Title Temporal variation of urban surface and air ...

Title

Temporal variation of urban surface and air temperature

Advisor(s)

Hui, SCM; Li, Y

Author(s)

Yang, Xinyan; 杨芯岩

Citation

Issued Date

URL

Rights

2013

http://hdl.handle.net/10722/195964

Creative Commons: Attribution 3.0 Hong Kong License

Temporal variation of urban surface and air temperature

Submitted by

YANG, Xinyan 杨芯岩

For the Degree of Doctor of Philosophy

Abstract of this thesis entitled

ABSTRUCT

Temporal variation of urban surface and air temperature Submitted by

YANG, Xinyan

For the Degree of Doctor of Philosophy Department of Mechanical Engineering at The University of Hong Kong in October, 2013

The urbanization process alters the radiative, thermal, moisture and aerodynamic characteristics of a surface, which significantly affect the surface energy balance within the atmospheric boundary layer. Such modifications can lead to the so-called urban warming phenomenon, where the extent and rate of urban surface and air temperature is substantially higher than the corresponding rural region, which has caused serious concern in recent decades. However, the understanding of the causes of urban warming is incomplete, and the same applies to lack of effective mitigation strategies. Therefore, in order to have a complete understanding of the formation of urban warming, the present thesis focusses on the estimation of temporal variations of urban surface and air temperatures by using numerical simulations, analytical methods and field measurements. To better understand the mechanism(s) of urban surface temperature variation, a three-dimensional model that incorporates the energy exchange processes is first developed for a realistically complex city. In order to reduce the computational effort for the radiation heat transfer calculation, the compressed row storage scheme is applied, which permits the rigorous consideration of multiple reflections in a realistic urban area with hundreds of buildings. i

The developed surface energy balance model is then used to investigate the effects of the urban canopy geometry on urban albedo and surface temperature. The average urban albedo is less for a moderately compact city having high rise buildings with varying building heights than other cases. A cooler urban street surface temperature with smaller amplitude and earlier occurrence of the daily maximum temperature is observed in a high rise compact city than a low-rise sparse city. In order to understand quantitatively the causes of urban air warming, a new analytical zero-dimensional urban air temperature model is also developed, which is able to capture the features of the urban temperature variation. Results show that solar heat gain, evapotranspiration and the anthropogenic heat affect the mean air temperature, while heat storage and thermal convection affect the amplitude and phase shift of the daily cycle. A high-rise, high-density city generates low surface temperature, resulting in low air temperature during the day. The main conclusion of this study is that on the condition rural air temperature cycle is given, the mean temperature of the urban air and surface temperature is determined by the net heat gain and ventilation rate, and the amplitude and phase can be obtained from thermal storage and ventilation rate. Essentially, the net heat gain, thermal storage and ventilation are affected by urban morphology, and hence a city thermal environment can be designed. (419 words)

ii

TEMPORAL VARIATION OF URBAN SURFACE AND AIR TEMPERATURE

BY

YANG, XINYAN

DEPARTMENT OF MECHANICAL ENGINEERING THE UNIVERSITY OF HONG KONG 2013

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY AT THE UNIVERSITY OF HONG KONG

SUPERVISOR: PROF. YUGUO LI CO-SUPERVISOR: DR. SAM C. M. HUI

iii

DECLARATION

I declare that this thesis represents my own work, except where due acknowledgement is made, and that it has not been previously included in a thesis, dissertation or report submitted to this University or to any other institution for a degree, diploma or other qualifications.

Signed

________________________________ YANG, Xinyan

iv

ACKNOWLEDGMENT I would like first to express my sincere gratitude to my supervisor Prof. Yuguo Li for the continuous support and guidance over the last four years. His tireless work enthusiasm, original perspective, critical thinking and immense knowledge affect me deeply. I really enjoy talking and discussing with him no matter on the issue of academic problem or philosophy of life. He is a wise man that I could always profit from listening to him. I also thank my co-supervisor, Dr Sam Hui for his support.

I am indebted to Mr. Wing Kam Leung and Mr. Kwok Hung Tam who share their wisdom and experiences to provide me professional technical support in my experiment. I also would like to thank Mr. Edward Tsui who helps me a lot to negotiate with the real estate management to obtain approval for a field experiment.

I have been blessed to work in our friendly and cheerful group which is full of talented and nice people. I would like to thank Dr. Jian Hang, Dr. Lina Yang, Dr. Zhiwen Luo, Ms. Xiaoxue Wang and Mr. Kai Wang who have studied related topics with me; sharing and providing their valuable suggestions and knowledge on my field experiments and theoretical modeling. My sincere thanks also go to Dr. Jian Gong, Dr. Xiaolei Gao, Dr. Li Liu, Ms. Jiayi Wu, Mr. Lei Zhang, Mr. Jianjian Wei, Ms. Shang Wang and Ms. Shi Yin, for the stimulating discussion, for all the fun we have had.

This thesis would have remained a dream had it not been for my parents and my husband, who have always encouraged me on my dreams, and who have provided me a warm home full of love.

v

LIST OF CONTENTS Abstract

…………………………………………………………………….i

Declaration

…………………………………………………………………...iv

Acknowledgment .....................................................................................................v List of contents …………………………………………………………………...vi List of tables

…………………………………………………………………...xi

List of figures …………………………………………………………………..xii Nomenclature ………………………………………………………………...xviii Chapter 1

Introduction ....................................................................................1

1.1

Research background .....................................................................1

1.2

Objectives and scope of this study.................................................3

1.3

Structure of the thesis ....................................................................4

Chapter 2 2.1 2.1.1

Literature review ............................................................................7 Urban surface temperature .............................................................7 Roles of urban surface temperature in urban boundary layer climate ............................................................................................7

2.1.2

Urban surface temperature related to land cover/land use .............8

2.1.3

Impact of urban surface temperature ...........................................10

2.2

Urban air temperature ..................................................................11

2.2.1

Urban warming and canopy layer urban heat island....................11

2.2.2

Impact of urban air temperature...................................................15

2.3

Urban energy balance ..................................................................16

2.3.1

Urban surface energy balance ......................................................16

2.3.2

Urban canopy layer energy balance .............................................17

2.4

Urban morphology .......................................................................19

2.5

Construction materials .................................................................21

2.6

Anthropogenic heat flux ..............................................................22 vi

2.7

Existing studies and limitations of urban radiation balance modeling ......................................................................................24

2.8

Summary ......................................................................................25

Chapter 3

Urban surface temperature distribution ........................................26

3.1

Introduction ..................................................................................26

3.2

A three-dimensional urban surface energy model .......................27

3.2.1

Radiation scheme .........................................................................29

3.2.1.1

Shape factor and Gebhart absorption factor ................................29

3.2.1.2

Compressed row storage scheme .................................................30

3.2.1.3

Solar radiation calculation ...........................................................32

3.2.1.4

Longwave radiation model ..........................................................33

3.2.2

Convection model ........................................................................33

3.2.3

Heat conduction model ................................................................34

3.3

Model validation ..........................................................................36

3.3.1

Validation of the shape factor ......................................................36

3.3.2

Validation of the conduction sub-model ......................................36

3.3.3

Validation of the full model .........................................................37

3.4

Discussion ....................................................................................44

3.5

Summary ......................................................................................47

Chapter 4

Impact of urban morphology on urban albedo and urban surface temperature ..................................................................................48

4.1

Introduction ..................................................................................48

4.2

Model description ........................................................................49

4.2.1

Urban albedo calculation .............................................................50

4.2.2

Validation of the albedo calculation ............................................50

4.3

Scenario description .....................................................................53

4.3.1

Location description and meteorological data .............................53

4.3.2

Scenario description .....................................................................54 vii

4.4 4.4.1

Results and discussion .................................................................56 Scenario A - Building density ( H / L = 1 , plan area index

λ p = 0 - 0.79 ) ..............................................................................56 4.4.2

Scenario B - Building height (plan area index λp = 0.44 , H / W = 1 - 6 ) ..............................................................................61

4.4.3

Scenario C - Building stagger arrangement (plan area index

λp = 0.44 , H1 / W = 6 and H1 / H 2 = 6 : 1 - 6 : 6 ) .......................64 4.4.4

Relationship between sky view factor and street surface temperature ................................................................................ .68

4.4.5

Relationship between the average urban albedo and the surface temperature of the urban area ......................................................71

4.5

Surface temperature observation .................................................71

4.6

Summary ......................................................................................73

Chapter 5

Surface temperature distribution in an ideal courtyard ................75

5.1

Introduction ..................................................................................75

5.2

Energy balance of the courtyard air .............................................76

5.3

Results ..........................................................................................79

5.3.1

Base line scenario ........................................................................79

5.3.2

Effect of thermal mass .................................................................87

5.3.3

Effect of material conductivity ....................................................88

5.3.4

Effect of surface albedo ...............................................................91

5.3.5

Effect of courtyard height ............................................................92

5.4

Discussion ....................................................................................94

5.5

Summary ......................................................................................96

Chapter 6

The impact of urbanization on the urban air temperature ............97

6.1

Introduction ..................................................................................97

6.2

Zero-dimensional city air temperature model (zero-CAT) ..........98

viii

6.2.1

Model description ........................................................................98

6.2.2

Analytical solution .....................................................................101

6.2.3

Urban heat island intensity ........................................................102

6.3

Model validation ........................................................................103

6.3.1

Site description and meteorological data ...................................103

6.3.2

Validation result .........................................................................104

6.4

Results ........................................................................................106

6.4.1

Canopy geometry .......................................................................108

6.4.2

Construction material .................................................................110

6.4.3

Anthropogenic heat ....................................................................112

6.4.4

Air pollution ...............................................................................112

6.5

Discussion ..................................................................................112

6.5.1

Phase shift ..................................................................................113

6.5.2

Amplitude ..................................................................................116

6.6

Summary ....................................................................................117

Chapter 7

Effect of urban morphology on the urban air temperature .........119

7.1

Introduction ................................................................................119

7.2

Model description ......................................................................121

7.2.1

Improvement of the zero-CAT model .......................................121

7.2.2

Validation of the improved model .............................................123

7.3

Results and discussion ...............................................................127

7.3.1

Effect of urban geometry with constant airflow rate and without anthropogenic heat .....................................................................129

7.3.2

Effect of urban geometry with varied airflow rate and without anthropogenic heat .....................................................................134

7.3.3

Effect of urban geometry with varied airflow rate and anthropogenic heat .....................................................................139

7.3.3.1

Anthropogenic heat emission by transportation ........................140 ix

7.3.3.2 7.4

Anthropogenic heat emission by buildings ................................142 Traverse experiment ..................................................................144

7.4.1

Experiment description ..............................................................145

7.4.2

Results and discussion ...............................................................149

7.5 Chapter 8

Summary ....................................................................................154 Conclusions ................................................................................156

8.1

Conclusions ................................................................................156

8.2

Limitations and future work ......................................................158

