Modification of current land uses in Sub-areas 1 to 4. ..... Conduction is the transfer and distribution of heat energy from atom to atom within a ...... in overhead wires. ...... 0.720. 0.738. 0.737. 0.734. 0.729. 0.724. 1.2. 0.718. 0.738. 0.738. 0.736.
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
By 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
i
UMI Number: 3382376
INFORMATION TO USERS
The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion.
______________________________________________________________ UMI Microform 3382376 Copyright 2009 by ProQuest LLC All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code.
_______________________________________________________________ ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106-1346
Copyright by Jun-Pill Kim 2009
ii
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. ii
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 iv
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.
v
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
vi
FIELD OF STUDY
Major Fields: City and Regional Planning Minor Fields: Land Use, Urban Heat Island, Remotely Sensed Data, Geographic Information System, Quantitative Methods.
vii
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 viii
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 REMOTELYSENSED 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 ix
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 x
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
xi
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 xii
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-windinfluence case............................................................................................... 123 Table 6.11. Weather data on February 25, 2006. ............................................................ 126 xiii
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
xiv
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 Subareas 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
xv
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
xvi
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 xvii
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 xviii
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 xix
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
xx
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 Figure 3.6. Weight ( d ij− p ) 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
xxiii
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
xxiv
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
Los Angeles, the concentration of O3 is often 240 ppbv2 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 3
Parts per billion (109) by volume 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 remotelysensed 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 Landsat5 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.
4
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). 6
Dry clay soil Saturated clay soil Asphalt Dense concrete
Density (σ), kg/m3 1.6*103 2.00*103 2.11*103 2.40*103
Heat capacity (C), J/m3/K 1.42 3.10 1.94 2.11
Thermal conductivity (k), W/m/k 0.25 1.58 0.75 1.51
Table 2.1. Physical properties of several materials (from Oke, 1987).
Figure 2.1 Urban heat island profile. 7
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 shortwave 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 upwelling radiation, is the fundamental energy balance at the urban surface. The downwelling 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 5
http://geography.uoregon.edu/envchange/clim_animations/ http://www.met.wau.nl/projects/jep/report/ecromp/node4.html#fig_ intro_radia
8
From Sun
Reflection
S↓
S↑
From clouds and atmosphere
L↓
Reflection and emission
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.
9
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
10
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. 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 7
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). 13
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). 14
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.
15
UHI intensity (°C)
Population ●: 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. 16
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). 17
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 18
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 19
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: 20
NDVI =
Band 4 − Band 3 Band 4 + Band 3
(2.3)
The fractional vegetation cover (Fr) is estimated as: Fr = N * 2 , where N* =
(2.4)
NDVI − NDVIo , 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
21
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
■: the thermal storage of urban canyon ( ΔQs )
♦: the latent heat flux (QE)
Time ●: sensible heat flux (QH)
*:
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.)
22
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) 23
(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)
24
(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. 25
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 27
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.
28
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.
29
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.
30
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.
xo Wind (u) yo
: Land use at (xo, yo)
:Neighboring land uses
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
31
(3.2)
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.
Input thermal energy,
T(xo, yo)
Output thermal energy, θOutput
θInput
θInput and θOutput: the unobserved input and output thermal energy at (xo, yo).
Figure 3.2. Basic thermal balance at location (xo, yo).
32
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.
33
Landsat-5 data (Six different dates through 2005 and 2006)
Radiometric and Geometric Corrections:
Extraction of spatial information: Land uses, NDVI and Remotely Sensed Temperature (RST)
Spatial Analysis: Estimate the parameters of RST models for six land uses
Consider both wind-effect and no-wind-effect
Land-use allocation optimization model that minimizes UHI/temperature impacts.
Figure 3.3. Flowchart of the major research steps.
34
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.
35
dij L1,k
L2,k
L3,k
L4,k
L5,k
L23,k
L24,k
L6,k Lj,k
dij: the distance between the pixel i and the center pixel j.
(a) Effects on temperature at j under calm conditions
dij Thermal energy transport by conduction
L1,k
L2,k
L3,k
L4,k
L5,k
L23,k
L24,k
L6,k Wind
Lj,k
(b) Effects on temperature at j under wind conditions. Figure 3.4. Grid system, temperature, land use and wind effects.
36
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
(c) Temperatures estimated from Landsat-5.
Figure 3.5. Hypothetical land use and temperature patterns.
37
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 illustrates the weight factor, d ij− p . 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 ( d ij− p ) and the NDVI variable, the effect of neighboring land use NDVIs on Tj can be summarized as follows:
38
E jNoWind = ∑ β k ⋅ [∑ k
i
NDVIi ⋅ LUik ⋅ N ij ] d ijp
(3.4)
where E jNoWind 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 j , RST = f {L( xo , y o )} + f {L( x k , y k )} + ε j = T j ,base + E jNoWind + ε j
(3.5)
where Tj, RST is the remotely sensed temperature at the center j, Tj, base is the temperature that is independent of neighboring land uses, E jNoWind 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.
39
30-p
30-p
30-p
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
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) Case of 24 neighboring grid cells Figure 3.6. Weight ( d ij− p ) based on distance from the central pixel.
40
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:
V jk = ∑ i
NDVIi ⋅ LUik ⋅ N ij dijp
(3.6)
The equation to be estimated is then: 6
T j ,RST = β o + ∑ β k ⋅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.
41
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
: Downwind side
: Upwind 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. 42
In addition, downwind neighboring land uses may also have an effect on cell j. Therefore, Equation (3.5) can be modified as:
T j ,RST = f {L( xo , yo )} + f {L( xk , yk )} + ε j
(3.8)
= T j ,base + E Upwind + E Downwind +ε j j j
where E Upwind and E Downwind are the effects of upwind and downwind land uses. j j
Wind effect
Distance weight
1
1
0
1
1
0
1
1
0
*
Weight matrix, wij
30-p
30-p
30-p
30-p
1
30-p
30-p
30-p
30-p
=
30-p
30-p
0
30-p
1
0
30-p
30-p
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
E Upwind = u α ⋅ ∑ β k ⋅[∑ j k =1
i
wij d ijp
⋅ NDVI i ⋅ LU ik ⋅ N ij ] (3.9)
6
= u α ⋅ ∑ β k ⋅ X jk k =1
43
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 ( E Downwind ) is described as follows: j 6
= ∑ β k' ⋅ [ ∑ E Downwind j k =1
(1 − wij )
i
d ijp
⋅ NDVI i ⋅ LU ik ⋅ N ij ]
(3.10)
6
= ∑ β k' ⋅ X 'jk k =1
' where βk are the parameters to be estimated, and X 'jk is the weighted NDVI
sum of land use k in cells downwind. Finally, Equation (3.8) can be rewritten as: 6
6
k =1
k =1
T j ,RST = β o + uα ⋅ ∑ β k ⋅ X jk + ∑ β k' ⋅ X 'jk + ε j where βo represents the intercept.
44
(3.11)
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.
48
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 16
http://www.csc.noaa.gov/crs/lca/faq_gen.html#LULC 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.
50
(b) A (3*3) convolution
(a) No convolution
(c) A (5*5) convolution
(d) A (7*7) convolution
: Water
: Urban area
: Impervious area
: Residential area
: Agricultural area
: Green area
Figure 4.3. Changes in land cover with different sizes of convolutions. 51
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.
53
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) TM (band 4) + TM (band 3) 18 Advanced Spaceborne Thermal Emission and Reflection Radiometer, http://asterweb.jpl.nasa.gov 17
Normalized difference vegetation index, NDVI =
54
T(x, y) =
T (k ) , 1 + (λ * T (k ) / ρ ) ⋅ ln ε TM6
(4.3)
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 recalibrated by using a new procedure and revised calibration parameters, because Landsat5 has aged and optical characteristics have changed since its launch in March, 1984 (Chander and Markham, 2003). This formula is: T(x, y) =
K2 , K ln( 1 + 1) Lλ
(4.4)
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 m ⋅ sr ⋅ μm 2
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).
55
Table 4.1 presents statistics for the estimated temperatures, based on these three methods.
Land uses (Number of observations) Water (142,219) Agriculture (305,217) Green (1,254,252) Residential (394,681) Impervious (503,593) Urban (54,966)
Temperature (°C) Method Malaret Sobrino USGS Malaret Sobrino USGS Malaret Sobrino USGS Malaret Sobrino USGS Malaret Sobrino USGS Malaret Sobrino USGS
Mean
Maximum
Minimum
28.26 29.77 25.59 30.07 30.93 27.29 31.23 32.05 28.38 34.58 35.68 31.58 35.57 37.06 32.55 35.56 37.64 32.58
53.32 55.66 51.92 44.56 46.78 41.71 41.68 42.72 38.66 45.60 47.49 42.84 53.86 56.22 52.63 50.43 52.74 48.35
24.23 25.01 21.86 20.29 21.22 18.31 24.23 25.04 21.86 21.29 22.25 19.21 17.76 19.62 16.03 7.49 9.23 26.96
Standard deviation 2.46 2.33 2.33 2.62 2.86 2.48 2.59 2.67 2.45 2.17 2.36 2.09 2.48 2.74 2.43 4.32 4.38 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
56
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. P ( X i − μ i > kσ i ) ≤
1 k2
(4.6)
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 (Xi - µi) for land use i is over k standard deviation is less than or equal to example, if k = 3, then the probability is 1
32
1 . For k2
= 1 , or 11%. Alternatively, if a normal 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 20
P(|Xi-μi| > 3σi) ≈ 0.0027 (0.27 %). 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 (Number of observations) Water (142,219) Agriculture (305,217) Green (1,254,252) Residential (394,681) Impervious (503,593) Urban (54,966)
Method (Number of outliers) Malaret (651) Sobrino (718) USGS (651) Malaret (5,475) Sobrino (9,151) USGS (8,403) Malaret (597) Sobrino (566) USGS (597) Malaret (1,540) Sobrino (788) USGS (911) Malaret (4,122) Sobrino (2,872) USGS (3,963) Malaret (978) Sobrino (981) USGS (881)
Temperature (°C) Mean
Maximum
Minimum
28.13 29.64 25.47 30.01 30.80 27.19 31.23 32.05 28.38 34.61 35.69 31.59 35.56 37.03 32.52 35.81 37.89 32.79
35.40 36.76 32.36 37.83 39.50 34.36 38.62 40.05 35.54 40.93 42.76 37.50 42.78 45.26 39.81 48.25 50.53 45.07
24.22 25.01 21.86 22.28 23.75 20.09 24.23 25.04 21.86 28.44 28.71 25.31 28.44 28.85 25.31 22.77 24.64 20.10
Standard deviation 2.13 1.95 1.99 2.49 2.64 2.30 2.58 2.66 2.45 2.11 2.33 2.06 2.33 2.62 2.29 3.78 3.85 3.72
Table 4.2. Temperature statistics after removing outliers (k = 3), August 1, 2005.
58
16000
The number of pixel
14000 12000 10000 8000 6000 4000 2000 0 20
22
24
26
28
30
32
34
Temperature
(a) Temperature distribution of water. 70000
The number of Pixel
60000 50000 40000 30000 20000 10000 0 22
24
26
28
30
32
34
36
38
40
Temperature
(b) Temperature distribution of residential areas. 200000 180000
The number of pixel
160000 140000 120000 100000 80000 60000 40000 20000 0 22
24
26
28
30
32
34
36
Temperature
(c) Temperature distribution of green areas. Figure 4.6. Temperature distributions after removing outliers, August 1, 2005. Continued 59
Figure 4.6 continued.
100000 90000
The number of pixel
80000 70000 60000 50000 40000 30000 20000 10000 0 25
27
29
31
33
35
37
39
41
Temperature
(d) Temperature distribution of impervious areas. 180000 160000
The number of pixel
140000 120000 100000 80000 60000 40000 20000 0 20
22
24
26
28
30
32
34
36
38
Temperature
(e) Temperature distribution of agricultural areas. 20000 18000
The number of pixel
16000 14000 12000 10000 8000 6000 4000 2000 0 20
25
30
35
40
Temperature
(e) Temperature distribution of urban areas. 60
45
Land use (Number of observations) Water (142,219) Agriculture (305,217) Green (1,254,252) Residential (394,681) Impervious (503,593) Urban (54,966) (a) Before removing outliers
Land use (Number of outliers)
NDVI Mean
Maximum
Minimum
Standard deviation
0.07
0.75
-0.94
0.3625
0.59
0.92
-0.18
0.1815
0.54
0.90
-0.02
0.1391
0.35
0.76
-0.32
0.1328
0.22
0.86
-0.90
0.1562
-0.01
0.64
-0.69
0.0801
Maximum
Minimum
Standard deviation
0.70
-0.61
0.3598
0.84
0.41
0.1082
0.79
0.27
0.1290
0.58
0.11
0.1194
0.49
-0.06
0.1441
0.09
-0.15
0.0600
NDVI Mean
Water 0.07 (145) Agriculture 0.63 (55, 941) Green 0.54 (26,498) Residential 0.35 (11,569) Impervious 0.22 (12,089) Urban area -0.02 (2,958) (b) After removing outliers (k = 2) Table 4.3. NDVI statistics, August 1, 2005.
