# Integrating Optical and Microwave Satellite Observations for High Resolution Land Surface Temperature and Soil Moisture Derivation and Drought Analyses

код для вставкиСкачатьINTEGRATING OPTICAL AND MICROWAVE SATELLITE OBSERVATIONS FOR HIGH RESOLUTION LAND SURFACE TEMPERATURE AND SOIL MOISTURE DERIVATION AND DROUGHT ANALYSES by Yu Li A Dissertation Submitted to the Graduate Faculty of George Mason University in Partial Fulfillment of The Requirements for the Degree of Doctor of Philosophy Earth System and Geoinformation Sciences Committee: _________________________________________ Dr. Donglian Sun, Dissertation Director _________________________________________ Dr. Xiwu Zhan, Committee Member _________________________________________ Dr. Chaowei Yang, Committee Member _________________________________________ Dr. Long S Chiu, Committee Member _________________________________________ Dr. Paul Houser, Committee Member _________________________________________ Dr. Anthony Stefanidis, Department Chair _________________________________________ Dr. Donna M. Fox, Associate Dean, Office of Student Affairs & Special Programs, College of Science _________________________________________ Dr. Peggy Agouris, Dean, College of Science Date: Summer Semester 2017 George Mason University Fairfax, VA __________________________________ Integrating Optical and Microwave Satellite Observations for High Resolution Land Surface Temperature and Soil Moisture Derivation and Drought Analyses A Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at George Mason University by Yu Li Master of Science Institute of Atmospheric Physics, Chinese Academy of Sciences & Chengdu University of Information Technology, 2012 Director: Donglian Sun, Professor Department of Earth System and Geoinformation Sciences Summer Semester 2017 George Mason University Fairfax, VA ProQuest Number: 10618964 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. ProQuest 10618964 Published by ProQuest LLC (2017 ). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106 - 1346 Copyright 2017 Yu Li All Rights Reserved ii DEDICATION This is dedicated to my amazing parents, Li Jianxi and Ju Yuqiong, my beloved and sweetest turtle Mohammad Mohtasham. iii ACKNOWLEDGEMENTS I would like to thank all my committee members, this dissertation would not be achieved by their valuable guidance. I owe my sincerest gratitude to my Dissertation Chair Dr. Donglian Sun. She is the kind of person that would provide people with all the convenience and concerns she could. She is an intelligent and elegant professor, and guides me through this process hand by hand. I could not be able to finish my Ph.D. journey without her support and encouragement. I’m very proud of her and thank her for everything. I’m grateful to my co-adviser, Dr. Xiwu Zhan. As a talented scientist, he would share his wisdom and help me through each step. His passionate attitude inspires me to be dedicated to my dissertation. I would like to thank Dr. Paul Houser. I always feel impressed by the way he looks into a scientific aspect and how he would use particular approaches to make contributions to this society. His expert view changed me, made me a different but better student. I would like to thank Dr. Long S Chiu, for his strong background knowledge of remote sensing and always willing to help me to understand different matters. I would like to thank Dr. Chaowei Yang. He is a genius and has an ability to link science for practical daily life. Thank them a lot. I owe the deepest gratitude Dr. Ruixin Yang, Dr. Matt Rice, and Department Chair Dr. Anthony Stefanidis. They offered me significant help so that I can pass through the dark time of my Ph.D. Their generous help would be appreciated all my life. Thank them. Thank my advisor Prof. Daren Lü and Prof. Jinli Liu in China. It is a big honor to be their student and able to communicate with the top scientists in China frequently. Their humor, enthusiasm of life, and wisdom always inspire me. Thank my parents and my turtle Mohammad, for their unconditional love and full support. They are my family and make me feel safe and fortunate. Thank all my friends in Northern Virginia. My girlfriends Manzhu Yu, Manqi Li, Jiexia Wu, and Yun Li, feel so blessed to know them and be friends with them, thank them for always be here for me whenever I have difficulties. Thank my friends Han Qin, Mengchao Xu, Fei Hu, Min Shao, thank them for all the joy and fun. My friends in China, Yan Yan, Xiao Xiao, Dongxu Yao, Yuan Yuan, thank them for being such a loyal friend and big support. iv TABLE OF CONTENTS Page List of Tables ................................................................................................................... viii List of Figures .................................................................................................................... ix List of Equations ............................................................................................................... xii List of Abbreviations ....................................................................................................... xiv Abstract ............................................................................................................................ xvi Chapter 1 Introduction ................................................................................................... 1 1.1 LST derivation from satellite observations .......................................................... 1 1.2 High-resolution LSTs ........................................................................................... 5 1.3 Practical usage of HR LST observations.............................................................. 7 1.3.1 Soil moisture retrieval ................................................................................... 7 1.3.2 Drought analysis ........................................................................................... 8 1.4 Structure of the dissertation................................................................................ 10 Chapter 2 2.1 Literature review ......................................................................................... 12 LST retrieval ...................................................................................................... 12 2.1.1 LST retrieval from infrared observations ................................................... 12 2.1.2 LST retrieval from MW observations ......................................................... 14 2.1.3 The integration of TIR and passive WM observations ............................... 16 2.2 LST downscaling approaches............................................................................. 18 2.3 Soil moisture derivation ..................................................................................... 21 2.4 Drought indicators .............................................................................................. 25 Chapter 3 Objective of this study ................................................................................ 30 3.1 Synergistic study on MW and TIR LST ............................................................ 30 3.2 Derivation of HR LST ........................................................................................ 32 3.3 Application of HR LST ...................................................................................... 33 3.4 Hypothesis .......................................................................................................... 34 Chapter 4 Methodology for LST integration ............................................................... 35 v 4.1 Merging LSTs from MW and TIR data ............................................................. 35 4.1.1 Data ............................................................................................................. 35 4.1.1.1 Microwave data ....................................................................................... 36 4.1.1.2 Thermal Infrared Data ............................................................................. 36 4.1.2 Algorithms for retrieving LST from passive microwave data .................... 37 4.1.2.1 The single-channel algorithm .................................................................. 38 4.1.2.2 The four-channel algorithm ..................................................................... 38 4.1.2.3 The five-channel algorithm ..................................................................... 38 4.1.2.4 The five-channel algorithm with auxiliary data ...................................... 39 4.2 Regression Tree algorithm ................................................................................. 42 4.3 GWR-based gap-filling algorithm ...................................................................... 44 4.4 Results from AMSR-E to MODIS calibration ................................................... 