Land-Use Planning and the Urban Heat Island Effect

Home , Suburbanization, Urban heat island

LAND-USE PLANNING AND THE URBAN HEAT ISLAND EFFECT

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Jun-Pill Kim, M.C.R.P.

Graduate Program in City and Regional Planning

THE OHIO STATE UNIVERSITY

2009

Dissertation Committee:

Jean-Michel Guldmann, Advisor

Carolyn J. Merry

Philip A. Viton

Jun-Pill Kim

2009

ABSTRACT

Local climate changes due to urbanization have been well documented. These

changes are epitomized by the concept of the “Urban Heat Island” (UHI), which

represents temperature differences between urban and rural areas. In urban areas, the UHI

effect is a critical factor for air quality and public health. It results in higher peak energy

demand because of the use of air conditioning in Summer. Higher temperatures increase

health risks to city dwellers, because increased air temperatures are associated with

secondary air pollutants, such as ozone (O3). Recent research on the UHI, including

theoretical models and statistical analyses, has resulted in a better understanding of

climate modifications in urban areas. The purpose of this research is to further develop

statistical models of local temperature changes, using Landsat-5 satellite remote-sensing

data. The temperature at any location and for any land use is modeled as a function of the pattern of land uses around this location. These models are estimated with data pertaining to the Columbus, Ohio, metropolitan area (CMA). Their applicability to land-use planning and regulation is illustrated by simulating hypothetical land-use changes in part of the CMA, and computing the resulting temperature effects. The results clearly demonstrate that it is possible to reduce temperatures in residential and urban areas through a judicious siting of green areas.

Dedicated to my parents and my brother,

my daughter and son, and my wife,

Na-Yun Kim

iii

ACKNOWLEDGMENTS

The writing of a dissertation is obviously not possible without the personal and practical support of numerous people. Thus, my sincere gratitude goes to my parents, my family, all my friends, and professors at The Ohio State University for their love, support, and patience over the last few years.

First and foremost, I wish to express my deep appreciation to my adviser,

Professor Jean-Michel Guldmann, for his guidance and inspiration in completing this dissertation. His encouragements and careful guidance will never be forgotten. He always read and responded to the drafts of each chapter of my work more quickly than I could have hoped. In the same vein, I want to thank Professor Philip A. Viton for his support and encouragement on my research. I would like to thank Professor Carolyn J. Merry for her valuable instruction in data processing and precise comments. She has always been with me whenever I needed her help. I would also like to thank Professor Jennifer-Evans

Cowley for giving me the opportunity to work with her on the Hurricane Katrina rehabilitation project.

I would like to recognize the endless support of my parents. They always believe in and encourage what I do. I would like to thank my daughter, MiRi, and son, Song-Joo, for providing me pleasure whenever I was discouraged. Finally, these acknowledgements

would not be complete without heartfelt thanks to my wife, Na-Yun Kim, who supported me in everything. I would not have completed my Ph.D. program without her support.

VITA

February, 1997………………………………B.S. Environmental Engineering, The KwangWoon University, Republic of Korea

August, 1999………………………………..M.E. Environmental Engineering, Pennsylvania State University, University Park, Pennsylvania

December, 2002…………………………….M.S. Civil Engineering (Remote Sensing), The Ohio State University, Columbus, Ohio

January, 2003 – June, 2003…………………Graduate Research Associate, Agricultural, Environmental & Development Economics, The Ohio State University, Columbus, Ohio

January, 2004 – December, 2005…………...Internship in the Auditor’s Office of Delaware County

August, 2006………………………………...M.C.R.P, City and Regional Planning, The Ohio State University, Columbus, Ohio

April, 2008 – March, 2009………………….Graduate Research Associate, City and Regional Planning, The Ohio State University, Columbus, Ohio

FIELD OF STUDY

Major Fields: City and Regional Planning Minor Fields: Land Use, Urban Heat Island, Remotely Sensed Data, Geographic Information System, Quantitative Methods.

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TABLE OF CONTENTS

ABSTRACT ...... II

ACKNOWLEDGMENTS ...... IV

VITA ...... VI

TABLE OF CONTENTS ...... VIII

LIST OF TABLES ...... XII

LIST OF FIGURES ...... XXI

CHAPTER 1 INTRODUCTION ...... 1

CHAPTER 2 LITERATURE REVIEW ...... 5

2.1 OVERVIEW OF THE URBAN HEAT ISLAND (UHI) ...... 5

2.2 BASIC THERMODYNAMICS OF THE UHI...... 8

2.3 THE NATURE OF THE UHI...... 13

2.4 RESEARCH ON THE UHI...... 17

2.5 THE NEED FOR A NEW APPROACH TO UHI MODELING...... 29

CHAPTER 3 METHODOLOGY ...... 30

3.1. THEORETICAL BACKGROUND AND PROCEDURE...... 30

3.2. LANDSAT-5 GRID - BASED APPROACH...... 35

3.2.1. TEMPERATURES UNDER CALM (NO-WIND) CONDITIONS. .... 38

3.2.2. TEMPERATURES UNDER WIND CONDITIONS...... 42

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CHAPTER 4 DATA SOURCES AND PROCESSING ...... 45

4.1. DATA SOURCES...... 45

4.2. TEMPERATURE AND LAND-USE DATA ANALYSIS...... 52

4.3. MEASURED AND ESTIMATED TEMPERATURES...... 62

CHAPTER 5 EXPLORATORY ANALYSIS ...... 68

5.1. GENERAL DESCRIPTION OF COLUMBUS, OHIO...... 68

5.1.1. CLIMATE...... 68

5.1.2. POPULATION...... 75

5.2. RELATIONSHIP BETWEEN NDVI AND TEMPERATURE...... 76

5.2.1. DESCRIPTION OF THE NDVI...... 76

5.2.2. BASIC RELATIONSHIPS BETWEEN NDVI AND REMOTELY-

SENSED TEMPERATURE (RST)...... 81

5.2.3. LAND-USE SPECIFIC RELATIONSHIPS BETWEEN NDVI AND

REMOTELY-SENSED TEMPERATURES (RST)...... 85

CHAPTER 6 RESULTS AND ANALYSIS...... 92

6.1. NO-WIND-EFFECT ANALYSIS...... 92

6.1.1. LAND-USE NDVI MODELS IN THE NO-WIND-EFFECT CASE. . 97

6.1.1.1. MODELS FOR AUGUST 1, 2005...... 99

6.1.1.2. NDVI MODELS ACROSS THE YEAR 2005 - 2006...... 107

6.1.2. LAND-USE AREA MODELS IN THE NO-WIND-EFFECT CASE. ....

...... 111

6.1.2.1. MODELS FOR AUGUST 1, 2005...... 113

6.1.2.2. AREA MODELS ACROSS THE YEAR 2005-2006...... 120

6.1.3. MODEL COMPARISON IN THE NO-WIND-EFFECT CASE...... 122

6.2. WIND-EFFECT ANALYSIS...... 125

6.2.1. LAND-USE NDVI MODELS...... 125

6.2.2. LAND-USE AREA MODELS...... 144

6.2.3. MODEL COMPARISON IN THE WIND-EFFECT CASE FOR

FEBRUARY 25, 2006...... 160

6.2.4. ALTERNATIVE UPWIND AND DOWNWIND CONFIGURATIONS.

...... 162

6.3. SUMMARY...... 164

CHAPTER 7 APPLICATION OF THE MODEL ...... 168

7.1. OVERVIEW...... 168

7.2. IMPACT ANALYSIS ...... 171

7.2.1. THE PILOT TEST AREA...... 171

7.2.2. MODIFICATION OF CURRENT LAND USES...... 176

CHAPTER 8 CONCLUSIONS ...... 188

BIBLIOGRAPHY ...... 193

APPENDIX A REMOTELY-SENSED TEMPERATURES DERIVED WITH THREE

METHODS ON SIX DIFFERENT DATES ...... 203

APPENDIX B THE BEAUFORT WIND FORCE SCALE...... 209

APPENDIX C NDVI MODELS FOR DIFFERENT DATES WITH NO ACCOUNT

FOR WIND EFFECTS...... 212

APPENDIX D LAND-USE AREA MODELS FOR DIFFERENT DATES IN THE NO

WIND-EFFECT CASE...... 246

APPENDIX E WIND VARIATIONS AT THE FOUR MEASURING STATIONS. .. 279

APPENDIX F ANALYSIS OF THE REMOTELY-SENSED TEMPERATURE (RST)

AND NDVI VARIABLE...... 283

APPENDIX G LAND-USE OPTIMIZATION ...... 308

LIST OF TABLES

Table ...... Page

Table 2.1. Physical properties of several materials (from Oke, 1987)...... 7

Table 2.2. Radiative properties of several materials (from Oke, 1987) ...... 10

Table 4.1. Comparison of temperatures derived from three different methods on August 1,

2005...... 56

Table 4.2. Temperature statistics after removing outliers (k = 3), August 1, 2005...... 58

Table 4.3. NDVI statistics, August 1, 2005...... 61

Table 4.4. The five measuring stations in the CMA...... 62

Table 4.5. Comparison between the measured and the estimated temperatures...... 64

Table 4.6. Sum of the mean square errors at the five measuring stations...... 65

Table 4.7. Comparison between measured temperature and RST...... 66

Table 5.1 General monthly weather characteristics for the Columbus Metropolitan Area

(CMA)...... 69

Table 5.2. Observed monthly mean temperatures over the years 1976-2007 (°C)...... 70

Table 5.3. Population in Columbus, Ohio...... 75

Table 5.4. Basic statistics of NDVI in the Columbus Metropolitan Area (August 1, 2005).

...... 78

Table 5.5. Simple linear regression between RST and NDVI across all CMA pixels. .... 82

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Table 5.6. Log-log regression between RST and NDVI across all CMA pixels...... 83

Table 5.7. Linear relationships between the Box-Cox variables NDVI(µ) and RST(λ)...... 84

Table 5.8. Comparison of the R2 obtained for the linear, log-log, and Box-Cox models. 87

Table 5.9. Linear regression model between NDVI and RST for individual land uses. .. 88

Table 5.10. Log-log regression model for individual land uses...... 89

Table 5.11. Linear relationships between the Box-Cox variables NDVI(µ) and RST(λ) for

individual land uses...... 90

Table 6.1. Regression results for the NDVI models on August 1, 2005...... 100

Table 6.2. NDVI statistics for the independent variables on August 1, 2005...... 103

Table 6.3. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on

August 1, 2005...... 105

Table 6.4. R2s of the NDVI models across the year 2005-2006...... 108

Table 6.5. Statistics on NDVI for the six land uses for the whole Columbus Metropolitan

Area (CMA)...... 110

Table 6.6. Land-use area statistics for the independent variables on August 1, 2005. ... 114

Table 6.7. Regression results for the land-use are models on August 1, 2005...... 115

Table 6.8. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on

August 1, 2005...... 118

Table 6.9. R2s of the land-use area models across the year 2005-2006...... 120

Table 6.10. Comparison of the R2 values of the NDVI and area models in the no-wind-

influence case...... 123

Table 6.11. Weather data on February 25, 2006...... 126

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Table 6.12. R2s for different wind effects (α), buffer sizes (θ) and distance exponents (p)

on February 25, 2006...... 129

Table 6.13. Results for the highest R2 NDVI models on February 25, 2006...... 133

Table 6.14. NDVI statistics for the independent variables on February 25, 2006...... 137

Table 6.15. NDVI elasticity statistics under wind effect when (a) Tj = RST and (b) Tj =

estimated temperatures on August 1, 2005...... 140

Table 6.16. R2s for different wind effects (α), buffer sizes (θ) and distance exponents (p)

on February 25, 2006...... 146

Table 6.17. Regression results for the land-use area models under wind-effect case on

February 25, 2006...... 149

Table 6.18. Land-use area statistics for the independent variables on February 25, 2006.

...... 153

Table 6.19. Area elasticity statistics under wind-effect case when (a) Tj = RST and

(b) Tj = estimated temperatures on February 25, 2006...... 156

Table 6.20. Comparison of the highest R2s and wind effects on February 25, 2006...... 161

Table 6.21. Comparison of results for various upwind and downwind configuration

scenarios on February 25, 2006...... 163

Table 6.22. Comparison of the highest R2s of the wind-effect and no-wind-effect models

on February 25, 2006...... 164

Table 6.23. The highest R2s of the NDVI and area models in the no-wind-influence case.

...... 166

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Table 6.24. Highest R2s and (θ, p) for the NDVI and area models in the no-wind-effect

case across the year 2005-2006...... 167

Table 7.1. Distribution of the six land uses within the CMA on August 1, 2005

(1,641*1,605 = 2,633,805 cells)...... 170

Table 7.2. Comparison between remotely-sensed temperatures (TRST) and

model-estimated temperatures (Test) in the pilot test area...... 172

Table 7.3. Sub-area size, number of land-use cells and number of relocated cells...... 177

Table 7.4. Statistics for model-estimated temperatures for residential areas in Sub-areas 1

and 2 before and after land-use reallocation...... 180

Table 7.5. Ratios and differences of model-estimated temperatures for residential cells in

Sub-areas 1 and 2...... 183

Table 7.6. Statistics for model-estimated temperatures (Test) before and after land-use

reallocation in Sub-areas 3 and 4...... 184

Table 7.7. Ratios and differences of model-estimated temperatures for urban cells in Sub-

areas 3 and 4...... 187

Table A.1. Remotely sensed temperatures after removing outliers (k = 3)

on February 25, 2006...... 204

Table A.2. Remotely sensed temperatures after removing outliers (k = 3)

on April 11, 2005...... 205

Table A.3. Remotely sensed temperatures after removing outliers (k = 3)

on May 13, 2005...... 206

Table A.4. Remotely sensed temperatures after removing outliers (k = 3)

on September 2, 2005...... 207

Table A.5. Remotely sensed temperatures after removing outliers (k = 3)

on November 21, 2005...... 208

Table B.1. The Beaufort wind force scale...... 210

Table C.1. R2 for various (θ, p) combinations for each NDVI land-use model on February

25, 2006...... 214

Table C.2. Regression results for the NDVI models on February 25, 2006...... 216

Table C.3. NDVI statistics for the independent variables on February 25, 2006...... 217

Table C.4. Elasticity statistics when (a) Tj = RST and and (b) Tj = estimated temperatures

on February 25, 2006...... 218

Table C.5. R2 for various (θ, p) combinations for each NDVI land-use model on April 11,

2005...... 220

Table C.6. Regression results for the NDVI models on April 11, 2005...... 222

Table C.7. NDVI statistics for the independent variables on April 11, 2005...... 223

Table C.8. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on

April 11, 2005...... 224

Table C.9. R2 for various (θ, p) combinations for each NDVI land-use model on May 13,

2005...... 226

Table C.10. Regression results for the NDVI models on May 13, 2005...... 228

Table C.11. NDVI statistics for the independent variables on May 13, 2005...... 229

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Table C.12. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on

May 13, 2005...... 230

Table C.13. R2 for various (θ, p) combinations for each NDVI land-use model on August

1, 2005...... 232

Table C.14. R2 for various (θ, p) combinations for each NDVI land-use model on

September 2, 2005...... 234

Table C.15. Regression results for the NDVI models on September 2, 2005...... 236

Table C.16. NDVI statistics for the independent variables on September 2, 2005...... 237

Table C.17. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on

September 2, 2005...... 238

Table C.18. R2 for various (θ, p) combinations for each NDVI land-use model on

November 21, 2005...... 240

Table C.19. Regression results for the NDVI models on November 21, 2005...... 242

Table C.20. NDVI statistics for the independent variables on November 21, 2005...... 243

Table C.21. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on

November 21, 2005...... 244

Table D.1. R2 for various (θ, p) combinations for each area land-use model on February

25, 2005...... 247

Table D.2. Regression results for the area models on February 25, 2006...... 249

Table D.3. Area statistics for the independent variables on February 25, 2006...... 250

Table D.4. Elasticity statistics when (a) Tj = RSTs and (b) Tj = estimated temperatures on

February 25, 2006...... 251

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Table D.5. R2 for various (θ, p) combinations for each area land-use model on April 11,

2005...... 253

Table D.6. Regression results for the area models on April 11, 2005...... 255

Table D.7. Area statistics for the independent variables on April 11, 2005...... 256

Table D.8. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on

April 11, 2005...... 257

Table D.9. R2 for various (θ, p) combinations for each area land-use model on May 13,

2005...... 259

Table D.10. Regression results for the area models on May 13, 2005...... 261

Table D.11. Area statistics for the independent variables on May 13, 2005...... 262

Table D.12. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on

May 13, 2005...... 263

Table D.13. R2 for various (θ, p) combinations for each area land-use model on August 1,

2005...... 265

Table D.14. R2 for various (θ, p) combinations for each area land-use model on

September 2, 2005...... 267

Table D.15. Regression results for the area models on September 2, 2005...... 269

Table D.16. Area statistics for the independent variables on September 2, 2005...... 270

Table D.17. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on

September 2, 2005...... 271

Table D.18. R2 for various (θ, p) combinations for each area land-use model on

November 21, 2005...... 273

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Table D.19. Regression results for the area models on November 21, 2005...... 275

Table D.20. Area statistics for the independent variables on November 21, 2005...... 276

Table D.21. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on

November 21, 2005...... 277

Table F.1. Cross-tabulations between remotely sensed temperature (RST, °C) and NDVI

on February 25, 2006...... 286

Table F.2. Statistics on remotely sensed temperature (RST, °C) cross-tabulated with

positive, zero, and negative NDVI values on February 25, 2006...... 287

Table F.3. Cross-tabulations between remotely sensed temperature (RST, °C) and NDVI

on April 11, 2005...... 290

Table F.4. Statistics on remotely sensed temperature (RST, °C) cross-tabulated with

positive, zero, and negative NDVI values on April 11, 2005...... 291

Table F.5. Cross-tabulations between remotely sensed temperature (RST, °C) and NDVI

on May 13, 2005...... 294

Table F.6. Statistics on remotely sensed temperature (RST, °C) cross-tabulated with

positive, zero, and negative NDVI values on May 13, 2005...... 295

Table F.7. Cross-tabulations between remotely sensed temperature (RST, °C) and NDVI

on August 1, 2005...... 298

Table F.8. Statistics on remotely sensed temperature (RST, °C) cross-tabulated with

positive, zero, and negative NDVI values on August 1, 2005...... 299

Table F.9. Cross-tabulations between remotely sensed temperature (RST, °C) and NDVI

on September 2, 2005...... 302

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Table F.10. Statistics on remotely sensed temperature (RST, °C) cross-tabulated with

positive, zero, and negative NDVI value on September 2, 2005...... 303

Table F.11. Cross-tabulations between remotely sensed temperature (RST, °C) and NDVI

on November 21, 2005...... 306

Table F.12. Statistics on remotely sensed temperature (RST, °C) cross-tabulated with

positive, zero, and negative NDVI value on November 2, 2005...... 307

LIST OF FIGURES

Figure ...... Page

Figure 2.1 Urban heat island profile...... 7

Figure 2.2. Radiation balance at the surface...... 9

Figure 2.3. Temperature distribution (from Oke, 1987)...... 14

Figure 2.4. Effects of urban area u on its surrounding areas (from Landsberg et al., 1972).

...... 14

Figure 2.5. Relationships between maximum UHI intensity and population (from

Landsberg, 1979)...... 16

Figure 2.6. The UBL and the UCL (from Oke, 1976)...... 20

Figure 2.7. The diurnal energy balance for urban, suburban, and rural areas (from

Christen et al., 2003.) ...... 22

Figure 2.8. Short-wave radiative heating and long-wave cooling (from Oke, 1982)...... 23

Figure 2.9. The sky view factor in the UC (from Oke, 1982)...... 24

Figure 2.10. Maximum heat island intensity and H/W (from Oke, 1981)...... 25

Figure 3.1. Illustration of the proposed approach...... 31

Figure 3.2. Basic thermal balance at location (xo, yo)...... 32

Figure 3.3. Flowchart of the major research steps...... 34

Figure 3.4. Grid system, temperature, land use and wind effects...... 36

xxi

Figure 3.5. Hypothetical land use and temperature patterns...... 37

− p Figure 3.6. Weight ( dij ) based on distance from the central pixel...... 40

Figure 3.7. The effect of neighboring land uses on the temperature at j when θ = (3 * 3).

...... 42

Figure 3.8. Weight matrix with wind effect...... 43

Figure 4.1. Landsat dataset for the Columbus Metropolitan Area (CMA)...... 46

Figure 4.2. Six land-use types in the Columbus Metropolitan Area (CMA) on August 1,

2005...... 48

Figure 4.3. Changes in land cover with different sizes of convolutions...... 51

Figure 4.4. Temperature distribution in the Columbus Metropolitan Area (CMA) on

August 1, 2005...... 52

Figure 4.5. Overlaying temperature layer on land-use layer...... 53

Figure 4.6. Temperature distributions after removing outliers, August 1, 2005...... 59

Figure 4.7. The locations of the five measuring stations...... 63

Figure 5.1. Monthly mean temperature variation at the measuring station in West Dublin.

...... 72

Figure 5.2. Monthly mean temperatures at the five measuring stations during the year

2005...... 74

Figure 5.3 Wavelength distribution...... 76

Figure 5.4 Effect of vegetation health on NDVI...... 79

Figure 5.5. Variations of mean NDVI by land-use types (April 2005 – February 2006) . 80

Figure 6.1. Measuring stations and surrounding areas (1,641*1,605 = 2,633,805 cells). 93

xxii

Figure 6.2. Distribution of central cells across land uses when θ = 11...... 95

Figure 6.3. Cell buffer pattern when θ = 5...... 95

Figure 6.4. Comparison of the R2s of the best NDVI models in the no-wind-effect case.

...... 108

Figure 6.5. Illustration of the land-use area collinearity issue...... 112

Figure 6.6. Comparison of the R2s of the best land-use area models ...... 121

Figure 6.7. Matrix of wind direction from the West when θ = 5...... 128

Figure 6.8. Alternative upwind and downwind configurations when θ = 5...... 162

Figure 7.1. The pilot test area for impact analysis on August 1, 2005...... 173

Figure 7.2. Comparison between remotely-sensed (TRST) and model-estimated (Test)

temperatures for the pilot test area...... 174

Figure 7.3. Modification of current land uses in Sub-areas 1 to 4...... 178

Figure 7.4. Changes in temperatures in Sub-areas 1 and 2...... 181

Figure 7.5. Changes in temperatures in Sub-areas 3 and 4...... 185

Figure 8.1. Illustration of a green roof-top...... 192

Figure E.1. Hourly wind speed measurement at the four measuring stations on February

25, 2006...... 280

Figure E.2. Hourly wind speed measurement at the four measuring stations on April 11,

2005...... 280

Figure E.3. Hourly wind speed measurement at the four measuring stations on May 13,

2005...... 281

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Figure E.4. Hourly wind speed measurement at the four measuring stations on August 1,

2005...... 281

Figure E.5. Hourly wind speed measurement at the four measuring stations on September

2, 2005...... 282

Figure E.6. Hourly wind speed measurement at the four measuring stations on November

21, 2005...... 282

Figure F.1. Plotting of NDVI and RST (°C) observations on February 25, 2006...... 284

Figure F.2. Plotting of NDVI and RST (°C) observations on April 11, 2005...... 288

Figure F.3. Plotting of NDVI and RST (°C) observations on May 13, 2005...... 292

Figure F.4. Plotting of NDVI and RST (°C) observations on August 1, 2005...... 296

Figure F.5. Plotting of NDVI and RST (°C) observations on September 2, 2005...... 300

Figure F.6. Plotting of NDVI and RST (°C) observations on November 2, 2005...... 304

Figure G.1. Simple lattice for the optimization model...... 310

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CHAPTER 1

INTRODUCTION

Urbanization and urban sprawl are the dominant factors in regional landscape

evolution across the world, and can significantly affect local climate. Rapid urbanization

results from the large-scale development of commercial, manufacturing and

transportation areas, leading to the emergence of the urban heat island (UHI) effect,

whereby urbanized areas are characterized by temperatures higher than those of the

surrounding rural areas. In major cities all over the world, including Phoenix,

Washington, Shanghai and Tokyo, the maximum temperatures in July have been steadily

increasing at a rate of 0.56°C to 0.83°C every ten years over the last 30 to 80 years.1

Green spaces, that have lower temperatures, are being replaced by land uses that have higher thermal contents, such as central business districts (CBD), commercial areas and dense housing. The increased heat in urban areas requires an increase in the amount of energy used for cooling buildings, leading to a deterioration of air quality and negative health effects. For instance, higher temperatures increase the generation of ozone (O3)

pollution (Lo and Quattrochi, 2003; Cardelino and Chameides, 2000). For example, in

1 http://eetd.lbl.gov/HeatIsland/ 1

2 Los Angeles, the concentration of O3 is often 240 ppbv at 32°C, while its National

Ambient Air Quality Standard (NAAQS) is 120 ppbv. Ozone concentration may increase

from a desired to an unacceptable level with a temperature increase of just 10-15°C

(Rosenfeld, 1996). The UHI can contribute up to 3°C within this range.

According to the U.S. Department of Energy (1996), one sixth of the electricity in

the U.S. is consumed to cool buildings, at an annual cost of $40 billion. Mitigation plans

for the UHI could save approximately $10 billion in annual energy costs. The resulting

decrease in atmospheric pollutants, such as ozone and smog, would save another $5

billion through reduction in medical costs3. To promote sustainable development in urban

areas, local governments should adopt appropriate policies. Green spaces have clearly a

pivotal role in influencing building temperatures and energy consumptions (Stull, 1988),

by reducing the UHI effect. The evapotranspiration of plants helps improve air quality

and reduce urban air temperatures (Sturman, 1998). Green spaces alleviate photochemical

reactions and reduce hydrocarbons emitted from power plants, because of lower energy

needs. Despite the substantial costs of the UHI in urban areas, few cities have tried to

develop comprehensive programs to reduce urban warming (Rodgers et al., 2001), partly because there is little research on the relationship between the structure of urban areas and the UHI effects. Rodgers et al. (2001) believe that the UHI is more related to urban

design, than to development density. If the relationship between city form and the extent of the UHI were known, it would be possible to identify “thermally efficient” models of urban development.

2 Parts per billion (109) by volume 3 http://satellite.zodiak.com/desti nation/framesversion/greenhouse/greenho use.html 2

The urban heat island effect is one of the atmospheric phenomena that clearly

require further research. However, there have been many factors inhibiting such research,

including the complexity of the urban atmosphere and of the energy and mass balances

related to various land uses, the lack of a clear theoretical framework, and the lack of

temperature data in cities (Oke, 1982). However, the present availability of remotely-

sensed data makes it possible to overcome these difficulties. A satellite-based

methodology is used to estimate urban temperatures and to classify land use/land cover

(LULC). Remotely-sensed thermal imagery can provide a time-synchronized grid of

temperature data over a whole city, and distinctive differences in the temperatures of individual buildings (Nichol, 1996).

The objective of this research is to uncover the relationship between land-use and ground-based temperature patterns in urban areas, making use of data for the Columbus

Metropolitan Area (CMA). Land-use and temperature distributions derived from Landsat-

5 satellite data, and a Geographical Information System (GIS) are used to visualize and analyze the interactions between temperature and land use. A new methodology is proposed, combining thermal balance concepts with statistical methods, to estimate how changes in land uses affect local temperatures.

The remainder of this dissertation is organized as follows. Chapter 2 consists of a literature review, including the basics on the UHI and existing research on the interactions between land use and the UHI. Chapter 3 presents the theoretical/methodological framework, making use of basic thermodynamics and statistics. Chapter 4 describes data sources and processing. Chapter 5 presents

3 exploratory analysis of the CMA data, to help understand the climate of the CMA, including basic relationships between NDVI and local temperatures. Chapter 6 presents modeling results and their critical analysis. Chapter 7 illustrates potential applications of the modeling approach for land-use planning. Chapter 8 presents conclusions and outlines areas for further research.

CHAPTER 2

LITERATURE REVIEW

In this chapter, research on the urban heat island (UHI) is reviewed and a new

approach using remotely-sensed data is outlined. After an overview of the UHI, the basic thermodynamics and the nature of the UHI are discussed. Research on the UHI is then reviewed, and a brief outline of the UHI model proposed in this research is presented.

2.1 OVERVIEW OF THE URBAN HEAT ISLAND (UHI)

The surface of the earth has experienced various changes because of anthropogenic activities over the past half century, including mostly deforestation and urbanization (Ownes et al., 1998). In the United States, urban areas have rapidly increased since World War II, because economic growth has increased the housing supply and suburbanization (Adams, 1984).

The expansion of urban areas has been an important factor in environmental impacts related to microclimate. Natural land covers are replaced by urban materials, such as concrete, glass and metal. Natural features, including vegetation, water bodies and soil, enhance the retention of thermal energy by a natural mechanism called 5

evapotranspiration (Rodgers et al., 2001), which reduces the amount of thermal energy reaching surface features and the amount of heat re-emitted into the atmosphere.

However, anthropogenic activities have resulted in changes in surface energy balances, with an increase in sensible heat flux instead of latent heat flux (Stull, 1988).

Table 2.1 presents the thermal properties of construction materials, which have a larger heat capacity than vegetation and other natural features, resulting in the absorption

of a large quantity of heat energy into urban surfaces during the daytime. This absorbed

thermal energy is then slowly released in the urban regions during the late afternoon and night. This excess heat energy produces urban and suburban temperatures 1°C to 6°C higher than those in rural areas (Rodgers et al., 2001).

The urban heat island (UHI) can be described as a pattern of temperatures higher in urban areas than in the surrounding areas (Montavez et al., 2000). Figure 2.1 illustrates this temperature distribution. The major concern related to the UHI is air pollution.

Higher temperatures increase ozone (O3) pollution (Lo and Quattrochi, 2003), because

elevated temperatures can trigger the chemical reactions that form ozone (Cardelino and

Chameides, 2000).

Volatile organic compounds (VOCs) are one of the precursors of O3, emitted in

part by vehicles. Warmer temperatures can increase O3 formation from VOCs. A 1°F rise

over 70 °F can increase the potential ozone formation by approximately 3% (USDOE,

1996). A temperature reduction of 3°F in urban areas is estimated to ameliorate air quality in a way that would be roughly equivalent to the substitution of electric vehicles for gasoline vehicles (USDOE, 1996).

Density (σ), Heat capacity (C), Thermal conductivity (k),

kg/m3 J/m3/K W/m/k Dry clay soil 1.6*103 1.42 0.25 Saturated clay soil 2.00*103 3.10 1.58 Asphalt 2.11*103 1.94 0.75 Dense concrete 2.40*103 2.11 1.51

Table 2.1. Physical properties of several materials (from Oke, 1987).

Figure 2.1 Urban heat island profile.

2.2 BASIC THERMODYNAMICS OF THE UHI

The surface energy balance is composed of radiative and non-radiative components (Oke, 1982). Radiative components include incoming and outgoing short- wave and long-wave radiations, and non-radiative components include sensible heat flux, latent heat flux, and the change in energy storage in water.4

The incoming energy flux, Q*, consists of the net effect of incoming and outgoing

long- and short-wave radiations. Figure 2.2 illustrates the radiation balance at the surface,

which can be summarized with the equation5:

Q* = (S↑ + S↓) + (L↑ + L↓) (2.1) where Q* is the net energy flux, S↑ is the short-wave radiation reflected by the surface,

S↓ is the short-wave radiation from the sun (both direct and diffuse), L↑ is the long-wave

radiation reflected and emitted by the surface and L↓ is the incoming long-wave radiation

from clouds and atmosphere. Net radiation, the sum of the down-welling and the up-

welling radiation, is the fundamental energy balance at the urban surface. The down-

welling radiation has been described as a direct heating radiation. The up-welling

radiation has two components: the reflected short-wave radiation and the re-radiated

long-wave radiation. The up-welling radiation has an important role in decreasing urban

temperature.

4 http://geography.uoregon.edu/envchange/clim_animations/ 5 http://www.met.wau.nl/projects/jep/report/ecromp/node4.html#fig_ intro_radia 8

From Sun Reflection From clouds Reflection and atmosphere and emission

S↓ S↑ L↓ L↑

Figure 2.2. Radiation balance at the surface.

The surface albedo is also one of the important factors in radiative components affecting urban temperatures (Oke, 1987). It is defined as the ratio of the down-welling to the up-welling of solar irradiances. It is subject to considerable spatial and temporal variations, and is an indicator of land-cover change. Table 2.2 presents the radiative properties of several materials.

Albedo (α) Emissivity (ε)

Asphalt 0.05 – 0.20 0.95

Concrete 0.10 – 0.35 0.71 – 0.91

Urban areas 0.10 – 0.27 0.85 – 0.96

Soils: wet to dry 0.05 – 0.40 0.98 – 0.90

Grass: long to short 0.16 – 0.26 0.90 – 0.95

Table 2.2. Radiative properties of several materials (from Oke, 1987)

With regard to the non-radiative components in the UHI, the sensible heat flux

and the latent heat flux are two major factors (Terjung and O’Rourke, 1980). The sensible

heat flux (QH) is a direct heating flux, and is a function of surface and air temperatures.

However, the latent heat flux (QE) is energy that is stored in water vapor. It is a function

of surface wetness and relative humidity. Finally, the net effect of the non-radiative components can be summarized as follows (Oke, 1982).

* Q = QE + QH + ΔQs (2.2)

* where Q is the surface net radiant flux and ΔQs is the thermal storage. ΔQs is usually

assumed greater in the city than in its surrounding areas, because building materials have

larger thermal conductivity (k)6 and heat capacity (C)7. These two properties are sometimes combined as the thermal admittance or thermal inertia, kC 8 (Oke, 1982).

Understanding energy transfer mechanisms is critical in studying the UHI and in designing sustainable urban forms, because energy cannot be lost, but only changes its form. In the UHI, light energy is converted into thermal energy that increases temperatures in urban areas.9 There are three important ways to transfer energy between

materials: convection, conduction and radiation.10 Advection is also important when dealing with the energy balance of the UHI.

Convection is the transfer of heat by the motion of a fluid. When the sun’s energy reaches the earth's surface, it is transferred to the air, which results in the temperature

increase of the air. This heated air moves upward by buoyancy. The warm rising air cools

down when it reaches higher altitudes, and the cooler air begins to sink. When this air

reaches the surface again, it is re-heated, and goes back to the original rising column. The

circulation of the mantle inside the Earth is a good example of convection.

Conduction is the transfer and distribution of heat energy from atom to atom

within a substance. Conduction occurs via collisions between atoms and molecules. This

transfer takes place mostly in solids. However, conduction can occur in fluids. For

example, a spoon in a cup of hot soup becomes warmer because the heat from the soup is

conducted and transferred to the spoon.

6 Thermal conductivity: A measurement of the rate at which heat passes through a material. 7 Thermal capacity: The amount of heat that a material can store. 8 Thermal inertia: A measurement of the response of a material to temperature changes. 9 http://science.nasa.gov/newhome/headlines/essd21jul98_1.htm 10 http://www.free-definition.com/Free-convection.html 11

Radiation can directly transport energy through space without any kind of matter.

Sunlight is a good example of radiation. The sun transfers its energy over 93 million miles in space.

Heat advection is the horizontal movement of heat by the wind. Advection refers to the horizontal transport of heat and pollutants. This phenomenon can be defined as

“the process of transport of an atmospheric element or property just from the mass motion (velocity field) of the atmosphere.” 11

11 http://www.wmo.ch/web/gcos/terre/variable.html 12

2.3 THE NATURE OF THE UHI.

The differences in energy and stability between urban and rural areas produce

differences in the warming and cooling rates in those areas. This causes the distinctive

diurnal air temperature pattern that generates the UHI, and these differences control the

intensities of the UHI (Oke, 1982).

Figure 2.3 shows the typical hourly variations of urban and rural air temperatures

under calm weather conditions. In rural areas, the net radiative energy and heat energy

leave the surface at about sunset. As the temperature decreases, the cooling rate also

declines. This exponential decay continues until sunrise. Then, solar heating generates a

sensible heat flux. This sensible heat flux merges with radiative energy from the surface,

which is the remnant of the nocturnal radiative inversion, and these cumulative energy

flows increase air temperatures. The warming rate declines until mid-afternoon, when the

maximum temperature occurs.

The UHI is a nocturnal phenomenon due to different urban and rural cooling rates,

rather than heating rates (Oke, 1982). As shown in Figure 2.3, the rates of warming and

cooling in urban areas are smaller than those in rural areas, except in the latter half of the

night. Heat intensity ( ΔTu−r ), the difference in temperatures between urban and rural

areas, starts increasing in the late afternoon and first part of the night, and then declines to

zero by noon. At around sunset, the cooling rate of the rural environment is larger than

that of urban areas. This result suggests that the spatial distribution of the UHI is related

to the distribution of surface land uses with different cooling rates. The UHI intensity could be reduced if the urban cooling rate were slightly greater (Oke, 1982).

Figure 2.3. Temperature distribution (from Oke, 1987).

(a) Wind effect

(b) No wind effect.

Figure 2.4. Effects of urban area u on its surrounding areas (from Landsberg et al., 1972).

The UHI has an influence on the overlying atmosphere. If ideal conditions occur, such as calm wind, flat open terrain, and cloudless sky, the vertical thermal modification takes the form of a dome. In reality, however, winds are not calm for a long time. Thus, the more normal form would be entrained in the direction of the wind (Oke, 1982). In

Figure 2.4-(a), the shape and size of the surrounding area (u’) is controlled by the wind.

In Figure 2.4-(b), u’ is defined as the surrounding area affected by the urban area (u) under no wind conditions (Landsberg et al., 1972).

The characteristics of the UHI are related to both the intrinsic nature of the city, such as its size, population, building density and land uses, and external factors, such as climate, weather and seasons (Oke, 1982). Also, there is a close relationship between

UHI intensity and population (Landsberg, 1979; Lo and Faber, 1997). Figure 2.5 shows this relationship for European, Australian and North American cities. The geographical locations of cities are important, including the nature of soils, the presence of water, topographical features, vegetation and land uses. There is also a relationship between

UHI intensity and area city size (Oke, 1982).

Statistical studies show that the most important meteorological variables for UHI intensity are wind speed and cloud cover (Chandler, 1965; Duckworth and Sandberg,

1954). The relationship between UHI intensity and wind speed is non-linear. A low cloud cover is more effective than a high cloud cover in reducing UHI intensity.

UHI intensity (°C)

Populatio n

●: cities in North America ○: cities in Europe +: cities in Australia

Figure 2.5. Relationships between maximum UHI intensity and population (from Landsberg, 1979).

In cities that are located in temperate latitudes, there is a seasonal variation in the

UHI. The UHI frequently occurs with the highest intensity in summer and autumn,

although the largest heating requirements take place in winter (Chandler, 1965; Lee,

1979). This finding suggests that anthropogenic heat is not a primary factor that causes

the UHI (Oke, 1982).

In tropical regions, the wet–dry season difference is more significant than the winter–summer difference. According to studies by Adebayo (1987) and Jauregui (1997), there is a larger heat island effect in the dry season. This finding is consistent with a larger thermal admittance in the rural environment due to moist soils. Tereshchenko and

Filonov (2001) find negative heat island effects during the rainy seasons in Guadalajara,

Mexico.

2.4 RESEARCH ON THE UHI.

In 1833, Luke Howard was the first to report that air temperature in a city is

higher than in the surrounding rural areas. Initially, research on the UHI focused on urban

effects, describing how the UHI has an effect on air pollution (Oke, 1982). However, the

focus of UHI research has since shifted to understanding the UHI process.

Many attempts have been made to model urban development in connection to the

UHI (Arthur et al., 2003). Oke (1982) has summarized the knowledge about the intensity,

spatial and vertical structure, dynamics, and determinants of the UHI. He also has

reviewed temperature patterns near the surface. However, there are still many inherent

limits in studying the UHI, such as the complexity of the urban atmosphere (i.e., energy

balances and land uses) and the difficulty to measure temperatures in cities. Urban areas are composed of many elements, such as gardens, lawns, and paved areas (Oke, 1982;

Suckling, 1980; Doll et al., 1985). These various elements have different radiative and thermal properties, and they also interact with one another (Oke, 1989). These interactions result in radiative exchange and advection at a small scale.

Different physical properties of UHIs characterize different cities. Despite a similar climate, Nasrallah et al. (1990) find that the UHI for Kuwait City is less intense than that for Phoenix, Arizona. They explain this difference in terms of the form and location of the city on the Arabian Gulf. Magee et al. (1999) and Kumar et al. (2001) find unusual seasonal patterns of UHIs in winter for Fairbanks, Alaska, and Mumbai, India. In

Reykjavik, Iceland, a tendency for negative heat island intensities, with warmer temperatures in rural areas than in urban areas, is found in the summer (Steinecke, 1999).

Changes in air temperature within urban areas are closely related to urban

geometry (Yamashita et al., 1986; Westendorf et al., 1989; Eliasson, 1992 and 1994; Goh

and Chang, 1999; and Mont´avez et al., 2000). Attempts have been made to simulate the

dependence of the UHI on urban geometry and the differences in thermal admittance

(Arnfield, 1990; Oke et al., 1991; Johnson et al., 1991; Swaid, 1993). Todhunter (1990)

also investigates the role of canyon orientation and asymmetry, with an emphasis on the

role of the diurnal pattern of solar radiation. Oke et al. (1991) focus on geometry, and also emphasize differences in thermal admittance that may have equal significance.

Moreover, the moisture content of soils in rural areas has thermal admittances similar to those of urban building materials. This may be the reason why the small (and even negative) UHI intensities occur in moist tropical locations.

Other important factors that control the UHI are site factors (Ackerman, 1985;

Goldreich, 1992; Kuttler et al., 1996), humidity differences between urban and rural areas

(Holmer and Eliasson, 1999), and advection due to the temperature gradient between urban and rural areas (Haeger-Eugensson and Holmer, 1999). Moreover, there are arguments about advective effects on the UHI. Oke (1982) assumes that horizontal advection is negligible in calculations of the urban energy balance. However, Tapper et al. (1981) state that advective effects by the local wind in winter are likely to affect the

UHI, and suggest that they should be included in the calculations of urban energy balances.

Scale is an important concept for understanding how different elements of the urban surface interact with adjacent atmospheric layers. The smaller the scale, the less the

variability of the urban surface (Schmid and Oke, 1992). Urban climatology should

consider the heterogeneity and complexity of variables at different scales (Cionco and

Ellefsen, 1998). For example, building walls and the elements located between buildings can be defined as an urban canyon (UC). UCs and the roofs of the neighboring buildings define blocks. Blocks scale up to neighborhoods, land-use zones, and, finally, the entire city. At the same scale, each unit also interacts with adjacent units by small-scale advection (Ching et al., 1983). Therefore, defining the urban surface according to scale is important to explain energy balances (Arnfield, 2003).

An important distinction is related to the urban boundary layer (UBL) and the urban canopy layer (UCL), as shown in Figure 2.6 (Oke, 1976). Although the two UHIs created by these layers have different scales and processes, both are measured by the difference in temperature between urban and surrounding areas. This distinction has been a guiding principle in all types of urban climate research since the urban heat model was proposed by Oke (1976).

The UCL extends roughly from ground to roof level. UCL processes are controlled by the micro-scale, representing site-specific characteristics. In contrast, UBL processes, taking place above roof level, are a local or a meso-scale phenomenon that is controlled by larger spatial and temporal scales. Meso-scale phenomena are affected by the urban surface or land uses (Arnfield, 2003).

The lowest portion of the UBL can be regarded as a roughness sublayer (Roth et al., 1989b). The mixing effect of turbulence disappears at some height. The roughness of individual elements is not important any more, and a new layer is created. This layer is

sometimes called the constant-flux layer (Roth, 2000). In other words, the layer is stable

at a certain height, which is enough to measure energy fluxes.

Figure 2.6. The UBL and the UCL (from Oke, 1976).

Remotely-sensed data from satellites represent additional potential for UHI research (Carlson et al., 1981; Nichol, 1996). Arthur and Carlson (2000) use a multiple linear regression model to detect the impact of urban development on surface temperatures from multispectral satellite data. They show how surface developments affect parameters derived from Landsat data, such as the fractional vegetation cover and surface temperature. In this research, the fractional vegetation is regarded as the most important variable, and the NDVI (Normalized Difference Vegetation Index) is used to estimate the fractional vegetation. The NDVI is defined by the relationship between the red band (band 3: 0.63-0.69 µm) and the near infrared band (band 4: 0.76-0.90 µm), with:

Band 4−Band 3 NDVI= (2.3) Band 4+Band 3

The fractional vegetation cover (Fr) is estimated as:

Fr = N *2 , (2.4)

NDVI− NDVIo where N* = , NDVIs is the NDVI of a 100 % vegetation cover, NDVIo NDVIs − NDVIo is the NDVI of bare soil and NDVI is the value for the given pixel.

However, thermal remote sensing has some drawbacks. It tends to overestimate the intensity of UHIs, because of the heterogeneous nature of the urban surface detected by a satellite sensor (Roth et al., 1989a). Voogt and Oke (1997) address this issue by comparing the measured temperature at the surface with the remotely-sensed temperature. As expected, the measured temperature can significantly differ from the surface temperature estimated by the remote sensor. The resolution of the sensor is naturally an important determinant of the precision of the estimates.

The UHI has been approached as the difference between urban and rural energy balances since the 1970s (Oke, 1982; Arnfield, 2003). Figure 2.7 depicts the differences in energy balance in urban, suburban and rural areas. The sensible heat flux and the latent heat flux per unit surface area are represented in Figure 2.7. According to Terjung and

O’Rourke (1980), the sensible heat flux and the outgoing long-wave radiation are the two primary factors in the UHI. As shown in Figure 2.8, about 60% of the daytime radiant surplus is removed by the convective sensible heat flux, and about 30% is conducted into

the urban canyon ( ΔQs ). At night, approximately 90% of the net radiative heat flux is released to the sky from the urban canyon in the form of long-wave radiation.

Many other variables, such as moisture content and thermal properties of the soil, can have an effect on the sharing of heat between soil and atmosphere. The ratio between sensible and latent heat fluxes, called Bowen’s ratio ( β ), heavily depends on surface

moisture content (Oke, 1982). Typical values of β in rural areas are in the range from

0.4 to 0.8. When the surface is dry, β is 1.5 or greater in the mid-latitudes (Bailey,

1977).

Time Time Time

■: the thermal storage of urban canyon ( ΔQs ) ●: sensible heat flux (QH) *: ♦: the latent heat flux (QE) Q the surface net radiant flux density ( )

Figure 2.7. The diurnal energy balance for urban, suburban, and rural areas (from Christen et al., 2003.)

Figure 2.8. Short-wave radiative heating and long-wave cooling (from Oke, 1982).

On the other hand, modeling of the energy balance in urban areas is difficult due to their heterogeneous nature (Oke, 1982). In spite of the complicated structure of the urban environment, there have been studies considering the more dominant surface features, such as urban canyons (Nunez and Oke, 1980). The urban canyon (UC) consists of the surfaces of buildings, the street, the enclosed air volume, the open airspace at roof level, and roads. Energy fluxes may occur horizontally in UCs (Arnfield, 2003). At night, net long-wave radiation (L*) takes place and is proportional to the size of the sky view

factor (Ψs) in the UC (Oke, 1982). Figure 2.9 shows a diagram defining the sky view

factor. The relationship between width (W), height (H) and the incident degree of solar

radiation can be represented as follows (Oke, 1982):

Ψs =cos(β) (2.5)

Equation (2.5) shows that the incident solar radiation and the loss of long-wave radiation to the sky depend on the urban geometry.

Figure 2.9. The sky view factor in the UC (from Oke, 1982).

Oke (1981) has tried to find the relationships between the maximum intensity of the UHI and the height/width ratio of the street canyons (H/W). He has observed these relationships in 31 cities located in North America, Europe and Australia. As shown in

Figure 2.10, the relationships between the maximum intensity of the UHI (Tu-r(max)) and

H/W can be summarized as follows.

Tu-r(max) = 7.45 + 3.97·ln(H/W) (2.6)

UHI intensity (°C)

H/W

•: cities in North America ○: cities in Europe +: cities in Australia

Figure 2.10. Maximum heat island intensity and H/W (from Oke, 1981).

The energy flux also depends on moisture availability (Oke, 1982). When both

the city and its rural surroundings are wet, the differences in energy flux are small.

However, in drier conditions, impervious areas in urban areas, such as roads, parking lots and the roofs of buildings, lead to high surface temperatures and produce a large amount

of sensible heat flux, even at night (Asaeda and Ca, 1993). The impervious areas also reduce the amounts of water storage in the subsurface and of evapotranspiration at the surface (Oke and Cleugh, 1987) and are able to convert radiant energy into sensible heat energy.

The release of anthropogenic heat is also important in urban areas (Oke et al.,

1991). Studies of anthropogenic heat flux are relatively straightforward (Arnfield, 2003).

Swaid and Hoffman (1990–91) analyze the impact of the anthropogenic heat flux on air temperature. Steinecke (1999) finds that the city-wide average anthropogenic heat flux is approximately 35 W/m2 in the case of Reykjavik, Iceland. Ichinose et al. (1999) estimate

the anthropogenic heat flux in residential areas in Tokyo, Japan, at 30 W/m2 in the

summer and 1,590 W/m2 in winter.

According to Estournel et al. (1983), pollutants have a significant impact on urban

temperature. Industrial aerosol and photochemical smog can attenuate solar irradiance.

There has been a 33% decrease in solar radiation in Hong Kong over a 35-year period, which cannot be explained by natural phenomena (Stanhill and Kalma, 1995). In the case

of Central Mexico City, which experiences serious air pollution, an average 22% decline

in solar irradiation has been detected (J´auregui and Luyando, 1999). The reduction is

larger in winter than in summer, with a 0-10% reduction rate on top of the UC (Peterson

and Stoffel, 1980). However, long-wave radiation in daytime can be greater because of

emissions of long-wave radiation from solar-heated air pollutants (Rouse et al., 1973).

The effect of typical pollutants on the incident long-wave radiation and solar fluxes can

be positive or negative (Arnfield, 1982). Finally, the difference in long-wave radiation

between urban and rural areas is less than 5% (White et al., 1978).

It is during the 1990s that knowledge derived from research on UHIs and related

climate modifications has started to be used for the design of a thermally efficient urban

model (Sturman, 1998). Urban development should consider both microclimatic

26 variations and prospective impacts. However, Evans and Deschiller (1996) demonstrate the difficulty in applying such knowledge to real urban development, using examples from Buenos Aires.

Several studies have focused on methods to minimize the effect of the UHI. Two major factors must be considered to improve the urban environment: albedo and vegetation. Bretz et al. (1998) examine the effect of highly reflective materials in decreasing the absorption of solar radiation. According to Taha et al. (1997), the impact of a 15% increase in albedo would be a decrease in air temperatures of approximately

2.8°C over the central areas of Los Angeles. Also, a 15% increase in vegetation cover would lead to a similar result. Finally, the results show that simultaneous increases in albedo and vegetation cover would decrease air temperatures by 2-5°C over the Los

Angeles urban region.

Vegetation in urban areas reduces the UHI effect and the amount of energy needed for cooling. Shaw and Bible (1996) provide a general overview of this approach.

Akbari et al. (1997) also conclude that vegetation clearly has an important role for urban temperatures and energy use. Trees intercept rainfall, mitigate pollution and reduce wind speed. They also provide shaded areas and decrease temperature by evapotranspiration.

More detailed research about the effect of vegetation on the balance of surface energy is available in Grimmond et al. (1996).

There is likely to be a relationship between the amount of trees and energy consumption (Sturman, 1998). However, it is very difficult to uncover this relationship

(Kjelgren and Montague, 1998). The thermal properties of the surrounding environment

have a large effect on the response of trees. For example, higher temperatures on asphalt

surfaces cause decreased evapotranspiration from leaves. In other cases, some plants emit

biogenic hydrocarbon, which leads to an increase in ozone concentration, although the

reduction in temperature would decrease photochemical activity (Sturman, 1998).

The design of a new urban development should then be a compromise between the ideas of the architects, environmental engineers, and urban planners. It is very crucial that these professionals are educated about the importance of climatic factors for urban design and planning (Evans and Deschiller, 1996). Cooperation or consensus building through discourse and education must be achieved, because technical issues cannot be separated from social, economic, and political issues, and stakeholders who have different viewpoints must engage in analytical reviews and decision-making processes.

Corburn (2009) reports on such a co-production in the case of the UHI in New York City,

that has contributed to a more scientifically legitimate decision-making process that is

publicly transparent and accountable for. Golany (1996) describes a set of basic factors

that can be used for an urban design that is thermally efficient, including the site selection

of individual dwellings and an urban layout for a given climate. Adjustments should be

made in response to the prospective impacts of several factors, such as airflow and shade.

2.5 THE NEED FOR A NEW APPROACH TO UHI MODELING.

Despite the substantial costs of the UHI in urban areas, no city has tried to

develop comprehensive programs to reduce urban warming (Rodgers et al., 2001). It is therefore not surprising that little research has been conducted on the relationship

between the design of a city and its physical properties for absorbing heat. Earlier studies

have mostly focused on general UHI concepts, the differences in energy balances

between urban and rural areas and the role of urban geometry. UHI models try to

measure, observe and analyze how the rapid growth of urban areas has impacted the

region's microclimate and air quality (Oke, 1982).

