The production of warm rain in shallow maritime cumulus clouds

Quarterly Journal of the Royal Meteorological Society

Q. J. R. Meteorol. Soc. 139: 20–31, January 2013 A

The production of warm rain in shallow maritime cumulus clouds Alan M. Blyth,a * Jason H. Lowenstein,b† Yahui Huang,b Zhiqiang Cui,b Stewart Daviesb‡ and Kenneth S. Carslawb b

a National Centre for Atmospheric Science, School of Earth and Environment, University of Leeds, UK Institute for Climate and Atmospheric Science, School of Earth and Environment, University of Leeds, UK

*Correspondence to: A. M. Blyth, National Centre for Atmospheric Science, School of Earth and Environment, University of Leeds, Leeds, LS2 9JT, UK. E-mail: [email protected] † Current affiliation: OwnEnergy Inc., Brooklyn, NY, USA. ‡ Current affiliation: Viridor Waste Management Ltd, Exeter, UK.

The problem of the production of warm rain by collision and coalescence has been studied for over half a century and several processes have been suggested to explain the observed production, which is more rapid than generally possible with models. A straightforward scenario in relatively shallow maritime cumulus clouds is one where cloud drops simply grow by condensation and coalescence, with no appeal to enhancement due to entrainment or turbulence or indeed the presence of giant and ultragiant aerosols that may exist in the boundary layer. However, it is difficult in a field experiment to measure the concentrations of aerosols and the time evolution of the droplet size distribution or reflectivity in individual clouds. The Rain in Cumulus Over the Ocean (RICO) field experiment overcame some of these difficulties due to the abundance of clouds and the statistical sampling strategy at all significant altitudes. In this article, we present the results of the rate of increase in the radar reflectivity in a couple of cases. Comparisons with a cloud model strongly suggest that the development of warm rain can be explained using the observed aerosol distribution alone. Sensitivity studies suggested that giant and ultragiant aerosols c 2012 were unimportant for the production of rain in these clouds. Copyright Royal Meteorological Society Key Words: giant aerosols; cloud microphysics model; collision and coalescence; aircraft and radar observations Received 6 October 2011; Revised 1 February 2012; Accepted 16 April 2012; Published online in Wiley Online Library 14 June 2012 Citation: Blyth AM, Lowenstein JH, Huang Y, Cui Z, Davies S, Carslaw KS. 2013. The production of warm rain in shallow maritime cumulus clouds. Q. J. R. Meteorol. Soc. 139: 20–31. DOI:10.1002/qj.1972

1.

Introduction

This article is concerned with observations and modelling of the development of precipitation in clouds with temperatures greater than 0 ◦ C (warm rain). It is essential to be able to quantify the production of warm rain and therefore to understand the processes involved, because warm rain plays an important part in the hydrological cycle of the planet. For example, a significant fraction of precipitation in the Tropics is associated with warm rain (Johnson et al., 1999). Also, the development of c 2012 Royal Meteorological Society Copyright

precipitation in mixed-phase clouds can also depend on the existence of supercooled raindrops formed through the warm rain process (e.g. Koenig, 1963; Blyth and Latham, 1993; Huang et al., 2008; Cui et al., 2011). Furthermore, precipitation from warm, shallow clouds has been shown to be important in moistening the free troposphere (Masunaga and Kummerow, 2006). Many climate models predict the onset of warm rain when the mean droplet radius becomes greater than a threshold value (Rotstayn and Liu, 2005), and the more sophisticated schemes now possible in numerical weather prediction models (Lim and Hong, 2010; Morrison