48 4.4.1 Implementation of the single-channel algorithm ........................................ 49 4.4.2 Implementation of the four-channel algorithm ........................................... 50 4.4.3 Implementation of the new proposed five-channel algorithm .................... 51 4.4.4 data Implementation of the new proposed five-channel algorithm with auxiliary 52 4.5 Results from AMSR-2 to GOES calibration ...................................................... 54 Chapter 5 Derivation of high-resolution LST.............................................................. 56 5.1 The regression-based LST downscaling algorithms .......................................... 56 5.2 The SRR-based LST downscaling algorithms ................................................... 57 5.2.1 The multi-images SRR ................................................................................... 58 5.2.1.1 The POCS-based SRR............................................................................. 58 5.2.1.2 The ML-based SRR................................................................................. 60 5.2.2 The single-image SRR .................................................................................... 62 5.2.2.1 Example-based SRR................................................................................ 62 5.2.2.2 Self-similarity-based SRR ....................................................................... 65 Chapter 6 6.1 Applications ................................................................................................ 67 Soil moisture derivation ..................................................................................... 67 6.1.1 Variables input to SM models..................................................................... 67 6.1.2 Temporal compositing and spatial resampling ........................................... 68 vi 6.1.3 Models for HR soil moisture estimates ....................................................... 68 6.1.2.1 The Universal Triangle Model ................................................................ 69 6.1.2.2 The Basic Model ..................................................................................... 69 6.1.2.3 The Refined Model.................................................................................. 71 6.2 Drought analyses ................................................................................................ 73 6.2.1 SM anomaly calculation ............................................................................. 74 6.2.2 Comparison with traditional indices and model outputs............................. 74 Chapter 7 Results ......................................................................................................... 76 7.1 Integrated LSTs .................................................................................................. 76 7.2 HR LST derivation ............................................................................................. 81 7.2.1 Regression-based derivation ....................................................................... 81 7.2.2 MISR-based derivation ............................................................................... 82 7.2.3 SISR-based derivation ................................................................................ 84 7.3 Soil moisture ...................................................................................................... 86 7.4 Drought analyses and case study........................................................................ 86 7.4.1 Drought in California .................................................................................. 86 7.4.2 Drought in contiguous U.S. ........................................................................ 91 7.4.3 Continuous drought monitoring .................................................................. 92 7.4.4 Case study: drought in 2012 ....................................................................... 94 Chapter 8 Evaluations .................................................................................................. 99 8.1 Validation of the integrated LST against SurfRad observations ........................ 99 8.2 Validation of the GWR-based gap-filled LST ................................................. 109 8.3 Downscaled results ........................................................................................... 111 8.3.1 Comparison with fine-resolution satellite data ......................................... 111 8.3.2 Evaluation against the SurfRad observations ........................................... 112 8.4 Validation of the soil moisture against SCAN observations ............................ 113 Chapter 9 Conclusion and Discussions ..................................................................... 116 References ....................................................................................................................... 120 vii LIST OF TABLES Table Page Table 1. Typical TIR sensors for LST observations and the onboard satellite information. ........................................................................................................................................... 13 Table 2. The channel selection for different microwave LSTs. ........................................ 41 Table 3. Different AMSR-2 Ascending LST retrieving models in autumn and analyses. 42 Table 4. LST derived from AMSR-E with the single-channel algorithm vs. MODIS LST in daytime.......................................................................................................................... 49 Table 6. LST derived from AMSR-E the single-channel algorithm vs. MODIS LST in nighttime ........................................................................................................................... 50 Table 6. LST derived from the AMSR-E with the four-channel algorithm vs. MODIS LST during daytime .......................................................................................................... 51 Table 7. LST derived from the AMSR-E with the four-channel algorithm vs. MODIS LST during nighttime ........................................................................................................ 51 Table 8. LST derived from the AMSR-E with the new proposed five-channel algorithm vs. MODIS LST during daytime ....................................................................................... 52 Table 9.LST derived from the AMSR-E with the new proposed five-channel algorithm vs. MODIS LST during night time ................................................................................... 52 Table 10. LST derived from AMSR-E ascending data with the new proposed fivechannel and auxiliary data, compared with MODIS LST product during daytime, 2007. 53 Table 11. LST derived from AMSR-E descending data with the new proposed fivechannel and auxiliary data, compared with MODIS LST product during nighttime, 2007. ........................................................................................................................................... 53 Table 12. LST derived from AMSR-2 Ascending data with new proposed five-channel and auxiliary data, compared with the GOES 1.5h before noon LST, 2013. ................... 54 Table 13. LST derived from AMSR-2 descending data with the new proposed fivechannel with auxiliary data, compared with the GOES 1.5h after sunrise LST, 2013. .... 55 Table 14. Different soil moisture models and the AICC values over California. ............. 71 Table 15. SurfRad sites for algorithm validation .............................................................. 99 Table 16. Scan sites for algorithm validation ................................................................. 114 viii LIST OF FIGURES Figure Page Figure 1.The outline of this dissertation. .......................................................................... 11 Figure 2. An example: part of the RT structure and regression models from AMSR-E and MODIS descending LST M5P training for autumn 2007. ................................................ 43 Figure 3. The regular process of gap-filling algorithm. .................................................... 45 Figure 4. (a) Cloud free MODIS LST, (b) the combined LST based on MODIS and AMSR-E data, (c) LST from the selected region (Figure 4a, inside the purple square) of MODIS observations, (d) the regular gap-filling method apply for (c), (e) LST from the selected region (Figure 4b, inside the purple square) of the combined observation, (f) the regular gap-filling method apply for (e), (h) the GWR-based filling algorithm applied to fill the gaps of the purple square, during nighttime/descending pass on December 15, 2008................................................................................................................................... 