61
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.
Station West Dublin OSU Airport CIA Bolton Airport RBA
Latitude – Longitude (Coordinate on image) 40 4' 4" - 83 10' 53" (180, 505) 40 05' - 83 05' (461, 454) 39 59' - 82 53' (1021, 837) 39 54' - 83 08' (303, 1129) 39 49' - 82 56' (865, 1451)
CIA: Columbus International Airport.
RBA: Rickenbacker Airport
Table 4.4. The five measuring stations in the CMA.
21
http://www.wunderground.com/download/index.asp (West Dublin) and http://cdo.ncdc.noaa.gov/qclcd/QCLCD?prior=N (Other measuring stations)
62
Land Use Agriculture Green Urban Agriculture Imperviousness
Figure 4.7. The locations of the five measuring stations.
63
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.
Station
Time (AM)
West Dublin
10:00
OSU Airport
9:53
CIA
9:51
Bolton Airport
9:57
RBA
9:55
Wind speed (m/sec) 0 (N, 0°) 1.79 (NW, 300°) 1.79 (N, 0°) 0 (N, 0°) 0 (N, 0°)
Temperature (°C)
ET (°C) Malaret Sobrino
26.56
28.44
29.17
25.73
27.8
28.59
29.63
26.16
28
37.03
39.15
33.95
27
27.98
28.71
25.31
28
39.79
41.95
36.72
*: 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
USGS
0°= north, 90°= east, 180° = south and 270° = west (in terms of clockwise).
64
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. The method that has the smallest sum of mean square errors, (Tmeasured − Testimated)
2
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, Stations
Land use
West Dublin OSU Airport Columbus International Airport. Bolton Airport Rickenbacker Airport
Green Green Urban Green Impervious Total Sum
(Tmeasured − Testimated)2 Malaret 3.53 0.62 81.54 0.96 139.00 225.66
Sobrino 6.81 3.35 124.32 2.92 194.60 332.01
Table 4.6. Sum of the mean square errors at the five measuring stations.
65
USGS 0.69 2.69 35.40 2.85 76.03 117.66
Date
February, 25 (2006)
April, 11 (2005)
May, 13 (2005)
Station
Time (AM)
West Dublin
9:58
OSU Airport
9:53
CIA
9:51
Bolton Airport
9:51
RBA
9:56
West Dublin
10:00
OSU Airport
9:53
CIA
9:51
Bolton Airport
9:58
RBA
9:55
West Dublin
9:58
OSU Airport
9:53
CIA
9:51
Bolton Airport
9:59
RBA
9:55
MT: Measured temperatures.
Wind speed (m/sec) 9.39 (WNW, 300º) 8.49 (WNW, 290º) 8.05 (WNW, 290º) 7.60 (WNW, 300º) 6.26 (WNW, 300º) 1.34 (SSE, 150º) 2.68 (VR) 3.13 (VR) 3.13 (ENE, 60º) 2.68 (ENE, 70º) 2.68 (SSE,150º) 4.47 (SE, 120º) 4.47 (SE,140º) 3.13 (SE,140º) 2.68 (SE,130º)
MT (°C) RST (°C) 8
10.87
8.3
8.93
8.9
10.39
8.0
9.90
9
10.87
17.5
20.98
18.3
18.31
18.9
24.03
20.0
21.86
18
25.31
16
21.42
17.8
19.66
18.3
24.46
18.0
22.73
18
26.59
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.
Date
August, 1 (2005)
September, 2 (2005)
November,21 (2005)
Station
Time (AM)
West Dublin
10:00
OSU Airport
9:53
CIA
9:51
Bolton Airport RBA
9:57 9:55
West Dublin
10:00
OSU Airport
9:53
CIA
9:51
Bolton Airport
7:19
RBA
9:55
West Dublin OSU Airport CIA
10:00 9:53 9:51
Bolton Airport
9:52
RBA
9:57
Wind speed (m/sec) 0 (N, 0°) 1.79 (WNW, 300º) 1.79 (N, 0°) 0 0 1.57 (E, 90º) 4.47 (W, 280º) 4.92 (W, 280º) 0 3.13 (SE, 220º) 0 0 0 2.68 (WNW, 330º) 0
67
MT (°C) RST (°C) 26.56
25.73
27.8
26.16
28.9
33.95
27 28
25.31 36.72
26.5
24.46
25
23.60
25.6
30.32
17
24.03
23
32.76
7 4.4 4.4
8.93 8.44 8.93
3
10.39
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
Month 1 2 3 4 5 6 7 8 9 10 11 12 Years on record
Average Temperature (°C) -2.2 -0.6 5.0 11.1 16.7 21.7 23.9 22.8 18.9 12.2 6.1 0.6
Average number of clear days 4 4 5 5 6 6 7 7 9 10 5 4
Average number of rainy days 13 11 14 13 13 11 11 9 8 9 12 13
Average precipitation (cm) 7.1 5.8 7.9 8.6 9.7 9.9 11.7 8.4 6.9 5.3 7.6 6.9
48
44
54
48
Table 5.1 General monthly weather characteristics for the Columbus Metropolitan Area (CMA).27 25 26
Records for Columbus. National Weather Service. Retrieved on 2008-11-16. http://www.wunderground.com/history/airport/KCMH/1970/1/31/MonthlyHistory.html
69
Year 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
Month 1 24 12 19 21 29 23 21 30 24 22 30 30 27 37 38 30 32 34 21 29 28 28 37 31 27 29 35 23 24 31 41 34
2 38 27 17 20 25 34 29 34 37 26 33 35 29 28 38 36 37 28 30 28 31 36 40 37 32 35 36 27 32 34 34 21
3 46 46 34 45 37 40 40 43 32 44 43 44 40 42 45 44 41 38 40 43 35 42 43 37 NA 38 42 43 44 37 41 48
4 51 55 51 50 49 56 47 48 50 57 54 52 50 48 51 56 52 50 54 51 50 48 53 55 NA 57 55 55 53 54 57 51
5 58 67 60 61 63 60 67 58 58 63 64 66 63 56 59 71 60 62 58 61 61 57 67 65 65 63 59 61 67 59 61 67
6 71 68 71 70 68 71 66 69 73 67 71 72 70 67 70 75 67 70 74 73 72 70 71 74 74 71 74 68 70 75 70 73
NA: Not Available.
Table 5.2. Observed monthly mean temperatures over the years 1976-2007 (°C).28 Continued.
27 28
http://www.weatherbase.com/weather/weatherall.php3?s=82427&refer=&units=us http://www.census.gov/population/www/documentation/twps0027/twps0027.html
70
Table 5.2 continued.
Month Year 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
7 72 76 74 72 76 72 74 77 71 73 75 76 77 70 74 78 73 76 75 76 73 74 74 80 72 74 78 74 74 77 77 73
8 68 72 73 72 76 70 69 76 73 71 71 74 75 67 72 75 69 75 72 78 74 70 76 73 72 75 76 74 71 77 76 78
9 62 68 70 65 69 62 63 67 63 67 69 67 65 63 66 66 65 65 65 64 66 65 71 68 64 64 71 65 68 70 64 71
71
10 48 52 52 54 51 51 56 55 60 58 56 49 47 51 55 56 52 53 56 56 55 55 56 55 57 56 54 53 55 56 53 62
11 34 45 44 44 41 41 45 44 41 48 42 48 44 42 46 41 45 43 48 38 37 40 46 47 41 49 42 48 46 46 46 45
12 25 30 34 35 33 30 40 25 39 26 33 36 32 20 37 36 35 33 39 29 37 34 38 35 24 38 33 34 33 30 40 36
10.00
Monthly mean temperature, Ԩ
5.00 0.00 Jan ‐5.00
Feb Mar
‐10.00 ‐15.00 1975
1980
1985
1990
1995
2000
2005
2010
Year (a) From January to March
Monthly mean temperature, Ԩ
25.00
20.00
15.00
Apr May Jun
10.00
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. 72
Figure 5.1continued.
Monthly mean temperature, Ԩ
30.00
25.00 Jul Aug
20.00
Sep
15.00 1975
1980
1985
1990
1995
2000
2005
2010
Year (c) From July to September.
20.00
Monthly mean temperature, Ԩ
15.00 10.00 5.00
Oct Nov
0.00
Dec ‐5.00 ‐10.00 1975
1980
1985
1990
1995
2000
2005
Year (d) From October to December. 73
2010
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
Bolton Bolton Rickenbacker RBA Airport
25
Columbus CIAInternational Airport
Monthly mean temperature, Ԩ
20
OSU Airport OSU Airport W Dublin W Dublin
15
10
5
0 1 ‐5
2
3
4
5
6
7
8
9
10
11
Month
Figure 5.2. Monthly mean temperatures at the five measuring stations during the year 2005.
74
12
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 (%) 1850 17,882 195.7 1860 18,554 3.8 1870 31,274 68.6 1880 51,647 65.1 1890 88,150 70.7 1900 125,560 42.4 1910 181,511 44.6 1920 237,031 30.6 1930 290,564 22.6 1940 306,087 5.3 1950 375,901 22.8 1960 471,316 25.4 1970 539,677 14.5 1980 564,871 4.7 1990 632,910 12.0 2000 711,470 12.4 30 Table 5.3. Population in Columbus, Ohio. 29 30
U.S. Rank 37 49 42 33 30 28 29 28 28 26 28 28 21 19 16 15
American FactFinder. United States Census Bureau. 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 32
http://en.wikipedia.org/wiki/Normalized_Difference_Vegetation_Index 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 nearinfrared 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): NDVI =
band 4 − band 3 band 4 + band 3
(5.1)
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 (Number of observations) Water (142,219) Agriculture (305,217) Green (1,254,252) Residential (394,681) Impervious (503,593) Urban (54,966)
NDVI Mean
Maximum
Minimum
0.07 0.59 0.54 0.35 0.22 -0.01
0.75 0.92 0.90 0.76 0.86 0.64
-0.94 -0.18 -0.02 -0.32 -0.90 -0.69
Standard deviation 0.3625 0.1815 0.1391 0.1328 0.1562 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
‐0.2
‐0.4
April 2005
Ag: Agriculture
May 2005
August 2005
September 2005
Resi: Residential
November 2005
February 2006
Time
Imp: Impervious
Figure 5.5. Variations of mean NDVI by land-use types (April 2005 – February 2006)
80
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. 81
Date*
R2
Equation
April 11, 2005 May 13, 2005 August 1, 2005 September 2, 2005 November 21, 2005 February 25, 2006
0.002 0.07 0.45 0.24 0.01 0.06
51.54 + 0.61·NDVI 56.42 – 2.99·NDVI 72.94 – 9.43·NDVI 65.03 – 6.15·NDVI 37.25 + 1.21·NDVI 35.79 + 3.52·NDVI
t-statistics (a0, a1) (4,857.60, 70.36) (6,189.44, -439.28) (7,657.84, -1,455.60) (6,550.38, -908.71) (4,916.42, 194.64) (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
Date*
R2
Equation
April 11, 2005 May 13, 2005 August 1, 2005 September 2, 2005 November 21, 2005 February 25, 2006
0.001 0.05 0.37 0.18 0.01 0.01
3.95 + 0.04·log(NDVI) 3.98 – 0.06·log(NDVI) 4.15 – 0.19·log(NDVI) 4.07 – 0.12·log(NDVI) 3.65 + 0.04·log(NDVI) 3.67 + 0.12·log(NDVI)
t-statistics (ln(α), β) (86,372.3, 193.15) (76,148.8, -363.77) (68,039.4, -1,238.1) (63,461.5, -763.76) (79,060.7, 207.51) (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 (λ )
⎧ ( RST + 30) λ − 1 ⎪ =⎨ λ ⎪ln(RST + 30) ⎩
⎧ ( NDVI + 1) μ − 1 and NDVI ( μ ) = ⎪⎨ μ ⎪ if λ = 0 ⎩ln(NDVI + 1)
if λ ≠ 0
if μ ≠ 0
(5.5)
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: ( RST ) ( λ ) = a 0 + a1 ⋅ ( NDVI ) ( μ ) + ε
(5.6)
The Box-Cox transformation provides a continuum between the linear model (λ = µ = 1) and the double-log linear model (λ→0, µ→0). A chi-squared (χ2) 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 (0.05) = 10.596, it is clear that, in all cases, the Box-Cox model Table 5.7. As χ 2df
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.