Warm Rain in Shallow Maritime Cumulus Clouds

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et al., 2009) depend on the accuracy of the representation and therefore our understanding of the processes (Lim and Hong, 2010). One of the earliest modelling studies of the warm rain process was performed by Twomey (1966). The results of the calculations showed that the times for rain were slightly longer than the 15 minutes or so observed in warm oceanic clouds. Twomey offered the explanation that the times would be reduced if regions of high liquid water content persisted in the cloud even for a short period such as a minute. There have been significant modelling developments recently that address the issue of explaining the rate of production of precipitation in warm cumulus clouds with sophisticated models (e.g. Lasher-Trapp et al., 2005; Grabowski et al., 2010). Increasingly, the models are able to include those significant processes that have been investigated individually over the years. vanZanten et al. (2011) presented results of an inter-comparison between 12 large-eddy simulations and also observations made in the Rain In Cumulus over the Ocean (RICO) experiment. They found that the ensemble average of the simulations reproduced the profiles of cloud and rain water and, to a lesser extent, the concentration of raindrops. There were significant differences between the models of surface precipitation rates, for example, particularly for the models with more simplified microphysics schemes. There have been three principal areas of research into trying to solve this problem: growth on giant aerosols (GA) and ultragiant aerosols (UGA) (e.g. Ochs, 1978; Johnson, 1982; Lasher-Trapp et al., 2001; Feingold et al., 1999; Zhang et al., 2006; Jensen and Lee, 2008), enhancement of growth of a few of the largest cloud droplets due to entrainment and mixing (e.g. Baker et al., 1980; Telford and Chai, 1980; Cooper, 1989; Chaumat and Brenguier, 2001; Pawlowska and Brenguier, 2003; Lasher-Trapp et al., 2005) and increase in the growth rate of drops due to turbulent enhancement of the collision efficiencies (Srivastava, 1989; Shaw, 1998; Pinsky et al., 1999; Wang et al., 2008). It is appealing to believe in the simplest solution: that the rate of production of rain can be explained with the aerosol particles that exist in the boundary layer, including the giant and ultragiant particles. Giant (1 µm ≤ ddry ≤ 10 µm) and ultragiant aerosol particles (ddry > 10 µm) have been shown to play a significant role in the onset of the coalescence process and hence the production of warm rain (e.g. Ochs, 1978; Johnson, 1982; Lasher-Trapp et al., 2001). Giant aerosols were first reported by Woodcock (1953), who found that size distributions measured over the sea near Hawaii were very sensitive to wind speed. Exton et al. (1985), Leeuw (1986) and O’Dowd et al. (1996), for example, have presented further data supporting Woodcock’s observations. Johnson (1982) examined the influence of UGA on the formation of warm rain and concluded that ‘naturally occurring giant and ultragiant aerosol particles can play an important role in precipitation initiation’. A number of other modelling studies (e.g. Ochs and Semonin, 1979) have shown that these largest aerosol particles play a significant role in the initial development of warm rain. Further support was supplied by Beard and Ochs (1993), for example. Caylor and Illingworth (1987) found that radar observations of the early development of differential reflectivity, ZDR , and reflectivity could be explained by using UGA. Lasher-Trapp et al. (2001) calculated drop growth on UGA by continuous

collection in a high-resolution, three-dimensional simulated cloud and found that the altitudes and magnitudes of the observed first echoes could be explained by UGA. Blyth et al. (2003) analysed radar and aircraft data collected during the Small Cumulus Microphysics Study (SCMS) and concluded that GA and UGA were sufficient to explain the radar and aircraft observations, without including other mechanisms such as turbulence or entrainment and mixing. Previous studies have shown that GA and UGA are less important for precipitation formation in clouds with a low concentration of cloud condensation nuclei (CCN) (e.g. Johnson, 1982; Feingold et al., 1999; Zhang et al., 2006). Recently, Cheng et al. (2009) investigated the effects of CCN and giant CCN (GCCN) on the development of precipitation in the clouds observed during RICO using the Regional Atmospheric Modeling System in Large Eddy Simulation mode. They found, like others above, that the GCCN had a larger influence when there was a higher concentration of CCN. Jensen and Lee (2008) examined the relative importance of smaller aerosols (rdry < 0.5 µm) and giant and UGA on the warm rain-rate variability in marine stratocumulus clouds, using a cloud model with simple dynamics and sophisticated microphysics. It is the most accurate microphysical treatment of warm rain development thus far using a scheme with no artificial broadening. They found that when the wind speed was greater than 4–5 m s−1 the concentration and sizes of giant sea-salt particles determined the resulting rainfall rate in the marine stratocumulus clouds that they modelled. The number of smaller drops in the peak formed on CCN determined how much a large drop formed on a giant sea-salt aerosol was allowed to grow. They also found that turbulent enhancement of collisions and effects of broad spectra due to mixing had minor influences on the development of precipitation in the clouds they modelled. Furthermore, there was a stronger dependence on the giant aerosol size distribution than was found by Feingold et al. (1999), which Jensen and Lee (2008) believed was due to the slight artificial broadening caused by the numerical scheme. The prescribed dynamics and lack of entrainment and sedimentation is a limitation of their results. Hudson et al. (2011) found a correlation between the concentration of giant nuclei and the concentration of drops in the cloud with diameter greater than about 150 µm at altitudes greater than 2.4 km. However, Reiche and Lasher-Trapp (2010) compared results from parcel model calculations with radar observations made during RICO and determined that the cloud depth (likely influenced by the humidity of the environment; Nuijens et al., 2009) was the most important factor for the production of rain, regardless of the amount of giant aerosol or the observed droplet number concentration present on a given day. Minor et al. (2011) similarly found that the role of giant aerosols in the formation of warm rain was minor by analysing early echo development in more than 70 RICO clouds. The development of precipitation after the formation of the embryos depends on the cloud dynamics. Burnet and Brenguier (2010) examined data collected in the 10 August cloud during SCMS and highlighted how sensitive the onset of precipitation is to cloud dynamics. Two clouds collapsed after reaching an altitude of 3 km above sea level, without producing any precipitation, while the third one reached a higher level of 4 km and produced significant precipitation. Cooper et al. (2011) used a parcel model with an accurate calculation of the condensation and coalescence, run along