47 Figure 5. (a) MODIS LST from the selected region (Figure 4a, inside the red square) of MODIS observations, (b) AMSR-E LST from the selected region (Figure 4b, inside the red square) of the combined observation, (c) the regular method to fill gaps of (b), (d) the GWR-based filling algorithm applied to fill the gaps of (b), during nighttime/descending pass on December 15, 2008. ............................................................................................. 48 Figure 6. An example of training data. (a) The MODIS 5-km LSTs observations; (b) the selected region for HR version of image; (c) bicubic spline interpolation for the full coverage HR image; (d) LR version of the image. ........................................................... 63 Figure 7. (a) USDM weekly drought condition map. (b) Normalized Monthly accumulated precipitation over California (32 - 42°N, 114 - 125 °W) retrieved from TRMM, and normalized monthly accumulated precipitation seasonal decomposition by Loess, from Jan 2003 to Dec 2014.................................................................................... 72 Figure 8. (a)Cloud free MODIS LST, (b) the derived AMSR-E LST based on Fivechannel algorithm,(c) the combined LST based on MODIS and AMSR-E, (d) the integrated LST from MODIS and AMSR-E, during daytime on December 5, 2008. ...... 77 Figure 9. (a)Cloud free MODIS LST , (b)the derived AMSR-E LST, (c)the combined LST based on MODIS under clear sky and AMSR-E under clouds, (d)the integrated LST from MODIS and AMSR-E, during nighttime on June 2, 2008. ...................................... 78 Figure 10. (a) Cloud free GOES LST at 1.5h before noon, (b) the AMSR-2 Ascending LST, (c) GOES and AMSR-2 combined LST, and (d) the integrated LST from GOES and AMSR-2 on October 22, 2015. ......................................................................................... 79 Figure 11. (a) Cloud free GOES LST at 1.5 h after sunrise, (b) the AMSR-2 descending LST, (c) the GOES and AMSR-2 combined LST, and (d) the integrated LST from GOES and AMSR-2 on August 3, 2015....................................................................................... 80 ix Figure 12. Spatial distribution of (a) MODIS LST, (b) AMSR-E LST, (c) TsHARP, (d) traditional GWR downscaled LST, and (e)the GWR Gap-filling algorithm downscaled LST for the image at the same time (Oct 2, 2008). ........................................................... 81 Figure 13. Spatial distribution of (a) AMSR-E around 1: 30 p.m. LST, (b1) previous day of AMSR-E around 1: 30 p.m. LST, (c1) ML downscaled LST retrieval based on (a) and (b1), (d1) POCS downscaled LST retrieval based on (a) and (b1); (b2) same day of AMSR-E around 10: 30 a.m. LST, (c2) ML downscaled LST retrieval based on (a) and (b2), (d2) POCS downscaled LST retrieval based on (a) and (b2). Date: February 14, 2008................................................................................................................................... 83 Figure 14.Spatial distribution of downscaled LST from different SISR methods: (a) Example-based method (b) Self-similarity method. Date: 1:30 p.m., February 14, 2008. 84 Figure 15. An example for different SR methods: (a) Original LR image (10 km). (b) Example-based method (c) Self-similarity based method. LST data is 1.5h AMSR-2 LST before noon for August 9, 2015. ....................................................................................... 85 Figure 16. An example: The final HR AMSR-E LST compared with MODIS LST during daytime on December 8, 2008 .......................................................................................... 85 Figure 17. The final HR AMSR-2 LST compared with GOES 1.5h after sunrise LST on March 29, 2015 ................................................................................................................. 86 Figure 18. Drought condition from different indicators. From top to bottom: USDM classification, VTCI, VHI, model output, soil moisture anomalies based on ―Triangle Model‖, basic model output, and the refined model. Anomaly of Soil moisture content. 89 Figure 19. The temporal correlation coefficient maps between the USDM drought classifications and the triangle model (top panel), the basic model (middle panel), the refined model (bottom) outputs. ....................................................................................... 91 Figure 20. Contiguous U.S.Drought condition from different indicators. From top to bottom: the USDM classification, VTCI, VHI, ESI, NLDAS model output, soil moisture anomalies based on the refined model, and the soil moisture percentile based on the refined model. ................................................................................................................... 92 Figure 21. An example of weekly USDM observation compared with daily SM anomalies. First column: weekly USDM observations. Soil moisture anomalies observations in the continuous 8 days (from June 3 to June 10) (Second column) based on previous LST and (Third column) based on the new derived Example-based LST. ........ 93 Figure 22. Main Drought area in 2012.............................................................................. 94 Figure 23. (a) USDM weekly drought condition map over the twelve states in 2012. (b) The average soil moisture anomalies over the twelve states. ........................................... 96 Figure 24. (a) The USDM classification (b) soil moisture anomalies based on the refined model in Texas, and (c) the 1-km resolution soil moisture anomalies (drought conditions) on the west Texas. Date: May 8, 2012 .............................................................................. 97 Figure 25. 2012 Corn Future historical prices. The figure obtained from TDAmeritrade. ........................................................................................................................................... 98 Figure 26. Scatter plots of MODIS and AMSR-E LST against the SurfRad Observations in 2008. ......................................................................................................................... 102 Figure 27. Scatterplots of the comparison of LST from AMSR-E ascending /daytime retrievals and ground-based measurements at six SurfRad sites in 2008. ...................... 103 x Figure 28. Scatterplots of the comparison of LST from AMSR-E descending /nighttime retrievals and ground-based measurements at six SurfRad sites in 2008. ...................... 105 Figure 29. Scatter plots of GOES LST product and the retrieved AMSR-2 LST vs. SurfRad observations in 2015 during daytime (a) and nighttime (b). ............................ 106 Figure 30. Scatterplots of the comparison of LST from AMSR-2 ascending /daytime retrievals and ground-based measurements at six SurfRad sites in 2015. ...................... 107 Figure 31. Scatterplots of the comparison of LST from AMSR-2 descending /nighttime retrievals and ground-based measurements at six SurfRad sites in 2015. ...................... 108 Figure 32. An comparison between gap-filling LST and Terra LST. (a) Cloud free GOES LST at 1.5h before noon, (b) the AMSR-2 ascending LST, (c) GOES and AMSR-2 combined LST, (d) the integrated LST from GOES and AMSR-2, (e)Terra descending LST, (f) the difference between images based retrieval on June 18, 2015. .................... 109 Figure 33. The histogram of the difference between gap-filling LSTs and Terra LSTs in figure 32f. ........................................................................................................................ 110 Figure 34. A sample set for comparing the gap-filling LSTs with MODIS/TERRA at 1km for 2015. .................................................................................................................... 110 Figure 35. A sample set for comparing with MODIS at 1-km for 2008, based on examplebased SRR (a), self-similarity SRR (b). .......................................................................... 111 Figure 36. Scatter plots of the AMSR-E LST vs. SurfRad observations in 2008 during daytime/ascending (a) LSTs retrieved from Example-Based SRR and (b) LSTs retrieved from Self-Similarity-Based SRR. ................................................................................... 112 Figure 37. Scatter plots of the AMSR-2 LST vs. SurfRad observations in 2015 during daytime (a) LSTs retrieved from Example-Based SRR and (b) LSTs retrieved from SelfSimilarity-Based SRR. .......................................................................................................... 113 Figure 38. Scatter plots of soil moisture retrievals from the refined model compare with SCAN sites. ..................................................................................................................... 115 xi LIST OF EQUATIONS Equation Page Equation 1. Rayleigh-Jeans approximation of Planck’s function ....................................... 