*
2
Date
R
(λ, μ)
Equation
April 11, 2005 May 13, 2005 August 1, 2005 September 2, 2005 November 21, 2005 February 25, 2006
0.003 0.10 0.50 0.27 0.01 0.01
(2.75, 3.2) (1.25, 3.6) (-0.25, 2.3) (07.5, 2.0) (3.0, 2.5) (3.01, 0.7)
19,558.64 – 444.14·NDVI(µ) 114.88 – 4.74·NDVI(µ) 2.58 - 0.04·NDVI(µ) 27.00 – 1.75·NDVI(µ) 19,168.46 + 1,045.28·NDVI(µ) 19,131.73 + 1,558.96·NDVI(µ)
Loglikelihood ratio (LKR) -2,225,849 -2,033,350 -2,156,851 -2,310,414 -958,204 -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).
84
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.
86
Central land use (Number of observations)
Water
Agricultural
Green
Residential
Impervious
Urban
Model’s R2 Date February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21
*: The highest R2 is marked in red.
Simple linear
Log-log
Box-Cox
0.49* 0.52 0.36 0.17 0.19 0.04 0.004 0.04 0.15 0.63 0.30 0.0003 0.01 0.001 0.14 0.50 0.23 0.06 0.01 0.0001 0.04 0.23 0.07 0.01 0.01 0.04 0.07 0.13 0.06 0.0002 0.02 0.002 0.0004 0.002 0.0001 0.007
0.48 0.53 0.36 0.18 0.20 0.03 0.005 0.04 0.15 0.61 0.27 0.003 0.02 0.0008 0.13 0.49 0.21 0.05 0.02 0.0008 0.03 0.22 0.06 0.01 0.02 0.03 0.06 0.12 0.05 0.003 0.02 0.006 0.002 0.005 0.002 0.01
0.49 0.54 0.37 0.18 0.21 0.05 0.004 0.04 0.17 0.60 0.32 0.001 0.012 0.002 0.18 0.53 0.26 0.07 0.014 0.0002 0.05 0.24 0.08 0.07 0.01 0.05 0.08 0.13 0.07 0.0008 0.01 0.03 0.001 0.0007 0.008 0.002
Table 5.8. Comparison of the R2 obtained for the linear, log-log, and Box-Cox models.
87
Central land use (Number of observations) Water (54,877)
Agricultural (690,263)
Green (1,055,777)
Residential (310,592)
Impervious (463,075)
Urban (59,222)
Date
R2
Equation
February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21
0.49 0.52 0.36 0.17 0.19 0.04 0.004 0.04 0.15 0.63 0.30 0.0003 0.01 0.001 0.14 0.50 0.23 0.06 0.01 0.0001 0.04 0.23 0.07 0.01 0.01 0.04 0.07 0.13 0.06 0.0002 0.02 0.002 0.0004 0.002 0.0001 0.007
7.52 + 10.17NDVI 18.25 + 11.22NDVI 17.32 + 6.44NDVI 25.41 + 2.65NDVI 23.33 + 2.42NDVI 7.26 + 1.43NDVI 9.43 + 0.88NDVI 22.23 - 2.13NDVI 23.07 - 3.38NDVI 33.77 - 10.89NDVI 27.46 - 5.35NDVI 8.78 - 0.17NDVI 9.42 + 1.43NDVI 21.84 - 0.37NDVI 23.31 - 3.80NDVI 35.05 - 12.46NDVI 28.83 - 6.34NDVI 7.85 + 2.35NDVI 10.41 + 1.45NDVI 23.67 + 0.17NDVI 24.74 - 2.79NDVI 34.22 - 7.58NDVI 29.87 - 4.11NDVI 8.73 + 1.54NDVI 10.27 + 1.40NDVI 24.36 - 3.10NDVI 25.06 - 3.79NDVI 33.79 - 5.71NDVI 29.73 - 4.27NDVI 9.14 + 0.16NDVI 8.66 + 8.85NDVI 22.91 + 2.57NDVI 23.74 + 0.95NDVI 32.60 + 2.48NDVI 27.87 + 1.09NDVI 7.67 + 3.74NDVI
Table 5.9. Linear regression model between NDVI and RST for individual land uses. 88
Central land use Water (54,877)
Agricultural (690,263)
Green (1,055,777)
Residential (310,592)
Impervious (463,075)
Urban (59,222)
Date
R2
Equation
February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21
0.48 0.53 0.36 0.18 0.20 0.03 0.005 0.04 0.15 0.61 0.27 0.003 0.02 0.0008 0.13 0.49 0.21 0.05 0.02 0.0008 0.03 0.22 0.06 0.01 0.02 0.03 0.06 0.12 0.05 0.003 0.02 0.006 0.002 0.005 0.002 0.01
3.63 + 0.24·log(NDVI + 1) 3.88 + 0.21·log(NDVI + 1) 3.86 + 0.14·log(NDVI + 1) 4.02 + 0.05·log(NDVI + 1) 3.98 + 0.04·log(NDVI + 1) 3.62 + 0.03·log(NDVI + 1) 3.67 + 0.03·log(NDVI + 1) 3.96 - 0.05·log(NDVI + 1) 3.97 – 0.08·log(NDVI + 1) 4.17– 0.26·log(NDVI + 1) 4.06– 0.13·log(NDVI + 1) 3.66 – 0.005·log(NDVI + 1) 3.67 + 0.05·log(NDVI + 1) 3.95 – 0.007·log(NDVI + 1) 3.98 – 0.09·log(NDVI + 1) 4.20 – 0.31·log(NDVI + 1) 4.08 – 0.16·log(NDVI + 1) 3.63 + 0.08·log(NDVI + 1) 3.70 + 0.05·log(NDVI + 1) 3.98 + 0.009·log(NDVI + 1) 4.00 – 0.06·log(NDVI + 1) 4.17 - 0.16·log(NDVI + 1) 4.09 – 0.09·log(NDVI + 1) 3.65 + 0.05·log(NDVI + 1) 3.69 + 0.05·log(NDVI + 1) 3.99 – 0.05·log(NDVI + 1) 4.01 – 0.08·log(NDVI + 1) 4.15 – 0.10·log(NDVI + 1) 4.09 – 0.08·log(NDVI + 1) 3.67 + 0.007·log(NDVI + 1) 3.65 + 0.31·log(NDVI + 1) 3.96 + 0.09·log(NDVI + 1) 3.98 + 0.05·log(NDVI + 1) 4.13 + 0.06·log(NDVI + 1) 4.05 + 0.05·log(NDVI + 1) 3.62 + 0.16·log(NDVI + 1)
Table 5.10. Log-log regression model for individual land uses.
89
Central land use
Water (54,877)
Agricultural (690,263)
Green (1,052,731)
Date
R2
(λ, μ)
February 25
0.49
(0.00, 0.6)
April 11
0.54
(-0.50, 0.7)
May 13
0.37
(-1.55, 0.3)
August 1
0.18
(-3.00, 2.9)
September 2
0.21
(-0.82, 2.9)
November 21
0.05
(2.75, 0.9)
February 25
0.004
(3.00, 0.9)
April 11
0.04
(-0.25, 1.1)
May 13
0.17
(-2.50, 2.5)
August 1
0.598
(-1.36, 1.1)
September 2
0.32
(2.00, 2.1)
November 21
0.001
(3.00, 0.5)
February 25
0.012
(3.02, 0.9)
April 11
0.002
(2.00, 2.9)
May 13
0.18
(0.5, 2.9)
August 1
0.53
(-1.25, 3.6)
September 2
0.26
(0.25, 4.0)
November 21
0.07
(3.01, 2.1)
Equation 3.62 + 0.2·NDVI(µ) 1.71 + 0.03·NDVI(µ) 1.65 + 0.057·NDVI(µ) 1.47 + 0.048·NDVI(µ) 1.13 + 0.006·NDVI(µ) 7,645.56 + 818.90·NDVI(µ) 20,533.24 + 1222.39·NDVI(µ) 6.32 – 0.47·NDVI(µ) 0.399 – 0.00002·NDVI(µ) 0.71 – 0.004·NDVI(µ) 1635.00 – 198.67·NDVI(µ 19684.37 – 461.81·NDVI(µ) 20,488.19 + 2160.54·NDVI(µ) 1344.24 – 13.58·NDVI(µ) 12.58 0.31·NDVI(µ) 0.79 0.0005·NDVI(µ) 7.03 0.10·NDVI(µ) 18,261.71 – 2,513.51·NDVI(µ)
Log-likelihood ratio (LKR) -41,197.8 -54,398.9 -38,848.5 -34,478.4 -27624.6 -20,174.6 -223,243 -295,663 -295,620 -256,440 -291,741 -142,405 -181,025 -485,895 -496,221 -551,067 -481,333 -208,175
Table 5.11. Linear relationships between the Box-Cox variables NDVI(µ) and RST(λ) for individual land uses. Continued. 90
Table 5.11 continued.
Central land use
Residential (310,592)
Impervious (463,074)
Urban (59,222)
Date
R2
(λ, μ)
February 25
0.014
(3.00, 0.3)
April 11
0.0002
(3.00, 2.9)
May 13
0.05
(3.00, 3.9)
August 1
0.24
(2.99, 2.1)
September 2
0.08
(3.00, 2.9)
November 21
0.07
(3.01, 0.90)
February 25
0.01
(3.09, 0.5)
April 11
0.05
(1.75, 2.1)
May 13
0.08
(0.5, 3.9)
August 1
0.13
(1.00, 0.9)
September 2
0.07
(3.00, 1.3)
November 21
0.0008
(3.00, 1.3)
February 25
0.01
(3.02, 0.5)
April 11
0.03
(3.00, 0.5)
May 13
0.001
(3.01, 1.3)
August 1
0.0007
(3.00, 0.5)
September 2
0.008
(3.00, 0.3)
November 21
0.002
(3.01, 0.7)
91
Equation 1,703.44 – 134.81·NDVI(µ) 51,919.29 – 336.37·NDVI(µ) 54279.43 – 3836.42·NDVI(µ) 86,990.25 – 20,749.6·NDVI(µ) 70930.74 – 8261.54·NDVI(µ) 18,261.71 – 2,513.51·NDVI(µ) 503.68 – 10.64·NDVI(µ) 623.15 – 56.51·NDVI(µ) 12.82– 0.28·NDVI(µ) 62.79 – 5.80·NDVI(µ) 71,754.68 – 15,074.3·NDVI(µ) 20,129.34 – 7.62·NDVI(µ) 19,877.11 – 7,693.36·NDVI(µ) 50757.94 – 2,361.06·NDVI(µ) 52,770.64 – 1,435.96·NDVI(µ) 82,801.19 – 5,006.99·NDVI(µ) 66,262.49 – 1,212.64·NDVI(µ) 18451.11 – 2,470.43·NDVI(µ)
Log-likelihood ratio (LKR) -9,565.9 -151,952 -139,231 -184,914 -213,880 -208,175 -181,495 -421,119 -371,241 -378,634 -475033 -206,811 -79,106.3 -93,284.3 -82,429.0 -81,818 -96,335.7 -76,159
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 : Columbus International Airport
: Bolton Airport
:Rickenbacker Airport
Figure 6.1. Measuring stations and surrounding areas (1,641*1,605 = 2,633,805 cells). 93
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.
35
See 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
2
1641
2 2 : Central cell
Figure 6.3. Cell buffer pattern when θ = 5. 95
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).
96
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
T j , RST = β o + ∑ β k ⋅ 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 (Tj,base), V jk = ∑ d ij− p ⋅ NDVIi ⋅ LU ik ⋅ N ij represents the distance-weighted NDVI land-use i
variable, i is the index of a neighboring pixel around the central pixel j, dij− p 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 ⎢ ⎥ ⎢ ⎢T2, RST ⎥ ⎢V2,1 ⎥ ⎢V ⎢T ⎢ 3, RST ⎥ ⎢ 3,1 ⎢ M ⎥=⎢ ⎢ ⎥ ⎢ ⎢T j , RST ⎥ ⎢V j ,1 ⎢ M ⎥ ⎢ ⎢ ⎥ ⎢ ⎢⎣Tm, RST ⎥⎦ ⎢⎣Vm,1 (m *1)
V1, 2
V1,3
V1, 4
V1,5
V2, 2
V2,3
V2, 4
V2,5
V3, 2
V3,3
V3, 4
V3,5
M
M
V j,2
V j ,3
V j ,4 M
Vm, 2
M Vm,3
Vm, 4
V j ,5 Vm,5
(m * 6)
V1,6 ⎤ ⎡ε ⎤ ⎥ ⎡ β1 ⎤ ⎢ 1 ⎥ V2, 6 ⎥ ⎢ ⎥ ε 2 ⎢ ⎥ β V3,6 ⎥ ⎢ 2 ⎥ ⎢ε 3 ⎥ ⎥ ⎢β 3 ⎥ ⎢ ⎥ ⎥⋅ ⎢ ⎥ + ⎢ M ⎥ ⎥ β V j ,6 ⎥ ⎢ 4 ⎥ ⎢ε j ⎥ ⎢β ⎥ ⎢ ⎥ ⎥ ⎢ 5⎥ ⎢ M ⎥ ⎥ ⎢⎣ β 6 ⎥⎦ ⎢ ⎥ Vm, 6 ⎥⎦ ⎣ε m ⎦ (6 *1)
(6.2)
where m is the number of observations for a given land use from Landsat-5, Tj,RST is the jth remotely-sensed temperature observation and εj is the jth 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.