References

…………………………………………………………………160

Appendix Performance of the new storage scheme .............................................184 List of publications ..............................................................................................186

x

LIST OF TABLES Table 3.1 Summary of the statistical performance of the full model validation. RMSE values of the previous evaluation by the model TUF-3D also presented here. Description of each statistics can be found in Grimmond et al. (2010). ...................................................................................................41 Table 3.2 Performance comparison between the two simplified radiation calculation scheme a) by using realistic surface radiative properties; b) when the whole urban surfaces covered by white painting (albedo=0.61, emissivity=0.82). .......................................................................................46 Table 4.1 Urban canopy geometry of the study scenarios. ....................................55 Table 5.1 Input data for the modeling study. .........................................................80 Table 5.2 The difference Td  Tb between the peak/daytime (trough/nighttime) courtyard air temperatures Tb of the baseline case and Td with doubled values for the studied parameter. ...............................................................95 Table 6.1 Input parameters of Kowloon Peninsula for the numerical and analytical zero – CAT scheme..................................................................................105 Table 6.2 Urban are temperature changes by modified urbanization features. ...107 Table 7.1 The input parameters of Kowloon Peninsula in the summer time for the improved zero – CAT scheme validation. ...............................................125 Table 7.2 Four types of urban morphology. ........................................................128 Table 7.3 Prediction results for the LRLD and HRHD cases with a constant airflow rate and no anthropogenic heat. ...................................................130 Table 7.4 Parameters of the urban morphology and the predicted airflow rate for the LRLD case and HRHD case. .............................................................138 Table 7.5 Photographs and fisheye photos of five study areas (a) King’s Park Rise (KP), (b) Mong Kok, (c) Tsim Sha Tsui in which next to the Kowloon Park road (TST_KP), (d) Tsim Sha Tsui (TST) and (e) Tsim Sha Tsui East (TST_E). The sky view factor is the average value of each place. ..........150 Table 7.6 A summary of the statistics of the observed air temperature for six study areas on 16 and 17 September 2012. .......................................................151

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LIST OF FIGURES Figure 1.1 Research scope of this study. The boxes filled with blue and red color represent the approaches are applied in this thesis to analyze the impact of urbanization features on the canopy layer and surface layer urban warming, respectively. The purple box means such urbanization feature is involved in the analysis of both of the two urban warming types. .............................6 Figure 2.1 Annual averaged temperature trend for different cities (Data source: Hughes, 1991; Sala et al., 2000; Gaffin et al., 2008; Jones et al., 2008; Kataoka et al., 2008; HKO, 2012a). ..........................................................13 Figure 2.2 Annual mean temperature anomalies for the city of Beijing and Wuhan (Data Source: Ren et al., 2007). .................................................................14 Figure 2.3 Typical variation of (a) urban and rural air temperature, (b) cooling/warming rates, and (c) heat island intensity under ‘ideal’ weather condition (Oke, 1987). ...............................................................................14 Figure 2.4 Schematic illustration of the volumetric averaging approach to urban energy balance (Roberts et al., 2006). The energy balance of the canopy layer is Q * QF  QH  QE  QS  QA . Note the different notation: Q * is the net radiation; QH is the sensible heat flux; QE is the latent heat flux;

QS the storage; QA  Qin  Qout the advective flux; and QF the anthropogenic heat flux. ............................................................................18 Figure 3.1 (a) An example urban area calculated by the MUST scheme. The surrounded imaginary walls are not shown here for clarity. G is the heat conduction, S is the absorbed shortwave radiation and L is the longwave radiation. (b) Predicted surface temperature distribution at 10 a.m., 16 Jul 2009 in Hong Kong....................................................................................28 Figure 3.2 Compressed row storage scheme (modified after Smailbegovic et al. (2005)) which divided a two-dimensional sparse matrix into three onedimensional arrays AN , AJ and AI , represented the non-zero values of the spars matrix, the column position of the original matrix and the pointer, respectively. ...............................................................................................31 Figure 3.3 Comparison between the observed and calculated temporal surface temperature profiles. (a) Bare soil; (b) Asphalt. ........................................37 xii

Figure 3.4 The average (a) roof and (b) road diurnal surface temperature predicted by MUST for 15 August 1992, compared with the local and microscale observation results as well as TEB and TUF-3D models. .........................39 Figure 3.5 Observed and MUST simulated wall facets temperature (north-, south, west- and east- facing walls) profiles for the Vancouver light industrial site during a sunny period (YD 225-231, 1992). ..............................................39 Figure 3.6 Observed and MUST simulated energy balance components for the Vancouver light industrial site in 15 August 1992. ..................................41 Figure 3.7 RMES (W m-2) for (a) net all-wave radiation, (b) sensible heat flux and (c) heat storage by time of day, night and transition time periods. Squares and triangles are RMES S and RMES U , respectively. .................43 Figure 4.1 Definition of the urban geometry parameters.......................................49 Figure 4.2 Comparison of the simulation results by MUST scheme and the observation data according to Kanda et al. (2005a) for three kinds of plan area index in autumn (a) plan area index 0.25, (b) plan area index 0.44, and (c) plane area index 0.6. ......................................................................52 Figure 4.3 The occurrence of the hottest day of Hong Kong during the recent decades. ......................................................................................................53 Figure 4.4 Relationship between the average urban albedo and the plan area index of Scenario A in (a) summer and (b) winter. .............................................58 Figure 4.5 Relationship between the sky view factor and the plan area index of Scenario A..................................................................................................59 Figure 4.6 The percentage of street area being sunlit for different plan area index at solar noon of Scenario A in summer and winter....................................59 Figure 4.7 Street surface temperature in terms of the (a) average temperature, (b) phase shift, and (c) temperature amplitude for different plan area index of Scenario A in summer and winter..............................................................60 Figure 4.8 Relationship between the average urban albedo and the H / W ratio of Scenario B in (a) summer and (b) winter. ..................................................62 Figure 4.9 Street surface temperature in terms of the (a) mean temperature, (b) phase shift, and (c) temperature amplitude for different H / W of Scenario B in summer and winter. ............................................................................63

xiii

Figure 4.10 Relationship between H / W ratio and the sky view factor of Scenario B. ................................................................................................................64 Figure 4.11 Relationship between the average urban albedo and the abnormity extent ( H1 / H 2 ) of Scenario C in (a) summer and (b) winter. ...................66 Figure 4.12 Street surface temperature in terms of the (a) mean temperature, (b) phase shift, and (c) temperature amplitude for different abnormity extent H 1 / H 2 of Scenario C in summer and winter. ...........................................67

Figure 4.13 The relationship between the sky view factor and the street surface temperature, which in terms of the (a) mean temperature, (b) phase shift, and (c) temperature amplitude in summer and winter. ..............................70 Figure 4.14 Top: digital photo of the target district and the selected surface points 1-8 for showing the temperature profile. Middle: an infrared camera photo at 4:00 p.m. on 13 September 2010. Bottom: the temporal surface temperature profiles of the chosen surface points 1-8. ..............................72 Figure 5.1 The simple courtyard model. ................................................................77 Figure 5.2 Illustration of the heat transfer and ventilation process in the simple courtyard model. ........................................................................................77 Figure 5.3 The 3D surface temperature distribution [Baseline scenario, summer] (a) at 8 a.m., (b) 12 p.m., (c) 16 p.m., and (d) 20 p.m. ..............................81 Figure 5.4 The 3D surface temperature distribution [Baseline scenario, winter]. (a) 8 a.m., (b) 12 p.m., (c) 16 p.m., and (d) 20 p.m. ........................................82 Figure 5.5 Temporal thermal environment in the courtyard [Baseline scenario, summer] (a) Surface temperature and solar radiation, (b) Microscale heat island intensity. ..........................................................................................84 Figure 5.6 The diurnal variation of the ground surface heat flux [Baseline scenario, summer]. ....................................................................................................85 Figure 5.7 Temporal thermal environment in the courtyard [Baseline scenario, winter] (a) Surface temperature and solar radiation, (b) Microscale heat island intensity. ..........................................................................................86 Figure 5.8 The diurnal variation of the ground surface heat flux [Baseline scenario, summer]. ....................................................................................................87 Figure 5.9 The diurnal courtyard thermal environment under different material conductivity in summer. (a) courtyard air temperature (b) microscale heat xiv

island intensity. The peak and trough locations are shown by solid circles. ...................................................................................................................90 Figure 5.10 The diurnal variation of heat flux as affected by changing wall/ground-slab conductivity in summer, including net radiation (Qnet), conductive heat flux (Qcond) and convective heat flux (Qconv). .............91 Figure 5.11 The diurnal variation of temperature as affected by courtyard geometry (a) summer; (b) winter. The peak and trough locations are shown by solid circles. ...............................................................................93 Figure 6.1 Energy balance scheme of the city. ......................................................98 Figure 6.2 Performance of the numerical and analytical solution of zero-CAT model. ......................................................................................................105 Figure 6.3 Relationship between the non-dimensional number  and the phase shift with varied convective heat transfer number  and certain constant time  (   1.07 ). .............................................................................109 Figure 6.4 Relationship between the non-dimensional number  and the coefficient of temperature amplitude with varied convective heat transfer number  and certain time constant  (   1.07 ). ...........................110 Figure 6.5 Relationship between the time constant  and the coefficient of temperature amplitude with

constant

non-dimensional

number 

(   1.456 ). .............................................................................................111 Figure 6.6 Relationship between the time constant  and the phase shift with constant non-dimensional number  and convective heat transfer number

 (   1.456 ,   1.10 ). .........................................................................111 Figure 6.7 Relationship between the non-dimensional number  and the phase shift with varied convective heat transfer number  and certain time constant  (   3.66 ). ..............................................................................114 Figure 6.8 Relationship between time constant  and the phase shift with varied convective heat transfer number  and constant non-dimensional number

 (   1.456 ). .........................................................................................114 Figure 6.9 Relationship between the time constant  and the coefficient of temperature amplitude with varied convective heat transfer number  and constant non-dimensional number  (   1.456 )....................................117 xv