The present research focuses on developing methods for minimizing the UHI

phenomenon through the configuration of alternative urban land-use patterns. According

to Rodgers et al. (2001), the UHI may be more related to the urban land-use layout than

to the density of development, although it is commonly assumed that the UHI is related to

the density of development. If the relationship between patterns of land uses and

temperatures can be better understood and quantified, it should be possible to design

“thermally efficient” cities. The goal of this research is to develop such quantitative

relationships and to demonstrate their use for planning and design.

CHAPTER 3

METHODOLOGY

This chapter presents the proposed modeling approach, based on statistical

techniques and remotely sensed grid data. Land use/land cover (LULC) and temperature

data, derived from Landsat-5 data, are used to develop a model relating temperatures and land-use patterns. A brief description of thermal dynamics is presented first. This chapter also shows how statistical methods can be used to analyze thermal dynamics with remotely sensed data sets. Two cases, with and without wind effect, are considered.

3.1. THEORETICAL BACKGROUND AND PROCEDURE.

Research on the climatic consequences of land use/land cover (LULC) alterations has concentrated primarily on urbanization (Asaeda and Ca, 1993; Taha et al.,1997;

Arnfield, 2003). However, there are few studies based on data derived from satellites and

on how changes in LULC at a specific location affect the temperature at that location. A

further question is related to the impact of changes in neighboring land uses surrounding

a specific location on the change in temperature at that location.

To answer these questions, the surface temperature at a location (xo, yo), T(xo, yo), is assumed to be a function of both the land use at (xo, yo) and the neighboring land uses.

Wind effects must be also considered. This approach is illustrated in Figure 3.1, which

points to the relationship:

T(xo, yo) = f {L(xo, yo), L(xk, yk), u, ε} (3.1) where L(xo, yo) is a vector of variables for land use at location (xo, yo), L(xk, yk) is a vector

of variables for neighboring land uses, u is the wind effect, and ε includes other variables

that are not observed.

Wind (u)

:Neighboring land uses : Land use at (xo, yo)

Figure 3.1. Illustration of the proposed approach.

The general idea under no-wind-effect is to formulate and estimate equations of the

following form for the temperature at a given location:

T(xo, yo) = (β1*LU1) + (β2*LU2) + …. + (βn*LUn) + ε (3.2)

31 where β’s are parameters to be estimated, based on land uses (LU), such as roads, agricultural areas, and forests, and ε represents other unobserved variables, such as the urban canyon effect and atmospheric conditions (i.e., air humidity).

The notion of thermal balance is used to estimate the effect of land use on temperature at (xo, yo). Figure 3.2 depicts a simple model for the thermal balance at (xo, yo). The main heat transfer occurs along the wind direction and is called advection. To model this transfer, each grid cell must be in a steady state, with constant wind direction and velocity, thus with no variations in temperatures within the grid cells (Incropera,

1990). In other words, the grid cell temperatures estimated with remotely sensed data (30 m * 30 m) must be constant for a given grid cell.

T(x , y ) Input thermal energy, o o Output thermal energy,

θInput θOutput

θInput and θOutput: the unobserved input and output thermal energy at (xo, yo).

Figure 3.2. Basic thermal balance at location (xo, yo).

The mathematical expression of the thermal balance at location (xo, yo) is:

Tobs(xo, yo) = T(xo, yo) + (θInput – θOutput)

= f{L(xo, yo)} + f{L(xk, yk)} + ε (3.3)

where Tobs(xo, yo) is the observed temperature measured with remotely sensed data at (xo,

yo), T(xo, yo) is the base temperature at (xo, yo) that depends on the cell’s unique land use,

which can be estimated from remotely sensed data, and θInput and θOutput are the thermal energy inputs and outputs, which cannot be observed with remotely sensed data. If θInput

is larger than θOutput, Tobs(xo, yo) is higher than T(xo, yo). The reverse also holds. If the

output thermal energy is equal to the input thermal energy, Tobs(xo, yo) is equal to the base

temperature associated with the land use at (xo, yo). In this study, T(xo, yo) is assumed to

be a function of land use at (xo, yo), and (θInput – θOutput) is assumed to be related to neighboring land uses. The input (θInput) and output (θOutput) of thermal energy may be

represented as functions of wind and neighboring land-use effects, and ε includes the

unobserved effects.

Given this basic knowledge, a remotely sensed data set is used to find the

relationship between land uses and local temperature. Figure 3.3 presents the major steps

of this research.

Landsat-5 data Radiometric and (Six different dates through 2005 and 2006) Geometric Corrections:

Extraction of spatial information: Land uses, NDVI and Remotely Sensed

Temperature (RST)

Spatial Analysis: Estimate the parameters of RST models for six Consider both wind-effect land uses and no-wind-effect

Land-use allocation optimization model that minimizes UHI/temperature impacts.

Figure 3.3. Flowchart of the major research steps.

3.2. LANDSAT-5 GRID - BASED APPROACH.

Landsat-5 data is provided for square grid cells. The size of each cell is 30 m * 30

m. Consider a buffer θ defined by (n * n) grid cells (n ≥ 3), centered on cell (j, k). The

value of “n” will be determined after comparing the errors that the estimated parameters

produce. Figure 3.4 presents a grid system when n = 5: Li,k represents land use k in cell i, where k is one of six land uses (k = 1 → 6), and i is a pixel around the center pixel j.

Two independent variables, wind effect and land-use effect, are used to explain

the variations in local temperature in the grid system. Figure 3.4-(a) depicts the effect of

neighboring land uses on the temperature at j, Tj, under calm conditions (no-wind-effect).

In this case, all neighboring land uses equally affect the Tj. On the other hand, as

illustrated in Figure 3.4-(b), when there is a wind effect, the land uses located on the

upwind side are assumed to have larger effects on Tj due to advection. Neighboring land

uses that are located next to the center pixel also affect Tj through air thermal conduction.

The differences between base temperatures and estimated temperatures are

explained by the effects of neighboring land uses. Base temperatures are defined as

temperatures that are independent of neighboring land uses. For example, as shown in

Figure 3.5, the actual water temperature measured by Landsat-5 data in Figure 3.5-(c) is

higher than its base temperature in Figure 3.5-(b), because of the effects of the higher

temperatures in the surrounding urban areas. However, the actual urban temperatures are

lower than their base temperature because of the lower water temperature in their surroundings.

dij

L1,k L2,k L3,k L4,k L5,k

L6,k

Lj,k

L L 23,k 24,k

dij: the distance between the pixel i and the center pixel j.

(a) Effects on temperature at j under calm conditions

dij

L1,k L2,k L3,k L4,k L5,k Thermal energy transport by conduction

L6,k

Wind Lj,k

L23,k L24,k

(b) Effects on temperature at j under wind conditions.

Figure 3.4. Grid system, temperature, land use and wind effects.

Urban Urban Urban 35ºC 35ºC 35ºC

Urban Water Urban 35ºC 25ºC 35ºC

Urban Urban Urban 35ºC 35ºC 35ºC

(a) Land use distribution (b) Base Temperature

34ºC 34ºC 34ºC

34ºC 28ºC 34ºC

34ºC 34ºC 34ºC

Figure 3.5. Hypothetical land use and temperature patterns.

3.2.1. TEMPERATURES UNDER CALM (NO-WIND) CONDITIONS.

The temperature at a given location is related to the land use at that location and

the surrounding land uses. Various land uses have different amounts of green spaces,

which results in different Normalized Difference Vegetation Index (NDVI) values. Using

linear regression, relationships between NDVI values and surface temperatures have been

studied by Goetz (1997), Gallo and Owen (1999), Raynolds et al. (2008), and Wilson et

al. (2003). Assuming a linear relationship between NDVI and surface temperature, the parameters that represent the effect of each land use can be estimated.

The degree to which neighboring land uses have an effect on the temperature at the center location depends on the distance between the center pixel and the neighboring pixel. The

distances (dij) between the center pixel (j) and each cell (i) must be considered. Figure 3.6

− p illustrates the weight factor, dij . The optimal value of p can be determined by

maximizing the model fit.

The NDVI index, derived from Landsat-5 data, is used as the land-use variable.

The NDVI is defined as the ratio (band 4- band 3)/(band 4+ band 3). Any pixel in each

band ranges from 0 to 255 in a gray scale. Therefore, -1 ≤ NDVI ≤ 1. Bands 3 and 4 are

used to estimate NDVI, because these two bands have large differences in spectral

reflectance for photosynthesis. The more green leaves, the more reflectance for band 4.

NDVI represents the share of green space in one pixel. Combining the distance weight

− p ( dij ) and the NDVI variable, the effect of neighboring land use NDVIs on Tj can be

summarized as follows:

NDVI E NoWind = β ⋅[ i ⋅ LU ⋅ N ] j ∑ k ∑ p ik ij (3.4) k i dij

NoWind where E j is the effect of neighboring land uses on the temperature at the central

pixel j, the β’s and p are the parameters to be estimated, i is the index of the neighboring

cells that are considered, and k is the land use in cell i, LUik = 1 if all i has land-use k, = 0

otherwise, and Nij =1 if i belongs to the buffer of cell j, = 0 otherwise.

More green space decreases temperature and the green space area in one pixel can

be represented by the NDVI values derived from the Landsat data. Based on previous

research (Wilson et. al., 2003), under calm weather conditions, one could assume a linear

relationship between NDVI values and local temperatures, with:

T = f {L(x , y )}+ f {L(x , y )}+ ε j, RST o o k k j (3.5) NoWind =T j,base + E j + ε j

where Tj, RST is the remotely sensed temperature at the center j, Tj, base is the temperature

NoWind that is independent of neighboring land uses, E j is the effect of neighboring land

uses in Equation (3.4), and εj is an error term, representing all the other effects that cannot be observed. Equation (3.5) suggests that the difference between the Tj, RST and the Tj, base can be explained by the effect of neighboring land uses.

-p -p -p 30 30 30

30-p 1 30-p

30-p 30-p 30-p

(a) Case of eight neighboring grid cells.

60-p 60-p 60 -p 60-p 60-p

-p 60-p 30 30-p 30-p 60-p

-p -p 1 -p -p 60 30 30 60

60-p 30-p 30-p 30-p 60-p

60-p 60-p 60-p 60-p 60-p

(b) Case of 24 neighboring grid cells

− p Figure 3.6. Weight ( dij ) based on distance from the central pixel.

Linear regression is used to estimate Equation (3.5). The Columbus Metropolitan

Area (CMA) includes (1,641*1,605) pixels of Landsat-5 data, and each pixel is classified as one of six land uses. Therefore, six distinct parameters (β’s) must be estimated for

each land use. For example, six parameters for “urban areas” need to be estimated. All

the pixels classified as urban areas at different locations are used to estimate the

parameters. Define:

NDVI V i LU N jk =∑ p ⋅ ik ⋅ ij (3.6) i dij

The equation to be estimated is then:

6 Tj,RST = βo + ∑βk ⋅V jk +ε j (3.7) k=1

The intercept βo represents an estimate of the unknown Tbase temperature. It is likely that

the parameters βk vary over the year, that is, the impacts of adjacent land uses may be different on hot days with high temperatures, than on cooler days. As data will be obtained that span the whole year, such variations will be uncovered.

3.2.2. TEMPERATURES UNDER WIND CONDITIONS.

In considering wind effects, the main heat transfer occurs along the wind direction and is called advection. As illustrated in Figure 3.7, the important neighboring land uses affecting the temperature at the central cell j are located upwind. To use the advection model, each grid cell must be in a steady state, with constant wind direction and velocity

(Incropera, 1990). In this case, a weight matrix explaining the effects of neighboring land uses located upwind must be considered.

dij

Wind (u) Lj,k

: Upwind side : Downwind side

Figure 3.7. The effect of neighboring land uses on the temperature at j when θ = (3 * 3).

Figure 3.8 suggests how to develop a weight matrix with wind effects on Tj, RST,

using binary coefficients 0 and 1, and the distances from the central pixel. Land uses that

are located upwind are assigned a value of 1 and all the others are assigned a value of 0.

In addition, downwind neighboring land uses may also have an effect on cell j. Therefore,

Equation (3.5) can be modified as:

Tj,RST = f {L(xo , yo )}+ f {L(xk , yk )}+ε j Upwind Downwind (3.8) =Tj,base + E j + E j +ε j

Upwind Downwind where E j and E j are the effects of upwind and downwind land uses.

Wind effect Distance weight Weight matrix, wij

1 1 0 30-p 30-p 30-p 30-p 30-p 0

-p 1 1 0 * 30-p 1 30-p = 30 1 0

-p -p -p -p -p 1 1 0 30 30 30 30 30 0

Figure 3.8. Weight matrix with wind effect.

Previous studies (Chandler, 1965; Duckworth and Sandberg, 1954) suggest that the relationship between temperature and wind effect is non-linear. The following is proposed to describe the upwind effect:

6 w EUpwind = uα ⋅ β ⋅[ ij ⋅ NDVI ⋅ LU ⋅ N ] j ∑ k ∑ d p i ik ij k=1 i ij (3.9) 6 α = u ⋅∑ β k ⋅ X jk k=1

where u is the wind speed, α and β’s are parameters to be estimated, wij is the wind effect

(0: no wind effect and 1: wind effect), as illustrated in Figure 3.8, and X jk is the weighted

NDVI sum of land use k in cells upwind. The effect of neighboring land uses downwind

Downwind ( E j ) is described as follows:

6 (1− w ) E Downwind = β ' ⋅[ ij ⋅ NDVI ⋅ LU ⋅ N ] j ∑ k ∑ d p i ik ij k =1 i ij (3.10) 6 = β ' ⋅ X ' ∑ k jk k =1

where β ' are the parameters to be estimated, and X ' is the weighted NDVI k jk

sum of land use k in cells downwind. Finally, Equation (3.8) can be rewritten

as:

6 6 α ' ' Tj,RST = βo + u ⋅∑βk ⋅ X jk + ∑βk ⋅ X jk + ε j (3.11) k=1 k=1

where βo represents the intercept.

CHAPTER 4

DATA SOURCES AND PROCESSING

This chapter provides first a description of the data and their sources for the

Columbus Metropolitan Area (CMA). An analysis of the spatial distribution of remotely sensed temperatures and land uses is next presented. Finally, temperature data derived from Landsat-5 are also compared with measured data.

4.1. DATA SOURCES.

The satellite data used in this study include Landsat-5 Thematic Mapper (TM) images, dated April 11, 2005, May 13, 2005, August 1, 2005, September 2, 2005,

November 21, 2005 and February 25, 2006. As illustrated in Figure 4.1, image data is from path 19 and row 32 of the satellite track. The original image size is 7864*7207, the coordinates of the upper left corner are (241530.0 m, 4574370.0 m), and those of the lower right are (477420.0 m, 4358190.0 m). The Landsat-5 image is rectified to a common UTM coordinate system, WGS 84 and zone number 17 north. The original spatial resolution of the image band (band 1- 5) is (30 m*30 m). In the case of the TM thermal band (band 6), the size of a pixel is (120 m*120 m). The thermal band data are 45 resampled to fit the spatial resolution of the other image bands, with a pixel size of

30 m*30 m.

Figure 4.1. Landsat dataset for the Columbus Metropolitan Area (CMA).12

12 http://landsat.ohiolink.edu/GEO/LS7/ 46

The atmospheric correction for the original image was performed by using the

model MODTRAN (Moderate Resolution Atmospheric Transmission).13 This

atmospherically corrected image is reduced to a size of 1,641*1,605 (2,389.45 km2), so as

to include the City of Columbus and its metropolitan area. The (X, Y) coordinates of the upper left corner are (3085558.0 m, 4452735.0 m) and those of the lower right are

(356678.0 m, 4403535.0 m).

Land-use/cover patterns for August 1, 2005, are mapped using Landsat-5 TM

data, as presented in Figure 4.2. With the aid of Erdas Imagine software, a supervised

classification using a maximum likelihood algorithm is used to classify land-use/cover

types for the Columbus Metropolitan Area (CMA). An accuracy assessment was

performed and the accuracy is about 82.31%.14

The six different land uses are: water bodies (i.e., lakes and rivers), agricultural

areas, green areas (i.e., forest, pasture and lawn), residential areas, impervious areas (i.e.,

road and parking lot), and urban areas (i.e., commercial and downtown areas). Most

studies of the UHI usually use five to eight land use categories, depending on the specific

situations, such as the historical city core or 5-12 story apartments in residential areas

(Unger et al., 2001; Asmat et al., 2003; Hawkins et al., 2004; Mote and Grady, 2003;

Akinaru and Akira, 1996; Li et al., 2005).

13 MODTRAN is a computer software program designed to model atmospheric propagation of electromagnetic radiation and is used for performing atmospheric correction of the original Landsat data. 14 300 points in the classified image are compared to the land uses on aerial photographies (2-m grid size). 47

: Water : Urban area : Impervious area

: Agricultural area : Residential area : Green area

Figure 4.2. Six land-use types in the Columbus Metropolitan Area (CMA) on August 1, 2005.

Before performing an image classification, the terms “Land Use” and “Land

Cover” must be clearly defined. In most cases, these two terms tend to be exchangeable.

Both land use and land cover (LULC) are closely related to the regional climate in

complex ways, including the radiation balance between the land surface and the

atmosphere. However, they are clearly different.

“Land Cover” focuses on the detailed ground material itself, such as vegetation

(i.e., grass and trees), water (i.e., rivers and lakes), large structures (skyscraper) and other

features that cover the ground. Digital sensors mounted on satellites are designed to

collect multiple wavelengths of light, and statistical analysis of these wavelength bands

of data can provide the ground truth, the land cover.15

On the other hand, “Land Use” is related to human activities on the land

surface,16 and refers to the economic uses of the land, such as commercial (i.e., stores,

office buildings and parking lots), agricultural and industrial (i.e., factories and plants).

No spectral basis exists for the determination of land uses from satellite data.

Therefore, it is necessary to discriminate land use from land cover in satellite

data. For this purpose, different sizes of convolutions, such as a (3*3), a (5*5) and a (7*7)

array of cell data, can be used. Figure 4.3-(a), where no convolution is used, depicts a

bridge (impervious area) on the Scioto River and shows detailed land covers. However, as the size of the convolution window is increased, the more predominant land features are shown, such as in Figure 4.3-(b) and -(c). Finally, in Figure 4.3-(d), with a (7*7)

15 http://www.csc.noaa.gov/crs/lca/faq_gen.html#LULC 16 http://www.cara.psu.edu/land/lu-primer/luprimer01.asp 49

convolution, the bridge cannot be discriminated and is classified as water and forest,

because the dominant land covers are the river and the forest within this 7 * 7 grid.

LULCs must be selected according to the purpose of the study. If land covers are

the more important factors, one can classify remotely sensed data with no convolution or

with a (3*3) convolution. However, if land uses are more important factors, larger

convolutions, such as (5*5) and (7*7) grids, can be used. With the increase in the size of

the window, small areas of land covers will be incorporated into the dominant land uses.

For example, small green spaces in parking lots are classified as a part of the impervious

areas.

The original data set (no convolution) is appropriate in this study, because it provides information on land cover, which is closer to the land use in the real world.

Because this study focuses on the changes in temperatures that result from the changes in land use, using land cover prevents the loss of information due to the generalization provided by a convolution.

(a) No convolution (b) A (3*3) convolution

: Water : Urban area : Impervious area

: Residential area : Agricultural area : Green area

Figure 4.3. Changes in land cover with different sizes of convolutions.

4.2. TEMPERATURE AND LAND-USE DATA ANALYSIS.

To detect the UHI phenomenon over the Columbus Metropolitan Area (CMA), remotely sensed temperatures (RST) derived from Landsat-5 data are used. Figure 4.4 presents the temperature distribution in the CMA on August 1, 2005, as estimated by the

USGS method (Chander and Markham, 2003). It very clearly shows that urban areas, such as downtown Columbus and commercial areas, have higher temperatures than their surrounding environments.

: 23-27 °C : 28-33 °C : 34-38°C : 34-38°C

Figure 4.4. Temperature distribution in the Columbus Metropolitan Area (CMA) on August 1, 2005. 52

The thermal band in Landsat-5 is used to find the relationship between land-use characteristics and RST. As shown in Figure 4.5, the thermal temperatures of various land uses can be obtained by overlaying the radiant temperature layer on a land-use/cover layer derived from Landsat-5.

Temperature layer

Same number of rows Land-use layer

Same number of columns

Figure 4.5. Overlaying temperature layer on land-use layer.

To estimate temperatures, three different methods are employed: the Malaret method (1985), the Sobrino method (2004), and the USGS method (2003). The Malaret method converts the digital number (DN) in the thermal band into RST with the following equation (Malaret et al., 1985).

T(k) = 209.831 + 0.834DN – 0.00133DN2 (4.1) where T(k) is the Kelvin temperature and DN is the digital number. However, the temperatures derived from Equation (4.1) are only referenced to a black body.

To avoid this problem, the emissivity (ε) must be considered, based on the nature

of land uses, because the thermal band for the Thematic Mapper sensor on Landsat-5

measures the amount of emitted energy from each pixel. A procedure to estimate the

emissivity from TM images is to use the NDVI17, and the NDVI Thresholds Method –

NDVITHM (Sobrino et al., 2004).

(a) NDVI < 0.2 or NDVI > 0.5

If NDVI < 0.2, the pixel is bare soil. Finding the typical emissivity of soil is difficult

(Sobrino et al., 2004). Thus, a possible solution is to use the mean value for the

emissivities of soils in the ASTER spectral library.18 The mean value of 49 soil types is

0.973, with a standard deviation of 0.004. On the other hand, the NDVI values larger than

0.5 are considered as fully vegetated. The emissivity of vegetation is typically 0.99.

(b) 0.2 ≤ NDVI ≤ 0.5

In this case, the pixel is composed of a mixture of bare soil and vegetation. Emissivity

can be estimated as follows (Sobrino et al., 2004):

εTM6 = 0.004Pv + 0.986 (4.2) where εTM6 is the emissivity of band 6 (thermal band) for the Thematic Mapper sensor on

2 ⎡ NDVI − NDVImin ⎤ Landsat-5 and Pv is the vegetation proportion, Pv = ⎢ ⎥ . According to ⎣ NDVImax − NDVImin ⎦

Artis and Carnhan (1982), the emissivity-corrected surface temperature at a point (x, y) can be computed as:

TM (band 4) − TM (band 3) 17 Normalized difference vegetation index, NDVI = TM (band 4) + TM (band 3) 18 Advanced Spaceborne Thermal Emission and Reflection Radiometer, http://asterweb.jpl.nasa.gov

T(k) T(x, y) = , (4.3) 1+ (λ *T(k) / ρ) ⋅ lnε TM6 where λ is the wavelength of emitted radiance, 11.5 μm (Markham and Barker, 1987),

T(x, y) is the emissivity-corrected temperature in Kelvin (K) at (x, y), T(k) is the temperature derived from Equation (4.1), ρ= h * c/σ (1.438 * 10-2 mK), σ = the

Bolzmann constant (1.38 * 10-23 J/K), h is the Planck constant (6.626 * 10-34J·sec), and c

is the velocity of light (2.998 * 108 m/sec).

Finally, the USGS recommends a different method to estimate radiant temperatures, which has been effective as of May 5, 2003. Landsat-5 TM data must be re- calibrated by using a new procedure and revised calibration parameters, because Landsat-

5 has aged and optical characteristics have changed since its launch in March, 1984

(Chander and Markham, 2003). This formula is:

K T(x, y) = 2 , (4.4) K ln( 1 +1) Lλ

where T(x, y) is the temperature in Kelvin (K), K1 is the calibration constant (607.76

W ), K2 is the calibration constant (1260.56 K), and Lλ is the spectral radiance at m2 ⋅sr⋅μm

sensor’s aperture (unitless). Also, the spectral radiance at sensor’s aperture is:

Lλ(x, y) = Grescale * Qcal + Brescale (4.5)

where Lλ(x, y) is the spectral radiance at sensor’s aperture at (x, y), Qcal is the digital

number at (x, y), Grescale = 0.055158 and Brescale = 1.2378 (Chander and Markham, 2003).

Table 4.1 presents statistics for the estimated temperatures, based on these three methods.

Land uses Temperature (°C) (Number of Method Standard Mean Maximum Minimum observations) deviation Malaret 28.26 53.32 24.23 2.46 Water Sobrino 29.77 55.66 25.01 2.33 (142,219) USGS 25.59 51.92 21.86 2.33 Malaret 30.07 44.56 20.29 2.62 Agriculture Sobrino 30.93 46.78 21.22 2.86 (305,217) USGS 27.29 41.71 18.31 2.48 Malaret 31.23 41.68 24.23 2.59 Green Sobrino 32.05 42.72 25.04 2.67 (1,254,252) USGS 28.38 38.66 21.86 2.45 Malaret 34.58 45.60 21.29 2.17 Residential Sobrino 35.68 47.49 22.25 2.36 (394,681) USGS 31.58 42.84 19.21 2.09 Malaret 35.57 53.86 17.76 2.48 Impervious Sobrino 37.06 56.22 19.62 2.74 (503,593) USGS 32.55 52.63 16.03 2.43 Malaret 35.56 50.43 7.49 4.32 Urban Sobrino 37.64 52.74 9.23 4.38 (54,966) USGS 32.58 48.35 26.96 4.16

Table 4.1. Comparison of temperatures derived from three different methods on August 1, 2005.

However, there are some unusual temperature estimates, over 50°C and about 7°C on August 1, 2005. The measurement of temperatures is likely to incur more errors than land uses, because only the thermal band is used (5 bands are used for land-use

classification). There are two error sources during the conversion of radiance to

temperature: sensor properties (calibration) and atmospheric scatter (MODTRAN is used

to reduce this error). The calibration error is difficult to quantify, but some studies

indicate that this is significant and requires recalibration with on-site data, such as aircraft

observations. The error from MODTRAN is usually assumed to be low. These

temperature data can be treated as outliers. To detect outliers, the Chebyshev inequality

can be used, because the probability distribution of the temperatures for any land use is

not known. For any positive value k, the probability that an observation lies beyond k

standard deviations from the mean can be computed as follows.

1 P( X − μ > kσ ) ≤ (4.6) i i i k 2

where Xi is the temperature of a specific land use i, and µi and σi are the mean temperature and its standard deviation for this specific land use i.

Equation (4.6) indicates that the probability that a certain temperature deviation

1 (Xi - µi) for land use i is over k standard deviation is less than or equal to . For k 2

example, if k = 3, then the probability is 1 = 1 , or 11%. Alternatively, if a normal 32 9

distribution is assumed, which is consistent with the OLS assumption made in the

forthcoming regression analyses, the corresponding probability is 2.7 * 10-3, or 0.27%.19

Table 4.2 and Figure 4.6 present temperature data and their distribution after removing

outliers for the August 1, 2005 image.20

19 P(|Xi-μi| > 3σi) ≈ 0.0027 (0.27 %). 20 See Appendix A for other dates. 57

In the case of NDVI, which ranges from -1 to 1, k = 2 is selected, because the standard deviation of water (0.3625) multiplied by three is greater than one. If NDVI ≥

0.5, the pixel is considered as fully vegetated (e.g., forests). A pixel is composed of a

mixture of bare soil and vegetation when 0.2 ≤ NDVI < 0.5. If NDVI < 0.2, a pixel is

generally assumed to represent bare soil, with no vegetation. In the case of developed

areas (residential, impervious and urban areas), it is unlikely that NDVI > 0.5 or NDVI <

0. NDVI values over 2σ from their mean values are defined as outliers. Table 4.3 presents

NDVI values before and after removing outliers.

Land uses Method Temperature (°C) (Number of (Number of Standard Mean Maximum Minimum observations) outliers) deviation Malaret (651) 28.13 35.40 24.22 2.13 Water Sobrino (718) 29.64 36.76 25.01 1.95 (142,219) USGS (651) 25.47 32.36 21.86 1.99 Malaret (5,475) 30.01 37.83 22.28 2.49 Agriculture Sobrino (9,151) 30.80 39.50 23.75 2.64 (305,217) USGS (8,403) 27.19 34.36 20.09 2.30 Malaret (597) 31.23 38.62 24.23 2.58 Green Sobrino (566) 32.05 40.05 25.04 2.66 (1,254,252) USGS (597) 28.38 35.54 21.86 2.45 Malaret (1,540) 34.61 40.93 28.44 2.11 Residential Sobrino (788) 35.69 42.76 28.71 2.33 (394,681) USGS (911) 31.59 37.50 25.31 2.06 Malaret (4,122) 35.56 42.78 28.44 2.33 Impervious Sobrino (2,872) 37.03 45.26 28.85 2.62 (503,593) USGS (3,963) 32.52 39.81 25.31 2.29 Malaret (978) 35.81 48.25 22.77 3.78 Urban Sobrino (981) 37.89 50.53 24.64 3.85 (54,966) USGS (881) 32.79 45.07 20.10 3.72

Table 4.2. Temperature statistics after removing outliers (k = 3), August 1, 2005.

16000

14000

l 12000

10000

8000

6000

The number of pixe of The number 4000

2000

0 20 22 24 26 28 30 32 34 Temperature

(a) Temperature distribution of water.

70000

60000

l 50000

40000

30000

ThePixe of number 20000

10000

0 22 24 26 28 30 32 34 36 38 40 Temperature

(b) Temperature distribution of residential areas.

200000 180000 160000 l 140000 120000 100000 80000 60000 The number of pixe of The number 40000 20000 0 22 24 26 28 30 32 34 36 Temperature

Figure 4.6. Temperature distributions after removing outliers, August 1, 2005. Continued

Figure 4.6 continued.

100000 90000 80000 l 70000 60000 50000 40000 30000 The number of pixe of The number 20000 10000 0 25 27 29 31 33 35 37 39 41 Temperature

(d) Temperature distribution of impervious areas.

180000

160000

140000 l 120000

100000

80000

60000 The number of pixe The number 40000

20000

0 20 22 24 26 28 30 32 34 36 38 Temperature

(e) Temperature distribution of agricultural areas.

20000 18000 16000 l 14000 12000 10000 8000 6000 The number of pixe of The number 4000 2000 0 20 25 30 35 40 45 Temperature

(e) Temperature distribution of urban areas.

Land use NDVI (Number of Standard Mean Maximum Minimum observations) deviation Water 0.07 0.75 -0.94 0.3625 (142,219) Agriculture 0.59 0.92 -0.18 0.1815 (305,217) Green 0.54 0.90 -0.02 0.1391 (1,254,252) Residential 0.35 0.76 -0.32 0.1328 (394,681) Impervious 0.22 0.86 -0.90 0.1562 (503,593) Urban -0.01 0.64 -0.69 0.0801 (54,966) (a) Before removing outliers

NDVI Land use Standard (Number of outliers) Mean Maximum Minimum deviation Water 0.07 0.70 -0.61 0.3598 (145) Agriculture 0.63 0.84 0.41 0.1082 (55, 941) Green 0.54 0.79 0.27 0.1290 (26,498) Residential 0.35 0.58 0.11 0.1194 (11,569) Impervious 0.22 0.49 -0.06 0.1441 (12,089) Urban area -0.02 0.09 -0.15 0.0600 (2,958) (b) After removing outliers (k = 2)

Table 4.3. NDVI statistics, August 1, 2005.

4.3. MEASURED AND ESTIMATED TEMPERATURES.

After estimating temperatures with the three different methods, these estimated

temperatures are compared with true ground measurements. Five measuring stations are

available in the CMA, as depicted in Figure 4.7. They are maintained by the National

Oceanic and Atmospheric Administration (NOAA) and Weather Underground, Inc.21

Measured weather data, such as temperatures, and wind speeds and directions, can be downloaded for these five meteorological stations.

Table 4.4 presents the station locations, with latitude and longitude, and the land use where the meteorological station is located (as of August, 2005). These stations are located near the Columbus International Airport and OSU Airport, and outside I-270 (the other three stations), the beltway surrounding the City of Columbus.

Latitude – Longitude Station Land Use (Coordinate on image) West Dublin 40 4' 4" - 83 10' 53" (180, 505) Agriculture OSU Airport 40 05' - 83 05' (461, 454) Green CIA 39 59' - 82 53' (1021, 837) Urban Bolton Airport 39 54' - 83 08' (303, 1129) Agriculture RBA 39 49' - 82 56' (865, 1451) Imperviousness CIA: Columbus International Airport. RBA: Rickenbacker Airport

Table 4.4. The five measuring stations in the CMA.

21http://www.wunderground.com/download/index.asp (West Dublin) and http://cdo.ncdc.noaa.gov/qclcd/QCLCD?prior=N (Other measuring stations) 62

Figure 4.7. The locations of the five measuring stations.

Table 4.5 presents the measured temperature at the five stations on August 1,

2005, and the temperatures at the same locations estimated from the satellite data. Wind

directions are specified by degrees azimuth.22 Temperatures at around 10 AM (local) are

used for comparison, because the Landsat-5 satellite passes through Ohio at around 10

AM. As shown in Table 4.5, the three methods provide close approximations for the agricultural and green areas. However, there are large differences for the urban and

impervious areas.

Time Wind speed Temperature ET (°C) Station (AM) (m/sec) (°C) Malaret Sobrino USGS 0 West Dublin 10:00 26.56 28.44 29.17 25.73 (N, 0°) 1.79 OSU Airport 9:53 27.8 28.59 29.63 26.16 (NW, 300°) 1.79 CIA 9:51 28 37.03 39.15 33.95 (N, 0°) 0 Bolton Airport 9:57 27 27.98 28.71 25.31 (N, 0°) 0 RBA 9:55 28 39.79 41.95 36.72 (N, 0°) *: MS: Measuring Station. Time: Measuring time ET: Estimated Temperature at points where MS* are located.

Table 4.5. Comparison between the measured and the estimated temperatures.

22 0°= north, 90°= east, 180° = south and 270° = west (in terms of clockwise).

According to Voogt and Oke (1997), there are some differences between the measured and the estimated temperatures because of the heterogeneous nature of the urban surface detected by a satellite sensor, especially in urban areas. As shown in

Table 4.6, three measuring stations (West Dublin, OSU airport and Bolton

Airport) are classified as green areas and the other two are classified as urban areas and impervious areas. The former three stations display almost the same measured and estimated temperatures. However, the latter two stations display significant differences.

2 The method that has the smallest sum of mean square errors,(Tmeasured−Testimated) over the five stations was selected. As shown in Table 4.6, the USGS method has the smallest sum of mean square errors. Finally, the comparisons between the measured and the estimated temperatures, and the wind speed on different days (image dates) are presented in Table 4.7.

Mean square error, 2 Stations Land use (Tmeasured−Testimated) Malaret Sobrino USGS West Dublin Green 3.53 6.81 0.69 OSU Airport Green 0.62 3.35 2.69 Columbus International Airport. Urban 81.54 124.32 35.40 Bolton Airport Green 0.96 2.92 2.85 Rickenbacker Airport Impervious 139.00 194.60 76.03 Total Sum 225.66 332.01 117.66

Table 4.6. Sum of the mean square errors at the five measuring stations.

Time Wind speed Date Station MT (°C) RST (°C) (AM) (m/sec) 9.39 West Dublin 9:58 8 10.87 (WNW, 300º) 8.49 OSU Airport 9:53 8.3 8.93 (WNW, 290º) February, 25 8.05 CIA 9:51 8.9 10.39 (2006) (WNW, 290º) 7.60 Bolton Airport 9:51 8.0 9.90 (WNW, 300º) 6.26 RBA 9:56 9 10.87 (WNW, 300º) 1.34 West Dublin 10:00 17.5 20.98 (SSE, 150º) 2.68 OSU Airport 9:53 18.3 18.31 (VR) April, 11 3.13 CIA 9:51 18.9 24.03 (2005) (VR) 3.13 Bolton Airport 9:58 20.0 21.86 (ENE, 60º) 2.68 RBA 9:55 18 25.31 (ENE, 70º) 2.68 West Dublin 9:58 16 21.42 (SSE,150º) 4.47 OSU Airport 9:53 17.8 19.66 (SE, 120º) May, 13 4.47 CIA 9:51 18.3 24.46 (2005) (SE,140º) 3.13 Bolton Airport 9:59 18.0 22.73 (SE,140º) 2.68 RBA 9:55 18 26.59 (SE,130º) MT: Measured temperatures. RST: Remotely Sensed Temperature by the USGS method.

Table 4.7. Comparison between measured temperature and RST.23

Continued

23 See Appendix A. 66

Table 4.7 continued.

Time Wind speed Date Station MT (°C) RST (°C) (AM) (m/sec) 0 West Dublin 10:00 26.56 25.73 (N, 0°) 1.79 OSU Airport 9:53 27.8 26.16 August, 1 (WNW, 300º) (2005) 1.79 CIA 9:51 28.9 33.95 (N, 0°) Bolton Airport 9:57 0 27 25.31 RBA 9:55 0 28 36.72 1.57 West Dublin 10:00 26.5 24.46 (E, 90º) 4.47 OSU Airport 9:53 25 23.60 (W, 280º) September, 2 4.92 (2005) CIA 9:51 25.6 30.32 (W, 280º) Bolton Airport 7:19 0 17 24.03 3.13 RBA 9:55 23 32.76 (SE, 220º) West Dublin 10:00 0 7 8.93 OSU Airport 9:53 0 4.4 8.44 November,21 CIA 9:51 0 4.4 8.93 (2005) 2.68 Bolton Airport 9:52 3 10.39 (WNW, 330º) RBA 9:57 0 4 10.87

CHAPTER 5

EXPLORATORY ANALYSIS

This chapter presents an overall description of the weather in the Columbus

Metropolitan Area (CMA). The relationship between NDVI and remotely sensed temperature (RST) is analyzed, using various regression models.

5.1. GENERAL DESCRIPTION OF COLUMBUS, OHIO.

5.1.1. CLIMATE.

The climate in Columbus, Ohio, is similar to that of nearby cities, including

Chicago, Illinois and Toledo, Ohio.24 Columbus deals with a variety of weather situations every year, such as tornadoes, blizzards, winter storms and severe thunderstorms. For example, the last tornado hitting the Columbus Metropolitan Area (CMA) occurred on

October 11, 2006, and was rated an F2 on the Fujita scale. The last major snow storm, with a snow accumulation of 51.82 cm, was recorded on March 8, 2008, during a blizzard that affected a large portion of the Midwest, resulting in power outages across central

Ohio.

24 http://en.wikipedia.org/wiki/Climate_of_Columbus%2C_Ohio 68

Table 5.1 presents the general weather characteristics of the CMA. The region is

dominated by a humid continental climate, characterized by hot, muggy summers and

cold, dry winters. The hottest temperature ever recorded in the CMA is 41°C on July 21,

1934 and July 14, 1936.25 The coldest temperature ever recorded is –30°C, on January

19, 1994.

Table 5.2 presents monthly mean temperatures since 1976. Figure 5.1 presents a

graphical illustration of these data sets, which are derived from the measuring station in

West Dublin. 26

Average Average Average Average Month Temperature number of clear number of rainy precipitation (°C) days days (cm) 1 -2.2 4 13 7.1 2 -0.6 4 11 5.8 3 5.0 5 14 7.9 4 11.1 5 13 8.6 5 16.7 6 13 9.7 6 21.7 6 11 9.9 7 23.9 7 11 11.7 8 22.8 7 9 8.4 9 18.9 9 8 6.9 10 12.2 10 9 5.3 11 6.1 5 12 7.6 12 0.6 4 13 6.9 Years on 48 44 54 48 record

Table 5.1 General monthly weather characteristics for the Columbus Metropolitan Area (CMA).27

25 Records for Columbus. National Weather Service. Retrieved on 2008-11-16. 26 http://www.wunderground.com/history/airport/KCMH/1970/1/31/MonthlyHistory.html 69

Month Year 1 2 3 4 5 6 1976 24 38 46 51 58 71 1977 12 27 46 55 67 68 1978 19 17 34 51 60 71 1979 21 20 45 50 61 70 1980 29 25 37 49 63 68 1981 23 34 40 56 60 71 1982 21 29 40 47 67 66 1983 30 34 43 48 58 69 1984 24 37 32 50 58 73 1985 22 26 44 57 63 67 1986 30 33 43 54 64 71 1987 30 35 44 52 66 72 1988 27 29 40 50 63 70 1989 37 28 42 48 56 67 1990 38 38 45 51 59 70 1991 30 36 44 56 71 75 1992 32 37 41 52 60 67 1993 34 28 38 50 62 70 1994 21 30 40 54 58 74 1995 29 28 43 51 61 73 1996 28 31 35 50 61 72 1997 28 36 42 48 57 70 1998 37 40 43 53 67 71 1999 31 37 37 55 65 74 2000 27 32 NA NA 65 74 2001 29 35 38 57 63 71 2002 35 36 42 55 59 74 2003 23 27 43 55 61 68 2004 24 32 44 53 67 70 2005 31 34 37 54 59 75 2006 41 34 41 57 61 70 2007 34 21 48 51 67 73 NA: Not Available.

Table 5.2. Observed monthly mean temperatures over the years 1976-2007 (°C).28

Continued.

27 http://www.weatherbase.com/weather/weatherall.php3?s=82427&refer=&units=us 28 http://www.census.gov/population/www/documentation/twps0027/twps0027.html 70

Table 5.2 continued.

Month Year 7 8 9 10 11 12 1976 72 68 62 48 34 25 1977 76 72 68 52 45 30 1978 74 73 70 52 44 34 1979 72 72 65 54 44 35 1980 76 76 69 51 41 33 1981 72 70 62 51 41 30 1982 74 69 63 56 45 40 1983 77 76 67 55 44 25 1984 71 73 63 60 41 39 1985 73 71 67 58 48 26 1986 75 71 69 56 42 33 1987 76 74 67 49 48 36 1988 77 75 65 47 44 32 1989 70 67 63 51 42 20 1990 74 72 66 55 46 37 1991 78 75 66 56 41 36 1992 73 69 65 52 45 35 1993 76 75 65 53 43 33 1994 75 72 65 56 48 39 1995 76 78 64 56 38 29 1996 73 74 66 55 37 37 1997 74 70 65 55 40 34 1998 74 76 71 56 46 38 1999 80 73 68 55 47 35 2000 72 72 64 57 41 24 2001 74 75 64 56 49 38 2002 78 76 71 54 42 33 2003 74 74 65 53 48 34 2004 74 71 68 55 46 33 2005 77 77 70 56 46 30 2006 77 76 64 53 46 40 2007 73 78 71 62 45 36

10.00

5.00 Ԩ 0.00 Jan ‐5.00 Feb Monthly mean temperature, temperature, Mar ‐10.00

‐15.00 1975 1980 1985 1990 1995 2000 2005 2010 Year

(a) From January to March

25.00

20.00 Ԩ

15.00 Apr May Monthly mean temperature, temperature, 10.00 Jun

5.00 1975 1980 1985 1990 1995 2000 2005 2010 Year

(b) From April to June

Figure 5.1. Monthly mean temperature variation at the measuring station in West Dublin.

Continued.

Figure 5.1continued.

30.00

Ԩ 25.00

Jul Aug 20.00 Monthly mean temperature, temperature, Sep

15.00 1975 1980 1985 1990 1995 2000 2005 2010 Year

20.00

15.00

Ԩ 10.00

5.00 Oct Nov 0.00 Monthly mean temperature, temperature, Dec ‐5.00

‐10.00 1975 1980 1985 1990 1995 2000 2005 2010 Year

(d) From October to December.

Figure 5.2 illustrates the variations of monthly mean temperatures at the five measuring stations during the year 2005: Bolton, Rickenbacker, Columbus International airport, OSU airport and West Dublin.

30 BoltonBolton

Rickenbacker RBA 25 Airport Columbus CIAInternational Airport 20 OSUOSU Airport Airport

Ԩ W Dublin 15 W Dublin

10 Monthly mean temperature, temperature,

0 123456789101112

‐5 Month

Figure 5.2. Monthly mean temperatures at the five measuring stations during the year 2005.

5.1.2. POPULATION.

According to the 2000 Census29, 711,470 people, 301,534 households, and

165,240 families resided in the city in 2000, with a population density of 1,306.4/km².

There were 327,175 housing units at an average density of 600.8/km². The racial composition of the city was White (67.93%), African American (24.47%), Native

American (0.29%), Asian (3.44%), Pacific Islander (0.05%), other races (1.17%), and two or more races (2.65%). 2.46% of the population was Hispanic. Table 5.3 presents

Columbus decennial population and its change over 1850-2000. The populations and rankings are based on the boundaries of the city at the time of each census.

Year Population Decennial Change (%) U.S. Rank 1850 17,882 195.7 37 1860 18,554 3.8 49 1870 31,274 68.6 42 1880 51,647 65.1 33 1890 88,150 70.7 30 1900 125,560 42.4 28 1910 181,511 44.6 29 1920 237,031 30.6 28 1930 290,564 22.6 28 1940 306,087 5.3 26 1950 375,901 22.8 28 1960 471,316 25.4 28 1970 539,677 14.5 21 1980 564,871 4.7 19 1990 632,910 12.0 16 2000 711,470 12.4 15 Table 5.3. Population in Columbus, Ohio.30

29 American FactFinder. United States Census Bureau. 30 http://www.census.gov/population/www/documentation/twps0027/twps0027.html 75

5.2. RELATIONSHIP BETWEEN NDVI AND TEMPERATURE.

5.2.1. DESCRIPTION OF THE NDVI.

The Normalized Difference Vegetation Index (NDVI) is a simple numerical indicator that is used to analyze remote sensing measurements and estimate the green vegetation content of objects observed on the ground.31 Plants absorb solar radiation in the photosynthetically active radiation (PAR) spectral region (0.4 – 0.7 µm, bands 1 through 3 in Landsat-5) and use it as source of energy for photosynthesis.

Figure 5.3 Wavelength distribution.32

31 http://en.wikipedia.org/wiki/Normalized_Difference_Vegetation_Index 32 http://www.satelliteimpressions.com/landsat.html 76

As illustrated in Figure 5.3, this spectral band is the red band (band-3),

approximately 0.6 µm – 0.7 µm. On the other hand, the cell structure of a leaf strongly

reflects near-infrared light (0.7 µm - 1.1 µm). The more leaves a plant has, the more the near infrared reflectance. In general, if there is much more reflected radiation in near- infrared wavelengths than in visible wavelengths, the vegetation in that pixel is likely to be dense, for instance a forest. If there is very little difference, then the vegetation may be sparse, such as tundra or desert (Sellers, 1985).

In the case of Landsat data set, the equation defining NDVI is (Arthur and

Carlson, 2000):

band 4 − band 3 NDVI = (5.1) band 4 + band 3

where band-3 (0.6 µm – 0.7 µm) and band-4 (0.7 µm - 1.1 µm) are the spectral bands of

Landsat data. Mathematically, the sum and the difference of the two spectral bands

contain the same information as the original data sets. Calculations of NDVI for a given

pixel always result in a number that ranges from -1 to 1. A zero or negative NDVI means

no vegetation, and a high NDVI close to one indicates the highest possible density of

green leaves.

As illustrated with NDVI data for the CMA in Table 5.4, each cell of land use has

a unique value of NDVI, ranging from -1 to 1. For example, water and urban areas do not

have much vegetation and, therefore, these areas have lower NDVI values, which are

negative or slightly positive. If the NDVI value is less than 0.2, a pixel is considered as

having no vegetation (Sobrino et al., 2004). On the other hand, agricultural and green

areas have a lot of vegetation and their NDVI values are closer to 1. NDVI values higher 77

than 0.5 are usually considered as fully vegetated cells. Finally, if 0.2 ≤ NDVI ≤ 0.5, the

pixel is a mixture of vegetation and other objects on the ground.

Land use NDVI (Number of Standard Mean Maximum Minimum observations) deviation Water (142,219) 0.07 0.75 -0.94 0.3625 Agriculture (305,217) 0.59 0.92 -0.18 0.1815 Green (1,254,252) 0.54 0.90 -0.02 0.1391 Residential (394,681) 0.35 0.76 -0.32 0.1328 Impervious (503,593) 0.22 0.86 -0.90 0.1562 Urban (54,966) -0.01 0.64 -0.69 0.0801

Table 5.4. Basic statistics of NDVI in the Columbus Metropolitan Area (August 1, 2005).

However, the NDVI values of a given area do change. As shown in Figure 5.4, healthy vegetation (left) absorbs most of the visible light and reflects a large portion of the near-infrared light, with NDVI = 0.72. 33 However, unhealthy or sparse vegetation

(right) reflects more visible light and less near-infrared light, with NDVI = 0.14.

Figure 5.5 displays the variations of NDVI for six land uses from April 2005 to

February 2006.

33 (0.5-0.08)/(0.5+0.08) 78

Figure 5.4 Effect of vegetation health on NDVI.34

34 http://earthobservatory.nasa.gov/Features/MeasuringVegetation/measuring_vegetation_2.php 79

NDVI

0.8 Water Ag Green Resi Imp Urban 0.6

0.4

0.2

‐0.2

‐0.4 April May August September November February 2005 2005 2005 2005 2005 2006 Time

Ag: Agriculture Resi: Residential Imp: Impervious

Figure 5.5. Variations of mean NDVI by land-use types (April 2005 – February 2006)

5.2.2. BASIC RELATIONSHIPS BETWEEN NDVI AND REMOTELY-SENSED

TEMPERATURE (RST).

To study the thermal environment of a city, it is critical to obtain area-wide temperature data. Remotely sensed temperature (RST) combined with land-use

information from satellites may be very useful to understand the surface conditions of

urban areas. Until recently, the resolution of satellite information was limited to several

tens of meters. However, it is now becoming possible to obtain resolutions of about 1 m.

NDVI and RST are the primary data that can be derived from satellites. There have been several studies on the relationship between NDVI and RST (Artis and

Carnahan, 1982; Nichol, 1996; Gallo and Owen, 1999; Dash et. al., 2002; Arthur et al.,

2003; Li et al., 2005; Raynolds, 2008; Yashwant et al., 2008). Most studies focus on estimating linear relationships between NDVI and RST. According to Donglian and

Menas (2007), this relationship depends on the season and time-of-day. For example, the correlation between NDVI and RST is positive in winter, but strong negative correlations are found during the warm season.

Table 5.5 presents the estimation of the linear relationship between RST and

NDVI at the six different times in 2005 and 2006 for all image data cells of the CMA, with:

RST = a0 + a1 ⋅ NDVI +ε (5.2)

where a0 and a1 are the parameters estimated. The USGS method is used to derive the remotely sensed temperature data. This relationship does not consider the effects of neighboring cells and land-use patterns.

t-statistics Date* R2 Equation (a0, a1) April 11, 2005 0.002 51.54 + 0.61·NDVI (4,857.60, 70.36) May 13, 2005 0.07 56.42 – 2.99·NDVI (6,189.44, -439.28) August 1, 2005 0.45 72.94 – 9.43·NDVI (7,657.84, -1,455.60) September 2, 2005 0.24 65.03 – 6.15·NDVI (6,550.38, -908.71) November 21, 2005 0.01 37.25 + 1.21·NDVI (4,916.42, 194.64) February 25, 2006 0.06 35.79 + 3.52·NDVI (3,639.40, 405.91) *: Number of observed pixels at all dates: 2,633,805 (1,641*1,605).

Table 5.5. Simple linear regression between RST and NDVI across all CMA pixels.

The relationship between RST and NDVI can also be represented by a multiplicative function, with:

RST +30 =α ⋅(NDVI +1)β ⋅eε (5.3)

The logarithmic transformation yields the linear model:

ln(RST +30) = ln(α) + β ⋅ln(NDVI+1) +ε (5.4) where α and β are the parameters to be estimated. Adding positive constants to RST and

NDVI guarantees positive values. The results are presented in Table 5.6.

The Landsat dataset for August 1, 2005 provides the highest R2 for both specifications. A higher accuracy is obtained during Summer (August 1, 2005 and

September 2, 2005), when the vegetation is fully grown. A low accuracy characterizes the results for April 11, 2005, May 13, 2005, November 21, 2005 and February 25, 2006.

NDVI has a negative effect in Spring and Summer (May 13, August 1 and September 2,

2005) and a positive one in winter (February 25, 2006 and November 21, 2005). When vegetation is fully grown, more vegetation (NDVI ↑) has clearly a cooling effect (RST ↓), as expected. 82

t-statistics Date* R2 Equation (ln(α), β) April 11, 2005 0.001 3.95 + 0.04·log(NDVI) (86,372.3, 193.15) May 13, 2005 0.05 3.98 – 0.06·log(NDVI) (76,148.8, -363.77) August 1, 2005 0.37 4.15 – 0.19·log(NDVI) (68,039.4, -1,238.1) September 2, 2005 0.18 4.07 – 0.12·log(NDVI) (63,461.5, -763.76) November 21, 2005 0.01 3.65 + 0.04·log(NDVI) (79,060.7, 207.51) February 25, 2006 0.01 3.67 + 0.12·log(NDVI) (91,305.0, 485.41) *: Number of observed pixels at all dates: 2,633,805 (1,641*1,605).

Table 5.6. Log-log regression between RST and NDVI across all CMA pixels.