98
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.
99
Central land use (Number of pixels)
Water (54,166)
Agriculture (678,313)
Green (681,220)
Residential (310,170)
Impervious (461,847)
Urban (59,110)
Neighboring land use Intercept Water Agriculture Green Residential Impervious Urban Intercept Water Agriculture Green Residential Impervious Urban Intercept Water Agriculture Green Residential Impervious Urban Intercept Water Agriculture Green Residential Impervious Urban Intercept Water Agriculture Green Residential Impervious Urban Intercept Water Agriculture Green Residential Impervious Urban
Parameter (β's) 24.04 0.07 0.14 0.12 0.64 1.80 -7.52 35.70 -2.79 -1.47 -1.47 -0.93 -1.50 1.02 37.66 -2.30 -1.20 -1.22 -1.00 -1.26 -1.94 35.31 -1.93 -1.00 -0.93 -0.60 -0.47 -1.29 34.96 1.36 -0.97 -0.85 -0.50 -0.36 -0.22 36.09 0.94 -0.83 -0.53 0.57 -1.21 6.62
t-statistics 1513.14 22.09 22.56 36.18 91.81 165.46 -45.10 4706.0 -151.18 -1279.2 -916.96 -96.59 -186.87 9.06 5609.60 -512.29 -1338.2 -1472.0 -528.39 -391.43 -20.54 2896.36 -217.67 -210.11 -471.93 -253.84 -99.06 -16.55 4391.94 93.31 -242.43 -365.31 -142.53 -88.75 -5.36 684.46 15.66 -45.88 -40.10 22.83 -43.74 90.53
Table 6.1. Regression results for the NDVI models on August 1, 2005.
100
R2 (θ, p)
0.57 (9, 0.3)
0.80 (9, 0.5)
0.78 (7, 0.3-0.4)
0.61 (7, 0.3)
0.40 (9, 0.5-0.6)
0.19 (25, 0.6)
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
Central land use (MT)
Neighboring land use
NDVI weighted sum Mean
Minimum
Water -0.87 -8.54 Agriculture 0.59 -0.04 Green 2.69 0 Water (25.59°C) Residential 0.78 0 Impervious 0.39 -3.50 Urban -0.003 -2.99 Water 0.01 -1.53 Agriculture 3.81 -0.09 Green 1.72 0 Agriculture (27.29°C) Residential 0.06 -0.05 Impervious 0.12 -0.73 Urban 0.0004 -0.44 Water 0.05 -2.38 Agriculture 1.68 -0.06 Green 5.23 0.03 Green (28.38°C) Residential 0.39 -0.17 Impervious 0.30 -0.88 Urban 0.0004 -0.68 Water 0.06 -2.80 Agriculture 0.24 -0.11 Green 1.66 0 Residential (31.58°C) Residential 2.23 -0.06 Impervious 1.08 -1.24 Urban 0.002 -0.96 Water 0.01 -4.00 Agriculture 0.44 -0.11 Green 1.22 0 Impervious (32.55°C) Residential 0.92 -0.17 Impervious 1.38 -2.84 Urban -0.003 -2.33 Water 0.01 -4.72 Agriculture 0.76 -0.02 Green 1.59 0 Urban (32.58°C) Residential 0.96 0 Impervious 1.55 -1.17 Urban -0.11 -1.94 MT: Mean Temperature with remotely-sensed temperatures (RST).
Maximum 9.90 12.42 15.12 9.94 6.65 0.33 2.38 8.11 7.13 2.88 2.83 0.83 5.74 11.01 11.06 7.28 4.95 0.83 5.82 8.34 9.78 7.52 5.18 1.07 3.77 8.01 8.46 6.49 4.85 1.23 2.55 13.19 11.91 7.24 4.82 1.20
Table 6.2. NDVI statistics for the independent variables on August 1, 2005.
103
Standard deviation 3.45 1.14 2.98 1.10 0.69 0.04 0.07 2.11 1.25 0.16 0.24 0.01 0.26 1.88 2.24 0.74 0.50 0.01 0.27 0.57 1.68 1.30 0.75 0.03 0.19 0.82 1.34 0.86 0.74 0.07 0.26 1.10 1.48 0.76 0.72 0.25
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:
εi = (
∂T j Tj
)/(
∂V ji V ji
) = βi ⋅
V ji Tj
(6.9)
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
Central land use
Water
Agriculture
Green
Residential
Impervious
Urban
Neighboring land use Impervious Residential Green Agriculture Water Urban Agriculture Green Impervious Residential Water Urban Green Agriculture Residential Impervious Water Urban Green Residential Impervious Agriculture Water Urban Green Impervious Agriculture Residential Water Urban Impervious Green Urban Agriculture Residential Water
Elasticity (εi) Mean
Minimum
Maximum
0.025 0.018 0.012 0.003 -0.003 0.001 -0.214 -0.093 -0.006 -0.002 -0.001 0.000 -0.231 -0.074 -0.013 -0.012 -0.004 0.000 -0.051 -0.043 -0.016 -0.008 -0.004 -0.000 -0.033 -0.015 -0.014 -0.014 6*10-6 10-5 -0.058 -0.027 -0.025 -0.021 0.017 3*10-5
-0.258 0.000 0.000 -0.000 -0.025 -0.092 -0.516 -0.440 -0.153 -0.095 -0.267 -0.021 -0.584 -0.556 -0.261 -0.203 -0.504 -0.056 -0.349 -0.164 -0.080 -0.324 -0.397 -0.040 -0.294 -0.055 -0.305 -0.110 -0.227 -0.009 -0.360 -0.277 -0.538 -0.418 0.000 -0.164
0.375 0.227 0.075 0.071 0.029 0.919 0.005 0.000 0.042 0.002 0.164 0.025 -0.001 0.003 0.006 0.044 0.224 0.046 0.000 0.001 0.023 0.003 0.221 0.045 0.000 0.043 0.004 0.003 0.210 0.020 0.053 0.000 0.234 0.001 0.123 0.083
Standard deviation 0.043 0.025 0.014 0.006 0.010 0.012 0.127 0.069 0.012 0.005 0.008 0.000 0.113 0.086 0.025 0.020 0.023 0.001 0.054 0.025 0.011 0.020 0.019 0.001 0.038 0.008 0.027 0.013 0.010 0.000 0.028 0.026 0.061 0.031 0.013 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.
Central land use
Water
Agriculture
Green
Residential
Impervious
Urban
Neighboring land use Impervious Residential Green Agriculture Water Urban Agriculture Green Impervious Residential Water Urban Green Agriculture Residential Impervious Water Urban Green Residential Impervious Agriculture Water Urban Green Impervious Agriculture Residential Urban Water Impervious Green Urban Residential Agriculture Water
Elasticity (εi) Mean
Minimum
Maximum
0.025 0.018 0.012 0.003 -0.003 0.001 -0.213 -0.093 -0.006 -0.002 -0.001 4*10-5 -0.231 -0.074 -0.013 -0.012 -0.004 -8*10-6 -0.051 -0.042 -0.016 -0.008 -0.004 5*10-7 -0.033 -0.015 -0.014 -0.014 2*10-6 10-5 -0.057 -0.027 -0.023 0.017 -0.020 4*10-5
-0.185 0.000 0.000 -0.000 -0.025 -0.111 -0.501 -0.419 -0.143 -0.090 -0.269 -0.014 -0.558 -0.547 -0.245 -0.210 -0.621 -0.052 -0.348 -0.148 -0.076 -0.325 -0.490 -0.041 -0.263 -0.053 -0.305 -0.103 -0.008 -0.184 -0.184 -0.231 -0.539 0.000 -0.483 -0.143
0.333 0.209 0.070 0.066 0.028 0.559 0.004 0.000 0.029 0.002 0.110 0.024 -0.001 0.002 0.005 0.036 0.132 0.036 0.000 0.001 0.016 0.003 0.135 0.036 0.000 0.029 0.003 0.003 0.014 0.130 0.050 0.000 0.201 0.110 0.001 0.065
(b) Tj = Temperatures with the regression models. 106
Standard deviation 0.042 0.025 0.014 0.006 0.010 0.011 0.126 0.069 0.012 0.005 0.008 0.000 0.112 0.086 0.025 0.020 0.023 0.001 0.054 0.025 0.011 0.020 0.019 0.001 0.038 0.008 0.027 0.013 0.000 0.008 0.027 0.026 0.056 0.013 0.032 0.008
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
Land use
Water Agriculture Green Residential Impervious Urban
April 11
May 13
0.80 (9, 0.4) 0.08 (9, 0.2) 0.16 (11, 0.1) 0.26 (13, 0.2) 0.29 (13, 0.5) 0.14 (47, 0.7)
0.70 (9, 0.3) 0.21 (7, 0.4) 0.36 (7, 0.1) 0.34 (9, 0.4) 0.23 (9, 0.3) 0.08 (33, 0.5)
R2 (θ, p) 2005 September August 1 2 0.57 0.50 (9, 0.3) (11, 0.4) 0.80 0.49 (9, 0.5) (11, 0.4) 0.78 0.52 (7, 0.3) (9, 0.4) 0.61 0.32 (7, 0.3) (9, 0.4) 0.40 0.23 (9, 0.5) (13, 0.5) 0.19 0.09 (25, 0.6) (29, 0.8)
November 21 0.13 (9, 0.2) 0.03 (41, 0.1) 0.09 (7, 0.2) 0.15 (13, 0.4) 0.07 (25, 0.6) 0.12 (23, 0.7)
2006 February 25 0.83 (11, 0.5) 0.04 (39, 0.5) 0.12 (23, 0.5) 0.28 (13, 0.4) 0.21 (17, 0.4) 0.23 (17, 0.5)
Table 6.4. R2s of the NDVI models across the year 2005-2006.
0.9
R2
0.8 0.7 Water
0.6
Agriculture 0.5
Green
0.4
Residential Impervious
0.3
Urban
0.2 0.1
Time
0 April 11 2005
May 13 2005
August 1 September November February 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 (Number of observations) Water (54,037)
Agricultural (675,486)
Green (1,038,081)
Residential (309,896)
Impervious (461,539)
Urban (59,181)
Date
Mean
Minimum
Maximum
Standard deviation
February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21 February 25 April 11 May 13 August 1 September 2 November 21
-0.18 -0.15 0.07 0.07 0.05 -0.11 0.12 0.17 0.24 0.59 0.56 0.18 0.17 0.27 0.42 0.54 0.54 0.26 0.14 0.26 0.36 0.35 0.36 0.22 0.09 0.18 0.25 0.22 0.24 0.17 -0.03 -0.003 0.03 -0.01 0.004 -0.01
-0.88 -1.00 -1.00 -0.94 -0.93 -0.89 -0.68 -0.73 -0.42 -0.18 -0.71 -0.90 -0.5 -1.00 -0.41 -0.02 -0.33 -0.90 -0.90 -1.00 -0.32 -0.32 -0.33 -0.92 -0.81 -0.92 -0.64 -0.90 -0.93 -0.92 -0.64 -0.74 -0.64 -0.69 -0.81 -0.61
0.49 0.66 0.85 0.75 0.78 0.57 0.68 1.00 0.89 0.92 0.95 0.74 0.71 0.80 0.83 0.90 0.98 0.89 0.57 0.74 0.80 0.76 0.86 0.89 0.70 0.76 0.76 0.86 0.85 0.80 0.47 0.68 0.71 0.64 0.81 0.68
0.20 0.26 0.27 0.36 0.37 0.22 0.10 0.15 0.20 0.18 0.19 0.14 0.10 0.15 0.17 0.14 0.14 0.14 0.09 0.12 0.11 0.13 0.14 0.10 0.11 0.16 0.16 0.16 0.17 0.15 0.07 0.09 0.09 0.08 0.10 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:
T j ,RST = β o + ∑ β k ⋅ [∑ k
i
Area ⋅ LU ik ⋅ N ij ] d ijp
(6.10)
The weighted sum of the land-use areas around the central cell j (Vj,k) is defined as:
V jk = ∑ i
Area ⋅ LU ik ⋅ N ij d ijp
(6.11)
where i represents the index of a neighboring pixel around the central pixel j, dij− p 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:
VRingA = 16 * 900*
1 7,200 1 14,400 , VRingB = 8 * 900* p = = p p 30 30 p 60 60
(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
Central land use
Water
Agriculture
Green
Residential
Impervious
Urban
Neighboring land use Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban
Weighted sum of neighboring land uses (m2) Mean
Minimum
Maximum
1094.1 13.40 64.06 25.80 30.21 1.78 3.76 1439.4 301.64 18.61 51.85 4.76 20.26 390.02 2061.3 132.70 147.96 6.20 4.50 12.39 76.05 1035.0 97.18 4.30 21.13 149.45 332.70 371.84 1782.5 100.85 3.59 29.60 35.91 41.65 199.32 1064.5
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1229.5 189.78 328.12 293.49 313.50 148.36 631.87 1820.1 920.09 742.77 798.14 769.55 1580.3 1858.5 2758.5 1694.8 1693.1 1142.7 291.88 279.91 326.79 1219.7 315.72 205.23 1813.1 1691.3 1858.5 1762.8 2758.5 1752.0 278.31 411.80 343.50 259.22 444.37 1374.6
Standard deviation 100.44 22.36 67.74 34.85 43.48 6.87 19.85 223.44 182.77 44.87 94.27 27.53 79.30 348.66 388.83 218.71 213.69 34.19 16.70 22.47 66.88 65.04 64.25 12.92 95.70 231.54 339.09 300.49 372.87 180.68 16.63 40.48 40.89 33.80 79.01 93.95
Table 6.6. Land-use area statistics for the independent variables on August 1, 2005. 114
Central land use (Number of pixels)
Water (54,142)
Agriculture (672,859)
Green (1,037,789)
Residential (309,864)
Impervious (461,516)
Urban (59,145)
Neighboring land use
Parameter (β's)
t-statistics
Intercept Water Agriculture Green Residential Impervious Intercept Water Agriculture Green Residential Impervious Intercept Water Agriculture Green Residential Impervious Intercept Water Agriculture Green Residential Impervious Intercept Agriculture Green Residential Impervious Urban Intercept Agriculture Green Residential Impervious Urban
27.93 -0.004 0.003 0.006 0.022 0.025 28.23 -0.008 -0.001 0.001 0.003 0.015 22.94 -0.003 0.001 0.002 0.003 0.007 24.41 -0.03 0.002 -0.008 0.006 0.014 11.20 0.005 0.005 0.006 0.009 0.007 -5.36 0.027 0.019 0.023 0.050 0.024
23.27 -3.85 3.32 6.23 23.12 23.8 177.79 -56.02 -16.92 15.32 25.11 150.06 138.02 -42.57 14.8 29.82 53.81 107.65 97.19 -119.81 9.96 -38.77 30.73 64.84 145.95 179.79 172.64 223.11 311.21 224.83 -4.39 27.27 19.25 23.59 55.07 26.91
Table 6.7. Regression results for the land-use are models on August 1, 2005.