3 Equation 2. The relation between TB and physical temperature T..................................... 3 Equation 3. Radiance transfer model for passive microwave remote sensing of LST ....... 3 Equation 4. The empirical model of LST and emissivity at vertical and horizontal polarizations ........................................................................................................................ 4 Equation 5. The SVAT Model .......................................................................................... 23 Equation 6. The enhanced SVAT model .......................................................................... 24 Equation 7. The VCI model .............................................................................................. 27 Equation 8. The VTCI model............................................................................................ 28 Equation 9. The single channel algorithm ........................................................................ 38 Equation 10. The four-channel LST model ...................................................................... 38 Equation 11. Five-channel LST model ............................................................................. 39 Equation 12. Five-channel LST model with auxiliary data .............................................. 39 Equation 13. The judge of rain existence.......................................................................... 40 Equation 14. The non-stationary relationship between AMSR-E and MODIS with auxiliary data ..................................................................................................................... 46 Equation 15. 5km LST downscaled based on GWR......................................................... 46 Equation 16. Image model ................................................................................................ 58 Equation 17. Simplified Image model .............................................................................. 58 Equation 18. POCS process .............................................................................................. 59 Equation 19. LR images from the degrading of HR images ............................................. 59 Equation 20. The projectiona LR image ........................................................................... 60 Equation 21. ML reconstruction ....................................................................................... 60 Equation 22. The pseudo-inverse result of ML ................................................................ 60 Equation 23. The initial image of ML method ................................................................. 61 Equation 24. Each estimation with the BPF function ....................................................... 61 Equation 25. The total probability of an observed LR image ........................................... 61 Equation 26. The probability of HR patches .................................................................... 64 Equation 27. The matrix of transition probability between HR patches........................... 64 Equation 28. The transition probability matrix between HR and LR patches .................. 64 Equation 29. The image pyramid ...................................................................................... 66 Equation 30. The Universal Triangle Model .................................................................... 69 Equation 31. The basic soil moisture regression model ................................................... 70 Equation 32. The refined soil moisture regression model ................................................ 73 Equation 33. Soil moisture anomalies .............................................................................. 74 xii Equation 34. LST conversion from SurfRad observations ............................................. 100 Equation 35. Approximate emissivity............................................................................. 100 Equation 36. Mean Bias Error ........................................................................................ 103 Equation 37. Standard Deviation .................................................................................... 104 xiii LIST OF ABBREVIATIONS Advanced Microwave Scanning Radiometer.......................................................... AMSR-2 Atmosphere-Land Exchange Inverse .........................................................................ALEXI Back-Projection Function .............................................................................................. BPF Brightness Temperature ................................................................................................... TB Decision Trees ................................................................................................................. DT Evapotranspiration Stress Index ......................................................................................ESI Geographically Weighted Regression.......................................................................... GWR Geostationary Operational Environmental Satellite ................................................... GOES High Resolution .............................................................................................................. HR Land Surface Temperature ............................................................................................ LST Low Resolution ............................................................................................................... LR Maximum Likelihood .....................................................................................................ML Mean Absolute Errors ..................................................................................................MAE Microwave .................................................................................................................... MW Moderate Resolution Imaging Spectroradiometer ...................................................MODIS Multi-Images Super-Resolution .................................................................................. MISR National Agricultural Statistics Service ...................................................................... NASS National Drought Mitigation Center .........................................................................NDMC National Oceanic and Atmospheric Administration ................................................. NOAA National Soil Survey Center ...................................................................................... NRCS Normalized Difference Vegetation Index ...................................................................NDVI North American Land Data Assimilation System .................................................. NLDAS Projection Onto Convex Sets ......................................................................................POCS Root Mean Square Error .............................................................................................RMSE Single Image Super Resolution .................................................................................... SISR Soil Climate Analysis Network ................................................................................. SCAN Soil Moisure ..................................................................................................................... SM Special Sensor Microwave/Imager ............................................................................ SSM/I Standard Deviation.......................................................................................................... StD Super Resolution Reconstruction .................................................................................. SRR SURFace RADiation Budget Network .............................................................. SURFRAD Thermal Infrared ............................................................................................................ TIR U.S. Drought Monitor ............................................................................................... USDM United States Department of Agriculture ...................................................................USDA Vegetation Health Index ................................................................................................ VHI xiv ABSTRACT INTEGRATING OPTICAL AND MICROWAVE SATELLITE OBSERVATIONS FOR HIGH RESOLUTION LAND SURFACE TEMPERATURE AND SOIL MOISTURE DERIVATION AND DROUGHT ANALYSES Yu Li, Ph.D. George Mason University, 2017 Dissertation Director: Dr. Donglian Sun Land Surface Temperature (LST) and soil moisture are among the most crucial state variables that impact the regional and global hydrological and energy cycle and thus are required to initialize hydrological and numerical weather prediction models. Soil moisture status is also critical to agricultural activities and