c 2012 Royal Meteorological Society Copyright

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multiple trajectories produced by a high-resolution threedimensional cloud model, and showed that rain could be produced in cumulus clouds due to the broadening of the droplet size distribution (DSD) caused by the variability in droplet trajectories arriving at a given location and time in a cumulus cloud. Different growth histories were experienced by the droplets due to entrainment and mixing, as originally envisioned by Baker and Latham (1979). Burnet and Brenguier (2010) also showed how difficult it is to make observations of the development of precipitation with aircraft and radar. This difficulty was addressed to some extent in the RICO field experiment (Rauber et al., 2007), because of the statistical sampling strategy. The purpose of the present study is to examine new observations made during RICO of the development of rain in two cases on 9 December 2004 and 14 January 2005 of relatively shallow, warm, maritime cumulus clouds, with the help of an axisymmetric, bin-resolved, dual-moment cloud model. In section 2, there is a description of the RICO field experiment and the model used in the study. Section 3 describes the aerosol size distributions that were measured over long legs in the boundary layer. Comparisons between the observations and the model are presented in section 4 and results from sensitivity studies are presented in section 5, where the concentration of CCN is increased and compared with and without GA and UGA. Conclusions are given in section 6. All times are given in Coordinated Universal Time (UTC) and altitudes are given as altitude above mean sea level (MSL).

Position Indicator (PPI) mode and was able to complete a full volume scan in 3–4 min. The beam width was 0.91◦ and range gates were every 150 m. Data gathered with the radar and NCAR C-130 aircraft will be presented in this article. Aerosol size distributions (ASDs) presented in this article were measured by a PMS Passive Cavity Aerosol Spectrometer Probe (PCASP/SPP-200: Kin and Boatman, 1990; Strapp et al., 1992) and a PMS Forward Scattering Spectrometer Probe (FSSP/SPP-100), which were calibrated to measure particles with diameters 0.14 µm < d < 2.75 µm and 3.1 µm < d < 46.5 µm, respectively. The CCN distribution was measured with the CCN spectrometer (Hudson and Mishra, 2007). The DSDs were measured by the FSSP, two-dimensional optical array cloud probe (2D-C, 42 µm ≤ d ≤ 1.6 mm with image reconstruction) and PMS two-dimensional optical array precipitation probe (2D-P, 145 µm ≤ d ≤ 12.7 mm with image reconstruction). Values of liquid water content presented in the article are from the integrated FSSP size distribution, checked against the other liquid-water-content probes. Details of the calibration methods and corrections applied to the data and uncertainties have been determined by the extensive research performed by Knollenberg (1981), Baumgardner (1983), Dye and Baumgardner (1984), Baumgardner et al. (1985, 1992), Brenguier and Amodei (1989), Baumgardner and Spowart (1990), Korolev et al. (1991), Brenguier et al. (1994), Wendisch et al. (1996), Baumgardner and Korolev (1997), Brenguier et al. (1998) and Korolev et al. (1998).

2.

The RICO field experiment was different from previous projects (e.g. the Small Cumulus Microphysics Study: Blyth et al., 2003) designed to study the development of warm rain in cumulus clouds in two critical ways. Firstly, the aircraft penetrated a large number of clouds at a constant altitude before moving to a different altitude, rather than chasing individual clouds and attempting to sample the growth phase of a single cloud at different altitudes. Secondly, the radar scanned many clouds rapidly at a constant elevation angle during RICO, rather than attempting to coordinate with the aircraft and sample single clouds by varying the elevation angle at several appropriate azimuth angles. It is notoriously difficult to measure an individual cloud with radar and/or aircraft from its early stages through to the onset of precipitation unless the clouds are anchored to particular features, such as a mountain range. However, in RICO many clouds could be tracked with the radar over the critical development stages of their lifetime and cloud DSDs were measured with the aircraft at all altitudes of the clouds at all stages of their development, including near the top of ascending turrets. RICO took place over the Atlantic Ocean off the Caribbean islands of Antigua and Barbuda, from 15 November 2004 to 24 January 2005. Several observational platforms were used, including the National Center for Atmospheric Research (NCAR) dual-polarization and dual-wavelength radar SPolKa, the NCAR C-130, University of Wyoming King Air and UK BAe 146 research aircraft and the Seward Johnson research vessel. The radar scanned clouds in Plan

The Model of Aerosols and Chemistry in Convective Clouds (MAC3) is an axisymmetric bin-resolved, dual-moment (i.e. mass and number) cloud model. The dynamics and microphysics within MAC3 are based on the cloud model of Reisin et al. (1996). Further development of the model was carried out by Yin et al. (2005) and by Cui et al. (2006), after which the model was given the current name. MAC3 carries four hydrometeors (drops, ice crystals, graupel particles and ice aggregates) in 34 mass-doubling size bins per hydrometeor and includes detailed microphysics for both warm and mixed-phase processes. Droplets range in diameter from approximately 3 µm–8 mm. The warm-phase microphysical processes include nucleation, condensation and evaporation, collision and coalescence, break-up and sedimentation (Yin et al., 2005). The droplet response to entrainment and mixing is homogeneous in nature; when a droplet is exposed to subsaturated air it simply shrinks or completely evaporates, depending on its size. The stochastic collection model of Tzivion et al. (1987a) is used to represent collection. The model was used by Feingold et al. (1999), for example, which Jensen and Lee (2008) suggested produced slight artificial broadening, as mentioned in the Introduction. The solution is based on a multi-moment approach that conserves cloud water and also solves for drop concentration. Equations for both drop mass and number concentration are solved within each bin. The kernels are from Long (1974) for d < 0.1 mm, Ochs et al. (1986) for 0.1 ≤ d ≤ 0.6 mm and Low and List (1982a,b) for d > 0.6 mm (Tzivion et al., 1987a). Tzivion et al. (1987a) concluded that the numerical spectral broadening in MAC3 is small. They compared the calculated spectrum with theoretical solutions for the constant kernel, Golovins kernel (Golovin, 1963) and hydrodynamic kernel