115
R2 (θ, p)
0.64 (11, 1.3)
0.48 (13, 1.1)
0.34 (11, 0.9)
0.55 (11, 1.3)
0.44 (11, 0.9)
0.26 (17, 1.3)
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
Central land use
Water
Agriculture
Green
Residential
Impervious
Urban
Neighboring land use Water Residential Agriculture Impervious Green Impervious Green Agriculture Residential Water Green Impervious Residential Agriculture Water Residential Impervious Green Water Agriculture Impervious Residential Green Agriculture Urban Urban Impervious Residential Agriculture Green
Elasticity (εi) Mean
Minimum
Maximum
Standard deviation
-0.1628 0.0212 0.0017 0.0280 0.0149 0.0264 0.0147 -0.0791 0.0016 -0.0011 0.1321 0.0340 0.0145 0.0126 -0.0021 0.2063 0.0431 -0.0203 -0.0049 0.0010 0.4825 0.0735 0.0537 0.0261 0.0216 0.8031 0.3037 0.0299 0.0255 0.0216
-0.2085 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1163 0.0000 -0.1922 0.0446 0.0000 0.0000 0.0000 -0.1862 0.1424 0.0000 -0.1075 -0.3647 0.0000 0.2175 0.0000 0.0000 0.0000 0.0000 0.4624 0.0000 0.0000 0.0000 0.0000
-0.0707 0.2300 0.0254 0.2457 0.0796 0.3722 0.0498 -0.0328 0.0556 0.0000 0.2184 0.3530 0.1929 0.0689 0.0000 0.3205 0.1384 0.0000 0.0000 0.0255 0.8677 0.3607 0.3167 0.3374 0.6206 4.0342 0.9285 0.1781 0.3410 0.2300
0.0257 0.0273 0.0029 0.0384 0.0158 0.0461 0.0088 0.0166 0.0038 0.0059 0.0296 0.0477 0.0235 0.0117 0.0084 0.0165 0.0276 0.0188 0.0187 0.0018 0.0856 0.0596 0.0564 0.0410 0.0394 0.1802 0.1082 0.0242 0.0348 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.
Central land use
Water
Agriculture
Green
Residential
Impervious
Urban
Neighboring land use Water Impervious Residential Green Agriculture Agriculture Impervious Green Residential Water Green Impervious Residential Agriculture Water Residential Impervious Green Water Agriculture Impervious Residential Green Agriculture Urban Urban Impervious Residential Agriculture Green
Elasticity (εi) Mean
Minimum
Maximum
Standard deviation
-0.1625 0.0277 0.0212 0.0149 0.0017 -0.0788 0.0263 0.0146 0.0016 -0.0011 0.1314 0.0340 0.0145 0.0126 -0.0021 0.2059 0.0430 -0.0203 -0.0049 0.0010 0.4809 0.0733 0.0536 0.0260 0.0215 0.7891 0.3000 0.0296 0.0252 0.0213
-0.1983 0.0000 0.0000 0.0000 0.0000 -0.1055 0.0000 0.0000 0.0000 -0.2291 0.0446 0.0000 0.0000 0.0000 -0.2092 0.1638 0.0000 -0.0963 -0.4188 0.0000 0.2581 0.0000 0.0000 0.0000 0.0000 0.5559 0.0000 0.0000 0.0000 0.0000
-0.1036 0.2426 0.2109 0.0752 0.0249 -0.0341 0.3114 0.0435 0.0642 0.0000 0.1779 0.3201 0.1821 0.0634 0.0000 0.2714 0.1305 0.0000 0.0000 0.0220 0.6854 0.3619 0.3278 0.3098 0.3828 1.1942 0.5681 0.1954 0.3676 0.2336
0.0253 0.0381 0.0270 0.0157 0.0029 0.0156 0.0452 0.0087 0.0038 0.0059 0.0270 0.0469 0.0235 0.0115 0.0085 0.0137 0.0274 0.0187 0.0191 0.0018 0.0809 0.0597 0.0565 0.0410 0.0385 0.1104 0.1031 0.0240 0.0350 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.
Land use
Water Agriculture Green Residential Impervious Urban
April 11
May 13
0.78 (17, 1.2) 0.04 (15, 1.3) 0.19 (11, 1.0) 0.38 (13, 1.1) 0.36 (25, 1.5) 0.26 (25, 1.3)
0.74 (15, 1.3) 0.10 (13, 1.3) 0.23 (11, 1.0) 0.42 (13, 1.5) 0.36 (17, 1.3) 0.27 (21, 1.3)
R2 (θ, p) 2005 September August 1 2 0.64 0.56 (11, 1.3) (13, 1.4) 0.48 0.32 (13, 1.1) (17, 1.2) 0.34 0.37 (11, 0.9) (15, 1.5) 0.55 0.36 (11, 1.3) (11, 0.9) 0.44 0.31 (11, 0.9) (11, 0.7) 0.26 0.21 (17, 1.3) (17, 1.1)
November 21 0.16 (11, 1.5) 0.06 (37, 1.8) 0.06 (35, 1.7) 0.17 (17, 1.3) 0.11 (21, 1.2) 0.17 (13, 1.2)
Table 6.9. R2s of the land-use area models across the year 2005-2006. 120
2006 February 25 0.82 (23, 1.5) 0.05 (23, 0.7) 0.14 (47, 1.7) 0.35 (25, 1.7) 0.28 (29, 1.4) 0.20 (15, 1.3)
R2 0.9 0.8 0.7 Water
0.6
Agriculture Green
0.5
Residential Impervious
0.4
Urban 0.3 0.2 0.1
Time
0 April 11 2005
May 13 2005
August 1 September 2005 2, 2005
November February 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
Central land use
Water
Agriculture
Green
Residential
Impervious
Urban
Date April 11, 2005 May 13, 2005 August 1, 2005 September 2, 2005 November 21, 2005 February 25, 2006 April 11, 2005 May 13, 2005 August 1, 2005 September 2, 2005 November 21, 2005 February 25, 2006 April 11, 2005 May 13, 2005 August 1, 2005 September 2, 2005 November 21, 2005 February 25, 2006 April 11, 2005 May 13, 2005 August 1, 2005 September 2, 2005 November 21, 2005 February 25, 2006 April 11, 2005 May 13, 2005 August 1, 2005 September 2, 2005 November 21, 2005 February 25, 2006 April 11, 2005 May 13, 2005 August 1, 2005 September 2, 2005 November 21, 2005 February 25, 2006
Input variables Land-use NDVI areas 0.80 0.78 0.70 0.74 0.57 0.64 0.50 0.56 0.13 0.16 0.83 0.82 0.08 0.04 0.21 0.10 0.80 0.48 0.49 0.32 0.03 0.06 0.04 0.05 0.16 0.19 0.36 0.23 0.34 0.78 0.52 0.37 0.09 0.06 0.12 0.14 0.26 0.38 0.34 0.42 0.61 0.55 0.32 0.36 0.15 0.17 0.28 0.35 0.29 0.36 0.23 0.36 0.40 0.44 0.23 0.31 0.07 0.11 0.21 0.28 0.14 0.26 0.19 0.26 0.19 0.21 0.12 0.17 0.20 0.23 0.08 0.27
R2 difference (NDVI-Area) 0.02 -0.04 -0.07 -0.06 -0.03 0.01 0.04 0.11 0.32 0.17 -0.03 -0.01 -0.03 0.13 0.44 0.15 0.03 -0.02 -0.12 -0.08 0.06 -0.04 -0.02 -0.07 -0.07 -0.13 -0.04 -0.08 -0.04 -0.07 -0.12 -0.07 -0.12 -0.05 0.03 -0.19
ρ
1
0.94
0.94
0.94
0.94
-0.37
ρ: Rank correlation coefficient.
Table 6.10. Comparison of the R2 values of the NDVI and area models in the no-windinfluence 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:
ρ = 1−
6 ⋅ ∑ di2
n(n 2 − 1)
(6.20)
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 37
http://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient. 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.
Stations
Time (AM)
West Dublin
9:58
The Ohio State University Airport
9:53
Columbus International Airport
9:51
Bolton Airport
9:51
Rickenbacker Airport
9:56
MT: Measured temperature.
Wind speed (m/sec) 9.39 (WNW, 300º) 8.49 (WNW, 290º) 8.05 (WNW, 290º) 7.60 (WNW, 300º) 6.26 (WNW, 300º)
MT (°C) RST (°C) 8
10.87
8.3
8.93
8.9
10.39
8.0
9.90
9
10.87
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:
T j , RST = T j ,base + u α ⋅ ∑ β k ⋅ [∑ k
i
wij d ijp
⋅ NDVI i ⋅ LU ik ⋅ N ij ]
+ ∑ γ k ⋅ [∑ k
i
(1 − wij ) d ijp
NDVI i ⋅ LU ik ⋅ N ij ] + ε j
= T j ,base + ∑ β k ⋅ (u α ⋅ X jk ) + ∑ γ k ⋅ X 'j ,k + ε j k
k
126
(6.21)
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, wij = 0 if not, γk and NDVI i',k are the parameter estimates and NDVI values for land use k at cell i in the no-wind-influence area,
X j ,k = ∑ i
wij d
p ij
⋅ NDVIi ⋅ LUik ⋅ Nij and X 'j ,k = ∑ i
(1 − wij ) d ijp
NDVIi ⋅ LUik ⋅ Nij . In Equation
(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 linear in the variables uα·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
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
Wind
: upwind side
:downwind side
Figure 6.7. Matrix of wind direction from the West when θ = 5.
128
p 0.1 0.2 0.3 0.4 0.5 0.6 0.7
p 0.1 0.2 0.4 0.6 0.8 1.0 1.4
7*7 0.810 0.808 0.806 0.801 0.793 0.782 0.768
31 * 31 0.040 (-0.55) 0.040 (-0.62) 0.04 (-0.47) 0.040 (-0.67) 0.04 (-1.86) 0.002 (-13.68) 0.039 (1.29)
Size of buffer (θ) 9*9 11 * 11 13 * 13 0.820 0.820 0.813 0.821 0.821 0.815 0.821 0.823 0.818 0.819 0.821 0.823 0.815 0.823 0.822 0.808 0.819 0.822 0.796 0.811 0.818 (a) Water (α = 0.01 in all cases).