productivities that are relevant to our food security. Accurate LST and soil moisture data products with the highest possible spatial resolution are needed for hydrological and meteorological sciences and agricultural decision makers. Thermal satellite sensors, such as the Moderate Resolution Imaging Spectroradiometer (MODIS) onboard NASA’s Earth Observing System (EOS) satellites and the Geostationary Operational Environmental Satellite (GOES) Imager, can provide LST data products under clear sky conditions with moderate to high spatial resolution, but lack the capability under cloudy conditions. Passive Microwave (MW) satellite sensors, such as the Advanced Microwave Scanning Radiometer (AMSR)-E or AMSR-2 can detect surface parameters even in the presence of cloud, but the spatial resolution of the MW sensors are typically low. Utilizing the advantages of multiple instruments on multi-platforms - the potential for improving these products is a viable approach - which has been used in many areas of applications. To obtain consistent LST observations, a new algorithm is developed to derive LST from AMSR-E and AMSR-2 under cloudy conditions and merged with the LSTs from MODIS and GOES Imager in clear sky conditions. A Geographically Weighted Regression (GWR) based gap-filling algorithm is further proposed to fill the remained passing gaps in the merged observations. A SuperResolution-Retrieval (SRR) method is examined to derive high resolution LST from the above merged gap filled LST data. The resulting LST data products with high spatial resolution and complete spatial coverage are them used to feed into a soil moisture retrieval model to derive high resolution high coverage surface soil moisture data products. Anomalies of the soil moisture data products are finally used to map drought areas for the California and Contiguous United States. Comprehensive evaluation of the LST data derived from AMSR-E/AMSR2, MODIS/GOES, and their merging is conducted by comparing them against LST products from fine resolution satellites as well as ground measurements from SURFace RADiation Budget Network (SurfRad). The comparison results illustrate that the high resolution LST data derived from the MW and TIR merged LST data using the SRR method is significantly superior to the individual satellite sensor data products. Soil moisture data obtained from the soil models using high-resolution and highcoverage LST data are evaluated in two ways: (1) direct comparison against the in-situ soil moisture measurements collected from the U.S. Department of Agriculture (USDA) Soil Climate Analysis Network (SCAN), and (2) indirect comparison of the drought are as mapped with the soil moisture anomalies against the official U.S. Drought Monitor (USDM). Results indicated that the derived soil moisture data has good agreement with the SCAN measurements for most of the sites. The agreement of the drought maps from the soil moisture anomalies is compatible with several other conventionally used drought indices. The drought maps are generated daily and have high spatial coverage (1km) and thus could better serve the decision makers with better spatial and temporal details. In addition to generating superior LST and soil moisture data products for science and social users, this study has the following scientific findings: (1) For MW LST estimates, the five-channel algorithm could be better than other methods; (2) The slow changing surface state variables (e.g. vegetation cover type, Normalized Difference Vegetation Index – NDVI, and elevation) contain significant information for downscaling coarse resolution to high resolution LST; (3) Conditions of auxiliary data like precipitation, soil texture, topography, and surface types contribute to the accuracy of soil moisture model, and complement to the impact of LST; (4) Accumulated precipitation impact the soil moisture model more significant than instantaneous rainfall data; (5) Soil moisture data derived from the Refined Model had advantages in deriving drought area maps over the soil moisture from either the Triangle Model or the Basic Model based on comparison with the USDM drought maps. CHAPTER 1 INTRODUCTION 1.1 LST derivation from satellite observations LST is a rapid response variable that can provide proxy information regarding rapidly evolving surface soil moisture and crop stress conditions, indicating significant changes in vegetation structure or reduction in biomass (Moran et al. 1994). The sparse distribution of weather stations makes LST observation a daunting task, and LST impact can not be immediately detected. This issue could be solved with satellite sensed data. The Microwave (WM) and Thermal Infrared (TIR) sensors onboard remote sensing satellites are the primary tools for LST observation, and they can obtain surface parameters continually. MW radiation are highly sensitive to the dielectric constant of water and soil, and TIR sensors have the ability to infer information on soil moisture. Comparing with MW radiation, TIR radiation are highly affected by clouds and their direct sensitivity to liquid water are relatively low. On the contrary, cloud backscattering has less influence on MW. MW can penetrate clouds and be applied for both day and night. However, optical images can provide higher spatial resolution. Thus, an ideal land parameter measurement is to combine multi-sensors to get more information. Integration of MW and TIR data promises to improve the measurement, mapping, and monitoring of surface properties. 1 Passive MW sensors usually have a coarser spatial resolution (typically about 2550km), which allow them to monitor surface variables on a daily basis all over the earth. EOS is a Low Earth (or polar) Orbit (LEO) whereas GOES is a geostationary orbit while only a few in situ surface measurements are available for such cost and coverage. MW LST depends on the distribution of Brightness Temperature (TB) and emissivity as well as the spectral band of measurement (Becker and Li, 1995). However, the assumptions or simplifications and atmospheric effects degrade both the feasibility and the accuracy of the derived LST. Thus LST retrieval models from MW data should be developed by focusing on both simplifying the parameterization of the radiative transfer model and developing the emissivity relationships between different frequencies and polarizations (Li et al. 2013). Any physical object with a temperature above absolute zero (unit: K) emits energy of some magnitude (Rayleigh-Jeans approximation of Planck’s function in microwave region is shown in Eq.1, where Rayleigh-Jeans applies for long wavelength). The emitted microwave radiation can be expressed in terms of TB. TB is the inverse of the Planck function, that equals to its emissivity (subscript p denotes the signal polarization: vertical or horizontal) multiplied by its physical temperature T ( can be neglected). LST then can be retrieved from observed TB using various algorithms which account for the atmospheric effect and for the surface spectral emissivity, including empirical statistical methods, neural networks, and physical models (Weng et al. 1998). 2 Equation 1. Rayleigh-Jeans approximation of Planck’s function B , T c14T c2 Equation 2. The relation between TB and physical temperature T TB = epT + (1 - ep )Tsky The theoretical basis for passive MW LST retrieval is based on the thermal radiance of the ground and its transfer from the ground through the atmosphere to the remote sensor. Generally speaking, the ground is not a blackbody. Thus ground emissivity has to be considered for computing the passive microwave radiance emitted by the ground. The atmosphere has important effects on the received radiance at the remote sensor level. Considering all these effects, the general radiance transfer equation for passive MW remote sensing of LST can be formulated as follows (Mao et al. 2007a, b): Equation 3. Radiance transfer model for passive microwave remote sensing of LST B f (Tf ) f ( ) f B f ( LST ) f ( )(1 f ) B f (Ta ) B f (Ta ) Where Ta↓ is downward atmospheric brightness temperature, and Ta↑ is upward atmospheric brightness temperature, Tf is the brightness temperature at frequency f, τf is the atmospheric transmittance in frequency f at viewing direction θ (zenith angle from nadir), and εf is the ground emissivity. Bf(LST)is the ground radiance, and Bf(Ta↓)and Bf(Ta↑) are the downwelling and upwelling path radiances, respectively. An empirical linear relationship (Fily et al. 2003, Mialon et al. 2007) between emissivity at vertical and horizontal polarizations was found: εV = aεH + b, where εV/εH stands for surface emissivity at vertical and horizontal polarization, respectively, and a and b are the linear regression coefficients. Therefore LST can be derived: 3 Equation 4. The empirical model of LST and emissivity at vertical and horizontal polarizations LST [Tbv aTbH (1 b a) f ( )Ta (1 a)Ta ] / (b f ( )) In