under the working title of "Modelling marine stratocumulus and its radiative properties".

204

8.2. FUTURE WORK

In addition to the LEM studies, there is also the possibility of using the ACPIM to look at the effects of aerosol composition in the context of marine stratocumulus. The role of composition was considered briefly in Dearden et al [3] for the idealised trade wind cumulus case (sea-salt versus ammonium sulphate), and was only found to have a very small impact on cloud droplet number concentrations due to the relatively strong dynamical forcing. However composition is likely to be more important in layer clouds where vertical velocities are weaker, particularly in coastal stratocumulus decks that are also more likely to be influenced by anthropogenic emissions. By running the ACPIM as a Lagrangian parcel model for a range of updraught speeds typical of those associated with marine stratocumulus, it is possible to perform simulations with different aerosol compositions, and the relationship between composition and number of droplets activated could be parameterised such that the effect of composition can be included in bulk 3-D simulations which permit feedbacks between microphysics, radiation and dynamics. Recommendations for follow-up work based on the specific outcomes of the papers presented in this thesis are listed as follows. * There is some suggestion in the findings from the 2nd paper [3] that a diagnostic relationship for droplet number may be just as suitable as a prognostic treatment for simulations of liquid clouds. However it is important to note the caveat of no dynamical feedbacks in relation to this particular case, so future work should explore if this result holds within a more realistic dynamical framework, as this may have important implications for optimising the computational cost of microphysics schemes. This question is already being explored to some degree within the VOCALS LEM modelling work, although it should also be considered in other cloud regimes as well where possible. * It would be very useful to conduct a dedicated microphysics intercomparison focussing purely on bin microphysics schemes within the 1-D framework based on the Factorial Method. The aim should be to quantify and compare the sensitivity of each bin scheme based on changes in the assumed collection efficiency, number of size bins, and numerical considerations such as the choice of advection scheme and bin structure describing the evolution of particle size distributions. This would 205


help to identify the key factors that control differences between bin schemes and therefore where future research efforts should be focused. * The different precipitation rates noted in the idealised warm cloud study in chapter 5 imply differences in rain evaporation rates between microphysics schemes. This may have potentially significant consquences in terms of evaporative cooling of the sub-cloud layer. This is likely to be a potentially important feedback mechanism in models with more complete dynamics; although quantification of such feedback effects were beyond the scope of the study, it is something that should be studied in future work. * Future work should also consider ways to improve the representation of ice growth rates in numerical models, as the prognostic treatment of ice density in ACPIM, whilst preferable over the constant bulk density assumption, was found to struggle when attempting to reproduce the relatively rapid growth rates seen in the in-situ observations from the ICE-L case study. More laboratory work is needed to account for this such that the representation of ice growth rates in microphysics models can be improved. * The recent DeMott et al scheme for primary ice nucleation [7] represents a significant step forward in parameterizing heterogeneous ice nucleation by accounting for both aerosol number concentrations as well as temperature. However its use is only strictly valid between -15 C and -35 C. The shallow convective cloud considered in chapter 7 is a good example of a case where ice was observed at temperatures greater than -10 C. Thus where possible, future field campaigns should continue to target mixed-phase clouds within a similar temperature range in order to improve our understanding of factors influencing ice initiation within this relatively warm regime.

8.3

Final thoughts

Application of the Factorial Method has been a key part of this work, both in the idealised warm cloud study in chapter 5 and the ICE-L wave cloud modelling in chapter 206

8.4. REFERENCES

6. The main advantage of the Factorial Method in the context of this study has been in its ability to help isolate the dominant microphysical and/or meteorological variables in a given cloud, and also the ability to isolate and quantify the potentially crucial interactions between variables, and how these interactions evolve as a function of time through the evolution of a cloud from its creation to its dissipation. Such an analysis technique should prove to be very useful for future studies intending to disentangle the effects of aerosol from the effects of meteorology. One of the key results of this thesis is that it has been shown how dynamical factors can overshadow concerns of microphysical complexity when using numerical models to simulate aerosol-cloud interactions. In terms of the ice phase, both the ICE-L and APPRAISE modelling work have demonstrated how relatively subtle errors in the representation of the cloud macrostructure can have significant consequences for the simulation of mixed-phase processes. Since the macrostructure is dictated largely by dynamical considerations, it is imperative that numerical models strive to improve the accuracy of the meteorological representation in order to justify improvements in model microphysics. Historically, dynamical considerations have arguably been treated separately from the effects of microphysics resulting in little synergy between the two areas of atmospheric research, but the work highlighted in this thesis shows that increasingly the two must be considered together if we are to further our understanding of aerosol-cloud interactions, specifically in terms of how we choose to implement such coupling in numerical models and the extent to which we need to take the issue of microphysical complexity to be able to capture the key interactions. Based on the results presented in this thesis, it is possible to conceive that in future generations of numerical models, microphysics schemes will possess the ’intelligence’ to selectively determine the appropriate level of complexity to simulate a given cloud based on knowledge of aerosol properties and the local dynamics of the cloud environment.

8.4

References

[1] P. J. Connolly et al., “Cloud-resolving simulations of intense tropical Hector thunderstorms: Implications for aerosol-cloud interactions”, Quarterly Journal of the Royal Meteorological Society. 132, 3079–3106. (2006). 207


[2] M. E. B. Gray et al., “Version 2.3 of the Met Office Large Eddy Model: Part II. Scientific Documentation”, APR Turbulence and Diffusion Note 276, Met Office, 52 pp. (2001). [3] C. Dearden et al., “Evaluating the effects of microphysical complexity in idealised simulations of trade wind cumulus using the Factorial Method”, Atmospheric Chemistry and Physics. 11, 2729–2746. (2011). [4] S. A. Twomey, “The Nuclei of Natural Cloud Formation. Part II: The Supersaturation in Natural Clouds and the Variation of Cloud Droplet Concentrations”, Geofisica pura e applicata. 43, 227–242. (1959). [5] E. Kessler, “On the distribution and continuity of water substance in atmospheric circulations”, Meteorological Monographs. 10. (1969). [6] A. Seifert and K. D. Beheng, “A double-moment parameterization for simulating autoconversion, accretion and selfcollection”, Atmospheric Research. 59, 265–281. (2001). [7] P. J. DeMott et al., “Predicting global atmospheric ice nuclei distributions and their impacts on climate”, Proceedings of the National Academy of Sciences of the United States of America. 107, 11217–11222. (2010).

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APPENDIX

A REPRINT: INVESTIGATING THE SIMULATION OF CLOUD MICROPHYSICAL PROCESSES IN NUMERICAL MODELS USING A 1-D DYNAMICAL FRAMEWORK

Full reference as follows: Dearden, C.: Investigating the simulation of cloud microphysical processes in numerical models using a one-dimensional dynamical framework., Atmos. Sci. Lett., 10, 207-214, 2009.

209

ATMOSPHERIC SCIENCE LETTERS Atmos. Sci. Let. 10: 207–214 (2009) Published online in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/asl.239

Investigating the simulation of cloud microphysical processes in numerical models using a one-dimensional dynamical framework Christopher Dearden* School of Earth, Atmospheric and Environmental Science, University of Manchester, Manchester, UK

*Correspondence to: Christopher Dearden, School of Earth, Atmospheric and Environmental Science, University of Manchester, Room 3.16, Simon Building, Oxford Road, Manchester M13 9PL, UK. E-mail: christopher.dearden@ postgrad.manchester.ac.uk Received: 25 January 2009 Revised: 7 July 2009 Accepted: 20 August 2009

Abstract This paper describes the method by which the performance of a suite of microphysics schemes of varying levels of complexity can be compared within an idealised framework. The purpose is to establish the level of microphysical sophistication required for the successful simulation of liquid clouds in operational models, paying particular attention to the required level of coupling with aerosols. Initial results from a lagrangian parcel model are able to demonstrate the importance of the treatment of droplet activation in dual moment schemes for predicting droplet number qualitatively. Subsequent testing within a one-dimensional (1D) column model using the existing factorial method (FM) will aim to quantify the importance of microphysical complexity on precipitation and cloud albedo relative to the effects of meteorology. Copyright  2009 Royal Meteorological Society Keywords:

clouds; microphysics; parcel model

1. Introduction The level of microphysical complexity implemented within a numerical weather prediction (NWP) model or climate model is an important consideration because model complexity has to be balanced alongside cost implications, ultimately determined by computational limitations. It is important to capture liquid phase processes accurately not just because they determine the structure of warm clouds but also because liquid droplets can exist at temperatures below 0 ◦ C in the form of supercooled water, which plays a role in ice formation through homogeneous and heterogeneous freezing mechanisms (Cantrell and Heymsfield, 2005). Consequently, an accurate representation of the liquid phase should be achieved first, as a precursor to an eventual improved treatment of the ice phase. Because aerosols in the atmosphere are known to reduce the size of the energy barrier required for the phase transition of water, a study of liquid phase microphysics is incomplete without consideration of the role of cloud condensation nuclei (CCN). The effect of CCN can lead to the modification of cloud properties on the large scale: the albedo of warm clouds is enhanced in the presence of CCN by virtue of an increase in the surface area of droplets (Twomey, 1959). Such interactions, known as aerosol indirect effects, can have important consequences for the net cloud radiative forcing and hence climate. Aerosol indirect effects may also be important for weather, as they can prolong the lifetime of a cloud by increasing the liquid water content due to a suppression in the drizzle rate (Albrecht, 1989). However, observational evidence is not always consistent with this (Coakley Copyright  2009 Royal Meteorological Society

and Walsh, 2002), suggesting that the specifics of the meteorology may be important. This makes it difficult to isolate the aerosol effects and identify those that may be worthy of parameterization. In recent years, considerable advances in understanding have been made in accounting for CCN properties on droplet activation (McFiggans et al., 2006), and detailed process models have been designed to investigate the remaining uncertainty surrounding the role of organic compounds (Topping et al., 2005a, 2005b). Such process models can be used to inform and constrain the development of microphysics schemes that either describe the bulk properties of hydrometeors (‘bulk schemes’) or resolve the hydrometeor size distribution explicitly by breaking it down into discrete size bins (‘bin schemes’). However, the performance of these schemes still needs to be considered under a range of thermodynamic environments to establish whether the additional microphysical complexity can consistently add any skill to the model. Bulk schemes work by assuming some form of the particle size distribution based on aircraft observations. Typically, the distribution is based on a gamma function, which is in turn a function of particle diameter, D: nx (D) = nx 0 D αx exp(−λx D)

(1)

where the class of hydrometeor is denoted by x , nx is the number distribution, nx 0 is the intercept parameter, αx is the shape parameter [which when set to zero, reduces Equation (1) to an exponential distribution] and λx is the slope parameter. The

208

C. Dearden

size–mass relationship is specified as: Mx (D) = cx D dx

(2)

where Mx is the particle mass and cx and dx are constants. The moments M of the particle size distribution are given by: ∞ D k nx (D)dD (3) Mk = −∞

where k can take any real value and denotes the k th moment of the size distribution. The number concentration corresponds to k = 0, and mass mixing ratio to k = dx , where dx for a spherical hydrometeor is equal to three. Thus, the moments return useful information regarding bulk cloud properties. Single moment schemes solve for the mixing ratio, related to the third moment, whereas dual moment schemes predict number concentration as well and so are doubly expensive because they must hold twice the number of prognostic variables. By predicting number as well as mass, dual moment treatments of cloud water must include a rate equation describing the activation of droplets and thus have the ability to parameterize the effects of aerosol. This study will attempt to quantify this advantage and decide whether the application of a dual moment bulk scheme can be warranted for the simulation of the liquid phase.