43 * 43 0.040 (-1.11) 0.040 (-0.55) 0.040 (-1.17) 0.040 (-0.52) 0.040 (-1.41) 0.040 (-1.25) 0.040 (-0.24)
Size of buffer (θ) 47 * 47 51 * 51 0.040 0.040 (-1.08) (-1.06) 0.040 0.041 (-0.53) (-1.55) 0.041 0.041 (-1.43) (-1.26) 0.041 0.042 (-0.59) (-0.46) 0.041 0.042 (-1.13) (-0.79) 0.041 0.041 (-2.75) (-2.16) 0.041 0.041 (0.01) (0.01) (b) Agriculture.
15 * 15 0.803 0.806 0.810 0.814 0.817 0.820 0.819
55 * 55 0.041 (-1.04) 0.041 (-1.71) 0.042 (-0.63) 0.042 (-0.45) 0.042 (-1.20) 0.042 (-1.15) 0.042 (0.01)
63 * 63 0.042\ (-1.01) 0.042 (-1.56) 0.043 (-0.59) 0.043 (-0.47) 0.043 (-0.94) 0.043 (-3.43) 0.043 (0.01)
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. p 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3
p 0.2 0.4 0.5 0.6 0.7 0.8 1.0
39 * 39 0.129 (-3.46) 0.131 (-7.43) 0.133 (-9.37) 0.133 (-9.45) 0.130 (-8.95) 0.127 (-8.14) 0.121 (-1.26) 0.113 (-2.87)
43 * 43 0.128 (-3.23) 0.132 (-7.39) 0.134 (-9.60) 0.134 (-9.79) 0.132 (-9.26) 0.129 (-8.43) 0.123 (-7.45) 0.115 (-6.46)
Size of buffer (θ) 47 * 47 51 * 51 0.128 0.127 (-3.04) (-2.87) 0.132 0.131 (-7.36) (-7.33) 0.134 0.134 (-9.79) (-9.79) 0.135 0.135 (-10.34) (-10.07) 0.133 0.134 (-9.55) (-9.79) 0.130 0.131 (-8.68) (-8.95) 0.124 0.125 (-7.66) (-8.95) 0.116 0.112 (-6.62) (-1.61) (c) Green areas.
11 * 11 0.271 (0.56) 0.271 (1.67) 0.270 (2.34) 0.268 (2.54) 0.266 (2.71) 0.263 (2.87) 0.257 (3.00)
13 * 13 0.272 (0.43) 0.273 (1.56) 0.273 (2.24) 0.272 (2.45) 0.271 (2.64) 0.268 (2.81) 0.264 (3.00)
Size of buffer (θ) 15 * 15 17 * 17 0.269 0.266 (0.32) (0.23) 0.268 0.269 (0.79) (0.71) 0.272 0.271 (1.31) (0.94) 0.273 0.272 (2.38) (2.31) 0.272 0.272 (2.58) (2.53) 0.270 0.271 (2.76) (2.72) 0.267 0.268 (3.00) (3.00) (d) Residential areas.
55 * 55 0.126 (-2.71) 0.131 (-7.27) 0.134 (-10.14) 0.135 (-10.56) 0.134 (-10.07) 0.132 (-9.17) 0.126 (-3.58) 0.117 (-6.94)
59 * 59 0.126 (-2.58) 0.130 (-7.23) 0.134 (-10.27) 0.134 (-10.76) 0.133 (-10.28) 0.131 (-9.37) 0.127 (-8.23) 0.118 (-7.05)
19 * 19 0.263 (-0.07) 0.267 (0.64) 0.269 (0.87) 0.271 (1.41) 0.271 (2.47) 0.271 (2.68) 0.269 (2.99)
23 * 23 0.257 (-0.22) 0.262 (1.01) 0.264 (0.76) 0.267 (1.01) 0.269 (1.57) 0.270 (2.61) 0.269 (2.95) Continued.
130
Table 6.12 continued.
0.8 1.0 1.2 1.4 1.6 1.8 2.0
p 0.2 0.3 0.4 0.5 0.6 0.8 1.0
15 * 15 0.208 (2.58) 0.207 (1.75) 0.205 (1.81) 0.204 (2.32) 0.200 (2.33) 0.196 (2.33) 0.19 (2.33)
9*9 0.230 (0.62) 0.229 (0.90) 0.224 (0.63) 0.215 (0.89) 0.202 (0.01) 0.173 (0.01) 0.156 (0.01)
Size of buffer (θ) 25 * 25 29 * 29 33 * 33 0.209 0.208 0.206 (0.73) (0.70) (0.69) 0.211 0.210 0.209 (1.25) (0.98) (1.00) 0.212 0.211 0.212 (1.81) (1.34) (1.81) 0.212 0.211 0.212 (1.84) (2.32) (2.33) 0.209 0.211 0.211 (2.33) (2.33) (2.33) 0.206 0.207 0.209 (2.33) (2.33) (2.33) 0.200 0.201 0.203 (2.33) (2.33) (2.33) (e) Impervious areas.
37 * 37 0.204 (0.67) 0.207 (1.01) 0.211 (1.35) 0.212 (1.85) 0.212 (2.34) 0.209 (2.33) 0.204 (2.33)
45 * 45 1.99 (0.94) 0.205 (1.01) 0.209 (1.36) 0.212 (1.85) 0.212 (2.34) 0.210 (2.33) 0.205 (2.33)
Size of buffer (θ) 13 * 13 17 * 17 0.230 0.221 (-3.25) (-0.17) 0.233 0.227 (-10.21) (-0.16) 0.233 0.233 (-16.28) (-1.70) 0.233 0.233 (0.71) (0.46) 0.224 0.232 (0.91) (0.83) 0.194 0.207 (1.50) (1.52) 0.173 0.183 (0.01) (1.58) (f) Urban areas.
21 * 21 0.207 (-0.62) 0.215 (-0.29) 0.222 (0.37) 0.229 (0.04) 0.230 (-2.42)) 0.211 (1.14) 0.188 (1.87)
25 * 25 0.191 (-0.31) 1.99 (-0.03) 0.208 (0.34) 0.217 (0.13) 0.222 (-0.28) 0.210 (0.53) 0.189 (1.85)
11 * 11 0.232 (-7.94) 0.233 (-12.46) 0.233 (0.56) 0.226 (0.76) 0.215 (0.94) 0.185 (0.01) 0.165 (0.01)
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 (Number of pixels)
Upwind Water (54,142)
Downwind
Upwind Agriculture (618,405)
Downwind
Upwind Green (986,326)
Downwind
Neighboring land use α Intercept Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban α Intercept Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban α Intercept Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban
β’s 0.01 8.13 1.01 0.001 0.21 0.88 0.95 1.40 0.71 0.33 -0.39 0.78 0.66 -4.21 -0.46 9.46 0.36 -0.17 0.15 0.74 0.19 1.42 0.10 -0.002 -0.03 0.12 0.25 0.08 -10.07 9.48 8.04E+10 -3.15E+9 9.44E+8 5.12E+10 2.69E+10 -3.43E+10 33.644 -5.44 -9.43 19.81 30.79 0.72
t-statistics 490.28 162.21 0.03 12.46 23.62 31.16 8.37 93.06 9.51 -20.54 18.95 19.38 -17.69 1487.42 27.62 -25.40 32.40 40.25 12.16 13.06 19.69 -0.75 -17.69 16.56 39.69 2.27 2388.84 134.67 -9.23 56.59 91.25 48.00 -5.34 -6.62E+10 -16.36 -55.39 35.81 52.60 0.13
R2 (θ, p)
0.823 (11, 0.4)
0.040 (51, 0.6)
0.135 (47, 1.5)
Table 6.13. Results for the highest R2 NDVI models on February 25, 2006. Continued. 133
Table 6.13 continued. Central land use (Number of pixels)
Upwind Residential (309,718)
Downwind
Upwind Impervious (459,196)
Downwind
Upwind Urban (59,169)
Downwind
Neighboring land use α Intercept Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban α Intercept Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban α Intercept Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban
134
β’s 2.24 10.36 0.02 -0.005 -0.002 0.004 0.004 0.04 1.22 -0.35 -0.38 0.31 0.43 3.30 1.81 10.49 0.73 -0.21 -0.07 0.31 -0.002 0.86 26.54 -10.56 -4.60 9.36 2.59 39.42 0.56 10.64 0.81 -0.07 -0.05 0.76 -1.26 2.36 2.31 -2.13 0.83 4.11 -4.20 3.29
t-statistics 2059.92 112.26 -32.75 -43.93 68.62 39.33 45.22 74.30 -22.25 -54.86 35.04 39.45 38.80 1917.53 507.11 -35.32 -22.92 56.98 -3.71 47.74 100.01 -38.61 -32.98 41.33 15.24 45.82 310.20 16.17 -1.35 -1.62 15.38 -48.28 87.73 14.16 -12.35 7.33 24.33 -45.31 28.76
R2 (θ, p)
0.273 (13, 0.5)
0.212 (25, 1.2)
0.233 (11, 0.4)
The equations that represent the relationship between the NDVI areas and local temperature can be summarized as follows:
TWater = 8.13 + u0.01·[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
- 0.39· NDVI *
Green
+ 0.78· NDVI *
+ 0.66· NDVI *
Re si
Im p
* Ag
– 4.21· NDVI *
] (6.22)
Urban
TAg = 9.46 + u-0.46·[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
- 0.03· NDVI *
Green
+ 0.12· NDVI*
+ 0.25· NDVI *
Re si
Im p
* Ag
+ 0.08· NDVI *
] (6.23)
Urban
TGreen = 9.48 + u-10.07·[(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 *
Water
+ 30.79· NDVI *
Im p
- 5.44· NDVI
+ 0.72· NDVI *
* Ag
Urban
- 9.43· NDVI *
Green
+ 19.81· NDVI*
Re si
]
(6.24)
TResi = 10.36 + u2.24·[0.02·NDVIWater - 0.005·NDVIAg - 0.002·NDVIGreen +0.004·NDVIResi
+ 0.004·NDVIImp+ 0.04·NDVIUrban] + [1.22· NDVI *
Water
- 0.38· NDVI *
Green
+ 0.31· NDVI *
Re si
+ 0.43· NDVI *
Im p
-0.35· NDVI
* Ag
+ 3.30· NDVI *
Urban
]
(6.25)
TImp = 10.49 + u1.81·[0.73·NDVIWater - 0.21·NDVIAg - 0.07·NDVIGreen + 0.31·NDVIResi
- 0.002·NDVIImp + 0.86·NDVIUrban] + [26.54· NDVI *
Water
- 4.60· NDVI *
Green
+ 9.36· NDVI*
Re si
+ 2.59· NDVI *
Im p
135
- 10.56· NDVI
+ 39.42· NDVI *
Urban
* Ag
] (6.26)
TUrban = 10.64 + u0.56·[0.81 NDVIWater – 0.07 NDVIAg – 0.05 NDVIGreen + 0.76·NDVIResi
– 1.26 NDVIImp + 2.36 NDVIUrban] + [2.31· NDVI *
Water
+ 0.83· NDVI *
Green
+ 4.11· NDVI *
Re si
- 4.20· NDVI *
Im p
- 2.13· NDVI
+ 3.29· NDVI *
* Ag
Urban
]
(6.27)
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 *
Landuse
are the sum of the NDVI areas of the upwind
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
Central land use
Wind side
Upwind Water
Downwind
Upwind Agriculture Downwind
Upwind Green Downwind
Neighboring land use Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban
NDVI weighted sum Mean -1.67 0.08 0.36 0.10 -0.004 -0.006 -1.17 0.08 0.32 0.09 0.009 -0.003 -0.04 1.73 2.32 0.21 0.32 -0.007 -0.04 1.51 2.22 0.21 0.32 -0.008 -2.74E-4
0.007 0.19 0.002 0.003 -3.85E-5 -2.83E-4
0.006 0.01 0.002 0.002 -3.83E-5
Standard deviation 1.64 0.17 0.47 0.20 0.21 0.03 1.28 0.18 0.42 0.18 0.19 0.02 0.36 0.83 1.25 0.40 0.42 0.05 0.35 0.77 1.20 0.38 0.42 0.06 0.002 0.005 0.10 0.004 0.003 2.19E-4 0.002 0.005 0.008 0.004 0.003 2.23E-4
Minimum Maximum -5.01 -0.39 -1.43 -0.41 -2.49 -1.91 -3.83 -0.56 -1.77 -0.36 -1.90 -1.51 -13.56 -0.98 -1.527 -0.27 -1.83 -2.07 -12.71 -0.85 -0.05 -0.30 -1.82 -2.61 -0.07 -0.01 -0.50 -0.007 -0.02 -0.008 -0.07 -0.007 -0.01 -0.007 -0.02 -0.01
2.46 2.49 4.26 2.04 1.83 0.11 1.78 2.85 3.47 1.74 1.51 0.12 0.78 9.90 9.37 5.30 3.92 0.63 0.72 8.74 9.10 4.77 3.89 0.47 0.02 0.07 0.76 0.04 0.04 0.007 0.01 0.06 0.06 0.04 0.04 0.006
Table 6.14. NDVI statistics for the independent variables on February 25, 2006. Continued. 137
Table 6.14 continued.