Figure 7.1 Illustration of the energy balance scheme of the city .........................121 Figure 7.2 Diurnal profile of anthropogenic heat in summer, similar to the study by Ichinose et al. (1999). .........................................................................126 Figure 7.3 Validation results of the improved zero-dimensional model. ............126 Figure 7.4 Diurnal air temperatures of four types of urban morphology with a constant airflow rate and no anthropogenic heat. ....................................131 Figure 7.5 Diurnal heat fluxes per plan surface area of four types of urban morphology with constant airflow rate and no anthropogenic heat: (a) Nature, (b) Concrete, (c) LRLD, and (d) HRHD. ....................................131 Figure 7.6 Diurnal surface temperatures of four types of urban morphology with constant airflow rate and no anthropogenic heat. ....................................133 Figure 7.7 Diurnal heat fluxes per total surface area of four types of urban morphology with constant airflow rate and no anthropogenic heat: (a) Nature, (b) Concrete, (c) LRLD, and (d) HRHD. ....................................134 Figure 7.8 Diurnal air temperatures of LRLD and HRHD cases with predicted airflow rate and no anthropogenic heat....................................................139 Figure 7.9 Hourly fractional traffic profiles for weekdays for US (Hallenbeck et al., 1997). .................................................................................................141 Figure 7.10 The air temperature with and without the anthropogenic heat emission by vehicles for LRLD case and HRHD case. ..........................................141 Figure 7.11 The air temperature with and without the anthropogenic heat emission by buildings for LRLD case and HRHD case. .........................................144 Figure 7.12 Map of Hong Kong and study area of Kowloon Peninsula ..............147 Figure 7.13 Detailed diagram of vehicle equipped with sensors (Temperature sensor, CO sensor and Radiometer). ........................................................147 Figure 7.14 The route of the survey and six study areas which are King’s Park Rise (KP), Mong Kok, Tsim Sha Tsui in which next to the Kowloon Park road (TST_KP), Tsim Sha Tsui (TST), Tsim Sha Tsui East (TST_E) and flyover. .....................................................................................................148 Figure 7.15 Observed air temperatures in the six study areas for two days (16 and 17 September 2012). ................................................................................151 Figure 7.16 . Observation results of the air temperature declination from sunset 6:00 p.m. at the day 16 September to the sunrise 6:00 a.m. at the day 17

xvi

September. The vertical axis shows the measured air temperature at a certain hour minus the air temperature at 6:00 p.m. the sunset. ..............152

xvii

NOMENCLATURE A

surface area or plan area of urban [m2]

Af

roof area [m2]

An

natural surface area [m2]

Ap

pavement area [m2]

At

total urban surface area [m2]

cb

specific heat of building material [J kg-1 K-1]

cM

heat capacity of wall materials or soil [J kg-1 K-1]

cp

heat capacity of air [J kg-1 K-1]

cr

specific heat of road material [J kg-1 K-1]

dn

day number of the year [-]

D

thermal diffusivity [m2 s-1]

E

heat source [J]

Et 0

the measured evapotranspiration [m]

E0

eccentricity correction factor of the earth’s orbit [-]

Fij

shape factor [-]

Fsky

sky view factor of the urban [-]

G ij

Gebhart absorption factor [-]

h fg

latent heat of water vapor [J kg-1]

hin

convective heat transfer coefficient at interior surfaces [W m-2. K-1]

hrad

radiation heat transfer coefficient [ W m2 K-1]

hurban

urban control volume height [m] xviii

h0

exterior convective heat transfer coefficient [W m-2. K-1]

I df

diffuse solar radiation [W m-2]

I dr

direct solar radiation [W m-2]

I sc

solar constant (=1367) [W m-2]

k

thermal conductivity [W m-1 K-1]

kb

thermal conductivity of the building [W m-1 K-1]

kr

thermal conductivity of the road [W m-1 K-1]

m

mass of the urban material [kg]

n

air change rate per second [s-1]

N

air change rate per hour [h-1 or ACH]

N  N

number of rays in polar and azimuth angle, respectively [-]

P

proportion of road surface area to the total urban surface area [-]

1 P

proportion of building surface area to the total urban surface area [-]

Pat

transmittance of atmosphere [-]

q

ventilation flow rate [m3 s-1]

qanthro

anthropogenic heat flux, [J m-2]

qcond

conductive heat flux, [J m-2]

qconv

convective heat flux, [J m-2]

qevp

evapotranspiration heat flux, [J m-2]

q rad

long wave radiation heat flux, [J m-2]

qsol

solar radiation heat flux, [J m-2]

Q

energy leaving black surface Ai [W]

Qij

total energy leaving black surface Ai that reaches surface Aj [W] xix

t

time [h]

t dp

dew point temperature [℃]

tm

hour from midnight [h]

Tb

sub-surface temperature of the building [K]

TB

urban material temperature rise [K]

Tc

canopy air temperature [K]

TE

air temperature rise due to anthropogenic heat flux [K]

Tgrd

sub-surface temperature of the natural and pavement surface [K]

Ti

urban air temperature [K]

Tin

indoor air temperature [K]

Tinner

interior wall surface temperature [K]

Tr

sub-surface temperature of the road [K]

Ts

urban surface temperature [K]

Tsky

sky temperature [K]

Tsoil

monthly average soil temperature [K]

T0

rural or ambient air temperature [K]

Tco

heat island intensity between the canopy and ambient air [K]

U eff

effective wind speed [m s-1]

vi

mean urban wind speed [m s-1]

v0

mean rural wind speed [m s-1]

V

volume of an indoor space or a courtyard [m3]

xb

building wall depth where daily temperature variation is ignored [m]

xx

x r

road depth where daily temperature variation is ignored [m]

Greek symbols



surface albedo/urban albedo [-]

r

reference urban albedo [-]



canopy rotation angle [o]

s

slope of the surface [o]



heat transfer dimensionless number [-]



emissivity [-]



polar angle [o]

a

solar altitude [o]

 az

surface azimuth angle [o]

 in

solar incidence angle [o]

z

solar zenith angle [o]



reflectivity [-]

 air

air density [kg m-3]

b

building material density [kg m-3]

H O

water density [kg m-3]

M

density of wall materials or soil [kg m-3]

r

road material density [kg m-3]



convective heat transfer number [-]



Stefan-Boltzmann constant (=5.669×10-8) [W m-2 K-1]



time constant [h]



azimuth angle [o]



solar azimuth [o]

2

xxi



absorptivity [-]

xxii

CHAPTER 1

INTRODUCTION

1.1 Research background Urbanization is the physical growth of urban areas as a result of the migration of villagers into cities to search for employment and a higher standard of living. One of the serious problems produced by the urbanization process is the distinct urban climate due to the replacement of natural land surface by artificial structures including roads, buildings and other infrastructure, along with the anthropogenic heat and pollution emission from buildings, transportation and human activities, (Oke, 1997; Grimmond, 2007). The airflow, energy and water exchanges are modified. When wind passes through an urban area, the buildings act as blocks to alter the wind profile and reduce the wind speed in the canopy (Britter & Hanna, 2003; Hang et al., 2009). The downward transport of momentum by turbulent stress dominantes the exchange in the urban canopy (Belcher et al., 2003; Coceal and Belcher, 2004). The relatively poor urban ventilation dilutes and removes inefficiently the heat and pollution generated by the urban area. Another well-known urban effect on the local climate is urban warming. The extent and rate of temperature increase is substantially larger than in non-urban areas, which means the urban surface temperature and near-surface air temperature is almost always warmer than the surrounding rural areas (Oke, 1973). Many observations verified the phenomenon with different urban features in different parts of the world, from the low-rise and low-density village of Barrow, located in the Arctic (Hinkel et al., 2003), to high-rise and high-density cities such as Hong Kong, which experience a monsoon-influenced humid subtropical climate (HKO, 2012a). The urban surface is the only medium to absorb solar radiation at city scale, and it then warms up the air by sensible heat transfer. The surface temperature could be extremely high in summer time, especially for desert areas, e.g. the asphalt surface temperature can reach 68 oC in Phoenix, Arizona (Harrington et al., 1995) and nearly 60 oC in Haifa (Swaid and Hoffman, 1989). The urban surface temperature may threaten the health of humans as well as being a thermal comfort issue. An early study conducted by Moritz and Henriques (1947)

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pointed out that a surface temperature of 44 oC is critical in the causation of hyperthermic edema in that six hours contact may produce a second-degree burn. Many studies have reported that, in summer, contact between feet and urban surfaces may cause burns which can be serious enough for people to be admitted to hospital. These patients mainly fall in the categories of children, the incapacitated, restrained, or sensory deficient (Harrington et al., 1995; Al-Qattan, 2000; Sinha et al., 2006). Also, such high surface temperatures may threaten the safety of urban residents, since the road surface temperature is hot enough to melt asphalt, and car accidents are caused by this problem every year. Furthermore, vehicle tires age faster in such a hot environment, which makes them more prone to catastrophic failure (NHTSA, 2013). Same as the urban surfaces, the urban air also experience warmer temperature than its surrounding rural counterpart, which has a serious impact on the health and comfort of the urban inhabitants. Previous studies reveal that the risk of contracting infectious diseases is increased due to urban warming (Khasnis and Nettleman, 2005). These diseases include the herpangina and hand-footmouth disease (Urashima et al., 2003), the vector-borne disease (Githeko et al., 2000) and so on. People also believe that the heat is related to mortality as it causes heat exhaustion, heat cramps, heart attacks and stroke (Kilbourne, 1997; McMichael et al., 2002). The underlying physical causes of urban warming are complex. The urbanization process alters the radiative, thermal, moisture and aerodynamic characteristics of the surface, which significantly impact the surface energy balance within the atmospheric boundary layer. Therefore, understanding the surface energy balance of an urban area, and making a comparison with pre-urban, more practically the rural area is the key to improving the knowledge of the physical mechanisms behind urban modification, and further solving the urban warming problem. Extensive studies have been devoted to such complex underlying physical causes of urban warming by numerical and experimental approaches (Arnfield, 2003; Rizwan et al., 2008; Fujibe, 2011). Many studies have been devoted to develop a surface energy balance model for different applications (Grimmond, 2010), most of which aim to couple with a mesoscale atmospheric model for

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accurate weather forecasts and climate change information (Masson, 2000; Kusaka et al., 2001; Martilli et al., 2002). Only a few focus on microscale temporal distributions of urban surface temperature (Krayenhoff and Voogt, 2007; Asawa et al., 2008). The temperature distrubution is highly inhomogeneous. Thus, the major obstacle for model development at the microscale is the quadratic memory requirement in radiation calculation for the surface temperature prediction. Also, the affecting parameters are too numerous, for example, the external weather, the built structure, the anthropogenic factors and so on. Thus, full consideration of the energy balance model is always complicated, which can not lead to a simple result for in depth analysis. Above all, scientific understanding of the causes of urban warming remains incomplete; and the reason is the lack of an effective and simple strategy to analyze clearly the causes of urban warming (Arnfield, 2003; Hamdi and Schayes, 2008). Therefore, we carried out this study in an attempt to improve our understanding of the urban surface and air temperature variation profiles for different urban features using the knowledge of the energy balance at urban surfaces, and further establish a better understanding of the urban warming phenomenon. We are mostly interested in the parameters in the design and operation of a city. The findings can be useful in both a) improving the knowledge of the mechanisms of the urban thermal environment, and b) providing suggestions and solutions for urban planning to take advantage of urban features to achieve a sustainable development of the city.

1.2 Objectives and scope of this study The presented study is devoted to providing a further understanding of the urban warming phenomenon by analyzing the urban surface and air temperature variation profiles for different urban features with the knowledge of the energy balance of the urban area. Various methods are involved in the study, including numerical simulation, theoretical analysis and field measurements in order to analyze and quantify the impact of different design parameters on urban thermal environment. It is expected that the outcome can provide effective design and prediction tools as well as establish optimum mitigation strategies for a better thermal environment of the urban area.

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These are the specific objectives of this study: 1.