Finally, the Box-Cox transformation can be used, with:

⎧(RST + 30)λ −1 ⎧(NDVI+1)μ −1 (λ) ⎪ if λ ≠ 0 ( ) ⎪ if μ ≠ 0 RST = ⎨ λ and NDVI μ = ⎨ μ (5.5) ⎪ ⎪ ⎩ln(RST + 30) if λ = 0 ⎩ln(NDVI+1) if μ = 0 where NDVI(µ) and RST(λ) are the Box-Cox transformed variables for NDVI and RST. A linear regression analysis is next performed on the transformed variables:

(λ ) (μ ) (RST ) = a0 + a1 ⋅(NDVI ) + ε (5.6)

The Box-Cox transformation provides a continuum between the linear model (λ = µ = 1)

2 and the double-log linear model (λ→0, µ→0). A chi-squared (χ ) test indicates whether the optimal model is significantly different from the double-log model (λ→0, µ→0). The log-likelihood ratio (LKR) is computed as follows:

LKR = 2·[LK(m) – LK(0)] (5.7) where LK(m) is the log-likelihood of the selected model (λ, µ), and LK(0) is the log-likelihood of the model with (λ→0, µ→0). If the two models are equivalent, then LKR follows a χ2 distribution with 2 degrees of freedom. 83

The Box-Cox results are presented in *: Number of observed pixels at all dates: 2,633,805

(1,641*1,605).

2 Table 5.7. As χ2df (0.05) = 10.596, it is clear that, in all cases, the Box-Cox model

is superior to the double-log one. It is also clear that the R2s for the Box-Cox model are,

in most cases, superior to those obtained with the linear and double-log models, except

November 21, 2005, and February 25, 2006.

Log- Date* R2 (λ, μ) Equation likelihood ratio (LKR) April 11, 2005 0.003 (2.75, 3.2) 19,558.64 – 444.14·NDVI(µ) -2,225,849 May 13, 2005 0.10 (1.25, 3.6) 114.88 – 4.74·NDVI(µ) -2,033,350 August 1, 2005 0.50 (-0.25, 2.3) 2.58 - 0.04·NDVI(µ) -2,156,851 September 2, 2005 0.27 (07.5, 2.0) 27.00 – 1.75·NDVI(µ) -2,310,414 November 21, 2005 0.01 (3.0, 2.5) 19,168.46 + 1,045.28·NDVI(µ) -958,204 February 25, 2006 0.01 (3.01, 0.7) 19,131.73 + 1,558.96·NDVI(µ) -957,054 *: Number of observed pixels at all dates: 2,633,805 (1,641*1,605).

Table 5.7. Linear relationships between the Box-Cox variables NDVI(µ) and RST(λ).

5.2.3. LAND-USE SPECIFIC RELATIONSHIPS BETWEEN NDVI AND

REMOTELY-SENSED TEMPERATURES (RST).

As previously discussed, changes in land use/land cover (LULC) have an influence on meteorological variables, such as temperature. For example, conversion of

natural land to farmland changes surface roughness, albedo, leaf conductance and other properties, such as the exchanges of water and energy between the land surface and the atmosphere (Pielke et al., 2002). To account for these effects, the analysis of the relationships between land uses and RST is conducted at the six different dates. Table 5.8

presents a summary comparison of the R2 obtained from estimating the same three

models as used in Section 5.2.2 without distinction of land use. Table 5.9 presents the

results for the simple linear regression model between NDVI and RST, Table 5.10 those

for the double-log regression model, and Table 5.11 for the Box-Cox model. Similar

patterns of R2 values are obtained for the three models. The highest R2 is usually obtained in Summer (August 1 and September 2). As indicated in Table 5.8, the Box-Cox models have the highest R2s in most cases. In Table 5.11, the log-likelihood ratio (LKR) test

indicates that the Box-Cox estimation is superior to the double-log one in all cases.

Water has always a positive NDVI effect. The agricultural areas NDVI has a

negative effect, except on February 25, 2006, for all three models. The higher the NDVI,

the lower the temperature. The green areas NDVI has also a negative effect, except

during the winter season (February 25 and November 21). The models for agricultural

and green areas have higher R2s in Summer (August 1 and September 2) and lower R2s in

Winter (February 25 and November 21) for all specifications. The residential areas NDVI

85 has a negative effect on May 13, August 1 and September 2, and a positive one on

February 25, April 11 and November 21 for the double-log and linear models, and a negative effect in all cases for the Box-Cox model. The impervious areas NDVI has a positive effect on February 25 and November 21, and a negative effect for the other dates for the double-log and linear models, and a negative one in all cases for the Box-Cox model. The urban areas NDVI model has the lowest R2 throughout the year.

Central land use Model’s R2 (Number of Date Simple linear Log-log Box-Cox observations) February 25 0.49* 0.48 0.49 April 11 0.52 0.53 0.54 May 13 0.36 0.36 0.37 Water August 1 0.17 0.18 0.18 September 2 0.19 0.20 0.21 November 21 0.04 0.03 0.05 February 25 0.004 0.005 0.004 April 11 0.04 0.04 0.04 May 13 0.15 0.15 0.17 Agricultural August 1 0.63 0.61 0.60 September 2 0.30 0.27 0.32 November 21 0.0003 0.003 0.001 February 25 0.01 0.02 0.012 April 11 0.001 0.0008 0.002 May 13 0.14 0.13 0.18 Green August 1 0.50 0.49 0.53 September 2 0.23 0.21 0.26 November 21 0.06 0.05 0.07 February 25 0.01 0.02 0.014 April 11 0.0001 0.0008 0.0002 May 13 0.04 0.03 0.05 Residential August 1 0.23 0.22 0.24 September 2 0.07 0.06 0.08 November 21 0.01 0.01 0.07 February 25 0.01 0.02 0.01 April 11 0.04 0.03 0.05 May 13 0.07 0.06 0.08 Impervious August 1 0.13 0.12 0.13 September 2 0.06 0.05 0.07 November 21 0.0002 0.003 0.0008 February 25 0.02 0.02 0.01 April 11 0.002 0.006 0.03 May 13 0.0004 0.002 0.001 Urban August 1 0.002 0.005 0.0007 September 2 0.0001 0.002 0.008 November 21 0.007 0.01 0.002 *: The highest R2 is marked in red.

Table 5.8. Comparison of the R2 obtained for the linear, log-log, and Box-Cox models.

Central land use (Number of Date R2 Equation observations) February 25 0.49 7.52 + 10.17NDVI April 11 0.52 18.25 + 11.22NDVI Water May 13 0.36 17.32 + 6.44NDVI (54,877) August 1 0.17 25.41 + 2.65NDVI September 2 0.19 23.33 + 2.42NDVI November 21 0.04 7.26 + 1.43NDVI February 25 0.004 9.43 + 0.88NDVI April 11 0.04 22.23 - 2.13NDVI Agricultural May 13 0.15 23.07 - 3.38NDVI (690,263) August 1 0.63 33.77 - 10.89NDVI September 2 0.30 27.46 - 5.35NDVI November 21 0.0003 8.78 - 0.17NDVI February 25 0.01 9.42 + 1.43NDVI April 11 0.001 21.84 - 0.37NDVI Green May 13 0.14 23.31 - 3.80NDVI (1,055,777) August 1 0.50 35.05 - 12.46NDVI September 2 0.23 28.83 - 6.34NDVI November 21 0.06 7.85 + 2.35NDVI February 25 0.01 10.41 + 1.45NDVI April 11 0.0001 23.67 + 0.17NDVI Residential May 13 0.04 24.74 - 2.79NDVI (310,592) August 1 0.23 34.22 - 7.58NDVI September 2 0.07 29.87 - 4.11NDVI November 21 0.01 8.73 + 1.54NDVI February 25 0.01 10.27 + 1.40NDVI April 11 0.04 24.36 - 3.10NDVI Impervious May 13 0.07 25.06 - 3.79NDVI (463,075) August 1 0.13 33.79 - 5.71NDVI September 2 0.06 29.73 - 4.27NDVI November 21 0.0002 9.14 + 0.16NDVI February 25 0.02 8.66 + 8.85NDVI April 11 0.002 22.91 + 2.57NDVI Urban May 13 0.0004 23.74 + 0.95NDVI (59,222) August 1 0.002 32.60 + 2.48NDVI September 2 0.0001 27.87 + 1.09NDVI November 21 0.007 7.67 + 3.74NDVI

Table 5.9. Linear regression model between NDVI and RST for individual land uses.

Central Date R2 Equation land use February 25 0.48 3.63 + 0.24·log(NDVI + 1) April 11 0.53 3.88 + 0.21·log(NDVI + 1) Water May 13 0.36 3.86 + 0.14·log(NDVI + 1) (54,877) August 1 0.18 4.02 + 0.05·log(NDVI + 1) September 2 0.20 3.98 + 0.04·log(NDVI + 1) November 21 0.03 3.62 + 0.03·log(NDVI + 1) February 25 0.005 3.67 + 0.03·log(NDVI + 1) April 11 0.04 3.96 - 0.05·log(NDVI + 1) Agricultural May 13 0.15 3.97 – 0.08·log(NDVI + 1) (690,263) August 1 0.61 4.17– 0.26·log(NDVI + 1) September 2 0.27 4.06– 0.13·log(NDVI + 1) November 21 0.003 3.66 – 0.005·log(NDVI + 1) February 25 0.02 3.67 + 0.05·log(NDVI + 1) April 11 0.0008 3.95 – 0.007·log(NDVI + 1) Green May 13 0.13 3.98 – 0.09·log(NDVI + 1) (1,055,777) August 1 0.49 4.20 – 0.31·log(NDVI + 1) September 2 0.21 4.08 – 0.16·log(NDVI + 1) November 21 0.05 3.63 + 0.08·log(NDVI + 1) February 25 0.02 3.70 + 0.05·log(NDVI + 1) April 11 0.0008 3.98 + 0.009·log(NDVI + 1) Residential May 13 0.03 4.00 – 0.06·log(NDVI + 1) (310,592) August 1 0.22 4.17 - 0.16·log(NDVI + 1) September 2 0.06 4.09 – 0.09·log(NDVI + 1) November 21 0.01 3.65 + 0.05·log(NDVI + 1) February 25 0.02 3.69 + 0.05·log(NDVI + 1) April 11 0.03 3.99 – 0.05·log(NDVI + 1) Impervious May 13 0.06 4.01 – 0.08·log(NDVI + 1) (463,075) August 1 0.12 4.15 – 0.10·log(NDVI + 1) September 2 0.05 4.09 – 0.08·log(NDVI + 1) November 21 0.003 3.67 + 0.007·log(NDVI + 1) February 25 0.02 3.65 + 0.31·log(NDVI + 1) April 11 0.006 3.96 + 0.09·log(NDVI + 1) Urban May 13 0.002 3.98 + 0.05·log(NDVI + 1) (59,222) August 1 0.005 4.13 + 0.06·log(NDVI + 1) September 2 0.002 4.05 + 0.05·log(NDVI + 1) November 21 0.01 3.62 + 0.16·log(NDVI + 1)

Table 5.10. Log-log regression model for individual land uses.

Central land Log-likelihood Date R2 (λ, μ) Equation use ratio (LKR) 3.62 + February 25 0.49 (0.00, 0.6) -41,197.8 0.2·NDVI(µ) 1.71 + April 11 0.54 (-0.50, 0.7) -54,398.9 0.03·NDVI(µ) 1.65 + May 13 0.37 (-1.55, 0.3) -38,848.5 Water 0.057·NDVI(µ) (54,877) 1.47 + August 1 0.18 (-3.00, 2.9) -34,478.4 0.048·NDVI(µ) 1.13 + September 2 0.21 (-0.82, 2.9) -27624.6 0.006·NDVI(µ) 7,645.56 + November 21 0.05 (2.75, 0.9) -20,174.6 818.90·NDVI(µ) 20,533.24 + February 25 0.004 (3.00, 0.9) -223,243 1222.39·NDVI(µ) 6.32 – April 11 0.04 (-0.25, 1.1) -295,663 0.47·NDVI(µ) 0.399 – May 13 0.17 (-2.50, 2.5) -295,620 Agricultural 0.00002·NDVI(µ) (690,263) 0.71 – August 1 0.598 (-1.36, 1.1) -256,440 0.004·NDVI(µ) 1635.00 – September 2 0.32 (2.00, 2.1) -291,741 198.67·NDVI(µ 19684.37 – November 21 0.001 (3.00, 0.5) -142,405 461.81·NDVI(µ) 20,488.19 + February 25 0.012 (3.02, 0.9) -181,025 2160.54·NDVI(µ) 1344.24 – April 11 0.002 (2.00, 2.9) -485,895 13.58·NDVI(µ) 12.58 - May 13 0.18 (0.5, 2.9) -496,221 Green 0.31·NDVI(µ) (1,052,731) 0.79 - August 1 0.53 (-1.25, 3.6) -551,067 0.0005·NDVI(µ) 7.03 - September 2 0.26 (0.25, 4.0) -481,333 0.10·NDVI(µ) 18,261.71 – November 21 0.07 (3.01, 2.1) -208,175 2,513.51·NDVI(µ)

Table 5.11. Linear relationships between the Box-Cox variables NDVI(µ) and RST(λ) for individual land uses. Continued.

Table 5.11 continued.

Central land Log-likelihood Date R2 (λ, μ) Equation use ratio (LKR) 1,703.44 – February 25 0.014 (3.00, 0.3) -9,565.9 134.81·NDVI(µ) 51,919.29 – April 11 0.0002 (3.00, 2.9) -151,952 336.37·NDVI(µ) 54279.43 – May 13 0.05 (3.00, 3.9) -139,231 Residential 3836.42·NDVI(µ) (310,592) 86,990.25 – August 1 0.24 (2.99, 2.1) -184,914 20,749.6·NDVI(µ) 70930.74 – September 2 0.08 (3.00, 2.9) -213,880 8261.54·NDVI(µ) 18,261.71 – November 21 0.07 (3.01, 0.90) -208,175 2,513.51·NDVI(µ) 503.68 – February 25 0.01 (3.09, 0.5) -181,495 10.64·NDVI(µ) 623.15 – April 11 0.05 (1.75, 2.1) -421,119 56.51·NDVI(µ) 12.82– May 13 0.08 (0.5, 3.9) -371,241 Impervious 0.28·NDVI(µ) (463,074) 62.79 – August 1 0.13 (1.00, 0.9) -378,634 5.80·NDVI(µ) 71,754.68 – September 2 0.07 (3.00, 1.3) -475033 15,074.3·NDVI(µ) 20,129.34 – November 21 0.0008 (3.00, 1.3) -206,811 7.62·NDVI(µ) 19,877.11 – February 25 0.01 (3.02, 0.5) -79,106.3 7,693.36·NDVI(µ) 50757.94 – April 11 0.03 (3.00, 0.5) -93,284.3 2,361.06·NDVI(µ) 52,770.64 – May 13 0.001 (3.01, 1.3) -82,429.0 Urban 1,435.96·NDVI(µ) (59,222) 82,801.19 – August 1 0.0007 (3.00, 0.5) -81,818 5,006.99·NDVI(µ) 66,262.49 – September 2 0.008 (3.00, 0.3) -96,335.7 1,212.64·NDVI(µ) 18451.11 – November 21 0.002 (3.01, 0.7) -76,159 2,470.43·NDVI(µ)

CHAPTER 6

RESULTS AND ANALYSIS

This chapter presents the estimation results for the regression models developed in Chapter 3 to delineate the relationships between local temperatures and land-use patterns under two different scenarios: wind and no-wind effects. Models are first estimated for six different dates in 2005-2006, while ignoring the wind factor and using alternatively land-use NDVI and land-use area variables. Model R2s (goodness-of-fit) are compared across time and across model specification. Next, the wind factor is introduced into the model for February 25, 2006 when there is a relatively strong wind, and the results are compared to those for the same date when the wind factor is ignored. The overall implications of the results are discussed.

6.1. NO-WIND-EFFECT ANALYSIS.

Based on the methodology proposed in Chapter 3, the parameters that represent the local effect of each land use are estimated. For this purpose, Landsat-5 data and weather data derived from measuring stations are combined, as shown in Figure 6.1.

There are five weather measuring stations within the Columbus Metropolitan Area 92

(CMA). However, they do not all measure the same wind speed on the same day. For example, at around 10AM on August 1, 2005, three measuring stations, West Dublin,

Bolton Airport and Rickenbacker Airport (RBA), recorded no wind speed. However, the other two stations, OSU Airport and Columbus International Airport (CIA), recorded

1.79 m/sec wind speed from the North.

: West Dublin : The Ohio State University (OSU) Airport : Bolton Airport

: Columbus International Airport :Rickenbacker Airport

Figure 6.1. Measuring stations and surrounding areas (1,641*1,605 = 2,633,805 cells).

Although the five measuring stations observe different wind speeds and directions, the speed differences are small. Therefore, the Beaufort wind force scale, created in 1805 by Sir Francis Beaufort, a British admiral and hydrographer, is used to select a wind speed that applies to the whole area.35 This is an empirical measure based mainly on observed sea conditions. On the Beaufort scale, a wind speed of 1.79 m/sec belongs to category 2, “Light breeze.” In this research, this condition is considered as a

“calm” condition. The wind speed on August 1, 2005, is assumed to be zero for the whole area.

Figure 6.2 presents the distribution of central land-use cells when the buffer is of dimension θ = 11. In this case, there are 2,601,445 cells that can be used to estimate the land-use parameters. In Figure 6.3, the total number of central cells when θ = 5 is equal to

2,620,837 (1,637*1,601). The first central cell must be located at (3, 3) and the last central cell at (1,639, 1,603). The first two cells and the last two cells in each row and column cannot be considered as central cells. Figure 6.3 illustrates how the total number of central cells depends on the size of the buffer matrix.

35See Appendix A 94

Urban, Water, 59,181 54,037

Impervious, 461,539 Agriculture, 672,686

Residential, 319,896

Green, 1,034,106

Total: 2,601,445

Figure 6.2. Distribution of central cells across land uses when θ = 11.

2 1605

1641

: Central cell

Figure 6.3. Cell buffer pattern when θ = 5.

Two different input variables are used: NDVI and AREA. The NDVI measure has been selected because the six land uses (water, agricultural, green, residential, impervious and urban areas) have varying amounts of vegetation, across space and over time. The higher the NDVI in any one cell, the larger the amount of vegetation in that cell. On the other hand, the AREA measure represents the amount of any specific land use, irrespective of the amount of vegetation, and thus represents the effects of non-vegetation factors.

There are several variables that may affect local temperatures, such as urban canyon effects, types of anthropogenic activities, thermal conductivity, advection by the temperature gradient, sky view factor, albedo, soil moisture, cloudiness and air humidity. The NDVI variable only represents the effects of vegetation. However, the other variables mentioned above, that are not related to vegetation, affect local temperatures. The AREA-based models can be presumed to better represent these other effects than the NDVI models, especially in the more developed areas

(residential, impervious and urban).

6.1.1. LAND-USE NDVI MODELS IN THE NO-WIND-EFFECT CASE.

To estimate the land-use parameters, Equation (3.7) can be transformed into:

6 Tj,RST = βo + ∑βk ⋅V jk + ε j (6.1) k=1

where Tj,RST is the remotely sensed temperature at the center cell j, βo is the intercept

− p (Tj,base), V jk =∑dij ⋅ NDVIi ⋅ LUik ⋅ Nij represents the distance-weighted NDVI land-use i

− p variable, i is the index of a neighboring pixel around the central pixel j, dij is the

distance factor between the central and neighboring pixel, k is the land-use index (k:

1→6), LUik = 1 if cell i is occupied by land-use k, = 0 otherwise, Nij = 1 if i belongs to the

buffer of cell j, = 0 otherwise, and εj is the error term.

Remotely-sensed data provide a large number of observations for each land use.

The relationship can be represented in matrix form by Equation (6.2):

⎡T1,RST ⎤ ⎡V1,1 V1,2 V1,3 V1,4 V1,5 V1,6 ⎤ ⎡ε ⎤ ⎢ ⎥ ⎢ ⎥ β 1 T V V V V V V ⎡ 1 ⎤ ⎢ ⎥ ⎢ 2,RST ⎥ ⎢ 2,1 2,2 2,3 2,4 2,5 2,6 ⎥ ε 2 ⎢β ⎥ ⎢ ⎥ ⎢T ⎥ ⎢V V V V V V ⎥ ⎢ 2 ⎥ ⎢ε ⎥ ⎢ 3,RST ⎥ ⎢ 3,1 3,2 3,3 3,4 3,5 3,6 ⎥ 3 ⎢β3 ⎥ ⎢ ⎥ ⎢ M ⎥ = ⎢ M M ⎥⋅ ⎢ ⎥ + ⎢ M ⎥ ⎢ ⎥ ⎢ ⎥ β 4 (6.2) T V V V V V V ⎢ ⎥ ⎢ε ⎥ ⎢ j,RST ⎥ ⎢ j,1 j,2 j,3 j,4 j,5 j,6 ⎥ ⎢β ⎥ ⎢ j ⎥ ⎢ ⎥ ⎢ ⎥ 5 M M M ⎢ ⎥ ⎢ M ⎥ ⎢ ⎥ ⎢ ⎥ ⎣⎢β6 ⎦⎥ ⎢ ⎥ T V V V V V V ε ⎣⎢ m,RST ⎦⎥ ⎣⎢ m,1 m,2 m,3 m,4 m,5 m,6 ⎦⎥ ⎣ m ⎦ (m*1) (m*6) (6*1)

where m is the number of observations for a given land use from Landsat-5, Tj,RST is the

th th j remotely-sensed temperature observation and εj is the j error term. 97

For example, when θ = 7, the number of observations for water cells is 54,294.

All the land-use parameters β’s can be estimated by ordinary least square (OLS)

regression, under the assumption of normality and homoskedasticity for the error term.

Also, there is enough variability over space in the non-observed factors to make any

possible correlation between the land-use variables and the error term negligible. For

instance, in urban areas, the street canyon effect highly depends on local building-road geometries, that vary considerably.

Each of the six land uses is considered separately to determine the optimal combination (θ, p) that yields the highest R2, because the purpose of this research is to be

able to predict the changes in temperatures resulting from different neighboring land-use

arrangements. The whole land-use effect (R2) at any one location (central cell) is more

important than the effects of individual land uses separately. The t-statistics, which

measure the precision of each estimated parameter, are less important. Indeed, because

land uses are spatially interrelated, changing one land use at a given location is not

possible without changing land uses at other locations. Thus, it is the forecast of the

impact of the whole change that is important.

For NDVI models on August 1, 2005, Table C.13 in Appendix C presents the R2s for various combination of (θ, p). The highest R2s are obtained when θ ∈ [7 – 9] and p∈

[0.3 - 0.6] for all land uses, except urban areas. Distance exponents (p) less than one

suggest that it is the extended land-use pattern around the central pixel, rather than only

the adjacent pixels, that is more important to explain local temperatures.

6.1.1.1. MODELS FOR AUGUST 1, 2005.

Table 6.1 presents the estimated parameters for the NDVI land-use models with

the highest R2 among various combination of (θ, p) for August 1, 2005. The model results suggest that temperatures in undeveloped areas, e.g., water, agricultural and green areas, can be well explained by the NDVI in neighboring cells. However, model results for developed areas, e.g., impervious and urban areas, display lesser accuracy. Notably, the model for urban areas needs the largest buffer size θ [21 – 35] to best explain temperatures, and still displays the lowest accuracy (R2 ≈ 0.19), probably because these

areas are very heterogeneous, with variable urban canyon effects and anthropogenic

activities.

Central land use Neighboring Parameter R2 t-statistics (Number of pixels) land use (β's) (θ, p) Intercept 24.04 1513.14 Water 0.07 22.09 Agriculture 0.14 22.56 Water 0.57 Green 0.12 36.18 (54,166) (9, 0.3) Residential 0.64 91.81 Impervious 1.80 165.46 Urban -7.52 -45.10 Intercept 35.70 4706.0 Water -2.79 -151.18 Agriculture -1.47 -1279.2 Agriculture 0.80 Green -1.47 -916.96 (678,313) (9, 0.5) Residential -0.93 -96.59 Impervious -1.50 -186.87 Urban 1.02 9.06 Intercept 37.66 5609.60 Water -2.30 -512.29 Agriculture -1.20 -1338.2 Green 0.78 Green -1.22 -1472.0 (681,220) (7, 0.3-0.4) Residential -1.00 -528.39 Impervious -1.26 -391.43 Urban -1.94 -20.54 Intercept 35.31 2896.36 Water -1.93 -217.67 Agriculture -1.00 -210.11 Residential 0.61 Green -0.93 -471.93 (310,170) (7, 0.3) Residential -0.60 -253.84 Impervious -0.47 -99.06 Urban -1.29 -16.55 Intercept 34.96 4391.94 Water 1.36 93.31 Agriculture -0.97 -242.43 Impervious 0.40 Green -0.85 -365.31 (461,847) (9, 0.5-0.6) Residential -0.50 -142.53 Impervious -0.36 -88.75 Urban -0.22 -5.36 Intercept 36.09 684.46 Water 0.94 15.66 Agriculture -0.83 -45.88 Urban 0.19 Green -0.53 -40.10 (59,110) (25, 0.6) Residential 0.57 22.83 Impervious -1.21 -43.74 Urban 6.62 90.53

Table 6.1. Regression results for the NDVI models on August 1, 2005.

100

Based on the parameters in Table 6.1, the equations representing the relationships

between the NDVI variables and local temperature can be summarized as follows:

TWater = 24.04 + 0.07·NDVIWater + 0.14·NDVIAg + 0.12·NDVIGreen

+ 0.64·NDVIResi + 1.80·NDVIImp - 7.52·NDVIUrban (6.3)

TAg = 35.70 - 2.79·NDVIWater - 1.47·NDVIAg - 1.47·NDVIGreen

- 0.93·NDVIResi - 1.50·NDVIImp + 1.02·NDVIUrban (6.4)

TGreen = 37.66 – 2.30·NDVIWater – 1.20·NDVIAg – 1.22·NDVIGreen

- NDVIResi – 1.26·NDVIImp – 1.94·NDVIUrban (6.5)

TResi = 35.31 -1.93·NDVIWater - NDVIAg - 0.93·NDVIGreen

- 0.60·NDVIResi - 0.47·NDVIImp - 1.29·NDVIUrban (6.6)

TImp = 34.96 + 1.36·NDVIWater – 0.97·NDVIAg – 0.85·NDVIGreen

- 0.50·NDVIResi - 0.36·NDVIImp - 0.22·NDVIUrban (6.7)

TUrban = 36.09 + 0.94·NDVIWater - 0.83·NDVIAg - 0.53·NDVIGreen

+ 0.57·NDVIResi - 1.21·NDVIImp + 6.62·NDVIUrban (6.8)

where TLand use is the temperature for a given land use at the central pixel, NDVILand use is the weighted sum of the NDVIs of the neighboring land uses, depending on (θ, p). Ag represents agriculture, Resi residential areas and Imp impervious areas. The estimated parameters can be interpreted as follows.

Equation (6.3) explains the temperature of water. The intercept is 24.04 °C (Tbase) which is, by far, the lowest base temperature for all land uses. All the neighboring land

101

uses, except urban, have positive NDVI coefficients, which suggests that the more

vegetation in these land uses, the higher the water temperature. As shown in Figure 5.5,

mean NDVIs for urban areas throughout the year 2005 - 2006 are negative, which implies

that urban areas have also a positive effect on water temperature. However, it is not

desirable to focus only on whether the product of the coefficient and the NDVI value is

positive or negative. The focus must be on the direction of change. In Equation (6.4) for

agriculture, all land uses have a negative NDVI effect, except urban, which suggests that

the more vegetation, the lower the temperature. In the case of green and residential areas

[Equations (6.5) and (6.6)], all surrounding land uses have negative NDVI effects. For all

three land uses, an increasing vegetative cover in the surrounding areas has mostly a

cooling effect. In the case of impervious areas [Equation (6.7)], all the neighboring land

uses, except water, have negative NDVI coefficients, also implying that the more

vegetation in the surrounding areas, the greater the cooling effect on impervious areas.

Finally, for urban areas in Equation (6.8), except for water, residential and urban areas,

the NDVI effects are negative. The low R2 is probably due to the complexity of urban

structures, with different materials having different thermal contents, and with diverse

anthropogenic activities and local wind effects in urban canyons.

Table 6.2 presents statistics for the independent variables (the weighted NDVI sum of neighboring land uses) of the models presented in Table 6.1. These statistics vary across central land uses and neighboring land uses, as expected.

102

NDVI weighted sum Central land use Neighboring land (MT) use Standard Mean Minimum Maximum deviation Water -0.87 -8.54 9.90 3.45 Agriculture 0.59 -0.04 12.42 1.14 Water Green 2.69 0 15.12 2.98 (25.59°C) Residential 0.78 0 9.94 1.10 Impervious 0.39 -3.50 6.65 0.69 Urban -0.003 -2.99 0.33 0.04 Water 0.01 -1.53 2.38 0.07 Agriculture 3.81 -0.09 8.11 2.11 Agriculture Green 1.72 0 7.13 1.25 (27.29°C) Residential 0.06 -0.05 2.88 0.16 Impervious 0.12 -0.73 2.83 0.24 Urban 0.0004 -0.44 0.83 0.01 Water 0.05 -2.38 5.74 0.26 Agriculture 1.68 -0.06 11.01 1.88 Green Green 5.23 0.03 11.06 2.24 (28.38°C) Residential 0.39 -0.17 7.28 0.74 Impervious 0.30 -0.88 4.95 0.50 Urban 0.0004 -0.68 0.83 0.01 Water 0.06 -2.80 5.82 0.27 Agriculture 0.24 -0.11 8.34 0.57 Residential Green 1.66 0 9.78 1.68 (31.58°C) Residential 2.23 -0.06 7.52 1.30 Impervious 1.08 -1.24 5.18 0.75 Urban 0.002 -0.96 1.07 0.03 Water 0.01 -4.00 3.77 0.19 Agriculture 0.44 -0.11 8.01 0.82 Impervious Green 1.22 0 8.46 1.34 (32.55°C) Residential 0.92 -0.17 6.49 0.86 Impervious 1.38 -2.84 4.85 0.74 Urban -0.003 -2.33 1.23 0.07 Water 0.01 -4.72 2.55 0.26 Agriculture 0.76 -0.02 13.19 1.10 Urban Green 1.59 0 11.91 1.48 (32.58°C) Residential 0.96 0 7.24 0.76 Impervious 1.55 -1.17 4.82 0.72 Urban -0.11 -1.94 1.20 0.25 MT: Mean Temperature with remotely-sensed temperatures (RST).

Table 6.2. NDVI statistics for the independent variables on August 1, 2005.

103

The elasticity (ε) for each equation and variable is estimated to measure the

relative importance of individual NDVI land-use effects on local temperatures. The

elasticity (εi) in Equation (6.1) is defined:

∂Tj ∂V ji V ji ε i = ( )/ ( ) = βi ⋅ (6.9) Tj V ji Tj where Vji is the weighted NDVI sum for the neighboring land use i around central cell j,

and Tj is the temperature at j. For Tj, two different temperature measures are used to estimate the elasticity: RST and the temperature estimated (Test) by Equations (6.3)

through (6.8).

As indicated in Table 6.3, the two approaches to estimate temperature (Tj = RST

and Tj = Test) lead to similar elasticity means. Water has negative effects on all

neighboring land uses (ε ≤ 0), indicating that increasing water area can reduce local temperatures. Agriculture and green areas have negative effects on the local temperatures

of all land uses (-0.235 < ε < -0.051), except water (ε > 0). The highest elasticity values

for these two areas are -0.214 for agricultural areas onto themselves and -0.231 for green

areas onto themselves. This result implies that increasing neighboring green and

agricultural areas around green and agricultural areas is the most effective tool to

decrease local temperatures. For residential, impervious and urban areas, increasing green

areas is also the most effective way to reduce local temperatures. However, water has no

effects on the temperatures of these areas, and increasing neighboring impervious areas

has negative effects on these three areas.

104

Elasticity (ε ) Neighboring i Central land use land use Standard Mean Minimum Maximum deviation Impervious 0.025 -0.258 0.375 0.043 Residential 0.018 0.000 0.227 0.025 Green 0.012 0.000 0.075 0.014 Water Agriculture 0.003 -0.000 0.071 0.006 Water -0.003 -0.025 0.029 0.010 Urban 0.001 -0.092 0.919 0.012 Agriculture -0.214 -0.516 0.005 0.127 Green -0.093 -0.440 0.000 0.069 Impervious -0.006 -0.153 0.042 0.012 Agriculture Residential -0.002 -0.095 0.002 0.005 Water -0.001 -0.267 0.164 0.008 Urban 0.000 -0.021 0.025 0.000 Green -0.231 -0.584 -0.001 0.113 Agriculture -0.074 -0.556 0.003 0.086 Residential -0.013 -0.261 0.006 0.025 Green Impervious -0.012 -0.203 0.044 0.020 Water -0.004 -0.504 0.224 0.023 Urban 0.000 -0.056 0.046 0.001 Green -0.051 -0.349 0.000 0.054 Residential -0.043 -0.164 0.001 0.025 Impervious -0.016 -0.080 0.023 0.011 Residential Agriculture -0.008 -0.324 0.003 0.020 Water -0.004 -0.397 0.221 0.019 Urban -0.000 -0.040 0.045 0.001 Green -0.033 -0.294 0.000 0.038 Impervious -0.015 -0.055 0.043 0.008 Agriculture -0.014 -0.305 0.004 0.027 Impervious Residential -0.014 -0.110 0.003 0.013 Water 6*10-6 -0.227 0.210 0.010 Urban 10-5 -0.009 0.020 0.000 Impervious -0.058 -0.360 0.053 0.028 Green -0.027 -0.277 0.000 0.026 Urban -0.025 -0.538 0.234 0.061 Urban Agriculture -0.021 -0.418 0.001 0.031 Residential 0.017 0.000 0.123 0.013 Water 3*10-5 -0.164 0.083 0.008 (a) Tj = RST

Table 6.3. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on August 1, 2005. Continued.

105

Table 6.3 continued.

Elasticity (ε ) Neighboring i Central land use land use Standard Mean Minimum Maximum deviation Impervious 0.025 -0.185 0.333 0.042 Residential 0.018 0.000 0.209 0.025 Green 0.012 0.000 0.070 0.014 Water Agriculture 0.003 -0.000 0.066 0.006 Water -0.003 -0.025 0.028 0.010 Urban 0.001 -0.111 0.559 0.011 Agriculture -0.213 -0.501 0.004 0.126 Green -0.093 -0.419 0.000 0.069 Impervious -0.006 -0.143 0.029 0.012 Agriculture Residential -0.002 -0.090 0.002 0.005 Water -0.001 -0.269 0.110 0.008 Urban 4*10-5 -0.014 0.024 0.000 Green -0.231 -0.558 -0.001 0.112 Agriculture -0.074 -0.547 0.002 0.086 Residential -0.013 -0.245 0.005 0.025 Green Impervious -0.012 -0.210 0.036 0.020 Water -0.004 -0.621 0.132 0.023 Urban -8*10-6 -0.052 0.036 0.001 Green -0.051 -0.348 0.000 0.054 Residential -0.042 -0.148 0.001 0.025 Impervious -0.016 -0.076 0.016 0.011 Residential Agriculture -0.008 -0.325 0.003 0.020 Water -0.004 -0.490 0.135 0.019 Urban 5*10-7 -0.041 0.036 0.001 Green -0.033 -0.263 0.000 0.038 Impervious -0.015 -0.053 0.029 0.008 Agriculture -0.014 -0.305 0.003 0.027 Impervious Residential -0.014 -0.103 0.003 0.013 Urban 2*10-6 -0.008 0.014 0.000 Water 10-5 -0.184 0.130 0.008 Impervious -0.057 -0.184 0.050 0.027 Green -0.027 -0.231 0.000 0.026 Urban -0.023 -0.539 0.201 0.056 Urban Residential 0.017 0.000 0.110 0.013 Agriculture -0.020 -0.483 0.001 0.032 Water 4*10-5 -0.143 0.065 0.008

(b) Tj = Temperatures with the regression models.

106

6.1.1.2. NDVI MODELS ACROSS THE YEAR 2005 - 2006.

The estimation procedure presented in the previous section with data for August 1,

2005, has been applied to the other five days with available data over 2005-2006 (April

11, May 13, September 2, November 21, 2005, and February 25, 2006). The detailed

results are presented in Appendix C, including the sensitivity analysis over the parameters (θ, p), the regression results for the best models, statistics of the independent variables, and elasticity analyses. The results are summarized here.

The seasonal variations of the NDVI do appear to affect the accuracy of the models. Table 6.4 presents the R2s for the NDVI models for the different land uses, for

the optimal combinations of (θ, p), and Figure 6.4 illustrates these results graphically.

Except for water, the highest R2s for each land use are obtained on August 1, 2005, when

the vegetation is fully grown. The late winter (February 25, 2006) models have uniformly

higher R2 than the early winter (November 21, 2005) models. These differences might be

due to the general temperature level in the CMA at these times, but further analyses

would be necessary to confirm this hypothesis. As illustrated in Table 6.4 and Figure 5.5,

the patterns of the R2s for the five land uses, except water, are similar to the NDVI

pattern.

107

R2 (θ, p) Land use 2005 2006 September November February April 11 May 13 August 1 2 21 25 0.80 0.70 0.57 0.50 0.13 0.83 Water (9, 0.4) (9, 0.3) (9, 0.3) (11, 0.4) (9, 0.2) (11, 0.5) 0.08 0.21 0.80 0.49 0.03 0.04 Agriculture (9, 0.2) (7, 0.4) (9, 0.5) (11, 0.4) (41, 0.1) (39, 0.5) 0.16 0.36 0.78 0.52 0.09 0.12 Green (11, 0.1) (7, 0.1) (7, 0.3) (9, 0.4) (7, 0.2) (23, 0.5) 0.26 0.34 0.61 0.32 0.15 0.28 Residential (13, 0.2) (9, 0.4) (7, 0.3) (9, 0.4) (13, 0.4) (13, 0.4) 0.29 0.23 0.40 0.23 0.07 0.21 Impervious (13, 0.5) (9, 0.3) (9, 0.5) (13, 0.5) (25, 0.6) (17, 0.4) 0.14 0.08 0.19 0.09 0.12 0.23 Urban (47, 0.7) (33, 0.5) (25, 0.6) (29, 0.8) (23, 0.7) (17, 0.5)

Table 6.4. R2s of the NDVI models across the year 2005-2006.

R2 0.9

0.8

0.7 Water 0.6 Agriculture 0.5 Green

0.4 Residential Impervious 0.3 Urban 0.2

0.1

0 Time

April 11 May 13 August 1 September November February 2005 2005 2005 2, 2005 21, 2005 25, 2006

Figure 6.4. Comparison of the R2s of the best NDVI models in the no-wind-effect case.

108

Agricultural, green and residential areas display very similar patterns, with R2s

peaking on August 1 and bottoming on November 21. The R2s of urban areas do not

change much throughout the year, most likely because they have always low NDVI

values. The highest R2 is obtained in Winter (February 25, 2006). Also, urban areas need

the largest buffer (θ) to achieve the best R2s, which are still low when compared to the

other land uses. Impervious areas have patterns similar to urban areas, but with higher

R2s. Finally, water has its highest R2s in Winter (February 21, 2006 and November 21,

2005), and this cannot be explained by the seasonal variations in NDVI values.

Table 6.5 presents statistics on the NDVIs at the six different dates. The NDVIs

display a marked heterogeneity, corresponding to seasonal variations. Based on previous

studies, the largest increase in NDVI occurs in Spring (April and May), because of temperature rise and moisture availability (Tucker et al., 2001; Slayback et al., 2003).

Concurrent increases in temperature and precipitation during Summer may improve light

use efficiency for photosynthesis and moisture availability for plants, and thus leads to an

increase in plant growth, resulting in larger NDVIs and better accuracy for the models in

the Summer (August and September).

109

Central land use Standard (Number of Date Mean Minimum Maximum deviation observations) February 25 -0.18 -0.88 0.49 0.20 April 11 -0.15 -1.00 0.66 0.26 Water May 13 0.07 -1.00 0.85 0.27 (54,037) August 1 0.07 -0.94 0.75 0.36 September 2 0.05 -0.93 0.78 0.37 November 21 -0.11 -0.89 0.57 0.22 February 25 0.12 -0.68 0.68 0.10 April 11 0.17 -0.73 1.00 0.15 Agricultural May 13 0.24 -0.42 0.89 0.20 (675,486) August 1 0.59 -0.18 0.92 0.18 September 2 0.56 -0.71 0.95 0.19 November 21 0.18 -0.90 0.74 0.14 February 25 0.17 -0.5 0.71 0.10 April 11 0.27 -1.00 0.80 0.15 Green May 13 0.42 -0.41 0.83 0.17 (1,038,081) August 1 0.54 -0.02 0.90 0.14 September 2 0.54 -0.33 0.98 0.14 November 21 0.26 -0.90 0.89 0.14 February 25 0.14 -0.90 0.57 0.09 April 11 0.26 -1.00 0.74 0.12 Residential May 13 0.36 -0.32 0.80 0.11 (309,896) August 1 0.35 -0.32 0.76 0.13 September 2 0.36 -0.33 0.86 0.14 November 21 0.22 -0.92 0.89 0.10 February 25 0.09 -0.81 0.70 0.11 April 11 0.18 -0.92 0.76 0.16 Impervious May 13 0.25 -0.64 0.76 0.16 (461,539) August 1 0.22 -0.90 0.86 0.16 September 2 0.24 -0.93 0.85 0.17 November 21 0.17 -0.92 0.80 0.15 February 25 -0.03 -0.64 0.47 0.07 April 11 -0.003 -0.74 0.68 0.09 Urban May 13 0.03 -0.64 0.71 0.09 (59,181) August 1 -0.01 -0.69 0.64 0.08 September 2 0.004 -0.81 0.81 0.10 November 21 -0.01 -0.61 0.68 0.09

Table 6.5. Statistics on NDVI for the six land uses for the whole Columbus Metropolitan Area (CMA).

110

6.1.2. LAND-USE AREA MODELS IN THE NO-WIND-EFFECT CASE.

Equation (6.1), based on the weighted sum of NDVI for neighboring land uses, is

modified to include a different set of input variables, the six neighboring land-use areas:

Area T = β + β ⋅[ ⋅ LU ⋅ N ] (6.10) j ,RST o ∑ k ∑ p ik ij k i dij

The weighted sum of the land-use areas around the central cell j (Vj,k) is defined as:

Area Vjk =∑ p ⋅ LUik ⋅ Nij (6.11) i dij

− p where i represents the index of a neighboring pixel around the central pixel j, dij is the distance factor between the central and neighboring pixel, p is the distance exponent, and

Area is the area of any one cell (30 m *30 m = 900 m2).

However, there is, for each observation, a perfect linear relationship:

VWater + VAg + VGreen + VResi + VImp + VUrban = Constant (6.12)

This can be easily explained by considering the buffer illustrated in Figure 6.5 with dimension θ = 5. The neighboring cells are made of two rings, A and B. All the 16 cells in Ring A have their areas (30*30 = 900) weighted by the same distance factor 60-p, and

this also applied to the 8 cells in Ring B, but with the factor 30-p. It follows that the

distance weighted sums of land areas for the three rings (including the central cell) are:

1 14,400 1 7,200 V =16*900* = , V = 8*900* = RingA 60p 60p RingB 30 p 30p (6.13)

VCenter = 900

where VRingA and VRingB are the weighted sum for Rings A and B. Whatever the mix of

land uses in each ring, their sum is fixed. Therefore, the left-side component of Equation

111

(6.12) is always, whatever the land use mix within the buffer, equal to the sum VRingA +

VRingB + VCenter, which only depends on the distance exponent (p), and is therefore fixed.

:Ring A : Ring B

(a) Rings A and B.

60-p 60-p 60-p 60-p 60-p

60-p 30-p 30-p 30-p 60-p

60-p 30-p 1 30-p 60-p

60-p 30-p 30-p 30-p 60-p

60-p 60-p 60-p 60-p 60-p

(b) Distance weights.

Figure 6.5. Illustration of the land-use area collinearity issue.

112

6.1.2.1. MODELS FOR AUGUST 1, 2005.

To avoid the multi-collinearity problem implied by Equation (6.12), only five of

the six land-use variables can be used in the model. The neighboring land use deemed least important in explaining temperature is excluded. Table 6.6 presents statistics on the independent variables of the models, and Table 6.7 presents the models with the highest

R2 values.

113

Weighted sum of neighboring land uses (m2) Neighboring Central land use land use Standard Mean Minimum Maximum deviation Water 1094.1 0 1229.5 100.44 Agriculture 13.40 0 189.78 22.36 Green 64.06 0 328.12 67.74 Water Residential 25.80 0 293.49 34.85 Impervious 30.21 0 313.50 43.48 Urban 1.78 0 148.36 6.87 Water 3.76 0 631.87 19.85 Agriculture 1439.4 0 1820.1 223.44 Green 301.64 0 920.09 182.77 Agriculture Residential 18.61 0 742.77 44.87 Impervious 51.85 0 798.14 94.27 Urban 4.76 0 769.55 27.53 Water 20.26 0 1580.3 79.30 Agriculture 390.02 0 1858.5 348.66 Green 2061.3 0 2758.5 388.83 Green Residential 132.70 0 1694.8 218.71 Impervious 147.96 0 1693.1 213.69 Urban 6.20 0 1142.7 34.19 Water 4.50 0 291.88 16.70 Agriculture 12.39 0 279.91 22.47 Green 76.05 0 326.79 66.88 Residential Residential 1035.0 0 1219.7 65.04 Impervious 97.18 0 315.72 64.25 Urban 4.30 0 205.23 12.92 Water 21.13 0 1813.1 95.70 Agriculture 149.45 0 1691.3 231.54 Green 332.70 0 1858.5 339.09 Impervious Residential 371.84 0 1762.8 300.49 Impervious 1782.5 0 2758.5 372.87 Urban 100.85 0 1752.0 180.68 Water 3.59 0 278.31 16.63 Agriculture 29.60 0 411.80 40.48 Green 35.91 0 343.50 40.89 Urban Residential 41.65 0 259.22 33.80 Impervious 199.32 0 444.37 79.01 Urban 1064.5 0 1374.6 93.95

Table 6.6. Land-use area statistics for the independent variables on August 1, 2005.

114

Central land use Neighboring Parameter t-statistics R2 (θ, p) (Number of pixels) land use (β's) Intercept 27.93 23.27 Water -0.004 -3.85 Water Agriculture 0.003 3.32 0.64 (54,142) Green 0.006 6.23 (11, 1.3) Residential 0.022 23.12 Impervious 0.025 23.8 Intercept 28.23 177.79 Water -0.008 -56.02 Agriculture Agriculture -0.001 -16.92 0.48 (672,859) Green 0.001 15.32 (13, 1.1) Residential 0.003 25.11 Impervious 0.015 150.06 Intercept 22.94 138.02 Water -0.003 -42.57 Green Agriculture 0.001 14.8 0.34 (1,037,789) Green 0.002 29.82 (11, 0.9) Residential 0.003 53.81 Impervious 0.007 107.65 Intercept 24.41 97.19 Water -0.03 -119.81 Residential Agriculture 0.002 9.96 0.55 (309,864) Green -0.008 -38.77 (11, 1.3) Residential 0.006 30.73 Impervious 0.014 64.84 Intercept 11.20 145.95 Agriculture 0.005 179.79 Impervious Green 0.005 172.64 0.44 (461,516) Residential 0.006 223.11 (11, 0.9) Impervious 0.009 311.21 Urban 0.007 224.83 Intercept -5.36 -4.39 Agriculture 0.027 27.27 Urban Green 0.019 19.25 0.26 (59,145) Residential 0.023 23.59 (17, 1.3) Impervious 0.050 55.07 Urban 0.024 26.91

Table 6.7. Regression results for the land-use are models on August 1, 2005.

115

Based on the parameters in Table 6.7, the equations representing the relationships between land-use areas and local temperatures can be summarized as follows:

TWater = 27.93 - 0.004·AREAWater + 0.003·AREAAg + 0.006·AREAGreen

+ 0.022·AREAResi + 0.028·AREAImp (6.14)

TAg = 28.23 - 0.008·AREAWater - 0.001·AREAAg + 0.001·AREAGreen

+ 0.003·AREAResi + 0.015·AREAImp (6.15)

TGreen = 22.94 – 0.003·AREAWater + 0.001·AREAAg + 0.002·AREAGreen

+ 0.003 AREAResi + 0.007·AREAImp (6.16)

TResi = 24.41 -0.03·AREAWater + 0.002·AREAAg - 0.008·AREAGreen

+ 0.006·AREAResi + 0.014·AREAImp (6.17)

TImp = 11.2 + 0.005·AREAAg + 0.005·AREAGreen + 0.006·AREAResi

- 0.009·AREAImp + 0.007·AREAUrban (6.18)

TUrban = -5.36 + 0.027·AREAAg + 0.019·AREAGreen + 0.023·AREAResi

+ 0.05·AREAImp + 0.024·AREAUrban (6.19)

where AREALand use is the weighted area sum of neighboring land uses, and TLand Use is the temperature for a given land use at the central cell.

116

Equation (6.14) explains the temperature of water. Urban areas are not included in

this model because of their very small elasticity. All the neighboring land uses, except water, have positive coefficients, which suggests that the more of these land uses around water, the higher the water temperature. In Equation (6.15) for agriculture, urban areas

are also excluded. Green, residential and impervious areas have positive effects on the

local temperature of agricultural areas, but water and agricultural areas have negative

effects. In the case of green areas in Equations (6.16), all the surrounding land uses,

except water, have positive effects on local temperature, except water. For residential

areas in Equation (6.17), water and green areas have negative effects on local temperature.

Urban areas have been removed from the model. Agricultural, residential and impervious areas have positive effects.

Equation (6.18) represents the model for impervious areas. The water area is not used in this model. All the neighboring land uses, except impervious areas, have positive coefficients, implying that the larger these areas, the higher the temperature of impervious areas. Finally, for urban areas in Equation (6.19), water is not considered. All land uses have positive coefficients, implying that all neighboring land uses have a positive effect on the temperature.

Table 6.8 presents elasticity statistics for the independent variables (weighted area sum of neighboring land uses) of the models presented in Table 6.7.

117

Elasticity (ε ) Central land Neighboring i use land use Standard Mean Minimum Maximum deviation Water -0.1628 -0.2085 -0.0707 0.0257 Residential 0.0212 0.0000 0.2300 0.0273 Water Agriculture 0.0017 0.0000 0.0254 0.0029 Impervious 0.0280 0.0000 0.2457 0.0384 Green 0.0149 0.0000 0.0796 0.0158 Impervious 0.0264 0.0000 0.3722 0.0461 Green 0.0147 0.0000 0.0498 0.0088 Agriculture Agriculture -0.0791 -0.1163 -0.0328 0.0166 Residential 0.0016 0.0000 0.0556 0.0038 Water -0.0011 -0.1922 0.0000 0.0059 Green 0.1321 0.0446 0.2184 0.0296 Impervious 0.0340 0.0000 0.3530 0.0477 Green Residential 0.0145 0.0000 0.1929 0.0235 Agriculture 0.0126 0.0000 0.0689 0.0117 Water -0.0021 -0.1862 0.0000 0.0084 Residential 0.2063 0.1424 0.3205 0.0165 Impervious 0.0431 0.0000 0.1384 0.0276 Residential Green -0.0203 -0.1075 0.0000 0.0188 Water -0.0049 -0.3647 0.0000 0.0187 Agriculture 0.0010 0.0000 0.0255 0.0018 Impervious 0.4825 0.2175 0.8677 0.0856 Residential 0.0735 0.0000 0.3607 0.0596 Impervious Green 0.0537 0.0000 0.3167 0.0564 Agriculture 0.0261 0.0000 0.3374 0.0410 Urban 0.0216 0.0000 0.6206 0.0394 Urban 0.8031 0.4624 4.0342 0.1802 Impervious 0.3037 0.0000 0.9285 0.1082 Urban Residential 0.0299 0.0000 0.1781 0.0242 Agriculture 0.0255 0.0000 0.3410 0.0348 Green 0.0216 0.0000 0.2300 0.0254 (a) Tj = RST

Table 6.8. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on August 1, 2005.

Continued.

118

Table 6.8 continued.

Elasticity (ε ) Central land Neighboring i use land use Standard Mean Minimum Maximum deviation Water -0.1625 -0.1983 -0.1036 0.0253 Impervious 0.0277 0.0000 0.2426 0.0381 Water Residential 0.0212 0.0000 0.2109 0.0270 Green 0.0149 0.0000 0.0752 0.0157 Agriculture 0.0017 0.0000 0.0249 0.0029 Agriculture -0.0788 -0.1055 -0.0341 0.0156 Impervious 0.0263 0.0000 0.3114 0.0452 Agriculture Green 0.0146 0.0000 0.0435 0.0087 Residential 0.0016 0.0000 0.0642 0.0038 Water -0.0011 -0.2291 0.0000 0.0059 Green 0.1314 0.0446 0.1779 0.0270 Impervious 0.0340 0.0000 0.3201 0.0469 Green Residential 0.0145 0.0000 0.1821 0.0235 Agriculture 0.0126 0.0000 0.0634 0.0115 Water -0.0021 -0.2092 0.0000 0.0085 Residential 0.2059 0.1638 0.2714 0.0137 Impervious 0.0430 0.0000 0.1305 0.0274 Residential Green -0.0203 -0.0963 0.0000 0.0187 Water -0.0049 -0.4188 0.0000 0.0191 Agriculture 0.0010 0.0000 0.0220 0.0018 Impervious 0.4809 0.2581 0.6854 0.0809 Residential 0.0733 0.0000 0.3619 0.0597 Impervious Green 0.0536 0.0000 0.3278 0.0565 Agriculture 0.0260 0.0000 0.3098 0.0410 Urban 0.0215 0.0000 0.3828 0.0385 Urban 0.7891 0.5559 1.1942 0.1104 Impervious 0.3000 0.0000 0.5681 0.1031 Urban Residential 0.0296 0.0000 0.1954 0.0240 Agriculture 0.0252 0.0000 0.3676 0.0350 Green 0.0213 0.0000 0.2336 0.0251

(b) Tj = Temperatures estimated with the regression models.