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2.1.

Description of data and methods The RICO field experiment

2.2.

MAC3 model


and produced very good agreement for both mass and number distributions. Tzivion et al. (1987b) studied the behaviour of the solution with the number of bins, with bin numbers being 36, 72, 108 and 144, and three kernels (Golovin, Long and Hall). As the number of bins increased, better convergence to the case of 144 bins was obtained. The solution of 144 bins approached the exact solution. For 36 bins (which is closest to the 43 bins of MAC3) there was a very small acceleration for Golovins kernel and a slightly larger acceleration for the Long and Hall kernels. MAC3 is an axisymmetric model and the axisymmetry is a limitation for the cloud dynamics. The model cannot be used to simulate clouds in strong wind shear. In a weak wind shear environment, however, Ogura (1963), Murry (1970) and Soong and Ogura (1973) found that the clouds simulated in an axisymmetric model were similar to those in a three-dimensional model (Wilhelmson and Ogura, 1972), providing the initial and boundary conditions in the two models were the same (Soong and Ogura, 1973). The model carries aerosol particles in 43 bins with dry diameters ranging up to 39.7 µm. All aerosol particles are assumed to be ammonium sulphate. Aerosol particles with diameters less than 0.24 µm grow via condensation according to the Köhler equation. Once the ambient supersaturation exceeds the critical supersaturation for particles in this size range, they are activated and placed in the cloud droplet bins, where further growth occurs based on the condensational growth equation. For dry aerosol particles with diameters greater than 0.24 µm, a factor k0 is used to calculate the initial sizes of the droplets at 100% RH. This parameter is given by k0 = 5.8w−0.12 a−0.214 , where w is the vertical velocity in m s−1 and a is the dry radius of the aerosol particle in micrometres. The parameter k0 is then multiplied by the dry radius of the aerosol particle to determine the initial size for which the droplet will be introduced into the cloud droplet bins at 100% RH (Yin et al., 2005). For example, with a vertical velocity of 0.1 m s−1 , a dry aerosol particle of diameter 2.48 µm will be assigned a value of k0 = 7.2, and introduced into the cloud droplet bins as a 18.16 µm drop. This is significantly smaller than 122.8 µm, the diameter of this particle at its equilibrium size at 100% RH. k0 is used to compensate for the lag in growth of the largest aerosol particles. The parameter is also used in cloud, at every grid point. MAC3 was initialized with the appropriate observed subcloud ASD. In particular, a parcel model was used to produce the ASD at 95% RH that best matched the observations and then the distribution was converted to its dry size using the Köhler equation for input for MAC3. In order to initiate convection, a warm bubble was used in conjunction with the relevant clear-air sounding. The grid spacing was 60 m in the horizontal and 120 m in the vertical. The radial and vertical domains were 6 km and 4.8 km, respectively.

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Figure 1. Aerosol size distributions measured by the PCASP and FSSP (solid lines) on 9 December 2004 and 14 January 2005 (lower and upper curves, respectively), below cloud base. Note that there is an unexplained step change in the PCASP concentrations at a diameter of approximately 0.2 µm.

sampling statistics. These were shown to be similar to measurements made by a Giant Nuclei Impactor system (Colon-Robles et al., 2006). The particles measured by the FSSP were deliquesced (Colon-Robles et al., 2006), so the raw distribution was converted to the dry sizes to produce the distributions for the two cases discussed in this article (Figure 1) using the Köhler equation, assuming the measured particles are NaCl and the mass of water is according to the ambient temperature and RH. RH values typically ranged between 75% and 85%. It has been shown that the composition of the larger aerosol particles (e.g. d > 1 µm) found in a marine environment are predominately sea salt (O’Dowd et al., 1999; Peter et al., 2008). The dry ASDs from 14 and 18 January 2005, the days when the average horizontal wind speed measured during the circles was greatest and weakest, respectively, were presented, along with the dry sea-salt distributions measured by Woodcock (1953), by Lowenstein et al. (2010). There was good agreement with the Woodcock distributions when compared at similar wind speeds. 4. Development of warm rain 4.1. Case 1: 14 January 2005