contributions of a number of factors to changes in surface precipitation from mixed phase convective cloud. For brevity, the key aspects of the method are now described. Factors are chosen to reflect those variables whose effects require evaluation, for example, CCN concentration, or initial temperature profile. If k factors are considered at two levels (corresponding to a high value and a low value), this would give a 2k factorial design. In the case of three factors, labelled A, B and C respectively, eight simulations would be needed. Each simulation is labelled according to the level of the factors used, such that a high value of the factors A, B and C is denoted by a lowercase letter a, b and c respectively, and the low value is denoted by the absence of the corresponding letter. The case when all three factors are considered at their low levels is denoted as (1). Thus, the eight treatment combinations in standard order can be written as (1), a, b, ab, c, ac, bc and abc. From this it can be seen that three degrees of freedom are associated with the main effects of A, B and C , and four degrees of freedom are associated with the interactions between AB, AC, BC and ABC. The main effect of A can be obtained from the average of the four treatment combinations where A is at the high level, minus the average of the four treatment combinations where A is at the low level. In standard notation, this can be written as: (a + ab + ac + abc) [(1) + b + c + bc] − 4 4 1 = [a + ab + ac + abc − (1) − b − c − bc] (4) 4

A=

2. Methodology The methodology adopted for this work is based on testing the performance of a suite of microphysics schemes of increasing levels of sophistication within a common 1D framework. Such a framework enables control over atmospheric thermodynamic variables, while allowing the performance of the schemes to be analysed in isolation from systematic errors that can arise from elsewhere. Because CCN lead to the formation of liquid droplets in the atmosphere, specific consideration will be given to establishing the sensitivity of cloud properties to changes in aerosol properties such as concentration and composition. This will be achieved through the factorial method (FM), which involves systematically exploring the phase space of thermodynamic and microphysical variables to assess the impact on precipitation reaching the ground. This will enable an assessment to be made concerning the importance of aerosol effects in the context of changing meteorological conditions, and therefore whether any robust conclusions concerning cloud–aerosol interactions can be reached. Equally as importantly, the minimum requirements needed to simulate these aerosol effects in numerical models will also be ascertained. The FM is described in Teller and Levin (2008), where its application is demonstrated using the Tel Aviv University 2D (TAU 2D) cloud resolving model to investigate the relative Copyright  2009 Royal Meteorological Society

The effects of B and C are obtained in a similar manner, yielding: 1 [b + ab + bc + abc − (1) − a − c − ac] (5) 4 1 C = [c + ac + bc + abc − (1) − a − b − ab] (6) 4 B=

The effects of the two-factor interactions (namely AB, AC and BC ) are computed thus. The AB interaction can be thought of as one-half of the difference between the average A effects at the two levels of B : 1 (average A effect at high B value) AB = 2 −(average A effect at low B value) 1 AB = [abc − bc + ab − b − ac + c − a + (1)] 4 (7) Following similar logic, the AC and BC interactions are given by: 1 [(1) − a + b − ab − c + ac − bc + abc] (8) 4 1 BC = [(1) + a − b − ab − c − ac + bc + abc] (9) 4 AC =

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The remaining effect, the interaction of all three factors (ABC ), is defined as the average difference between the AB interaction for the two levels of C : 1 ABC = [abc − bc − ac + c − ab + b + a − (1)] 4 (10) The terms in square brackets in the above equations are known as the contrasts in the treatment combinations. The contrasts are useful to evaluate as they are required to calculate the sums of squares for each of the effects. In general, the sum of squares for any effect is calculated by: SS =

1 2k

× (Contrast)2

(11)

The relative contribution of each effect to the total variance can be quantified in terms of a percentage of the total sum of squares, where the total is given by: SST = SSA + SSB + SSC + SSAB + SSAC + SSBC + SSABC

(12)

The reader is referred to Montgomery (2005) for the general case where more than three factors need to be evaluated. The factors chosen for this particular study are: (1) Updraught speed (to explore the effects on the number of droplets activated at cloud base) (2) Initial temperature profile (to explore the effect of cloud base temperature on droplet activation) (3) Aerosol composition (to explore the impact of increases in organic material in both internal and external mixing states) (4) Aerosol size (to establish the impact of increasingly larger CCN) (5) Aerosol concentration (to investigate the relationship between increases in aerosol number and the rate of autoconversion) A 1D column model (described in Section 3.3) with prescribed forcing and a fixed vertical resolution will be used to drive a suite of microphysics schemes to investigate the impact of each of the above factors on surface precipitation. The impact on the cloud albedo will also be considered in terms of the effective radius of droplets, an important quantity for climate models to predict as it determines the cloud radiative forcing. The importance of the microphysical factors (aerosol composition, size and concentration) relative to the effects of meteorology (updraught speed and temperature profile) will be judged in terms of their role in explaining the total variance. The FM will be applied to both bin and bulk microphysics schemes in the same 1D framework, including a dual moment liquid scheme with the option of prognostic aerosol, and a less computationally demanding single moment Copyright  2009 Royal Meteorological Society

treatment of liquid. Results from the bulk schemes will be compared in turn with those from the bin scheme, to establish whether they are capable of producing similar sensitivities. As the complexity of the bulk schemes reduces, so does the potential to represent aerosol–cloud interactions. However, this may not be a limiting factor if the effects of aerosol are shown from the bin scheme to be insignificant compared with the effects of meteorology. Ultimately, the tests will identify the level at which aerosols need to be represented within a bulk microphysics scheme for the purpose of simulating liquid phase processes. Once the comparison of the microphysics schemes has been conducted in the 1D framework, the bulk schemes will be engineered into a 3D cloud resolving model and a series of warm and mixed phase case studies will be performed in a mesoscale framework. This will qualitatively demonstrate whether any improvements in model skill can be had by increasing the complexity of the microphysics. Figure 1 shows a flowchart that summarises the methodology through from start to finish.

3. Model description 3.1. The bulk schemes The bulk microphysics will be based on the existing scheme of Morrison et al. (2005). It includes a dual moment representation of cloud liquid droplets, rain, cloud ice, snow and graupel, with assumed size distributions of the form given in Equation (1). Within the Morrison scheme, various options are available to specify the treatment of droplet activation and the representation of aerosol. This built-in flexibility will be exploited to develop a hierarchy of bulk schemes, starting from relatively simple microphysics, with each subsequent scheme benefiting from an incremental increase in complexity. This will allow any improvements in performance between schemes to be easily traceable and attributable. Details of the proposed hierarchy are now presented, along with a discussion of the added functionality each scheme provides relative to its predecessor. 3.1.1. Single moment liquid water and rain

As the Morrison scheme uses a dual moment approach for all hydrometeors, a version of the scheme will be developed that simplifies the treatment of liquid water and rain to single moment; consequently droplet number must be prescribed. Typically in single moment schemes, it is specified as a constant, for example, Thompson et al. (2004). Although a single moment scheme cannot account for the effects of aerosol composition or size, the effects of aerosol concentration can be explored by proxy through changes in the prescribed droplet number. Atmos. Sci. Let. 10: 207–214 (2009) DOI: 10.1002/asl

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Figure 1. Flowchart illustrating the application of the factorial method to assess the importance of cloud–aerosol interactions in the context of a changing meteorology with reference to an explicit bin scheme. 3.1.2. Single moment liquid water, dual moment rain

The use of a dual moment scheme for rain will facilitate the simulation of the thermodynamic indirect effect (Lohmann and Feichter, 2005), because the predicted number concentration for rain will have an effect on the collection rate of cloud droplets by falling rain drops. This could be significant for cases of deep convection, where the amount of supercooled water that freezes homogeneously leads to the release of latent heat. The degree of latent heating can result in a more vigorous convective updraft, allowing higher cloud top heights to be achieved. Comparison with the single moment rain scheme will help to decide whether a dual moment treatment of rain is necessary. 3.1.3. Dual moment liquid water, dual moment rain

The transition from prescribed droplet number concentration to a prognostic treatment has consequences for the simulation of the mixed phase, because it provides the opportunity to investigate the possibility of a riming indirect effect, first proposed by Lohmann and Feichter (2005). An explicit treatment of droplet activation is also required. Particular attention will be Copyright  2009 Royal Meteorological Society

given to assessing the sensitivity of total precipitation to the handling of cloud droplet activation. The influence of aerosols will initially be accounted for using the activation spectrum relation (Rogers and Yau, 1989), which relates droplet number N to supersaturation ratio, s: N = cs k

(13)

where c and k are constants that depend on the type of airmass and s = (qv /qsat − 1) × 100%, where qv is the (supersaturated) vapour mixing ratio and qsat is the saturation mixing ratio. This requires the Morrison scheme to be able to predict supersaturations explicitly. Currently a saturation adjustment method is used, whereby excess water vapour above saturation is instantaneously removed and converted to the liquid phase. Such a method is justified within a mesoscale framework, where model timesteps are typically longer than the growth rate of droplets through condensation of the available water vapour. However, this technique never permits a supersaturation to be maintained, thus rendering it incompatible with Equation (13). Consequently to study droplet activation based on Equation (13) in the 1D framework, the saturation Atmos. Sci. Let. 10: 207–214 (2009) DOI: 10.1002/asl


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adjustment method must be replaced with a diffusional growth equation which is specified in Pruppacher and Klett (1997): (qv /qsat − 1) dm = CF dt ρAB

(14)

where dm/dt is the rate of change of mass due to evaporation/condensation, AB is a function of temperature, C = D/2 assuming spherical particles and F is the ventilation coefficient (in this study, ventilation effects are ignored for cloud droplets). To account for changes in aerosol composition in this scheme, N–s relationships for different aerosol types can be constructed off-line using the binresolved microphysics scheme with droplet activation based on Kohler theory. From the N–s relations, N–w parameterizations for different aerosol types can then be developed in the manner of Twomey (1959), such that the droplet number will depend on updraft speed w rather than the resolved supersaturation. 3.1.4. Dual moment liquid water and rain, with prognostic treatment of aerosol

While the previous schemes attempt to account for the effects of aerosols on some level, they do so noninteractively. The use of a prognostic dual moment scheme for aerosols addresses this limitation, such that the effect of aerosol transport on cloud properties is handled explicitly and so does not need to be parameterized. The dual moment aerosol scheme would hold mass and number concentration as prognostic variables, and provided that the spread was known, the number size distribution of the aerosols present could be represented by a log–normal function (Jacobson, 2005). The effects of aerosol size can then be explored by changing the spread of the log–normal function. A potential problem arises in that after activation of droplets, the aerosol size distribution will adjust back to a log–normal function, which may not be realistic. The issue of whether or not it is sufficient to reduce number and mass of aerosol and recalculate the parameters based on a log-normal relationship will be investigated. As well as internal mixtures, it will be possible to account for external mixtures in this scheme, by simply adding more prognostic variables to reflect different aerosol species.

3.2. The bin scheme The bin scheme used to validate the performance of the bulk schemes is based on the aerosol–cloud precipitation interaction model (ACPIM), which is in the final stages of development at the University of Manchester. It is a state of the art microphysical process model that accounts for multi-component aerosol thermodynamic properties in different mixing states, with droplet activation from Kohler theory. The microphysics is initialized assuming a log–normal aerosol size distribution, Copyright  2009 Royal Meteorological Society

thus requiring inputs for the geometric mean diameter, the spread and the total aerosol number. ACPIM is particularly suited to studying the effects of aerosol composition on cloud because it uses results from the ADDEM model (aerosol diameter-dependent equilibrium model), described in detail in Topping et al. (2005a, 2005b), to obtain the equilibrium behaviour of multi-component aerosols. ADDEM allows for a treatment of the effect of curvature (the Kelvin effect) in determining the hygroscopic properties of mixed inorganic/organic aerosols, and uses the general form of the Kohler equation housed within an iterative loop with a guaranteed convergence scheme to solve for the new equilibrium state. This allows accurate equilibrium vapour pressures to be computed for a wide range of internal and external mixtures, which can then be fed as inputs into ACPIM to study the effects of composition on cloud properties. Although the focus of this paper is on the effects of CCN, the ACPIM also allows the insoluble fraction of aerosol to be specified, thus making it a suitable scheme to study heterogeneous freezing processes (Connolly et al., 2009). This opens up the possibility of a future study to quantify the importance of ice nuclei (IN) effects on mixed phase cloud using the FM.