order to develop good LST algorithms for passive microwave sensors AMSR-E and AMSR-2, several algorithms were selected here for comparison. Visible and infrared sensors are more frequently used in detecting LST. Correspondingly, there are more studies on TIR satellite sensors for LST retrieval. Usually, TIR imaging provides higher spatial resolution of surface information. TIR sensors receive Top of Atmosphere (TOA) radiances. Both emission and reflection happened in day and emission in night time (Tomlinson et al. 2011). Same as microwave, Planck’s law is used to derive blackbody/TB from TOA radiance. TOA radiances are then converted to LST by correcting for three main effects, namely, atmospheric attenuation, angular effects and surface spectral emissivity values. Within TIR wavelengths, most attenuation is due to water vapor and aerosols. Thus, one of the disadvantages of these TIR-based approaches is that LST can be retrieved only under clear sky conditions. Integration of MW and TIR data has potential to improve the measurement, mapping, and monitoring of surface properties. The new product will have the capacity to detect LST under nearly all weather conditions (except for the raining condition, when MW is influenced by the attenuation). Converting MW LSTs to TIR LSTs is not an easy task. This is due to (1) LSTs retrieved at a given location might be acquired by the same polar-orbit satellite on different days or (2) LSTs retrieved at different locations in the same day correspond to different local solar times of observation and different View Zenith Angles (VZAs), (3) let alone LSTs retrieved from different polar-orbit satellites. 4 Moreover, as the LST varies along with time and VZA, there is no comparability among LSTs of one pixel retrieved on different days or LSTs of different pixels on the same day. Therefore these LSTs are not simply replaceable with each other; a comprehensive study should carry out for merging two LSTs. TIR based LST reflects an average value of the soil temperature from the land surface to a particular depth (depending on the frequency used to retrieve LST) underneath the surface, whereas MW based LST is the skin temperature with several microns of depth (Li et al. 2013). The Diurnal Temperature Range (DTR) changes soil water content, which affects the thermal inertia as well as the daily temperature range. To address these issues, angular normalization (Li et al. 1999) and temporal normalization (Sun et al. 2006) must be developed to produce a consistent LST product under all weather conditions. Considering the complementarily of passive MW and TIR data, a physics-based model for retrieving LSTs and an efficient model of combining LSTs should be developed. 1.2 High-resolution LSTs High-resolution (HR) remote sensing satellite imageries are beneficial in many fields, such as military, hazard assessment, and surface information. The coarse resolution limits the usage of LST application. High spatial and temporal resolution of LST data is a necessary input for modeling or analyzing surface conditions. Unfortunately, the resolution trade-off effect usually causes a high temporal resolution with a low spatial resolution. Traditionally, to improve the observed spatial resolution is 5 to decrease the physical sizes of sensors (Park et al. 2003; Zhang et al. 2014) at the cost of noisy and expensive imagery. Hence, using the sensors/data that are already available is a better way to obtain HR imagery. Such post-processing approach is called SuperResolution Reconstruction (SRR). The main idea is to use the available low-resolution (LR) image(s) to reconstruction HR image(s). In this dissertaion, the term "downscaling" means to enhance the spatial resolution of an observation. The Atmosphere-Land Exchange Inverse (ALEXI) model (Anderson et al. 1997) is one of the few diagnostic LSMs designed to exploit the high temporal resolution of observations provided by geostationary satellites. The radiometric temperature data input into ALEXI is obtained from Geostationary Operational Environmental Satellite (GOES). GOES mainly monitors the land surface of Northern America and Southern America. The GOES-based retrievals of LST are currently implemented with a gap-filling algorithm to estimate evapotranspiration (ET) at spatial resolutions of about 4 km twice a day (Sun and Pinker 2003; Sun et al. 2013). ALEXI uses the morning and midmorning (1 to 1.5 h after sunrise and before local noon) surface temperature as its driving input because this is the signature in the diurnal surface temperature wave most closely correlated with soil moisture content (Anderson et al. 2007a). ALEXI requires clear-sky conditions during the time interval for obtaining the surface temperature data and for satisfying model assumptions of linear sensible heat rise during the morning boundary layer growth phase (Anderson et al. 2007b). The consistent HR LST is a desire to serve as an input for ALEXI model, the LST downscaling approaches thus should be investigated. 6 1.3 Practical usage of HR LST observations Soil moisture is one of the key variables that impacts global and regional weather, climate, flash flood and river flow forecasts. It controls energy exchange between the surface and atmosphere through evaporation and transpiration. Soil moisture status is critical to agricultural and natural water resources management. Drought is considered to be the most severe natural hazard in terms of impact, duration, and spatial extent (Kousky 2014). Satellite remote sensing capabilities have been greatly improved for decades and served as the main method for drought monitoring and prediction. Drought may occur unnoticeably and varyingly, and lack of information to drought may lead to severe disaster. The damage was extensive but the impact to livestock and farm production is uncountable (Wilhite et al. 2000). Numerous drought indices have been developed by using readily available satellite data such as precipitation, LST and NDVI, etc. Among this data, soil moisture content is a direct reflection for land surface dryness or wetness condition, thus it is an important variable for drought monitoring. 1.3.1 Soil moisture retrieval Since it is hard to measure soil moisture over large area directly, Leese et al. (2001) concluded it’s better to monitor soil moisture with combination of in-situ model and remote sensed variables respond to soil moisture. In this dissertation, the HR LST is served as the input variable that responds to soil moisture. Vegetation indices are based on the unique spectral signature of green vegetation in the red and near infrared portions 7 of the spectrum and form the basis for quantitative assessment of vegetation condition using satellite data. So far, different Vegetation Indices (VIs) were developed for different proposes. They include the Normalized Diference Vegetation Index (NDVI), Transformed Vegetation Index (TVI), Difference Vegetation Index (DVI), Soil Adjusted Vegetation Index (SAVI), Atmospherically Resistant Vegetation Index (ARVI), and Vegetation Condition Index (VCI). The microwave-optical/IR synergistic approach is an efficient method to improve the current drought related soil moisture products with several advantages including simplicity and no need of ground measurements. The study in this dissertation focuses on the development and validation of the synergistic approach. 1.3.2 Drought analysis Drought has external forcing factors like El Niño and the Southern Oscillation (ENSO), land use change (Aral Sea, deforestation), and global warming; it is likely to be triggered by anomalous tropical sea surface temperatures (SSTs). La Nina-like SST anomalies might lead to drought in North America, El-Nino-like SSTs might bring in drought in East China, and southward shift of the warmest SSTs in the Atlantic and warming in the Indian Ocean might cause Sahel droughts in Africa (Dai 2013). Drought may be enhanced and prolonged by local passive and active feedbacks. Extreme hydrological processes are often dynamic and destructive. It is important to monitor such extreme processes and predicts their impact. Satellite remote sensing data with global covers is a promising and economical tool for gaining dependent surface parameters to monitor drought. 