Neighboring land use
Central land use
Upwind Residential Downwind
Upwind Impervious Downwind
Upwind Urban Downwind
Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban
NDVI weighted sum Mean -0.007 0.07 0.410 0.62 0.27 -0.004 -0.008 0.06 0.36 0.39 0.23 -0.004 -0.001 0.008 0.02 0.01 0.11 -0.001 -0.001 0.007 0.02 0.01 0.02 -0.001 -0.02 0.08 0.17 0.14 0.15 -0.22 -0.02 0.07 0.15 0.12 0.15 -0.14
138
Minimum Maximum -3.25 -0.39 -1.51 -0.90 -1.68 -0.65 -3.05 -0.70 -1.29 -0.33 -1.46 -0.58 -0.25 -0.07 -0.06 -0.02 -0.79 -0.14 -0.22 -0.05 -0.06 -0.02 -0.11 -0.13 -3.96 -2.39 -0.66 -0.31 -3.79 -5.16 -3.66 -1.07 -0.25 -0.26 -3.31 -4.33
1.34 3.00 3.56 2.43 1.81 0.42 1.01 2.58 3.05 1.81 1.83 0.40 0.04 0.21 0.23 0.14 0.75 0.04 0.03 0.18 0.22 0.12 0.14 0.05 0.19 4.75 3.73 1.73 2.20 1.61 0.21 3.35 3.56 2.04 1.74 1.03
Standard deviation 0.11 0.14 0.41 0.38 0.24 0.02 0.11 0.12 0.36 0.29 0.21 0.02 0.01 0.01 0.02 0.02 0.12 0.003 0.009 0.01 0.02 0.01 0.02 0.003 0.17 0.17 0.29 0.17 0.36 0.30 0.16 0.16 0.26 0.17 0.32 0.24
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 and εdown = -0.337)39. 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
Central land use
Neighboring land use
Upwind Water
Downwind
Upwind Agriculture Downwind
Upwind Green Downwind
Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban
Elasticity Mean
Minimum
Maximum
-0.6882 0.00001 0.0107 0.0116 -0.0095 -0.0021 -0.33699 0.00334 -0.01781 0.00936 -0.00466 0.00276 -0.0007 -0.0122 0.0142 0.0063 0.0024 -0.0004 -0.00046 -0.00033 -0.00710 0.00261 0.00827 -0.00007 -0.0026 -0.0019 0.0161 0.0118 0.0059 0.0001 -0.00114 -0.00348 -0.01748 0.00472 0.00699 0.00001
-4.5712 -0.0003 -0.1933 -0.1390 -1.3328 -0.8251 -2.37726 -0.14012 -0.21914 -0.15326 -0.94671 -0.30836 -1.3612 -0.4531 -0.5898 -0.5635 -0.2019 -1.2478 -0.28224 -0.01288 -0.37754 -0.41456 -0.87782 -0.14658 -3.1877 -0.0988 -0.2449 -0.1125 -0.3760 -0.2506 -0.74362 -0.13667 -0.65558 -0.11535 -0.33243 -0.00671
0.4335 0.0003 0.1318 0.2391 0.2125 0.0686 0.23211 0.13693 0.40983 0.15169 0.18437 1.48093 0.0362 0.4347 0.8311 1.1794 0.4913 0.6453 0.32386 0.01343 0.20670 0.94773 1.81500 0.15588 0.2492 0.0957 0.5492 0.5753 0.4569 0.7259 0.07548 0.13577 0.37929 0.33201 0.80683 0.00336
Standard deviation 0.8928 0.0000 0.0140 0.0221 0.0605 0.0164 0.45884 0.00873 0.02612 0.01843 0.04095 0.02179 0.0081 0.0069 0.0085 0.0121 0.0036 0.0048 0.00470 0.00019 0.00430 0.00518 0.01206 0.00071 0.0285 0.0015 0.0091 0.0172 0.0078 0.0012 0.01016 0.00271 0.00900 0.00692 0.00907 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. Central land uses
Neighboring land uses
Upwind
Residential
Downwind
Upwind
Impervious
Downwind
Upwind
Urban
Downwind
Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban
Elasticity Mean
Minimum
Maximum
Standard deviation
-0.0025 -0.0035 -0.0083 0.0240 0.0105 -0.0017 -0.0013 -0.0021 -0.0133 0.0112 0.0091 -0.0013 -0.0077 -0.0070 -0.0070 0.0207 -0.0009 -0.0048 -0.0052 -0.0074 -0.0098 0.0130 0.0042 -0.0046 -0.0056 -0.0013 -0.0020 0.0238 -0.0418 -0.1205 -0.0050 -0.0104 0.0087 0.0357 -0.0407 -0.0345
-3.5269 -0.4590 -0.1772 -0.9402 -0.7800 -3.3135 -1.2726 -0.1282 -0.5434 -0.3979 -0.6279 -2.6677 -5.2930 -0.9450 -0.5064 -1.6132 -0.1296 -4.1410 -3.0983 -1.5587 -0.7958 -0.9324 -0.4645 -4.3389 -2.2423 -0.7987 -0.4393 -6.3527 -16.1003 -27.2625 -2.6316 -6.2719 -1.9266 -8.3554 -13.1755 -11.1392
0.3725 0.0956 0.3928 0.4583 0.6970 5.0273 1.3524 0.1394 0.5621 0.3603 0.6610 3.2178 0.4223 0.9519 0.9094 1.1528 0.1172 3.8259 1.7695 1.4694 0.8178 0.9605 0.3718 4.3564 0.5394 0.8639 0.4791 6.5201 18.6095 29.1896 1.1564 4.9784 2.7128 6.7373 21.4935 11.2973
0.0408 0.0074 0.0087 0.0147 0.0102 0.0278 0.0195 0.0046 0.0140 0.0083 0.0090 0.0175 0.0851 0.0127 0.0082 0.0219 0.0016 0.0391 0.0509 0.0140 0.0119 0.0142 0.0057 0.0370 0.0542 0.0122 0.0110 0.1566 0.4683 1.1668 0.0535 0.1061 0.0483 0.1963 0.4613 0.3644
Continued. 141
Table 6.15 continued. Central land use
Neighboring land use
Upwind Water Downwind
Upwind Agriculture Downwind
Upwind Green Downwind
Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban
Elasticity Mean
Minimum
Maximum
-0.76393 0.00545 0.01603 0.00313 -0.00194 -0.00021 -0.54685 0.00485 0.01439 0.00292 -0.00143 -0.00010 -0.00227 0.03033 0.02012 0.00109 0.00110 -0.00002 -0.00224 0.02648 0.01932 0.00107 0.00109 -0.00002 -0.00001 0.00006 0.00065 0.00001 0.00057 0.00001 -0.00001 0.00005 0.00006 0.00002 0.00009 0.0001
-9.38407 -0.09999 -0.10671 -0.04445 -0.26360 -0.06407 -6.44633 -0.14655 -0.16087 -0.03867 -0.26623 -0.02375 -1.00540 -0.01813 -0.01630 -0.00185 -0.00754 -0.00620 -0.84298 -0.01568 -0.00048 -0.00184 -0.00900 -0.00690 -0.00585 -0.00020 -0.00349 -0.00002 -0.00004 -0.00001 -0.00441 -0.00008 -0.00010 -0.00002 -0.00004 -0.00001
0.22890 0.14544 0.17967 0.05009 0.03524 0.00334 0.17467 0.16145 0.14583 0.04327 0.04085 0.00504 0.03952 0.18499 0.07917 0.02222 0.01257 0.00153 0.03666 0.15391 0.08205 0.02196 0.01192 0.00112 0.00069 0.00065 0.00258 0.00006 0.00003 0.00001 0.00046 0.00055 0.00023 0.00005 0.00004 0.00000
(b) Tj =Temperatures estimated with the regression models.40
Standard deviation 1.28733 0.01150 0.02036 0.00586 0.01264 0.00133 0.96573 0.01211 0.02007 0.00569 0.01234 0.00064 0.02073 0.01501 0.01070 0.00193 0.00141 0.00012 0.02082 0.01363 0.01039 0.00186 0.00137 0.00014 0.00011 0.00004 0.00035 0.00001 0.00000 0.00000 0.00009 0.00004 0.00003 0.00001 0.00000 0.00000
Continued.
40
Estimated Temperature with Equations (6.11) through (6.16).
142
Table 6.15 continued.
Central land uses
Neighboring land uses
Upwind
Residential
Downwind
Upwind
Impervious
Downwind
Upwind
Urban
Downwind
Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban
Elasticity Mean
Minimum
Maximum
Standard deviation
-0.0024 -0.0035 -0.0082 0.0239 0.0105 -0.0017 -0.0012 -0.0021 -0.0132 0.0112 0.0090 -0.0013 -0.0070 -0.0069 -0.0069 0.0205 -0.0009 -0.0046 -0.0048 -0.0073 -0.0096 0.0128 0.0041 -0.0044 -0.0056 -0.0015 -0.0021 0.0271 -0.0721 -0.1634 -0.0049 -0.0150 0.0099 0.0418 -0.0770 -0.0458
-3.1918 -0.1855 -0.0881 -0.0618 -0.1653 -0.3666 -2.2389 -0.1075 -0.1381 -0.0165 -0.0929 -0.2623 -9.3130 -0.2278 -0.0730 -0.2259 -0.1376 -1.5918 -4.4761 -0.2474 -0.1132 -0.0536 -0.1517 -1.2861 -3.1176 -0.1735 -0.0689 -9.3610 -122.2751 -1151.377 -4.1552 -8.6036 -5.3760 -78.9271 -211.1948 -372.4061
0.2192 0.0224 0.0348 0.0858 0.0652 0.1291 0.1048 0.0238 0.1099 0.0485 0.0713 0.1145 19.2831 0.3488 0.1223 0.1395 0.0451 0.1447 19.1882 0.1935 0.1257 0.0922 0.1807 0.1598 0.9729 0.4884 0.0661 3.1895 77.9774 3623.1703 4.3174 14.9490 9.0713 54.8049 122.5940 772.8028
0.0366 0.0072 0.0084 0.0139 0.0090 0.0095 0.0179 0.0044 0.0137 0.0080 0.0081 0.0071 0.0867 0.0111 0.0074 0.0184 0.0011 0.0156 0.0632 0.0119 0.0102 0.0116 0.0042 0.0133 0.0598 0.0045 0.0043 0.0658 1.0201 16.9884 0.0720 0.1012 0.0525 0.5279 1.6234 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:
T j , RST = T j ,base + u α ⋅ ∑ β k ⋅ [∑ k
i
wij d ijp
⋅ AREA ⋅ LU ik ⋅ N ij ]
+ ∑ γ k ⋅ [∑ k
i
(1 − wij ) d ijp
⋅ AREA ⋅ LU ik ⋅ N ij ] + ε j
= T j ,base + ∑ β k ⋅ (u α ⋅ X jk ) + ∑ β k' ⋅ X 'jk + ε j k
where X j ,k = ∑ i
wij d ijp
(6.28)
k
⋅ AREA ⋅ LU ik ⋅ N ij and X 'j ,k = ∑ i
(1 − wij ) d ijp
⋅ AREA ⋅ LU ik ⋅ N ij .
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
p 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
p 0.8 0.9 1.0 1.1 1.2 1.3 1.4
7*7 0.748 (0.01) 0.744 (0.01) 0.740 (0.01) 0.736 (0.01) 0.731 (0.01) 0.727 (0.01) 0.721 (0.01) 0.716 (0.01)
13 * 13 0.039 0.039 0.039 0.038 0.038 0.037 0.037
15 * 15 0.816 (0.01) 0.817 (0.01) 0.817 (0.01) 0.816 (0.01) 0.815 (0.01) 0.813 (0.01) 0.811 (0.01) 0.809 (0.01)
Size of buffer (θ) 17 * 17 19 * 19 0.815 0.812 (-1.54) (-1.54) 0.816 0.814 (0.01) (-1.60) 0.817 0.816 (0.01) (0.01) 0.818 0.818 (0.01) (0.01) 0.818 0.819 (0.01) (0.01) 0.818 0.819 (0.01) (0.01) 0.815 0.818 (0.01) (0.01) 0.814 0.816 (0.01) (0.01) (a) Water.
23 * 23 0.803 (0.01) 0.807 (0.01) 0.811 (0.01) 0.814 (0.01) 0.817 (0.01) 0.819 (0.01) 0.819 (0.01) 0.818 (0.01)
Size of buffer (θ) 25 * 25 45 * 45 49 * 49 53 * 53 0.047 0.048 0.048 0.048 0.047 0.048 0.048 0.048 0.046 0.048 0.048 0.048 0.046 0.048 0.048 0.048 0.046 0.048 0.048 0.048 0.045 0.048 0.048 0.048 0.045 0.048 0.048 0.048 (b) Agriculture (α = 0.01 in all cases).