3.3. The 1D driver model This study employs the kinematic driver model (KiD; Shipway, 2009) to force the microphysics and initiate cloud formation. The KiD model operates in a 1D column with a fixed number of vertical levels and provides an ideal test bed for intercomparison of different microphysics schemes, based on a common advection component. The KiD model comes complete with a suite of test cases, the most simple of which consists of a single warm updraft, sinusoidal in time and constant in height, to advect vapour and hydrometeors in the vertical. Instantaneous cloud-related diagnostics, including hydrometeor mass mixing ratios, number concentration and surface precipitation, can be output at selected time intervals for subsequent analysis. The KiD model does not account for the effects of entrainment into the cloudy updraft; its main purpose is to provide a flexible framework that facilitates the testing and comparison of different microphysical treatments given a prescribed vertical velocity. While the importance of accurate atmospheric dynamics is recognized, it is first necessary to gain a fundamental understanding of the pure microphysical behaviour, and this is most easily achieved under relatively simple dynamical forcing. Subsequent work will then build on this understanding by introducing the effects of entrainment, in full 3D case studies of warm clouds with a cloud resolving model. Prior to inclusion within the KiD model, the microphysics schemes will first be developed and tested within a closed lagrangian parcel model. Such a framework does not allow for the effects of sedimentation to be studied, hence why the KiD model must be used Atmos. Sci. Let. 10: 207–214 (2009) DOI: 10.1002/asl

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to fulfil the needs of this study. However, a parcel model provides a suitable platform for comparing the different treatments of droplet activation, and how this determines the resulting number of droplets activated both at cloud base and within the cloud itself. The ability of the bulk schemes to capture accurate droplet concentrations will be a key factor in how they perform in a 1D column model; on this subject the parcel model can provide very useful insight. Some preliminary results are now discussed.

4. Initial parcel model results The parcel model has been used to compare droplet number as predicted by the bulk scheme with that from the bin scheme. In the bulk microphysics scheme, Equation (13) is used for droplet activation. However, parcel model tests show that the resolved treatment of supersaturation requires a timestep of 0.1 s or better for stability. To overcome this problem, activation of droplets can be predicted from the Twomey (1959) approximation, which is based solely on updraft speed and thus is not restricted by the choice of model timestep. Table I demonstrates the validity of the Twomey approximation for predicting cloud base droplet number concentrations. The predicted droplet number is compared under a range of updraft speeds and for activation parameters corresponding to both maritime and continental conditions. In all cases, the parcel model ascent was initialised with a temperature of 300 K, a relative humidity of 95% and a pressure of 1000 mb. The values predicted by the Twomey approximation lie within 10–20% of those predicted from the resolved supersaturation approach. The agreement improves at higher updraft speeds, and at lower values of c. However, while the Twomey approximation is sufficient to capture cloud base droplet number, once in cloud, the processes of condensation and subsequent collision/coalescence become important. This is demonstrated using ACPIM in parcel model mode, as shown in Figure 2. In this run, aerosols are assumed to Table I. Cloud base droplet number concentration (Nc), as a function of updraft speed for (top) maritime conditions (c = 120/cc and k = 0.4) and (bottom) continental conditions (c = 1000/cc and k = 0.5).

Cloud base Nc (Twomey approximation) Cloud base Nc (resolved supersaturation)

Cloud base Nc (Twomey approximation) Cloud base Nc (resolved supersaturation)

10 m/s

3 m/s

1 m/s

0.1 m/s

120/cc

120/cc

96/cc

54/cc

120/cc

115/cc

85/cc

47/cc

10 m/s

3 m/s

1 m/s

0.1 m/s

1000/cc

719/cc

517/cc

259/cc

900/cc

623/cc

429/cc

204/cc

Copyright  2009 Royal Meteorological Society

Figure 2. A parcel expansion from the ACPIM model, showing aerosol number concentration versus temperature.

consist solely of ammonium sulphate, with a geometric mean diameter of 60.e−9m, a spread of 0.1 and a total aerosol number of 100.e+6. A fixed updraft speed of 1 m/s was prescribed, starting from an initial temperature of 300 K, a relative humidity of 95% and a pressure of 1000 mb. It can be seen how aerosol number reduces by an amount between 20–25% due to activation of droplets at cloud base, above which no further activation occurs because the supersaturation in the parcel reduces as the existing droplets grow by condensation. A similar parcel ascent was replicated with bulk microphysics, for the same initial thermodynamic conditions, and with the activation parameters c = 100 and k = 0.4. Figure 3 shows how the Twomey approximation applied to in-cloud activation of droplets (blue line) would lead to a considerable overestimate of droplet number. When the supersaturation is resolved explicitly in the bulk scheme (Figure 3; red line), droplet number above cloud base stays roughly constant initially and then rapidly reduces as the droplets grow big enough for self-collection and accretion processes to become important. However, autoconversion of droplets to rain acts to reduce droplet mass and number, which in turn reduces the sink of water vapour (Figure 4a), allowing the supersaturation within the parcel to slowly increase again (Figure 4b). Because the activity spectrum relation (Equation 13) does not account for the depletion of CCN, anomalous new droplets are activated within the supersaturated environment. Figure 3 illustrates that the resolved supersaturation approach is clearly more desirable than the Twomey approach for droplet activation because it accounts for condensation/deposition as a sink of water vapour and thus allows for a more realistic treatment of droplet activation when existing condensate is present (i.e. within cloud). However, it requires a very short timestep for stablility, rendering it impractical for Atmos. Sci. Let. 10: 207–214 (2009) DOI: 10.1002/asl


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where δ = qv − qsat , T is temperature, τc and τr are the phase relaxation timescales associated with cloud droplets and rain respectively, (∂T /∂t)RAD is the radiative heating rate (which is zero in the parcel model), g is the gravitational acceleration, w is the vertical velocity and cp is the specific heat of air at constant pressure. Solving Equation (15) for dδ/dt = 0 yields a diagnostic relationship for the maximum supersaturation available for droplet activation within the current timestep, which is given by: dqsat δ=− dT

Figure 3. Parcel expansion with bulk microphysics, showing droplet number concentration versus temperature. The red line corresponds to a resolved treatment of supersaturation for droplet activation; the blue line represents the predicted droplet number when the Twomey approximation is used (i.e. based solely on updraft speed).

use in operational models. A compromise can be struck by restricting the use of the Twomey approach to cloud base activation only. When in cloud, it is possible to approximate the result achieved with the resolved supersaturation approach without the restriction of very small timesteps; such an approach involves consideration of the prognostic equation for supersaturation, δ (Morrison et al., 2005), which in the absence of the ice phase, is given by: 1 1 dδ =− + δ dt τc τr dqsat gw ∂T − − dT ∂t RAD cp

(15)

∂T ∂t

gw − cp RAD

1 1 + τc τr

−1

(16)

Equation (16) can be used for in-cloud activation of new droplets, by expressing δ as a percentage supersaturation ratio and inserting into Equation (13). Then if the potential number of newly activated droplets predicted by Equation (13) is less than the number that already exists, no additional droplets are activated within the timestep. To prevent unrealistically large droplet numbers when the phase relaxation timescale is long, the potential number of newly activated droplets is not allowed to exceed that obtained by the Twomey approach. The result is shown in Figure 5, which compares predicted droplet number with resolved supersaturation in red with the diagnosed equilibrium supersaturation for in-cloud activation given by Equation (16) in blue. Qualitatively the agreement is much better than in Figure 3, with the added advantage that the equilibrium supersaturation method is not limited to small timesteps.

5. Summary The FM of Teller and Levin (2008) is to be employed within the 1D kinematic driver model with state-ofthe-art bin microphysics and aerosol. The use of the 1D model is intended to aid in the identification of the key processes at work, providing isolation from non-linear interactions and systematic bias that may

Figure 4. Plots from the bulk parcel model with resolved supersaturation. (a) (left) The first moment of the liquid droplet size distribution [= Nc(αc + 1)/λc , where Nc is the droplet number concentration], plotted as a function of temperature of the rising parcel. The first moment is proportional to the sink of water vapour. (b) (right): Saturation ratio versus temperature. Copyright  2009 Royal Meteorological Society


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Acknowledgements The author would like to thank Dr. Paul Connolly, University of Manchester, for supplying the ACPIM model, and Dr. Ben Shipway, UK Met Office, for supplying the KiD model.

References

Figure 5. Parcel model output comparing predicted droplet number with resolved treatment of supersaturation for droplet activation (red) with the diagnosed equilibrium supersaturation method for activation (blue).

arise from other aspects of a model. The method will seek to separate the significance of aerosol effects on clouds from the effects of meteorology, and thus dictate the minimum level of complexity that needs to be incorporated into a bulk microphysics scheme to successfully simulate liquid clouds. Where possible, the potential for tuning aspects of a single moment liquid scheme to a bin scheme will be explored, as a cost-effective alternative to the more expensive dual moment options. Initial results from a parcel model provide useful insight into the effects of changing the treatment of droplet activation in the bulk scheme and show a potential weakness in schemes that do not include an explicit representation of aerosol. To investigate the impacts on surface precipitation, the microphysics schemes must be engineered into the KiD model where sedimentation between vertical levels is permitted. Thus, future work will focus on applying the FM within the KiD framework for a range of updraft speeds and temperatures, to help quantify the benefits of increasing microphysical complexity based on the metrics of surface precipitation and effective radius. Particular attention will be given to establishing the benefits of a prognostic aerosol scheme in bulk schemes. The importance of entrainment will be addressed by performing 3D case studies of warm clouds, to see if the conclusions from the FM/1D experiments are upheld given more realistic dynamical forcing.

Copyright  2009 Royal Meteorological Society

Albrecht BA. 1989. Aerosols, cloud microphysics, and fractional cloudiness. Science 245(4923): 1227–1230. Cantrell W, Heymsfield A. 2005. Production of ice in tropospheric clouds – A review. Bulletin of the American Meteorological Society 86(6): 795–807. Coakley JA, Walsh CD. 2002. Limits to the aerosol indirect radiative effect derived from observations of ship tracks. Journal of the Atmospheric Sciences 59: 668–680. Connolly PJ, Möhler O, Field PR, Saathoff H, Burgess R, Choularton T, Gallagher M. 2009. Studies of heterogeneous freezing by three different desert dust samples. Atmospheric Chemistry and Physics 9: 2805–2824. Jacobson MK. 2005. Fundamentals of Atmospheric Modelling, 2nd edn. Cambridge University Press: Cambridge. Lohmann U, Feichter J. 2005. Global indirect aerosol effects: a review. Atmospheric Chemistry and Physics 5: 715–737. McFiggans G, Artaxo P, Baltensperger U, Coe H, Facchini MC, Feingold G, Fuzzi S, Gysel M, Laaksonen A, Lohmann U, Mentel TF, Murphy DM, O’Dowd CD, Snider JR, Weingartner E. 2006. The effect of physical and chemical aerosol properties on warm cloud droplet activation. Atmospheric Chemistry and Physics 6: 2593–2649. Montgomery DC. 2005. Design and Analysis of Experiments. John Wiley: New York. Morrison H, Curry JA, Khvorostyanov VI. 2005. A new doublemoment microphysics parameterization for application in cloud and climate models. Part I: description. Journal of the Atmospheric Sciences 62(6): 1665–1677. Pruppacher HR, Klett JD. 1997. Microphysics of Clouds and Precipitation. Kluwer Academic Publishers: Norwell, USA. Rogers RR, Yau MK. 1989. A Short Course in Cloud Physics, 3rd edn. Butterworth and Heinemann: Oxford. Shipway BJ. 2009. Kinematic driver for microphysics intercomparison, UK Met Office. http://appconv.metoffice.com/microphysics/index. shtml. Teller A, Levin Z. 2008. Factorial method as a tool for estimating the relative contribution to precipitation of cloud microphysical processes and environmental conditions: method and application. Journal of Geophysical Research-Atmospheres 113(D2) 13 pp. Thompson G, Rasmussen RM, Manning K. 2004. Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part I: description and sensitivity analysis. Monthly Weather Review 132(2): 519–542. Topping DO, McFiggans GB, Coe H. 2005a. A curved multicomponent aerosol hygroscopicity model framework: part 1 – inorganic compounds. Atmospheric Chemistry and Physics 5: 1205–1222. Topping DO, McFiggans GB, Coe H. 2005b. A curved multicomponent aerosol hygroscopicity model framework: part 2 – including organic compounds. Atmospheric Chemistry and Physics 5: 1223–1242. Twomey SA. 1959. The nuclei of natural cloud formation. Part II: the supersaturation in natural clouds and the variation of cloud droplet concentrations. Pure and Applied Geophysics 43: 243–249.