8 The American Meteorological Society (1997) defined four commonly accepted drought types as meteorological, hydrological, agricultural, and socioeconomic drought due to their differences in duration, regions, needs, and disciplinary approaches. Meteorological drought refers to region based analyses. It measures the degree of dryness relative to average amount and duration of historical records. Hydrological drought happens when the amount of precipitation is not enough to maintain surface water. It is rainfall, land use, and water storage dependent. Socioeconomic drought occurs with low availability of water for humans. Agricultural drought is a period when soil moisture is insufficient to meet evapotranspirative demands to sustain crop growth. Drought disrupts cropping processes, reduces breeding, and highly affects environment and economies. This dissertation will analyze agricultural drought, which occurs over a large area, and its uncertain impact lasts until harvest season. Agricultural interest in drought is important in much of the U.S. In fact, there is considerable interest in indices that used to monitor agricultural drought. Drought condition is a subjective judgment, government agencies within National Oceanic and Atmospheric Administration (NOAA) and United States Department of Agriculture (USDA) teamed up with the National Drought Mitigation Center (NDMC) to produce a weekly drought monitor (DM) data product that incorporates climate data and professional input from all levels and is well known as the U.S. Drought Monitor (USDM). The USDM maps are consensus product based on several indicators and key variables, and the final maps are adjusted manually by experts over the country (Svoboda et al. 2002). The USDM drought conditions are classified into five classes based on a 9 ranking percentile approach: (1) D0 - abnormally, (2) D1 - moderate, (3) D2 - severe, (4) D3 - extreme, and (5) D4 -exceptional dry conditions. They are utilized as (1) D0-D4 (CPC Soil Moisture Model percentile≤30%), (2) D1-D4 (percentile≤20%), (3) D2-D4 (percentile ≤ 10%), (4) D3-D4 (percentile ≤ 5%), and (5) D4 (percentile ≤ 2%) (Xia et al. 2014). The DM product is based on several indicators, mainly including the (Palmer Drought Index) PDI, Standardized Precipitation Index (SPI), Keetch-Byram drought index (KBDI), North American Land Data Assimilation System (NLDAS) soil moisture output, Streamflow, Precipitation Anomalies. In growing season, it includes Crop Moisture Index (CMI), Vegetation Health Index (VHI), Evapotranspiration Stress Index (ESI), Mesonets, and reports from USDM authors. Some other ancillary indicators are the Surface Water Supply Index (SWSI), reservoir levels, snowpack conditions from SNOTEL/(Natural Resources Conservation Service (NRCS)), groundwater levels determined from wells, USDA reported crop status, and direct in situ soil moisture measurements(Svoboda et al. 2002). The weekly DM maps are currently distributed at http://droughtmonitor.unl.edu/ with relatively coarse resolution.They served as one of the criteria to determine eligibility for relief of aggravation due to drought condition. It’s necessary to find a simple and reasonable model for drought monitoring comparable to the USDM drought classifications, and to explore the possibilities for linking a real-time index with surface wetness condition in a fine resolution. 1.4 Structure of the dissertation 10 The remaining chapters of the dissertation contain the following topics. Chapter 2 provides a literature review for merging, downscaling LST, soil moisture, and drought study. Chapter 3 discusses the objective of this study. Chapter 4 describes the methodology of integrating MW and TIR LST. Chapter 5 aims to downscale LSTs. The regression-based method as well as SRR techniques - both multi-images and single image super-resolution will be stated. Chapter 6 will conduct the application with the integrated HR LST. Chapter 7 exhibits the results for each objective. Chapter 8 evaluates the results against fine-resolution satellite data and ground-based LST. Chapter 9 presents the conclusion and discussion. An outline of this dissertation is showing in Figure 1. MW sensed data Infrared LST MW LST Ancillary data Machine learning Integrated LST Downscaling HR LST Validation against In-site measurements Evaluation Validation against Fine-resolution satellite observations Evaluated against USDM SM models Drought Monitoring Evaluation Figure 1.The outline of this dissertation. 11 Validation against popular drought indices CHAPTER 2 LITERATURE REVIEW Brief background information was given in the previous section. This section will review and discuss the relevant studies. 2.1 LST retrieval 2.1.1 LST retrieval from infrared observations In general, the TIR wavelength used for LST measurements is the between 8 and 15 μm. Prosperous algorithms are developed, to give a few examples: single TIR channel method (Hook et al. 1992); the split-window method (McMillin et al. 1975); Multichannel method (Sun et al. 2003); Multi-angle method (Chedin 1982); the physicalbased day/night operational method (Wan et al. 1997); the temperature and emissivity separation (TES) method (Gillespie et al. 1998); the multi-temporal physical method (Li et al. 2011); the Kalman filter physical method (Masiello et al. 2013) and the two-step retrieval method (TSRM) (Ma et al. 2000). These methods usually require other auxiliary information from the atmosphere (such as atmospheric water vapor content) or atmospheric correction, and it has strict requirement for observation time and angle. All the LSTs derivation are matched with the acquisition time of satellites. Geostationary satellite sensors - that remains the position relative to the Earth - like GOES Imager or the Spinning Enhanced Visible and InfraRed Imager (SEVIRI) can provide LST observations in a shorter period at the cost of coarse spatial resolution. The 12 sun-synchronous satellite sensors like MODIS or the Advanced Very High Resolution Radiometer (AVHRR) - that pass the Earth at the same local solar time - can measure LSTs for a higher spatial resolution with restricted daily visits. Table 1 provides the typical TIR sensors for LST measurements. Other TIR sensors such as the Hyperspectral Infrared Imager (HyspIRI) and the National Polar-orbiting Operational Environmental Satellite System (NPOESS) are planning to launch in the near future. Notable use of LST measurements are derived from TIR sensors globally. For example, Gallo et al. (1993) used AVHRR data to investigate Urban Heat Island (UHI) based on the surface temperature and vegetation index for 37 cities in the United States. Stathopoulou and Cartalis (2007) explored LSTs across the major cities in Greece using Landsat ETM+ data. Pinker et al. (2009) evaluated GOES LSTs over the USA. Among the TIR sensors, MODIS sensor is the compromise between regular image acquisition and reasonable spatial resolution (Tomlinson et al. 2011). Table 1. Typical TIR sensors for LST observations and the onboard satellite information. Sensor Satellite Spatial resolutiona GOES Imager GOES 4 km Spectral bandwidth (μm) Equator passing timeb Availble since Every 3 hours 1974 10.2-11.2; 11.5-12.5 07:30,19:30; c AVHRR NOAA 10.3-11.3; 02:30,14:30; 11.5-12.5 02:20,14:20; 1.1km 1979 01:40,13:40. 13 Landsat ETM+ Landsat 7 60 m d 10.4-12.5 10:00 1999 e 1999 22:30;10:30 2000 01:30;13:30 2002 8.125-8.475; 8.475-8.825; ASTER Terra 90 m 8.925–9.275; 10.25–10.95; 10.95–11.65 10.78-11.28; MODIS Terra 1 km 11.77-12.27 10.78-11.28; MODIS Auqa 1 km 11.77-12.27 AATSR Envisat 1 km 11; 12 10:00 2004 SEVIRI Meteosat-8 3 km 10.8; 12 Every 15 minutes 2005 AVHRR MetOP 1.1 km 09:30 2006 10:00 2016 10.3-11.3; 11.5-12.5 SLSTR Sentinel-3 1 km 10.85 a Given as approximate resolution. The time here is approximate local solar time. If available, left time is for descending node, right time is for ascending node. c The detail of AVHRR passing time onboard NOAA satellites can be foundin: https://www.ngdc.noaa.gov/ecosys/cdroms/AVHRR97_d1/avhrr.htm d Usually resampled to 30 m. e ASTER onboard Terra, and data are scheduled to acquire. b 2.1.2 LST retrieval from MW observations There are fewer cases that passive MW has been used for LST measurement. McFarland et al. (1990) are one of the first research teams that use linear regression 14 models to derive surface temperature for crop/range, moist soils, and dry soils from the Special Sensor Microwave/Imager (SSM/I) TB. They used 85 GHz vertical polarization TB as primary channel for LST correlation, 19 GHz for compensating the influence of surface water, and the difference between 37 and 22 GHz for atmospheric water vapor content correction. Njoku et al. (1993) further used a more appropriate the neural network method for LST retrieval, indicating a nonlinear relation should be established among passive MW and land parameters. Njoku and Li (1997) later applied the MW measurements at the range of 6 -18 GHz frequency to derive LST. The retrieved surface temperature except for bare soils can reach the accuracy of 2 °C. Davis et al. (1995) applied the Bayesian methodology to retrieve LST with prior information like noise of sensor, uncertainties of model, probability distributions of the estimation, and ancillary data. Later their method is improved by Basist et al. (1998) based on semiempirical techniques. Aires et al. (2001) developed a new neural network and variant assimilation method at 19 - 85GHz from SSM/I, with the theoretical Root Mean Square Error (RMSE) of LST retrieval over globe is 1.3 K in clear-sky conditions and 1.6 K in cloudy scenes. Chen et al. (2011) established a linear relation between AMSR-E 6.9 GHz Microwave Polarization Difference Index (MPDI) intervals at 0.04, 0.02 and 0.01 based on five land cover types and observation temperatures from meteorological observation stations over Guangdong Province to derive LST under bad weather conditions during the snow disaster of Southern China in 2008. Sun et al. (2012) applied Regression Tree (RT) methods to stratify regression models for LST retrieval. 