To numerically simulate the temporal surface temperature distribution for a group of buildings;

2.

To investigate the relationship between the urban albedo and surface temperature variation profile with the urban morphology;

3.

To mathematically model the urban air temperature with the consideration of the urban characteristics;

4.

To understand the relationship between the urban air temperature and the urban morphology;

5.

To measure the urban surface and air temperature variation for different urban regions.

1.3 Structure of the thesis The work reported in this thesis is a result of efforts to gain better understanding of the temporal variation of urban surface and air temperature. Figure 1.1 shows the possible methodologies for studying the impact of urbanization on the urban warming phenomenon, and the blocks with a colored background represent the strategies used, which include numerical models, field experiments and remote sensing, as well as corresponding features of urbanization for analysis. This thesis contains of eight chapters, which are summarized as follows: Chapter 1 introduces the background and the significance of the study, and also provides an overview of the thesis. Chapter 2 gives a brief summary of previous studies on relevant topics. Chapter 3 introduces a three-dimensional urban energy model for predicting and understanding surface temperature distribution. Chapter 4 describes the impact of canopy geometry on urban albedo and surface temperature, especially for high-rise and high-density urban morphology. Chapter 5 focuses on predicting and understanding the temporal threedimensional exterior surface temperature distribution in an ideal courtyard. Chapter 6 builds a zero-dimensional City Air Temperature (zero-CAT) model to analyze the urbanization impact on the urban heat island effect. 4

Chapter 7 investigates the effect of urban morphology on the urban air temperature by using an improved zero-dimensional City Air Temperature model (zero-CAT) and field experiment. Chapter 8 draws the conclusions of the study and also outlines future work.

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Figure 1.1 Research scope of this study. The boxes filled with blue and red color represent the approaches are applied in this thesis to analyze the impact of urbanization features on the canopy layer and surface layer urban warming, respectively. The purple box means such urbanization feature is involved in the analysis of both of the two urban warming types. 6

CHAPTER 2 2.1

LITERATURE REVIEW

Urban surface temperature

2.1.1 Roles of urban surface temperature in urban boundary layer climate The urban surface temperature is one of the most important parameters in the study of urban climatology. The sun is the sole heat source of the EarthAtmosphere system. After absorption and reflection by clouds and atmosphere, nearly half the solar energy reaches the Earth’s surface, leading to a rise in the ocean and land surface temperatures, and further affecting the air temperature and the energy exchanges of the lowest part of the urban atmosphere. The modification of the surface arises from the introduction of artificial surface characteristics due to urbanization leading to changes in radiative, thermal, moisture and aerodynamic properties in the urban area compared to the rural surroundings (Oke, 1987; Voogt & Oke, 2003). Such extensive transformation may give rise to micro, local or even mesoscale changes in climate, for example, the thermal and wind environment of the boundary layer, precipitation patterns, ecological environment and so on. Compared with the surrounding rural area, the urban areas generally provide warmer surface conditions, which are defined as the urban surface heat island. The first observation of urban surface heat island was conducted by Rao (1972) by low resolution satellite imaging. Since then, various thermal infrared remote sensing methods of different platforms, e.g. satellite, aircraft and ground based were used to make observations of urban surface heat island. Although Roth et al. (1989) suggested that bias may exist due to the viewing restrictions of the urban surface structure by the instrumentation which was further confirmed by other studies (Voogt, 1995; Voogt and Oke, 1998; Roth, 2012), previous research found that the magnitude of the urban surface heat island is related to the season and time of day. The greatest intensity always occurs in the warm season during daytime, in particular during calm, clear days, especially for large, flat roof buildings or open areas, and lowest intensity occurs at night (Roth et al., 1989; Voogt, 1995; Hung et al., 2006; Wang et al., 2007). However, some studies found that the intensity of the daytime urban surface heat island was weak or even

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negative (Carnahan and Larson, 1990; Stathopoulou and Cartalis, 2009). This is probably because of the lag of urban surface warming due to the heat storage capacity of building materials, and also because of the use of rural areas for comparison since there is a relationship between the normalized difference vegetation index and the surface temperature (Gallo et al., 1993; Weng et al., 2004; Yuan and Bauer, 2007). In general, the urban surface heat island is a surface energy balance phenomenon, and many studies try to use a modeling approach to evaluate the generation mechanisms (Johnson et al., 1991; Oke et al., 1991). However, compared to the urban air heat island, less research has been carried out on urban surface heat island. The solar radiation warms the building fabric and ground surface, and the maximum temperature difference between the air and the building surfaces may reach 12-14 oC (Nakamura and Oke, 1988). Therefore, thermally induced airflow occurs, which develops from the temperature difference between the surface and ambient air. There is no doubt that the contribution of the buoyancy force is very dominant when the prevailing wind is absent (Kim and Baik, 2001; Luo, 2010). Relatively few studies have been devoted to this aspect by numerical, field experiment and laboratory approaches (Sini et al., 1996; Uehara et al., 2000; Kim and Baik, 2001; Xie et al., 2007). Recently, Yang and Li (2009) studied city ventilation due to thermal behavior of urban surfaces by measuring the temporal surface temperature distribution. The results illustrated that the city ventilation driven by the building thermal buoyancy in Hong Kong is very intense due to the large surface areas and high temperature differences with ambient air. Luo and Li (2011) further paid attention to the interactive structure of the slope flow and wall flow, and reached the conclusion that the buoyancy-driven flow system plays an important role in city ventilation. 2.1.2 Urban surface temperature related to land cover/land use The surface temperature on Earth can vary dramatically. The lowest natural temperature ever recorded on the surface of the Earth was -89.2 oC at the Soviet Vostok Station in Antarctica, on July 21, 1983, while the hottest spot in 2004 and 2005 was the Lut desert of Iran, which reached 70.7 oC (Hudson, 2008; NASA, 2006). The reasons for such differences in the surface temperatures are related to the weather condition, thermal physical properties of the surface, wind

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conditions, geometry and so on, all of which affect the energy balance of the surface (Nunez and Oke, 1977; Bärring et al., 1985; Dickinson, 1988; Swaid and Hoffman, 1990; Johnson et al., 1991; Herb et al., 2008; Swaid, 1993; Yang et al., 2012). Taha et al (1992) conducted a measurement of albedo and surface temperature for eight surfaces on a roof at Lawrence Berkeley Laboratory. The results indicated that high-albedo materials could have a large impact on surface temperature regime in that the surface temperature of typical roofing material was about 40 oC warmer than air, while there was a difference of only 5 oC for highalbedo coatings at solar noon. Researchers also found that a vegetated area has similar a cooler surface temperature against the high-albedo surfaces during the summer daytime (Niachou et al., 2001; Sonne, 2006; Takebayashi and Moriyama, 2007), although the principle is quite different in that evapotranspiration plays a more important role for the vegetated area, rather than the reduced heat absorption for the high-albedo materials. As reviewed by Voogt (2003), many studies have evaluated the relationship between the spatial structure of urban thermal patterns and urban surface characteristics, due to its importance for regional planning and urban ecology (Carlson and Arthur, 2009; Grimmond et al., 2010). The thermal infrared imaging is an efficient and feasible method, which enables the spatial and temporal urban surface temperature pattern to be studied over a whole city by providing high resolution data, although it is often limited by time, atmospheric conditions and the geometry seen by the sensor (Roth et al., 1989; Nichol, 1995; Voogt and Oke, 1997; Dousset and Gourmelon, 2003; Voogt and Oke, 2003; Weng et al., 2004). It is an indirect measurement approach that detects the emission and reflection of radiation surfaces by considering different surface radiation properties (Voogt and Oke, 2003). The observation results indicated that the urban surface temperature correlated with the distribution of land use and land cover in that the urban surface temperature is positively correlated with the impervious surface fraction but negatively correlated with the green vegetation fraction (Voogt, 1995; Lo et al., 1997; Weng, 2001; Weng et al., 2004; Lu and Weng, 2006; Weng et al., 2007).

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2.1.3 Impact of urban surface temperature Human-biometeorology studies the importance and the interrelationship of the weather conditions, climate and air quality on human health (Mayer, 1993; Höppe, 1999). For the evaluation of the thermal component of the urban climate, the mean radiative temperature Tmrt is an important indicator to govern the human energy balance and assess thermal comfort with the application of a thermal index, such as predicted mean vote (PMV), standard effective temperature (SET*) and physiologically equivalent temperature (PET) (Höppe, 1999; Matzarakis et al., 1999, 2007; Thorsson et al., 2007; Vanos et al., 2010). The physical meaning of

Tmrt is a temperature that sums up all shortwave and longwave radiation flux for the human energy balance. Thus, the urban surface temperature is involved in the determination of Tmrt , and also the human thermal comfort. Studies have found that it is the most influencing factor on windless summer days as a result of the intense heat stresses from shortwave and longwave radiation (Höppe, 1999; Matzarakis et al., 1999). In some extreme cases, the urban surface temperature may threaten the health of humans not only the issue of thermal comfort. In summer, contact between feet and naturally heated surfaces may cause burns serious enough for people to be admitted to the hospital. Such patients fall mainly in the categories of children, the incapacitated, restrained, or sensory deficient (Harrington et al., 1995; Al-Qattan, 2000; Sinha et al., 2006). Measurement shows that asphalt pavement was hot enough to cause burns during the day in summer, and it even caused a second-degree burn within 35 seconds from 10:00 a.m. to 5:00 p.m. (Harrington et al., 1995). Such hot urban surfaces may also cause damage to or have unexpected effects on animals. A recent report shows that the pads of a dog’s feet may be burned and blistered by the hot pavement (AccuWeather, 2012). Ruano et al. (1999) believe that the surface temperature affects the evolution and maintenance of chemical signals, which relate to the ability to exploit food resources in ants. Transportation plays an important role in many countries since their economies and social structures rely on the continued availability of the road network. In terms of the consequences for safety and environmental concerns, the road surface temperature is of significant importance (Chapman et al., 2001, 2006). For cities in cold climates, it is particularly dangerous during the early

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winter or after a period of warm weather when snow falls on a warm road. Initially the snow would melt, followed by refreezing if the warm road is overwhelmed by the cold air above (White et al., 2006; Mass and Steed, 2002). In summer, the surface temperature is hot enough to melt asphalt, causing problems to roads, which then need emergency repair. Car accidents related to this problem happen every year. Also, tires age faster in such a hot environment, which causes them to be more prone to catastrophic failure (NHTSA, 2013). For the Formula One car race, the surface temperature of the circuit may reach 100 oC in dry weather. Racing drivers therefore need to choose different types of tire according to the weather conditions to ensure the tire operates at an optimal temperature, e.g. intermediate tires and wettires for cool and wet circuit conditions, respectively (Tomba, 2008).