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APPENDIX

B REPRINT: EVALUATING THE EFFECTS OF MICROPHYSICAL COMPLEXITY IN IDEALISED SIMULATIONS OF TRADE WIND CUMULUS USING THE FACTORIAL METHOD

Full reference as follows: Dearden, C., Connolly, P. J., Choularton, T. W. and Field, P. R.: Evaluating the effects of microphysical complexity in idealised simulations of trade wind cumulus using the Factorial Method., Atmos. Chem. Phys., 11, 2729-2746, 2011.

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Atmos. Chem. Phys., 11, 2729–2746, 2011 www.atmos-chem-phys.net/11/2729/2011/ doi:10.5194/acp-11-2729-2011 © Author(s) 2011. CC Attribution 3.0 License.

Atmospheric Chemistry and Physics

Evaluating the effects of microphysical complexity in idealised simulations of trade wind cumulus using the Factorial Method C. Dearden1 , P. J. Connolly1 , T. W. Choularton1 , and P. R. Field2 1 University 2 Met

of Manchester, School of Earth, Atmospheric and Environmental Sciences, UK Office, Atmospheric Processes and Parametrization, Exeter, UK

Received: 28 September 2010 – Published in Atmos. Chem. Phys. Discuss.: 11 October 2010 Revised: 16 March 2011 – Accepted: 17 March 2011 – Published: 23 March 2011

Abstract. The effect of microphysical and environmental factors on the development of precipitation in warm idealised cloud is explored using a kinematic modelling framework. A simple one-dimensional column model is used to drive a suite of microphysics schemes including a flexible multimoment bulk scheme (including both single and dual moment cloud liquid water) and a state-of-the-art bin-resolved scheme with explicit treatments of liquid and aerosol. The Factorial Method is employed to quantify and compare the sensitivities of each scheme under a set of controlled conditions, in order to isolate the effect of additional microphysical complexity in terms of the impact on surface precipitation. At relatively low updraught speeds, the sensitivity of the bulk schemes was found to depend on the assumptions made with regards the treatment of droplet activation. It was possible to achieve a much closer agreement between the single and dual moment bulk schemes by tuning the specified droplet number concentration in the single moment scheme, suggesting that a diagnostic representation of droplet number may be an acceptable alternative to the more expensive prognostic option. However the effect of changes in CCN concentration were found to produce a relatively stronger effect on precipitation in the bulk schemes compared to the bin scheme; this is believed to be a consequence of differences in the treatment of drop growth by collision and coalescence. Collectively, these results demonstrate the usefulness of the Factorial Method as a model development tool for quantitatively comparing and contrasting the behaviour of microphysics schemes of differing levels of complexity within a specified parameter space.

Correspondence to: C. Dearden ([email protected])

1

Introduction

Shallow convective clouds play an important role in the global circulation and the hydrological cycle of the Earth system. Sub-tropical marine shallow cumuli, capped by the trade wind inversion, transport moisture vertically within the cloud layer, where it is subsequently detrained and transported to the tropics by the trade winds to fuel deep convection within the Inter Tropical Convergence Zone (ITCZ). The development of precipitation in trade wind cumuli is believed to be sensitive to cloud condensation nuclei (CCN) concentrations by virtue of aerosol-cloud interactions, and such interactions could potentially have important climatological consequences (Wang and McFarquhar, 2008). Yet the overall magnitude of this sensitivity is poorly understood. Twomey (1977) showed that an increase in CCN concentration under a fixed liquid water content can lead to higher cloud droplet number concentrations but a reduction in overall droplet size. Albrecht (1989) later suggested that the reduction in size of cloud droplets as a result of the Twomey effect could potentially act to reduce the precipitation efficiency of marine boundary layer clouds. However the extent to which aerosols are able to modify cloud macroscopic properties in a buffered system such as the Earth’s atmosphere is likely to be more subtle than a consideration of microphysical processes alone would suggest (Stevens and Feingold, 2009). In principle, numerical models are useful tools to help establish and understand the complex nature of the interaction between aerosols, clouds and precipitation in the context of the trade wind regime. However, the macrostructure of shallow maritime convective cloud is poorly represented in the current generation of General Circulation Models (GCMs), and consequently such large-scale models are not a suitable basis upon which to explore such links. This has been shown most recently in a study by Medeiros and Stevens (2010), who used a conditional sampling technique to demonstrate that GCMs struggle to produce a satisfactory macrophysical

Published by Copernicus Publications on behalf of the European Geosciences Union.

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representation of the shallow cumulus cloud regime when validated against reanalysis data. The poor representation of shallow convection in GCMs stems from their reliance upon convective parameterizations, which is also believed to be responsible for the uncertainty surrounding global estimates of the climate sensitivity (Bony and Dufresne, 2005). Instead it is more appropriate to use Large Eddy Simulations (LES) at convection-permitting resolutions of 100 m or less to investigate the extent to which cloud microphysical processes influence the cloud macrostructure. Field campaigns such as the Rain In shallow Cumulus over the Ocean project (RICO, Rauber et al., 2007) and the INDian Ocean EXperiment (INDOEX, Heymsfield and McFarquhar, 2001) play an important role in constraining and validating LES models, (e.g., Abel and Shipway, 2007; Wang and McFarquhar, 2008). In particular, the LES intercomparison study of van Zanten et al. (2011) based on the RICO field study suggests that differences in the representation of microphysical processes is the main reason for the large variation in the timing and amount of precipitation produced between models. LES models based on bulk microphysical parameterizations typically operate by assuming a functional form of the hydrometeor size distribution and solve prognostic equations representing the moments of the distribution, namely the mass mixing ratio for single-moment (1-m) schemes and additionally number concentration for dual-moment (2-m). Bulk schemes are cheaper to run than explicit bin schemes, but must make simplifying assumptions in order to ensure computational efficiency. As the reliance on bulk microphysics schemes is likely to continue in the future, it is becoming increasingly necessary to develop objective methods of validating their performance. This has typically been achieved via comparison against explicit bin-resolved microphysics within simple kinematic driver models. For example the study of Morrison and Grabowski (2007) used a 2-D kinematic framework to assess the performance of 2-m bulk microphysics in terms of simulating warm clouds using an explicit bin scheme as a benchmark, where both schemes assume a fixed background aerosol size distribution. They considered idealised representations of a shallow cumulus regime and a stratocumulus regime. However such regimes can themselves cover a broad range of environmental conditions, and it is important to assess the sensitivity of the microphysics to variations in the meteorological conditions as well. The observational study of Nuijens et al. (2009) assessed the sensitivity of precipitation from shallow cumulus during RICO to variations in the meteorological environment, and concluded that subtle variations in the meteorological conditions can have a strong influence on precipitation, even speculating that this may be a stronger control on precipitation than aerosol effects alone. It is fair to say that in general, the need to account for changes in meteorology when using LES models to evaluate microphysical sensitivities has been somewhat overlooked. Recent exceptions include the work of Wang and McFarquhar (2008) and Atmos. Chem. Phys., 11, 2729–2746, 2011

Teller and Levin (2008). In the case of the latter, the Factorial Method (FM) was used to quantify the sensitivity of precipitation in simulations of mixed-phase convective cloud when both meteorological and microphysical factors occur synergistically. The technique of isolating the effects of individual factors in the context of atmospheric modelling was pioneered by Stein and Alpert (1993). Dearden (2009) proposed to expand the use of the FM across a hierarchical suite of microphysics schemes within a one dimensional kinematic framework, consisting of a bulk scheme with the choice of both 1-m and 2-m liquid water, and an explicit bin scheme with prognostic treatment of aerosol, capable of accounting for the effects of aerosol composition. Such a method allows the macroscopic forcing conditions to be easily constrained, and is adopted here in relation to quantifying the impact of microphysical complexity on precipitation development in the context of idealised shallow cumulus cloud. The sensitivity of the bulk schemes can be quantified and compared to that of the bin scheme such that it may be possible to isolate those meteorological regimes where the additional microphysical complexity is warranted. It is important to note that the nature of the 1-D kinematic framework is such that it does not permit feedbacks between microphysics and dynamics and thus does not provide a complete representation of cloud dynamics. Whilst the importance of feedback effects are recognised, they also make it difficult to isolate differences that arise purely from the treatment of microphysics and potentially other factors (such as the numerical treatment of advection), and so an idealised study in the absence of feedbacks is beneficial in terms of identifying and understanding the potential limitations of simpler bulk parameterizations. The simplicity of the driver model also allows for a greater number of sensitivity tests to be performed compared to 3-D simulations due to the reduced computational burden. Finally simple 1-D frameworks have very recently been used to develop our understanding of rain formation in shallow cumulus clouds (Seifert and Stevens, 2010), and also to develop improved parameterizations of rain evaporation for use in dual-moment bulk schemes (Seifert, 2008), which demonstrates their usefulness as a tool for advancing our understanding in this area. This paper is organised as follows. A description of the microphysics and the idealised driver model are presented in Sect. 2. Section 3 considers the details of the experimental design based on the FM. The results from each microphysics scheme are analysed and compared in Sect. 4, and the potential implications of these findings are addressed in Sect. 5, including a discussion of how feedbacks between microphysics and dynamics may potentially modify the sensitivities shown.

www.atmos-chem-phys.net/11/2729/2011/

C. Dearden et al.: Evaluating the effects of microphysical complexity using the Factorial Method 2 Model configuration The suite of microphysical schemes considered for testing are embedded within a 1-D column framework, within which the initial temperature and humidity profiles are prescribed, along with the vertical velocity field responsible for producing the supersaturation necessary for cloud formation. The hierarchy of microphysical complexity ranges from a fully explicit treatment of liquid water and aerosol to a bulk parameterization of warm rain processes with the option of both 2-m and 1-m cloud liquid water. A detailed description of each of the schemes considered is now given, starting with the bin microphysics. 2.1

Bin microphysics

The bin scheme used in this study is the Aerosol-CloudPrecipitation-Interaction-Model (ACPIM), developed at the University of Manchester. ACPIM is a state-of-the-art process model that has been created primarily to study the effects of aerosol on mixed-phase cloud as part of the core modelling suite for the Aerosol Properties Processes And InfluenceS on the Earth’s climate (APPRAISE) project. For the purpose of this study its use is restricted to liquid-only processes. The ACPIM model supports a prognostic treatment of aerosol, allowing the effects of the aerosol size distribution and also composition to be explored; this feature was used in the simulations performed for this study. Activation of droplets in ACPIM is based on Köhler theory. 147 mass bins are used to resolve the liquid drop size distribution, and 154 are used for aerosol. The ambient supersaturation is resolved using a variable sub-step to ensure it is captured to a sufficient level of accuracy, regardless of the choice of the main model timestep. Each aerosol bin solves prognostic equations for the mass and number of aerosols. Condensation occurs continuously via the droplet growth equation (Pruppacher and Klett, 1997), where the equilibrium vapour pressure is supplied by Köhler theory using data from a thermodynamic model (ADDEM, Topping et al., 2005). The growth equation is solved explicitly using the Variablecoefficient Ordinary Differential Equation solver (VODE) available from the netlib repository (www.netlib.org). Initial growth of the cloud droplets is dominated by the diffusional growth equation, and subsequent growth to rain drop size through the collision-coalescence process is handled by explicitly solving the 2-D stochastic collection equation (Bott, 2000), with the collision efficiency based on the look up table by Hall (1980). In the version of ACPIM used for this study, the efficiency of coalescence is taken to be unity, such that the overall collection efficiency is equal to the Hall collision efficiency. In terms of gas kinetic effects, the condensation coefficient in all cases is taken to be unity, based on Laaksonen et al. (2005). For this study, a single log-normal aerosol size distribution is used with a geometric standard deviation of 1.28, and a geometric mean diameter of 0.06 microns. These values www.atmos-chem-phys.net/11/2729/2011/