Figure 2 shows the liquid water content, LWC, plotted as a function of altitude for many different clouds penetrated on 14 January 2005. Several clouds were penetrated near their top at any one level during the long legs, while others were penetrated nearer their middle. The values of LWC from the FSSP never exceeded about 1 g m−3 and are significantly less than the adiabatic value at all altitudes, deviating by increasing amounts with altitude, as found by 3. Sub-cloud aerosol size distributions Warner (1955). Values of the vertical wind speed w in the same clouds typically ranged between −4 and +4 m s−1 The NCAR C-130 aircraft typically flew 60-km diameter (Figure 3). The maximum updraught speed increased with circles at altitudes below cloud base. During these periods, altitude up to an altitude of 1.7 km, where it reached slightly measurements were made of the sub-cloud ASD and the greater than 8 m s−1 . The 14 January ASD shown in Figure 1 (Lowenstein CCN distribution. Concentrations of giant and ultragiant aerosols were determined from FSSP measurements et al., 2010) was used as input in MAC3. The model was averaged over the long intervals, thus providing good initiated with the atmospheric sounding taken at Barbuda at c 2012 Royal Meteorological Society Copyright

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1718 UTC, 14 January (see Figure 4). Figure 5 shows radialheight diagrams of LWC, wind speed and direction and reflectivity calculated by the model every 3 min over a period of 15 min. The altitude of the cloud base for the simulation was zCB ≈ 550 m and the average cloud-top ascent rate was 2.6 m s−1 , values which are similar to the observed values of approximately 500 m and 2.2 m s−1 (measured with the radar), respectively. The maximum updraught speed slightly above cloud base at 4 min was approximately 5 m s−1 , which is about the same as the maximum updraught speed measured slightly above cloud base. These values only show that the model produces a sensible cloud. The maximum model value of concentration of cloud droplets at this time was 160 cm−3 , but this increased to about 220 cm−3 a minute later, which is similar to the maximum number concentration of droplets measured by the FSSP. The model cloud top is at an altitude of about 1.6 km at 7 min (Figure 5). The maximum updraught speed is 6 m s−1 in the centre of the cloud and a downdraught of −1.5 m s−1 has developed at the edge of the cloud. The maximum value of LWC (in the cloud core on the axis of the model; R = 0 km) is about 1.5 g kg−1 . In the comparison between observations and model radar reflectivity discussed below, model values at R = 420 m are used. The cloud at this location is still well within the updraught, but the liquid water content is much reduced from the value in the core, due to entrainment. The values of LWC and w are closer to the observations. By 10 min, the cloud top has ascended to about 2.4 km. The values of w and LWC in the cloud core are about

9 m s−1 and 2.9 g kg−1 , respectively, while the maximum reflectivity is 15 dBZ. The concentration of droplets and the liquid water content, and hence the reflectivity, decrease with radial distance from the core of the cloud as a result of entrainment. The maximum values of LWC and w at 10 min at R = 420 m are about 2.1 g kg−1 and 5 m s−1 , respectively. The reflectivity in the model cloud is 35 dBZ at 13 min and z ≈ 2 km, and the contours have started to descend towards the surface. The value of LWC in the core of the cloud has reached a peak of about 2.3 g kg−1 while at R = 420 m it is about 1.2 g kg−1 . By 16 min, the core values of w and LWC have decreased to 5 m s−1 and 1.4 g kg−1 , respectively, while at R = 420 m they are about 1 m s−1 and 0.3 g kg−1 , respectively. The cloud top reached its maximum altitude of 3.2 km and the reflectivity in the core reached a magnitude of about 45 dBZ at z = 1.25 km. Observations of the time rate of change of radar reflectivity were made by the SPolKa radar in a cloud tracked from 2002:10 to 2052:10 UTC on 14 January 2005. Figure 6(a) shows the resulting time–height diagram constructed from the maximum reflectivity values in the cloud during PPI scans. The diagram begins when the radar top is at its minimum altitude. The reflectivity is likely dominated by Bragg scatter (most often produced by fluctuations in water vapour; Baker and Brenguier, 2007) for Z < 10 dBZ (Knight and Miller, 1993), so comparisons with model-produced Rayleigh reflectivity (dependent on the concentration and sixth power of the size of the drops) cannot be made for times less than about 8 min. The maximum rate of increase in radar reflectivity during this time period at 2 km is approximately 15–30 dBZ from one observation point to the next: a time period of about 4.5 min thus a rate of 3.3 dBZ min−1 . However, the value determined from the interpolation scheme used to produce Figure 6(a) suggests a greater value of about 5 dBZ min−1 . The reflectivity subsequently increased to a value of 45 dBZ at 20 min between about 0.5 and 2 km. The time–height diagram of model-produced radar reflectivity at radius R = 420 m is shown in Figure 6(b). As described above, the cloud properties reproduced by the model are similar to those observed in clouds penetrated on this day, although the value of LWC is greater in the model for a few minutes of the simulation, which might have caused the rates of increase of reflectivity to be greater (Twomey, 1966). Also, it is important to note that although model diagnostics show there is very little horizontal transport of the particles from the high liquid-water core to the cloud at R = 420 m, it cannot be completely ruled out. As shown in Figure 6, the two-dimensional model is able to reproduce (i) the general shape of the observed radar reflectivity time–height diagram, (ii) the altitude of the first occurrence of the 15 dBZ echo (z ≈ 2 km) and (iii) the maximum reflectivity (45 dBZ). The model rate of increase of reflectivity at R = 420 m, in the development stages (15–30 dBZ) when raindrops are just beginning to form, is greater than but comparable to the observations. At 420 m radial distance, the reflectivity increases from 15–35 dBZ in about 4 min, giving a rate of approximately 5 dBZ min−1 . This is larger than the observed rate of about 3.3 dBZ min−1 . The reason for this is most likely to be the greater value of model LWC compared with the observations. The rate of increase of reflectivity increases towards the centre of the model (R = 0 m) due to the increasing values of LWC.