2.2 Urban air temperature 2.2.1 Urban warming and canopy layer urban heat island Due to rapid urbanization, urban warming has become a serious problem (Oke, 1987; Rizwan et al., 2008). Long-term temperature records from large cities indicate a substantial warming situation (Hughes, 1991; Sala et al., 2000; Ren et al., 2007; Gaffin et al., 2007; Jones et al., 2008; Kataoka et al., 2009; Fujibe, 2009, 2011). Figure 2.1 and Figure 2.2 show the annual averaged temperature trend for different cities, and the features of the rate of increase are quite varied. For the city of Hong Kong, the annual averaged temperature has an average rise of 0.12 o

C per decade from 1885 to 2011, and the rate of increase became faster in the

latter half of the 20th century (HKO, 2012a). Both the cities of Beijing and Wuhan experienced a cooling trend in the 1960s and significant warming occurred after mid-1980, with 1998 being the warmest year in the recorded period (Ren et al., 2007). Among all the cities, the warming trend for Tokyo was much higher than for other cities in that the linear increasing trend was 3 oC per century from 1901 to 2008 (Fujibe, 2011). Also, the studies conducted in the city of Tokyo, Hong Kong, Wuhan et al. show that the increased minimum temperature plays a more important role in the increase of the mean temperature compared to the maximum temperature (Ichinose, 2001; Ren et al., 2007; Fujibe, 2011), which further illustrates the decrease in the diurnal temperature range.

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The contribution of urban warming to global warming has been controversial. Some research has suggested that urbanization has no effect or only a slight effect on the globally averaged temperature trend (Jones et al., 1990; Peterson, 2003; Parker, 2004), while others found a substantial contribution of the urbanization to the global climate (DeGaetano and Allen, 2002; Kim and Baik, 2002; Kataoka et al., 2009). However, one thing is certain, the city has an impact at regional and local scales in that urban regions experience warmer temperatures than rural surroundings in what is now called the canopy-layer urban heat island effect, which has long been recognized dating back to the pioneering work by Howard in 1818. The canopy-layer urban heat island is the most studied among all heat island types. The change in urban air temperature is due to the heat induced into the canopy layer through sensible heat flux from the building surface and also the heat generated in the canopy. The urban heat island varies in a consistent manner during a 24-hour period (Figure 2.3) and extensive studies in the literature are devoted to understanding the physical basis by theoretical and numerical approaches (Arnfield, 2003; Unger, 2004; Grimmond, 2007; Roth, 2007; Rizwan et al., 2008; Grimmond et el., 2010; Stewart, 2011; Roth, 2012). After sunrise, the urban air temperature begins to rise at a much slower speed than in the surrounding rural area. The rural air temperature always reaches its maximum temperature earlier than the urban air temperature. During the day, the difference between the rural and urban air temperature is quite small and in some cases observations may even show negative urban heat island intensity. However, in the afternoon, the urban heat island begins to develop well, and it always reaches a maximum a few hours after sunset. In general, the urban heat island is a nocturnal phenomenon and is most pronounced in calm and clear weather conditions in the dry season due to the distinct cooling rate difference between the built-up area and open rural space. The urban air temperature illustrates significant spatial and temporal variability. Observations reveal that the “cliffs” or the lower temperatures are associated with parks, water surfaces and open areas, while the “peak” is always located in the urban center (Bärring et al., 1985; Oke, 1987; Eliasson, 1996; Goh and Chang, 1999; Wong and Yu, 2005; Erell and Williamson, 2007). Since various microscale factors may affect the air temperature, the climate records may also be contaminated, especially for long-term climatological time series, in that 12

these data are unrepresentative of the variations in weather and climate in socalled homogeneous climate time series, because of the changing factors of instruments, observing practices, station locations and environment (Jones et al., 1985; Peterson et al., 1998; Mahmood et al., 2006; Runnalls and Oke, 2006; Fujibe, 2011). Thus, climatologists have made many efforts to better understand, detect and compensate for the biases produced by the inhomogeneity (Peterson et al., 1998; Changnon and Kunkel, 2006; Runnalls and Oke, 2006).

Figure 2.1 Annual averaged temperature trend for different cities (Data source: Hughes, 1991; Sala et al., 2000; Gaffin et al., 2008; Jones et al., 2008; Kataoka et al., 2008; HKO, 2012a).

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Figure 2.2 Annual mean temperature anomalies for the city of Beijing and Wuhan (Data Source: Ren et al., 2007).

Figure 2.3 Typical variation of (a) urban and rural air temperature, (b) cooling/warming rates, and (c) heat island intensity under ‘ideal’ weather condition (Oke, 1987).

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2.2.2 Impact of urban air temperature The heating, ventilation and air conditioning (HVAC) system is widely used to maintain and improve indoor comfort, and the urban heat island has potential impact on its operation performance. On the one hand, the urban warming phenomenon increases the cooling load of buildings; while on the other hand, it reduces the energy demand for heating (LCCP, 2002; Akasaka et al., 2002; Watkins et al. 2002). A great amount of research is devoted to the study of the impact of the urban air temperature on the energy consumption of buildings in different kinds of climate, for example the Mediterranean climate with hot and dry summers, cooler winters and rainy weather (Hassid et al., 2000; Santamouris et al., 2001; Xu et al., 2012), the hot and humid subtropical climate (Akasaka, 2002; Kondo and Kikegawa, 2003; Lam et al., 2010; Chan, 2011; Qi et al., 2012), temperate oceanic climate (Watkins et al., 2002; Kolokotroni et al., 2006, 2007) and also combinational climates (Christenson et al., 2005; Frank, 2005). The results reveal that the urban heat island has a positive effect on building energy consumption in cold climates, but a negative effect in tropical climates (Scott et al., 1994; Crawley, 2008). Also, the increased and reduced energy consumption in summer and winter respectively can be swapped through the year for temperate climates (Wang et al., 2010). The warmer urban environment has a serious impact on the health of the urban inhabitants. Previous studies reveal that the risk of contracting infectious diseases is increased due to urban warming (Khasnis and Nettleman, 2005). These disease include the herpangina and hand-foot-mouth disease (Urashima et al., 2003), the vector-borne disease (Githeko et al., 2000) and so on. What is more, it is believed that the heat is related to mortality as it causes heat exhaustion, heat cramps, heart attacks and stroke (Kilbourne, 1997; Mcmichael et al., 2002). For example, the heat wave in July 1980 in St Louis and Kansas City caused an increase in deaths of 57% and 64%, respectively (Jones et al., 1982); during summer 1995 in Chicago, the medical examiner’s office reported 437 heat-related deaths, and in 1999 the second deadliest heat wave of the decade resulted in at least 80 deaths (Semenza et al., 1996; Whitman et al., 1997; Naughton et al., 2007). Extreme thermal conditions have also led to a large number of excess deaths in the city of Shanghai, Seoul, Paris and so on (Dhainaut et al., 2003; Tan et al., 2007; Kalkstein et al., 2008). As the frequency and intensity of heat waves 15

will increase in the future (Meehl and Tebaldi, 2004), a series of heat warning systems have been developed and implemented to lessen the impact of heat in the care of elderly or vulnerable people (Tan et al., 2007; Kovats and Hajat, 2008; Kailkstein et al., 2008).

2.3

Urban energy balance The modification of the Earth’s surface due to processes of urbanization,

e.g. the increased urban surface area, the use of impervious and high heat capacity materials, the reduction of evapotranspiration, the increased runoff and so on, significantly alters the surface energy balance and the dynamic and thermodynamic nature of the boundary layer. Combined with anthropogenic heat emission and pollutants, all of these processes lead to distinct urban climates (Oke, 1987; Grimmond, 2007). It can be seen that the interrelationship between urbanization and local effects on the climate is complex. Therefore, in order to better comprehend the thermal environment of the urban area and to provide suggestions for practical applications, it is important to fully understand the range of possible physical mechanisms affecting the changes. 2.3.1 Urban surface energy balance The energy balance of the surface is the physical process that determines the surface fluxes of temperature and moisture. Energy conservation can be expressed as,

S   S   L  L  H  G  LE  0 .

(2.1)

S  and S  are the incoming and outgoing shortwave radiation respectively. L and L are the downward and upward longwave radiation respectively. H is the sensible heat flux into the boundary layer, G is the conductive heat flux into the urban fabric, and LE is the latent heat due to the evaporation of water. The energy budget of artificial surfaces, such as asphalt and concrete, is quite different from that of natural surfaces due to the different thermal and radiation properties. Anandakumar (1999) studied the energy budget components of a dry asphalt surface by observation. Throughout the year, the ground conductive heat flux G is found to be of larger magnitude than that of the sensible heat flux H . During the cool season, most of the net radiation is transformed into

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G , while in the warm season, a great amount of heat is transferred into H as the incoming energy is higher. Similar findings are verified by other studies, which reveal that the artificial materials cause very large sensible heat fluxes during a typical summer day, which often continue positive although are smaller after sunset, especially for asphalt, which releases the largest amount of H compared with various other pavement surfaces (Kotani and Sugita, 2005; Herb et al., 2008; Takebayashi and Moriyama, 2012). In contrast, H is greatly reduced in grassy areas or bare soil surfaces due to evapotranspiration, especially during

the

growing season when almost all the incoming heat is partitioned into G and LE (Kotani and Sugita, 2005; Takebayashi and Moriyama, 2012). Also, both the high-albedo material surfaces and grassy surfaces are able to dramatically reduce the peak and daily total energy received by increasing the S  , as well as by the shading effect and increasing the latent heat flux LE , respectively, and provide further benefits to the indoor environment in summer if such material is used for building fabric (Del Barrio, 1998; Sailor, 2008; Meyn and Oke, 2009; Scherba et al., 2011). 2.3.2 Urban canopy layer energy balance The energy budget of the urban canopy layer is governed by the site conditions of the immediate environment, which include canopy geometry, material, wind, wetness and so on. It is complex to derive the spatial arrangement of individual energy sources and sinks when we try to understand the canopy layer climate, and thus acceptable approximation is required when discussing the total building-air volume (Oke, 1987; Grimmond et al., 1991). A local-scale soilbuilding-air volume concept is adopted (Figure 2.4) in which the bottom is the depth at which surface zero net heat flux occurs over the period of concern while the upper boundary of this volume is just above roof level or the measurement level (Oke, 1987; Roberts et al., 2006). The energy balance is then the sum of the energy balance of the individual urban surfaces suitably weighted by surface area. The feature of the volumetric averaging approach is that the different characteristic of the energy balance and surface temperature of different points on the urban surface is lost and the precise dependence on surface morphology cannot be examined (Nunez and Oke, 1977; Voogt and Oke, 1998; Harman, 2003).

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There are many studies in the literature of the energy budget of the urban canopy layer. Both experiments and modeling reveal that the timing and magnitude of the energy exchange on different surfaces are significantly different. This is related to the patterns of net radiation receipt (Oke, 1987; Mills, 1991; Yang and Li, 2010; Kantzioura and Zoras, 2012). The east-facing wall is the first surface to become irradiated. After midday, it is in shadow, but it does experience a second peak when the opposite wall reaches its maximum irradiation. The floor is sunlit only during the middle of the day and only the uppermost part of the wall can be sunlit if the canopy is deep.