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are based on the bimodal distribution defined in the RICO model intercomparison study (van Zanten et al., 2011); the giant mode was found to have minimal impact on precipitation for the range of CCN concentrations considered. In terms of the aerosol composition, pure sea-salt was assumed in all cases. Tests with ammonium sulphate were also performed, although the effect on precipitation was found to be small, with only a slight increase in rain at lower updraught speeds. 2.2

Bulk microphysics

The bulk scheme is based on a liquid-only version of the scheme described in Morrison et al. (2005), such that the two classes of hydrometeor considered are cloud liquid water and rain. The scheme is a flexible multi-moment scheme, allowing the choice of either a 1-m or 2-m treatment for liquid droplets. The scheme also contains different options for the treatment of droplet activation in the 2-m liquid case. Saturation adjustment is used in the bulk schemes, such that any water vapour present above 100% relative humidity is assumed to instantaneously condense onto existing cloud droplets. Such an assumption is appropriate because the mass of water vapour above saturation is typically much smaller than the mass of cloud water. The autoconversion and accretion schemes used in all cases are those of Khairoutdinov and Kogan (2000), henceforth referred to as the KK scheme. A radius of 25 microns is used to separate the cloud liquid water and rain categories. The microphysical process rates in the KK scheme are formulated via multiple nonlinear regression of simulated spectra from LES studies of marine boundary layer clouds, and so are considered to be an appropriate choice for this study. Self-collection of rain drops is also accounted for, and is based on the parameterization specified in Seifert and Beheng (2001). Self-collection of rain drops is potentially an important process; indeed the LES study of shallow convection by Stevens and Seifert (2008) suggests that bulk schemes which do not include a parameterization of self-collection are more likely to exhibit higher evaporation rates due to having rain drop spectra that contain higher concentrations of smaller rain drops. In all cases, a 2-m scheme is used for rain. Dearden (2009) had originally proposed to include a 1-m treatment for rain as well, but this was not included in the final experimental design because it was not possible to identify a single value of the rain intercept parameter that was appropriate for different values of droplet number concentration. The benefits of 2-m rain over 1-m rain have been well documented recently, e.g. in the studies by Morrison et al. (2009), although Shipway and Hill (2011) and references therein suggest that 2-m rain schemes with an invariant shape parameter can suffer from the problem of excessive size-sorting. The particle size distribution for both rain and cloud liquid water is defined by a gamma distribution (Straka, 2009) of the form

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n(D) = N0 D µ e−λD

(1)

where n(D) is the number concentration for a given particle diameter size D; the integral of Eq. (1) with respect to D gives the total number concentration, NT . N0 is the intercept parameter, λ is the slope parameter and µ is the shape parameter. N0 is determined as a function of the total number concentration N0 =

NT λµ+1 0(µ + 1)

(2)

For rain, µ is set to zero, which reduces Eq. (2) to an exponential distribution (Marshall and Palmer, 1948), such that N0 = NT λ. Terminal fall speeds for rain are given by the following Vr (D) = (ρ0 /ρ)gr ar D br efr D ,

(3)

where ρ0 is the density of air at sea level, and the constants ar , br , fr and gr are set to 841, 0.8, 0.0 and 0.54 respectively, following Liu and Orville (1969). The different combinations of the bulk scheme are now presented, starting with the simplest level of complexity. 2.2.1

1-m liquid, 2-m rain

In the simplest treatment considered here, only one prognostic variable is used to represent cloud liquid water (the mass mixing ratio), and the droplet number concentration is taken as a constant in the calculation of the intercept parameter in Eq. (2). The experimental set up of the 1-m scheme is such that the assumed droplet number concentration is taken to be equal to the CCN concentration, with the implicit assumption that all available CCN activate to form cloud droplets. 2.2.2

2-m liquid (Twomey activation), 2-m rain

Moving from 1-m to 2-m liquid grants the ability to predict droplet number, thus requiring an explicit term representing activation of cloud droplets. The consequence of this is that in the 2-m scheme, not all available CCN are necessarily activated for a given updraught speed, which may lead to lower droplet number concentrations when compared to the 1-m scheme. The first treatment of droplet activation considered is based on the parameterization of Twomey (1959), which in Rogers and Yau (1989) is approximated as: NCCN ≈ 0.88c2/(k+2) [7.10−2 w 3/2 ]k/(k+2)

(4)

where w is the grid-scale vertical velocity in cms−1 and the number concentration of active CCN is NCCN , in cm−3 . The variables c and k are activation parameters where c represents the number concentration of CCN active at 1% supersaturation and k represents the ease with which droplets form. In this study, a value of 0.4 is used for k based on measurements of tropical maritime airmasses (Pruppacher and Klett, 1997).

Atmos. Chem. Phys., 11, 2729–2746, 2011

2.2.3

2-m liquid (Abdul-Razzak activation), 2-m rain

The second option for droplet activation is based on the parameterization of Abdul-Razzak et al. (1998), henceforth identified as A-R, which assumes a single log-normal aerosol size distribution for a given chemical composition, requiring knowledge of the geometric mean radius of aerosol particles and the standard deviation. This information is then used to parameterise the maximum supersaturation in the rising air parcel given the vertical velocity, which in turn determines the fraction of aerosols activated to form cloud droplets. The aerosol log-normal parameters used are the same as those employed to initialise the bin model, as is the assumed chemical composition. By repeating the 2-m liquid simulations using the A-R scheme for droplet activation, it will be possible to quantify the benefits of explicitly specifying the aerosol log-normal parameters, albeit assuming a fixed form. Dearden (2009) had originally proposed the option of a prognostic treatment of aerosol for the bulk scheme; however this was not considered due to time constraints. The possibility of a 2-m aerosol scheme coupled to the 2-m bulk microphysics will be revisited in future work on the subject. The only difference between the 2-m schemes is in terms of the droplet activation scheme used. For cloud base activation, droplet number in the A-R scheme is determined as a function of both the updraught speed and the aerosol properties. This is different from the Twomey approach, which determines cloud base droplet number based on the updraught speed and the value of the chosen c and k parameters. In both the Twomey and A-R cases, in-cloud activation is also permitted, and is based on a diagnostic calculation of the in-cloud equilibrium supersaturation within the current timestep. This diagnostic relation is a feature of the Morrison scheme, and should a supersaturation be diagnosed, incloud activation is allowed to occur via the specified activation scheme. 2.3

Driver model configuration

The bulk microphysics are driven using the 1-D Kinematic Driver Model, KiD (Shipway and Hill, 2011) whilst the ACPIM microphysics is currently embedded within its own 1-D column model. To obtain consistency with ACPIM, some changes have been made to the standard KiD model to ensure consistency between driver models, thus ensuring that both bin and bulk microphysics schemes can be compared rigorously. The details of the necessary changes in the KiD model are now presented. 2.3.1

Advection

The advection scheme common to both driver models is a 4th order, positive definite, monotonic scheme (Bott, 1989, 1992). The Bott scheme is used to advect vapour and liquid water. The default advection scheme in the KiD model is the www.atmos-chem-phys.net/11/2729/2011/


2.3.2

Initialisation of thermodynamics

(5)

Equation (5) is solved based on Press et al. (2007) in both KiD and ACPIM.

3 Experimental design 3.1

Initial conditions and idealised forcing

The forcing for the idealised warm shallow cumulus case is based on the “warm1” configuration as defined in the KiD documentation which can be downloaded from http: //appconv.metoffice.com/microphysics/doc.html. It consists of a single updraught, constant in height and sinusoidal in time: w1 sin(π t/t2 ) if t < t2 , w(z,t) = (6) 0.0 if t > t2 The timescale t2 is dependent upon the peak updraught speed, w1 , such that t2 = 1200/w1 . For a peak updraught speed of 0.5 ms−1 , this would result in the vertical velocity field reducing to zero after 2400 s. Thus values of w1 greater www.atmos-chem-phys.net/11/2729/2011/

w =4m/s 1

w =2m/s

4.5

1

w =1m/s 1

4

w1=0.5m/s

3.5 3 2.5 2 1.5 1 0.5 0 0

500

1000

1500 2000 Time (seconds)

2500

3000

3500

Fig. 1. Vertical velocity fields as a function of time, as applied to Fig. 1. Vertical the velocity fields asequally a function of time, as applied 1-D column at every vertical level.to the 1-D column equally at every v level.

Both models accept inputs for potential temperature and vapour mixing ratio at specified height levels; this defines the initial thermodynamic profiles. These points are then linearly interpolated onto the model vertical grid at every level. The model then converts from potential temperature to absolute temperature to pass to the microphysics, for which it needs the pressure field. Pressure is obtained by solving the following first-order differential based on the hydrostatic equation and the ideal gas law: dp −pg = dz RT

5

Magnitude of vertical velocity (m/s)

Total Variance Diminishing (TVD) scheme of Leonard et al. (1993) known as ULTIMATE, but for the purpose of this study the Bott scheme is used for consistency with ACPIM. There is no advection of potential temperature in the column; indeed the potential temperature and pressure fields are held fixed such that the microphysics is not permitted to influence the evolution of the dynamics. This was deemed necessary such that the pure microphysical behaviour of each scheme could be compared fairly, in the absence of thermodynamic feedbacks. A slight caveat is in the handling of sedimentation. The ACPIM driver model is configured to combine sedimentation with vertical advection due to air motion in a single calculation, which is handled using the 4th order Bott scheme. In KiD, sedimentation of cloud liquid water and rain is handled within the Morrison microphysics scheme itself using a timesplit 1st order upwind method, where a size threshold of 50 microns diameter is used to separate cloud liquid water from rain. The potential implications of these differences are addressed in Sect. 4.3.

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than 0.5 ms−1 would reduce the timescale over which the updraught is applied. The evolution of the updraught velocity with time for different values of w1 is plotted in Fig. 1, as 36 applied equally at every vertical level. The warm1 case is based on the composite profile used to initialise models for the GCSS RICO intercomparison. However, as noted in Shipway and Hill (2011), there is a slight issue with simulations based on the warm1 profile in that the resulting profile of liquid water content decreases with height after reaching a maximum above cloud base, which is not necessarily realistic for a warm shallow convective cloud. This is a consequence of the fact that the whole column is lifted in response to the vertical velocity field, where at a given timestep the applied vertical velocity is the same at every gridpoint. The relative humidity reaches a peak at around 750 m; at grid points above this height, the relative humidity begins to decrease such that the amount of water vapour available for condensation is reduced, leading to a slight reduction in liquid water content with height. Despite this, and given the highly idealised nature of the 1-D framework to begin with, the warm1 profile still acts as a suitable basis upon which to conduct a comparison of different microphysics schemes. The reader is made aware that in the 1-D intercomparison of Shipway and Hill (2011), the lowest levels of the warm1 profile were made slightly drier, to produce a liquid water content profile that increased with height and an overall reduction in liquid water path. This produced a reduction in surface precipiation totals relative to the original warm1 profile, given the same peak updraught velocity. Changes in temperature are considered such that the warm1 profile is shifted to cooler temperatures resulting in a constant cooling with height whilst keeping the relative humidity fixed. The result is such that changes in Atmos. Chem. Phys., 11, 2729–2746, 2011

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C. Dearden et al.: Evaluating the effects of microphysical complexity using the Factorial Method RICO

Table 1. Design matrix for the general 23 factorial design.