119

6.1.2.2. AREA MODELS ACROSS THE YEAR 2005-2006.

Table 6.9 presents the R2s of the best land-use area models for the six days with

available data over 2005-2006, estimated under the no-wind-influence hypothesis. The

optimal combinations of (θ, p) are also indicated. Figure 6.6 illustrates these results graphically. The buffer size (θ) ranges from 11 to 29, and the distance exponent (p) ranges mostly from 0.9 to 1.7.

The highest R2s for agricultural, residential and impervious areas are obtained on

August 1, 2005. The highest R2 for green areas takes place on September 2, 2005. Water areas have the highest R2 among all six land uses at all times, except November 21, 2005,

and their R2 peaks on February 25, 2006. The R2s for urban areas range from 0.17 to 0.27

throughout the year. The lowest R2s for all land uses are obtained on November 21, 2005.

R2 (θ, p) Land use 2005 2006 September November February April 11 May 13 August 1 2 21 25 0.78 0.74 0.64 0.56 0.16 0.82 Water (17, 1.2) (15, 1.3) (11, 1.3) (13, 1.4) (11, 1.5) (23, 1.5) 0.04 0.10 0.48 0.32 0.06 0.05 Agriculture (15, 1.3) (13, 1.3) (13, 1.1) (17, 1.2) (37, 1.8) (23, 0.7) 0.19 0.23 0.34 0.37 0.06 0.14 Green (11, 1.0) (11, 1.0) (11, 0.9) (15, 1.5) (35, 1.7) (47, 1.7) 0.38 0.42 0.55 0.36 0.17 0.35 Residential (13, 1.1) (13, 1.5) (11, 1.3) (11, 0.9) (17, 1.3) (25, 1.7) 0.36 0.36 0.44 0.31 0.11 0.28 Impervious (25, 1.5) (17, 1.3) (11, 0.9) (11, 0.7) (21, 1.2) (29, 1.4) 0.26 0.27 0.26 0.21 0.17 0.20 Urban (25, 1.3) (21, 1.3) (17, 1.3) (17, 1.1) (13, 1.2) (15, 1.3)

Table 6.9. R2s of the land-use area models across the year 2005-2006.

120

R2 0.9

0.8

0.7

Water 0.6 Agriculture

0.5 Green Residential 0.4 Impervious Urban 0.3

0.2

0.1

0 Time

April 11 May 13 August 1 September November February 2005 2005 2005 2, 2005 21, 2005 25, 2006

Figure 6.6. Comparison of the R2s of the best land-use area models in the no-wind-effect case.

121

6.1.3. MODEL COMPARISON IN THE NO-WIND-EFFECT CASE.

The previous sections have presented, in detail, the results of estimating Equation

(3.7) with two different input variables: NDVI and land-use areas. The accuracy of the

NDVI models depends on the amount of vegetation, which varies with the seasons. In contrast, the land-use area models are independent of changes in vegetation.

Table 6.10 presents a summary of the highest R2s for the two models over all six

dates in 2005-2006. In the case of water, both models display similar results with a slight

advantage to the area model. The highest R2s for both models are obtained on February

25. For agricultural and green areas, the NDVI models clearly perform better than the

area models, except in Winter (November 21 and February 25) and early Spring (April

11), where both models perform equally poorly. This result suggests that the temperatures

of agricultural and green areas are sensitive to vegetation around them. With regard to

residential, impervious and urban areas, the area models perform better than the NDVI

models, except for the residential model on August 1 and the urban model on November

21. This is probably due to the effects of other variables, unrelated to vegetation, in these

three areas.

These findings suggest that both models could be used for different types of areas:

developed and undeveloped. The NDVI models are more effective in estimating

temperatures in undeveloped areas, such as agricultural and green areas, especially in the

Summer. However, the land-use area model has better fits in more developed areas in

most cases, including residential, impervious and urban areas.

122

Input variables Central land R2 difference Date Land-use ρ use NDVI (NDVI-Area) areas April 11, 2005 0.80 0.78 0.02 May 13, 2005 0.70 0.74 -0.04 August 1, 2005 0.57 0.64 -0.07 Water 1 September 2, 2005 0.50 0.56 -0.06 November 21, 2005 0.13 0.16 -0.03 February 25, 2006 0.83 0.82 0.01 April 11, 2005 0.08 0.04 0.04 May 13, 2005 0.21 0.10 0.11 August 1, 2005 0.80 0.48 0.32 Agriculture 0.94 September 2, 2005 0.49 0.32 0.17 November 21, 2005 0.03 0.06 -0.03 February 25, 2006 0.04 0.05 -0.01 April 11, 2005 0.16 0.19 -0.03 May 13, 2005 0.36 0.23 0.13 August 1, 2005 0.78 0.34 0.44 Green 0.94 September 2, 2005 0.52 0.37 0.15 November 21, 2005 0.09 0.06 0.03 February 25, 2006 0.12 0.14 -0.02 April 11, 2005 0.26 0.38 -0.12 May 13, 2005 0.34 0.42 -0.08 August 1, 2005 0.61 0.55 0.06 Residential 0.94 September 2, 2005 0.32 0.36 -0.04 November 21, 2005 0.15 0.17 -0.02 February 25, 2006 0.28 0.35 -0.07 April 11, 2005 0.29 0.36 -0.07 May 13, 2005 0.23 0.36 -0.13 August 1, 2005 0.40 0.44 -0.04 Impervious 0.94 September 2, 2005 0.23 0.31 -0.08 November 21, 2005 0.07 0.11 -0.04 February 25, 2006 0.21 0.28 -0.07 April 11, 2005 0.14 0.26 -0.12 May 13, 2005 0.19 0.26 -0.07 August 1, 2005 0.19 0.21 -0.12 Urban -0.37 September 2, 2005 0.12 0.17 -0.05 November 21, 2005 0.23 0.20 0.03 February 25, 2006 0.08 0.27 -0.19 ρ: Rank correlation coefficient. Table 6.10. Comparison of the R2 values of the NDVI and area models in the no-wind- influence case.

123

Rank correlation coefficients (ρ) between the R2s of both models are calculated for each land use. If there are no tied ranks, the correlation coefficient is36:

6⋅ d 2 ρ =1− ∑ i (6.20) n(n2 −1)

where di is the difference between the ranks of a given observation date and n is the number of observations (dates). This coefficient measures the match between two rankings, and assesses its significance. The coefficient ranges from -1 to 1: the two rankings are the same if ρ = 1, the rankings are completely independent if ρ = 0, and the rankings are opposite if ρ = -1.

As shown in Table 6.10, the rank correlation coefficients for all land uses, except urban areas, are very close to 1, indicating a close match. However, for urban areas, the coefficient of -0.37, suggests that there is little match between the NDVI and area models. Areas models for urban areas have higher R2s than NDVI models, except on

November 21, 2005.

There are many sources of variations for temperatures in urban areas because of

their heterogeneity37, which makes it difficult to estimate accurate models. The highest R2 is obtained on November 21 for the NDVI model, and on February 25 for the area model, in contrast to agricultural and green areas, which achieve their highest R2s in Summer

(August 1 and September 2) with both models.

The distance exponents (p) for the NDVI models are less than one, ranging from

0.1 to 0.8, implying that the extended neighboring land uses around the central cell in the

36 http://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient. 37 See Section 6.1.2. 124

buffer (θ), rather than the contiguous ones, are important in explaining local temperatures.

On the other hand, the distance exponents for the land-use area models range from 0.7 to

1.5, pointing to a stronger role for adjacent and proximate land uses in determining the

temperature at the central cell.

6.2. WIND-EFFECT ANALYSIS.

6.2.1. LAND-USE NDVI MODELS.

As represented by Equation (3.11), the relationship between wind effect and local

temperature is non-linear. Landsat-5 data, dated February 25, 2006, are used to estimate

the land-use parameters in the wind-effect case for several reasons. First, the differences

in wind speed and direction across the five measuring stations are the smallest among all

six dates, around 10 AM, when the Landsat satellite passes over the State of Ohio.38

Second, wind speeds are significantly lower at other dates, which makes it unlikely that wind would have a measurable effect on temperature. Third, all other dates are characterized by a heterogeneous wind field over the CMA, and wind directions would have to be estimated all over the CMA, a task beyond the scope of this research.

For the sake of simplicity, the mean wind speed and the same wind direction are used over the whole CMA area. Table 6.1 presents weather data on February 25, 2006.

All the five measuring stations provide different wind speeds, but almost the same wind

direction. Wind speeds belong to category 4 or 5 in the Beaufort wind force scale, which

defines them as moderate or fresh breezes. Wind direction is assumed to be from the

38 See Table 4.7. 125

West, because of small angular differences from the true West (270º) at the five

measuring stations. In the following, the wind speed is assumed to be equal to the mean wind speed (7.95 m/sec), and the wind direction is assumed from the West.

Wind speed Stations Time (AM) MT (°C) RST (°C) (m/sec) 9.39 West Dublin 9:58 8 10.87 (WNW, 300º) The Ohio State University 8.49 9:53 8.3 8.93 Airport (WNW, 290º) 8.05 Columbus International Airport 9:51 8.9 10.39 (WNW, 290º) 7.60 Bolton Airport 9:51 8.0 9.90 (WNW, 300º) 6.26 Rickenbacker Airport 9:56 9 10.87 (WNW, 300º) MT: Measured temperature. RST: Remotely-sensed temperature.

Table 6.11. Weather data on February 25, 2006.

To estimate the land-use parameters in the non-linear model, Equation (3.11) is

transformed into Equation (6.21). If the wind effect exponent (α) is taken as given, the

basic equation then becomes linear, with:

w T = T + uα ⋅ β ⋅[ ij ⋅ NDVI ⋅ LU ⋅ N ] j,RST j,base ∑ k ∑ p i ik ij k i dij (1− w ) + γ ⋅[ ij NDVI ⋅ LU ⋅ N ] + ε ∑ k ∑ p i ik ij j (6.21) k i dij α ' = T j,base + ∑ β k ⋅(u ⋅ X jk ) + ∑γ k ⋅ X j,k + ε j k k

126 where wij is the matrix of upwind indices illustrated in Figure 6.7, with wij = 1 if cell i is upwind of central cell j, w = 0 if not, γ and NDVI ' are the parameter estimates and ij k i,k

NDVI values for land use k at cell i in the no-wind-influence area,

w (1− w ) X ij NDVI LU N X ' ij NDVI LU N j,k = ∑ p ⋅ i ⋅ ik ⋅ ij and j,k = ∑ p i ⋅ ik ⋅ ij . In Equation i dij i dij

(6.21), the distance exponents (p) and the wind effect exponent (α) are modified iteratively until the sum of the squared errors, e’·e, is minimized, where e is the vector of residuals, e = [ε1 ε2 ε3 ε4 ….. εm]. The six land uses are considered separately when testing for various (α, θ, p). For each iteration (i.e., combination of α, θ and p), the model is

α ' linear in the variables u ·Xj,k and X j,k , and can therefore be estimated by OLS.

Note that a similar upwind-downwind partitioning could be easily implemented if the wind were to blow from the East, North, or South. In the case of diagonal directions

(NE, NW, SE, SW), a diagonal partitioning could be implemented. For instance, if the wind were to blow from the NW, then the SW-NE diagonal could be used to separate the upwind and downwind buffers.

Table 6.12 presents the R2s for various (α, θ, p), and highlights the parameter estimates for the best models. The highest R2s occur mostly when α ∈[-16.28 - 2.24],

θ∈[11 - 51] and p∈[0.4 – 1.5] across all land uses. Distance exponents (p) are generally less than one, except for green and impervious areas, implying that the extended surrounding land uses are more important to explain the local temperature than just the contiguous ones.

127

1 1 1 0 0

1 1 1 0 0 Wind

1 1 1 0 0

: upwind side :downwind side

Figure 6.7. Matrix of wind direction from the West when θ = 5.

128

Size of buffer (θ) p 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 0.1 0.810 0.820 0.820 0.813 0.803 0.2 0.808 0.821 0.821 0.815 0.806 0.3 0.806 0.821 0.823 0.818 0.810 0.4 0.801 0.819 0.823 0.821 0.814 0.5 0.793 0.815 0.823 0.822 0.817 0.6 0.782 0.808 0.819 0.822 0.820 0.7 0.768 0.796 0.811 0.818 0.819 (a) Water (α = 0.01 in all cases).

Size of buffer (θ) p 31 * 31 43 * 43 47 * 47 51 * 51 55 * 55 63 * 63 0.040 0.040 0.040 0.040 0.041 0.042\ 0.1 (-0.55) (-1.11) (-1.08) (-1.06) (-1.04) (-1.01) 0.040 0.040 0.040 0.041 0.041 0.042 0.2 (-0.62) (-0.55) (-0.53) (-1.55) (-1.71) (-1.56) 0.04 0.040 0.041 0.041 0.042 0.043 0.4 (-0.47) (-1.17) (-1.43) (-1.26) (-0.63) (-0.59) 0.040 0.040 0.041 0.042 0.042 0.043 0.6 (-0.67) (-0.52) (-0.59) (-0.46) (-0.45) (-0.47) 0.04 0.040 0.041 0.042 0.042 0.043 0.8 (-1.86) (-1.41) (-1.13) (-0.79) (-1.20) (-0.94) 0.002 0.040 0.041 0.041 0.042 0.043 1.0 (-13.68) (-1.25) (-2.75) (-2.16) (-1.15) (-3.43) 0.039 0.040 0.041 0.041 0.042 0.043 1.4 (1.29) (-0.24) (0.01) (0.01) (0.01) (0.01) (b) Agriculture.

Parenthesis: wind effect (α)

Table 6.12. R2s for different wind effects (α), buffer sizes (θ) and distance exponents (p) on February 25, 2006.

Continued. 129

Table 6.12 continued.

Size of buffer (θ) p 39 * 39 43 * 43 47 * 47 51 * 51 55 * 55 59 * 59 0.129 0.128 0.128 0.127 0.126 0.126 0.9 (-3.46) (-3.23) (-3.04) (-2.87) (-2.71) (-2.58) 0.131 0.132 0.132 0.131 0.131 0.130 1.1 (-7.43) (-7.39) (-7.36) (-7.33) (-7.27) (-7.23) 0.133 0.134 0.134 0.134 0.134 0.134 1.3 (-9.37) (-9.60) (-9.79) (-9.79) (-10.14) (-10.27) 0.133 0.134 0.135 0.135 0.135 0.134 1.5 (-9.45) (-9.79) (-10.07) (-10.34) (-10.56) (-10.76) 0.130 0.132 0.133 0.134 0.134 0.133 1.7 (-8.95) (-9.26) (-9.55) (-9.79) (-10.07) (-10.28) 0.127 0.129 0.130 0.131 0.132 0.131 1.9 (-8.14) (-8.43) (-8.68) (-8.95) (-9.17) (-9.37) 0.121 0.123 0.124 0.125 0.126 0.127 2.1 (-1.26) (-7.45) (-7.66) (-8.95) (-3.58) (-8.23) 0.113 0.115 0.116 0.112 0.117 0.118 2.3 (-2.87) (-6.46) (-6.62) (-1.61) (-6.94) (-7.05) (c) Green areas.

Size of buffer (θ) p 11 * 11 13 * 13 15 * 15 17 * 17 19 * 19 23 * 23 0.271 0.272 0.269 0.266 0.263 0.257 0.2 (0.56) (0.43) (0.32) (0.23) (-0.07) (-0.22) 0.271 0.273 0.268 0.269 0.267 0.262 0.4 (1.67) (1.56) (0.79) (0.71) (0.64) (1.01) 0.270 0.273 0.272 0.271 0.269 0.264 0.5 (2.34) (2.24) (1.31) (0.94) (0.87) (0.76) 0.268 0.272 0.273 0.272 0.271 0.267 0.6 (2.54) (2.45) (2.38) (2.31) (1.41) (1.01) 0.266 0.271 0.272 0.272 0.271 0.269 0.7 (2.71) (2.64) (2.58) (2.53) (2.47) (1.57) 0.263 0.268 0.270 0.271 0.271 0.270 0.8 (2.87) (2.81) (2.76) (2.72) (2.68) (2.61) 0.257 0.264 0.267 0.268 0.269 0.269 1.0 (3.00) (3.00) (3.00) (3.00) (2.99) (2.95) (d) Residential areas. Continued.

130

Table 6.12 continued.

Size of buffer (θ)

15 * 15 25 * 25 29 * 29 33 * 33 37 * 37 45 * 45 0.208 0.209 0.208 0.206 0.204 1.99 0.8 (2.58) (0.73) (0.70) (0.69) (0.67) (0.94) 0.207 0.211 0.210 0.209 0.207 0.205 1.0 (1.75) (1.25) (0.98) (1.00) (1.01) (1.01) 0.205 0.212 0.212 0.211 0.211 0.209 1.2 (1.81) (1.81) (1.81) (1.34) (1.35) (1.36) 0.204 0.211 0.212 0.212 0.212 0.212 1.4 (2.32) (2.32) (2.33) (1.84) (1.85) (1.85) 0.200 0.209 0.211 0.211 0.212 0.212 1.6 (2.33) (2.33) (2.33) (2.33) (2.34) (2.34) 0.196 0.206 0.207 0.209 0.209 0.210 1.8 (2.33) (2.33) (2.33) (2.33) (2.33) (2.33) 0.19 0.200 0.201 0.203 0.204 0.205 2.0 (2.33) (2.33) (2.33) (2.33) (2.33) (2.33) (e) Impervious areas.

Size of buffer (θ) p 9 * 9 11 * 11 13 * 13 17 * 17 21 * 21 25 * 25 0.230 0.232 0.230 0.221 0.207 0.191 0.2 (0.62) (-7.94) (-3.25) (-0.17) (-0.62) (-0.31) 0.229 0.233 0.233 0.227 0.215 1.99 0.3 (0.90) (-12.46) (-10.21) (-0.16) (-0.29) (-0.03) 0.224 0.233 0.233 0.233 0.222 0.208 0.4 (0.63) (0.56) (-16.28) (-1.70) (0.37) (0.34) 0.215 0.226 0.233 0.233 0.229 0.217 0.5 (0.89) (0.76) (0.71) (0.46) (0.04) (0.13) 0.202 0.215 0.224 0.232 0.230 0.222 0.6 (0.01) (0.94) (0.91) (0.83) (-2.42)) (-0.28) 0.173 0.185 0.194 0.207 0.211 0.210 0.8 (0.01) (0.01) (1.50) (1.52) (1.14) (0.53) 0.156 0.165 0.173 0.183 0.188 0.189 1.0 (0.01) (0.01) (0.01) (1.58) (1.87) (1.85) (f) Urban areas.

131

Water has the highest R2 ≈ 0.82 with a buffer θ = 11, a wind speed effect α = 0.01, and a distance exponent of 0.4. Water has always the same optimal wind exponent for any combination (θ, p). The water wind factor u0.01 ≈ 1 when u = 50 m/sec, suggesting that water temperature is hardly modified by wind. The wind exponents for agricultural and green areas have always negative values (α < 0), implying that the stronger the wind, the lower the temperature. In the case of residential and impervious areas, wind appears to be an important factor explaining temperatures, with larger exponents (α > 1.0). For urban areas, the wind effect from the surrounding areas is not negligible (α = 0.56). There are many variables affecting urban temperatures. Urban areas have usually lower NDVI values, with less ability to control their temperatures due to little evapotranspiration from vegetation. Moreover, many buildings block the wind, resulting in the inhibition of cooling effects. However, wind could blow excess heat away from urban areas (Parker,

2004).

The regression results for the best (α, θ, p) combination for each land use are presented in Table 6.13. As expected, upwind land uses have larger effects on local temperatures than those on the downwind side.

132

Central land use Neighboring R2 β’s t-statistics (Number of pixels) land use (θ, p) α 0.01

Intercept 8.13 490.28 Water 1.01 162.21 Agriculture 0.001 0.03 Green 0.21 12.46 Upwind Residential 0.88 23.62 Water Impervious 0.95 31.16 0.823 (54,142) Urban 1.40 8.37 (11, 0.4) Water 0.71 93.06 Agriculture 0.33 9.51 Green -0.39 -20.54 Downwind Residential 0.78 18.95 Impervious 0.66 19.38 Urban -4.21 -17.69 α -0.46

Intercept 9.46 1487.42 Water 0.36 27.62 Agriculture -0.17 -25.40 Green 0.15 32.40 Upwind Residential 0.74 40.25 Agriculture Impervious 0.19 12.16 0.040 (618,405) Urban 1.42 13.06 (51, 0.6) Water 0.10 19.69 Agriculture -0.002 -0.75 Green -0.03 -17.69 Downwind Residential 0.12 16.56 Impervious 0.25 39.69 Urban 0.08 2.27 α -10.07

Intercept 9.48 2388.84 Water 8.04E+10 134.67 Agriculture -3.15E+9 -9.23 Green 9.44E+8 56.59 Upwind Residential 5.12E+10 91.25 Green Impervious 2.69E+10 48.00 0.135 (986,326) Urban -3.43E+10 -5.34 (47, 1.5) Water 33.644 -6.62E+10 Agriculture -5.44 -16.36 Green -9.43 -55.39 Downwind Residential 19.81 35.81 Impervious 30.79 52.60 Urban 0.72 0.13

Table 6.13. Results for the highest R2 NDVI models on February 25, 2006.

Continued.

133

Table 6.13 continued.

Central land use Neighboring R2 β’s t-statistics (Number of pixels) land use (θ, p) α 2.24

Intercept 10.36 2059.92 Water 0.02 112.26 Agriculture -0.005 -32.75 Green -0.002 -43.93 Upwind Residential 0.004 68.62 Residential Impervious 0.004 39.33 0.273 (309,718) Urban 0.04 45.22 (13, 0.5) Water 1.22 74.30 Agriculture -0.35 -22.25 Green -0.38 -54.86 Downwind Residential 0.31 35.04 Impervious 0.43 39.45 Urban 3.30 38.80 α 1.81

Intercept 10.49 1917.53 Water 0.73 507.11 Agriculture -0.21 -35.32 Green -0.07 -22.92 Upwind Residential 0.31 56.98 Impervious Impervious -0.002 -3.71 0.212 (459,196) Urban 0.86 47.74 (25, 1.2) Water 26.54 100.01 Agriculture -10.56 -38.61 Green -4.60 -32.98 Downwind Residential 9.36 41.33 Impervious 2.59 15.24 Urban 39.42 45.82 α 0.56

Intercept 10.64 310.20 Water 0.81 16.17 Agriculture -0.07 -1.35 Green -0.05 -1.62 Upwind Residential 0.76 15.38 Urban Impervious -1.26 -48.28 0.233 (59,169) Urban 2.36 87.73 (11, 0.4) Water 2.31 14.16 Agriculture -2.13 -12.35 Green 0.83 7.33 Downwind Residential 4.11 24.33 Impervious -4.20 -45.31 Urban 3.29 28.76

134

The equations that represent the relationship between the NDVI areas and local temperature can be summarized as follows:

0.01 TWater = 8.13 + u ·[1.01·NDVIWater + 0.001·NDVIAg + 0.21·NDVIGreen + 0.88·NDVIResi

* * + 0.95·NDVIImp + 1.40·NDVIUrban] + [0.71· NDVI + 0.33· NDVI Water Ag

* * * * - 0.39· NDVI + 0.78· NDVI + 0.66· NDVI – 4.21· NDVI ] (6.22) Green Resi Im p Urban

-0.46 TAg = 9.46 + u ·[0.36·NDVIWater - 0.17·NDVIAg + 0.15·NDVIGreen + 0.74·NDVIResi

* * + 0.19·NDVIImp + 1.42·NDVIUrban] + [0.10· NDVI - 0.002· NDVI Water Ag

- 0.03· NDVI * + 0.12· NDVI* + 0.25· NDVI * + 0.08· NDVI * ] (6.23) Green Resi Im p Urban

-10.07 TGreen = 9.48 + u ·[(8.04E+10)·NDVIWater - (3.15E+9) NDVIAg + (9.44E+8) NDVIGreen

+ (5.12E+10)·NDVIResi + (2.69E+10)·NDVIImp - (3.43E+10)·NDVIUrban]

+ [33.64· NDVI * - 5.44· NDVI * - 9.43· NDVI * + 19.81· NDVI* Water Ag Green Resi

+ 30.79· NDVI * + 0.72· NDVI * ] (6.24) Im p Urban

2.24 TResi = 10.36 + u ·[0.02·NDVIWater - 0.005·NDVIAg - 0.002·NDVIGreen +0.004·NDVIResi

* * + 0.004·NDVIImp+ 0.04·NDVIUrban] + [1.22· NDVI -0.35· NDVI Water Ag

- 0.38· NDVI * + 0.31· NDVI* + 0.43· NDVI * + 3.30· NDVI * ] (6.25) Green Resi Im p Urban

1.81 TImp = 10.49 + u ·[0.73·NDVIWater - 0.21·NDVIAg - 0.07·NDVIGreen + 0.31·NDVIResi

* * - 0.002·NDVIImp + 0.86·NDVIUrban] + [26.54· NDVI - 10.56· NDVI Water Ag

- 4.60· NDVI * + 9.36· NDVI* + 2.59· NDVI * + 39.42· NDVI * ] (6.26) Green Resi Im p Urban

135

0.56 TUrban = 10.64 + u ·[0.81 NDVIWater – 0.07 NDVIAg – 0.05 NDVIGreen + 0.76·NDVIResi

* * – 1.26 NDVIImp + 2.36 NDVIUrban] + [2.31· NDVI - 2.13· NDVI Water Ag

+ 0.83· NDVI * + 4.11· NDVI* - 4.20· NDVI * + 3.29· NDVI * ] (6.27) Green Resi Im p Urban

where TLand use is the temperature for a given land use at the central pixel j, u is the wind

* speed, and NDVILand Use and NDVI are the sum of the NDVI areas of the upwind Landuse and downwind sides surrounding the center j, respectively.

Equation (6.22) explains the temperature of water. The intercept is 8.13, which is the lowest for all land uses. All the neighboring land uses on the upwind side have positive coefficients, implying that the more vegetation, the higher the water temperature. In

Equation (6.23) for agriculture, all upwind land uses, except agriculture, have a positive effect. Also, agriculture and green areas have positive effects from the downwind side. In the case of green areas [Equation (6.24)], upwind agriculture and urban areas, and downwind agriculture and green areas have negative effects. In the case of residential areas [Equation (6.25)], upwind and downwind agriculture and green have negative

NDVI coefficients, implying that the more vegetation in surrounding areas, the greater the cooling effect on residential areas. Equation (6.26) describes the temperature of impervious areas. Agriculture and green areas in the upwind and downwind sides have negative coefficients. For urban areas in Equation (6.27), the intercept is 10.64, which is the highest of all land uses. Agriculture and impervious areas upwind and downwind have negative coefficients. Table 6.14 presents statistics for the NDVI variables.

136

NDVI weighted sum Central land Neighboring Wind side use land use Standard Mean Minimum Maximum deviation Water -1.67 -5.01 2.46 1.64 Agriculture 0.08 -0.39 2.49 0.17 Green 0.36 -1.43 4.26 0.47 Upwind Residential 0.10 -0.41 2.04 0.20 Impervious -0.004 -2.49 1.83 0.21 Urban -0.006 -1.91 0.11 0.03 Water Water -1.17 -3.83 1.78 1.28 Agriculture 0.08 -0.56 2.85 0.18 Green 0.32 -1.77 3.47 0.42 Downwind Residential 0.09 -0.36 1.74 0.18 Impervious 0.009 -1.90 1.51 0.19 Urban -0.003 -1.51 0.12 0.02 Water -0.04 -13.56 0.78 0.36 Agriculture 1.73 -0.98 9.90 0.83 Green 2.32 -1.527 9.37 1.25 Upwind Residential 0.21 -0.27 5.30 0.40 Impervious 0.32 -1.83 3.92 0.42 Urban -0.007 -2.07 0.63 0.05 Agriculture Water -0.04 -12.71 0.72 0.35 Agriculture 1.51 -0.85 8.74 0.77 Green 2.22 -0.05 9.10 1.20 Downwind Residential 0.21 -0.30 4.77 0.38 Impervious 0.32 -1.82 3.89 0.42 Urban -0.008 -2.61 0.47 0.06 Water -2.74E-4 -0.07 0.02 0.002 Agriculture 0.007 -0.01 0.07 0.005 Green 0.19 -0.50 0.76 0.10 Upwind Residential 0.002 -0.007 0.04 0.004 Impervious 0.003 -0.02 0.04 0.003 Urban -3.85E-5 -0.008 0.007 2.19E-4 Green Water -2.83E-4 -0.07 0.01 0.002 Agriculture 0.006 -0.007 0.06 0.005 Green 0.01 -0.01 0.06 0.008 Downwind Residential 0.002 -0.007 0.04 0.004 Impervious 0.002 -0.02 0.04 0.003 Urban -3.83E-5 -0.01 0.006 2.23E-4

Table 6.14. NDVI statistics for the independent variables on February 25, 2006.

Continued.

137

Table 6.14 continued.

NDVI weighted sum Central land Neighboring use land use Standard Mean Minimum Maximum deviation Water -0.007 -3.25 1.34 0.11 Agriculture 0.07 -0.39 3.00 0.14 Green 0.410 -1.51 3.56 0.41 Upwind Residential 0.62 -0.90 2.43 0.38 Impervious 0.27 -1.68 1.81 0.24 Urban -0.004 -0.65 0.42 0.02 Residential Water -0.008 -3.05 1.01 0.11 Agriculture 0.06 -0.70 2.58 0.12 Green 0.36 -1.29 3.05 0.36 Downwind Residential 0.39 -0.33 1.81 0.29 Impervious 0.23 -1.46 1.83 0.21 Urban -0.004 -0.58 0.40 0.02 Water -0.001 -0.25 0.04 0.01 Agriculture 0.008 -0.07 0.21 0.01 Green 0.02 -0.06 0.23 0.02 Upwind Residential 0.01 -0.02 0.14 0.02 Impervious 0.11 -0.79 0.75 0.12 Urban -0.001 -0.14 0.04 0.003 Impervious Water -0.001 -0.22 0.03 0.009 Agriculture 0.007 -0.05 0.18 0.01 Green 0.02 -0.06 0.22 0.02 Downwind Residential 0.01 -0.02 0.12 0.01 Impervious 0.02 -0.11 0.14 0.02 Urban -0.001 -0.13 0.05 0.003 Water -0.02 -3.96 0.19 0.17 Agriculture 0.08 -2.39 4.75 0.17 Green 0.17 -0.66 3.73 0.29 Upwind Residential 0.14 -0.31 1.73 0.17 Impervious 0.15 -3.79 2.20 0.36 Urban -0.22 -5.16 1.61 0.30 Urban Water -0.02 -3.66 0.21 0.16 Agriculture 0.07 -1.07 3.35 0.16 Green 0.15 -0.25 3.56 0.26 Downwind Residential 0.12 -0.26 2.04 0.17 Impervious 0.15 -3.31 1.74 0.32 Urban -0.14 -4.33 1.03 0.24

138

Table 6.15 presents the elasticities of local temperature with regard to the upwind and the downwind land use NDVI, with two different temperature (Tj) estimates: remotely-sensed (TRST) and model-estimated (Test). Water has negative mean elasticities for all land uses (ε < 0), implying that increasing water area reduces local temperatures.

Water has the largest negative effect on its own temperature in both cases (εup = -0.688

39 and εdown = -0.337) . The elasticity for agriculture suggests that upwind green areas (εup

= 0.014) and downwind impervious areas (εdown = 0.008) have the largest positive effects.

Water and agricultural areas on both sides have negative effects. For green areas, upwind water (εup = -0.002) and downwind agriculture (εdown = -0.003) have the largest negative effects. Green areas themselves have the largest positive elasticities on both sides.

For the more developed areas (residential, impervious and urban areas), increasing green areas is an effective tool to decrease local temperatures. Residential areas have the largest positive effects (εup = 0.024 and εdown = 0.011), and green areas have the largest cooling effects (εup = -0.008 and εdown = -0.013). Residential areas have the largest positive effect on the temperature of impervious areas (εup = 0.02 and εdown =

0.013). Water, agricultural and green areas have cooling effects on impervious areas. In the case of urban areas, residential areas also have positive effects on urban temperatures.

Upwind green areas have a negative effect on urban temperatures.

39 When Tj = RST. 139

Elasticity Central land Neighboring

use land use Standard Mean Minimum Maximum deviation Water -0.6882 -4.5712 0.4335 0.8928 Agriculture 0.00001 -0.0003 0.0003 0.0000 Green Upwind 0.0107 -0.1933 0.1318 0.0140 Residential 0.0116 -0.1390 0.2391 0.0221 Impervious -0.0095 -1.3328 0.2125 0.0605 Water Urban -0.0021 -0.8251 0.0686 0.0164 Water -0.33699 -2.37726 0.23211 0.45884 Agriculture 0.00334 -0.14012 0.13693 0.00873 Green -0.01781 -0.21914 0.40983 0.02612 Downwind Residential 0.00936 -0.15326 0.15169 0.01843 Impervious -0.00466 -0.94671 0.18437 0.04095 Urban 0.00276 -0.30836 1.48093 0.02179 Water -0.0007 -1.3612 0.0362 0.0081 Agriculture -0.0122 -0.4531 0.4347 0.0069 Green 0.0142 -0.5898 0.8311 0.0085 Upwind Residential 0.0063 -0.5635 1.1794 0.0121 Impervious 0.0024 -0.2019 0.4913 0.0036 Urban -0.0004 -1.2478 0.6453 0.0048 Agriculture Water -0.00046 -0.28224 0.32386 0.00470 Agriculture -0.00033 -0.01288 0.01343 0.00019 Green -0.00710 -0.37754 0.20670 0.00430 Downwind Residential 0.00261 -0.41456 0.94773 0.00518 Impervious 0.00827 -0.87782 1.81500 0.01206 Urban -0.00007 -0.14658 0.15588 0.00071 Water -0.0026 -3.1877 0.2492 0.0285 Agriculture -0.0019 -0.0988 0.0957 0.0015 Green 0.0161 -0.2449 0.5492 0.0091 Upwind Residential 0.0118 -0.1125 0.5753 0.0172 Impervious 0.0059 -0.3760 0.4569 0.0078 Urban 0.0001 -0.2506 0.7259 0.0012 Green Water -0.00114 -0.74362 0.07548 0.01016 Agriculture -0.00348 -0.13667 0.13577 0.00271 Green -0.01748 -0.65558 0.37929 0.00900 Downwind Residential 0.00472 -0.11535 0.33201 0.00692 Impervious 0.00699 -0.33243 0.80683 0.00907 Urban 0.00001 -0.00671 0.00336 0.00002 (a) Tj = RST

Table 6.15. NDVI elasticity statistics under wind effect when (a) Tj = RST and (b) Tj = estimated temperatures on August 1, 2005.

Continued.

140

Table 6.15 continued.

Elasticity Central land Neighboring

uses land uses Standard Mean Minimum Maximum deviation Water -0.0025 -3.5269 0.3725 0.0408 Agriculture -0.0035 -0.4590 0.0956 0.0074 Green -0.0083 -0.1772 0.3928 0.0087 Upwind Residential 0.0240 -0.9402 0.4583 0.0147 Impervious 0.0105 -0.7800 0.6970 0.0102 Urban -0.0017 -3.3135 5.0273 0.0278 Residential Water -0.0013 -1.2726 1.3524 0.0195 Agriculture -0.0021 -0.1282 0.1394 0.0046 Green -0.0133 -0.5434 0.5621 0.0140 Downwind Residential 0.0112 -0.3979 0.3603 0.0083 Impervious 0.0091 -0.6279 0.6610 0.0090 Urban -0.0013 -2.6677 3.2178 0.0175 Water -0.0077 -5.2930 0.4223 0.0851 Agriculture -0.0070 -0.9450 0.9519 0.0127 Green -0.0070 -0.5064 0.9094 0.0082 Upwind Residential 0.0207 -1.6132 1.1528 0.0219 Impervious -0.0009 -0.1296 0.1172 0.0016 Urban -0.0048 -4.1410 3.8259 0.0391 Impervious Water -0.0052 -3.0983 1.7695 0.0509 Agriculture -0.0074 -1.5587 1.4694 0.0140 Green -0.0098 -0.7958 0.8178 0.0119 Downwind Residential 0.0130 -0.9324 0.9605 0.0142 Impervious 0.0042 -0.4645 0.3718 0.0057 Urban -0.0046 -4.3389 4.3564 0.0370 Water -0.0056 -2.2423 0.5394 0.0542 Agriculture -0.0013 -0.7987 0.8639 0.0122 Green -0.0020 -0.4393 0.4791 0.0110 Upwind Residential 0.0238 -6.3527 6.5201 0.1566 Impervious -0.0418 -16.1003 18.6095 0.4683 Urban -0.1205 -27.2625 29.1896 1.1668 Urban Water -0.0050 -2.6316 1.1564 0.0535 Agriculture -0.0104 -6.2719 4.9784 0.1061 Green 0.0087 -1.9266 2.7128 0.0483 Downwind Residential 0.0357 -8.3554 6.7373 0.1963 Impervious -0.0407 -13.1755 21.4935 0.4613 Urban -0.0345 -11.1392 11.2973 0.3644

Continued.

141

Table 6.15 continued.

Elasticity Central land Neighboring

use land use Standard Mean Minimum Maximum deviation Water -0.76393 -9.38407 0.22890 1.28733 Agriculture 0.00545 -0.09999 0.14544 0.01150 Green 0.01603 -0.10671 0.17967 0.02036 Upwind Residential 0.00313 -0.04445 0.05009 0.00586 Impervious -0.00194 -0.26360 0.03524 0.01264 Urban -0.00021 -0.06407 0.00334 0.00133 Water Water -0.54685 -6.44633 0.17467 0.96573 Agriculture 0.00485 -0.14655 0.16145 0.01211 Green 0.01439 -0.16087 0.14583 0.02007 Downwind Residential 0.00292 -0.03867 0.04327 0.00569 Impervious -0.00143 -0.26623 0.04085 0.01234 Urban -0.00010 -0.02375 0.00504 0.00064 Water -0.00227 -1.00540 0.03952 0.02073 Agriculture 0.03033 -0.01813 0.18499 0.01501 Green 0.02012 -0.01630 0.07917 0.01070 Upwind Residential 0.00109 -0.00185 0.02222 0.00193 Impervious 0.00110 -0.00754 0.01257 0.00141 Urban -0.00002 -0.00620 0.00153 0.00012 Agriculture Water -0.00224 -0.84298 0.03666 0.02082 Agriculture 0.02648 -0.01568 0.15391 0.01363 Green 0.01932 -0.00048 0.08205 0.01039 Downwind Residential 0.00107 -0.00184 0.02196 0.00186 Impervious 0.00109 -0.00900 0.01192 0.00137 Urban -0.00002 -0.00690 0.00112 0.00014 Water -0.00001 -0.00585 0.00069 0.00011 Agriculture 0.00006 -0.00020 0.00065 0.00004 Green 0.00065 -0.00349 0.00258 0.00035 Upwind Residential 0.00001 -0.00002 0.00006 0.00001 Impervious 0.00057 -0.00004 0.00003 0.00000 Urban 0.00001 -0.00001 0.00001 0.00000 Green Water -0.00001 -0.00441 0.00046 0.00009 Agriculture 0.00005 -0.00008 0.00055 0.00004 Green 0.00006 -0.00010 0.00023 0.00003 Downwind Residential 0.00002 -0.00002 0.00005 0.00001 Impervious 0.00009 -0.00004 0.00004 0.00000 Urban 0.0001 -0.00001 0.00000 0.00000 40 (b) Tj =Temperatures estimated with the regression models.

Continued.

40 Estimated Temperature with Equations (6.11) through (6.16).

142

Table 6.15 continued.

Elasticity Central land Neighboring

uses land uses Standard Mean Minimum Maximum deviation Water -0.0024 -3.1918 0.2192 0.0366 Agriculture -0.0035 -0.1855 0.0224 0.0072 Green -0.0082 -0.0881 0.0348 0.0084 Upwind Residential 0.0239 -0.0618 0.0858 0.0139 Impervious 0.0105 -0.1653 0.0652 0.0090 Urban -0.0017 -0.3666 0.1291 0.0095 Residential Water -0.0012 -2.2389 0.1048 0.0179 Agriculture -0.0021 -0.1075 0.0238 0.0044 Green -0.0132 -0.1381 0.1099 0.0137 Downwind Residential 0.0112 -0.0165 0.0485 0.0080 Impervious 0.0090 -0.0929 0.0713 0.0081 Urban -0.0013 -0.2623 0.1145 0.0071 Water -0.0070 -9.3130 19.2831 0.0867 Agriculture -0.0069 -0.2278 0.3488 0.0111 Green -0.0069 -0.0730 0.1223 0.0074 Upwind Residential 0.0205 -0.2259 0.1395 0.0184 Impervious -0.0009 -0.1376 0.0451 0.0011 Urban -0.0046 -1.5918 0.1447 0.0156 Impervious Water -0.0048 -4.4761 19.1882 0.0632 Agriculture -0.0073 -0.2474 0.1935 0.0119 Green -0.0096 -0.1132 0.1257 0.0102 Downwind Residential 0.0128 -0.0536 0.0922 0.0116 Impervious 0.0041 -0.1517 0.1807 0.0042 Urban -0.0044 -1.2861 0.1598 0.0133 Water -0.0056 -3.1176 0.9729 0.0598 Agriculture -0.0015 -0.1735 0.4884 0.0045 Green -0.0021 -0.0689 0.0661 0.0043 Upwind Residential 0.0271 -9.3610 3.1895 0.0658 Impervious -0.0721 -122.2751 77.9774 1.0201 Urban -0.1634 -1151.377 3623.1703 16.9884 Urban Water -0.0049 -4.1552 4.3174 0.0720 Agriculture -0.0150 -8.6036 14.9490 0.1012 Green 0.0099 -5.3760 9.0713 0.0525 Downwind Residential 0.0418 -78.9271 54.8049 0.5279 Impervious -0.0770 -211.1948 122.5940 1.6234 Urban -0.0458 -372.4061 772.8028 3.8002

143

6.2.2. LAND-USE AREA MODELS.

To avoid the multi-collinearity problem discussed in Section 6.1.2, the same land uses included in the land-use area models in the no-wind-effect case are used here. Urban areas are excluded for water, agricultural, green and residential areas. Water is excluded for impervious and urban areas. Equation (6.21) for the NDVI models is transformed into:

α wij T j,RST = T j,base + u ⋅∑β k ⋅[∑ p ⋅ AREA⋅ LU ik ⋅ Nij ] k i dij (1− w ) + γ ⋅[ ij ⋅ AREA⋅ LU ⋅ N ]+ ε ∑ k ∑ p ik ij j k i dij

α ' ' =Tj,base + ∑βk ⋅(u ⋅ X jk ) + ∑βk ⋅ X jk +ε j (6.28) k k

w (1− w ) X ij AREA LU N X ' ij AREA LU N where j,k = ∑ p ⋅ ⋅ ik ⋅ ij and j,k = ∑ p ⋅ ⋅ ik ⋅ ij . i dij i dij

Table 6.16 presents the R2 values for various combinations of (α, θ, p). Most land uses, except green areas, have a small wind exponent (α = 0.01), indicating that local temperature is hardly impacted by wind in the area models. The distance exponents for the highest R2s are larger than 1, except for agricultural areas, indicating a dominant effect from adjacent areas on local temperatures. Water has the highest R2 ≈ 0.82 with a buffer θ = 19, a wind speed effect α = 0.01, and a distance exponent of 1.2. Agricultural areas have always the same wind exponent (0.01) and low R2s (< 0.05), and they need large buffers to achieve the highest R2. Green areas have always a negative wind

144 exponent (α < 0), implying that the stronger the wind, the lower the temperature. The highest R2 is 0.145 when (θ, p) = (43, 1.5). Residential areas have the same wind exponent (0.01) for most combinations of (θ, p), with the highest R2 = 0.348 when (θ, p)

= (25, 1.7). For impervious areas, the wind exponent in most cases is 0.01, with the highest R2 = 0.278 when (θ, p) = (33, 1.5). The wind exponents for urban areas are always equal to 0.01, with the highest R2 = 0.2 when (θ, p) = (17, 1.4).

145

Size of buffer (θ) p 7 * 7 15 * 15 17 * 17 19 * 19 23 * 23 27 * 27 0.748 0.816 0.815 0.812 0.803 0.792 0.8 (0.01) (0.01) (-1.54) (-1.54) (0.01) (-2.58) 0.744 0.817 0.816 0.814 0.807 0.798 0.9 (0.01) (0.01) (0.01) (-1.60) (0.01) (-2.01) 0.740 0.817 0.817 0.816 0.811 0.803 1.0 (0.01) (0.01) (0.01) (0.01) (0.01) (-1.05) 0.736 0.816 0.818 0.818 0.814 0.807 1.1 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) 0.731 0.815 0.818 0.819 0.817 0.812 1.2 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) 0.727 0.813 0.818 0.819 0.819 0.815 1.3 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) 0.721 0.811 0.815 0.818 0.819 0.815 1.4 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) 0.716 0.809 0.814 0.816 0.818 0.818 1.5 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (a) Water.

Size of buffer (θ) p 13 * 13 25 * 25 45 * 45 49 * 49 53 * 53 61 * 61 0.8 0.039 0.047 0.048 0.048 0.048 0.047 0.9 0.039 0.047 0.048 0.048 0.048 0.047 1.0 0.039 0.046 0.048 0.048 0.048 0.047 1.1 0.038 0.046 0.048 0.048 0.048 0.047 1.2 0.038 0.046 0.048 0.048 0.048 0.047 1.3 0.037 0.045 0.048 0.048 0.048 0.047 1.4 0.037 0.045 0.048 0.048 0.048 0.047 (b) Agriculture (α = 0.01 in all cases).

Table 6.16. R2s for different wind effects (α), buffer sizes (θ) and distance exponents (p) on February 25, 2006.

Continued.

146

Table 6.16 continued.

Size of buffer (θ) p 27 * 27 35 * 35 43 * 43 47 * 47 51 * 51 55 * 55 0.139 0.139 0.138 0.137 0.136 0.135 1.1 (-2.80) (-2.628) (-3.49) (-4.09) (-3.77) (-3.29) 0.140 0.140 0.139 0.139 0.138 0.137 1.2 (-5.28) (-3.68) (-2.79) (-2.63) (-2.63) (-2.62) 0.141 0.142 0.142 0.141 0.140 0.139 1.3 (-4.00) (-8.90) (-5.42) (-4.64) (-23.13) (-3.06) 0.141 0.143 0.143 0.143 0.144 0.142 1.4 (-3.87) (-2.89) (-3.79) (-20.49) (-14.45) (-4.64) 0.141 0.144 0.145 0.144 0.144 0.144 1.5 (-18.76) (-9.30) (-6.02) (-3.06) (-3.48) (-3.15) 0.100 0.102 0.145 0.145 0.145 0.145 1.6 (-98.47) (-98.60) (-36.84) (-26.11) (-19.62) (-15.59) 0.140 0.143 0.104 0.104 0.105 0.105 1.7 (-3.08) (-3.57) (-4940.3) (-2052.9) (-986.7) (-547.8) (c) Green areas.

Size of buffer (θ) p 17 * 17 25 * 25 29 * 29 33 *33 37 * 37 45 * 45 0.345 0.340 0.336 0.332 0.328 0.320 1.3 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) 0.346 0.345 0.341 0.337 0.332 0.328 1.4 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) 0.347 0.346 0.344 0.341 0.339 0.334 1.5 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) 0.345 0.348 0.348 0.347 0.346 0.344 1.7 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) 0.345 0.348 0.348 0.347 0.347 0.346 1.8 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) 0.340 0.347 0.348 0.348 0.348 0.347 1.9 (0.5369) (0.01) (0.01) (0.01) (0.01) (0.01) 0.332 0.341 0.343 0.344 0.345 0.346 2.1 (1.23) (1.19) (1.18) (1.17) (1.16) (1.15) (d) Residential areas. Continued.

147

Table 6.16 continued.

Size of buffer (θ)

17 * 17 21 * 21 25 * 25 33 * 33 37 * 37 45 * 45 0.271 0.274 0.274 0.270 0.266 0.259 1.1 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) 0.270 0.275 0.277 0.275 0.273 0.259 1.3 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) 0.270 0.274 0.277 0.276 0.275 0.268 1.4 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) 0.268 0.274 0.277 0.278 0.277 0.274 1.5 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) 0.265 0.271 0.275 0.278 0.277 0.275 1.6 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) 0.263 0.269 0.273 0.276 0.277 0.276 1.7 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) 0.255 0.262 0.266 0.271 0.272 0.272 1.9 (0.277) (0.25) (0.231) (0.40) (0.38) (0.356) (e) Impervious areas.

Size of buffer (θ) p 9 * 9 13 * 13 17 * 17 21 * 21 25 * 25 29 * 29 1.0 0.194 0.198 0.195 0.189 0.183 0.178 1.1 0.193 0.199 0.197 0.193 0.188 0.184 1.2 0.192 0.199 0.199 0.196 0.191 0.187 1.3 0.192 0.199 0.199 0.198 0.195 0.191 1.4 0.190 0.199 0.200 0.199 0.196 0.194 1.5 0.187 0.198 0.200 0.200 0.198 0.197 1.6 0.185 0.196 0.199 0.200 0.199 0.198 1.7 0.184 0.194 0.198 0.199 0.199 0.198 (f) Urban areas (α = 0.01 in all cases).

148

Table 6.17 presents the estimated land-use parameters for the land-use area models with the highest R2 among the various combinations of (α, θ, p).

Central land use Neighboring R2 β’s t-statistics (Number of pixels) land use (θ, p) α 0.01

Intercept 17.169 27.745 Water -0.008 5.756 Agriculture 0.0008 1.510 Upwind Green 0.004 5.455 Water Residential 0.007 8.568 0.819 (53,542) Impervious -0.0009 -1.970 (19, 1.2) Water -0.01 -21.967 Agriculture -0.003 -5.266 Downwind Green -0.003 -6.674 Residential 0.002 4.693 Impervious -0.001 -1.919 α 0.01

Intercept 5.034 52.273 Water 0.0004 12.229 Agriculture 0.0008 29.607 Upwind Green 0.001 40.357 Agriculture Residential 0.002 55.333 0.048 (626,273) Impervious 0.001 31.471 (45, 1.0) Water -0.00002 -0.588 Agriculture 0.0004 13.643 Downwind Green 0.0003 12.286 Residential 0.0009 29.633 Impervious 0.0006 18.697 α -6.019

Intercept -4.626 -13.751 Water -3595.1 -38.478 Agriculture 2581.7 30.035 Upwind Green 3101.4 36.293 Green Residential 5238.2 60.851 0.145 (992,531) Impervious 3741.7 39.226 (43, 1.5) Water -0.002 -4.707 Agriculture 0.009 26.974 Downwind Green 0.008 23.884 Residential 0.02 44.380 Impervious 0.015 37.468 Table 6.17. Regression results for the land-use area models under wind-effect case on February 25, 2006. Continued.

149

Table 6.17 continued.