Figure 2.4 Schematic illustration of the volumetric averaging approach to urban energy balance (Roberts et al., 2006). The energy balance of the canopy layer is

Q * QF  QH  QE  QS  QA . Note the different notation: Q * is the net radiation; QH is the sensible heat flux; QE is the latent heat flux; QS the storage;

QA  Qin  Qout the advective flux; and QF the anthropogenic heat flux.

The energy balance for the whole volume is relatively smooth and symmetrical (Nunez and Oke, 1977; Arnfield, 2003). For the built-up area, the latent heat flux is much smaller than QS since these sites have limited vegetation cover. Therefore, the storage heat flux QS is a very important term in the surface energy balance. A series of observations conducted in light industrial

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sites in Vancouver and Mexico City, both of which have scant vegetation, illustrate that around half of the incoming Q * goes into warming the urban fabric during the day, and only a small amount is convected into the lower atmosphere by QH . At night, QS is the sole source of energy for the control volume. It is so efficient for the urban area that it supports a consistently upward-directed convective heat flux at all times of the day and night, contributing to the heat island in the air (Grimmond and Oke, 1999; Oke et al., 1999). The energy sharing between QS and QH may be different for different urban areas. Arnfield (2003) proposed a hypothesis that it may be related to the canopy aspect ratio whereby QH is produced through the canopy top decreasing as the aspect ratio increases.

While Oke et al. (1999) pointed out that the ability of storage heat is related to the characteristic surface morphology and also its materials.

2.4 Urban morphology The canopy geometry may significantly influence the thermal environment of the urban area by providing solar shading for pedestrians and at the same time becoming a heat trap due to the multiple reflection between the urban surfaces (Terjung and Louie, 1973) and the reduced sky radiation (Oke et al., 1991; Arnfield, 1990). The impact of urban canopy geometry on radiation heat flux is the essential reason for the surface temperature difference. Many previous studies have already investigated the relationship between either the sky view factor or the height to width ratio (building height/street width H / W ), which are two parameters used to express the urban geometry, and the street temperature derived by either measurement or numerical modeling. For field observations, there are many ways to measure the surface temperature, e.g. by air-borne infrared thermographs (Bärring et al., 1985; Niachou et al., 2008; Kantzioura et al., 2012), by automobile traverses (Eliasson, 1996; Upmanin, 1999) or by in-situ measurements (Pearlmutter et al., 1999; Santamouris et al., 1999; Bourbia and Awbi, 2004; Johansson, 2006; Niachou et al., 2008; Bourbia and Boucheriba, 2010). For the sky view factor measurement, the fish-eye lens photographs are always applied (Bärring et al., 1985; Eliasson, 1996; Bourbia and Boucheriba, 2010). The measurement results from different studies are rather contradictory

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because the sky view factor of the urban canopy has a different effect on the street surface temperature, which can be positive (Pearlmutter et al., 1999; Bourbia and Awbi, 2004; Bourbia and Boucheriba, 2010), negative (Eliasson, 1992) or even have no effect (Lindberg et al., 2003). Similar confusing findings are also presented by Upmanis and Chen (1999) and Unger (2004). The former study pointed out that the relationship changes according to the season, day and location, the characteristics of which may contribute to the confusing results. In fact, this phenomenon is quite feasible since the experimental method is limited both in time and space, and easily influenced by the environment, all of which may lead to the failure to capture the general temperature variation trend. Therefore, numerical simulation is a suitable method to understand the complicated causal mechanisms. A simple way to numerically assess the effect of canopy geometry on street surface temperature is to conduct the simulation during a calm and cloudless night, with the absence of the solar shading effect and the turbulent heat flux (Arnfield, 1990; Johnson et al., 1991; Oke et al., 1991). The results show that the street canopy geometry alone has a significant effect on cooling rates, since the radiation intensity declines with the reduction of the sky view factor (increase of the H / W ratio). Recent research has begun to involve the complicated daytime shadow distribution into the urban surface energy balance models by applying either an analytical scheme (Sakakibara, 1996; Masson, 2000; Kanda et al., 2005a; Kusaka et al., 2001) or a ray tracing method (Krayenhoff & Voogt, 2007; Asawa et al. 2008). The simulation results show that the surface temperature of the urban street depends on the canopy geometry due to the reduced sky view factor and complicated daytime shadow which contribute to the formation of the urban heat island (Sakakibara, 1996). The buildings act as blocks affecting the wind flow pattern in the urban area, which relates to the urban geometry, in particular, the height to width ratio. Oke (1987) identified three flow regimes when the wind direction is perpendicular to the street axis, e.g. isolated roughness flow, wake interference flow and skimming flow. Kim and Baik (1999, 2001) further characterized the flow regimes into five patterns according to various aspect ratios and thermal effects of the canopy. Also, based on field measurements and mathematical modeling results, the wind speeds within the urban canopy are usually reduced compared to surrounding rural area with the same height, which may contribute to the 20

accumulation of heat and pollution, especially for the secondary street in which the ventilation and air exchange mainly depend on the vertical flow rate (Britter and Hanna, 2003; Coceal and Belcher, 2004, 2005; Hang et al., 2009; Hang and Li, 2010). Investigations have revealed that variability of building heights as well as the utility of the elevated level of space are efficient mitigation strategies to intensify urban ventilation to some extent (Kanda, 2006; Hang and Li, 2010).

2.5 Construction materials The thermal and radioactive properties of artificial materials applied in the urban area are quite different compared to rural land cover, by changing the albedo and emissivity, and increasing the thermal admittance and water-proofing (Oke, 1987; Grimmond, 2007). Mitigation strategies aiming to improve the indoor and outdoor thermal quality in terms of construction materials mainly include two parts, green urban surfaces and high-albedo surfaces. The green roof is an old but also innovative concept. The earliest green roof can be dated to the ancient civilizations of the Tigris and Euphrates River valleys. The most famous example must be the Hanging Gardens of Babylon in the seventh and eighth centuries BC. At that time, the function of planting on roofs was mainly for pleasure and attractiveness. In recent decades, people have begun to realize the potential benefits of the green roof from the ecological and social points of view, and many studies have been conducted to investigate the energy performance of the extensive green roof (designed to be ecological and sustainable with minimum maintenance) by modeling (Del Barrio, 1997; Kumar and Kaushik, 2005; Lazzarin et al., 2005; Sailor, 2008; Feng et al., 2010) and experimental approaches (Niachou et al., 2001; Lazzarin et al., 2005; Sonne, 2006; Santamouris et al., 2007; Takebayashi and Moriyama, 2007; Teemusk and Mander, 2009). Studies have revealed that the green roof can improve the thermal environment

not

only by the

insulation

effect

and

intensifying

the

evapotranspiration process but also by its shading effect (Akbari et al., 1997; Rosenfeld et al., 1998; Kumar and Kaushik, 2005; Solecki et al., 2005). On the one hand, the green roof has a mitigating effect on the urban heat island by reducing the air temperature 0.5 oC (Brad, 2002) to 4.2 oC (Wong et al., 2003). On the other hand, studies have shown a positive impact of the green roof resulting in a saving on air conditioning energy consumption, which is related to the Leaf

21

Area Index (LAI) (Wong et al., 2003; Onmura, 2001; Kumar and Kaushik, 2005) as well as the insulation properties of the buildings. Studies have shown that the green roof has limited effect on energy saving for well insulated roofs (Niachou et al., 2001; Castleton et al., 2010). Painting the urban surface with light color or using high albedo material is another mitigation approach. Typical urban materials have an albedo in the range of 0.05 to 0.35 while for the white painted surfaces it can reach 0.9 to 0.95, which means that most of the incident solar radiation will be reflected back to the environment (Oke, 1987). Many researchers have demonstrated that a high-albedo building surface can be effective in reducing the surface and air temperature near the ground, and further reducing the energy consumption of the building (Sailor, 1995; Taha et al., 1997; Rosenfeld et al., 1998; Taha, 1999; Akbari et al., 2007; Ihara et al., 2008; Yang et al., 2012). However, some studies have shown that the impact of increasing the material albedo may not always be positive if the surface emissivity is reduced at the same time and roof insulation is absent (Simpson and Mcpherson, 1997). Also, increasing the ground surface albedo may result in increasing the amount of solar radiation penetration into the room through the window (Kikegawa et al., 2006).

2.6 Anthropogenic heat flux Waste heat released by human activities, also called anthropogenic heat, is a significant contributor to the urban energy balance, and play an important role in the formation of the urban heat island, especially during nighttime and winter time, when relative solar forcing is low (Klysik, 1996; Ichinose et al., 1999; Fan and Sailor, 2005; Offerle et al., 2006; Hinkel and Nelson, 2007). It is related to the energy consumption of urban area which falls in four categories, transportation, buildings, industry and, less importantly, human metabolism (Grimmond, 1992; Sailor, 2011). Many studies have tried to estimate anthropogenic heat emissions in the urban environment using, for example, inventory approaches (Klysik, 1996; Taha, 1997; Ichinose et al., 1999; Fan and Sailor, 2005), energy budget closure methods (Offerle et al., 2005) and building energy modeling approaches (Kondo and Kikegawa, 2003; Ohashi et al., 2007). The simulation results showed that the averaged magnitude of anthropogenic heat over a city is always less than 100 W m-2 (Klysik, 1996;

22

Grimmond, 1992), but there are large variation between different cities because of the local climate and economic development. Lee et al. (2009) found that the annual mean anthropogenic heat emission in the cities of Seoul, Incheon, and Gyeonggi are 55, 53, and 28 W m-2, respectively. Kimura and Takahashi (1991) determined that the anthropogenic heat in Tokyo varied between 50 and 85 W m-2, while Ichinose et al. (1999) found it can reach as much as 200 W m-2 in summer and 400 W m-2 in winter with a maximum of 1590 W m-2. Smith et al. (2009) reported anthropogenic heat of 10 W m-2 for non-central areas and 23 W m-2 in city centers. After investigation of six cities in the United States, Sailor and Lu (2004) reported anthropogenic heat of 60 W m-2 in summer and 75 W m-2 in winter. In general, the anthropogenic heat flux for a city center is always an order of magnitude higher than the average for that city (Sailor and Lu, 2004). Researchers have always relied on modeling schemes to evaluate the contribution of anthropogenic heat to the urban heat island intensity by adding a source term in the energy balance model (Taha, 1999; Fan and Sailor, 2005; Ohashi, 2007; Chen et al., 2009; Hu et al., 2012). Tong et al (2004) found that anthropogenic heat led to a temperature increase of around 0.5 oC during the day and 1-3 °C during the night in Beijing city center. In Tokyo, Ichinose et al. (1999) reported that waste heat resulted in a 2.5 oC temperature increase in winter and, furthermore, Ohashi et al. (2007) found out that it may cause a temperature rise of 1-2 oC or more in office areas during weekdays. The study conducted in Philadelphia suggested that anthropogenic heat contributed a temperature increase of about 0.8 oC and 2.5 oC for summer nights and winter nights, respectively (Fan and Sailor, 2005). In Barrow, Alaska, a city with extreme weather conditions, where anthropogenic energy is the dominant heat in winter due to the polar night, an in-situ measurement found that the urban air temperature is 2 oC warmer than the surrounding tundra and occasionally exceeds 6 oC (Hinkel and Nelson, 2007). Overall, it can be seen that anthropogenic heat does indeed contribute to the urban heat island, and it is therefore unwise to ignore the artificial heat source term in atmospheric models (Myrup et al., 1993; Hafner and Kidder, 1999).