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Figure 2. Liquid water content values calculated from the FSSP measurements made on the NCAR C130 in many different clouds on 14 January 2005 (crosses) with the liquid water content in an adiabatic parcel superimposed (solid line).

Figure 3. Vertical wind speed measured by the NCAR C130 in clouds sampled on 14 January 2005.


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Figure 4. Skew-T, log p sounding made by a radiosonde launched from Spanish Point, Barbados on 14 January 2005 beginning at 1718 UTC. The left-hand curve is dew-point temperature and the right-hand curve is temperature.

The profiles and maximum values of LWC and w measured on 9 December were similar to those measured on 14 January. The model was initiated with the atmospheric sounding taken at Barbuda on 9 December 2005, which was similar to the 14 January sounding (Figure 4) and the ASD measured on 9 December in the boundary layer during the 60 km circles was used as input for the model (see Figure 1). The altitude of cloud base in the simulation was zCB ≈ 550 m and the average cloud-top ascent rate was 2.6 m s−1 . The maximum model updraught speed slightly above cloud base was approximately 2 m s−1 , which is significantly less than the value in the 14 January simulation but similar to the measured value on this day. The maximum model value of concentration of cloud droplets was about 160 cm−3 , which was greater than the maximum value of 100 cm−3 measured by the FSSP. The maximum value of LWC at R = 0 km was about 2.5 g kg−1 near the top of the model cloud, which was greater than the maximum observed value

on the day. The maximum updraught speed is 7.5 m s−1 in the centre of the cloud, which is similar to the observed maximum updraught speed of 6 m s−1 . Parameter values at R = 180 m were smaller than at the core of the cloud, as expected. The maximum values of LWC and w at a model time of 10 min and R = 180 m are 2.2 g kg−1 and 6 m s−1 , respectively. Observations of the time rate of change of radar reflectivity were made by the SPolKa radar in a cloud tracked from 1825–1850 UTC on 9 December 2004. Figure 9(a) shows the resulting time–height diagram constructed from the maximum reflectivity values in the cloud during PPI scans. The observation points are coarser in vertical distance than for the 14 January case, because the cloud was further from the radar. They are separated by about 4 min in time and a vertical distance of just under 1 km. Inspection of the raw points suggests that the first 20 dBZ echo would most likely have occurred at an altitude of z ≈ 2.0 km at about 1835 UTC. The initial growth clearly occurred between points at about 12–15 min (Figure 9(a)). The slope of the 20–30 dBZ echo contours is almost vertical instead of slanted, most likely due to the poorer vertical resolution. The rate of increase in reflectivity ranges from about 2–3 dBZ min−1 . The model-produced time–height diagram of radar reflectivity is shown in Figure 9(b) for a radial distance R = 180 m. The rate of increase in reflectivity during the development stages is similar to the observations. There are some differences in the shape of the radar reflectivity echo, the reasons for which are largely discussed above. The model 20 dBZ radar reflectivity echo is first produced at z ≈ 2.5 km, which is slightly above the likely first location of the 20 dBZ echo in the observed cloud. The maximum reflectivity was about 40 dBZ, which is the same as the observations. The reflectivity increases from 20–30 dBZ at a rate of about 4.0 dBZ min−1 at R = 180 m. Figure 10 shows the DSDs observed in updraughts near the tops of different clouds at altitudes of 805 m, 1.5 km, 2.1 km and 2.6 km. The DSDs at the upper two levels are broad, extending to precipitation-sized drops. Figure 11 shows DSDs produced by MAC3 at the same altitudes as the observations and times given in the figure. The two later times were chosen, since the points were near the top of the model cloud and reflectivity values were