3000 T T

d

2500

Height (metres)

2000

1500

1000

Run

A

B

C

Labels

1 2 3 4 5 6 7 8

− + − + − + − +

− − + + − − + +

− − − − + + + +

(one) a b ab c ac bc abc

500

3.2.1 0 −5

0

5

10 15 20 Temperature (Degrees C)

25

General example: 23 design

30

Consider the following general example based on 3 factors, labelled A, B and C respectively, each at two levels, yieldFig. 2. Temperature (solid) and dew-point temperature (dashed) ing a 23 design. Thus eight treatment combinations (experiFig. 2. Temperature dew-point (dashed) profiles in ◦ Cand taken from the RICO profiles (solid) in ◦ C and taken from thetemperature RICO model intercomparison, ments) would be necessary to fulfill the requirements of the model intercomparison, and used initialiseThe the models. The additional profiles,and “RICO-2” and “RICOused to initialise thetomodels. additional profiles, “RICO-2” ◦ ◦ study.under To denote low and high values, the geometric notation 5”, are obtained by cooling the RICO profile uniformly in height by 2 C and 5 C respectively a “RICO-5”, are obtained by cooling the RICO profile uniformly in system is used such that “−” indicates low and “+” indicates fixed relative humidity. ◦ ◦ height by 2 C and 5 C respectively under a fixed relative humidity. high, and the eight runs required in the 23 design are given in Table 1. Table 1 also writes the treatment combinations based on the labelling system of lowercase letters, which in 37cloud height or depth. The standard order is written as (one), a, b, ab, c, ac, bc and abc. thermodynamics do not affect the In this system, the presence of a lowercase letter represents temperature profile used in this study is plotted in Fig. 2. In the high value of that factor, and the absence of a letter deall cases, the simulations are left to run for long enough until notes the low value. The label (one) is reserved for the case they have finished precipitating (typically two hours) and diwhen all factors are at their low value. Using the lowercase agnostic output is available at the end of each timestep (every letter labels, it is possible to write down expressions for the 5 s). The vertical grid spacing in both models is set to 30 m, main effects; that is, the average effect of each factor due to with 100 levels giving a domain height of 3 km. the change in value from low to high. Similar expressions 3.2 Experimental design for the Factorial Method for the interactions between main effects can also be derived. For full details on the calculation of the main effects and inThe experimental design based around the FM is now preteraction terms based on a general 23 design, the reader is sented. It should be noted that changes in meteorological facreferred to Dearden (2009) and references therein. Once the tors, namely the temperature profile and updraught velocity, main effects and interaction terms have been calculated, the are treated consistently in each scheme; however the choice relative contribution of each effect or interaction to the toof microphysical factors to explore depends on the level of tal variance can also be quantified in terms of a percentage complexity of the microphysics scheme in question. The facof the total sum of squares. The calculation of the sum of torial design is based around the 2n design, meaning two valsquares for a given effect or interaction term is also specified ues, arbitrarilly labelled “low” and “high”, are assigned to n in Dearden (2009). number of factors, and the effect of changing from the “low” to the “high” value is calculated for each factor. Values for 3.2.2 Factorial design for bin microphysics each factor are chosen such that the effect of moving from Table 2 summarises the factorial design for the ACPIM the “low” value to the “high” value acts to reduce the amount model. A 23 design is used, giving three factors in total, two of precipitation reaching the surface. Thus each factor can be of which, namely w1 and T , are meteorological in nature evaluated in terms of its percentage contribution to precipitaand represent vertical velocity and the ambient temperature tion suppression. In some cases, repetitions of the 2n design respectively. The remaining factor, CCN, is a microphysiare considered to allow the effect of more than one “high” cal factor which represents the number concentration of the value to be explored. aerosol present within the column at each vertical level. 36 numerical simulations are required to fulfill the design presented in Table 2. The CCN factor is designed to explore the Atmos. Chem. Phys., 11, 2729–2746, 2011



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3

Table 2. Summary of the factorial design for the bin microphysics.

2−m

Description

Values

w1 T CCN

Peak vertical velocity (ms−1 )

0.5, 1, 2, 4 RICO, RICO-2, RICO-5 50, 100, 200

Temperature Profile Aerosol no. concentration (/cc)

effect of increasing the aerosol number concentration from a starting value of 50/cc, whilst the geometric mean radius and standard deviation as defined in Sect. 2.1 are held constant.

Liquid water path (kg m−2)

Factor

2.5

bin 1−m

2

1.5

1

0.5

0

3.2.3

Factorial design for bulk microphysics −0.5

0 500 1000 1500 2000 2500 3000 3500 Table 3 summarises the factorial design for the bulk miTime (seconds) 3 crophysics, also based around a 2 design and requiring 135 simulations in each case. The reduced computational Fig. 3. Timeseries of liquid water path from the 1-m, 2-m A-R and Fig. bin 3. Timeseries of liquid water path from the 1-m, 2-m and bin schemes burden of the bulk parameterizations compared to the bin schemes in the absence of precipitation and A-R sedimentation, such in the abse precipitation and such that stays in the cloud. scheme is exploited to perform a more thorough exploration that sedimentation, all condensed water staysallincondensed the −1 cloud. water The results shown were The results with the following settings: wsettings: , T= =RICO−1and CCN=100/cc. 1 =2 ms w obtained with the following of the parameter space. The meteorological factors w1were andobtained T 1 2 ms , T = RICO and CCN = 100/cc. are defined to be the same as in the bin scheme, although the w1 factor covers a greater range of values. In the 2-m bulk scheme, the CCN factor relates to the maximum droplet numand sedimentation are permitted 38 to occur, any subsequent difber concentration permitted. For 2-m Twomey, this is equal ferences in cloud liquid water path can be attributable to the to the value of c in Eq. (4). For 2-m A-R, the CCN factor treatment of these processes. relates to the aerosol number concentration based on the uniFigure 4 shows time-height plots from the bin and 2-m Amodal log-normal distribution, as in the bin scheme. In the R schemes with precipitation and sedimentation enabled, for 1-m scheme, the CCN factor is simply the prescribed value −1 , T = RICO and CCN = 100/cc. In both cases, w = 2 ms 1 of droplet number, which implicitly assumes that all availthe dynamical forcing conditions produce a cloud whose able aerosol have activated to form cloud droplets. It should base is around 500 m and a top at 2 km. As the prescribed be noted that no attempt was made to tune the bulk schemes updraught reduces to zero, and in the absence of any pato the bin scheme prior to running the experiments. It should rameterised entrainment effects or negative vertical velocialso be recognised that the choice of c and k parameters in the ties, a thin residual layer of cloud is allowed to persist in a Twomey case implies a different aerosol spectrum compared steady state. Admittedly this is not realistic; indeed Seifert to that used in the other schemes, which could contribute to and Stevens (2010) showed that the finite lifetime of shaldifferences in droplet number concentration, most notably at low cumulus cloud is an important timescale in determinlow updraught speeds. ing precipitation efficiency. However this shortcoming does not impinge upon the ability of the model to reveal interesting differences in the behaviour of the chosen microphysics 4 Results schemes. Furthermore, the influence of the residual cloud layer on the precipitation rate is minimal because the droplets 4.1 Initial analysis of cloud fields that remain are too small for effective collision and coalescence to occur, and so there is no real concern of any possible To illustrate the equality of the driver models, tests were percontamination issues arising from this deficiency. formed based on both the bulk and bin microphysics with precipitation and sedimentation processes switched off, such To allow comparison of rain mixing ratios, the bin scheme that the only microphysical processes permitted are condendiagnoses rain based on those liquid drops greater than sation and evaporation. The resulting liquid water paths from 50 microns in diameter, in accordance with the KK scheme. each scheme are plotted in Fig. 3. It can be seen that the The results share some similarities with those of Seifert and curves agree so closely that they appear to be coincident, Stevens (2010), who used a similar 1-D model to compare which confirms the consistency of the forcing conditions bean alternate pair of bin and 2-m bulk microphysics schemes tween driver models (and also confirms the validity of the with each other, but some differences as well. For instance, saturation adjustment approach used in the bulk schemes). It both studies show that the bulk scheme is able to capture the can also be concluded from this result that, once precipitation height and time of rain formation reasonably well. However


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Table 3. Summary of the factorial design for the bulk microphysics. Factor

Description

Values

w1 T CCN

Peak vertical velocity (ms−1 ) Temperature Profile Aerosol number concentration /cc (2-m A-R) No. of droplets active at 1% supersaturation /cc (2-m Twomey) Droplet number concentration /cc (1-m)

0.5 to 4 in intervals of 0.25 RICO, RICO-2, RICO-5 50, 100, 200

Fig. 4. Comparison of cloud droplet number concentration (m−3 ), cloud mass mixing ratio (kg kg−1 ) and rain mixing ratio (kg kg−1 ) from −1 T = RICO and the 2-m A-R scheme (left) and the bin scheme (right). The results shown are taken −3 from simulations with w1 = 2 ms ,−1 Fig. 4. Comparison of cloud droplet number concentration (m ), cloud mass mixing ratio (kg kg ) CCN = 100/cc. −1

and rain mixing ratio (kg kg ) from the 2-m A-R scheme (left) and the bin scheme (right). The results shown are taken from simulations with w1 =2 ms−1 , T =RICO and CCN=100/cc.

in this particular study, Figs. 4 and 5 show that the bin simThis is achieved through the method of moment-conserving ulation converts more of the cloud to rain than the bulk fits, the mathematics of which are derived in Appendix A. scheme. Given that the liquid water paths are essentially 39 Figure 6 plots the evolution of the diagnosed shape paramthe same in the absence of precipitation processes as shown eter with height and time from the bin scheme. The magin Fig. 3, this suggests that the collision-coalescence pronitude of µ varies considerably through the evolution of the cess in the ACPIM bin scheme is more efficient at produccloud; around the onset of in-cloud rain formation, µ is close ing rain compared to the KK autoconversion and accretion to zero, but values of µ are consistently higher below cloud schemes. The implications of the larger rain water path in base. This result is important since a varying shape paramethe bin scheme are addressed later in Sect. 4.3. ter has implications for rates of sedimentation (Milbrandt and McTaggart-Cowan, 2010) and evaporation, which could be It should also be remembered that the bulk scheme uses significant in full 3-D simulations when feedbacks between an exponential size distribution for rain, which implicitly asmicrophysics and dynamics can influence the temperature of sumes a shape parameter of zero. It is possible to test the vathe sub-cloud layer. The deficiencies of assuming a fixed µ lidity of this assumption using the bin scheme; this is accomvalue of zero are also discussed in Stevens and Seifert (2008). plished by fitting a gamma function to the resolved size distribution and diagnosing µ for rain through consideration of those drops greater than or equal to 50 microns in diameter. Atmos. Chem. Phys., 11, 2729–2746, 2011


C. Dearden et al.: Evaluating the effects of microphysical complexity using the Factorial Method 3

2 2−m bulk (A−R) Bin

2−m bulk (A−R) Bin

1.8

2.5

1.6 Rain water path (kg m−2)

Cloud liquid water path (kg m−2)

2737

2

1.5

1

1.4 1.2 1 0.8 0.6 0.4

0.5

0.2 0 0

10

20

30

Time (minutes)

40

50

60

0 0

10

20

30

40

50

60

Time (minutes)

Fig. 5. Comparison of cloud liquid water path (left) and rain water path (right) in kgm−2 from the 2-m A-R scheme (dashed) and bin scheme (solid), for those shown Fig. 4. Fig. 5. simulations Comparison of in cloud liquid water path (left) and rain water path (right) in kgm−2 from the 2-m