Central land use Neighboring R2 β’s t-statistics (Number of pixels) land use (θ, p) α 0.01

Intercept -27.922 -91.578 Water -0.004 -10.079 Agriculture 0.022 63.610 Upwind Green 0.026 85.948 Residential Residential 0.034 113.953 0.348 (308,897) Impervious 0.031 95.427 (25, 1.7) Water -0.00009 -0.215 Agriculture 0.024 60.560 Downwind Green 0.021 61.696 Residential 0.030 89.881 Impervious 0.031 83.469 α 0.01 Intercept -33.939 -128.122 Agriculture 0.024 85.211 Upwind Green 0.032 118.727 Residential 0.038 138.745 Impervious Impervious 0.037 143.295 0.278 (457,888) Urban 0.012 40.924 (33, 1.5) Agriculture 0.029 87.234 Green 0.031 99.357 Downwind Residential 0.037 116.772 Impervious 0.040 132.895 Urban 0.015 41.643 α 0.01

Intercept 7.324 2.277 Agriculture 0.023 1.869 Green 0.0005 0.134 Upwind Residential 0.007 1.169 Urban Impervious 0.037 2.067 0.200 (59,145) Urban -0.008 1.261 (17, 1.4) Agriculture 0.031 8.832 Green 0.038 10.563 Downwind Residential 0.032 9.020 Impervious 0.065 20.062 Urban 0.022 6.824

150

The equations that represent the relationships between the land-use areas and local temperature can be summarized as follows:

0.01 TWater = 17.17 + u ·[-0.008·AREAWater + 0.0008·AREAAg + 0.004·AREAGreen

* * + 0.007·AREAResi - 0.0009·AREAImp ] + [-0.01· AREA - 0.003· AREA Water Ag

* * * -0.003· AREA + 0.002· AREA - 0.00104· AREA ] (6.29) Green Resi Im p

0.01 TAg = 5.03+ u ·[0.0004·AREAWater + 0.0008·AREAAg + 0.001·AREAGreen

* * + 0.002·AREAResi + 0.001·AREAImp ] + [-0.00002· AREA + 0.0004· AREA Water Ag

* * + 0.0003· AREA + 0.0009· AREA + 0.0006· AREA* ] (6.30) Green Resi Im p

-6.021 TGreen = -4.63 + u ·[-3595.1·AREAWater + 2581.7·AREAAg + 3101.4·AREAGreen

* * + 5238.2·AREAResi + 3741.7·AREAImp ] + [-0.002· AREA + 0.009· AREA Water Ag

* * * + 0.008· AREA + 0.02· AREA + 0.01· AREA ] (6.31) Green Re si Im p

0.01 TResi = -27.92 + u ·[-0.004·AREAWater + 0.022·AREAAg + 0.026·AREAGreen

* * + 0.034·AREAResi + 0.031·AREAImp ] + [-0.00009· AREA + 0.024· AREA Water Ag

* * * + 0.021· AREA + 0.03· AREA + 0.031· AREA ] (6.32) Green Resi Im p

0.01 TImp = -33.9394+ u ·[0.024·AREAAg + 0.032·AREAGreen + 0.038·AREAResi

* * + 0.037·AREAImp + 0.012·AREAUrban] + [0.029· AREA + 0.031· AREA Ag Green

* * * + 0.037· AREA + 0.04· AREA + 0.015· AREA ] (6.33) Resi Im p Urban

151

0.01 TUrban = 7.32+ u ·[0.023·AREAAg + 0.0005·AREAGreen + 0.007·AREAResi

* * + 0.037·AREAImp - 0.008·AREAUrban] + [0.031· AREA + 0.038· AREA Ag Green

* * * + 0.032· AREA + 0.065· AREA + 0.022· AREA ] (6.34) Resi Im p Urban

Equation (6.29) explains the temperature of water. Agricultural, green and residential areas on the upwind side have positive coefficients, and water and impervious areas have negative coefficients, implying that the more water and impervious areas, the higher the water temperature. In Equation (6.30) for agriculture, all upwind land uses have a positive effect. Downwind water has a negative coefficient, thus decreasing temperature. In the case of green areas [Equation (6.31)], upwind and downwind water areas have negative effects, but all other land uses have positive effects, both upwind and downwind. In the case of residential areas [Equation (6.32)], upwind and downwind water areas have negative coefficients, implying that the more water in the surrounding areas, the greater the cooling effect on residential areas. All other land uses, upwind and downwind, have positive effects. Equation (6.33) describes the temperature of impervious areas. Only upwind impervious areas have a negative coefficient. In the case of urban areas in Equation (6.34), all land-use coefficients, except upwind urban areas, are positive.

Table 6.18 presents statistics for the land-use area variables used in Equations

(6.29) through (6.34).

152

Weighted sum of neighboring land uses (m2) Central land Neighboring

use land use Standard Mean Minimum Maximum deviation Water 1,130.5 0 1,352.1 148.16 Agriculture 28.45 0 329.26 42.28 Green 104.56 0 449.03 100.04 Upwind Residential 36.83 0 395.78 47.65 Impervious 47.54 0 402.24 63.75 Urban 4.14 0 223.90 13.64 Water Water 181.12 0 378.98 131.01 Agriculture 25.22 0 313.67 39.05 Green 93.22 0 378.98 91.50 Downwind Residential 32.57 0 351.40 43.71 Impervious 42.98 0 333.11 56.61 Urban 3.80 0 236.03 13.22 Water 22.70 0 2,577.8 88.48 Agriculture 2,187.5 0 3,650.7 573.28 Green 1,103.1 0 2,606.0 439.09 Upwind Residential 101.35 0 1,938.8 175.54 Impervious 214.62 0 2,053.8 284.37 Urban 21.44 0 2,085.8 81.02 Agriculture Water 22.56 0 2,529.3 90.42 Agriculture 1,153.5 0 2,529.3 531.06 Green 1,024.2 0 2,396.7 410.85 Downwind Residential 98.39 0 1,15.6 167.21 Impervious 208.91 0 2,016.8 276.03 Urban 21.64 0 1,928.7 82.33 Water 2.51 0 175.74 8.23 Agriculture 42.74 0 181.21 32.04 Green 1,003.7 0 1,080.5 33.12 Upwind Residential 14.77 0 147.39 20.53 Impervious 18.10 0 151.05 21.22 Urban 1.26 0 113.58 4.21 Green Water 2.34 0 159.23 7.76 Agriculture 38.76 0 159.23 28.78 Green 87.59 0 156.13 29.64 Downwind Residential 13.03 0 128.09 18.20 Impervious 16.31 0 130.26 19.20 Urban 1.18 0 101.54 3.99

Table 6.18. Land-use area statistics for the independent variables on February 25, 2006.

Continued.

153

Table 6.18 continued.

Weighted sum of neighboring land uses (m2) Central land Neighboring uses land uses Standard Mean Minimum Maximum deviation Water 0.74 0 51.63 2.78 Agriculture 2.49 0 40.69 4.05 Green 12.56 0 53.05 10.53 Upwind Residential 920.80 0 949.21 10.210 Impervious 15.64 0 51.15 10.12 Urban 0.85 0 39.11 2.23 Residential Water 0.62 0 43.06 2.52 Agriculture 2.19 0 41.46 3.56 Green 10.80 0 42.90 8.99 Downwind Residential 15.91 0 40.36 8.46 Impervious 12.75 0 41.99 8.40 Urban 0.76 0 34.81 2.02 Water 2.08 0 157.61 8.58 Agriculture 14.77 0 139.59 19.64 Green 32.18 0 150.71 27.19 Upwind Residential 31.29 0 134.39 23.32 Impervious 968.95 0 1,050.1 29.03 Urban 8.32 0 140.41 13.61 Impervious Water 1.83 0 134.38 7.54 Agriculture 12.85 0 122.76 17.20 Green 28.89 0 131.54 24.11 Downwind Residential 27.17 0 116.43 20.18 Impervious 56.39 0 127.66 25.31 Urban 7.23 0 124.02 11.99 Water 1.11 0 117.96 6.12 Agriculture 10.09 0 160.65 15.63 Green 11.33 0 130.46 15.15 Upwind Residential 13.31 0 108.83 13.12 Impervious 68.24 0 160.80 30.83 Urban 961.99 0 1,066.1 37.42 Urban Water 1.06 0 134.64 6.10 Agriculture 8.34 0 128.28 13.14 Green 10.35 0 119.33 14.01 Downwind Residential 12.15 0 89.76 11.89 Impervious 57.17 0 134.22 26.27 Urban 45.55 0 134.64 31.74

154

Table 6.19 presents the elasticities of the upwind and the downwind land use areas on the local temperature, with two different temperature (Tj) estimates: remotely- sensed (TRST) and model-estimated (Test). Upwind and downwind water has usually negative mean elasticities for all land uses (-2.677 <ε < 0.001), implying that an increasing neighboring water area reduces local temperature. Water has the largest negative effect on itself (εup = -2.677 and εdown = -0.666 when T = TRST). The elasticities for agriculture suggest that all land uses, in both directions, have positive effects on agricultural area temperature. Upwind impervious and downwind agricultural areas have the largest positive effects on their own temperature. For green areas, upwind water has a negative elasticity (εup = -0.004), but other land uses have positive elasticities. Upwind and downwind green areas have the largest positive effects on the temperature of green areas. Residential areas have the largest positive effect (εup = 3.071 and εdown = 0.045) on their own temperature, and upwind and downwind water has zero elasticity. With regard to impervious areas, upwind urban areas and downwind impervious areas have the largest elasticity (εup = 3.653 and εdown = 0.221). However, downwind urban areas have the smallest elasticity on the downwind side. In the case of urban areas, upwind urban areas have a negative elasticity, and the other land uses have positive elasticities on both sides.

Among upwind elasticities, green areas have the smallest one.

155

Elasticity Central Neighboring

land use land use Standard Mean Minimum Maximum deviation Water -2.677 -14.603 -0.364 2.168 Agriculture 0.004 0.000 0.044 0.005 Upwind Green 0.057 0.000 0.443 0.050 Residential 0.040 0.000 0.852 0.042 Impervious -0.008 -0.331 0.000 0.012 Water Water -0.666 -4.958 0.000 0.793 Agriculture -0.011 -0.177 0.000 0.016 Downwind Green -0.049 -0.484 0.000 0.049 Residential 0.011 0.000 0.181 0.013 Impervious -0.009 -0.252 0.000 0.012 Water 0.001 -0.208 0.782 0.006 Agriculture 0.200 -7.967 8.256 0.087 Upwind Green 0.135 -6.640 7.713 0.069 Residential 0.017 -4.090 4.248 0.034 Impervious 0.024 -4.141 4.321 0.039 Agriculture Water 0.000 -0.013 0.027 0.000 Agriculture 0.048 -2.062 2.132 0.028 Downwind Green 0.038 -1.981 1.757 0.020 Residential 0.009 -1.519 2.951 0.018 Impervious 0.013 -2.651 2.733 0.021 Water -0.004 -1.362 0.063 0.017 Agriculture 0.045 -3.951 4.337 0.040 Upwind Green 1.247 -46.192 43.849 0.320 Residential 0.029 -0.556 3.242 0.040 Impervious 0.026 -1.164 3.248 0.032 Green Water 0.000 -0.091 0.002 0.002 Agriculture 0.039 -3.410 3.486 0.033 Downwind Green 0.076 -3.494 3.030 0.033 Residential 0.020 -0.450 2.169 0.028 Impervious 0.024 -1.221 3.608 0.029 (a) Tj = RST

Table 6.19. Area elasticity statistics under wind-effect case when (a) Tj = RST and (b) Tj = estimated temperatures on February 25, 2006.

Continued.

156

Table 6.19 continued.

Elasticity Central Neighboring

land use land use Standard Mean Minimum Maximum deviation Water 0.0001 -0.098 0.007 0.002 Agriculture 0.006 -0.431 0.778 0.010 Upwind Green 0.033 -2.215 2.028 0.031 Residential 3.071 -123.603 117.870 1.288 Impervious 0.047 -4.987 4.887 0.043 Residential Water 0.000 -0.001 0.004 0.000 Agriculture 0.005 -0.735 0.520 0.009 Downwind Green 0.022 -1.457 1.380 0.021 Residential 0.045 -2.741 2.616 0.026 Impervious 0.037 -3.299 3.075 0.032 Agriculture 0.0002 0.000 0.0004 0.0001 Green 0.038 -6.622 3.907 0.064 Upwind Residential 0.105 -11.127 7.166 0.117 Impervious 0.113 -9.450 6.978 0.107 Urban 3.653 -150.871 141.820 3.259 Impervious Agriculture 0.038 -6.649 8.136 0.069 Green 0.090 -8.835 7.291 0.109 Downwind Residential 0.095 -9.283 8.024 0.095 Impervious 0.221 -13.496 13.342 0.208 Urban 0.011 -5.196 5.141 0.056 Agriculture 0.028 -4.464 4.476 0.126 Green 0.001 -0.189 0.131 0.004 Upwind Residential 0.010 -1.390 1.447 0.046 Impervious 0.271 -19.215 18.396 0.753 Urban -0.780 -30.736 32.285 2.877 Urban Agriculture 0.028 -5.535 6.409 0.161 Green 0.044 -8.841 9.677 0.231 Downwind Residential 0.041 -4.753 4.759 0.162 Impervious 0.388 -25.837 24.924 1.098 Urban 0.095 -11.148 10.708 0.581

Continued.

157

Table 6.19 continued.

Elasticity Central Neighboring

land use land use Standard Mean Minimum Maximum deviation Water -2.570 -7.972 -0.615 2.123 Agriculture 0.003 0.000 0.033 0.004 Upwind Green 0.054 0.000 0.220 0.046 Residential 0.038 0.000 0.252 0.039 Impervious -0.007 -0.057 0.000 0.009 Water Water -0.649 -2.707 0.000 0.802 Agriculture -0.010 -0.114 0.000 0.014 Downwind Green -0.046 -0.267 0.000 0.043 Residential 0.011 0.000 0.076 0.012 Impervious -0.008 -0.065 0.000 0.010 Water 0.001 0.000 0.143 0.004 Agriculture 0.195 0.066 0.340 0.055 Upwind Green 0.132 0.000 0.306 0.052 Residential 0.017 0.000 0.280 0.029 Impervious 0.024 0.000 0.227 0.031 Agriculture Water 0.000 -0.006 0.000 0.000 Agriculture 0.046 0.000 0.104 0.022 Downwind Green 0.037 0.000 0.089 0.015 Residential 0.009 0.000 0.135 0.014 Impervious 0.013 0.000 0.128 0.017 Water -0.004 -0.516 0.000 0.015 Agriculture 0.044 0.000 0.193 0.034 Upwind Green 1.227 0.915 2.289 0.080 Residential 0.029 0.000 0.258 0.039 Impervious 0.026 0.000 0.204 0.030 Green Water 0.0001 -0.044 0.000 0.002 Agriculture 0.038 0.000 0.159 0.029 Downwind Green 0.075 0.000 0.211 0.027 Residential 0.020 0.000 0.198 0.027 Impervious 0.024 0.000 0.200 0.27 41 (b) Tj = Temperatures estimated with the regression models.

Continued.

41 Estimated Temperature with Equations (6.29) through (6.34).

158

Table 6.19 continued.

Elasticity Central Neighboring

land use land use Standard Mean Minimum Maximum deviation Water -0.001 -0.047 0.000 0.002 Agriculture 0.009 0.000 0.154 0.015 Upwind Green 0.054 0.000 0.244 0.047 Residential 5.071 4.776 8.362 0.184 Impervious 0.078 0.000 0.259 0.050 Residential Water -0.0001 -0.001 0.000 0.000 Agriculture 0.008 0.000 0.175 0.014 Downwind Green 0.036 0.000 0.175 0.031 Residential 0.075 0.000 0.207 0.039 Impervious 0.061 0.000 0.204 0.040 Agriculture 0.037 0.000 0.400 0.051 Green 0.103 0.000 0.639 0.090 Upwind Residential 0.112 0.000 0.470 0.080 Impervious 3.574 3.036 19.859 0.333 Urban 0.011 0.000 0.290 0.019 Impervious Agriculture 0.037 0.000 0.404 0.052 Green 0.088 0.000 0.734 0.077 Downwind Residential 0.093 0.000 0.391 0.067 Impervious 0.216 0.000 0.662 0.094 Urban 0.011 0.000 0.311 0.019 Agriculture 0.030 0.000 0.398 0.045 Green 0.001 0.000 0.009 0.001 Upwind Residential 0.011 0.000 0.135 0.011 Impervious 0.294 0.000 0.871 0.090 Urban -1.011 -4.592 -0.492 0.455 Urban Agriculture 0.034 0.000 0.528 0.054 Green 0.049 0.000 0.665 0.069 Downwind Residential 0.046 0.000 0.510 0.044 Impervious 0.427 0.000 0.959 0.141 Urban 0.155 0.000 1.595 0.184

159

6.2.3. MODEL COMPARISON IN THE WIND-EFFECT CASE FOR

FEBRUARY 25, 2006.

Table 6.20 presents the highest R2 for the two model specifications estimated with the data of February 25, 2006: the NDVI and area models. The differences between the models are marginal, one way or the other, except for residential and impervious areas, when the area model has an edge. Water has always the highest R2s, and agriculture the lowest ones. The rank correlation coefficient (ρ) for the model R2s is equal to 0.99.

The NDVI models display a range of wind exponents. However, most wind exponents in the land-use area models are close to zero, except green areas, which have the lowest exponents (-10.07 for the NDVI model and -6.02 for the land-use model). This consistent result implies that the greater the wind speed, the lower the temperatures in green areas. In both cases, water has the same low exponent (0.01), implying that the temperature of water surfaces is hardly modified by wind.

For the NDVI model, the distance exponent (p) is less than 1 for water, agricultural, residential and urban areas. These small exponents mean that the extended neighborhood land uses are more important to explain local temperature, rather than only the adjacent ones. The distance exponents for green and impervious areas are 1.5 and 1.2, respectively, implying that contiguous land uses are the more important factors. In the land-use area model case, the distance exponents for all land uses are greater than 1, with the largest equal to 1.7 for residential areas and the smallest to 1.0 for agricultural areas.

Adjacent land uses are more critical in the land-use area models.

160

Land use NDVI models Area models Water 0.823 (1) 0.819 (1) Agriculture 0.042 (6) 0.048 (6) Highest R2 Green 0.135 (5) 0.145 (5) (Rank) Residential 0.273 (2) 0.348 (2) Impervious 0.212 (4) 0.278 (3) Urban 0.233 (3) 0.200 (4) Water 0.01 0.01 Agriculture -0.46 0.01 Wind effect Green -10.07 -6.02 (α) Residential 2.24 0.01 Impervious 1.81 0.01 Urban 0.56 0.01

Table 6.20. Comparison of the highest R2s and wind effects on February 25, 2006.

161

6.2.4. ALTERNATIVE UPWIND AND DOWNWIND CONFIGURATIONS.

All earlier results in the wind-effect case are based on the upwind/downwind configuration presented in Figure 6.7 (the “original scenario”). To check for the possibility that alternative upwind/downwind configurations may lead to significantly different and better results, the configurations presented in Figure 6.8 are considered.

0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 1 1 0 0 0

1 1 1 0 0 1 1 1 0 0

0 0 0 0 0 1 1 0 0 0

0 0 0 0 0 1 0 0 0 0

(a) Scenario 1 (b) Scenario 2

: Upwind : Downwind

Figure 6.8. Alternative upwind and downwind configurations when θ = 5.

Table 6.21 presents the R2s for the three different scenarios, using the land-use area model [Equation (6.21)] applied to residential and urban central cells. The results point to almost no difference in the effects of the upwind/downwind configurations.

162

Residential (25, 1.7) Urban(17, 1.4) Original Scenario 0.3471 0.2003 Scenario 1 0.3472 0.1998 Scenario 2 0.3477 0.2002

Table 6.21. Comparison of results for various upwind and downwind configuration scenarios on February 25, 2006.

163

6.3. SUMMARY.

Table 6.22 compares the models with and without a wind effect for the six land- use patterns and two sets of exploratory variables. The highest R2s for the six land uses in both cases and with both variables are almost the same on February 25, 2006, and the differences are very small. We may therefore conclude that the conceptually simpler no- wind-effect analysis, with only land use variables, is an acceptable way of predicting temperature. However, this conclusion is contingent on the data for February 25, 2006, and further analyses would be necessary to confirm or infirm this conclusion.

Land use NDVI Model Land-Use Area Model No-Wind- effect Wind-effect No-Wind- effect Wind-effect 0.83 0.82 0.82 0.82 Water (11, 0.5)* (11, 0.4) (23, 1.5) (19, 1.2) 0.04 0.04 0.05 0.05 Agriculture (39, 0.5) (51, 0.6) (23, 0.7) (45, 1.0) 0.12 0.14 0.14 0.15 Green (23, 0.5) (47, 1.5) (47, 1.7) (43, 1.5) 0.28 0.27 0.35 0.35 Residential (13, 0.4) (13, 0.5) (25, 1.7) (25, 1.7) 0.21 0.21 0.28 0.28 Impervious (17, 0.4) (25, 1.2) (29, 1.4) (33, 1.5) 0.23 0.23 0.20 0.20 Urban (17, 0.5) (11, 0.4) (15, 1.3) (17, 1.4) *: Size of buffer and distance exponent (θ, p) in parenthesis Table 6.22. Comparison of the highest R2s of the wind-effect and no-wind-effect models on February 25, 2006.

164

The size of buffer and distance exponent (θ, p) are naturally interrelated. If p is large, then one would expect the size of the buffer (θ) to be small, indicating that adjacent land uses are more important factors in determining local temperatures. The reverse also holds. However, green areas in the wind-effect case in both models require large θ and p as compared to the other land uses, implying that the extended neighboring land uses play a role in the determination of local temperatures, though with diminishing strength as distance increases. In most cases, wind-effect models need larger buffers (θ) to obtain the highest R2s, except for the NDVI model for urban areas and the area model for water in the no-wind-effect case. Both the NDVI and the area models for agriculture need the largest buffer to obtain their highest R2s. However, these R2s are the lowest ones among all land uses on February 25, 2005.

In the case of the distance exponents (p), there is little difference between wind and no-wind across the same model. For example, in the case of water in the NDVI models, the distance exponents are 0.5 for the no-wind-effect case and 0.4 for the wind- effect case, with almost the same R2s. However, the area model for water requires larger exponents (1.5, 1.2), implying a stronger role for the adjacent land uses.

Table 6.23 presents the highest R2s and the dates when these R2s are obtained in the no-wind-effect case across the year 2005-2006. Agricultural, green, residential and impervious areas have the highest R2s in Summer (August and September) with both models. However, water and urban areas have the highest R2s in Winter (February and

November). As mentioned previously, the NDVI models for undeveloped areas

(agricultural and green areas) have higher R2s than the area models, pointing to the

165 importance of the effects of vegetation on local temperatures (see Figure 6.4). However, with regard to areas that have less vegetation (impervious and urban areas), the area models have a slight advantage over the NDVI models, as the area models do not directly account for the amount of vegetation. The R2s for water areas in both models are almost the same.

R2s (date) Central land use NDVI Model Land-Use Area Model 0.83 0.82 Water (February 25, 2006) (February 25, 2006) 0.80 0.48 Agriculture (August 1, 2005) (August 1, 2005) 0.78 0.37 Green (August 1, 2005) (September 2, 2005) 0.61 0.55 Residential (August 1, 2005) (August 1, 2005) 0.40 0.44 Impervious (August 1, 2005) (August 1, 2005) 0.23 0.27 Urban (February 25, 2005) (February 25, 2006)

Table 6.23. The highest R2s of the NDVI and area models in the no-wind-influence case.

Table 6.24 presents the highest R2s and (θ, p) for both models across the year

2005-2006. The distance exponents (p) for the NDVI and area models do not fluctuate much throughout the year. For example, the distance exponents for green areas for the

NDVI models range from 0.1 to 0.5, thus focusing on the extended neighboring land uses

166 around the central cell in explaining local temperatures. On the other hand, the size of the buffers (θ) varies throughout the year. The NDVI models for water areas have buffers that do not fluctuate much in size, ranging from 9 to 11. However, The NDVI models for agricultural areas have buffer sizes ranging from 9 to 41.

R2 (θ, p) Land use 2005 2006 September November February April 11 May 13 August 1 2 21 25 0.80 0.70 0.57 0.50 0.13 0.83 NDVI (9, 0.4) (9, 0.3) (9, 0.3) (11, 0.4) (9, 0.2) (11, 0.5) Water 0.78 0.74 0.64 0.56 0.16 0.82 Area (17, 1.2) (15, 1.3) (11, 1.3) (13, 1.4) (11, 1.5) (23, 1.5) 0.08 0.21 0.80 0.49 0.03 0.04 NDVI (9, 0.2) (7, 0.4) (9, 0.5) (11, 0.4) (41, 0.1) (39, 0.5) Agriculture 0.04 0.10 0.48 0.32 0.06 0.05 Area (15, 1.3) (13, 1.3) (13, 1.1) (17, 1.2) (37, 1.8) (23, 0.7) 0.16 0.36 0.78 0.52 0.09 0.12 NDVI (11, 0.1) (7, 0.1) (7, 0.3) (9, 0.4) (7, 0.2) (23, 0.5) Green 0.19 0.23 0.34 0.37 0.06 0.14 Area (11, 1.0) (11, 1.0) (11, 0.9) (15, 1.5) (35, 1.7) (47, 1.7) 0.26 0.34 0.61 0.32 0.15 0.28 NDVI (13, 0.2) (9, 0.4) (7, 0.3) (9, 0.4) (13, 0.4) (13, 0.4) Residential 0.38 0.42 0.55 0.36 0.17 0.35 Area (13, 1.1) (13, 1.5) (11, 1.3) (11, 0.9) (17, 1.3) (25, 1.7) 0.29 0.23 0.40 0.23 0.07 0.21 NDVI (13, 0.5) (9, 0.3) (9, 0.5) (13, 0.5) (25, 0.6) (17, 0.4) Impervious 0.36 0.36 0.44 0.31 0.11 0.28 Area (25, 1.5) (17, 1.3) (11, 0.9) (11, 0.7) (21, 1.2) (29, 1.4) 0.14 0.08 0.19 0.09 0.12 0.23 NDVI (47, 0.7) (33, 0.5) (25, 0.6) (29, 0.8) (23, 0.7) (17, 0.5) Urban 0.26 0.27 0.26 0.21 0.17 0.20 Area (25, 1.3) (21, 1.3) (17, 1.3) (17, 1.1) (13, 1.2) (15, 1.3)

Table 6.24. Highest R2s and (θ, p) for the NDVI and area models in the no-wind-effect case across the year 2005-2006.

167

CHAPTER 7

APPLICATION OF THE MODEL

This chapter presents applications of the UHI statistical models to assess the temperature impacts of alternative land-use plans. The impact analyses are carried out in a small area of the CMA, with hypothetical rearrangements of land uses at the cell level.

Optimization models that delineate temperature-optimal land-use plans are outlined in

Appendix G, and their numerical implementability is discussed.

7.1. OVERVIEW.

The land-use area models estimated for August 1, 2005, are used in the following analyses, because (1) these models have the highest R2s among the six different dates, and (2) the relationships between land-use areas and local temperatures in developed areas have better fits than the NDVI models.42 These area models are presented in Table

6.7 and in Equations (6.14) – (6.19). The August 1, 2005, date is selected because the

UHI occurs with highest intensity in Summer (Chandler, 1965; Lee, 1979). However, a potentially interesting extension of this impact analysis would be to consider

42 See Table 6.10. 168 simultaneously several time periods across the year. This would, for instance, allow for considering the argument that the UHI might have beneficial impacts in Winter, by reducing the consumption of fuels or electricity for heating purposes.

The first research question investigated with the UHI models is: What are the impacts of alternative land-use patterns on local temperatures, while retaining the same total land-use area. The second research question is: What is the land-use arrangement that minimizes the UHI effect. To answer the first question, the UHI models are used in a simulation mode, computing the temperature of each cell. A pilot analysis is conducted over a small area of the CMA. To answer the second question, quadratic optimization models are formulated, and their computational feasibility is assessed. However, their numerical implementation will be the subject of further research. These models are presented in Appendix G.

Table 7.1 presents general land-use information for the six land uses within most of the Columbus Metropolitan Area (CMA), as derived from Landsat data on August 1,

2005. The existing land-use distribution is: 2.09% for water, 26.23% for agricultural areas, 40.01 % for green areas, 11.80% for residential areas, 17.63% for impervious areas and 2.25% for urban areas.

169

Land use Number of cells Area (km2) Percentage (%) Water 54,877 49.39 2.09 Agriculture 690,263 621.24 26.23 Green 1,055,777 950.20 40.01 Residential 310,592 279.53 11.80 Impervious 463,074 416.77 17.60 Urban 59,222 53.30 2.25 Total 2370.43 100.00

Table 7.1. Distribution of the six land uses within the CMA on August 1, 2005 (1,641*1,605 = 2,633,805 cells).

170

7.2. IMPACT ANALYSIS

7.2.1. THE PILOT TEST AREA.

Figure 7.1 presents the pilot test area, of size (60 * 60),43 located across the northwest side of the I-270 beltway. The six land uses are well-distributed: 2.16% for water, 7.08% for agricultural areas, 47.08% for green areas, 15.12% for residential areas,

26.76% for impervious areas, and 1.8% for urban areas. Much development has taken place recently in this area, but significant amounts of agricultural land remain that provide potential for future development.44

The following constraints apply to the allocation of land uses in this test area: (1) the border band of cells (i = 1→5, i = 56→60, j = 1→5, j = 56→60) around the 50*50 cells area cannot be modified; (2) changes in land uses can only take place within the

50*50 area; and (3) the total number of cells for each land use and each sub-area must remain the same, implying that reallocation takes place within each sub-area. These constraints must be met, because the purpose of this pilot test is to observe the impact of the spatial layout on local temperatures, but not the impacts of complete changes in land uses in the whole CMA. Considering a completely new land-use pattern was beyond the time/resources available for this study. Note that it might be easy to generate a land-use plan with minimal temperature, by using only green areas.

As indicated in Table 6.7, most land uses obtain their highest R2s when (θ, p) =

(11, 1.3), except urban areas [(θ, p) = (17, 1.3)]. Table 7.2 presents comparisons between remotely-sensed temperatures (TRST) and model-estimated temperatures (Test) for this

43 Row (326 - 385), Column (326 - 385) in the whole image. 44 http://www.dublin.oh.us/planning/community/index.php 171 pilot test area. Model-estimated temperatures are computed with Equations (6.17) through (6.19) for residential, impervious, and urban areas. The estimated relationship is:

TRST = α + β·Test + ε (7.1) where α and β are the parameters to be estimated, and ε is the error term.

The total number of central cells used for this pilot test is 2,500 (50 * 50). Figure

7.2 illustrates the regressions between the TRST and Test for the six land uses over the test area. As expected, the lowest R2 is obtained in the case of urban area temperatures.

Temperature statistics (°C) Central land uses R2 Models Standard (Number of cells) Mean Minimum Maximum deviation Water T 26.68 24.88 35.54 1.63 0.78 RST (54) Test 27.29 25.40 32.58 2.23 Agriculture T 29.31 25.31 36.72 2.10 0.68 RST (177) Test 28.18 26.84 30.91 0.65 Green T 29.21 24.88 36.33 1.87 0.62 RST (1,177) Test 25.62 24.63 26.72 0.28 Residential T 30.69 25.74 36.72 2.07 0.67 RST (378) Test 30.53 24.79 33.75 1.77 Impervious T 32.24 26.16 37.89 2.22 0.60 RST (669) Test 21.64 20.83 22.12 0.27 Urban T 34.72 31.95 37.50 1.42 0.25 RST (45) Test 28.08 25.69 30.80 1.34

Table 7.2. Comparison between remotely-sensed temperatures (TRST) and model-estimated temperatures (Test) in the pilot test area.

172

: Water : Urban area : Impervious area : Agricultural area : Residential area : Green area

Figure 7.1. The pilot test area for impact analysis on August 1, 2005.

173

35 y = 0.9757x + 1.3839 R² = 0.7772

RST 30 T

25 25 30 35

Test

(a) Water.

RST 30 T y = 2.8309x - 50.245 R² = 0.6766

25 25 30 35 Test

(b) Agricultural areas.

40 y = 5.2876x - 106.05 35 R² = 0.6187

RST 30 T 25

20 24 25 26 27

Test

Figure 7.2. Comparison between remotely-sensed (TRST) and model-estimated (Test) temperatures for the pilot test area. Continued. 174

Figure 7.2 continued.

40 y = 0.9533x + 1.8603 35 R² = 0.6741 RST T 30

25 20 25 30 35

Test

(d) Residential areas.

35 RST T 30 y = 6.3884x - 104.89 R² = 0.5994 25 20 21 22 23

Test

(e) Impervious areas.

39 y = 0.4431x + 21.871 37 R² = 0.2501

RST 35 T 33

31 25 27 29 31

Test

(f) Urban areas.

175

7.2.2. MODIFICATION OF CURRENT LAND USES.

Residential, impervious and urban areas can be classified as developed land uses, and these areas are selected for the pilot test, because (1) human activities usually take place in these areas, and (2) impervious and urban areas have the highest temperatures.

Water cells are retained as they are, because of the difficulty of relocating them. The focus of the analysis will be the impact of green areas on the temperature of the developed land uses.

As displayed in Figure 7.3 and Table 7.3, four different sub-areas have been selected for land-use modification, and four cells for Sub-area 1, six cells for Sub-area 2,

28 cells for Sub-area 3 and 36 cells in Sub-area 4 have been converted into green area cells (light green). Their current land uses have been relocated within the same sub-area.

Sub-areas 1 and 2 focus on the changes in residential temperatures resulting from an increase in green areas, with a couple of green cells inserted in the middle of residential areas. Sub-areas 3 and 4 focus on the temperature changes in predominantly impervious and urban areas, when made adjacent to green area cells. In both sub-areas, green areas are inserted in the middle of impervious areas and around urban areas. In all cases, the total number of cells for each land use in each sub-area remains the same as the one in the existing land-use pattern.

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Sub-area Land use Number of cells Number of relocated cells (Size) Water 0 0 Agricultural 0 0 1 Green 20 2 (6 * 7) Residential 12 2 Impervious 10 0 Urban 0 0 Water 0 0 Agricultural 0 0 2 Green 25 3 (10 * 5) Residential 19 3 Impervious 6 0 Urban 0 0 Water 0 0 Agricultural 4 0 3 Green 46 14 (11 * 15) Residential 26 0 Impervious 85 14 Urban 4 0 Water 4 0 Agricultural 3 0 4 Green 56 18 (10 * 15) Residential 8 0 Impervious 61 18 Urban 18 0 Total 407 74

Table 7.3. Sub-area size, number of land-use cells and number of relocated cells.

177

: switched green area cells.

Figure 7.3. Modification of current land uses in Sub-areas 1 to 4.

178

Figure 7.4 displays model-estimated temperatures before and after the relocation of the green area cells in the middle of the residential areas. Equation (6.17) is used to estimate the changes in temperatures. The switched cells have their temperatures marked in blue. Residential areas have been selected because (1) they represent most of the development, (2) they tend to constitute the leading edge of urban sprawl, and (3) most human activities take place in residential areas (Yeo, 2005). Table 7.4 presents comparative statistics for the temperatures of the residential areas in Sub-areas 1 and 2.

The temperatures of the residential areas decrease with the insertion of green area. As illustrated in Figure 7.4, the closer the residential area cells are to the new green area cells, the larger the temperature reduction. Overall, the mean residential area temperature in both sub-areas decreases by about 0.2°C.

Moreover, the ratios of the model-estimated temperatures before and after reallocation (Test-current/Test-modified) are presented in Table 7.5. A temperature ratio greater than one implies that the temperature decreases after the land-use change. Table 7.5 indicates that most ratios are slightly greater than one. These small changes are most likely due to the fact that only 2-3 green cells have been inserted into the residential fabric.

179

Temperature statistics (°C) Sub-area Standard Mean Minimum Maximum deviation T 30.41 29.48 30.94 0.49 1 est-current Test-modified 30.21 29.59 30.80 0.41 T 30.70 29.17 31.82 1.31 2 est-current Test-modified 30.51 29.59 31.60 1.32 Test-current: estimated temperatures with current land-use pattern. Test-modified: estimated temperatures with modified land-use pattern.

Table 7.4. Statistics for model-estimated temperatures for residential areas in Sub-areas 1 and 2 before and after land-use reallocation.

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21.36 30.94 30.82 21.30 25.94 21.16 25.74

21.31 30.90 30.76 30.34 21.21 25.83 25.76

21.30 30.85 30.65 30.20 25.83 25.82 25.73

21.22 21.25 30.34 29.92 25.80 25.82 25.78

25.77 25.80 29.78 29.48 25.75 25.83 21.15

25.80 25.83 25.67 25.67 25.70 25.84 21.18

Estimated temperatures with current land-use pattern.

21.35 30.79 30.70 21.29 25.95 21.17 25.75

21.31 30.67 25.96 30.24 21.22 25.84 25.77

21.29 30.61 25.92 30.21 29.91 25.84 25.74

21.22 21.23 30.25 30.01 29.73 25.84 25.79

25.84 25.80 29.80 29.59 25.76 25.85 21.13

25.65 25.64 25.67 25.68 25.71 25.85 21.17

Estimated temperatures with modified land-use pattern (a) Sub-area 1.

: Impervious area : Residential area : Green area : Switched green area cell

Figure 7.4. Changes in temperatures in Sub-areas 1 and 2.

Continued.

181

Figure 7.4 continued.

25.99 21.17 25.67 25.49 25.32 25.99 21.17 25.67 25.50 25.32

30.65 29.98 25.72 25.52 25.34 30.66 29.99 25.71 25.52 25.34

31.22 30.32 25.72 25.54 27.54 31.21 30.39 25.72 25.55 27.56

31.55 30.63 25.75 25.54 25.34 31.41 30.67 29.59 25.55 25.35

31.82 30.97 25.79 25.57 25.36 31.60 26.02 29.76 25.57 25.36

21.75 31.21 30.30 29.17 25.40 21.51 26.06 25.84 29.15 25.40

4 26.35 31.54 30.82 29.67 25.49 26.34 31.31 30.62 29.55 25.49

26.35 21.45 31.07 30.02 25.59 26.35 21.45 31.03 30.07 25.59

26.37 21.48 31.38 30.64 25.74 26.37 21.48 31.39 30.74 29.77

26.39 25.29 21.45 21.35 30.35 26.39 26.23 21.45 21.36 30.35

Estimated temperatures Estimated temperatures with current land-use pattern with modified land-use pattern

(b) Sub-area 2.

182

Temperature (°C) Sub-area Test-current - Test-modified Test-current/Test-modified Test-current Test-modified 30.94 30.79 0.15 1.005 30.82 30.7 0.12 1.004 30.9 30.67 0.23 1.007 30.34 30.24 0.10 1.003 30.85 30.61 0.24 1.008 1 30.2 30.21 -0.01 1.000 30.34 30.25 0.09 1.003 29.92 30.01 -0.09 0.997 29.78 29.8 -0.02 0.999 29.48 29.59 -0.11 0.996 30.65 30.66 -0.01 1.000 29.98 29.99 -0.01 1.000 31.22 31.21 0.01 1.000 30.32 30.39 -0.07 0.998 31.55 31.41 0.14 1.004 30.63 30.67 -0.04 0.999 31.82 31.6 0.22 1.007 29.17 29.15 0.02 1.001 2 31.54 30.62 0.92 1.030 30.82 30.62 0.20 1.007 29.67 29.55 0.12 1.004 31.07 31.03 0.04 1.001 30.02 30.07 -0.05 0.998 31.38 31.39 -0.01 1.000 30.64 30.74 -0.10 0.997 30.35 30.35 0.00 1.000

Table 7.5. Ratios and differences of model-estimated temperatures for residential cells in Sub-areas 1 and 2.

183

In contrast, Figure 7.5 illustrates the land-use modification, with switching of green cells, and the resulting temperature changes in Sub-areas 3 and 4. Equation (6.19) is used to estimate the changes in temperatures. Table 7.6 presents statistics on the temperatures of residential, impervious, and urban areas in Sub-areas 3 and 4 before and after green areas insertion. It is notable that urban area temperatures decrease by about

3°C in Sub-area 3 and 1.1°C in Sub-area 4. As displayed in Table 7.7, all the ratios (Test- current/Test-modified) are greater than one for the urban cells in both sub-areas. Surrounding urban areas by green areas clearly decreases urban area temperatures. With regard to residential areas, temperatures for both Sub-areas slightly increase. In the case of impervious areas, temperature reductions are observed for Sub-areas 3 and 4.

Temperature statistics (°C) Central Estimated Sub-area Standard land use temperature Mean Minimum Maximum deviation T 31.15 29.38 33.20 1.00 Residential est-current Test-modified 31.18 30.23 32.51 0.49 T 21.67 21.10 21.96 0.23 3 Impervious est-current Test-modified 21.47 21.16 21.86 0.19 T 30.27 29.78 30.83 0.45 Urban est-current Test-modified 27.31 26.81 27.86 0.45 T 30.00 28.82 31.00 0.64 Residential est-current Test-modified 30.19 29.32 31.42 0.66 T 21.50 21.20 21.67 0.12 4 Impervious est-current Test-modified 21.41 20.99 21.62 0.17 T 26.83 25.69 28.09 0.66 Urban est-current Test-modified 25.79 25.08 26.62 0.44

Table 7.6. Statistics for model-estimated temperatures (Test) before and after land-use reallocation in Sub-areas 3 and 4.

184

25.71 25.72 25.75 25.83 25.97 31.19 21.52 21.54 21.74 21.85 21.91 21.94 21.96 21.96 21.96

25.62 25.66 25.72 25.81 30.66 21.21 21.51 21.65 21.74 21.82 21.89 21.93 21.95 21.96 21.96

25.56 25.60 25.68 29.96 30.87 31.62 21.59 21.68 21.75 21.81 21.86 30.83 21.93 21.95 21.97

25.50 25.57 25.66 29.94 30.86 21.44 21.57 21.68 21.75 21.79 30.07 30.40 21.90 21.91 21.93

25.49 25.55 25.65 29.96 30.74 21.41 21.52 21.63 21.70 21.74 29.78 21.82 21.86 21.87 21.91

25.50 25.58 29.38 29.93 30.44 30.97 21.44 21.48 21.61 21.68 21.73 21.76 21.80 21.80 21.80

25.52 25.59 29.41 25.76 25.85 25.94 25.99 26.10 32.03 32.52 32.73 32.87 21.71 21.71 21.65

25.55 25.63 25.71 25.77 30.07 25.89 25.94 26.01 31.67 21.49 21.54 21.56 21.57 21.56 21.64

31.10 25.86 25.90 21.27 21.32 21.45 21.85 21.89 21.91 21.95 21.95 21.95 25.62 25.69 25.76

25.74 30.07 30.34 30.44 21.62 21.62 21.76 21.85 21.89 21.91 21.28 31.13 21.27 25.78 28.69

21.22 21.27 21.28 21.28 21.26 21.20 21.20 21.20 30.32 25.73 25.69 28.50 28.33 28.28 25.67

Estimated temperatures with current land-use pattern.

25.74 21.28 21.32 21.35 25.98 31.44 21.50 21.54 21.68 21.67 21.70 21.71 21.76 21.80 21.85

25.67 25.73 25.79 25.87 31.36 21.48 21.51 21.56 21.56 21.58 26.34 26.36 26.46 21.76 21.83

21.22 21.27 21.30 31.09 31.57 31.97 21.58 21.57 21.52 26.20 26.16 27.85 26.34 21.71 21.81

25.58 25.66 25.74 31.17 31.52 21.50 21.57 21.57 21.51 26.11 27.13 27.46 26.28 21.66 21.77

21.22 21.29 21.31 31.04 31.38 21.47 21.51 21.52 21.46 26.07 26.81 26.08 26.27 21.66 21.71

21.22 21.30 30.83 30.98 31.05 31.26 21.42 21.41 21.41 26.06 26.04 26.13 21.56 21.63 21.65

25.58 25.67 30.73 25.81 25.85 25.91 25.90 25.96 31.14 31.38 31.41 31.69 21.54 21.58 21.55

21.16 21.24 21.27 25.80 30.48 25.86 25.88 25.90 31.10 21.38 21.42 21.45 21.47 21.47 21.46

25.66 25.73 25.80 30.72 25.86 25.88 21.26 21.27 21.29 21.35 21.39 21.55 21.50 21.46 21.44

25.75 30.53 30.79 30.86 21.30 21.32 21.33 21.35 21.34 21.32 21.25 30.93 21.23 25.73 28.57

21.27 21.31 21.31 21.32 21.32 21.30 21.19 21.19 30.23 25.71 25.67 28.45 28.28 28.23 25.55 Estimated temperatures with modified land-use pattern. (a) Sub-area 3.

: Water : Urban area : Impervious area : Agricultural area : Residential area : Green area : Switched green area cell

Figure 7.5. Changes in temperatures in Sub-areas 3 and 4. Continued.

185

Figure 7.5 continued.

25.94 21.27 25.96 26.01 21.78 21.80 21.81 21.43 21.44 21.53 21.53 25.74 25.58 25.47

25.90 25.89 25.93 21.41 21.61 21.66 21.66 21.71 21.55 21.49 21.40 30.16 25.70 25.56 25.47

25.54 25.87 25.87 25.94 21.46 21.50 21.61 21.58 21.58 21.55 21.54 21.42 30.06 25.65 25.45

25.89 25.88 25.97 21.46 21.54 21.64 21.67 21.67 21.63 21.54 21.41 29.70 28.82 25.51 25.47

25.92 25.93 26.01 21.44 21.57 21.65 21.67 21.65 21.62 21.52 21.34 25.51 25.50 25.47

26.01 25.96 26.03 21.48 21.59 21.65 28.09 27.76 27.63 21.47 21.27 25.44 25.48 25.45

25.04 25.96 26.02 21.50 21.58 27.80 27.28 26.87 26.82 26.29 21.29 25.44 25.45 25.43

26.05 25.91 25.97 21.48 21.56 27.42 26.80 26.57 26.35 25.88 21.29 25.52 25.46 25.44 25.41

25.95 25.84 25.88 21.42 21.51 27.32 27.19 26.86 26.42 25.81 29.99 29.41 25.49 25.43 25.40

25.83 25.73 25.77 21.42 21.53 21.58 21.58 21.61 21.59 21.56 30.06 29.44 25.49 27.86 27.73

Estimated temperatures with current land-use pattern.

26.03 21.32 26.04 26.09 21.43 21.52 21.51 21.46 21.46 21.39 21.27 25.77 25.60 25.49

26.05 26.08 26.08 21.40 21.49 21.58 21.54 21.54 21.52 21.51 21.41 30.14 26.74 25.59 25.49

21.33 21.36 21.39 21.45 21.52 21.59 21.61 21.60 21.57 21.49 21.39 30.11 25.72 25.61 25.53

26.13 26.15 26.17 21.43 21.53 21.58 21.56 21.53 21.52 21.45 21.31 29.82 29.07 25.66 25.58

21.37 21.38 26.14 21.47 21.54 21.54 26.03 25.96 25.97 21.39 21.25 21.06 21.05 25.61

26.23 26.17 26.14 21.45 26.05 25.92 26.33 26.05 26.02 25.72 25.65 25.65 25.71 25.62

21.44 26.15 26.15 21.42 25.93 25.86 25.78 25.72 25.52 24.91 25.56 21.06 25.75 25.65

26.22 21.37 21.38 21.36 25.86 25.58 25.46 25.36 25.21 24.68 25.55 26.68 21.11 21.11 20.99

26.10 26.03 26.04 21.32 25.83 25.42 25.42 25.22 25.07 24.63 29.56 29.49 21.16 25.71 25.60

25.93 21.15 21.20 21.25 25.86 25.82 25.78 25.74 25.64 25.61 29.52 29.47 21.13 28.35 28.08

Estimated temperatures with modified land-use pattern. (b) Sub-area 4

186

Temperature (°C) Sub-area Test-current - Test-modified Test-current/Test-modified Test-current Test-modified 30.83 27.85 2.98 1.107 30.07 27.13 2.94 1.108 3 30.4 27.46 2.94 1.107 29.78 26.81 2.97 1.111 28.09 26.33 1.76 1.067 27.76 26.05 1.71 1.066 27.63 26.02 1.61 1.062 27.8 25.86 1.94 1.075 27.28 25.78 1.50 1.058 26.87 25.72 1.15 1.045 26.82 25.52 1.30 1.051 26.29 24.91 1.38 1.055 27.42 25.58 1.84 1.072 4 26.8 25.46 1.34 1.053 26.57 25.36 1.21 1.048 26.35 25.21 1.14 1.045 25.88 24.68 1.20 1.049 27.32 25.42 1.90 1.075 27.19 25.42 1.77 1.070 26.86 25.22 1.64 1.065 26.42 25.07 1.35 1.054 25.81 24.63 1.18 1.048

Table 7.7. Ratios and differences of model-estimated temperatures for urban cells in Sub- areas 3 and 4.

Because relatively small land-use changes have been made in the pilot test area

(less than 1% of the grid cells were modified), the changes in temperatures are fairly small and localized.

187

CHAPTER 8

CONCLUSIONS

The objective of this research was to develop and apply a methodology for delineating land-use patterns that help control the Urban Heat Island (UHI) effect to improve locational and land-use planning decision-making processes, including the conservation of green areas within developed areas. The central feature of this approach is the construction of statistical temperature models, using remote-sensing satellite data.

Such data are very useful because they overcome previous limitations on the study of the

UHI, including temperature and land-use data availability. Landsat-5 Thematic Mapper

(TM) data are used to investigate relationships between land uses and local temperatures.

The following research questions have been investigated: (1) How do land-use patterns in neighboring locations influence the temperature at any given location? (2)

What are the impacts of alternative land-use patterns on local temperatures, while retaining the same total area for each land use?

To answer these questions, data for the Columbus Metropolitan Area (CMA) have been used. The research has involved four phases: (1) Building a large database on land uses and temperature (RST) distributions at the level of 30 m * 30 m cells, with Landsat- 188

5 TM data for the CMA; (2) Developing a spatial framework to specify functional relationships between land uses and local temperatures; (3) Statistical estimations of these relationships; and (4) Using the estimated statistical models to assess the UHI effects of various land-use scenarios.

The statistical modeling approach involves linear regression analyses with NDVI and area land-use variables. Ordinary least square (OLS) regression is used for model estimation. Both sets of input variables are used to uncover the spatial relationships between neighboring land uses and local temperatures. Varying neighborhood buffer sizes (θ) and distance exponents (p) are considered to explain the spatial relationships between land uses and local temperatures, and the R2 coefficient is the primary criterion for model selection.

NDVI-band models turn out to be best for undeveloped areas (agricultural and green areas), while area models are better for developed areas (impervious and urban areas). The NDVI models have higher R2s when vegetation is fully grown, especially in

Summer (August and September). In the case of the NDVI models estimated with data for August 1, 2005, the R2s for agricultural and green areas are equal to 0.8 and 0.78.

However, the R2s for the same land uses with area models are equal to 0.48 and 0.34. On the other hand, land-use area models have higher R2s in more developed areas, which do not have much vegetation. For instance, the R2s for impervious and urban areas with area models on August 1, 2005, are 0.44 and 0.26, which are higher than for the NDVI models

(0.40 for impervious areas, 0.19 for urban areas).

189

In addition, wind effects are also considered in analyzing land-use relationships with local temperatures. Based on previous studies (Chandler, 1965; Duckworth and

Sandberg, 1954), the relationships between local temperatures and wind effects are assumed to be non-linear, and an exponent (α) is estimated for wind speed. In the case of the NDVI models estimated with data for the February 25, 2006, image, wind exponents for the six land uses range from -10.07 (green areas) to 2.24 (residential areas), implying different wind effects across land uses. However, all the wind exponents for area models are equal to 0.01, except for green areas (-6.02), suggesting that the wind effects on local temperatures are hard to capture. Moreover, various upwind/downwind buffer combinations have been considered, and almost the same R2s are obtained. With both the

NDVI and area models, there is very little difference in the R2s in the wind-effect and no- wind-effect cases, implying that land-use patterns are a much more determinative factor than wind in explaining local temperatures.

The distance exponent (p) and the buffer size (θ) are used in the NDVI and area models to test the effects of neighboring land uses. Wind-effect models need larger buffers (θ) to obtain their highest R2s, pointing to the importance of neighboring land uses. In the case of the NDVI models in the no-wind-effect case on August 1, 2005, all distance exponents are less than 1, implying that the extended neighborhood land uses are an important factor. In contrast, all distance exponents for area models for the August 1,

2005, image, except for green areas (0.9), are greater than 1, thus more focused on the effects of contiguous land uses. Area models need larger buffers to obtain higher R2s (θ:

190

11-13) than NDVI models (θ: 7-9), also implying the importance of the extended neighboring land uses.

Conservation and management planning guidelines can be derived from the type of simulation analyses presented in Chapter 7, which point to the impact of inserting green areas within developed areas. As illustrated in Figures 7.4 and 7.5, increasing green areas within residential, impervious and urban areas is an effective tool for reducing local temperatures. The impact of green areas can be particularly large in the case of impervious and urban areas with little vegetation, as demonstrated in Table 7.6. However, creating green areas is also difficult in highly developed commercial and downtown areas.

The insertion of green areas within parking lots could be useful to decrease the temperatures of such impervious areas. Green roof-tops can be another approach, as illustrated in Figure 8.1. They offer other environmental benefits, in addition to temperature reduction. Naturally-reduced temperatures will save energy for cooling buildings, resulting in better air quality. Also, green areas help capture and filter air pollutants. Green roof-tops are popular in many European countries (Germany), and a few U.S cities now provide incentives for green roof-tops (New York, Seattle, Portland, and Chicago).

191

Figure 8.1. Illustration of a green roof-top.

The possible use of the statistical models for optimal land-use allocation to individual cells is also illustrated in Chapter 7. Further research should focus on improving the statistical models and on developing feasible computational algorithms for optimization models delineating land-use patterns that minimize local temperatures. Such method could involve integer nonlinear programming or heuristic-based approaches. Also, while this research has focused only on the relationships between land uses and local temperatures, follow-up research and models should focus on the impacts of land-use patterns while accounting for socio-economic and environmental variables, and constraints related to mixed land uses and land-use contiguity.

192

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202

APPENDIX A

REMOTELY-SENSED TEMPERATURES DERIVED WITH

THREE METHODS ON SIX DIFFERENT DATES

203

To detect outliers, the Chebyshev theorem is used. For any positive value k, the probability that an observations lies beyond k standard deviations from the mean can be computed as follows:

1 P( X − μ > kσ ) ≤ i i i k 2 where Xi is the temperature of a specific land use i, and µi and σi are the mean temperature and its standard deviation for this specific land use i.