Q. J. R. Meteorol. Soc. 139: 20–31 (2013)

Note that the model reflectivity echo decays faster for t 17 min compared with the observed reflectivity values. This is due to a downdraught in the model cloud at R = 420 m which begins to develop at t = 17 min. Figure 7 shows the DSD measured by the aircraft in updraughts near the tops of different clouds on this day. The evolution of the DSD with increasing altitude is evident: the tail extends out to larger sizes as altitude increases. Figure 8 shows DSDs produced by MAC3 at the same three altitudes as in the observations and times indicated in the figure. Growth is mainly by condensation up to z = 1.33 km. Growth by collision and coalescence has occurred by z = 2.0 km, which is similar to the observations. The tails of the DSDs at 10 min extend out to diameters of about 1 mm at dN/d log D = 10−5 cm−3 . The model is able to reproduce the large-size tail of the observed DSD from d ∼ 70 µm to precipitation-sized drops. Rayleigh reflectivity calculated from each of these DSDs (Z ∼ 30 dBZ) compares well with the reflectivity measured by the radar at this point in time and space (Figure 6(a)). As mentioned above, the effect of entrainment is to decrease the size and concentration of the largest drops. 4.2. Case 2: 9 December 2004

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Figure 5. Contours of MAC3 values of liquid water content (thick lines) and reflectivity (thin lines) combined with wind vectors as a function of height and distance from the model axis from the 14 January 2005 run for 3 min intervals beginning at t = 4 min. The wind-speed scale is indicated in (a). The lowest value of LWC contour is 0.1 g kg−1 . Subsequent contours are 1, 2, 3 and 4 g kg−1 . Contours of reflectivity begin at −20 dBZ and increment by 10 dBZ.

comparable with the observations (Figure 9). It is possible to explain the development of the DSD up to about 1.5 km when condensation dominates. The tail of the DSD at 2.6 km, t = 25 min agrees quite well with the tail of the observed DSD. However, the size distribution between about

100 µm and 1 mm at z = 2.1 km, t = 24 min has lower concentrations than for the observations. It is possible, since the tail of the observed DSD at z = 2.1 km overlaps that observed at z = 2.6 km, that drops have fallen from a higher level.


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Figure 6. Time–height diagrams comparing the evolution of maximum reflectivity in a cloud observed on radar and produced by a two-dimensional axisymmetric cloud model. (a) Time–height diagram of observed maximum reflectivity from the SPolKa radar on 14 January 2005. The encircled colours indicate the location in time and space, and also the actual reflectivity where an observation was made. The solid black cross represents the location in space and time where and when the NCAR C130 aircraft penetrated the cloud. (b) Same as (a) except showing the evolution of reflectivity plotted at a radial distance of 420 m from the centre of the model cloud.

Figure 7. Overlay of selected observed DSDs at several altitudes for different clouds penetrated on 14 January 2005. The DSDs were measured at 805 m (A), 1.3 km (B) and 2.0 km (C). The gap in curve B occurs where there is a change of probe.

Figure 8. Overlay of model DSDs for a radial distance of 420 m from the model axis at z = 805 m, t = 4 min (dashed line), z = 1.3 km, t = 7 min (dotted line) and z = 2.0 km, t = 10 min (solid line).

the development stage of the cloud when the updraught has ceased and the liquid water content has decayed, the embryonic raindrops would not be able to grow. 5. Sensitivity studies Removing the aerosol size particles from the ASD with sizes larger than r = 0.5 µm had an insignificant effect on In this section, the concentration of CCN is varied and the rate of increase of reflectivity for values greater than the influence of giant and ultragiant aerosol particles is −10 dBZ, or on the maximum value in the standard 14 Janexamined. Figure 12 shows the effect on the concentration uary run, at the core and also at R = 420 m where LWC was of raindrops and reflectivity of increasing the concentration lower (not shown). This seems contradictory to the results of of all CCN used in the 14 January case by a factor of 7. Jensen and Lee (2008). However, there are two points. Firstly, The maximum reflectivity is similar to that attained in the the DSD calculated by MAC3 for this run was significantly standard run. However, the rain forms and falls to the ground different in the large-end tail in the lower part of the cloud about 3 min later. Rain is not significantly suppressed, but early in the run compared with the standard run. This was delayed. The main effect of the increase in concentration of not true at 10 min, higher in the cloud. Secondly, the equivCCN is that the rain lasts for a significantly shorter period of alent reflectivity in the calculations of Jensen and Lee (2008) time: the 30 dBZ echo intersects the ground for about 10 min was much less (approximately −13 dBZ) than the values in less than in the standard run. The dynamics of the cloud are the clouds discussed herein. There was a different result in important, as highlighted by Burnet and Brenguier (2010). the run with a large concentration of CCN and no GA or If the production of precipitation were delayed beyond UGA (Figure 13): the intensity of precipitation decreased c 2012 Royal Meteorological Society Copyright

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Figure 9. Time–height diagrams comparing the evolution of maximum reflectivity in a cloud observed on radar and produced by a two-dimensional axisymmetric cloud model. (a) Time–height diagram of observed maximum reflectivity from the SPolKa radar on 9 December 2004. The encircled colours indicate the location in time and space and also the actual reflectivity where an observation was made. The solid black cross represents the location in space and time where and when the NCAR C130 aircraft penetrated the cloud. (b) Same as (a) except showing the evolution of reflectivity plotted at a radial distance of 420 m from the centre of the model cloud.