A-R scheme (dashed) and bin scheme (solid), for those simulations shown in fig. 4

sensitive to vertical velocity; however in the other schemes, an increase in the magnitude of vertical velocity generally produces a reduction in the total amount of precipitation produced, with some minor exceptions to this pattern at low updraught speeds. This is a consequence of the ability of the other three schemes to predict droplet number; not all CCN are necessarily activated as cloud droplets for a given updraught. The reduction of precipitation towards larger up40draughts can be attributed to aerosol indirect effects, since stronger vertical velocities activate more CCN which in turn reduces the precipitation efficiency (the reader is reminded that by design, the maximum extent the column is lifted is the same regardless of the updraught speed; this explains why precipitation amounts do not increase with higher vertical velocities). It can also be seen that as vertical velocity is increased in the 2-m schemes, the total precipitation amounts begin to converge on those from the 1-m scheme. It is worthy of note that in some instances, an increase in w1 from 0.5 ms−1 to 1 ms−1 actually results in a slight increase in preFig. 6. Time-height plot of the diagnosed shape parameter for rain cipitation.through This is the because some of the 0.5 ms−1 simulations Time-heightfrom plot the of the diagnosed shape parameter from the bin scheme, obtained bin scheme, obtained through the method of momentare still producing small amounts of drizzle at the end of the of moment-conserving fits(see (seeAppendix appendixA). A).The Theplot plotshown shownis isfrom fromthethe CCN=50/cc case, with conserving fits integrations, and so have not quite finished precipitating by −1 ms and T CCN =RICO profile. = 50/cc case, with w1 = 0.5 ms−1 and T = RICO profile. the time the simulations are stopped. Thus precipitation totals appear slightly underestimated in these cases. All four schemes agree, at least in a qualitative sense, on a reduction 4.2 Comparison of total precipitation in precipitation amount as a function of cooling temperature. This is because under a fixed relative humidity, the available Table 4 shows the total precipitation amounts (in mm) for source of water vapour that is converted to liquid water dura subset of the total number of experiments from all four 41 ing condensation is reduced as the temperature profile cools. schemes. The nature of the table allows for comparison of each scheme as a function of changing CCN concentrations, Figures 7 and 8 plot the precipitation rate and accumulated precipitation totals respectively as a function of time, cloud base updraught speeds and temperature profiles. Befor those experiments highlighted in bold in Table 4. Figfore a more rigorous analysis of this data is performed using ure 7 reveals that all four schemes show a delay in the onset the FM, some broad observations can first be made. With regard the 1-m scheme, the assumption of a fixed droplet of precipitation as a function of reducing vertical velocity. number means that the total precipitation is essentially inThe timing of surface precipitation is quite similar between www.atmos-chem-phys.net/11/2729/2011/

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Fig. 8. Timeseries of accumulated surface precipitation (mm) from each scheme. Clockwise from top left: 1-m, 2-m Twomey, bin, 2-m A-R. Results are shown with CCN = 100/cc and T = RICO, for four different values of w1 .

Fig. 8. Timeseries of accumulated surface precipitation (mm) from each scheme. Clockwise from top left: 1-m, 2-m Twomey, bin, 2-m A-R. Results are shown with CCN=100/cc and T =RICO, for four Atmos. Chem. Phys., 11, 2729–2746, 2011 www.atmos-chem-phys.net/11/2729/2011/ different values of w1 .

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Table 4. Surface precipitation totals (mm) for each scheme as a function of CCN and w1 for three different temperature profiles, namely RICO (top); RICO-2 (middle); and RICO-5 (bottom). Those results highlighted in bold type are plotted in Figs. 7 and 8 as timeseries of surface precipitation rate and accumulated surface precipitation respectively. CCN RICO

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the bulk and bin schemes, with a slight tendency for the bulk scheme to produce fractionally earlier surface precipitation at lower updraught speeds. There is a relatively large jump in the peak precipitation rates between the 2-m bulk schemes and the bin scheme; consequently the bin scheme produces larger precipitation totals than the bulk schemes as confirmed by Fig. 8. It is interesting to note that in the KiD intercomparison study by Shipway and Hill (2011), the 1-m Morrison scheme was found to overestimate precipitation as validated against the explicit TAU bin model (Tzivion et al., 1987) in the same idealised framework. This is in contrast to the results shown here when comparing the Morrison bulk scheme with ACPIM, suggesting that differences between bin schemes can be as large as those between bulk schemes. A similar conclusion was also reached in the 3-D LES intercomparison of van Zanten et al. (2011), where the spread in precipitation amongst the three bin models considered was found to be as large as the variation between the bulk schemes. A possible explanation for the difference in this particular case is that the TAU-bin model accounts for the coalescence efficiencies of droplets based on the work of Ochs et al. (1986), which acts to reduce the number of suc-


cessful collisions involving collector drops in the size range 0.1 to 0.6 mm, whereas the version of ACPIM used in this study assumes a coalescence efficiency of unity for all drop sizes. A detailed investigation into the impact of collection efficiencies on surface precipitation in bin schemes is beyond the scope of this study; however this should be considered in future work to determine the extent to which the choice of collection kernel can account for differences in behaviour between bin schemes. 4.3

Factorial analysis: quantifying the effects of CCN, w1 and T (23 design)

The FM is now used to quantify the sensitivity of the schemes to the choice of microphysical and meteorological factors based on the data provided in Table 4. This section explores the relative importance of each factor as a function of time throughout the evolution of the cloud, and compares the sensitivities of each scheme to illustrate differences in behaviour. Calculation of the relative contributions for each factor and their interactions follows the methodology explained in Dearden (2009).

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Fig. 9. Relative contribution (%) timeseries plots for each scheme, considering the effects of changes in CCN, w1 and T , plus their combined interaction effects. The relative contribution is calculated as a percentage of the total variance associated with the change in precipitation at Fig. 9.The Relative contribution (%) timeseries plots for each scheme, considering thefrom effects changes the surface. contributions shown are based on the following changes: w1 from 0.5 ms−1 to 2 ms−1 ; CCN 50/ccof to 100/cc, andin T wRICO-2. and T , plus their combined interaction effects. The relative contribution is calculated as a perfromCCN, RICO to Clockwise from top left: 1-m, 2-m Twomey, bin, 2-m A-R. 1

centage of the total variance associated with the change in precipitation at the surface. The contributions shown are based on the following changes: w1 from 0.5 ms−1 to 2 ms−1 ; CCN from 50/cc to 100/cc, Figure 9 considers the effect of changes in each factor on change in CCN concentration, independent of the change in and T from RICO to RICO-2. Clockwise from top left: 1-m, 2-m Twomey, bin, 2-m A-R.

the metric of accumulated surface precipitation, and the relative importance of each factor in terms of the enhancement or suppression of surface precipitation is expressed as a percentage of the total variance as a function of time. Specifically, an increase in w1 is considered from 0.5 ms−1 to 2 ms−1 , along with a cooling of the temperature profile, T , from RICO to RICO-2, and an increase in CCN from 50/cc to 100/cc. Figure 9 shows that, in all four schemes, the change in precipitation is dominated by the change in vertical velocity in the early stages of cloud development. Beyond 40 minutes, the relative importance of the vertical velocity effect reduces and by the end of the simulations, the change in temperature produces the largest effect on the suppression of precipitation. However the schemes disagree on the extent of the relative importance of the CCN and temperature effects. It can be seen in Fig. 9 that the contribution of the CCN effect is largest in the 1-m scheme; this is a consequence of the experimental setup for the 1-m scheme where an assumption is made that the change in droplet number is equal to the Atmos. Chem. Phys., 11, 2729–2746, 2011

vertical velocity. For the 2-m bulk schemes, the contribution of the CCN effect is slightly reduced; this can be ex44plained as follows. For slowly increasing updraught speeds such as the 0.5 ms−1 case, the ability to predict droplet number results in competition for water vapour between growth of existing droplets and activation of new droplets; this is demonstrated by Dearden (2009) using a simple lagrangian parcel model. The presence of CCN that activate at relatively low updraught speeds act as a sink of water vapour through growth by condensation, resulting in fewer droplets being activated overall compared to the 1-m scheme where by design the droplet number concentrations are slightly higher. This explains why the 1-m scheme has the largest relative contribution from the effect of CCN according to Fig. 9. However the 2-m A-R scheme, which includes a parameterization for the maximum supersaturation based on the vertical velocity and the properties of the aerosol size distribution, shows less of a change in droplet number at low updraught speeds and therefore less of an impact on precipitation. Consequently www.atmos-chem-phys.net/11/2729/2011/


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Fig. 10. As for Fig. 9 but for an increase in w1 from 2 ms−1 to 4 ms−1 .

Fig. 10. As for Fig. 9 but for an increase in w1 from 2 ms−1 to 4 ms−1 . Fig. 9 shows that the 2-m A-R scheme improves the comparison with the bin scheme. However in more rapidly increasing updraughts, Fig. 10 shows that the benefit of predicting droplet number concentration is lost and the 2-m AR scheme produces largely the same sensitivity as the 1-m scheme. This is a consequence of the fact that, towards larger vertical velocities, the droplet number concentrations converge in the bulk schemes, thus producing very similar sensitivities. Some additional simulations with the 1-m scheme were also performed where the assumed droplet concentration at low updraught speeds was set to a value more representative of the predicted values from the 2-m A-R scheme. The results from these tests (not shown) reveal that tuning the droplet number concentration in the 1-m scheme allows the total precipitation values to match those produced by the 2-m A-R scheme, whilst also improving the agreement in terms of the relative contributions. This result suggests that a diagnostic representation of droplet number based on CCN number and updraught velocity would be sufficient to capture aerosol indirect effects for the chosen scenario. This has important implications when considering the balance between model complexity and computational efficiency, as it shows that in the absence of feedbacks at least, a prognostic variable for www.atmos-chem-phys.net/11/2729/2011/

droplet number may not be necessary, and that a diagnostic treatment of droplet number could help to minimise the cost of the scheme without compromising the ability of the model 45to capture the effects of aerosol. The remaining difference in sensitivities between the bin and 2-m A-R bulk scheme as shown in Figs. 9 and 10 can be explained by considering the effects of evaporation below cloud base. It has already been shown that the rain mass falling out of the cloud in the bin scheme is greater than in the bulk schemes (Fig. 4), but also that the bin scheme produces consistently larger amounts of surface precipitation. It is hypothesised that differences in collection efficiencies between the bulk and bin schemes are contributing to the different sensitivities to temperature and CCN, and specifically that larger rain drop sizes in the bin scheme are leading to an overall reduction in rain evaporation. To explore this hypothesis, a sensitivity test was performed with the 2-m A-R scheme where the rain fall speed parameter br is increased from the default value of 0.8 to 0.825 to facilitate larger rain drops, in order to test the impact on evaporation and the amount of rain that reaches the surface. Table 5 shows that the modification to the fallspeeds for rain in the bulk scheme leads to an increase in accretion, a reduction in rain evaporation, and in Atmos. Chem. Phys., 11, 2729–2746, 2011

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Table 5. Rain evaporation (kgm−2 ; top), accretion (kgm−2 ; middle) and surface precipitation (mm; bottom) accumulated over 2 h from the 2-m A-R scheme, as a function of CCN, w1 and T , and also from the 2-m A-R scheme with increased fallspeed parameter for rain, such that br = 0.825. The evaporation and accretion terms are calculated by integrating the process rates with height at each timestep, and then integrating these values in time over a 2 h period. RICO w1 0.5 ms−1 1.0 ms−1 2.0 ms−1 4.0 ms−1

RICO-2

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turn an increase in the total surface precipitation. Figure 11 shows the effect of this change on the relative contributions in the bulk scheme, and illustrates how the effect of CCN is reduced at the expense of the effect of temperature in accordance with the bin scheme. However it is also recognised that differences in the numerical treatment of sedimentation between the bin and bulk schemes (as discussed in Sect. 2.3.1) may be contributing to the difference in sensitivities as well. To explore this further, extra tests were performed with the bulk scheme where the existing first-order treatment of sedimentation was circumvented and replaced with increasingly higher order forward-difference approximations as specified in Jacobson (2005, p. 180), up to and including a fourthorder scheme for consistency with the bin model. Results from these tests (not shown) reveal that increasing the order of approximation from first to second order leads to a small increase in total surface precipitation (around 5%) over the range of bulk simulations considered. Subsequent increases to third and fourth order accuracy were found to have negligible impact on precipitation. These results suggest that the Atmos. Chem. Phys., 11, 2729–2746, 2011

1.14 1.08 1.07 1.07

1.25 1.21 1.20 1.20

use of a lower order treatment of sedimentation in the bulk scheme does not contribute significantly to the differences shown when comparing against the bin scheme.