February 25, 2006

Land uses Method Temperature (°C) (Number of (Number of Standard Mean Maximum Minimum observations) outliers) deviation Malaret (123) 6.05 15.67 -0.07 3.32 Water Sobrino (123) 7.74 17.51 1.56 3.33 (142,219) USGS (123) 5.68 14.18 0.27 2.92 Malaret (1,448) 10.43 15.15 5.78 1.55 Agriculture Sobrino (2,161) 12.04 16.62 7.14 1.59 (305,217) USGS (1,448) 9.54 13.71 5.45 1.37 Malaret (6,670) 10.59 14.62 6.93 1.31 Green Sobrino (6,163) 12.06 16.09 8.08 1.34 (1,254,252) USGS (6,670) 9.68 13.24 6.45 1.15 Malaret (4,053) 11.72 15.15 8.06 1.03 Residential Sobrino (4,480) 13.29 16.98 9.33 1.10 (394,681) USGS (4,053) 10.68 13.71 7.45 0.91 Malaret (8,337) 11.51 16.72 6.36 1.42 Impervious Sobrino (8.783) 13.14 18.19 7.59 1.46 (503,593) USGS (8,337) 10.49 15.11 5.95 1.25 Malaret (1,703) 9.70 22.28 -6.83 3.91 Urban Sobrino (1,704) 11.46 24.20 -5.47 3.96 (54,966) USGS (1,703) 8.90 20.09 -5.47 3.45

Table A.1. Remotely sensed temperatures after removing outliers (k = 3) asdf on February 25, 2006.

204

April 11, 2005.

Land uses Method Temperature (°C) (Number of (Number of Standard Mean Maximum Minimum observations) outliers) deviation Malaret (167) 18.32 31.56 9.18 4.34 Water Sobrino (176) 20.05 33.16 10.93 4.26 (142,219) USGS (182) 16.55 28.25 8.43 3.88 Malaret (5,469) 24.20 29.34 19.29 1.62 Agriculture Sobrino (5,976) 25.82 31.36 20.18 1.77 (305,217) USGS (7,148) 21.83 26.16 17.40 1.45 Malaret (7,856) 24.09 28.89 19.29 1.66 Green Sobrino (7,419) 25.36 30.83 19.97 1.75 (1,254,252) USGS (7,856) 21.74 26.16 17.40 1.51 Malaret (4,119) 26.31 31.56 21.29 1.63 Residential Sobrino (3,426) 27.53 33.05 21.99 1.73 (394,681) USGS (2,982) 23.75 28.67 18.76 1.53 Malaret (4,664) 26.34 34.56 18.27 2.52 Impervious Sobrino (4.314) 27.83 36.60 19.03 2.71 (503,593) USGS (5,067) 23.80 31.13 16.49 2.31 Malaret (1,152) 25.71 42.41 8.06 4.88 Urban Sobrino (1,157) 27.64 44.60 9.80 4.95 (54,966) USGS (1,158) 23.27 38.66 7.45 4.46

Table A.2. Remotely sensed temperatures after removing outliers (k = 3) fasd on April 11, 2005.

205

May 13, 2005.

Land uses Method Temperature (°C) (Number of (Number of Standard Mean Maximum Minimum observations) outliers) deviation Malaret (348) 19.59 28.89 13.55 2.95 Water Sobrino (391) 21.09 29.97 15.36 2.71 (142,219) USGS (348) 17.69 26.16 12.30 2.66 Malaret (4,740) 24.59 29.79 19.29 1.77 Agriculture Sobrino (2,933) 26.05 32.48 19.67 2.08 (305,217) USGS (4,740) 22.20 27.00 17.40 1.62 Malaret (3,748) 24.00 29.34 18.27 1.87 Green Sobrino (4,253) 24.95 31.26 18.70 2.04 (1,254,252) USGS (3,748) 21.66 26.58 16.49 1.70 Malaret (2,795) 26.31 31.56 21.29 1.66 Residential Sobrino (2,725) 27.29 32.72 21.77 1.72 (394,681) USGS (3,049) 23.78 28.26 19.20 1.52 Malaret (4,018) 26.65 34.14 19.29 2.33 Impervious Sobrino (3.668) 27.94 36.05 19.97 2.52 (503,593) USGS (4,475) 24.08 30.73 17.40 2.14 Malaret (898) 26.45 39.40 13.01 4.03 Urban Sobrino (905) 28.37 41.55 14.44 4.09 (54,966) USGS (925) 23.93 35.93 11.82 3.69

Table A.3. Remotely sensed temperatures after removing outliers (k = 3) sdfa on May 13, 2005.

206

September 2, 2005.

Land uses Method Temperature (°C) (Number of (Number of Standard Mean Maximum Minimum observations) outliers) deviation Malaret (901) 25.84 32.43 19.79 1.78 Water Sobrino (995) 27.33 33.61 21.55 1.57 (142,219) USGS (855) 23.34 29.50 17.40 1.65 Malaret (9,711) 27.11 32.87 21.29 1.76 Agriculture Sobrino (10,411) 27.95 34.36 21.50 1.89 (305,217) USGS (9,711) 24.51 29.91 19.20 1.63 Malaret (5,355) 28.08 33.72 22.28 1.90 Green Sobrino (5,282) 28.89 35.00 22.74 1.96 (1,254,252) USGS (5,355) 25.41 30.73 20.09 1.77 Malaret (3,266) 31.32 37.83 24.70 2.06 Residential Sobrino (2,658) 32.35 39.40 25.12 2.20 (394,681) USGS (3,266) 28.45 34.75 22.29 1.95 Malaret (5,788) 31.67 40.55 22.77 2.78 Impervious Sobrino (4,545) 33.03 42.79 23.14 3.02 (503,593) USGS (5,346) 28.78 37.11 20.09 2.65 Malaret (933) 30.95 47.92 13.55 5.17 Urban Sobrino (935) 32.94 50.20 14.97 5.25 (54,966) USGS (838) 28.14 43.95 11.82 4.89

Table A.4. Remotely sensed temperatures after removing outliers (k = 3) asdf on September 2, 2005.

207

November 21, 2005.

Land uses Method Temperature (°C) (Number of (Number of Standard Mean Maximum Minimum observations) outliers) deviation Malaret (832) 7.73 12.47 2.88 1.30 Water Sobrino (832) 9.37 14.27 4.33 1.29 (142,219) USGS (832) 7.16 11.34 2.89 1.15 Malaret (7,590) 9.72 14.09 5.21 1.21 Agriculture Sobrino (7,291) 11.14 15.36 6.33 1.33 (305,217) USGS (7,590) 8.92 12.77 4.94 1.06 Malaret (15,282) 9.34 13.55 4.63 1.17 Green Sobrino (16,209) 10.51 14.97 5.83 1.15 (1,254,252) USGS (15,282) 8.58 12.30 4.43 1.03 Malaret (5,876) 10.04 14.09 5.78 1.04 Residential Sobrino (5,462) 11.26 15.55 6.43 1.12 (394,681) USGS (5,876) 9.19 12.77 5.45 0.91 Malaret (10,411) 10.13 15.15 4.63 1.36 Impervious Sobrino (9,768) 11.50 17.14 5.74 1.45 (503,593) USGS (10,411) 9.27 13.71 4.43 1.20 Malaret (1,524) 8.77 22.77 -6.20 3.73 Urban Sobrino (1,527) 10.48 24.70 -4.79 3.79 (54,966) USGS (1,524) 8.08 20.54 -5.18 3.30

Table A.5. Remotely sensed temperatures after removing outliers (k = 3) afsd on November 21, 2005.

208

APPENDIX B

THE BEAUFORT WIND FORCE SCALE.

209

Wind Beaufort Speed Description On the Water On land number (m/sec) Calm. Smoke rises <0.3 Calm Flat. vertically. Wind motion visible in 1 0.3-1.5 Light air Ripples without crests. smoke. Small wavelets. Crests Light Wind felt on exposed 2 1.5-3.3 of glassy appearance, breeze skin. Leaves rustle. not breaking Large wavelets. Crests Leaves and smaller Gentle 3 3.3-5.5 begin to break; twigs in constant breeze scattered whitecaps motion. Dust and loose paper Moderate 4 5.5-8.0 Small waves. raised. Small branches breeze begin to move. Moderate (1.2 m) Branches of a moderate 8.0- Fresh 5 longer waves. Some size move. Small trees 10.8 breeze foam and spray. begin to sway. Large branches in motion. Whistling heard 10.8- Strong Large waves with foam in overhead wires. 6 13.9 breeze crests and some spray. Umbrella use becomes difficult. Empty plastic garbage cans tip over. Whole trees in motion. Effort needed to walk High wind, against the wind. 13.9- Moderate Sea heaps up and foam 77 Swaying of skyscrapers 17.2 Gale, Near begins to streak. may be felt, especially Gale by people on upper floors. Moderately high waves 17.2- with breaking crests Twigs broken from 8 Fresh Gale 20.7 forming spindrift. trees. Cars veer on road. Streaks of foam.

Table B.1. The Beaufort wind force scale.45 Continued.

45 http://en.wikipedia.org/wiki/Beaufort_scale

210

Table B.1 continued.

Wind Beaufort Speed Description On the Water On land number (m/sec) Larger branches break off trees, and some small High waves (6-7 m) trees blow over. 20.7- with dense foam. Wave Construction/temporary 9 Strong Gale 24.5 crests start to roll over. signs and barricades Considerable spray. blow over. Damage to circus tents and canopies. Very high waves. Large patches of foam from wave crests give Trees are broken off or the sea a white uprooted, saplings bent 24.5- Whole appearance. and deformed, poorly 10 28.4 Gale/Storm Considerable tumbling attached asphalt shingles of waves with heavy and shingles in poor impact. Large amounts condition peel off roofs. of airborne spray reduce visibility. Exceptionally high waves. Very large Widespread vegetation patches of foam, driven damage. More damage before the wind, cover to most roofing surfaces, 28.4- Violent 11 much of the sea asphalt tiles that have 32.6 storm surface. Very large curled up and/or amounts of airborne fractured due to age may spray severely reduce break away visibility. Considerable and widespread damage to Huge waves. Sea is vegetation, a few completely white with windows broken, Hurricane- foam and spray. Air is 12 ≥32.6 structural damage to force filled with driving mobile homes and spray, greatly reducing poorly constructed sheds visibility. and barns. Debris may be hurled about.

211

APPENDIX C

NDVI MODELS FOR DIFFERENT DATES WITH NO

ACCOUNT FOR WIND EFFECTS.

212

The six land uses are considered separately in determining the optimal combination of the size of the buffer and the distance exponent, (θ, p). Given the optimal

(θ, p) for each date and land use regression results are presented under the assumption of no-wind-effect, using the weighted NDVI land-use variables. Statistics on the independent variables and then elasticities area next presented.

213

February 25, 2006.

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 0.2 0.793 0.823 0.830 0.827 0.818 0.807 0.3 0.789 0.822 0.831 0.829 0.821 0.811 0.4 0.783 0.819 0.831 0.831 0.825 0.816 0.5 0.773 0.813 0.829 0.832 0.828 0.820 0.6 0.758 0.804 0.825 0.831 0.830 0.825 0.7 0.738 0.789 0.815 0.827 0.830 0.828 (a) Water

Size of buffer (θ) p 5 * 5 11 * 11 17 * 17 23 * 23 31 * 31 39 * 39 47 * 47 0.1 0.022 0.035 0.038 0.038 0.038 0.038 0.039 0.2 0.022 0.035 0.038 0.038 0.039 0.039 0.039 0.3 0.021 0.035 0.038 0.038 0.039 0.039 0.039 0.4 0.020 0.035 0.038 0.038 0.039 0.039 0.040 0.5 0.019 0.034 0.037 0.038 0.039 0.039 0.040 0.6 0.017 0.033 0.037 0.038 0.039 0.039 0.040 (b) Agriculture

Size of buffer (θ) p 11 * 11 13 * 13 17 * 17 23 * 23 27 * 27 31 * 31 35* 35 0.3 0.118 0.121 0.123 0.122 0.122 0.120 0.119 0.4 0.117 0.120 0.123 0.123 0.122 0.121 0.120 0.5 0.116 0.119 0.123 0.124 0.123 0.122 0.121 0.6 0.112 0.117 0.122 0.124 0.124 0.123 0.123 0.7 0.107 0.113 0.120 0.123 0.124 0.124 0.123 0.8 0.107 0.111 0.120 0.121 0.122 0.123 0.123 (c) Green Table C.1. R2 for various (θ, p) combinations for each NDVI land-use model on February 25, 2006. Continued.

214

Table C.1 continued.

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 17 * 17 0.1 0.201 0.246 0.268 0.274 0.273 0.270 0.266 0.2 0.198 0.244 0.267 0.274 0.274 0.271 0.268 0.3 0.193 0.241 0.265 0.274 0.275 0.273 0.270 0.4 0.185 0.235 0.262 0.273 0.275 0.274 0.271 0.5 0.174 0.226 0.256 0.269 0.274 0.274 0.273 0.6 0.159 0.211 0.245 0.263 0.270 0.272 0.272 0.7 0.142 0.191 0.228 0.249 0.261 0.266 0.269 0.8 0.123 0.166 0.202 0.227 0.243 0.253 0.259 (d) Residential area

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 17 * 17 0.1 0.156 0.185 0.199 0.204 0.206 0.205 0.204 0.2 0.154 0.183 0.198 0.204 0.206 0.206 0.205 0.3 0.151 0.181 0.197 0.203 0.206 0.206 0.206 0.4 0.146 0.178 0.195 0.202 0.206 0.207 0.207 0.5 0.139 0.172 0.191 0.200 0.204 0.206 0.207 0.6 0.130 0.164 0.184 0.195 0.201 0.204 0.206 0.7 0.119 0.152 0.174 0.187 0.195 0.200 0.203 0.8 0.107 0.137 0.159 0.175 0.185 0.191 0.196 (e) Impervious area

Size of buffer (θ) p 9 * 9 11 * 11 13 * 13 15 * 15 17 * 17 19 * 19 21 * 21 0.3 0.233 0.232 0.227 0.222 0.217 0.211 0.204 0.4 0.234 0.235 0.233 0.229 0.224 0.219 0.213 0.5 0.230 0.236 0.236 0.234 0.237 0.228 0.223 0.6 0.219 0.229 0.234 0.236 0.236 0.234 0.231 0.7 0.120 0.214 0.223 0.229 0.232 0.234 0.233 0.8 0.174 0.189 0.200 0.209 0.216 0.221 0.224 0.9 0.147 0.159 0.170 0.179 0.187 0.194 0.199 1.0 0.124 0.132 0.140 0.147 0.154 0.160 0.165 (f) Urban area

215

Central land uses Neighboring Parameters R2 t-statistics (Number of pixels) land uses (β's) (θ, p)

Intercept 8.13 523.22 Water 1.36 311.65 Agriculture 0.09 2.80 Water 0.83 Green -0.01 -0.63 (54,037) (11, 0.5) Residential 1.22 46.25 Impervious 1.23 51.30 Urban 0.19 1.28 Intercept 9.47 1706.67 Water 0.10 38.33 Agriculture -0.03 -30.15 Agriculture 0.04 Green 0.01 23.32 (634,376) (39, 0.5) Residential 0.18 64.45 Impervious 0.12 45.13 Urban 0.29 18.69 Intercept 9.46 2615.51 Water 0.45 149.00 Agriculture -0.03 -21.40 Green 0.12 Green -0.005 -7.53 (1,020,885) (23, 0.5) Residential 0.34 185.55 Impervious 0.28 129.58 Urban -0.21 -7.69 Intercept 10.37 2077.63 Water 0.95 155.09 Agriculture -0.25 -50.08 Residential 0.28 Green -0.17 -104.99 (309,759) (13, 0.4) Residential 0.26 132.74 Impervious 0.25 90.24 Urban 2.08 67.12 Intercept 10.45 2015.96 Water 0.77 214.31 Agriculture -0.25 -73.04 Impervious 0.21 Green -0.10 -61.82 (460,547) (17, 0.4) Residential 0.32 123.57 Impervious 0.03 13.70 Urban 0.99 83.78 Intercept 10.97 277.62 Water 1.75 28.99 Agriculture -1.29 -16.04 Urban 0.23 Green -0.04 -1.01 (59,151) (17, 0.5) Residential 2.64 34.20 Impervious -3.62 -82.92 Urban 6.19 115.90

Table C.2. Regression results for the NDVI models on February 25, 2006.

216

NDVI weighted sum Neighboring Central land uses land uses Standard Mean Minimum Maximum deviation Water -1.87 -5.55 2.17 1.79 Agriculture 0.1035 -0.4081 3.1694 0.19 Green 0.45 -1.46 4.85 0.54 Water Residential 0.13 -0.61 2.45 0.24 Impervious 0.00 -2.69 1.88 0.25 Urban -0.01 -2.28 0.09 0.04 Water -0.09 -23.67 1.29 0.64 Agriculture 3.99 -1.60 20.56 1.91 Green 5.42 -1.06 22.76 2.88 Agriculture Residential 0.47 -0.61 11.82 0.85 Impervious 0.74 -4.04 9.15 0.95 Urban -0.02 -4.70 1.35 0.11 Water -0.05 -11.15 2.07 0.37 Agriculture 1.26 -1.36 13.39 0.92 Green 3.67 -2.48 13.57 1.80 Green Residential 0.49 -0.80 7.60 0.75 Impervious 0.46 -3.46 6.27 0.60 Urban -0.01 -1.98 0.99 0.04 Water -0.02 -8.27 2.88 0.28 Agriculture 0.21 -0.66 8.69 0.37 Green 1.27 -2.14 10.29 1.15 Residential Residential 1.45 -0.94 6.13 0.95 Impervious 0.82 -3.70 4.97 0.66 Urban -0.01 -1.35 1.11 0.06 Water -0.09 -14.25 2.19 0.60 Agriculture 0.50 -3.43 12.10 0.73 Green 1.54 -3.45 12.98 1.54 Impervious Residential 1.08 -1.13 8.71 0.99 Impervious 1.28 -6.58 8.16 1.16 Urban -0.08 -7.31 1.61 0.21 Water -0.05 -5.45 0.24 0.2980 Agriculture 0.17 -2.14 6.80 0.27 Green 0.37 -0.44 5.05 0.48 Urban Residential 0.28 -0.14 2.88 0.28 Impervious 0.33 -3.93 2.99 0.54 Urban -0.30 -4.97 1.32 0.38

Table C.3. NDVI statistics for the independent variables on February 25, 2006. 217

Elasticity (ε ) Central land Neighboring i uses land uses Standard Mean Minimum Maximum deviation Water -1.023 -6.891 0.542 1.330 Agriculture 0.001 -0.027 0.037 0.002 Green 0.000 -0.007 0.008 0.000 Water Residential 0.020 -0.217 0.317 0.033 Impervious -0.014 -1.867 0.276 0.085 Urban 0.000 -0.111 0.007 0.002 Water -0.001 -1.553 0.368 0.010 Agriculture -0.012 -0.385 0.388 0.007 Green 0.005 -0.193 0.309 0.003 Agriculture Residential 0.008 -1.155 1.980 0.016 Impervious 0.009 -0.990 1.545 0.013 Urban 0.000 -1.583 1.193 0.006 Water -0.002 -3.031 0.144 0.028 Agriculture -0.004 -0.146 0.145 0.003 Green -0.001 -0.060 0.039 0.000 Green Residential 0.016 -0.234 0.971 0.024 Impervious 0.012 -0.689 1.425 0.017 Urban 0.000 -0.270 0.790 0.001 Water -0.003 -4.496 1.422 0.048 Agriculture -0.005 -0.539 0.197 0.009 Green -0.020 -0.436 0.722 0.020 Residential Residential 0.034 -1.061 0.433 0.022 Impervious 0.019 -1.417 1.180 0.016 Urban -0.002 -4.827 7.881 0.036 Water -0.012 -6.391 1.132 0.119 Agriculture -0.012 -1.306 1.302 0.022 Green -0.015 -0.789 1.506 0.017 Impervious Residential 0.032 -2.100 1.343 0.032 Impervious 0.003 -0.340 0.381 0.004 Urban -0.008 -6.004 6.845 0.067 Water -0.013 -2.735 0.942 0.088 Agriculture -0.022 -5.715 5.572 0.149 Green -0.001 -0.226 0.344 0.007 Urban Residential 0.076 -10.688 9.566 0.355 Impervious -0.108 -36.568 35.333 0.952 Urban -0.158 -36.457 41.852 1.419 (a) Tj = RST

Table C.4. Elasticity statistics when (a) Tj = RST and and (b) Tj = estimated temperatures on February 25, 2006. Continued.

218

Table C.4 continued.

Elasticity (ε ) Neighboring i Central land uses land uses Standard Mean Minimum Maximum deviation Water -1.166 -12.863 0.258 1.978 Agriculture 0.001 -0.016 0.033 0.002 Green 0.000 -0.006 0.003 0.000 Water Residential 0.019 -0.149 0.266 0.032 Impervious -0.013 -1.713 0.214 0.082 Urban 0.000 -0.086 0.002 0.001 Water 0.000 -0.343 0.012 0.007 Agriculture -0.012 -0.069 0.005 0.006 Green 0.005 -0.001 0.023 0.003 Agriculture Residential 0.008 -0.014 0.172 0.014 Impervious 0.009 -0.066 0.099 0.011 Urban 0.000 -0.174 0.038 0.003 Water -0.002 -1.228 0.087 0.022 Agriculture -0.004 -0.044 0.007 0.002 Green -0.002 -0.007 0.002 0.000 Green Residential 0.016 -0.050 0.206 0.024 Impervious 0.012 -0.203 0.157 0.016 Urban 0.000 -0.021 0.042 0.000 Water -0.003 -3.244 0.214 0.039 Agriculture -0.005 -0.251 0.034 0.009 Green -0.020 -0.210 0.070 0.019 Residential Residential 0.034 -0.039 0.133 0.021 Impervious 0.019 -0.200 0.106 0.014 Urban -0.003 -0.408 0.178 0.012 Water -0.011 -195.781 44.904 0.340 Agriculture -0.012 -0.862 0.166 0.019 Green -0.015 -0.153 0.316 0.015 Impervious Residential 0.031 -0.191 0.210 0.027 Impervious 0.003 -0.600 0.116 0.003 Urban -0.008 -2.508 0.143 0.027 Water -0.013 -3.769 2.749 0.094 Agriculture -0.028 -7.508 81.822 0.377 Green -0.002 -15.348 2.557 0.064 Urban Residential 0.116 -26.688 1.375E+3 5.665 Impervious -0.324 -7.829E+3 185.707 32.288 Urban -0.337 -3.007E+3 1.379E+3 15.326

(b) Tj = Temperatures estimated with the regression models.

219

April 11, 2005

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 0.1 0.775 0.793 0.794 0.788 0.778 0.766 0.2 0.773 0.793 0.795 0.790 0.780 0.770 0.3 0.770 0.792 0.796 0.792 0.783 0.773 0.4 0.766 0.790 0.799 0.794 0.787 0.778 0.5 0.758 0.787 0.796 0.795 0.790 0.782 0.7 0.729 0.767 0.785 0.792 0.792 0.789 (a) Water

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 17 * 17 0.1 0.065 0.072 0.075 0.074 0.071 0.067 0.063 0.2 0.064 0.072 0.076 0.075 0.072 0.068 0.064 0.3 0.064 0.072 0.076 0.076 0.073 0.070 0.063 0.4 0.063 0.071 0.076 0.076 0.074 0.071 0.064 0.5 0.061 0.070 0.075 0.076 0.075 0.073 0.066 0.6 0.059 0.067 0.074 0.076 0.076 0.074 0.064 0.8 0.054 0.060 0.066 0.071 0.073 0.073 0.063 (b) Agriculture

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 17 * 17 0.1 0.123 0.144 0.154 0.158 0.157 0.154 0.150 0.2 0.121 0.143 0.154 0.158 0.157 0.155 0.151 0.3 0.119 0.141 0.153 0.158 0.158 0.156 0.153 0.4 0.115 0.138 0.151 0.157 0.158 0.157 0.154 0.5 0.109 0.133 0.148 0.155 0.158 0.157 0.155 0.7 0.091 0.115 0.133 0.144 0.150 0.153 0.154 (c) Green Table C.5. R2 for various (θ, p) combinations for each NDVI land-use model on April 11, 2005. Continued.

220

Table C.5 continued.

Size of buffer (θ) p 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 17 * 17 19 * 19 0.1 0.232 0.252 0.260 0.261 0.259 0.255 0.251 0.2 0.230 0.251 0.260 0.262 0.260 0.257 0.253 0.3 0.227 0.249 0.259 0.262 0.261 0.259 0.255 0.4 0.222 0.246 0.258 0.262 0.262 0.260 0.257 0.5 0.213 0.240 0.254 0.260 0.262 0.261 0.259 0.6 0.201 0.230 0.247 0.256 0.259 0.260 0.259 0.7 0.184 0.214 0.233 0.246 0.252 0.256 0.257 0.8 0.164 0.192 0.213 0.228 0.2377 0.244 0.248 (d) Residential area

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 17 * 17 0.1 0.239 0.270 0.281 0.283 0.281 0.277 0.274 0.2 0.236 0.269 0.282 0.284 0.283 0.279 0.276 0.3 0.233 0.268 0.282 0.285 0.284 0.282 0.278 0.4 0.227 0.265 0.281 0.286 0.286 0.284 0.281 0.5 0.218 0.259 0.278 0.285 0.287 0.286 0.283 0.6 0.205 0.249 0.272 0.283 0.286 0.287 0.286 0.7 0.189 0.234 0.261 0.276 0.282 0.285 0.286 0.8 0.172 0.213 0.243 0.261 0.272 0.278 0.281 (e) Impervious area

Size of buffer (θ) p 21 * 21 29 * 29 37 * 37 43 * 43 47 * 47 51 * 51 55 * 55 0.3 0.111 0.119 0.121 0.122 0.122 0.122 0.120 0.4 0.113 0.122 0.124 0.125 0.126 0.126 0.124 0.5 0.115 0.125 0.128 0.130 0.130 0.130 0.129 0.6 0.117 0.128 0.132 0.134 0.135 0.135 0.134 0.7 0.115 0.129 0.134 0.137 0.139 0.139 0.139 0.8 0.109 0.125 0.133 0.137 0.139 0.141 0.141 0.9 0.097 0.116 0.125 0.131 0.134 0.136 0.137 1.0 0.080 0.099 0.110 0.117 0.120 0.123 0.125 (f) Urban area

221

Central land uses Neighboring Parameters R2 t-statistics (Number of pixels) land uses (β's) (θ, p) Intercept 18.61 893.71 Water 1.19 249.55 Water Agriculture 0.35 12.80 0.80 Green 0.14 11.99 (54,166) (9, 0.4) Residential 1.22 58.50 Impervious 1.76 77.86 Urban -1.96 -11.64 Intercept 22.46 6068.96 Water 0.73 52.44 Agriculture Agriculture -0.12 -135.02 0.08 Green -0.09 -120.03 (678,313) (9, 0.2) Residential 0.47 110.34 Impervious -0.16 -67.62 Urban 0.52 20.48 Intercept 21.98 5550.71 Water 0.26 110.56 Green Agriculture -0.03 -69.93 0.16 Green -0.04 -164.48 (1,038,081) (11, 0.1) Residential 0.17 274.68 Impervious 0.05 69.12 Urban -0.27 -19.26 Intercept 23.64 2664.24 Water 0.46 121.56 Residential Agriculture -0.13 -68.42 0.26 Green -0.10 -152.18 (309,759) (13, 0.2) Residential 0.07 98.48 Impervious 0.07 66.72 Urban -0.60 -33.54 Intercept 24.90 3401.50 Water 3.36 244.27 Impervious Agriculture -1.27 -181.38 0.29 Green -0.60 -184.24 (461,181) (13, 0.5) Residential 0.31 64.78 Impervious -0.21 -51.03 Urban -0.82 -22.56 Intercept 26.35 370.62 Water 1.62 28.26 Urban Agriculture -2.35 -47.75 0.14 Green -0.02 -1.09 (58,954) (47, 0.7) Residential 1.25 36.29 Impervious -1.68 -48.96 Urban 6.17 63.61

Table C.6. Regression results for the NDVI models on April 11, 2005.

222

NDVI weighted sum Neighboring Central land uses Standard land uses Mean Minimum Maximum deviation Water -2.15 -7.46 4.10 2.40 Agriculture 0.16 -0.55 5.02 0.33 Green 0.77 -1.46 6.62 0.94 Water Residential 0.25 -0.74 4.15 0.45 Impervious 0.07 -3.39 3.50 0.39 Urban -0.01 2.04 0.30 0.05 Water 0 -8.64 5.43 0.13 Agriculture 3.00 -6.42 21.84 2.03 Green 2.58 -5.48 20.91 2.49 Agriculture Residential 0.15 -1.21 11.42 0.47 Impervious 0.37 -8.20 16.78 0.86 Urban 0.003 -5.94 6.32 0.07 Water 0.01 -20.88 12.69 0.62 Agriculture 3.52 -5.83 35.93 3.22 Green 12.65 -11.54 49.79 6.80 Green Residential 1.54 -2.26 27.45 2.70 Impervious 1.51 -13.17 27.88 2.30 Urban 0.01 -4.28 9.61 0.10 Water 0.01 -19.93 9.11 0.69 Agriculture 0.90 -3.63 24.02 1.47 Green 5.32 -4.63 32.11 4.52 Residential Residential 6.33 -1.97 24.01 3.87 Impervious 3.99 -7.77 18.78 2.71 Urban 0.01 -3.75 6.07 0.15 Water -0.02 -5.88 1.68 0.24 Agriculture 0.32 -2.48 7.37 0.52 Green 0.99 -2.32 9.47 1.06 Impervious Residential 0.81 -0.74 5.86 0.75 Impervious 1.22 -3.81 8.38 0.85 Urban 0 -3.74 3.20 0.09 Water -0.09 -7.18 0.36 0.38 Agriculture 0.61 -0.82 6.83 0.55 Green 1.57 0 9.33 1.14 Urban Residential 1.13 -0.01 5.96 0.80 Impervious 1.60 -1.80 5.50 0.84 Urban -0.09 -2.47 1.73 0.26

Table C.7. NDVI statistics for the independent variables on April 11, 2005.

223

Elasticity (ε ) Central land Neighboring i uses (MT) land uses Standard Mean Minimum Maximum deviation Water -0.205 -0.867 0.254 0.245 Agriculture 0.003 -0.018 0.087 0.006 Green 0.006 -0.017 0.046 0.007 Water Residential 0.015 -0.051 0.223 0.025 Impervious 0.003 -0.548 0.294 0.039 Urban 0.001 -0.023 0.302 0.006 Water 0.000 -0.607 0.178 0.005 Agriculture -0.017 -0.153 0.045 0.012 Green -0.011 -0.096 0.045 0.011 Agriculture Residential 0.003 -0.038 0.223 0.010 Impervious -0.003 -0.150 0.094 0.007 Urban 0.000 -0.187 0.171 0.002 Water 0.000 -0.499 0.181 0.009 Agriculture -0.005 -0.058 0.010 0.005 Green -0.024 -0.118 0.042 0.013 Green Residential 0.012 -0.025 0.196 0.020 Impervious 0.003 -0.063 0.071 0.005 Urban 0.000 -0.132 0.055 0.001 Water 0.000 -0.926 0.200 0.017 Agriculture -0.005 -0.163 0.026 0.009 Green -0.023 -0.172 0.038 0.020 Residential Residential 0.018 -0.009 0.071 0.011 Impervious 0.012 -0.035 0.057 0.008 Urban 0.000 -0.146 0.132 0.004 Water -0.005 -1.984 0.264 0.051 Agriculture -0.018 -0.595 0.194 0.032 Green -0.026 -0.296 0.128 0.029 Impervious Residential 0.010 -0.015 0.077 0.010 Impervious -0.011 -0.139 0.061 0.008 Urban 0.000 -0.137 0.376 0.004 Water -0.008 -3.259 1.917 0.046 Agriculture -0.072 -13.241 12.962 0.292 Green -0.002 -0.224 0.230 0.004 Urban Residential 0.065 -8.464 7.569 0.176 Impervious -0.130 -19.571 20.419 0.449 Urban -0.033 -15.555 16.557 0.324 (a) Tj = RST

Table C.8. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on April 11, 2005. Continued.

224

Table C.8 continued.

Elasticity (ε ) Neighboring i Central land uses land uses Standard Mean Minimum Maximum deviation Water -0.203 -0.913 0.186 0.246 Agriculture 0.003 -0.017 0.083 0.006 Green 0.006 -0.014 0.045 0.007 Water Residential 0.015 -0.054 0.209 0.025 Impervious 0.003 -0.578 0.235 0.038 Urban 0.001 -0.025 0.209 0.006 Water 0.000 -0.382 0.152 0.005 Agriculture -0.017 -0.133 0.032 0.012 Green -0.011 -0.092 0.022 0.010 Agriculture Residential 0.003 -0.026 0.195 0.010 Impervious -0.003 -0.138 0.058 0.006 Urban 0.000 -0.156 0.132 0.002 Water 0.000 -0.331 0.129 0.008 Agriculture -0.005 -0.052 0.008 0.005 Green -0.024 -0.100 0.023 0.013 Green Residential 0.012 -0.018 0.176 0.020 Impervious 0.003 -0.032 0.061 0.005 Urban 0.000 -0.133 0.050 0.001 Water 0.000 -0.634 0.154 0.016 Agriculture -0.005 -0.152 0.018 0.009 Green -0.023 -0.157 0.026 0.020 Residential Residential 0.018 -0.006 0.067 0.011 Impervious 0.012 -0.025 0.052 0.008 Urban 0.000 -0.180 0.089 0.004 Water -0.005 -3.779 0.192 0.056 Agriculture -0.018 -0.627 0.110 0.032 Green -0.026 -0.304 0.060 0.029 Impervious Residential 0.010 -0.012 0.069 0.009 Impervious -0.011 -0.082 0.041 0.008 Urban 0.000 -0.124 0.109 0.003 Water -0.007 -0.987 0.023 0.034 Agriculture -0.065 -1.762 0.077 0.066 Green -0.001 -0.012 0.000 0.001 Urban Residential 0.060 -0.001 0.308 0.039 Impervious -0.117 -0.495 0.151 0.065 Urban -0.027 -1.366 0.381 0.081

(b) Tj = Temperatures estimated with the regression models.

225

May 13, 2005

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 0.1 0.658 0.694 0.700 0.694 0.683 0.670 0.2 0.656 0.693 0.702 0.697 0.687 0.674 0.3 0.650 0.692 0.703 0.699 0.690 0.679 0.4 0.641 0.688 0.702 0.702 0.694 0.684 0.5 0.627 0.680 0.700 0.702 0.698 0.689 0.6 0.607 0.665 0.692 0.699 0.699 0.693 0.7 0.580 0.642 0.676 0.690 0.695 0.693 (a) Water

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 0.1 0.210 0.211 0.201 0.186 0.170 0.154 0.2 0.210 0.212 0.203 0.188 0.173 0.157 0.3 0.209 0.212 0.204 0.191 0.176 0.161 0.4 0.208 0.213 0.206 0.194 0.180 0.166 0.5 0.206 0.212 0.208 0.197 0.184 0.171 0.6 0.203 0.211 0.209 0.201 0.189 0.177 0.7 0.199 0.209 0.209 0.203 0.194 0.183 0.8 0.195 0.204 0.207 0.204 0.197 0.189 (b) Agriculture

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 0.1 0.341 0.359 0.352 0.334 0.313 0.291 0.2 0.339 0.359 0.354 0.338 0.317 0.296 0.3 0.336 0.359 0.356 0.342 0.322 0.302 0.4 0.330 0.357 0.358 0.346 0.328 0.309 0.5 0.321 0.352 0.357 0.349 0.334 0.316 0.6 0.308 0.343 0.354 0.350 0.338 0.325 0.7 0.291 0.328 0.345 0.347 0.340 0.329 (c) Green Table C.9. R2 for various (θ, p) combinations for each NDVI land-use model on May 13, 2005. Continued.

226

Table C.9 continued.

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 0.1 0.318 0.339 0.335 0.320 0.302 0.286 0.2 0.316 0.340 0.340 0.323 0.306 0.290 0.3 0.313 0.340 0.339 0.327 0.311 0.296 0.4 0.306 0.338 0.341 0.330 0.316 0.301 0.5 0.294 0.338 0.340 0.333 0.321 0.307 0.6 0.278 0.322 0.336 0.333 0.324 0.313 0.7 0.257 0.304 0.324 0.328 0.323 0.315 0.8 0.233 0.279 0.304 0.314 0.315 0.311 (d) Residential area

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 17 * 17 0.1 0.210 0.227 0.229 0.226 0.220 0.214 0.208 0.2 0.210 0.227 0.230 0.227 0.222 0.216 0.210 0.3 0.207 0.226 0.231 0.229 0.224 0.218 0.212 0.4 0.203 0.225 0.231 0.230 0.226 0.220 0.215 0.5 0.198 0.222 0.231 0.231 0.229 0.223 0.218 0.6 0.190 0.216 0.228 0.230 0.228 0.225 0.221 0.7 0.179 0.207 0.222 0.227 0.228 0.226 0.223 0.8 0.167 0.194 0.211 0.219 0.223 0.223 0.222 (e) Impervious area

Size of buffer (θ) p 33 * 33 35 * 35 37 * 37 39 * 39 47 * 47 51 * 51 55 * 55 0.3 0.080 0.080 0.080 0.080 0.078 0.078 0.077 0.4 0.080 0.080 0.080 0.080 0.079 0.078 0.078 0.5 0.081 0.081 0.081 0.081 0.080 0.079 0.078 0.6 0.081 0.081 0.081 0.081 0.080 0.080 0.079 0.7 0.081 0.081 0.080 0.081 0.081 0.081 0.080 0.8 0.080 0.080 0.081 0.081 0.081 0.081 0.080 0.9 0.078 0.078 0.079 0.080 0.081 0.081 0.080 1.0 0.072 0.073 0.075 0.075 0.077 0.078 0.078 (f) Urban area

227

Central land uses Neighboring Parameters R2 t-statistics (Number of pixels) land uses (β's) (θ, p)

Intercept 15.86 1165.78 Water 0.28 70.56 Water Agriculture 0.52 52.64 0.70 Green 0.28 77.57 (54,166) (9, 0.3) Residential 0.82 107.08 Impervious 1.68 159.81 Urban -3.23 -19.81 Intercept 23.38 6563.55 Water -2.37 -76.11 Agriculture Agriculture -0.44 -223.75 0.21 Green -0.50 -309.33 (681,220) (7, 0.4) Residential 0.90 78.28 Impervious -0.41 -69.30 Urban 0.10 1.58 Intercept 23.45 5418.29 Water -0.75 -235.35 Green Agriculture -0.15 -205.57 0.36 Green -0.17 -570.88 (1,044,075) (7, 0.1) Residential 0.12 126.65 Impervious 0.14 120.10 Urban -0.93 -33.90 Intercept 23.82 1770.89 Water -1.64 -133.65 Residential Agriculture -0.38 -60.52 0.34 Green -0.34 -150.75 (310,038) (9, 0.4) Residential 0.08 31.72 Impervious 0.40 90.94 Urban -1.67 -29.44 Intercept 25.34 2966.07 Water 1.02 69.41 Impervious Agriculture -0.74 -210.01 0.23 Green -0.35 -201.21 (461,847) (9, 0.3) Residential -0.01 -4.57 Impervious -0.08 -33.72 Urban -0.56 -25.00 Intercept 23.23 409.28 Water 0.13 3.37 Urban Agriculture -0.56 -39.69 0.08 Green 0.03 5.44 (59,039) (33, 0.5) Residential 0.23 22.81 Impervious 0.12 10.24 Urban 0.37 8.03

Table C.10. Regression results for the NDVI models on May 13, 2005.

228

NDVI weighted sum Neighboring Central land uses Standard land uses Mean Minimum Maximum deviation Water -0.38 -6.35 7.72 2.36 Agriculture 0.45 -0.27 7.95 0.75 Green 2.25 -0.80 12.86 2.52 Water Residential 0.69 -0.13 9.23 1.01 Impervious 0.37 -1.89 5.97 0.71 Urban 0 -1.31 0.45 0.04 Water 0.01 -0.96 2.61 0.06 Agriculture 1.34 -1.44 7.26 0.94 Green 1.09 -0.97 6.49 1.16 Agriculture Residential 0.05 -0.16 3.75 0.17 Impervious 0.13 -1.77 5.79 0.33 Urban 0 -1.48 3.26 0.03 Water 0.09 -3.67 11.85 0.43 Agriculture 2.02 -1.08 20.08 2.13 Green 9.35 -3.27 23.45 4.98 Green Residential 0.85 -0.52 13.92 1.60 Impervious 0.74 -2.62 14.77 1.26 Urban 0 -1.66 7.42 0.05 Water 0.05 -2.09 4.83 0.20 Agriculture 0.23 -0.97 6.38 0.44 Green 1.61 -0.24 9.53 1.51 Residential Residential 2.18 -0.33 6.67 1.23 Impervious 1.22 -1.23 5.43 0.80 Urban 0.01 -0.78 1.66 0.04 Water 0.02 -4.89 5.13 0.21 Agriculture 0.56 -2.56 11.88 0.96 Green 1.72 -1.89 14.22 1.92 Impervious Residential 1.49 -0.40 9.32 1.35 Impervious 2.43 -3.57 14.36 1.34 Urban 0.04 -2.89 6.74 0.14 Water 0.04 -9.45 4.32 0.44 Agriculture 1.65 -0.60 13.37 1.51 Green 4.21 0 29.00 3.42 Urban Residential 2.89 0 17.76 2.05 Impervious 4.79 -0.88 12.17 1.83 Urban 0.25 -1.69 4.26 0.38

Table C.11. NDVI statistics for the independent variables on May 13, 2005.

229

Elasticity (ε ) Central land Neighboring i uses land uses Standard Mean Minimum Maximum deviation Water -0.010 -0.122 0.117 0.042 Agriculture 0.011 -0.009 0.197 0.020 Green 0.033 -0.015 0.197 0.037 Water Residential 0.028 -0.008 0.347 0.039 Impervious 0.031 -0.210 0.450 0.057 Urban 0.000 -0.077 0.243 0.008 Water -0.001 -0.301 0.116 0.007 Agriculture -0.027 -0.176 0.036 0.020 Green -0.025 -0.177 0.032 0.028 Agriculture Residential 0.002 -0.007 0.135 0.007 Impervious -0.003 -0.136 0.043 0.006 Urban 0.000 -0.008 0.017 0.000 Water -0.003 -0.432 0.173 0.017 Agriculture -0.014 -0.165 0.010 0.015 Green -0.075 -0.217 0.037 0.043 Green Residential 0.005 -0.004 0.077 0.008 Impervious 0.005 -0.022 0.110 0.008 Urban -0.000 -0.348 0.071 0.002 Water -0.004 -0.386 0.198 0.016 Agriculture -0.004 -0.121 0.022 0.007 Green -0.024 -0.169 0.005 0.023 Residential Residential 0.007 -0.002 0.025 0.004 Impervious 0.020 -0.031 0.087 0.013 Urban -0.001 -0.125 0.079 0.003 Water 0.001 -0.330 0.309 0.011 Agriculture -0.019 -0.492 0.117 0.033 Green -0.026 -0.262 0.043 0.030 Impervious Residential -0.001 -0.004 0.000 0.001 Impervious -0.008 -0.065 0.018 0.005 Urban -0.001 -0.201 0.100 0.003 Water 0.000 -0.069 0.031 0.003 Agriculture -0.042 -5.031 1.612 0.048 Green 0.006 -0.151 0.472 0.005 Urban Residential 0.028 -0.559 1.561 0.021 Impervious 0.025 -0.863 2.480 0.017 Urban 0.004 -0.147 0.426 0.007 (a) Tj = RST

Table C.12. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on May 13, 2005. Continued.

230

Table C.12 continued.

Elasticity (ε ) Neighboring i Central land uses land uses Standard Mean Minimum Maximum deviation Water -0.010 -0.126 0.109 0.041 Agriculture 0.011 -0.010 0.195 0.020 Green 0.033 -0.017 0.185 0.036 Water Residential 0.028 -0.007 0.318 0.038 Impervious 0.030 -0.261 0.381 0.057 Urban 0.000 -0.097 0.246 0.008 Water -0.001 -0.374 0.090 0.007 Agriculture -0.027 -0.158 0.026 0.020 Green -0.025 -0.163 0.020 0.028 Agriculture Residential 0.002 -0.006 0.128 0.007 Impervious -0.003 -0.115 0.030 0.006 Urban 0.000 -0.006 0.015 0.000 Water -0.003 -0.642 0.107 0.017 Agriculture -0.014 -0.149 0.007 0.015 Green -0.075 -0.205 0.023 0.042 Green Residential 0.005 -0.003 0.067 0.008 Impervious 0.005 -0.016 0.083 0.008 Urban -0.000 -0.446 0.063 0.002 Water -0.004 -0.524 0.126 0.016 Agriculture -0.004 -0.118 0.015 0.007 Green -0.024 -0.157 0.003 0.023 Residential Residential 0.007 -0.001 0.022 0.004 Impervious 0.020 -0.022 0.084 0.013 Urban -0.001 -0.130 0.053 0.003 Water 0.001 -0.243 0.171 0.009 Agriculture -0.018 -0.535 0.069 0.034 Green -0.026 -0.253 0.026 0.030 Impervious Residential -0.001 -0.004 0.000 0.001 Impervious -0.008 -0.049 0.011 0.004 Urban -0.001 -0.181 0.059 0.003 Water 0.000 -0.056 0.024 0.003 Agriculture -0.040 -0.457 0.014 0.040 Green 0.005 0.000 0.039 0.005 Urban Residential 0.027 0.000 0.147 0.018 Impervious 0.024 -0.005 0.057 0.009 Urban 0.004 -0.028 0.070 0.006

(b) Tj = Temperatures estimated with the regression models.

231

August 1, 2005.

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 0.1 0.513 0.558 0.565 0.558 0.545 0.530 0.2 0.510 0.558 0.568 0.562 0.550 0.535 0.3 0.503 0.556 0.569 0.565 0.555 0.541 0.4 0.490 0.550 0.568 0.568 0.560 0.548 0.5 0.470 0.537 0.562 0.567 0.563 0.553 0.6 0.442 0.514 0.548 0.560 0.561 0.555 0.7 0.408 0.479 0.521 0.542 0.550 0.550 (a) Water

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 0.1 0.784 0.801 0.796 0.777 0.752 0.725 0.2 0.783 0.802 0.798 0.781 0.758 0.732 0.3 0.780 0.801 0.800 0.785 0.764 0.740 0.4 0.777 0.800 0.802 0.789 0.770 0.749 0.5 0.771 0.798 0.803 0.794 0.777 0.758 0.6 0.764 0.794 0.802 0.797 0.784 0.768 0.7 0.754 0.786 0.799 0.799 0.790 0.777 (b) Agriculture

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 0.1 0.758 0.776 0.752 0.710 0.664 0.618 0.2 0.756 0.778 0.758 0.719 0.674 0.630 0.3 0.752 0.779 0.763 0.728 0.685 0.643 0.4 0.745 0.779 0.769 0.738 0.698 0.658 0.5 0.734 0.776 0.773 0.748 0.712 0.675 0.6 0.719 0.769 0.775 0.757 0.727 0.693 0.7 0.697 0.754 0.771 0.762 0.741 0.713 (c) Green

Table C.13. R2 for various (θ, p) combinations for each NDVI land-use model on August 1, 2005. Continued.

232

Table C.13 continued.

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 0.1 0.579 0.603 0.587 0.556 0.525 0.496 0.2 0.577 0.605 0.591 0.562 0.532 0.503 0.3 0.572 0.606 0.595 0.569 0.539 0.511 0.4 0.564 0.605 0.599 0.576 0.548 0.521 0.5 0.550 0.601 0.602 0.583 0.558 0.532 0.6 0.529 0.590 0.601 0.589 0.567 0.544 0.7 0.501 0.570 0.593 0.590 0.575 0.555 (d) Residential area

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 17 * 17 0.3 0.366 0.396 0.398 0.386 0.370 0.339 0.4 0.360 0.395 0.399 0.390 0.375 0.345 0.5 0.350 0.390 0.400 0.393 0.380 0.352 0.6 0.338 0.383 0.400 0.395 0.385 0.360 0.7 0.321 0.369 0.390 0.394 0.388 0.368 0.8 0.302 0.350 0.377 0.387 0.387 0.374 0.9 0.281 0.326 0.355 0.371 0.377 0.375 1.0 0.262 0.299 0.328 0.346 0.357 0.366 (e) Impervious area

Size of buffer (θ) p 15 * 15 21 * 21 25 * 25 35 * 35 45 * 45 55 * 55 0.3 0.173 0.183 0.181 0.173 0.165 0.155 0.4 0.176 0.186 0.185 0.178 0.171 0.163 0.5 0.178 0.188 0.188 0.183 0.178 0.170 0.6 0.180 0.188 0.189 0.186 0.183 0.177 0.7 0.180 0.182 0.185 0.185 0.184 0.180 0.8 0.176 0.168 0.173 0.176 0.176 0.175 0.9 0.166 0.148 0.154 0.160 0.161 0.161 1.0 0.159 0.128 0.134 0.140 0.142 0.142 (f) Urban area

233

September 2, 2005.

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 0.2 0.448 0.488 0.500 0.500 0.494 0.485 0.3 0.443 0.486 0.500 0.502 0.497 0.489 0.4 0.434 0.481 0.499 0.503 0.500 0.492 0.5 0.419 0.471 0.494 0.502 0.501 0.496 0.6 0.398 0.454 0.483 0.496 0.499 0.496 0.7 0.373 0.428 0.462 0.481 0.489 0.491 (a) Water

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 17 *17 0.1 0.456 0.481 0.490 0.490 0.485 0.478 0.469 0.2 0.454 0.480 0.490 0.491 0.487 0.480 0.473 0.3 0.451 0.479 0.490 0.492 0.489 0.483 0.476 0.4 0.447 0.477 0.490 0.493 0.491 0.486 0.480 0.5 0.441 0.473 0.488 0.493 0.492 0.489 0.484 0.6 0.432 0.466 0.484 0.492 0.493 0.491 0.488 0.7 0.421 0.456 0.477 0.488 0.492 0.492 0.491 0.8 0.408 0.442 0.466 0.480 0.487 0.491 0.491 (b) Agriculture

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 0.1 0.486 0.516 0.517 0.503 0.485 0.465 0.2 0.483 0.516 0.518 0.507 0.489 0.471 0.3 0.478 0.515 0.520 0.510 0.494 0.476 0.4 0.470 0.512 0.521 0.514 0.499 0.483 0.5 0.459 0.506 0.520 0.516 0.505 0.490 0.6 0.443 0.495 0.515 0.517 0.509 0.497 0.7 0.423 0.478 0.505 0.513 0.510 0.502 0.8 0.400 0.454 0.486 0.501 0.505 0.503 (c) Green Table C.14. R2 for various (θ, p) combinations for each NDVI land-use model on September 2, 2005. Continued.

234

Table C.14 continued.

Size of buffer (θ) p 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 17 * 17 19 * 19 0.1 0.311 0.312 0.305 0.294 0.284 0.274 0.265 0.2 0.311 0.314 0.307 0.297 0.287 0.277 0.269 0.3 0.311 0.315 0.309 0.299 0.290 0.281 0.272 0.4 0.311 0.316 0.311 0.303 0.294 0.285 0.277 0.5 0.304 0.315 0.313 0.306 0.298 0.289 0.281 0.6 0.295 0.310 0.312 0.307 0.300 0.293 0.286 0.7 0.280 0.301 0.307 0.305 0.301 0.295 0.289 0.8 0.260 0.285 0.295 0.298 0.296 0.293 0.289 (d) Residential area

Size of buffer (θ) p 9 * 9 11 * 11 13 * 13 15 * 15 17 * 17 19 * 19 21 * 21 0.1 0.229 0.229 0.227 0.225 0.223 0.220 0.218 0.2 0.229 0.230 0.229 0.227 0.224 0.222 0.220 0.3 0.230 0.231 0.230 0.228 0.226 0.224 0.222 0.4 0.230 0.232 0.232 0.230 0.228 0.226 0.224 0.5 0.229 0.232 0.233 0.232 0.230 0.228 0.226 0.6 0.225 0.231 0.232 0.232 0.231 0.229 0.228 0.7 0.219 0.227 0.230 0.231 0.230 0.229 0.228 0.8 0.208 0.218 0.224 0.226 0.227 0.227 0.226 (e) Impervious area

Size of buffer (θ) p 9 * 9 19 * 19 29 * 29 39 * 39 43 * 43 47 * 47 49 * 49 0.3 0.062 0.081 0.080 0.076 0.075 0.076 0.076 0.4 0.062 0.082 0.081 0.077 0.077 0.077 0.077 0.5 0.062 0.084 0.083 0.079 0.078 0.078 0.078 0.6 0.060 0.085 0.086 0.082 0.081 0.080 0.080 0.7 0.056 0.085 0.088 0.085 0.084 0.083 0.083 0.8 0.050 0.083 0.089 0.087 0.087 0.087 0.086 0.9 0.042 0.078 0.087 0.088 0.088 0.089 0.089 1.0 0.035 0.068 0.082 0.086 0.087 0.088 0.088 (f) Urban area

235

Central land uses Neighboring Parameters R2 t-statistics (Number of pixels) land uses (β's) (θ, p)

Intercept 22.06 1293.15 Water 0.07 22.00 Agriculture 0.15 22.19 Water 0.50 Green 0.13 38.23 (54,037) (11, 0.4) Residential 0.74 96.57 Impervious 1.28 114.77 Urban -3.68 -29.00 Intercept 27.97 3660.87 Water -0.54 -48.92 Agriculture -0.38 -595.30 Agriculture 0.49 Green -0.25 -302.75 (675,486) (11, 0.4) Residential 0.34 67.06 Impervious -0.05 -12.68 Urban -0.64 -13.60 Intercept 29.19 4070.22 Water -1.31 -236.80 Agriculture -0.61 -585.13 Green 0.52 Green -0.52 -602.83 (1,041,107) (9, 0.4) Residential 0.08 38.95 Impervious -0.01 -3.34 Urban -4.26 -61.43 Intercept 29.23 1611.84 Water -1.35 -100.02 Agriculture -0.58 -89.56 Residential 0.32 Green -0.50 -185.18 (310,038) (9, 0.4) Residential 0.03 9.77 Impervious 0.20 30.76 Urban -4.77 -52.05 Intercept 29.84 2516.77 Water 1.36 74.75 Agriculture -0.74 -154.29 Impervious 0.23 Green -0.50 -184.74 (461,181) (13, 0.5) Residential 0.13 29.2 Impervious 0.01 1.79 Urban -4.86 -100.26 Intercept 28.48 432.13 Water 1.00 5.17 Agriculture -1.66 -26.80 Urban 0.09 Green -0.43 -10.13 (59,038) (29, 0.8) Residential 3.60 45.75 Impervious -1.59 -19.72 Urban 5.85 33.80

Table C.15. Regression results for the NDVI models on September 2, 2005.