23

2.7 Existing studies and limitations of urban radiation balance modeling A modeling approach is an efficient way to understand the urban thermal climate or the potential for heat island mitigation, and many studies have been devoted to developing a surface energy balance model for different applications (Grimmond et al., 2010). Most of the existing urban-surface energy models aim to couple with a mesoscale atmospheric model for accurate weather forecasts and climate change information. They share similar factors that arise from using parametrized urban geometry, which does not give detailed information for individual buildings, and the radiation interactions are treated simply due to limitations of computer power (Masson, 2000; Kusaka et al., 2001; Martilli et al., 2002; Harman and Belcher, 2006; Oleson et al., 2008). Only a few models focus on microscale temporal distributions of urban surface temperature (Krayenhoff and Voogt, 2007; Asawa et al., 2008). The major obstacle for model development at the microscale is the radiation heat transfer calculation for the complex urban structure because a) it is time consuming, b) it is expensive on computer memory, and c) there are limited methods for evaluating both multiple reflection and the sunlit-shaded distribution. Kanda et al. (2005a) proposed a simple theoretical radiation scheme for regular building arrays. Such a special urban structure allows them to apply analytical methodologies to deal with the view factor and the sunlit-shaded distribution. Although it is a three-dimensional model, the surface of the urban geometry is still characterized by a single surface energy balance and the view factor by means of the face-averaged value. The drawback is obvious in that it cannot be used for a complex urban structure. The Temperature of Urban Facets in 3-D (TUF-3D) model developed by Krayenhoff and Voogt (2007) is a very detailed three-dimensional surface temperature prediction model which has greater surface resolutions by splitting the faces into smaller elements. The shape factor is calculated by determining whether the two patches can ‘see’ each other first, and then by using the exact plane parallel analytical equations combined with complicated view factor algebra. The ray tracing shading algorithm is adopted for the sunlit-shaded distributions. Both Krayenhoff and Vooght (2007) and Kanda et al. (2005a, 2005b) applied the radiosity approach for the multiple reflection

24

calculation, which directly solves a set of simultaneous linear energy balance equations involving the reflectivity, shape factor and the emission energy. On the one hand, a large amount of computer memory is required to store N 2 shape factors, or at least N 2 / 2 due to the reciprocity relation of the shape factor, for an environment with N cell surfaces. On the other hand, the calculation process is very time consuming. Even if an advanced iterative technique is applied, e.g. a progressive refinement algorithm method with the time complexity O(N), the time requirement is still substantial because the iteration should proceed for every timestep. More recently, a three-dimensional Computer Aided Design (3D-CAD) tool has been developed by Asawa et al. (2008) as a thermal design tool for use in planning outdoor spaces. This model considers not only the specular reflection but also the effect of tree shading. However, the radiation model is greatly simplified by only considering the first reflection and assuming the surface temperature of the surroundings is the same as the air temperature when conducting the longwave radiation calculation.

2.8 Summary Our literature studies have clearly demonstrated the importance of the urban thermal environment, more specifically the importance of the urban surface temperature and air temperature, to the quality of human life. Existing studies on the temporal variation of urban surface and air temperature have provided a starting point for understanding the urban thermal environment. However, regarding the hypothesized causes of the urban warming effect, although well described and confirmed by many observations, there is still not a satisfactory explanation of their roles, and so there is a great demand for further investigation and improvement of the analytical approaches. Therefore, we hope to address some of these problems in the present study by developing approaches which are efficient, accurate and simple enough in order to gain a better understanding of the temporal variation of urban surface and air temperature.

25

CHAPTER 3

URBAN SURFACE TEMPERATURE DISTRIBUTION

3.1 Introduction In this chapter, we develop a Model for Urban Surface Temperature (MUST) calculation that includes most of the energy exchange processes that contribute to the urban surface heat distribution in a realistically complex city, and which can provide predictions on a time scale from seconds to days. Compared with existing surface energy balance models, the MUST scheme has a complete three-dimensional shape with detailed information for individual buildings. Consistent with Krayenhoff and Voogt (2007), all of the urban surfaces are split into numerous cells, which means the entire urban landscape, including buildings and roads, is built based on a rectangular cube. The radiative and thermal properties of every cell surface are recorded. The discrete transfer method (Shah, 1979; Lockwood and Shah, 1981) is used for the shape factor estimation, and this is based on the concept of tracking the representative radiation rays with specified directions for every cell surface. Compared to the analytical methods, the benefit of the discrete transfer method is that each pair of shape factor from a specified cell surface can be calculated at one time, and there is no need to estimate the shape factors one after another after determining the geometric relationship of each pair. Gebhart absorption factor (Gebhart, 1971) is introduced in this study. The benefit of this scheme is that as long as the geometry and thermal properties of the urban environment remain the same, there is no need to carry out the iterative process at every timestep if the Gebhart absorption factor is estimated in advance. One major challenge for predicting a detailed surface temperature distribution in a realistic urban environment is the quadratic computer memory requirement necessary for calculating the surface thermal radiation transfer. The computer memory requirement is N 2 , where N is the total number of surface cells as mentioned above. The MUST scheme introduces a new storage strategy in which the computer resource costs increase linearly with N . This allows us to develop a detailed urban-surface heat balance model that predicts the temporal and three-dimensional surface temperatures in an urban environment that has a

26

complex morphology and allows for the further study of the impact of urban heat storage and the effect of improved surface coating and pavements.

3.2 A three-dimensional urban surface energy model The MUST scheme aims to predict the detailed urban-surface temperature distribution for any given day or location while using acceptable computer memory resources. It should present the distribution of buildings according to a realistic situation, which would allow for simplified scientific calculations. Figure 3.1 shows an example of the building cluster geometry used by the MUST scheme. It separates the urban environment into small, three-dimensional cells along the x, y and z coordinates. Each cell may contain one (e.g. in the centre of the wall), two (e.g. at the edge of the building) or at most three (at the corner of the building wall) effective calculation surfaces with five possible directions. Additionally, we define the property of every surface, such as roof, wall or road, to provide specific boundary conditions and determine different calculation processes. We construct an energy balance for each defined cell surface by considering the uniform temperature profile of each facet. The total energy balance should be closed over the layer. The canopy rotation angle is defined as the angle  between the north and the orientation that is parallel to the street. In the study, we focus primarily on a group of buildings and not an entire city. From the radiative point of view, the impact of the buildings outside the domain should be considered. Therefore, an imaginary boundary is established in order to imitate the continuous urban landscape. The imaginary boundaries are defined according to the three-dimensional urban energy balance model (TUF-3D) developed by Krayenhoff and Voogt (2007). The calculation domain is surrounded by walls with heights equal to the average building height. The control volume height is equivalent to the top of the roughness sub-layer, at which level turbulent heat flux has already been well mixed. The baseline of the volume is in the soil where net vertical heat flux can be ignored during the period of interest.

27

(a)

(b)

Figure 3.1 (a) An example urban area calculated by the MUST scheme. The surrounded imaginary walls are not shown here for clarity. G is the heat conduction, S is the absorbed shortwave radiation and L is the longwave radiation. (b) Predicted surface temperature distribution at 10 a.m., 16 Jul 2009 in Hong Kong.

28

3.2.1 Radiation scheme 3.2.1.1 Shape factor and Gebhart absorption factor An initial assumption is made that the surfaces considered here are Lambertian. An important coefficient, the shape factor or view factor, needs to be considered before the shortwave and longwave radiation budget is explained. The shape factor Fij is defined as the fraction of energy leaving a black surface element i that arrives at another black surface element j (Siegel and Howell, 1972). Initial calculations of this factor should be precise so that reasonable results for the radiation (both shortwave and longwave) can be attained. There are a number of methods for calculating the shape factor between any two surfaces, such as the law of solid-angle projection and the contour integration method (Yamazaki, 1983; Li and Fuchs, 1992). In this study, we utilize the discrete transfer method, which has the advantage of being easily coupled to a Computational Fluid Dynamics (CFD) solver (Shah, 1979; Lockwood and Shah, 1981; Cumber, 1995). The discrete transfer method is based on the concept of tracking the representatively directed radiation rays, similar to the Monte Carlo model. However, unlike the Monte Carlo model, in the discrete transfer method the beams are not randomly chosen and their directions are specified for each surface element by dividing the hemisphere into

N DTM  N  N equal segments, where N  and N  correspond to the values of the polar angle and the azimuth angle, respectively. Each subdivision is then

 

 2 N

,  

2 . The shape factor Fij is calculated as the fraction of total N

energy leaving black surface Ai that arrives at black surface A j . In order to evaluate the arriving energy, we need to calculate the intensity of each representative ray impinging at this surface A j from surface Ai for every subsolid angle and sum over the whole hemisphere of Ai . Also the surface is assumed to be Lambertian, which means the reflected or emitted radiation has equal intensity I 0 in all directions. Therefore, the energy leaving surface Ai that reaches surface A j is Qij  A j  I 0 cos i sin  i (sin  ) . The total energy leaving the black surface Ai , which is assumed as Q , is I 0Ai . So Fij can be calculated as:

29

Fij 

Qij Q



A j  cos  i sin  i (sin  )

Ai

,

(3.1)

where  i  (i  0.5) , i  1,..., N . Furthermore, Gebhart absorption factor is introduced for multiple reflection. The radiation of wavelength  upon a surface is either transmitted, reflected, or absorbed (Oke, 1987). Therefore, the radiation absorbed by a surface ( Ai ) includes the direct radiation from another surface ( A j ) and the indirect radiation from other surfaces by means of reflection. Gebhart absorption factor gives the percentage of energy emitted by a surface that is absorbed by another surface after reaching the absorbing surface by all possible paths (Gebhart, 1971). It is obtained by the following system of equations: Gij  Fij  j  k 1 Gkj  k Fik , N

(3.2)

where the surface element number i  1 to N and j  1 to N. The quantity Gij is the fraction of energy emitted by Ai that reaches A j and is absorbed. For longwave radiation and shortwave radiation, the values of Gij are different due to different absorptivity  and reflectivity  , and they are separately calculated. 3.2.1.2 Compressed row storage scheme The shape factor is important because it limits the calculations required for a large urban domain. Based on the definition of the shape factor, which is a twodimensional array, if there are N surfaces, then the size of the factor matrix is N 2 . For example, if there are 1,000 surfaces in the domain, then one million numbers need to be stored. Fortunately, most elements in the array are zero, which means it is a sparse matrix. Thus, a widely used scheme such as compressed row storage is introduced in this study to reduce the computer memory requirement (Figure 3.2) (Smailbegovic et al., 2005).