Figure 11. Same as Figure 8 but for 9 December 2004. The curves are z = 830 m, t = 10 min (dashed line), z ≈ 1.5 km, t = 14 min (dotted), z = 2.1 km, t = 24 min (thin solid) and z = 2.6 km, t = 25 min (thick solid). Figure 10. Same as Figure 7 but for 9 December 2004. The DSDs were measured at z = 833 m (A), 1.5 km (B), 2.1 km (C) and 2.6 km (D).

on two days during RICO off Antigua in the Caribbean. Unique statistical observations were made during RICO and the rain was delayed and it persisted for a shorter period of the sub-cloud and cloud parameters (Rauber et al., of time. The results of this sensitivity study are consistent 2007) with the NCAR C130 aircraft and SPolKa radar. with findings reported by Johnson (1982), Feingold et al. These observations were compared with the results from (1999) and Zhang et al. (2006), as discussed in the Introduc- MAC3, an axisymmetric, bin-resolved cloud microphysics tion. We conclude from these sensitivity simulations that the model that includes sedimentation. The results of the giant and ultragiant aerosol particles are not important in comparisons strongly suggest that the warm rain process the development of warm rain in these RICO clouds. How- in these relatively shallow, maritime clouds is a relatively ever, the results might be different for lower LWC values simple process of condensational growth of droplets formed than were possible in the model used in this study. on the sub-cloud aerosols, followed by stochastic collision and coalescence. Turbulent enhancement was not included 6. Summary and discussion in the model calculations. The result was found by Twomey (1966) almost 50 years ago using a simpler model. It is An analysis has been presented of the development of similar to the result found by Pawlowska and Brenguier warm rain in relatively shallow maritime clouds observed (2003) for stratocumulus clouds and lends support to their c 2012 Royal Meteorological Society Copyright

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example. They found that a broader DSD was produced by an ensemble average of trajectories than a single trajectory, showing the importance of the variability. The broadening is a result of increased supersaturation in updraughts with reduced concentrations of drops due to entrainment. Their results agreed with those of Jensen and Lee (2008) in showing that the growth of the largest drops was dependent on the concentration and size of drops in the main peak of the DSD. It is likely that the effects found by Cooper et al. (2011) would be much smaller in the shallower RICO clouds, which contained significantly fewer cloud drops. The results of this study represent a step forward in the long pursuit of explaining the warm rain process. Acknowledgements Figure 12. Maximum values produced by the MAC3 model run of the 14 January case with 7× aerosol loading as a function of time and height of (a) the concentration of raindrops (m−3 ), with a max value of 1379 l−1 , and (b) reflectivity (dBZ), with a max value of 51.4 dBZ. Contours are on a logarithmic scale of 1, 100, 500 and 1000 m−3 for (a) and −10 to 50 dBZ in increments of 10 dBZ for (b).

The authors thank the many people involved in RICO, particularly Drs Robert Rauber, Bjorn Stevens, Harry Ochs III and Charles Knight, for leading the project and for all the work involved in making it happen. We are grateful to Al Schanot, David Rogers, Jørgen Jensen and other scientists in EOL and NCAR for assistance with the NCAR C-130 data. We also thank Drs William Cooper, Jørgen Jensen, Sonia Lasher-Trapp and Justin Peter for many discussions and for providing much insight into the research. We are very grateful to Drs Lindsay Bennett and Ian Brooks, who provided expert help with many of the diagrams. We are very grateful to Dr Jean-Louis Brenguier and anonymous reviewers for providing critical reviews that improved the article. The second author acknowledges financial support provided by the Overseas Research Students Award Scheme (ORSAS). This work was supported by the Natural Environment Research Council under grant number NER/A/S/2003/00360. Data provided by NCAR/EOL under sponsorship of the National Science Foundation. http://data.eol.ucar.edu/ References

Figure 13. Same as Figure 12, but with the ASD cut at d = 1 µm. Maximum values of concentration of raindrops and reflectivity are 1485 l−1 and 49.8 dBZ.

parametrization of the precipitation process in boundarylayer clouds. However, giant and ultragiant aerosols were found to be unimportant for the formation of warm rain in the limited-sensitivity studies discussed here, even though they did affect the DSDs, as also found by Reiche and Lasher-Trapp (2010) and Minor et al. (2011). This is not inconsistent with the results of Jensen and Lee (2008), who performed accurate calculations of the development of raindrops in much shallower stratocumulus clouds. Entrainment and mixing is an integral part of the MAC3 model, but the net effect is to decrease the amount of warm rain in these relatively shallow maritime clouds, because of the reduced liquid water content. This highlights the issue raised by Twomey (1966) that the warm rain process is strongly dependent on the amount of cloud liquid water. Once embryos have been produced, the rate of growth can be significantly enhanced if high values are encountered even for periods of 1 min, as may occur, for example, if the particles move into high LWC cores of thermals (Blyth et al., 2005). The MAC3 model does not treat entrainment and mixing in as much detail as Cooper et al. (2011), for

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