236

NDVI weighted sum Neighboring Central land uses Standard land uses Mean Minimum Maximum deviation Water -1.06 -9.42 7.02 2.98 Agriculture 0.61 -0.43 10.99 1.04 Green 2.59 0 13.22 2.59 Water Residential 0.72 -0.05 8.86 0.96 Impervious 0.40 -2.75 5.82 0.64 Urban 0 -2.38 0.37 0.05 Water 0.02 -3.21 4.27 0.15 Agriculture 6.77 -1.16 15.97 3.87 Green 3.66 -0.04 14.25 2.46 Agriculture Residential 0.15 -0.08 5.58 0.37 Impervious 0.31 -3.10 6.58 0.56 Urban 0 -1.38 3.43 0.03 Water 0.05 -2.61 5.32 0.23 Agriculture 1.69 -0.29 10.96 1.73 Green 5.15 -0.08 11.14 2.19 Green Residential 0.43 -0.20 6.87 0.75 Impervious 0.35 -1.54 6.06 0.54 Urban 0 -0.65 2.86 0.02 Water 0.06 -2.62 4.23 0.24 Agriculture 0.28 -0.06 8.61 0.59 Green 1.78 -0.02 9.75 1.69 Residential Residential 2.19 -0.07 7.09 1.26 Impervious 1.15 -1.45 4.83 0.74 Urban 0 -0.79 1.48 0.04 Water 0.01 -4.75 3.39 0.21 Agriculture 0.60 -0.89 9.31 0.95 Green 1.60 -0.01 11.09 1.58 Impervious Residential 1.10 -0.29 6.90 0.94 Impervious 1.59 -2.58 5.46 0.78 Urban 0.01 -2.17 3.07 0.08 Water 0 -2.68 0.86 0.11 Agriculture 0.34 -0.31 5.20 0.45 Green 0.71 0 5.21 0.63 Urban Residential 0.43 0 2.96 0.33 Impervious 0.73 -0.87 2.17 0.32 Urban -0.03 -1.11 1.26 0.13

Table C.16. NDVI statistics for the independent variables on September 2, 2005.

237

Elasticity (ε ) Neighboring i Central land uses land uses Standard Mean Minimum Maximum deviation Water -0.004 -0.032 0.022 0.009 Agriculture 0.004 -0.003 0.071 0.007 Green 0.014 0.000 0.076 0.015 Water Residential 0.021 -0.002 0.246 0.027 Impervious 0.021 -0.167 0.249 0.032 Urban 0.001 -0.059 0.393 0.008 Water -0.001 -0.094 0.074 0.003 Agriculture -0.108 -0.426 0.020 0.067 Green -0.037 -0.161 0.000 0.025 Agriculture Residential 0.002 -0.001 0.069 0.005 Impervious -0.001 -0.014 0.007 0.001 Urban -0.000 -0.088 0.037 0.001 Water -0.003 -0.301 0.145 0.012 Agriculture -0.042 -0.384 0.007 0.044 Green -0.107 -0.265 0.002 0.050 Green Residential 0.001 -0.001 0.021 0.002 Impervious -0.000 -0.003 0.001 0.000 Urban -0.000 -0.507 0.120 0.003 Water -0.003 -0.244 0.150 0.013 Agriculture -0.006 -0.214 0.001 0.013 Green -0.033 -0.211 0.000 0.033 Residential Residential 0.002 -0.000 0.008 0.001 Impervious 0.008 -0.013 0.032 0.005 Urban -0.001 -0.288 0.162 0.006 Water 0.000 -0.290 0.177 0.012 Agriculture -0.017 -0.309 0.029 0.028 Green -0.029 -0.244 0.000 0.030 Impervious Residential 0.005 -0.002 0.034 0.004 Impervious 0.001 -0.001 0.002 0.000 Urban -0.001 -0.579 0.493 0.015 Water 0.000 -0.113 0.049 0.005 Agriculture -0.022 -6.509 7.416 0.064 Green -0.012 -3.223 3.512 0.028 Urban Residential 0.057 -6.615 5.268 0.061 Impervious -0.043 -4.376 5.676 0.055 Urban -0.008 -7.350 6.570 0.076 (a) Tj = RST

Table C.17. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on September 2, 2005. Continued.

238

Table C.17 continued.

Elasticity (ε ) Neighboring i Central land uses land uses Standard Mean Minimum Maximum deviation Water -0.004 -0.031 0.021 0.009 Agriculture 0.004 -0.003 0.068 0.007 Green 0.014 0.000 0.072 0.015 Water Residential 0.021 -0.002 0.228 0.027 Impervious 0.021 -0.145 0.251 0.032 Urban 0.001 -0.058 0.321 0.008 Water -0.001 -0.096 0.060 0.003 Agriculture -0.108 -0.277 0.015 0.066 Green -0.037 -0.146 0.000 0.025 Agriculture Residential 0.002 -0.001 0.066 0.005 Impervious -0.001 -0.013 0.005 0.001 Urban 0.000 -0.092 0.031 0.001 Water -0.003 -0.332 0.107 0.012 Agriculture -0.042 -0.298 0.006 0.044 Green -0.107 -0.248 0.001 0.049 Green Residential 0.001 -0.001 0.019 0.002 Impervious 0.000 -0.002 0.001 0.000 Urban 0.000 -0.825 0.087 0.003 Water -0.003 -0.261 0.110 0.013 Agriculture -0.006 -0.209 0.001 0.013 Green -0.033 -0.201 0.000 0.032 Residential Residential 0.002 0.000 0.007 0.001 Impervious 0.008 -0.010 0.032 0.005 Urban -0.001 -0.335 0.112 0.006 Water 0.000 -0.288 0.138 0.010 Agriculture -0.016 -0.316 0.020 0.028 Green -0.029 -0.231 0.000 0.030 Impervious Residential 0.005 -0.001 0.029 0.004 Impervious 0.001 -0.001 0.002 0.000 Urban -0.001 -1.044 0.264 0.014 Water 0.000 -0.105 0.028 0.004 Agriculture -0.021 -0.469 0.019 0.031 Green -0.011 -0.089 0.000 0.010 Urban Residential 0.054 0.000 0.284 0.037 Impervious -0.041 -0.130 0.052 0.018 Urban -0.006 -0.291 0.236 0.029

(b) Tj = Temperatures estimated with the regression models.

239

November 21, 2005

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 0.1 0.118 0.124 0.124 0.121 0.117 0.113 0.2 0.117 0.125 0.125 0.122 0.119 0.115 0.3 0.116 0.124 0.125 0.123 0.120 0.117 0.4 0.113 0.123 0.125 0.124 0.122 0.118 0.5 0.108 0.121 0.125 0.124 0.123 0.120 0.6 0.102 0.116 0.121 0.123 0.123 0.121 0.7 0.096 0.108 0.116 0.119 0.120 0.120 (a) Water

Size of buffer (θ) p 25 * 25 27 * 27 33 * 33 41 * 41 45 * 45 49 * 49 53 * 53 0.1 0.023 0.024 0.027 0.030 0.033 0.035 0.038 0.2 0.023 0.024 0.027 0.030 0.033 0.035 0.038 0.3 0.023 0.024 0.027 0.030 0.033 0.035 0.037 0.4 0.023 0.024 0.027 0.030 0.033 0.035 0.037 0.5 0.023 0.024 0.026 0.030 0.032 0.035 0.037 0.7 0.021 0.022 0.025 0.029 0.031 0.033 0.036 0.8 0.020 0.021 0.024 0.026 0.030 0.032 0.034 (b) Agriculture

Size of buffer (θ) p 5 * 5 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 0.1 0.087 0.089 0.088 0.085 0.082 0.079 0.2 0.086 0.089 0.089 0.086 0.083 0.080 0.3 0.086 0.089 0.089 0.087 0.084 0.081 0.4 0.085 0.089 0.089 0.088 0.085 0.083 0.5 0.084 0.089 0.089 0.088 0.086 0.084 0.6 0.082 0.087 0.089 0.089 0.087 0.086 0.7 0.079 0.085 0.087 0.088 0.088 0.087 0.8 0.076 0.082 0.085 0.086 0.087 0.086 (a) Green Table C.18. R2 for various (θ, p) combinations for each NDVI land-use model on November 21, 2005. Continued.

240

Table C.18 continued.

Size of buffer (θ) p 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 17 * 17 19 * 19 0.1 0.142 0.148 0.150 0.149 0.147 0.145 0.142 0.2 0.141 0.148 0.150 0.150 0.148 0.146 0.143 0.3 0.141 0.148 0.151 0.151 0.150 0.148 0.145 0.4 0.139 0.147 0.151 0.152 0.151 0.149 0.147 0.5 0.135 0.145 0.150 0.152 0.152 0.151 0.149 0.6 0.128 0.141 0.147 0.151 0.152 0.151 0.150 0.7 0.118 0.132 0.141 0.146 0.149 0.150 0.150 0.8 0.104 0.120 0.130 0.137 0.142 0.144 0.146 (b) Residential area

Size of buffer (θ) p 15 * 15 17 * 17 25 * 25 33 * 33 37 * 37 45 * 45 53 * 53 0.1 0.064 0.066 0.067 0.066 0.065 0.063 0.062 0.2 0.065 0.066 0.068 0.067 0.066 0.064 0.063 0.3 0.064 0.066 0.068 0.068 0.067 0.065 0.064 0.4 0.065 0.066 0.069 0.068 0.068 0.066 0.065 0.5 0.064 0.066 0.069 0.069 0.069 0.067 0.066 0.6 0.064 0.066 0.070 0.070 0.070 0.069 0.068 0.7 0.061 0.064 0.069 0.070 0.070 0.070 0.069 0.8 0.057 0.060 0.067 0.070 0.070 0.070 0.070 (c) Impervious area

Size of buffer (θ) p 17 * 17 23 * 23 27 * 27 31 * 31 35 * 35 37 * 37 39 * 39 0.3 0.098 0.096 0.093 0.091 0.089 0.089 0.088 0.4 0.104 0.101 0.099 0.096 0.095 0.094 0.094 0.5 0.109 0.108 0.105 0.103 0.102 0.101 0.101 0.6 0.112 0.113 0.112 0.110 0.109 0.109 0.110 0.7 0.110 0.116 0.116 0.116 0.116 0.116 0.116 0.8 0.101 0.111 0.115 0.117 0.118 0.119 0.120 0.9 0.085 0.098 0.103 0.108 0.111 0.113 0.114 1.0 0.069 0.080 0.085 0.090 0.095 0.097 0.098 (d) Urban area

241

Central land uses Neighboring Parameters R2 t-statistics (Number of pixels) land uses (β's) (θ, p)

Intercept 6.62 376.44 Water 0.0002 0.10 Agriculture 0.12 12.53 Water 0.13 Green 0.07 18.58 (54,166) (9, 0.2) Residential 0.35 39.43 Impervious 0.29 31.99 Urban -2.28 -33.33 Intercept 8.43 1400.43 Water 0.01 22.52 Agriculture 0.01 122.18 Agriculture 0.03 Green -0.001 -37.47 (631,571) (41, 0.1) Residential 0.0002 1.45 Impervious 0.001 9.80 Urban -0.01 -7.51 Intercept 7.55 2249.66 Water -0.16 -25.94 Agriculture 0.24 181.75 Green 0.09 Green 0.13 216.73 (1,044,075) (7, 0.2) Residential 0.26 116.85 Impervious 0.36 169.18 Urban -0.20 -4.00 Intercept 7.98 999.64 Water 0.11 9.92 Agriculture 0.09 20.70 Residential 0.15 Green -0.03 -20.39 (309,759) (13, 0.4) Residential 0.26 127.26 Impervious 0.40 157.33 Urban -1.42 -34.16 Intercept 8.51 1169.46 Water 0.29 35.00 Agriculture -0.03 -8.94 Impervious 0.07 Green -0.05 -22.37 (459,214) (25, 0.6) Residential 0.27 77.76 Impervious 0.28 91.75 Urban -1.57 -58.91 Intercept 9.78 217.27 Water 0.70 5.61 Agriculture -2.50 -31.44 Urban 0.12 Green -0.09 -1.98 (59,122) (23, 0.7) Residential 1.95 23.02 Impervious -2.82 -50.27 Urban 7.87 75.74

Table C.19. Regression results for the NDVI models on November 21, 2005.

242

NDVI weighted sum Neighboring Central land uses Standard land uses Mean Minimum Maximum deviation Water -3.73 -13.68 8.92 4.30 Agriculture 0.39 -0.58 12.09 0.75 Green 1.75 -0.13 14.29 2.12 Water Residential 0.56 -0.63 7.23 0.84 Impervious 0.29 -5.91 7.77 0.75 Urban -0.01 -5.79 1.38 0.09 Water -0.39 -169.57 15.20 5.95 Agriculture 63.92 -0.26 270.37 27.58 Green 99.19 -0.19 332.33 47.60 Agriculture Residential 9.25 -0.33 170.54 14.63 Impervious 15.87 -24.55 144.08 17.92 Urban 0.04 -42.80 16.16 0.98 Water 0.01 -3.88 6.63 0.13 Agriculture 0.94 -1.02 14.37 1.03 Green 3.83 -0.83 14.89 2.24 Green Residential 0.34 -0.75 7.19 0.64 Impervious 0.37 -2.13 9.85 0.64 Urban 0.001 -1.04 3.05 0.03 Water 0.003 -4.91 3.79 0.21 Agriculture 0.34 -0.65 12.22 0.56 Green 1.85 -0.33 12.95 1.60 Residential Residential 2.14 -0.65 8.07 1.21 Impervious 1.40 -2.19 7.29 0.96 Urban 0.001 -1.30 1.90 0.05 Water -0.04 -7.51 1.22 0.29 Agriculture 0.57 -0.60 8.63 0.69 Green 1.69 -0.17 10.70 1.41 Impervious Residential 1.14 -0.37 6.85 0.83 Impervious 1.56 -2.24 6.71 0.89 Urban -0.01 -2.99 1.36 0.10 Water -0.02 -2.78 0.15 0.14 Agriculture 0.20 -0.53 5.01 0.26 Green 0.44 -0.03 4.80 0.46 Urban Residential 0.33 -0.04 2.06 0.24 Impervious 0.59 -1.56 2.86 0.40 Urban -0.70 -2.10 1.15 0.19

Table C.20. NDVI statistics for the independent variables on November 21, 2005.

243

Elasticity (ε ) Neighboring i Central land uses land uses Standard Mean Minimum Maximum deviation Water 0.000 -0.001 0.000 0.000 Agriculture 0.006 -0.997 1.054 0.026 Green 0.016 -1.267 1.247 0.039 Water Residential 0.026 -2.228 2.045 0.048 Impervious 0.011 -2.103 1.407 0.036 Urban 0.003 -0.452 2.217 0.029 Water -0.001 -0.258 0.138 0.008 Agriculture 0.073 -2.251 2.191 0.055 Green -0.011 -0.546 0.624 0.011 Agriculture Residential 0.000 -0.048 0.046 0.001 Impervious 0.002 -0.314 0.303 0.004 Urban 0.000 -0.267 0.252 0.002 Water 0.000 -0.385 0.418 0.004 Agriculture 0.026 -2.894 3.925 0.042 Green 0.059 -2.778 2.719 0.066 Green Residential 0.010 -2.166 2.349 0.032 Impervious 0.015 -3.250 3.586 0.047 Urban 0.000 -0.305 0.493 0.001 Water 0.000 -0.190 0.215 0.004 Agriculture 0.004 -0.684 0.672 0.008 Green -0.006 -0.450 0.508 0.012 Residential Residential 0.061 -2.661 2.719 0.071 Impervious 0.061 -3.279 3.382 0.090 Urban 0.000 -3.431 4.464 0.019 Water -0.001 -0.478 0.320 0.011 Agriculture -0.002 -0.270 0.241 0.004 Green -0.010 -0.825 0.964 0.018 Impervious Residential 0.033 -2.094 2.054 0.051 Impervious 0.048 -3.005 3.005 0.067 Urban 0.002 -4.372 4.407 0.041 Water -0.002 -0.321 0.300 0.013 Agriculture -0.058 -12.135 12.735 0.396 Green -0.005 -0.817 0.717 0.023 Urban Residential 0.074 -6.570 6.491 0.320 Impervious -0.188 -19.466 21.993 0.966 Urban -0.031 -25.175 27.135 0.908 (a) Tj = RST

Table C.21. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on November 21, 2005. Continued.

244

Table C.21 continued.

Elasticity (ε ) Neighboring i Central land uses land uses Standard Mean Minimum Maximum deviation Water -0.000 -0.000 0.000 0.000 Agriculture 0.006 -0.007 0.165 0.012 Green 0.017 -0.001 0.129 0.020 Water Residential 0.026 -0.033 0.270 0.036 Impervious 0.011 -0.176 0.238 0.028 Urban 0.002 -0.861 0.729 0.028 Water -0.001 -0.252 0.018 0.008 Agriculture 0.070 -0.000 0.245 0.028 Green -0.011 -0.037 0.000 0.005 Agriculture Residential 0.000 -0.000 0.004 0.000 Impervious 0.002 -0.003 0.017 0.002 Urban -0.000 -0.019 0.049 0.001 Water -0.000 -0.155 0.075 0.002 Agriculture 0.026 -0.033 0.312 0.028 Green 0.058 -0.015 0.204 0.032 Green Residential 0.010 -0.025 0.194 0.019 Impervious 0.015 -0.108 0.314 0.025 Urban -0.000 -0.077 0.025 0.001 Water 0.000 -0.071 0.048 0.003 Agriculture 0.003 -0.007 0.112 0.006 Green -0.006 -0.050 0.001 0.006 Residential Residential 0.060 -0.022 0.206 0.032 Impervious 0.060 -0.098 0.264 0.039 Urban -0.000 -0.424 0.206 0.009 Water -0.001 -0.347 0.040 0.011 Agriculture -0.002 -0.031 0.002 0.002 Green -0.009 -0.067 0.001 0.008 Impervious Residential 0.033 -0.012 0.173 0.023 Impervious 0.047 -0.057 0.185 0.025 Urban 0.002 -0.309 0.368 0.016 Water -0.002 -0.267 3.291 0.018 Agriculture -0.077 -31.367 37.390 0.262 Green -0.006 -0.701 0.764 0.008 Urban Residential 0.085 -3.997 0.510 0.062 Impervious -0.238 -142.566 13.274 0.628 Urban -0.100 -84.724 816.873 3.423

(b) Tj = Temperatures estimated with the regression models.

245

APPENDIX D

LAND-USE AREA MODELS FOR DIFFERENT DATES IN

THE NO WIND-EFFECT CASE.

246

February 25, 2006.

Size of buffer (θ) p 17 * 17 19 *19 21 * 21 23 * 23 25 * 25 27 * 27 1.2 0.816 0.817 0.816 0.814 0.812 0.810 1.3 0.816 0.817 0.817 0.816 0.815 0.813 1.4 0.814 0.817 0.817 0.817 0.817 0.816 1.5 0.812 0.815 0.817 0.818 0.818 0.818 1.6 0.809 0.813 0.815 0.817 0.818 0.818 1.7 0.805 0.809 0.812 0.814 0.816 0.817 1.8 0.799 0.804 0.808 0.811 0.813 0.814 (a) Water

Size of buffer (θ) p 17 * 17 19 * 19 23 * 23 27 * 27 31 * 31 35 * 35 0.5 0.044 0.045 0.045 0.045 0.045 0.045 0.6 0.044 0.045 0.046 0.046 0.045 0.045 0.7 0.044 0.045 0.046 0.046 0.045 0.045 0.8 0.044 0.045 0.045 0.046 0.046 0.045 1.0 0.043 0.044 0.045 0.046 0.046 0.046 1.2 0.043 0.043 0.044 0.046 0.045 0.045 1.4 0.041 0.041 0.044 0.045 0.045 0.045 (b) Agriculture

Size of buffer (θ) p 35 * 35 39 * 39 43 * 43 47 * 47 51 * 51 55 * 55 1.3 0.136 0.136 0.135 0.135 0.134 0.133 1.5 0.138 0.138 0.138 0.138 0.138 0.138 1.6 0.138 0.139 0.139 0.140 0.140 0.140 1.7 0.138 0.139 0.140 0.141 0.141 0.141 1.8 0.138 0.139 0.140 0.141 0.141 0.141 1.9 0.137 0.138 0.139 0.140 0.141 0.141 2.0 0.137 0.137 0.138 0.139 0.140 0.140 (c) Green

Table D.1. R2 for various (θ, p) combinations for each area land-use model on February 25, 2005. Continued.

247

Table D.1 continued.

Size of buffer (θ) p 13 * 13 17 * 17 21 * 21 25 * 25 29 * 29 33 * 33 1.3 0.345 0.347 0.345 0.342 0.338 0.334 1.4 0.345 0.348 0.347 0.345 0.342 0.339 1.5 0.343 0.348 0.349 0.347 0.346 0.344 1.6 0.341 0.347 0.349 0.349 0.348 0.347 1.7 0.339 0.346 0.349 0.350 0.350 0.349 1.8 0.336 0.344 0.348 0.349 0.350 0.350 1.9 0.332 0.341 0.345 0.348 0.349 0.350 2.0 0.329 0.337 0.342 0.345 0.347 0.348 2.1 0.324 0.333 0.339 0.342 0.344 0.345 (d) Residential area

Size of buffer (θ) p 13 * 13 17 * 17 21 * 21 25 * 25 29 * 29 33 * 33 0.9 0.265 0.269 0.270 0.268 0.265 0.261 1.0 0.265 0.270 0.271 0.270 0.268 0.264 1.1 0.264 0.270 0.272 0.272 0.271 0.268 1.2 0.263 0.270 0.273 0.274 0.273 0.271 1.3 0.261 0.269 0.273 0.275 0.275 0.273 1.4 0.259 0.268 0.273 0.275 0.276 0.275 1.5 0.257 0.267 0.272 0.275 0.276 0.276 1.6 0.254 0.264 0.270 0.274 0.275 0.276 1.8 0.247 0.258 0.265 0.269 0.271 0.273 (e) Impervious area

Size of buffer (θ) p 13 * 13 15 * 15 17 * 17 19 * 19 21 * 21* 25 * 25 0.9 0.198 0.196 0.194 0.191 0.188 0.181 1.0 0.199 0.198 0.196 0.193 0.191 0.185 1.1 0.200 0.199 0.198 0.196 0.194 0.189 1.2 0.200 0.200 0.199 0.198 0.196 0.193 1.3 0.200 0.201 0.200 0.199 0.198 0.196 1.4 0.199 0.201 0.201 0.200 0.200 0.198 1.5 0.198 0.200 0.200 0.201 0.200 0.199 1.6 0.197 0.199 0.200 0.200 0.200 0.200 1.7 0.195 0.198 0.198 0.199 0.199 0.200 (f) Urban area

248

Central land uses Neighboring Parameters R2 t-statistics (Number of pixels) land uses (β's) (θ, p) Intercept 45.14 35.56 0.82 Water -0.04 -34.48 (23, 1.5) Water Agriculture -0.005 -4.76 (53,256) Green -0.002 -2.16 * Residential 0.01 12.94 0.83 (11, 0.5) Impervious -0.007 -5.35 Intercept 6.03 84.69 0.05 Water 0.00007 9.33 (23, 0.7) Agriculture Agriculture 0.0002 43.21 (657,986) Green 0.0003 54.84 Residential 0.0005 91.13 0.04* Impervious 0.0003 48.74 (39, 0.5) Intercept -21.82 -39.59 0.14 Water -0.02 -32.65 (47, 1.7) Green Agriculture 0.03 54.73 (986,326) Green 0.03 56.82 Residential 0.05 96.43 0.12* Impervious 0.04 70.10 (23, 0.5) Intercept -75.55 -161.97 0.35 Water -0.001 -2.42 (25, 1.7) Residential Agriculture 0.06 113.84 (308,897) Green 0.06 136.26 Residential 0.09 187.04 0.28* Impervious 0.08 160.33 (13, 0.4) Intercept -22.29 -174.18 0.28 Agriculture 0.017 167.51 (29, 1.4) Impervious Green 0.02 204.02 (458,515) Residential 0.02 249.64 Impervious 0.03 261.77 0.21* Urban 0.009 77.51 (17, 0.4) Intercept -6.92 -4.24 0.20 Agriculture 0.02 16.11 (15, 1.3) Urban Green 0.01 10.43 (59,158) Residential 0.02 11.28 Impervious 0.04 29.47 0.23* Urban 0.007 5.47 (17, 0.5) *: Input variable with NDVI

Table D.2. Regression results for the area models on February 25, 2006.

249

Central land uses Neighboring land-use area (m2) Neighboring (Mean land uses Standard Temperature) Mean Minimum Maximum deviation Water 1017.1 0 1133.2 69.05 Agriculture 14.74 0 145.77 18.50 Green 54.54 0 218.45 46.46 Water Residential 19.47 0 191.30 22.98 Impervious 25.14 0 202.03 29.05 Urban 2.24 0 97.79 5.81 Water 82.04 0 9248.0 320.59 Agriculture 7005.8 0 1295.8 2649.0 Green 4581.3 0 11638.0 2061.8 Agriculture Residential 364.51 0 9805.8 689.96 Impervious 841.94 0 9170.4 1236.1 Urban 81.87 0 9702.3 356.43 Water 1.74 0 93.02 4.66 Agriculture 29.75 0 123.09 20.76 Green 973.88 0.10 1024.2 21.45 Green Residential 10.28 0 101.49 13.78 Impervious 12.54 0 103.96 13.89 Urban 0.850 0 58.92 2.44 Water 1.36 0 84.46 4.30 Agriculture 4.68 0 71.69 6.70 Green 23.36 0 93.31 17.79 Residential Residential 936.72 0 986.07 16.91 Impervious 28.40 0 90.56 16.81 Urban 1.62 0 54.77 3.61 Water 5.90 0 392.44 21.16 Agriculture 41.56 0 349.47 52.17 Green 91.98 0 401.35 72.29 Impervious Residential 88.36 0 360.99 61.35 Impervious 1089.2 0 1311.9 75.80 Urban 23.64 0 361.66 34.88 Water 2.90 0 249.33 14.37 Agriculture 25.67 0 391.52 36.81 Green 29.16 0 303.6683 35.47 Urban Residential 35.24 0 225.86 30.16 Impervious 179.26 0 407.43 73.57 Urban 1056.0 0 1328.3 88.00

Table D.3. Area statistics for the independent variables on February 25, 2006. 250

Elasticity (ε ) Central land Neighboring i uses land uses Standard Mean Minimum Maximum deviation Water -10.3942 -54.5603 -1.6584 7.8899 Agriculture -0.0132 -0.1462 0.0000 0.0141 Water Green -0.0211 -0.1167 0.0000 0.0147 Residential 0.0418 0.0000 0.2951 0.0361 Impervious -0.0318 -0.4202 0.0000 0.0357 Water 0.0006 -0.0278 0.4331 0.0031 Agriculture 0.1810 -7.4716 7.7471 0.0934 Agriculture Green 0.1462 -8.7801 8.0191 0.0837 Residential 0.0204 -4.2630 5.7471 0.0411 Impervious 0.0283 -6.6213 6.4780 0.0489 Water -0.0038 -0.6390 0.0334 0.0125 Agriculture 0.0932 -8.2230 8.3439 0.0765 Green Green 3.1061 -114.7240 108.5509 0.8312 Residential 0.0523 -6.4094 5.3218 0.0706 Impervious 0.0533 -6.9360 6.6566 0.0636 Water -0.0002 -0.0517 0.0032 0.0009 Agriculture 0.0293 -3.6691 2.6857 0.0467 Green 0.1498 -6.6351 7.6692 0.1283 Residential Residential 7.8053 -313.7901 298.0227 3.4010 Impervious 0.2231 -17.2183 18.1343 0.1924 Urban 0.0746 -12.2140 9.1858 0.1203 Agriculture 0.1898 -19.5626 17.5666 0.2009 Green 0.2048 -13.3175 11.5572 0.1800 Impervious Residential 2.7379 -118.8563 113.5067 2.3570 Impervious 0.0220 -8.8604 7.9942 0.1038 Urban 0.0622 -9.8143 10.0568 0.2953 Agriculture 0.0461 -11.5857 9.1899 0.2455 Green 0.0568 -6.7634 6.9548 0.2267 Urban Residential 0.6987 -38.9310 46.3656 1.8740 Impervious 0.7210 -34.0680 32.1983 2.7931 Urban -10.3942 -54.5603 -1.6584 7.8899 (a) Tj = RST

Table D.4. Elasticity statistics when (a) Tj = RSTs and (b) Tj = estimated temperatures on February 25, 2006.

Continued.

251

Table D.4 continued.

Elasticity (ε ) Central land Neighboring i uses land uses Standard Mean Minimum Maximum deviation Water -10.0524 -32.3511 -2.7332 7.9261 Agriculture -0.0123 -0.0885 0.0000 0.0130 Water Green -0.0199 -0.0546 0.0000 0.0133 Residential 0.0398 0.0000 0.2209 0.0339 Impervious -0.0288 -0.1474 0.0000 0.0290 Water 0.0006 0.0000 0.0843 0.0025 Agriculture 0.1763 0.0183 0.3383 0.0699 Agriculture Green 0.1432 0.0000 0.3549 0.0631 Residential 0.0201 0.0000 0.4375 0.0366 Impervious 0.0278 0.0000 0.3028 0.0402 Water -0.0037 -0.3584 0.0000 0.0112 Agriculture 0.0915 0.0000 0.3865 0.0648 Green Green 3.0591 2.3455 5.5706 0.1769 Residential 0.0518 0.0000 0.4552 0.0664 Impervious 0.0526 0.0000 0.4137 0.0565 Water -0.0002 -0.0306 0.0000 0.0008 Agriculture 0.0289 0.0000 0.4679 0.0427 Green 0.1483 0.0000 0.6412 0.1189 Residential Residential 7.7396 7.0439 19.5133 0.4508 Impervious 0.2210 0.0000 0.6756 0.1299 Urban 0.0729 0.0000 0.7055 0.0953 Agriculture 0.1863 0.0000 0.8577 0.1526 Green 0.2021 0.0000 0.7880 0.1330 Impervious Residential 2.6797 2.1263 13.4097 0.2490 Impervious 0.0212 0.0000 0.5770 0.0341 Urban 0.0718 0.0000 0.9583 0.1000 Agriculture 0.0517 0.0000 0.6204 0.0655 Green 0.0631 0.0000 0.4685 0.0523 Urban Residential 0.7620 0.0000 1.1233 0.1707 Impervious 0.9627 0.4239 4.4093 0.4948 Urban -10.0524 -32.3511 -2.7332 7.9261

(b) Tj = Temperatures estimated with the regression models.

252

April 11, 2005.

Size of buffer (θ) p 9 * 9 13 * 13 15 * 15 17 * 17 19 * 19 21 * 21 0.8 0.753 0.775 0.776 0.774 0.770 0.766 1.0 0.747 0.774 0.777 0.777 0.775 0.773 1.1 0.744 0.773 0.777 0.778 0.778 0.776 1.2 0.741 0.772 0.777 0.779 0.779 0.778 1.3 0.737 0.769 0.776 0.779 0.780 0.780 1.4 0.732 0.766 0.774 0.778 0.780 0.780 1.5 0.727 0.763 0.771 0.776 0.779 0.780 1.6 0.722 0.758 0.767 0.773 0.777 0.779 (a) Water

Size of buffer (θ) p 7 * 7 11 * 11 15 * 15 17 * 17 19 * 19 23* 23 1.0 0.038 0.044 0.044 0.043 0.042 0.039 1.1 0.037 0.044 0.044 0.043 0.042 0.040 1.2 0.037 0.044 0.044 0.044 0.043 0.041 1.3 0.037 0.044 0.045 0.044 0.044 0.042 1.4 0.036 0.043 0.045 0.044 0.044 0.043 1.5 0.036 0.043 0.045 0.045 0.044 0.044 1.6 0.035 0.043 0.045 0.045 0.045 0.044 1.7 0.035 0.042 0.044 0.045 0.045 0.044 (b) Agriculture

Size of buffer (θ) p 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 17 * 17 0.6 0.176 0.184 0.185 0.182 0.179 0.174 0.8 0.175 0.184 0.186 0.185 0.181 0.178 0.9 0.174 0.183 0.186 0.185 0.183 0.179 1.0 0.173 0.183 0.187 0.186 0.184 0.181 1.1 0.172 0.182 0.186 0.186 0.185 0.182 1.2 0.171 0.182 0.186 0.187 0.185 0.184 1.4 0.168 0.179 0.185 0.186 0.186 0.183 (c) Green Table D.5. R2 for various (θ, p) combinations for each area land-use model on April 11, 2005. Continued.

253

Table D.5 continued.

Size of buffer (θ) p 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 21 * 21 0.8 0.352 0.370 0.374 0.373 0.368 0.352 0.9 0.350 0.369 0.374 0.374 0.370 0.356 1.0 0.349 0.368 0.374 0.374 0.372 0.360 1.1 0.347 0.366 0.374 0.375 0.373 0.363 1.2 0.345 0.364 0.373 0.375 0.374 0.366 1.3 0.342 0.362 0.371 0.375 0.375 0.369 1.4 0.340 0.360 0.370 0.374 0.375 0.372 1.5 0.337 0.358 0.368 0.372 0.374 0.373 1.6 0.335 0.355 0.365 0.371 0.373 0.374 (d) Residential area

Size of buffer (θ) p 9 * 9 13 * 13 17 * 17 25 * 25 29 * 29 33 * 33 1.0 0.340 0.353 0.355 0.350 0.346 0.341 1.1 0.336 0.353 0.356 0.353 0.349 0.345 1.2 0.352 0.352 0.356 0.355 0.352 0.348 1.3 0.334 0.351 0.356 0.357 0.355 0.352 1.4 0.332 0.350 0.356 0.358 0.357 0.355 1.5 0.329 0.348 0.355 0.359 0.359 0.357 1.6 0.327 0.346 0.354 0.359 0.359 0.358 1.7 0.324 0.343 0.352 0.358 0.359 0.359 1.8 0.320 0.340 0.349 0.357 0.358 0.35 (e) Impervious area

Size of buffer (θ) p 19 * 19 21 * 21* 23 * 23 25 * 25 29 * 29 33 * 33 0.9 0.251 0.250 0.249 0.248 0.244 0.239 1.0 0.253 0.252 0.252 0.251 0.248 0.244 1.1 0.254 0.254 0.254 0.253 0.251 0.248 1.2 0.255 0.255 0.256 0.255 0.254 0.252 1.3 0.255 0.256 0.256 0.257 0.256 0.254 1.4 0.254 0.256 0.256 0.257 0.257 0.256 1.5 0.253 0.254 0.256 0.256 0.257 0.257 1.6 0.251 0.253 0.254 0.255 0.256 0.256 1.7 0.248 0.250 0.252 0.253 0.254 0.255 (f) Urban area

254

Central land uses Neighboring Parameters R2 t-statistics (Number of pixels) land uses (β's) (θ, p) Intercept 25.91 31.21 0.78 Water -0.009 -17.69 (17, 1.2) Water Agriculture 0.002 3.90 (53,688) Green 0.005 9.94 * Residential 0.01 25.56 0.80 (9, 0.4) Impervious 0.006 11.27 Intercept 23.12 104.70 0.04 Water -0.02 -65.68 (15, 1.3) Agriculture Agriculture -0.0007 -4.31 (669,901) Green -0.003 -18.69 Residential 0.01 69.94 0.08* Impervious -0.003 -16.43 (9, 0.2) Intercept 19.68 134.77 0.19 Water -0.005 -70.78 (11, 1.0) Green Agriculture 0.001 16.78 (1,037,789) Green 0.0007 10.78 Residential 0.005 67.44 0.16* Impervious 0.002 29.63 (11, 0.1) Intercept 15.74 132.73 0.38 Water -0.007 -84.33 (13, 1.1) Residential Agriculture 0.00006 0.73 (309,718) Green 0.001 22.06 Residential 0.005 77.31 0.26* Impervious 0.005 72.24 (13, 0.2) Intercept -52.65 -177.95 0.36 Agriculture 0.03 121.07 (25, 1.5) Impervious Green 0.05 177.03 (459,196) Residential 0.06 224.82 Impervious 0.07 265.00 0.29* Urban 0.05 165.89 (13, 0.5) Intercept 0.53 0.46 0.26 Agriculture 0.01 12.40 (25, 1.3) Urban Green 0.01 20.12 (59,117) Residential 0.01 18.62 Impervious 0.03 47.53 0.14* Urban 0.009 11.92 (47, 0.7)

Table D.6. Regression results for the area models on April 11, 2005.

255

Land-use area (m2) Neighboring Central land uses Standard land uses Mean Minimum Maximum deviation Water 1285.9 0 1652.7 232.04 Agriculture 45.24 0 483.69 62.25 Green 173.21 0 716.53 157.08 Water Residential 62.08 0 624.12 75.83 Impervious 79.58 0 688.97 96.94 Urban 6.54 0 331.75 18.95 Water 1.817 0 278.48 9.00 Agriculture 1149.7 0 1328.3 101.88 Green 141.15 0 425.67 82.83 Agriculture Residential 8.88 0 343.53 20.61 Impervious 24.44 0 368.77 43.29 Urban 2.26 0 348.28 12.60 Water 12.86 0 1010.0 50.72 Agriculture 249.46 0 1200 224.39 Green 1654.3 0 2100 250.88 Green Residential 84.98 0 1094.5 140.75 Impervious 94.41 0 1096.5 137.23 Urban 3.86 0 732.5 21.42 Water 12.90 0 817.42 45.46 Agriculture 40.42 0 807.23 67.41 Green 221.93 0 909.07 183.66 Residential Residential 1256.7 0 1763.1 173.84 Impervious 273.88 0 885.81 173.17 Urban 14.21 0 616.21 38.64 Water 3.12 0 225.16 11.83 Agriculture 22.06 0 199.96 29.05 Green 48.87 0 227.83 40.96 Impervious Residential 49.12 0 208.26 35.36 Impervious 1009.5 0 1134.2 43.70 Urban 13.13 0 205.14 20.28 Water 6.52 0 379.39 24.66 Agriculture 45.28 0 455.32 54.33 Green 64.26 0 489.01 60.78 Urban Residential 67.15 0 361.20 47.30 Impervious 271.07 0 26.97 569.71 Urban 1091.6 0 1511.6 112.38

Table D.7. Area statistics for the independent variables on April 11, 2005.

256

Elasticity (ε ) Central land Neighboring i uses land uses Standard Mean Minimum Maximum deviation Water -0.7557 -1.7277 -0.1996 0.3210 Agriculture 0.0050 0.0000 0.0532 0.0066 Water Green 0.0471 0.0000 0.2074 0.0400 Residential 0.0414 0.0000 0.3435 0.0439 Impervious 0.0287 0.0000 0.2163 0.0327 Water -0.0015 -0.3791 0.0000 0.0080 Agriculture -0.0379 -0.0777 -0.0210 0.0042 Agriculture Green -0.0201 -0.0748 0.0000 0.0121 Residential 0.0054 0.0000 0.1884 0.0124 Impervious -0.0036 -0.0613 0.0000 0.0063 Water -0.0034 -0.3604 0.0000 0.0139 Agriculture 0.0136 0.0000 0.0761 0.0122 Green Green 0.0575 0.0238 0.1041 0.0104 Residential 0.0177 0.0000 0.2295 0.0285 Impervious 0.0094 0.0000 0.1116 0.0134 Water -0.0044 -0.3883 0.0000 0.0166 Agriculture 0.0001 0.0000 0.0022 0.0002 Residential Green 0.0142 0.0000 0.0829 0.0123 Residential 0.2665 0.1451 0.6048 0.0342 Impervious 0.0591 0.0000 0.2332 0.0367 Agriculture 0.0335 0.0000 1.2503 0.0461 Green 0.1026 0.0000 2.1603 0.0905 Impervious Residential 0.1208 0.0000 3.1172 0.0859 Impervious 2.9651 1.5858 248.1229 0.6310 Urban 0.0279 0.0000 23.8815 0.0686 Agriculture 0.0237 -4.7499 4.5034 0.0729 Green 0.0525 -6.3314 11.5893 0.1393 Urban Residential 0.0483 -4.9291 5.1607 0.1018 Impervious 0.4479 -45.6120 34.2676 0.8403 Urban 0.4770 -49.3835 46.8466 1.4765 (a) Tj = RST

Table D.8. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on April 11, 2005.

Continued.

257

Table D.8 continued.

Elasticity (ε ) Central land Neighboring i uses land uses Standard Mean Minimum Maximum deviation Water -0.7457 -1.3099 -0.3038 0.3024 Agriculture 0.0050 0.0000 0.0490 0.0066 Water Green 0.0467 0.0000 0.1662 0.0394 Residential 0.0410 0.0000 0.3094 0.0431 Impervious 0.0280 0.0000 0.1888 0.0317 Water -0.0015 -0.2811 0.0000 0.0078 Agriculture -0.0377 -0.0430 -0.0241 0.0032 Agriculture Green -0.0200 -0.0621 0.0000 0.0119 Residential 0.0054 0.0000 0.1737 0.0122 Impervious -0.0036 -0.0552 0.0000 0.0063 Water -0.0033 -0.3528 0.0000 0.0138 Agriculture 0.0135 0.0000 0.0645 0.0122 Green Green 0.0572 0.0266 0.0741 0.0096 Residential 0.0176 0.0000 0.2031 0.0283 Impervious 0.0093 0.0000 0.1050 0.0133 Water -0.0043 -0.3916 0.0000 0.0163 Agriculture 0.0001 0.0000 0.0022 0.0002 Residential Green 0.0142 0.0000 0.0619 0.0122 Residential 0.2657 0.1850 0.3581 0.0311 Impervious 0.0589 0.0000 0.1832 0.0364 Agriculture 0.0332 0.0000 0.3582 0.0462 Green 0.1020 0.0000 0.5124 0.0901 Impervious Residential 0.1202 0.0000 0.5068 0.0850 Impervious 2.9390 2.6407 5.7877 0.1285 Urban 0.0271 0.0000 0.4666 0.0422 Agriculture 0.0223 0.0000 0.2649 0.0283 Green 0.0485 0.0000 0.4009 0.0479 Urban Residential 0.0451 0.0000 0.2494 0.0307 Impervious 0.4217 0.0650 0.6873 0.1131 Urban 0.4390 0.2702 0.8934 0.0956

(b) Tj = Temperatures estimated with the regression models.

258

May 13, 2005.

Size of buffer (θ) p 9 * 9 13 * 13 15 * 15 17 * 17 19 * 19 21 * 21 0.9 0.725 0.737 0.733 0.728 0.721 0.715 1.1 0.720 0.738 0.737 0.734 0.729 0.724 1.2 0.718 0.738 0.738 0.736 0.733 0.729 1.3 0.715 0.737 0.739 0.738 0.735 0.732 1.4 0.711 0.735 0.738 0.739 0.737 0.735 1.5 0.707 0.733 0.737 0.739 0.738 0.737 1.6 0.703 0.730 0.735 0.738 0.738 0.738 (a) Water

Size of buffer (θ) p 9 * 9 11 * 11 13 * 13 15 * 15 17 * 17 21 * 21 0.9 0.096 0.096 0.096 0.094 0.090 0.082 1.0 0.096 0.097 0.097 0.094 0.091 0.083 1.1 0.095 0.097 0.097 0.095 0.092 0.086 1.2 0.095 0.097 0.097 0.096 0.093 0.087 1.3 0.094 0.097 0.098 0.096 0.094 0.089 1.4 0.093 0.097 0.097 0.097 0.095 0.090 1.6 0.091 0.095 0.097 0.097 0.096 0.092 (b) Agriculture

Size of buffer (θ) p 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 17 * 17 0.7 0.223 0.231 0.229 0.223 0.216 0.208 0.8 0.223 0.231 0.230 0.225 0.218 0.211 0.9 0.222 0.231 0.231 0.227 0.221 0.214 1.0 0.221 0.231 0.232 0.228 0.223 0.217 1.1 0.220 0.230 0.232 0.230 0.225 0.220 1.2 0.219 0.230 0.232 0.231 0.227 0.223 1.3 0.217 0.229 0.232 0.232 0.229 0.225 1.4 0.216 0.228 0.232 0.232 0.230 0.227 (c) Green Table D.9. R2 for various (θ, p) combinations for each area land-use model on May 13, 2005. Continued.

259

Table D.9 continued.

Size of buffer (θ) p 9 * 9 11 * 11 13 * 13 15 * 15 17 * 17 19 * 19 1.1 0.421 0.422 0.417 0.409 0.401 0.392 1.2 0.421 0.422 0.418 0.412 0.405 0.397 1.3 0.419 0.422 0.420 0.415 0.408 0.402 1.4 0.418 0.422 0.420 0.417 0.412 0.406 1.5 0.416 0.421 0.421 0.418 0.414 0.410 1.6 0.414 0.420 0.420 0.419 0.416 0.413 1.7 0.412 0.418 0.420 0.419 0.417 0.415 1.8 0.409 0.416 0.418 0.418 0.417 0.416 1.9 0.406 0.413 0.416 0.417 0.417 0.416 (d) Residential area

Size of buffer (θ) p 9 * 9 11 * 11 13 * 13 17 * 17 21 * 21 25 * 25 1.1 0.351 0.359 0.362 0.361 0.357 0.351 1.2 0.349 0.357 0.362 0.362 0.359 0.355 1.3 0.347 0.356 0.361 0.363 0.361 0.357 1.4 0.344 0.353 0.360 0.363 0.362 0.360 1.5 0.342 0.352 0.358 0.362 0.363 0.361 1.6 0.339 0.350 0.356 0.361 0.363 0.362 1.7 0.336 0.347 0.353 0.360 0.362 0.362 1.9 0.329 0.340 0.347 0.354 0.358 0.360 (e) Impervious area

Size of buffer (θ) p 17 * 17 19 * 19 21 * 21* 23 * 23 25 * 25 29 * 29 0.9 0.269 0.268 0.267 0.265 0.263 0.258 1.0 0.270 0.270 0.269 0.268 0.267 0.262 1.1 0.271 0.271 0.271 0.270 0.269 0.266 1.2 0.271 0.272 0.272 0.272 0.271 0.269 1.3 0.271 0.272 0.273 0.273 0.273 0.271 1.4 0.270 0.272 0.273 0.273 0.273 0.272 1.5 0.268 0.270 0.272 0.273 0.273 0.273 1.6 0.266 0.268 0.270 0.271 0.272 0.272 1.7 0.263 0.265 0.267 0.269 0.270 0.270 (f) Urban area

260

Central land uses Neighboring Parameters R2 t-statistics (Number of pixels) land uses (β's) (θ, p) Intercept 23.27 24.13 0.74 Water Water -0.006 -9.38 (15, 1.3) Agriculture 0.007 9.56 (53,843) Green 0.008 11.05 * Residential 0.02 27.89 0.70 (9, 0.3) Impervious 0.01 19.20 Intercept 21.76 89.59 0.10 Agriculture Water -0.03 -87.96 (13, 1.3) Agriculture 0.001 5.19 (672,859) Green -0.005 -27.01 Residential 0.01 52.03 0.21* Impervious -0.009 -8.49 (7, 0.4) Intercept 15.12 97.10 0.23 Green Water -0.004 -46.30 (11, 1.0) Agriculture 0.004 57.95 (1,037,789) Green 0.003 35.83 Residential 0.006 84.16 0.36* Impervious 0.006 80.67 (7, 0.1) Intercept -5.56 -13.52 0.42 Residential Water -0.04 -83.91 (13, 1.5) Agriculture 0.01 21.71 (309,718) Green 0.009 22.26 Residential 0.03 73.26 0.34* Impervious 0.04 86.15 (9, 0.4) Intercept -18.28 -114.17 0.36 Impervious Agriculture 0.02 123.45 (17, 1.3) Green 0.02 188.56 (460,517) Residential 0.03 223.00 Impervious 0.03 276.35 0.23* Urban 0.03 191.43 (9, 0.3) Intercept -8.83 -8.75 0.27 Urban Agriculture 0.01 20.73 (21, 1.3) Green 0.02 29.82 (59,128) Residential 0.02 27.21 Impervious 0.04 58.95 0.08* Urban 0.02 26.45 (33, 0.5) *: Input variable with NDVI.

Table D.10. Regression results for the area models on May 13, 2005.

261

Land-use area (m2) Neighboring Central land uses Standard land uses Mean Minimum Maximum deviation Water 1132.0 0 1328.3 131.30 Agriculture 22.62 0 254.67 32.97 Green 92.72 0 414.83 88.63 Water Residential 34.63 0 365.00 43.72 Impervious 43.01 0 390.76 55.36 Urban 3.18 0 190.29 9.99 Water 1.44 0 251.76 7.71 Agriculture 1126.7 0 1280.0 92.22 Green 121.80 0 379.99 75.75 Agriculture Residential 7.26 0 309.94 17.90 Impervious 20.84 0 332.58 38.64 Urban 1.91 0 318.98 11.31 Water 12.86 0 1010.1 50.72 Agriculture 249.46 0 1200.0 224.38 Green 1654.3 0 2100 250.88 Green Residential 84.98 0 1094.5 140.75 Impervious 94.41 0 1096.5 137.23 Urban 3.86 0 732.5 21.42 Water 2.18 0 140.26 7.89 Agriculture 6.21 0 134.59 10.77 Green 36.94 0 157.75 31.77 Residential Residential 965.03 0 1051.7 30.89 Impervious 46.96 0 153.86 30.52 Urban 2.15 0 98.67 6.10 Water 5.75 0 442.03 23.67 Agriculture 40.59 0 393.26 57.36 Green 90.17 0 450.72 82.55 Impervious Residential 94.86 0 420.52 71.81 Impervious 1117.6 0 1364.3 88.93 Urban 25.60 0 414.49 42.19 Water 5.04 0 330.72 20.84 Agriculture 37.47 0 440.82 47.57 Green 49.88 0 417.13 51.16 Urban Residential 54.45 0 312.89 40.72 Impervious 236.68 0 510.20 88.91 Urban 1079.2 0 1456.1 104.07

Table D.11. Area statistics for the independent variables on May 13, 2005.

262

Elasticity (ε ) Central land Neighboring i uses land uses Standard Mean Minimum Maximum deviation Water -0.4502 -0.6916 -0.1402 0.1148 Agriculture 0.0086 0.0000 0.0897 0.0122 Water Green 0.0393 0.0000 0.1921 0.0366 Residential 0.0353 0.0000 0.3411 0.0406 Impervious 0.0351 0.0000 0.2537 0.0425 Water -0.0019 -0.3892 0.0000 0.0109 Agriculture 0.0501 0.0271 0.0800 0.0049 Agriculture Green -0.0284 -0.1091 0.0000 0.0183 Residential 0.0038 0.0000 0.1416 0.0092 Impervious -0.0018 -0.0329 0.0000 0.0033 Water -0.0024 -0.2260 0.0000 0.0098 Agriculture 0.0497 0.0000 0.2547 0.0443 Green Green 0.2052 0.0848 0.3749 0.0402 Residential 0.0237 0.0000 0.3182 0.0383 Impervious 0.0268 0.0000 0.3077 0.0382 Water -0.0042 -0.3659 0.0000 0.0161 Agriculture 0.0027 0.0000 0.0611 0.0048 Residential Green 0.0142 0.0000 0.0812 0.0128 Residential 1.1540 0.7495 2.5843 0.0798 Impervious 0.0703 0.0000 0.2453 0.0447 Agriculture 0.0280 0.0000 0.3258 0.0410 Green 0.0895 0.0000 0.5211 0.0851 Impervious Residential 0.1041 0.0000 0.4841 0.0785 Impervious 1.5229 0.8663 6.7037 0.1431 Urban 0.0271 0.0000 1.7961 0.0462 Agriculture 0.0276 -0.9955 2.9632 0.0385 Green 0.0505 -0.7139 2.1162 0.0553 Urban Residential 0.0489 -0.7502 1.8208 0.0379 Impervious 0.4172 -8.8941 24.7872 0.1906 Urban 0.8786 -27.5480 80.9727 0.5015 (a) Tj = RST

Table D.12. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on May 13, 2005. Continued.