30

Figure 3.2 Compressed row storage scheme (modified after Smailbegovic et al. (2005)) which divided a two-dimensional sparse matrix into three onedimensional arrays AN , AJ and AI , represented the non-zero values of the spars matrix, the column position of the original matrix and the pointer, respectively.

The original two-dimensional matrix is divided into three one-dimensional arrays. The first array AN stores the non-zero values of the sparse matrix. The second array AJ which is equal in size to AN contains the column position of the original matrix and corresponds to the elements in AN . AI is a pointer array, and it records the number of the first non-zero element in every original row. When we find an element, for example A(i, j ) , we need to ascertain the section that initially contains AJ , and the formula for that is ( AI (i), AI (i  1)  1) . The next step is to figure out whether the column number j is contained in the above section in the AJ array. If not, then A(i, j ) equals zero. Otherwise, the value will be found in the AN array. The performance of the new storage scheme is discussed in the Appendix.

31

3.2.1.3 Solar radiation calculation The ray tracing scheme in the discrete transfer method is also used to determine the sunlit-shaded distributions. For each surface element, we specify the ray direction as directly opposite to the incidence of the sun. Along the ray path, if the ray impinges on other blocks or objects, then the sun’s rays cannot reach the surface, and the surface is considered sun-shaded. If the downwelling shortwave flux is non-zero at the surface, it is considered sunlit. To improve the resolution, each surface cell is further divided into 400 equal sub-cells to determine their sunlit or shaded status. The direct irradiance of a surface element i is calculated using Bouguer’s law (Yan and Zhao, 1986): 1 / sin  a

I dr  I sc E0 Pat

cos in ,

(3.3)

where I sc is the solar constant with a value of 1367 W m-2 (Frohlich and Brusa, 1981); Pat is the transmittance of the atmosphere;  a is the solar altitude;  in is the solar incidence angle given by cos  in  cos  s cos  z  sin  s sin  z cos(   az ) , where  z is the solar zenith angle,  is the solar azimuth,  s is the slope of the surface measured from the horizontal position, and  az is the surface azimuth angle, i.e., the normal surface deviation with respect to the local meridian; and E 0 is the eccentricity correction factor of the Earth’s orbit (Duffie and Beckman,1991), which is calculated as:

E0  1  0.033 cos(

2d n ). 365

(3.4)

According to the Berlage formula (Yan and Zhao, 1986), the diffuse irradiance of a surface element i is calculated as: I df  0.5Fis I sc sin  a

1 / sin

a 1  Pat , 1  1.4 ln Pat

(3.5)

where Fis is the shape factor of surface element i relative to the sky. Therefore, the absorbed shortwave radiation can be expressed as: S   (1   s )( I dr  I df ) ,

(3.6)

where  s is the albedo of the surface.

32

3.2.1.4 Longwave radiation model Longwave radiation includes the radiation from sky to the Earth’s surface and the radiation between surfaces. Concerning the radiation released to the sky, we adopt the model developed by Berdahl and Martin (1984) for the sky temperature calculation (Duffie and Beckman, 1991). It relates the sky temperature Tsky to the dry bulb air temperature Ti of the ambient air, the dew point temperature t dp and the hour from midnight t m :



2 Tsky  Ti 0.711  0.0056t dp  0.000073t dp  0.013 cos(15t m )



1/ 4

.

(3.7)

Using Stefan’s equation, longwave radiation in terms of surface i can be expressed as: 4 L  L    j 1 Lj G LjiTs4, j   iL FisTsky   iLTs4,i . N

(3.8)

3.2.2 Convection model To estimate the sensible heat flux, the conventional heat transfer expression is applied. Previous researches estimated the heat transfer coefficient by using either (1) the Monin-Obukhov similarity theory (MOST) over the urban canopy to parameterize the convective heat flux for heat exchange from the horizontal surfaces (Masson, 2000; Krayenhoff and Voogt, 2007), the canopy space (Kusaka et al., 2001) and the overall surface layer (Kanda et al., 2005b) or (2) the aerodynamic formulation method, which is based on wind-tunnel measurements for forced convection over flat plates (Masson, 2000; Krayenhoff and Voogt, 2007). The semi-empirical method of MOST, which is applicable to an infinitely homogeneous surface, is first applied by Masson (2000) over the urban canopy. It is based on the observation by Feigenwinter et al. (1999) in the city of Basel, Switzerland, which showed that the mechanical properties in the roughness sub-layer (from the ground to 2 to 5 times the height of the building) were similar to those in a rural surface layer. However, its application in an urban area, especially for a city with different building heights and densities, should be careful consideration, since the roughness sub-layer is always characterized by a horizontally non-uniform turbulence field due to local-scale advection. In most cases, it is only in the constant flux layer, which is above the roughness sub-layer,

33

that mean profiles obey semi-logarithmic laws and the Monin-Obukhov similarity applies (Roth, 2000). Recent studies utilized the scintillation method at this layer to measure the spatially averaged turbulent heat flux of the homogeneous urban surface by applying MOST (Kanda et al., 2002; Lagouarde et al., 2006). Therefore, since the MUST scheme is not applied only to idealized urban structures, it is not appropriate to use MOST widely to derive the sensible heat flux. For simplicity, the aerodynamic formulation method is applied for the estimation of the convective heat transfer coefficient. If we assume the air within the roughness sub-layer has no energy capacity, the total sensible heat flux equals the amount of mechanical energy enveloping the building that is integrated over the urban surface. Furthermore, it represents the turbulent heat flux between the surfaces and the boundary layer: H  h0 (Ts  Ti ) ,

(3.9)

where h0 is the external convective heat transfer coefficient which keeps constant during the simulation. To estimate the convective heat transfer coefficient, a classical and simple formula is applied relating to surface roughness rw,i and the effective wind speed U eff (z ) which is defined as a combination of the mean wind and the turbulent wind, and which considers the thermal production of turbulence (Lemonsu et al., 2004; Krayenhoff and Voogt, 2007):

h0  rw,i (11.8  4.2U eff ( z ))  4.0 ,

(3.10)

rw,i is assumed equal to 1.0. If the U eff (z ) for the roof surface and urban canopy layer equals to 2.0 and 1.0 m s-1, respectively, then the convective heat transfer coefficient equals approximately equals to 16.0 and 12.0 W m−2 K−1, respectively. 3.2.3 Heat conduction model Heat conduction through the ground and building envelopes is assumed to be one-dimensional, and thus the transient heat conduction equation is calculated as follows:

T   T   D  , t x  x 

(3.11)

where D is the thermal diffusivity, which varies for different layers of the wall and ground. In contrast to that reported by Masson (2000), the layer temperatures 34

are representative of the surface, not the middle of each layer. Therefore, if the number of layer surfaces including the uppermost and lowermost boundaries is i , there are k  i  1 segments between every two layer surfaces. By assuming the layers are of the same thickness, the explicit scheme for adjacent

layers of the

same material is:

D t  D t  Ti n1  1  2 k 2 Ti n  k 2 Ti n1  Ti n1 . x  x 





(3.12)

For layer surfaces which connect two different materials:

Ti n1  Ti n 

Dk t n D t (Ti 1  Ti n )  k 12 (Ti n  Ti n1 ) . 2 x x

Equations (3.12) and (3.13) can produce stable solutions if

(3.13)

Dt  0.5 . At x 2

either the exterior wall surface or the ground surface adjacent to urban air, the following boundary condition, which reflects the heat balance, is used:

S   L  L  H  G  0 , where G  k

Ts x

x 0

(3.14)

is the conductive heat flux into the buildings and ground. k

is the thermal conductivity of the wall material or the ground-surface material. Such thermal properties for typical materials used in building and urban construction can be found in Oke (1987). At the interior wall, the energy balance is:

k

T  hin (Tinner  Tin ) , x

(3.15)

where Tinner is the inside wall surface temperature and hin is the interior convective heat transfer coefficient, which equals 5 W m-1 K-1 and remains constant during the simulation. Tin is the indoor air temperature which can be either defined as constant or calculated using the indoor energy balance equation

 air c pV

Tin   hin (Tinner  Tin ) , where V is the volume of the indoor space. At a t

sufficient ground depth, the soil temperature is assumed to be constant and equivalent to the average monthly soil temperature Tsoil .

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3.3 Model validation 3.3.1 Validation of the shape factor The crucial factor in a surface radiation sub-model is the calculation of the shape factors. In addition to the discrete transfer method ray tracing scheme that calculates the shape factor in our model, we also need to determine the minimum number of rays required for satisfactory convergence. We evaluate our shape factor calculation method in an ideal rectangular room. The room surfaces were divided into 160 surface elements. For conservation, the shape factors of a surface element should add up to unity (one). It is found that 100 ×100 rays for each surface element offered a sufficient accuracy for our shape factor calculation within the ideal rectangular room geometry. 3.3.2 Validation of the conduction sub-model The ground conduction sub-model is used to predict the ground-surface temperature. The model is evaluated against the experimental work performed in Haifa between 18 and 22 January 1987 by Swaid and Hoffman (1989). The original purpose of the experiment was to validate a Surface Thermal Time Constant model (STTC) for predicting the ground-surface temperature in homogeneous and layered soils. The surface and subsurface ground temperatures were continuously recorded for the following materials: concrete, asphalt and bare soil. Simultaneously, meteorological data were also recorded. Data from 20-21 January, two days with clear skies and light wind, were used in the study by Swaid and Hoffman (1989), and these data are also used for validation in the present study. Bare soil and asphalt are the validation target materials, and all the forcing data, including dry-bulb temperature, wet-bulb temperature and solar radiation intensity, as well as the thermal properties of the materials, can be found in Swaid and Hoffman (1989). Initially, the soil temperature varies with depth, and thus the conductive heat flux is constant with depth, which is equal to the heat flux at the surface. Figure 3.3 shows the comparison between our predicted ground-surface temperature profile and the experimental data. The results for both bare soil and asphalt are comparable with the experimental data. The average (and the maximum) hourly difference between the predicted and measured surface

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temperature is 0.51 oC (1.76 oC) and 0.46 oC (1.81 oC) for bare soil and asphalt, respectively. This result shows that our ground-heat condition model performs adequately when predicting the temporal ground-surface temperature profile.

(a)

(b)

Figure 3.3 Comparison between the observed and calculated temporal surface temperature profiles. (a) Bare soil; (b) Asphalt. 3.3.3 Validation of the full model The MUST scheme is able to calculate not only the surface temperature of homogeneously distributed buildings but also the surface temperature of urban buildings with different heights and densities. However, because there is a lack of comprehensive and systematic observations in a non-uniform city, the observation data of the Vancouver light industrial site during a sunny period in 1992 are used

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as the forcing data set to validate the model. It is an ideal test site in that it contains composites of high-density, one- to three-story buildings with primarily flat roofs and a remarkable lack of vegetation (coverage area