4.4

Factorial analysis: the effect of increasing vertical velocity for a fixed temperature (22 design)

It is now prudent to explore the sensitivity of surface precipitation to different levels of change in the vertical velocity field. The sensitivities of each scheme can be compared through consideration of the total effect on precipitation suppression, as described in Sect. 3.2; the sign and magnitude of the result indicates the direction and significance of the induced change. In this case the factors considered are CCN and w1 , with a fixed background temperature and humidity based on the RICO profile, yielding a 22 design. The results from the following FM analysis are based on values of surface precipitation accumulated at the end of the model simulation. Following the logic from Sect. 3.2, the 22 design has www.atmos-chem-phys.net/11/2729/2011/


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in droplet number and is essentially insensitive to changes in updraught speed, which is clearly a limitation when com90 paring against the bin scheme (solid black line) under the 80 same conditions. In theory the sensitivity of the 1-m scheme to vertical velocity could be increased by using a diagnostic 70 relationship for droplet number concentration instead of the 60 assumption of a fixed value as used in this study. Both 2m schemes show an increase in suppression of rainfall as a 50 function of increasing vertical velocity, which in a qualitative 40 sense agrees with the bin scheme. However the 2-m Twomey scheme considerably overestimates the amount by which pre30 cipitation is suppressed. This can be understood by consid20 ering the total precipitation for the 50/cc case from Table 4. 10 The 2-m Twomey scheme produces relatively more precipitation than the other schemes at low updraught speeds, sug0 0 20 40 60 80 100 120 gesting that it activates fewer droplets at 50/cc. Thus when Time (minutes) the value of CCN is increased to 100/cc, the suppression of precipitation appears to be exaggerated. The implications of Fig. 11. As Fig. 9 but for the 2-m A-R scheme with modified fallthissuch arethat thatbr for this idealised case, a single value of k for g. 11. As Fig.speed 9 butparameter for the 2-m A-R scheme with modified fallspeed parameter for rain, for rain, such that br is increased from the default increased from the default of All 0.8 other to 0.825. All other fallspeed are unchanged. different CCN concentrations is not appropriate, and that the value of 0.8 tovalue 0.825. fallspeed parameters areparameters unchanged. value of k should change as a function of the assumed CCN concentration. This problem is alleviated in the 2-m A-R scheme, where knowledge of the aerosol composition and 0 log-normal size distribution is advantageous in obtaining a Bin 2−m (Twomey) better agreement with the bin scheme. 46 1−m −0.05 2−m (A−R) For values of w1 starting from 2 ms−1 (as shown in Fig. 13), all four schemes are in much better agreement in terms of the overall amount by which precipitation is sup−0.1 pressed. Thus it is difficult to justify the increased computational expense of a 2-m liquid scheme in this regime when a −0.15 1-m scheme performs in such a similar manner. 100

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Summary and discussion

The Factorial Method has been used to compare the sensitivities of warm shallow cumulus cloud as simulated by four different microphysics schemes of increasing levels of com0.5 1 1.5 2 2.5 3 3.5 4 plexity using an idealised 1-D column framework. The use Change in vertical velocity (from 0.5 m/s) of a simple driver model is intended to aid the comparison by removing the sensitivity to dynamical feedbacks, thus isolatFig. 12. Total effect on suppression of precipitation (in mm) from ing the pure microphysical behaviour. The chosen factors Fig. 12. Total each effectscheme on suppression of precipitation (in mm) scheme of changes as a function of changes in w1from andeach CCN, underasaa function −1 n w1 and CCN, under a fixed temperature (T =RICO). Changes in w are considered from 0.5 ms up include the magnitude of the cloud base vertical velocity, 1 fixed temperature (T = RICO). Changes in w1 are considered from −1 upintoCCN −1 o 4 ms−1 , and0.5 thems change is from 50/cc to 100/cc. the ambient temperature profile, and the assumed number 4 ms , and the change in CCN is from 50/cc to 100/cc. of aerosol available to act as CCN. The sensitivity of each scheme was assessed and quantified in terms of the suppression of precipitation at the surface, with the bin scheme used three degrees of freedom, such 47 that the total effect is equal as a benchmark in order to validate the performance of the to the sum of the effects of the two main factors plus their bulk schemes. interaction. The reader is reminded that all of the results found in this Figure 12 considers the total effect on precipitation restudy are specific to the particular test case in question, and sulting from repeated increases in w1 from a low value of future work will be necessary using the tools presented in this 0.5 ms−1 , plus the additional effect of an increase in CCN paper to determine the generality of our results. For the idefrom 50/cc to 100/cc. For the 1-m scheme, Fig. 12 illustrates alised case considered in this study where feedback effects that the reduction in precipitation is due solely to the change are neglected, the performance of the bulk schemes for cloud −0.25


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Fig. 13. As Fig. 12 but for changes in w starting from 2 ms−1 . Fig. 13. As Fig. 12 but for changes in w1 starting from 12 ms−1 .

base updraught speeds up to 2 ms−1 was found to depend on the assumptions made with regards the method of droplet activation. At updraughts larger than 2 ms−1 , all schemes activate most if not all of the available 48 CCN and so essentially reduce to the same droplet number concentrations. In this regime the 2-m bulk schemes were found to behave much like the 1-m bulk scheme. This suggests that for models with sufficient resolution, it is theoretically possible to optimise the balance between complexity and cost by allowing the model to choose the appropriate level of microphysical detail based on the magnitude of the cloud base updraught speed and knowledge of microphysical parameters such as aerosol number concentration and size. This stresses the importance of coupling the microphysics to a prognostic aerosol scheme to provide the necessary information. It should also be noted that it was possible to tune the 1-m scheme at low updraught speeds to produce essentially the same precipitation amounts and sensitivities as the 2-m scheme, by fixing the assumed droplet number concentration to match those of the predicted concentrations. This suggests that in the absence of feedbacks, a diagnostic relationship for droplet number may perform just as well as a prognostic treatment. This has obvious advantages in terms of computational efficiency given that one less prognostic variable would need to be advected. Further comparison of the schemes also highlighted some fundamental differences in behaviour worthy of comment. For instance the bin scheme consistently produced larger amounts of precipitation when compared to the bulk schemes, even in scenarios where all schemes produced very similar droplet number concentrations. A cooling of the temperature profile by 2 ◦ C under a fixed relative humidity was also found to produce a relatively higher contribution to precipitation suppression in the bin scheme compared to the bulk schemes. It was possible to enhance the dominance of the temperature effect in the bulk scheme and thus imAtmos. Chem. Phys., 11, 2729–2746, 2011

prove the agreement with the bin scheme by modifiying the fallspeed parameters for rain, which served to increase accretion, reduce evaporation and thus increase the surface precipitation. Differences in evaporation of rain between schemes may have important consequences in terms of dynamical feedbacks in full 3-D simulations, by modifying the extent of evaporative cooling of the sub-cloud layer. A consideration of such feedbacks is beyond the scope of this paper, but warrants further invesigation in future work. It is important to note that separate intercomparison studies comparing bin and bulk schemes using the KiD framework do not necessarily support the conclusion that bin schemes produce more precipiation than bulk schemes. Thus the enhanced sensitivity to temperature as seen in the ACPIM bin model may not be a general feature of bin schemes. Although it was shown that the bulk scheme could be effectively tuned to produce better agreement with this particular bin scheme, the same tuning may not necessarily improve the agreement relative to other bin schemes. Future work should therefore focus on investigating and understanding the origin of differences between bin schemes to increase confidence in their use as benchmarks against which simpler bulk parameterizations are validated. Suggested variables for investigation include the number of size bins used to resolve the liquid size distribution, the treatment of aerosol (whether a fixed log-normal mode or prognostic), the choice of collection kernel and the numerical treatment of advection. In light of these potential sources of differences, the need to constrain bin schemes with field observations and laboratory experiments is also recognised. A big caveat in producing these conclusions is the absence of entrainment and feedback effects in the 1-D framework. The 1-D framework does not account for entrainment mixing within the cloud, and in reality, the effect of entrainment mixing could to some extent counteract the change in temperature due to vertical advection. There is a growing suggestion within the available literature that the inclusion of feedback effects is likely to dampen the sensitivity of warm clouds to increases in aerosol loadings. For instance, the study by Jiang et al. (2006) used a 3-D LES modelling approach to compare the lifetime of polluted cumulus clouds to those of clean cumulus clouds when entrainment is allowed to occur. The results suggest the overall lifetime of both the polluted and clean clouds are statistically similar, and propose an evaporation-entrainment feedback mechanism which acts to dilute polluted clouds (i.e. reduce liquid water content) and therefore reduce the overall sensitivity of warm shallow cumuli to changes in aerosol concentration. Stevens and Feingold (2009) also argue that in reality, the sensitivity of clouds and precipitation to changes in aerosol concentration is on average weaker than a purely microphysical consideration alone would suggest, due to the capacity of the system to respond differentially to changes in aerosol, thereby acting to buffer the global system against such changes and reducing the overall effect. Stevens and Seifert (2008) even suggest www.atmos-chem-phys.net/11/2729/2011/

C. Dearden et al.: Evaluating the effects of microphysical complexity using the Factorial Method that the effect of increased aerosol loadings on shallow convection could in some instances lead to an enhancement of precipitation, since the delay in the onset of rain formation may allow the cloud to achieve a greater depth and therefore a higher liquid water path. Therefore the results of this study should be considered only as a starting point, with the recommendation that the techniques of factor separation be utilised in future work to help quantify the extent to which the sensitivities shown in this paper are modified within a more realistic dynamical framework. Appendix A Method of moment-conserving fits Diagnosis of the shape parameter for in the ACPIM model is based on the following methodology, which fits the resolved liquid size distribution for drop diameters greater than 50 microns to a gamma function. In general, the k-th moment of a size distribution n(D) is specified as: Z ∞ Mk = D k n(D)dD (A1) 0

where in this case n(D) is based on a gamma distribution as in Eq. (1). The k-th moment of a gamma distribution can be expressed analytically, and is given by: 0(µ + k + 1) (A2) λµ+k+1 Consequently the zeroth, first and second moments of a gamma distribution are written as follows: Mk = N0

0(µ + 1) λµ+1 0(µ + 2) ,M1 = N0 µ+2 λ 0(µ + 3) M2 = N0 µ+3 λ

M , 0 = N0

(A3)

The quantity F is now introduced and defined as the square of the first moment divided by the product of the second and zeroth moments: F=

M12 0(µ + 2)2 = M2 M0 0(µ + 1)0(µ + 3)

(A4)

Using the following property of gamma functions, 0(µ) = (µ − 1)0(µ − 1)

(A5)

it is possible to re-write the expression for F as follows: F=

(µ + 1)2 0(µ + 1)2 µ+1 = 0(µ + 1)(µ + 2)(µ + 1)0(µ + 1) µ + 2


(A6)

2745

Rearranging Eq. (A6) in terms of µ gives: µ=

1 − 2F F −1

(A7)

Equation (A7) is used to calculate the shape parameter µ, where the quantity F is obtained from the model microphysics based on explicit calculation of the of the P moments k resolved size distribution given by Mk = m i=1 Ni Di , where Ni and Di are the number concentration and diameter respectively for size category i, and m is the total number of size bins. Rain was diagnosed in the bin scheme using a diameter thresold of 50 microns for consistency with the bulk autoconversion scheme. Acknowledgements. The first author would like to thank Ben Shipway and Adrian Hill of the Met Office for their advice and feedback in setting up the KiD model. Thanks also to Hugh Morrison of NCAR, USA for supplying the latest version of the bulk microphysics code used in this study, and to the three anonymous reviewers whose comments helped to improve the final manuscript. Edited by: B. Stevens

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