27 * 27 0.792 (-2.58) 0.798 (-2.01) 0.803 (-1.05) 0.807 (0.01) 0.812 (0.01) 0.815 (0.01) 0.815 (0.01) 0.818 (0.01)
61 * 61 0.047 0.047 0.047 0.047 0.047 0.047 0.047
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.
p 1.1 1.2 1.3 1.4 1.5 1.6 1.7
p 1.3 1.4 1.5 1.7 1.8 1.9 2.1
27 * 27 0.139 (-2.80) 0.140 (-5.28) 0.141 (-4.00) 0.141 (-3.87) 0.141 (-18.76) 0.100 (-98.47) 0.140 (-3.08)
17 * 17 0.345 (0.01) 0.346 (0.01) 0.347 (0.01) 0.345 (0.01) 0.345 (0.01) 0.340 (0.5369) 0.332 (1.23)
35 * 35 0.139 (-2.628) 0.140 (-3.68) 0.142 (-8.90) 0.143 (-2.89) 0.144 (-9.30) 0.102 (-98.60) 0.143 (-3.57)
25 * 25 0.340 (0.01) 0.345 (0.01) 0.346 (0.01) 0.348 (0.01) 0.348 (0.01) 0.347 (0.01) 0.341 (1.19)
Size of buffer (θ) 43 * 43 47 * 47 0.138 0.137 (-3.49) (-4.09) 0.139 0.139 (-2.79) (-2.63) 0.142 0.141 (-5.42) (-4.64) 0.143 0.143 (-3.79) (-20.49) 0.144 0.145 (-6.02) (-3.06) 0.145 0.145 (-36.84) (-26.11) 0.104 0.104 (-4940.3) (-2052.9) (c) Green areas.
Size of buffer (θ) 29 * 29 33 *33 0.336 0.332 (0.01) (0.01) 0.341 0.337 (0.01) (0.01) 0.344 0.341 (0.01) (0.01) 0.348 0.347 (0.01) (0.01) 0.348 0.347 (0.01) (0.01) 0.348 0.348 (0.01) (0.01) 0.343 0.344 (1.18) (1.17) (d) Residential areas.
51 * 51 0.136 (-3.77) 0.138 (-2.63) 0.140 (-23.13) 0.144 (-14.45) 0.144 (-3.48) 0.145 (-19.62) 0.105 (-986.7)
55 * 55 0.135 (-3.29) 0.137 (-2.62) 0.139 (-3.06) 0.142 (-4.64) 0.144 (-3.15) 0.145 (-15.59) 0.105 (-547.8)
37 * 37 0.328 (0.01) 0.332 (0.01) 0.339 (0.01) 0.346 (0.01) 0.347 (0.01) 0.348 (0.01) 0.345 (1.16)
45 * 45 0.320 (0.01) 0.328 (0.01) 0.334 (0.01) 0.344 (0.01) 0.346 (0.01) 0.347 (0.01) 0.346 (1.15) Continued.
147
Table 6.16 continued.
1.1 1.3 1.4 1.5 1.6 1.7 1.9
p 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7
17 * 17 0.271 (0.01) 0.270 (0.01) 0.270 (0.01) 0.268 (0.01) 0.265 (0.01) 0.263 (0.01) 0.255 (0.277)
Size of buffer (θ) 21 * 21 25 * 25 33 * 33 0.274 0.274 0.270 (0.01) (0.01) (0.01) 0.275 0.277 0.275 (0.01) (0.01) (0.01) 0.274 0.277 0.276 (0.01) (0.01) (0.01) 0.274 0.277 0.278 (0.01) (0.01) (0.01) 0.271 0.275 0.278 (0.01) (0.01) (0.01) 0.269 0.273 0.276 (0.01) (0.01) (0.01) 0.262 0.266 0.271 (0.25) (0.231) (0.40) (e) Impervious areas.
37 * 37 0.266 (0.01) 0.273 (0.01) 0.275 (0.01) 0.277 (0.01) 0.277 (0.01) 0.277 (0.01) 0.272 (0.38)
45 * 45 0.259 (0.01) 0.259 (0.01) 0.268 (0.01) 0.274 (0.01) 0.275 (0.01) 0.276 (0.01) 0.272 (0.356)
9*9 0.194 0.193 0.192 0.192 0.190 0.187 0.185 0.184
Size of buffer (θ) 13 * 13 17 * 17 21 * 21 25 * 25 0.198 0.195 0.189 0.183 0.199 0.197 0.193 0.188 0.199 0.199 0.196 0.191 0.199 0.199 0.198 0.195 0.199 0.199 0.196 0.200 0.198 0.200 0.200 0.198 0.196 0.199 0.200 0.199 0.194 0.198 0.199 0.199 (f) Urban areas (α = 0.01 in all cases).
29 * 29 0.178 0.184 0.187 0.191 0.194 0.197 0.198 0.198
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 (Number of pixels)
Upwind Water (53,542)
Downwind
Upwind Agriculture (626,273)
Downwind
Upwind Green (992,531)
Downwind
Neighboring land use α Intercept Water Agriculture Green Residential Impervious Water Agriculture Green Residential Impervious α Intercept Water Agriculture Green Residential Impervious Water Agriculture Green Residential Impervious α Intercept Water Agriculture Green Residential Impervious Water Agriculture Green Residential Impervious
β’s 0.01 17.169 -0.008 0.0008 0.004 0.007 -0.0009 -0.01 -0.003 -0.003 0.002 -0.001 0.01 5.034 0.0004 0.0008 0.001 0.002 0.001 -0.00002 0.0004 0.0003 0.0009 0.0006 -6.019 -4.626 -3595.1 2581.7 3101.4 5238.2 3741.7 -0.002 0.009 0.008 0.02 0.015
t-statistics 27.745 5.756 1.510 5.455 8.568 -1.970 -21.967 -5.266 -6.674 4.693 -1.919 52.273 12.229 29.607 40.357 55.333 31.471 -0.588 13.643 12.286 29.633 18.697 -13.751 -38.478 30.035 36.293 60.851 39.226 -4.707 26.974 23.884 44.380 37.468
R2 (θ, p)
0.819 (19, 1.2)
0.048 (45, 1.0)
0.145 (43, 1.5)
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 (Number of pixels)
Upwind Residential (308,897)
Downwind
Upwind Impervious (457,888)
Downwind
Upwind Urban (59,145)
Downwind
Neighboring land use α Intercept Water Agriculture Green Residential Impervious Water Agriculture Green Residential Impervious α Intercept Agriculture Green Residential Impervious Urban Agriculture Green Residential Impervious Urban α Intercept Agriculture Green Residential Impervious Urban Agriculture Green Residential Impervious Urban
150
β’s 0.01 -27.922 -0.004 0.022 0.026 0.034 0.031 -0.00009 0.024 0.021 0.030 0.031 0.01 -33.939 0.024 0.032 0.038 0.037 0.012 0.029 0.031 0.037 0.040 0.015 0.01 7.324 0.023 0.0005 0.007 0.037 -0.008 0.031 0.038 0.032 0.065 0.022
t-statistics -91.578 -10.079 63.610 85.948 113.953 95.427 -0.215 60.560 61.696 89.881 83.469 -128.122 85.211 118.727 138.745 143.295 40.924 87.234 99.357 116.772 132.895 41.643 2.277 1.869 0.134 1.169 2.067 1.261 8.832 10.563 9.020 20.062 6.824
R2 (θ, p)
0.348 (25, 1.7)
0.278 (33, 1.5)
0.200 (17, 1.4)
The equations that represent the relationships between the land-use areas and local temperature can be summarized as follows:
TWater = 17.17 + u0.01·[-0.008·AREAWater + 0.0008·AREAAg + 0.004·AREAGreen *
+ 0.007·AREAResi - 0.0009·AREAImp ] + [-0.01· AREAWater - 0.003· AREA *
Ag
*
*
-0.003· AREAGreen + 0.002· AREAResi - 0.00104· AREA *
Im p
]
(6.29)
TAg = 5.03+ u0.01·[0.0004·AREAWater + 0.0008·AREAAg + 0.001·AREAGreen *
+ 0.002·AREAResi + 0.001·AREAImp ] + [-0.00002· AREAWater + 0.0004· AREA *
Ag
*
*
+ 0.0003· AREAGreen + 0.0009· AREAResi + 0.0006· AREA *
Im p
]
(6.30)
TGreen = -4.63 + u-6.021·[-3595.1·AREAWater + 2581.7·AREAAg + 3101.4·AREAGreen *
+ 5238.2·AREAResi + 3741.7·AREAImp ] + [-0.002· AREAWater + 0.009· AREA *
Ag
*
+ 0.008· AREAGreen + 0.02· AREA*Re si + 0.01· AREA *
Im p
]
(6.31)
TResi = -27.92 + u0.01·[-0.004·AREAWater + 0.022·AREAAg + 0.026·AREAGreen *
+ 0.034·AREAResi + 0.031·AREAImp ] + [-0.00009· AREAWater + 0.024· AREA *
Ag
*
*
+ 0.021· AREAGreen + 0.03· AREAResi + 0.031· AREA *
Im p
]
(6.32)
TImp = -33.9394+ u0.01·[0.024·AREAAg + 0.032·AREAGreen + 0.038·AREAResi *
+ 0.037·AREAImp + 0.012·AREAUrban] + [0.029· AREA * + 0.031· AREAGreen Ag
*
+ 0.037· AREAResi + 0.04· AREA *
Im p
*
+ 0.015· AREAUrban ] 151
(6.33)
TUrban = 7.32+ u0.01·[0.023·AREAAg + 0.0005·AREAGreen + 0.007·AREAResi *
+ 0.037·AREAImp - 0.008·AREAUrban] + [0.031· AREA * + 0.038· AREAGreen Ag
*
+ 0.032· AREAResi + 0.065· AREA *
Im p
*
+ 0.022· AREAUrban ]
(6.34)
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
Central land use
Neighboring land use
Upwind Water
Downwind
Upwind Agriculture Downwind
Upwind Green Downwind
Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban
Weighted sum of neighboring land uses (m2) Mean 1,130.5 28.45 104.56 36.83 47.54 4.14 181.12 25.22 93.22 32.57 42.98 3.80 22.70 2,187.5 1,103.1 101.35 214.62 21.44 22.56 1,153.5 1,024.2 98.39 208.91 21.64 2.51
42.74 1,003.7 14.77 18.10 1.26 2.34
38.76 87.59 13.03 16.31 1.18
Minimum Maximum 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1,352.1 329.26 449.03 395.78 402.24 223.90 378.98 313.67 378.98 351.40 333.11 236.03 2,577.8 3,650.7 2,606.0 1,938.8 2,053.8 2,085.8 2,529.3 2,529.3 2,396.7 1,15.6 2,016.8 1,928.7 175.74 181.21 1,080.5 147.39 151.05 113.58 159.23 159.23 156.13 128.09 130.26 101.54
Standard deviation 148.16 42.28 100.04 47.65 63.75 13.64 131.01 39.05 91.50 43.71 56.61 13.22 88.48 573.28 439.09 175.54 284.37 81.02 90.42 531.06 410.85 167.21 276.03 82.33 8.23 32.04 33.12 20.53 21.22 4.21 7.76 28.78 29.64 18.20 19.20 3.99
Table 6.18. Land-use area statistics for the independent variables on February 25, 2006. Continued. 153
Table 6.18 continued.
Neighboring land uses
Central land uses
Upwind Residential Downwind
Upwind Impervious Downwind
Upwind Urban Downwind
Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban Water Agriculture Green Residential Impervious Urban
Weighted sum of neighboring land uses (m2) Mean 0.74 2.49 12.56 920.80 15.64 0.85 0.62 2.19 10.80 15.91 12.75 0.76 2.08 14.77 32.18 31.29 968.95 8.32 1.83 12.85 28.89 27.17 56.39 7.23 1.11 10.09 11.33 13.31 68.24 961.99 1.06 8.34 10.35 12.15 57.17 45.55
154
Minimum Maximum 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
51.63 40.69 53.05 949.21 51.15 39.11 43.06 41.46 42.90 40.36 41.99 34.81 157.61 139.59 150.71 134.39 1,050.1 140.41 134.38 122.76 131.54 116.43 127.66 124.02 117.96 160.65 130.46 108.83 160.80 1,066.1 134.64 128.28 119.33 89.76 134.22 134.64
Standard deviation 2.78 4.05 10.53 10.210 10.12 2.23 2.52 3.56 8.99 8.46 8.40 2.02 8.58 19.64 27.19 23.32 29.03 13.61 7.54 17.20 24.11 20.18 25.31 11.99 6.12 15.63 15.15 13.12 30.83 37.42 6.10 13.14 14.01 11.89 26.27 31.74
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: remotelysensed (TRST) and model-estimated (Test). Upwind and downwind water has usually negative mean elasticities for all land uses (-2.677