263

Table D.12 continued.

Elasticity (ε ) Central land Neighboring i uses land uses Standard Mean Minimum Maximum deviation Water -0.4487 -0.6373 -0.2441 0.1138 Agriculture 0.0086 0.0000 0.0924 0.0122 Water Green 0.0391 0.0000 0.1617 0.0361 Residential 0.0351 0.0000 0.2968 0.0399 Impervious 0.0345 0.0000 0.2576 0.0417 Water -0.0019 -0.4540 0.0000 0.0109 Agriculture 0.0499 0.0340 0.0605 0.0033 Agriculture Green -0.0283 -0.0936 0.0000 0.0181 Residential 0.0038 0.0000 0.1388 0.0091 Impervious -0.0018 -0.0284 0.0000 0.0033 Water -0.0024 -0.2606 0.0000 0.0099 Agriculture 0.0495 0.0000 0.2280 0.0440 Green Green 0.2041 0.0953 0.2698 0.0364 Residential 0.0236 0.0000 0.2802 0.0380 Impervious 0.0267 0.0000 0.2809 0.0378 Water -0.0042 -0.3865 0.0000 0.0162 Agriculture 0.0027 0.0000 0.0613 0.0048 Residential Green 0.0141 0.0000 0.0650 0.0127 Residential 1.1508 0.9991 1.7449 0.0504 Impervious 0.0701 0.0000 0.2168 0.0443 Agriculture 0.0278 0.0000 0.3178 0.0411 Green 0.0891 0.0000 0.4716 0.0848 Impervious Residential 0.1037 0.0000 0.4675 0.0780 Impervious 1.5137 1.2578 2.5002 0.0706 Urban 0.0267 0.0000 0.4487 0.0441 Agriculture 0.0269 0.0000 0.3758 0.0358 Green 0.0491 0.0000 0.4428 0.0522 Urban Residential 0.0475 0.0000 0.2899 0.0349 Impervious 0.4058 0.0116 0.7084 0.1230 Urban 0.8451 0.5537 1.4733 0.1482

(b) Tj = Temperatures estimated with the regression models.

264

August 1, 2005.

Size of buffer (θ) p 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 1.1 0.623 0.638 0.637 0.630 0.619 1.2 0.621 0.637 0.638 0.633 0.624 1.3 0.619 0.636 0.639 0.635 0.628 1.4 0.617 0.635 0.639 0.637 0.631 1.5 0.614 0.633 0.639 0.638 0.634 1.6 0.611 0.631 0.638 0.638 0.636 1.8 0.604 0.625 0.634 0.637 0.637 (g) Water

Size of buffer (θ) p 9 * 9 11 * 11 13 * 13 15 * 15 17 * 17 21 * 21 0.7 0.475 0.482 0.481 0.475 0.466 0.447 0.8 0.474 0.482 0.482 0.477 0.470 0.452 0.9 0.472 0.482 0.483 0.480 0.473 0.457 1.0 0.471 0.482 0.484 0.481 0.476 0.462 1.1 0.469 0.481 0.484 0.483 0.479 0.467 1.2 0.467 0.479 0.484 0.484 0.481 0.462 1.3 0.464 0.477 0.483 0.484 0.482 0.475 1.5 0.458 0.472 0.480 0.482 0.480 0.479 (h) Agriculture

Size of buffer (θ) p 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 19 * 19 0.6 0.322 0.335 0.335 0.329 0.320 0.301 0.8 0.320 0.335 0.337 0.333 0.326 0.310 0.9 0.319 0.334 0.338 0.334 0.328 0.314 1.0 0.317 0.334 0.338 0.336 0.331 0.318 1.1 0.315 0.333 0.338 0.337 0.333 0.322 1.2 0.314 0.331 0.338 0.338 0.335 0.325 1.4 0.309 0.328 0.336 0.338 0.337 0.331 1.5 0.307 0.326 0.334 0.338 0.338 0.334 (i) Green Table D.13. R2 for various (θ, p) combinations for each area land-use model on August 1, 2005. Continued.

265

Table D.13 continued.

Size of buffer (θ) p 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 19 * 19 1.0 0.540 0.553 0.551 0.543 0.532 0.510 1.1 0.539 0.553 0.552 0.546 0.536 0.517 1.2 0.537 0.552 0.553 0.548 0.540 0.523 1.3 0.535 0.551 0.554 0.550 0.544 0.529 1.4 0.533 0.550 0.554 0.552 0.547 0.535 1.5 0.531 0.548 0.553 0.552 0.549 0.539 1.6 0.528 0.546 0.552 0.552 0.550 0.543 1.7 0.525 0.543 0.550 0.552 0.551 0.546 (j) Residential area

Size of buffer (θ) p 9 * 9 11 * 11 13 * 13 15 * 15 21 * 21 25 * 25 0.6 0.438 0.435 0.426 0.415 0.382 0.361 0.8 0.438 0.438 0.431 0.422 0.393 0.375 0.9 0.437 0.439 0.434 0.426 0.399 0.383 1.0 0.437 0.439 0.435 0.429 0.405 0.390 1.1 0.436 0.439 0.437 0.431 0.411 0.397 1.3 0.432 0.438 0.438 0.435 0.420 0.410 1.5 0.428 0.436 0.438 0.437 0.428 0.421 1.7 0.422 0.431 0.435 0.436 0.432 0.428 (k) Impervious area

Size of buffer (θ) p 13 * 13 17 * 17 21 * 21 23 * 23 25 * 25 27 * 27 0.9 0.259 0.258 0.255 0.254 0.248 0.248 1.0 0.259 0.259 0.258 0.256 0.254 0.252 1.1 0.259 0.260 0.260 0.259 0.257 0.255 1.2 0.258 0.261 0.261 0.260 0.259 0.258 1.3 0.257 0.261 0.262 0.262 0.261 0.260 1.4 0.255 0.260 0.262 0.262 0.262 0.261 1.5 0.253 0.259 0.261 0.262 0.262 0.261 1.6 0.251 0.257 0.260 0.261 0.261 0.261 1.7 0.248 0.254 0.258 0.259 0.259 0.259 (l) Urban area

266

September 2, 2005.

Size of buffer (θ) p 9 * 9 13 * 13 15 * 15 17 * 17 19 * 19 21 * 21 0.8 0.554 0.546 0.537 0.526 0.515 0.505 1.0 0.553 0.551 0.543 0.535 0.526 0.517 1.1 0.552 0.553 0.546 0.539 0.531 0.523 1.3 0.549 0.555 0.551 0.546 0.539 0.533 1.4 0.548 0.556 0.553 0.548 0.543 0.538 1.5 0.545 0.555 0.554 0.551 0.546 0.542 1.6 0.543 0.555 0.554 0.552 0.549 0.545 (a) Water

Size of buffer (θ) p 9 * 9 13 * 13 15 * 15 17 * 17 19 * 19 21 * 21 0.8 0.305 0.318 0.318 0.317 0.314 0.311 1.0 0.302 0.317 0.319 0.319 0.317 0.315 1.1 0.300 0.317 0.319 0.319 0.319 0.317 1.2 0.299 0.316 0.319 0.320 0.319 0.318 1.3 0.297 0.315 0.318 0.319 0.320 0.319 1.4 0.294 0.313 0.317 0.319 0.320 0.319 1.5 0.292 0.311 0.315 0.318 0.319 0.319 1.6 0.289 0.309 0.313 0.316 0.318 0.318 (b) Agriculture

Size of buffer (θ) p 7 * 7 11 * 11 15 * 15 19 * 19 23 * 23 27 * 27 1.0 0.342 0.364 0.361 0.351 0.340 0.329 1.1 0.340 0.364 0.362 0.354 0.344 0.334 1.2 0.338 0.364 0.364 0.357 0.349 0.339 1.4 0.334 0.362 0.365 0.362 0.356 0.349 1.5 0.331 0.360 0.366 0.364 0.359 0.354 1.6 0.329 0.358 0.365 0.365 0.362 0.357 1.7 0.326 0.356 0.364 0.365 0.363 0.360 1.8 0.323 0.353 0.362 0.364 0.364 0.362 (c) Green Table D.14. R2 for various (θ, p) combinations for each area land-use model on September 2, 2005. Continued.

267

Table D.14 continued.

Size of buffer (θ) p 7 * 7 9 * 9 11 * 11 13 * 13 15 * 15 17 * 17 0.8 0.344 0.356 0.357 0.352 0.345 0.337 0.9 0.342 0.356 0.358 0.354 0.347 0.340 1.0 0.341 0.355 0.358 0.355 0.350 0.343 1.1 0.340 0.354 0.358 0.356 0.352 0.346 1.2 0.338 0.353 0.358 0.357 0.353 0.349 1.3 0.336 0.352 0.357 0.357 0.355 0.351 1.4 0.334 0.350 0.356 0.357 0.356 0.353 1.5 0.332 0.348 0.355 0.357 0.356 0.354 1.6 0.330 0.346 0.353 0.356 0.355 0.355 (d) Residential area

Size of buffer (θ) p 9 * 9 11 * 11 13 * 13 17 * 17 21 * 21 33 * 33 0.5 0.305 0.307 0.303 0.292 0.281 0.244 0.6 0.305 0.307 0.304 0.294 0.283 0.249 0.7 0.305 0.308 0.306 0.297 0.286 0.253 0.8 0.304 0.308 0.307 0.299 0.289 0.258 0.9 0.304 0.308 0.307 0.301 0.292 0.263 1.0 0.303 0.308 0.308 0.303 0.295 0.269 1.1 0.302 0.307 0.308 0.304 0.298 0.274 1.2 0.301 0.307 0.308 0.306 0.300 0.279 1.3 0.299 0.306 0.308 0.307 0.302 0.283 (e) Impervious area

Size of buffer (θ) p 13 * 13 17 * 17 21 * 21 23 * 23 25 * 25 27 * 27 0.9 0.210 0.210 0.208 0.206 0.204 0.202 1.0 0.210 0.211 0.209 0.208 0.207 0.205 1.1 0.210 0.212 0.211 0.210 0.209 0.207 1.2 0.209 0.212 0.212 0.212 0.211 0.209 1.3 0.208 0.212 0.213 0.213 0.212 0.211 1.4 0.207 0.211 0.213 0.213 0.213 0.212 1.5 0.205 0.210 0.212 0.212 0.213 0.212 1.6 0.203 0.208 0.211 0.211 0.212 0.212 1.7 0.200 0.206 0.209 0.210 0.210 0.210 (f) Urban area

268

Central land uses Neighboring Parameters R2 t-statistics (Number of pixels) land uses (β's) (θ, p) Intercept 21.74 14.97 0.56 Water -0.0002 -0.17 (13, 1.4) Water Agriculture 0.008 6.35 (54,000) Green 0.01 9.48 * Residential 0.03 26.47 0.50 (11, 0.4) Impervious 0.03 19.85 Intercept 22.02 139.02 0.32 Water -0.002 -14.28 (17, 1.2) Agriculture Agriculture 0.0007 6.78 (666,895) Green 0.004 41.06 Residential 0.009 85.25 0.49* Impervious 0.01 94.57 (11, 0.4) Intercept -17.14 -30.36 0.37 Water 0.008 14.31 (15, 1.5) Green Agriculture 0.03 62.54 (1,032,003) Green 0.04 74.47 Residential 0.07 127.40 0.52* Impervious 0.07 130.89 (9, 0.4) Intercept 20.53 179.53 0.36 Water -0.002 -40.37 (11, 0.9) Residential Agriculture 0.0009 18.30 (309,864) Green 0.0009 20.69 Residential 0.003 79.49 0.32* Impervious 0.004 83.60 (9, 0.4) Intercept 15.42 188.37 0.31 Agriculture 0.001 59.97 (11, 0.7) Impervious Green 0.002 103.84 (461,516) Residential 0.002 149.56 Impervious 0.003 191.88 0.23* Urban 0.002 104.19 (13, 0.5) Intercept 8.39 6.10 0.21 Agriculture 0.008 7.35 (17, 1.1) Urban Green 0.01 13.43 (59,128) Residential 0.02 16.44 Impervious 0.04 36.91 0.09* Urban 0.008 8.94 (29, 0.8) *: Input variable with NDVI.

Table D.15. Regression results for the area models on September 2, 2005.

269

Land-use area (m2) Neighboring Central land uses Standard land uses Mean Minimum Maximum deviation Water 1040.6 0 1145.7 74.63 Agriculture 11.11 0 140.29 17.32 Green 49.64 0 241.76 50.24 Water Residential 19.45 0 214.75 25.53 Impervious 23.31 0 230.22 31.96 Urban 1.52 0 108.84 5.29 Water 3.64 0 485.10 16.78 Agriculture 1325.2 0 1652.7 175.52 Green 257.19 0 737.32 141.01 Agriculture Residential 17.22 0 608.80 37.62 Impervious 45.16 0 624.80 76.04 Urban 4.23 0 595.14 22.03 Water 1.89 0 145.67 6.97 Agriculture 36.67 0 176.05 31.66 Green 1010.4 0 1076.1 35.12 Green Residential 12.46 0 157.95 20.02 Impervious 14.02 0 153.89 19.55 Urban 0.622 0 91.26 2.97 Water 25.91 0 1662.8 94.48 Agriculture 77.52 0 1638.7 136.32 Green 444.48 0 1838.7 379.42 Residential Residential 1629.5 0 2691.1 360.81 Impervious 553.82 0 1793.8 358.87 Urban 27.28 0 1244.5 79.31 Water 52.41 0 4380.0 235.51 Agriculture 369.39 0 4049.6 565.73 Green 823.26 0 4499.5 827.41 Impervious Residential 903.99 0 4243.0 725.82 Impervious 3003.3 0 5399.5 900.25 Urban 247.02 0 4252.5 439.08 Water 9.86 0 733.36 44.66 Agriculture 77.34 0 1008.0 103.18 Green 98.94 0 908.49 110.81 Urban Residential 112.23 0 691.45 89.48 Impervious 509.97 0 1122.0 197.59 Urban 1291.1 0 2099.4 233.60

Table D.16. Area statistics for the independent variables on September 2, 2005.

270

Elasticity (ε ) Central land Neighboring i uses land uses Standard Mean Minimum Maximum deviation Water -0.0098 -0.0159 -0.0043 0.0013 Agriculture 0.0039 0.0000 0.0501 0.0061 Water Green 0.0248 0.0000 0.1380 0.0251 Residential 0.0260 0.0000 0.2688 0.0323 Impervious 0.0261 0.0000 0.2563 0.0345 Water -0.0003 -0.0440 0.0000 0.0015 Agriculture 0.0356 0.0171 0.0981 0.0066 Agriculture Green 0.0409 0.0000 0.1444 0.0222 Residential 0.0062 0.0000 0.1927 0.0131 Impervious 0.0187 0.0000 0.3951 0.0308 Water 0.0006 0.0000 0.0520 0.0023 Agriculture 0.0487 0.0000 0.4274 0.0433 Green Green 1.5616 0.9733 3.3834 0.1369 Residential 0.0312 0.0000 0.3884 0.0486 Impervious 0.0388 0.0000 0.6801 0.0529 Water -0.0022 -0.1649 0.0000 0.0082 Agriculture 0.0026 0.0000 0.0653 0.0047 Residential Green 0.0143 0.0000 0.0771 0.0128 Residential 0.1885 0.0835 0.4627 0.0399 Impervious 0.0729 0.0000 0.4314 0.0467 Agriculture 0.0137 0.0000 0.1813 0.0217 Green 0.0500 0.0000 0.3199 0.0520 Impervious Residential 0.0737 0.0000 0.4664 0.0589 Impervious 0.3121 0.0861 1.1160 0.0888 Urban 0.0158 0.0000 0.8978 0.0297 Agriculture 0.0114 -2.9064 2.3820 0.0258 Green 0.0264 -8.2040 7.8050 0.0668 Urban Residential 0.0345 -3.9650 3.3697 0.0371 Impervious 0.3069 -25.6248 24.5489 0.2599 Urban 0.3495 -38.6766 39.2415 0.4654 (a) Tj = RST

Table D.17. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on September 2, 2005.

Continued.

271

Table D.17 continued.

Elasticity (ε ) Central land Neighboring i uses land uses Standard Mean Minimum Maximum deviation Water -0.0097 -0.0116 -0.0067 0.0013 Agriculture 0.0039 0.0000 0.0495 0.0061 Water Green 0.0248 0.0000 0.1186 0.0249 Residential 0.0259 0.0000 0.2473 0.0320 Impervious 0.0259 0.0000 0.2257 0.0341 Water -0.0003 -0.0455 0.0000 0.0015 Agriculture 0.0354 0.0194 0.0466 0.0059 Agriculture Green 0.0408 0.0000 0.1129 0.0219 Residential 0.0062 0.0000 0.1922 0.0131 Impervious 0.0186 0.0000 0.2239 0.0303 Water 0.0006 0.0000 0.0578 0.0024 Agriculture 0.0485 0.0000 0.2434 0.0428 Green Green 1.5563 1.1475 1.7757 0.0979 Residential 0.0311 0.0000 0.3606 0.0484 Impervious 0.0387 0.0000 0.3705 0.0520 Water -0.0022 -0.1749 0.0000 0.0083 Agriculture 0.0026 0.0000 0.0580 0.0046 Residential Green 0.0142 0.0000 0.0641 0.0127 Residential 0.1877 0.0985 0.2995 0.0378 Impervious 0.0724 0.0000 0.2225 0.0457 Agriculture 0.0137 0.0000 0.1724 0.0218 Green 0.0498 0.0000 0.2919 0.0519 Impervious Residential 0.0732 0.0000 0.3465 0.0583 Impervious 0.3090 0.0947 0.5114 0.0799 Urban 0.0154 0.0000 0.2899 0.0277 Agriculture 0.0110 0.0000 0.1515 0.0146 Green 0.0256 0.0000 0.2324 0.0272 Urban Residential 0.0332 0.0000 0.1929 0.0241 Impervious 0.2951 0.0086 0.5223 0.0899 Urban 0.3319 0.2192 0.5893 0.0596 (b) Tj = Temperatures estimated with the regression models.

272

November 21, 2005.

Size of buffer (θ) p 9 * 9 11 * 11 13 * 13 15 * 15 17 * 17 19 * 19 1.1 0.158 0.156 0.154 0.152 0.149 0.146 1.3 0.158 0.158 0.156 0.155 0.153 0.150 1.4 0.158 0.158 0.157 0.156 0.154 0.152 1.5 0.158 0.159 0.158 0.157 0.155 0.154 1.6 0.157 0.159 0.158 0.158 0.157 0.156 1.7 0.157 0.159 0.159 0.158 0.158 0.157 1.8 0.157 0.159 0.159 0.159 0.158 0.158 1.9 0.156 0.158 0.159 0.159 0.159 0.158 (a) Water

Size of buffer (θ) p 25 * 25 33 * 33 37 * 37 41 * 41 45 * 45 49 * 49 1.2 0.055 0.055 0.054 0.053 0.053 0.052 1.4 0.056 0.057 0.056 0.056 0.054 0.054 1.6 0.057 0.058 0.058 0.058 0.058 0.058 1.8 0.056 0.058 0.059 0.059 0.059 0.059 1.9 0.056 0.058 0.059 0.059 0.059 0.059 2.0 0.056 0.058 0.059 0.059 0.059 0.059 2.1 0.055 0.057 0.058 0.059 0.059 0.059 2.2 0.054 0.056 0.057 0.058 0.058 0.058 (b) Agriculture

Size of buffer (θ) p 19 * 19 27 * 27 35 * 35 39 * 39 43 * 43 51 * 51 1.1 0.055 0.055 0.054 0.054 0.054 0.053 1.3 0.055 0.056 0.056 0.056 0.056 0.055 1.5 0.055 0.057 0.057 0.057 0.057 0.057 1.6 0.055 0.057 0.058 0.058 0.058 0.057 1.7 0.055 0.057 0.058 0.058 0.058 0.058 1.8 0.054 0.056 0.057 0.058 0.058 0.058 1.9 0.053 0.056 0.057 0.057 0.058 0.058 (c) Green Table D.18. R2 for various (θ, p) combinations for each area land-use model on November 21, 2005. Continued.

273

Table D.18 continued.

Size of buffer (θ) p 13 * 13 15 * 15 17 * 17 21 * 21 25 * 25 29 * 29 0.9 0.165 0.164 0.162 0.158 0.154 0.150 1.0 0.165 0.165 0.163 0.160 0.156 0.152 1.1 0.165 0.165 0.164 0.162 0.158 0.155 1.2 0.165 0.166 0.165 0.163 0.160 0.157 1.3 0.165 0.166 0.166 0.164 0.162 0.160 1.4 0.165 0.166 0.166 0.165 0.164 0.162 1.5 0.164 0.165 0.166 0.166 0.165 0.163 1.6 0.163 0.165 0.166 0.166 0.165 0.165 1.7 0.162 0.164 0.165 0.166 0.166 0.165 1.8 0.161 0.163 0.164 0.165 0.165 0.165 (d) Residential area

Size of buffer (θ) p 13 * 13 17 * 17 21 * 21 25 * 25 29 * 29 33 * 33 0.9 0.109 0.111 0.110 0.108 0.106 0.103 1.0 0.109 0.111 0.111 0.109 0.107 0.105 1.1 0.109 0.111 0.111 0.110 0.109 0.107 1.2 0.108 0.111 0.112 0.111 0.110 0.108 1.3 0.107 0.110 0.112 0.112 0.111 0.110 1.4 0.106 0.110 0.111 0.112 0.111 0.111 1.5 0.105 0.109 0.111 0.112 0.111 0.111 1.6 0.104 0.108 0.110 0.111 0.111 0.111 1.8 0.100 0.106 0.107 0.108 0.109 0.109 (e) Impervious area

Size of buffer (θ) p 9 * 9 11 * 11 13 * 13 17 * 17 21 * 21 23 * 23 0.9 0.169 0.172 0.172 0.167 0.161 0.158 1.0 0.168 0.172 0.173 0.171 0.164 0.162 1.1 0.168 0.172 0.173 0.171 0.167 0.165 1.2 0.167 0.172 0.174 0.173 0.169 0.168 1.3 0.166 0.171 0.173 0.173 0.171 0.170 1.4 0.165 0.170 0.173 0.174 0.173 0.172 1.5 0.163 0.169 0.172 0.174 0.174 0.173 1.6 0.161 0.168 0.171 0.173 0.174 0.174 1.7 0.160 0.166 0.169 0.172 0.173 0.174 1.8 0.157 0.164 0.167 0.170 0.172 0.173 (f) Urban area

274

Central land uses Neighboring Parameters R2 t-statistics (Number of pixels) land uses (β's) (θ, p) Intercept 41.67 16.97 0.16 Water -0.03 -14.35 (11, 1.5) Water Agriculture -0.02 -8.78 (54,142) Green -0.03 -12.73 * Residential -0.01 -6.23 0.13 (9, 0.2) Impervious -0.01 -4.84 Intercept -40.02 -42.96 0.06 Water -0.03 -24.34 (37, 1.8) Agriculture Agriculture 0.05 53.14 (637,392) Green 0.03 31.26 Residential 0.06 55.51 0.03* Impervious 0.03 28.29 (41, 0.1) Intercept -24.52 -32.77 0.06 Water -0.01 -17.54 (35, 1.7) Green Agriculture 0.04 59.99 (1,004,076) Green 0.03 43.48 Residential 0.04 55.81 0.09* Impervious 0.04 58.99 (7, 0.2) Intercept -7.34 -43.67 0.17 Water 0.002 14.49 (17, 1.3) Residential Agriculture 0.01 77.80 (309,452) Green 0.008 62.69 Residential 0.01 101.22 0.15* Impervious 0.01 98.45 (13, 0.4) Intercept -0.12 -1.31 0.11 Agriculture 0.003 49.54 (21, 1.2) Impervious Green 0.003 57.03 (459,881) Residential 0.004 79.32 Impervious 0.006 112.31 0.07* Urban -0.0002 -3.00 (25, 0.6) Intercept 8.26 6.61 0.17 Agriculture 0.004 4.27 (13, 1.2) Urban Green -0.002 -1.66 (59,169) Residential -0.002 -2.00 Impervious 0.01 16.73 0.12* Urban -0.004 -4.37 (23, 0.7) *: Input variable with NDVI.

Table D.19. Regression results for the area models on November 21, 2005.

275

Land-use area (m2) Neighboring Central land uses Standard land uses Mean Minimum Maximum deviation Water 985.61 0 1041.6 42.43 Agriculture 5.28 0 77.12 8.95 Green 26.40 0 141.11 28.46 Water Residential 10.97 0 126.30 15.08 Impervious 12.59 0 135.56 18.57 Urban 0.71 0 61.88 2.80 Water 0.38 0 42.53 1.41 Agriculture 939.36 0 970.80 15.13 Green 24.84 0 67.43 11.81 Agriculture Residential 1.83 0 53.12 3.43 Impervious 4.58 0 54.26 6.82 Urban 0.44 0 55.05 1.95 Water 1.43 0 84.74 4.14 Agriculture 25.43 0 110.14 18.69 Green 966.38 0.05 1011.5 19.72 Green Residential 8.67 0 90.74 12.23 Impervious 10.36 0 93.05 12.20 Urban 0.637 0 57.02 2.07 Water 6.74 0 424.96 22.44 Agriculture 22.70 0 396.18 34.94 Green 116.34 0 466.33 91.53 Residential Residential 1079.7 0 1331.3 85.96 Impervious 141.16 0 450.58 85.83 Urban 7.96 0 314.75 19.54 Water 11.78 0 842.55 45.45 Agriculture 82.95 0 750.20 109.88 Green 184.00 0 848.49 155.18 Impervious Residential 182.31 0 766.22 131.85 Impervious 1297.3 0 1770.3 163.06 Urban 49.36 0 758.95 76.73 Water 3.63 0 331.80 19.27 Agriculture 34.27 0 554.99 51.37 Green 36.74 0 417.72 48.07 Urban Residential 46.28 0 315.07 41.94 Impervious 247.30 0 564.12 104.59 Urban 1121.9 0 1490.1 125.57

Table D.20. Area statistics for the independent variables on November 21, 2005.

276

Elasticity (ε ) Central land Neighboring i uses land uses Standard Mean Minimum Maximum deviation Water -4.6516 -121.5235 128.0615 6.2100 Agriculture -0.0145 -3.1156 3.0305 0.0742 Water Green -0.1008 -10.5099 10.6885 0.3821 Residential -0.0209 -2.3938 2.0227 0.0476 Impervious -0.0200 -0.7637 2.8501 0.0389 Water -0.0018 -1.5727 1.7124 0.0133 Agriculture 5.5026 -188.9902 179.9776 6.1746 Agriculture Green 0.0858 -7.1115 6.1916 0.1219 Residential 0.0130 -4.3684 4.0099 0.0416 Impervious 0.0175 -4.3946 4.3692 0.0550 Water -0.0026 -1.5886 1.7423 0.0187 Agriculture 0.1338 -15.5250 13.4622 0.1826 Green Green 3.7134 -124.4964 118.4576 5.6282 Residential 0.0421 -9.2402 9.1114 0.1373 Impervious 0.0593 -9.9355 10.5060 0.1684 Water 0.0020 -0.9419 1.1025 0.0113 Agriculture 0.0298 -5.7784 7.9528 0.0892 Residential Green 0.1070 -12.0678 10.8197 0.2979 Residential 1.4877 -55.9922 54.0553 2.3303 Impervious 0.2073 -15.2837 14.6345 0.3437 Agriculture 0.0270 -5.7653 4.9978 0.0738 Green 0.0665 -8.1960 7.8702 0.1780 Impervious Residential 0.0841 -7.6852 7.1793 0.1633 Impervious 0.8619 -34.3672 32.9837 1.3016 Urban -0.0011 -0.3854 0.3968 0.0055 Agriculture 0.0158 -3.9640 2.7545 0.0851 Green -0.0068 -1.6185 1.5061 0.0406 Urban Residential -0.0101 -0.9406 1.1098 0.0395 Impervious 0.4076 -22.0267 22.5805 1.1429 Urban -0.4508 -20.0429 21.0632 1.8784 (a) Tj = RST

Table D.21. Elasticity statistics when (a) Tj = RST and (b) Tj = estimated temperatures on November 21, 2005. Continued.

277

Table D.21 continued.

Elasticity (ε ) Central land Neighboring i uses land uses Standard Mean Minimum Maximum deviation Water -4.7554 -5.4990 -3.0222 0.5546 Agriculture -0.0157 -0.2183 0.0000 0.0264 Water Green -0.1105 -0.6101 0.0000 0.1202 Residential -0.0210 -0.2074 0.0000 0.0272 Impervious -0.0200 -0.1757 0.0000 0.0277 Water -0.0018 -0.2882 0.0000 0.0069 Agriculture 5.4180 4.7369 8.3893 0.1314 Agriculture Green 0.0847 0.0000 0.2496 0.0425 Residential 0.0129 0.0000 0.3332 0.0239 Impervious 0.0172 0.0000 0.2197 0.0260 Water -0.0026 -0.2877 0.0000 0.0086 Agriculture 0.1320 0.0000 0.5229 0.0939 Green Green 3.6681 3.0515 7.0018 0.2064 Residential 0.0416 0.0000 0.4280 0.0579 Impervious 0.0578 0.0000 0.4836 0.0667 Water 0.0019 0.0000 0.1849 0.0070 Agriculture 0.0293 0.0000 0.4957 0.0456 Residential Green 0.1056 0.0000 0.4874 0.0889 Residential 1.4727 1.1298 2.1493 0.1013 Impervious 0.2044 0.0000 0.5979 0.1202 Agriculture 0.0264 0.0000 0.2640 0.0361 Green 0.0646 0.0000 0.3239 0.0570 Impervious Residential 0.0830 0.0000 0.3515 0.0588 Impervious 0.8405 0.6128 1.0398 0.0757 Urban -0.0010 -0.0242 0.0000 0.0017 Agriculture 0.0186 0.0000 0.2859 0.0275 Green -0.0077 -0.1092 0.0000 0.0107 Urban Residential -0.0109 -0.0946 0.0000 0.0099 Impervious 0.4384 0.0000 0.6239 0.1103 Urban -0.5907 -1.9566 -0.2564 0.2617

(b) Tj = Temperatures estimated with the regression models.

278

APPENDIX E

WIND VARIATIONS AT THE FOUR MEASURING

STATIONS.

279

February 25, 2006.

12 10 8 OSU 6 Bolton 4 CIA 2 Wind speed, m/sec Wind RBA 0 0 6 12 18 24 Time

CIA: Columbus International Airport. RBA: RickenBacker Airport. Figure E.1. Hourly wind speed measurement at the four measuring stations on February 25, 2006.

April 11, 2005.

8 7 6 5 OSU 4 3 Bolton 2 CIA Wind speed, m/sec Wind 1 RBA 0 0 6 12 18 24 Time

CIA: Columbus International Airport. RBA: RickenBacker Airport. Figure E.2. Hourly wind speed measurement at the four measuring stations on April 11, 2005.

280

May 13, 2005.

8 7 6 5 OSU 4 3 Bolton 2 CIA

Wind speed, m/sec Wind 1 RBA 0 0 6 12 18 24 Time

CIA: Columbus International Airport. RBA: RickenBacker Airport. Figure E.3. Hourly wind speed measurement at the four measuring stations on May 13, 2005.

August 01, 2005.

4.5 4 3.5 3 2.5 OSU 2 Bolton 1.5 1 CIA Wind speed, m/sec Wind 0.5 RBA 0 0 6 12 18 24 Time

CIA: Columbus International Airport. RBA: RickenBacker Airport. Figure E.4. Hourly wind speed measurement at the four measuring stations on August 1, 2005. 281

September 2, 2005.

9 8 7 6 5 OSU 4 Bolton 3 2 CIA

Wind speed, m/sec Wind 1 RBA 0 0 6 12 18 24 Time

CIA: Columbus International Airport. RBA: RickenBacker Airport. Figure E.5. Hourly wind speed measurement at the four measuring stations on September 2, 2005.

November 21, 2005.

9 8 7 6 5 OSU 4 Bolton 3 2 CIA Wind speed, m/sec Wind 1 RBA 0 0 6 12 18 24 Time

CIA: Columbus International Airport. RBA: RickenBacker Airport. Figure E.6. Hourly wind speed measurement at the four measuring stations on November 21, 2005.

282

APPENDIX F

ANALYSIS OF THE REMOTELY-SENSED TEMPERATURE

(RST) AND NDVI VARIABLE.

283

February 25, 2006.

(a) All land uses.

Figure F.1. Plotting of NDVI and RST (°C) observations on February 25, 2006.

Continued.

284

Figure F.1 continued.

(b) Individual land uses

285

NDVI

Positive Zero Negative Positive 2,391,986 40,280 197,097 RST Zero 0 0 0 Negative 856 84 3,502 (a) All land uses.

NDVI Water Agriculture Positive Zero Negative Positive Zero Negative Positive 13,357 1,410 40,110 669,688 9,365 11,131 RST Zero 0 0 0 0 0 0 Negative 0 0 0 52 5 22 (a) Water and agriculture

NDVI Green Residential Positive Zero Negative Positive Zero Negative Positive 1,045,050 4,794 5,912 296,210 4,725 9,595 RST Zero 0 0 0 0 0 0 Negative 7 5 9 48 0 14 (b) Green and residential

NDVI Impervious Urban Positive Zero Negative Positive Zero Negative Positive 355,760 17,249 89,526 11,921 2,737 40,823 RST Zero 0 0 0 0 0 0 Negative 335 15 189 414 59 3,268 (c) Impervious and urban

Table F.1. Cross-tabulations between remotely sensed temperature (RST, °C) and NDVI on February 25, 2006.

286

Land uses NDVI Number of RST (°C) Standard (Mean values observations deviation temperature) Mean Minimum Maximum Positive 13,357 8.45 1.85 16.04 1.70 Water Zero 1,410 8.06 2.89 15.11 1.67 (5.68°C) Negative 40,110 4.71 0.27 21.42 2.71 Positive 669,740 9.54 -8.61 16.04 1.39 Agriculture Zero 9,370 9.90 -3.52 15.11 1.65 (9.54°C) Negative 11,153 9.23 -5.19 15.11 1.82 Positive 1,045,057 9.67 -0.80 15.11 1.20 Green Zero 4,799 9.52 -1.33 14.65 1.71 (9.68°C) Negative 5,921 8.61 -0.80 14.18 2.11 Positive 296,258 10.66 -6.31 16.49 1.04 Residential Zero 4,725 10.22 0.80 15.11 1.37 (10.68°C) Negative 9,609 9.79 -2.97 14.65 1.73 Positive 356,095 10.45 -13.40 18.31 1.38 Impervious Zero 17,264 10.37 -10.97 18.31 1.65 (10.49°C) Negative 89,715 10.20 -11.57 21.86 2.19 Positive 12,335 8.80 -15.26 19.21 3.43 Urban Zero 2,796 9.37 -13.40 17.41 3.07 (8.90°C) Negative 44,091 8.16 -25.23 20.10 5.21

Table F.2. Statistics on remotely sensed temperature (RST, °C) cross-tabulated with positive, zero, and negative NDVI values on February 25, 2006.

287

April 11, 2005.

(a) All land uses.

Figure F.2. Plotting of NDVI and RST (°C) observations on April 11, 2005.

Continued. 288

Figure F.2 continued.

(b) Individual land uses.

289

NDVI

Positive Zero Negative Positive 2,476,227 14,757 142,639 RST Zero 0 0 0 Negative 5 1 176 (b) The whole area.

NDVI Water Agriculture Positive Zero Negative Positive Zero Negative Positive 17,031 732 37,114 682,798 2,083 5,382 RST Zero 0 0 0 0 0 0 Negative 0 0 0 0 0 0 (d) Water and agriculture

NDVI Green Residential Positive Zero Negative Positive Zero Negative Positive 1,052,935 707 2,126 306,025 968 3,602 RST Zero 0 0 0 0 0 0 Negative 0 0 0 0 0 0 (e) Green and residential

NDVI Impervious Urban Positive Zero Negative Positive Zero Negative Positive 397,406 7,992 57,676 20,032 2,275 36,739 RST Zero 0 0 0 0 0 0 Negative 0 0 0 5 1 176 (f) Impervious and urban

Table F.3. Cross-tabulations between remotely sensed temperature (RST, °C) and NDVI on April 11, 2005.

290

Land uses NDVI Number of RST (°C) Standard (Mean values observations deviation temperature) Mean Minimum Maximum Positive 17,031 20.11 11.35 35.54 2.55 Water Zero 732 18.97 11.35 32.76 2.26 (16.55°C) Negative 37,114 14.96 8.44 43.59 3.49 Positive 682,798 21.86 4.44 30.73 1.56 Agriculture Zero 2,083 22.43 15.11 29.50 1.87 (21.83°C) Negative 5,382 21.98 10.39 31.55 2.15 Positive 1,052,935 21.74 11.83 31.55 1.58 Green Zero 707 21.00 12.78 28.68 2.51 (21.74°C) Negative 2,126 19.31 10.39 28.26 2.95 Positive 306,025 23.73 9.42 33.96 1.63 Residential Zero 965 23.16 13.72 30.32 2.41 (23.75°C) Negative 3,602 22.15 9.90 31.55 2.93 Positive 397,406 23.66 2.38 40.58 2.26 Impervious Zero 7,992 24.65 8.44 38.28 2.80 (23.80°C) Negative 57,676 24.66 1.33 45.81 3.85 Positive 20,037 23.10 -3.51 38.66 3.91 Urban Zero 2,276 24.27 -1.87 37.50 3.75 (23.27°C) Negative 36,915 22.70 -12.78 42.84 5.95

Table F.4. Statistics on remotely sensed temperature (RST, °C) cross-tabulated with positive, zero, and negative NDVI values on April 11, 2005.

291

May 13, 2005

(a) All land uses.

Figure F.3. Plotting of NDVI and RST (°C) observations on May 13, 2005.

Continued.

292

Figure F.3 continued.

(b) Individual land uses.

293

NDVI

Positive Zero Negative Positive 2,543,058 9,083 81,663 RST Zero 0 0 0 Negative 0 0 1 (a) The whole area.

NDVI Water Agriculture Positive Zero Negative Positive Zero Negative Positive 25,519 483 28,875 688,817 508 938 RST Zero 0 0 0 0 0 0 Negative 0 0 0 0 0 0 (b) Water and agriculture

NDVI Green Residential Positive Zero Negative Positive Zero Negative Positive 1,055,213 124 440 309,934 166 492 RST Zero 0 0 0 0 0 0 Negative 0 0 0 0 0 0 (c) Green and residential

NDVI Impervious Urban Positive Zero Negative Positive Zero Negative Positive 431,748 5,062 26,264 31,827 2,740 24,654 RST Zero 0 0 0 0 0 0 Negative 0 0 0 0 0 1 (d) Impervious and urban

Table F.5. Cross-tabulations between remotely sensed temperature (RST, °C) and NDVI on May 13, 2005.

294

Land uses NDVI Number of RST (°C) Standard (Mean values observations deviation temperature) Mean Minimum Maximum Positive 25,591 19.70 13.72 34.36 2.19 Water Zero 483 18.94 14.18 34.36 2.46 (17.69°C) Negative 28,875 16.05 12.30 45.81 2.24 Positive 688,817 22.23 11.83 31.95 1.69 Agriculture Zero 508 22.57 17.41 27.01 1.59 (22.20°C) Negative 938 21.82 14.18 31.95 2.72 Positive 1,055,213 21.68 11.83 30.73 1.74 Green Zero 124 21.65 15.58 27.43 1.97 (21.66°C) Negative 440 18.60 14.18 26.16 2.67 Positive 309,934 23.75 11.83 33.96 1.62 Residential Zero 166 22.64 14.18 28.26 2.29 (23.78°C) Negative 492 21.51 14.18 28.26 2.96 Positive 431,748 24.03 8.93 42.46 2.14 Impervious Zero 5,062 25.46 11.83 42.84 2.93 (24.08°C) Negative 26,264 25.23 11.83 48.35 4.15 Positive 31,827 23.96 7.45 40.58 3.18 Urban Zero 2,740 24.58 8.44 40.96 3.56 (23.93°C) Negative 24,655 23.43 -0.80 42.46 5.13

Table F.6. Statistics on remotely sensed temperature (RST, °C) cross-tabulated with positive, zero, and negative NDVI values on May 13, 2005.

295

August 1, 2005.

(a) All land uses.

Figure F.4. Plotting of NDVI and RST (°C) observations on August 1, 2005.

Continued.

296

Figure F.4 continued.

(b) Individual land uses.

297

NDVI

Positive Zero Negative Positive 2,513,981 8,915 110,909 RST Zero 0 0 0 Negative 0 0 0 (a) The whole area.

NDVI Water Agriculture Positive Zero Negative Positive Zero Negative Positive 26,636 386 27,855 685,904 986 3,373 RST Zero 0 0 0 0 0 0 Negative 0 0 0 0 0 0 (b) Water and agriculture

NDVI Green Residential Positive Zero Negative Positive Zero Negative Positive 1,055,771 4 2 309,868 178 546 RST Zero 0 0 0 0 0 0 Negative 0 0 0 0 0 0 (c) Green and residential

NDVI Impervious Urban Positive Zero Negative Positive Zero Negative Positive 414,723 5,216 43,135 21,079 2,145 35,998 RST Zero 0 0 0 0 0 0 Negative 0 0 0 0 0 0 (d) Impervious and urban

Table F.7. Cross-tabulations between remotely sensed temperature (RST, °C) and NDVI on August 1, 2005.

298

Land uses NDVI Number of RST (°C) Standard (Mean values observations deviation temperature) Mean Minimum Maximum Positive 26,636 26.69 21.86 40.58 2.18 Water Zero 386 26.74 23.17 42.84 2.60 (25.59°C) Negative 27,855 24.52 21.86 51.92 1.93 Positive 685,904 27.26 18.31 40.58 2.46 Agriculture Zero 986 32.13 23.60 37.89 1.71 (27.29°C) Negative 3,373 32.11 25.74 41.71 1.78 Positive 1,055,771 28.38 21.86 38.66 2.45 Green Zero 4 29.07 27.43 32.76 2.48 (28.38°C) Negative 2 26.00 25.74 28.26 1.78 Positive 309,868 31.58 19.21 42.84 2.10 Residential Zero 178 31.27 26.16 39.05 2.10 (31.58°C) Negative 546 30.93 24.46 36.33 2.03 Positive 414,723 32.36 16.04 48.35 2.23 Impervious Zero 5,216 33.90 19.66 46.90 2.74 (32.55°C) Negative 43,135 34.16 19.21 52.62 3.40 Positive 21,079 32.7 14.18 47.63 3.09 Urban Zero 2,145 33.78 16.49 45.07 3.18 (32.58°C) Negative 35,998 32.40 6.96 48.35 4.71

Table F.8. Statistics on remotely sensed temperature (RST, °C) cross-tabulated with positive, zero, and negative NDVI values on August 1, 2005.

299

September 2, 2005.

(a) All land uses.

Figure F.5. Plotting of NDVI and RST (°C) observations on September 2, 2005.

Continued.

300

Figure F.5 continued.

(b) Individual land uses.

301

NDVI

Positive Zero Negative Positive 2,518,238 9,880 105,669 RST Zero 0 0 0 Negative 0 0 18 (a) The whole area.

NDVI Water Agriculture Positive Zero Negative Positive Zero Negative Positive 26,260 463 28,154 685,419 1,079 3,765 RST Zero 0 0 0 0 0 0 Negative 0 0 0 0 0 0 (b) Water and agriculture

NDVI Green Residential Positive Zero Negative Positive Zero Negative Positive 1,055,409 129 238 309,620 226 746 RST Zero 0 0 0 0 0 0 Negative 0 0 0 0 0 0 (c) Green and residential

NDVI Impervious Urban Positive Zero Negative Positive Zero Negative Positive 417,659 5,701 39,714 23,871 2,282 33,052 RST Zero 0 0 0 0 0 0 Negative 0 0 0 0 0 18 (d) Impervious and urban

Table F.9. Cross-tabulations between remotely sensed temperature (RST, °C) and NDVI on September 2, 2005.

302

Land uses NDVI Number of RST (°C) Standard (Mean values observations deviation temperature) Mean Minimum Maximum Positive 26,260 24.45 15.11 41.33 1.89 Water Zero 463 24.06 15.58 36.72 2.16 (23.34°C) Negative 28,154 22.52 15.58 49.43 1.74 Positive 685,419 24.49 10.39 36.33 1.84 Agriculture Zero 1,079 25.79 14.18 33.56 1.73 (24.51°C) Negative 3,765 25.87 16.95 33.96 1.77 Positive 1,055,409 25.41 10.39 35.15 1.84 Green Zero 129 25.97 22.73 29.50 1.29 (25.41°C) Negative 238 25.21 21.86 30.32 1.33 Positive 309,620 28.38 11.83 39.81 2.14 Residential Zero 226 27.87 24.03 33.16 1.92 (28.45°C) Negative 746 27.81 21.42 36.72 2.17 Positive 417,659 28.55 8.44 44.33 2.76 Impervious Zero 5,701 29.82 12.78 43.59 3.46 (28.78°C) Negative 39,714 30.33 12.78 50.86 3.89 Positive 23,871 27.84 5.95 42.09 4.46 Urban Zero 2,282 29.18 7.94 42.09 4.33 (28.14°C) Negative 33,070 27.80 -3.52 46.54 6.08

Table F.10. Statistics on remotely sensed temperature (RST, °C) cross-tabulated with positive, zero, and negative NDVI value on September 2, 2005.

303

November 2, 2005.

(a) All land uses.

Figure F.6. Plotting of NDVI and RST (°C) observations on November 2, 2005.

Continued.

304

Figure F.6 continued.

(b) Individual land uses.

305

NDVI

Positive Zero Negative Positive 2,450,408 34,813 135,924 RST Zero 0 0 0 Negative 9259 164 3,237 (a) The whole area.

NDVI Water Agriculture Positive Zero Negative Positive Zero Negative Positive 17,637 1,521 35,321 671,491 10,094 7,097 RST Zero 0 0 0 0 0 0 Negative 273 36 89 1,548 14 19 (b) Water and agriculture

NDVI Green Residential Positive Zero Negative Positive Zero Negative Positive 1,045,625 3,538 2,494 305,002 1,779 2,698 RST Zero 0 0 0 0 0 0 Negative 4,095 8 8 1,111 1 1 (c) Green and residential

NDVI Impervious Urban Positive Zero Negative Positive Zero Negative Positive 392,055 13,892 55,451 18,598 3,989 32,863 RST Zero 0 0 0 0 0 0 Negative 1,535 28 113 697 77 3,007 (d) Impervious and urban

Table F.11. Cross-tabulations between remotely sensed temperature (RST, °C) and NDVI on November 21, 2005.

306

Land uses NDVI Number of RST (°C) Standard (Mean values observations deviation temperature) Mean Minimum Maximum Positive 17,910 7.49 -4.07 16.04 1.68 Water Zero 1,557 7.13 -2.97 13.72 1.82 (7.16°C) Negative 35,410 6.91 -3.52 23.60 1.36 Positive 673,039 8.86 -6.88 14.65 1.31 Agriculture Zero 10,108 8.59 -3.52 12.78 1.37 (8.92°C) Negative 7,116 8.37 -2.97 14.18 1.38 Positive 1,049,720 8.48 -5.19 15.11 1.37 Green Zero 3,546 8.18 -4.07 11.83 1.38 (8.58°C) Negative 2,502 8.00 -3.52 11.83 1.38 Positive 306,113 9.08 -5.19 16.95 1.36 Residential Zero 1,780 8.80 -1.87 15.58 1.31 (9.19°C) Negative 2,699 8.50 -0.26 15.58 1.35 Positive 393,590 9.13 -9.79 21.42 1.58 Impervious Zero 13,920 9.22 -7.46 20.98 1.70 (9.27°C) Negative 55,564 9.39 -9.20 25.31 2.13 Positive 19,295 7.95 -15.88 19.66 3.18 Urban Zero 4,066 8.44 -15.26 19.66 2.85 (8.08°C) Negative 35,870 7.38 -24.52 21.42 4.98

Table F.12. Statistics on remotely sensed temperature (RST, °C) cross-tabulated with positive, zero, and negative NDVI value on November 2, 2005.

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APPENDIX G

LAND-USE OPTIMIZATION

308

A land-use optimization model is presented in this section, using the mathematical relationships between local temperatures and land-use areas estimated in Equations (6.3) to (6.8).This model takes the form of a quadratic program, with linear constraints. It allocates land uses to cells in a grid while minimizing a function of local temperatures.

To illustrate the problem, consider a rectangular lattice made of N * M cells (i =

1→N, j = 1→M), and a set of K land uses (k = 1→K). Figure G.1 presents such a lattice for M = N = 7. Consider the following binary decision variables:

⎧1 if land use k isassigned tocell (i, j) xijk = ⎨ (G.1) ⎩0 if not

Assume that the total number of cells for land use k (Nk) is fixed. In addition, one and only one land use must be assigned to any given cell (i, j). The constraints are then:

∑∑ xijk = N k ∀k (G.2) ij

∑ xijk = 1 ∀(i, j) (G.3) k

For the sake of simplicity, suppose that all land uses have the same buffer size 5 * 5 and the same distance exponent p. The area where land uses can be allocated is the blue sub-lattice (i = 3→5, j = 3→5) in Figure G.1. Consider a cell

(i, j) in this smaller lattice, and assume that it is occupied by land use q. One can compute the temperature Tijq at (i, j) as a linear function of the binary variables xijk. For example, the temperature at cell (3, 3) is computed as:

5 5 K Area T x [ ] 33q = βqo + ∑∑∑ ijk ⋅ βqk ⋅ p (G.4) ij===1 11k d33ij

309 where βqo and βqk are the regression coefficients linking neighboring land use areas to the

central cell temperature [see Equations (6.3)-(6.8)], d33ij is the distance between the centroids of cells (3, 3) and (i, j), p is the distance exponent, and Area is the area of any cell. Similarly, the temperature at cell (5, 5) with land use q is estimated as:

7 7 K Area T x [ ] 55q = βqo + ∑∑∑ ijk ⋅ βqk ⋅ p (G.5) ij===3 31k d55ij

j →

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (1, 7)

(2, 1)

Land use: q

i ↓

(5, 1) Land use: q

(7, 1) (7, 2) (7, 7)

Figure G.1. Simple lattice for the optimization model.

310

More generally, let (u, v) be the indices for a central cell in the blue lattice in

Figure G.1. The temperature at (u, v) for land use q is then:

u+2 v+2 K Area T x [ ] uvq = βqo + ∑∑∑ijk ⋅ βqk ⋅ p (G.6) i=u−2 j==v−21k duvij

Clearly, the temperature Tuvq is relevant only if land use q is actually assigned to (u, v) or equivalently, if xuvq = 1. As we do not know which land use is assigned to (u, v), the temperature at (u, v) must be formulated in a way that accounts for all possibilities.

Hence:

K Tuv = ∑Tuvq ⋅ xuvq (G.7) q=1

The products in Equation (G.7) will be equal to zero, except for the endogenously selected land use (i.e., xuvq = 1). If the goal is to minimize the overall average temperature in the lattice, then the problem becomes:

K Minimize T = ∑Tuv = ∑∑Tuvq ⋅ xuvq (G.8) u,v u,1v q= subject to constraints (G.2) and (G.3). As Tuvq is a linear function of the basic assignment variables xijk, the objective function in Equation (G.8) is quadratic in binary variables.

Alternatively, the goal might be to minimize the average temperature for a given land use q, with:

Minimize T q = ∑Tuvq ⋅ xuvq (G.9) u,v

311

Yet, another goal might be to minimize a weighted function of temperatures, with:

K Minimize T = ∑∑wq ⋅Tuvq ⋅ xuvq (G.10) u,1v q= where wq is the weight for land-use q temperature.

Once the proper constraints are generated, a variety of objective functions can be considered, as illustrated in Equations (G.8) to (G.10). Moreover, there can be other constraints in a land-use optimization model, such as contiguity or compactness for land uses, and minimum /maximum numbers of cells for some land uses across the whole urban area. Also, climatic/UHI goals could be combined with other socio-economic and environmental factors in the objective function.

Quadratic integer programs are very difficult to solve, and the above problem would have a very large numbers of variables for any real-world case study. Thus, a search for heuristic methods producing good solutions with acceptable computing time would be very useful. Work in this direction could start by transforming the binary variables into continuous and bounded variables, with:

0 ≤ xijk ≤ 1 (G.11)

Each cell could then be occupied by several land uses, and xijk would represent the share of cell (i, j) occupied by land use k. The problem would then be transformed into a continuous quadratic optimization problem, for which solution algorithms are available.

312