15 Conclusively, the satisfactory model is expected to retrieve the LSTs from a combination of TBs measured at different frequencies and polarization modes. 2.1.3 The integration of TIR and passive WM observations The TIR data can provide fine spatial resolution, but it loses efficiency when the land surface is fully or partly covered by clouds. Microwave observations have been functioned as promising tools for detecting land surface properties, for it is less affected by the atmosphere. However, microwave observations are limited by its coarse spatial resolution and validation is required. TIR and MW data can thus complement each other, and the combination of the two is a promising line of research for producing long-term LST products in near all weather conditions with a spatial resolution as fine as that of TIR data (Li et al. 2013). To merge the two data is to blend in the LST information for TIR imagery under cloudy pixels. Mao et al. (2007a) built regression models between the AMSR-E TB bands and MODIS LST products, the relations are based on LST above or below absolute zero (273k). The average retrieval LST error is about 2 - 3 °C relative to the MODIS LST products, and 89 GHz vertical polarization is the best single band. To enhance the accuracy of their algorithm, they later (Mao et al. 2007b) used neural network to retrieve LST from passive microwave AMSR-E data, and the average error is under 2°C. However, over 60% of the areas in MODIS LST product are influenced by weather, especially cloud (Kou et al. 2016). The MODIS LST itself contains certain errors when the air contains much cloud, atmospheric water content or rainfall. So the regression model between AMSR-E TB and MODIS LST products lacks some practical 16 significance. Li et al. (2013) concluded to combine and extract the two LSTs, a model must be developed to extract the surface temperature from passive microwave data at different frequencies, and of the thermal conductivity equation applied to soil. Jang et al. (2014) applied a simple pixel-wise empirical regression method to combine TIR LST and MW TB products. They downscaled 25 km MW data to sub-grid cell 5 km data. Due to their ignorance of spatial variability within coarse pixels, Kou et al. (2016) proposed to blend MODIS and AMSR-E LST data by using the Bayesian Maximum Entropy (BME) method. But it requires a large amount of data to obtain an accurate spatiotemporal random field of the variables. The key issue here is how to recover the LST at the spatial resolution of TIR data when a microwave pixel is fully or partly cloudy. Zhan et al. (2002) described a synergistic technique using optical/infrared frequency products to overcome the coarse spatial resolution of the MW satellite products. This method was later enhanced by Chauhan et al. (2003). They built the statistical relationships between near-surface soil moisture and optical-derived soil moisture indices. Merlin et al. (2008) applied these relations and transferred this method to a wider range of conditions. They tested their algorithms with data from the National Airborne Field Experiment 2006 (NAFE'06, 1 km resolution airborne L-band TB was gained in southeastern Australia). The overall Root Mean Square (RMS) difference between downscaled and observed soil moisture is relatively low. This method requires many surface parameters and micrometeorological data, thus it may not be available over large areas. 17 Surface parameters have all been obtained from visible and infrared reflectance and have been enhanced more recently by microwave imagery (Clevers and van Leeuwen 1996). They combined optical and radar data for crop growth monitoring and found radar data can improve acquiring information in crop growing season in particular with the absence of optical observation, but showing slight improvement when optical data are available. The MW-TIR synergistic approach is efficient to improve the current surface products with several advantages including simplicity and no need of ground measurements. 2.2 LST downscaling approaches Atkinson et al. (2013) summarized that there are mainly three approaches for remote sensing data downscaling. (1) Regression approaches. Those are the most straightforward and common method. (2) The Area To Point Prediction (ATPP). It will downscale the input coarse resolution variables via interpolation. (3) Super-resolution mapping. A variety of interpolation methods will be used to increase the spatial resolution while transforming it to a classification (Wan et al. 2010). Most LST downscaling studies are focused on the statistical downscaling of thermal satellite data (often known as Thermal Sharpening). Kustas et al. (2003) presented a simple generalized TIR image sharpening algorithm (TsHARP) by building the statistical relationships between LST and the NDVI developed at the coarser TIR pixel resolution, and then applied at the finer shortwave resolution. It is based on the assumption that a unique statistical relationship exists between Temperature (T) and 18 vegetation indices at multiple spatial scales, largely related to percent vegetation cover. It neglects the effects of spatial variability in soil moisture (e.g., water bodies in the image do not conform to the inverse T-NDVI relationship). Karnieli et al. (2010) exploited the strong inverse relationship between LST and vegetation indices from VIS/NIR data. According to their founding, dense vegetation cover and radiometric temperature tends to have negative correlation (cooling effect of transpiration). Anderson et al. (2011) applied the relationship between LST and NDVI at TIR pixel resolution to a finer shortwave resolution. However, this technique has limits when irrigation or senesced vegetation. Based on Anderson’s work, Gao et al. (2012) applied a data mining sharpener approach designed for application over widely varying landscapes to enhance TsHARP results, considering the relation between temperature and reflectances. A regression tree is used to build the relationship between temperature and reflectance at multiple spatial resolutions. This relationship is described by a local model using a moving-window technique. Ever since, single variables were added into the models, such as emissivity (Inamdar et al. 2009; Stathopoulou et al. 2009). Alternatively, the new retrieval methods are employing a LST predictor set (VIs, albedo, emissivity, land cover, slope, etc) (Zakšek et al. 2012). An adaptive regression and normalization method was proposed by Trishchenko et al. (2006) to downscale coarser resolution between MODIS/TERRA band 3 and band7 images from 500 to 250 m with an assumption that similarities or correlations exist among different MODIS bands.In this method, individual 500 m MODIS granules from bands 3, 4, 5, 6, and 7 were divided into intermediate 250 m spatial resolution images to 19 develop nonlinear regression relationships between dependent variables (band 3 and band 7) and independent variables (band 1, band 2, and NDVI). Song et al. (2014) proposed a method to retrieve HR 1-km soil moisture by downscaling 25-km AMSR-E TB using MODIS visible/infrared (VIS/IR) data. The method of retrieving land surface temperature with passive microwave is combined with the relationship between the MPDI and NDVI to obtain HR microwave TB and soil moisture. In Song’s research, the downscaled soil moisture is similar to the ground measurements during this period with RMSE less than 0.12, and it is more suitable to moderate to drier soil conditions with baresurface or covered by sparse vegetation (0.1 ≤ NDVI ≤ 0.5). The T-NDVI approach usually has high spatial resolution. The selection of auxiliary datasets (such as vegetation or topographic indices) as well as the generation and application of the empirical model are key to successfully retrieve HR LST. Also, this concept often is limited when auxiliary data and predictable data are not well correlated (such as NDVI and LST on an irrigation ground) (Sun et al. 2007). The statistical downscaling methods can perform better when carrying out with localization strategies (Zakšek, et al. 2012), such as GWR (Duan et al. 2016). The SRR can be categorized into two methods: Multi-Images Super-Resolution (MISR), and Single-Image Super-Resolution (SISR). Nasrollahi et al. (2014) summarized most SRR approaches in different fields. In recent years, the SRR for remote sensing images has mainly focused on multi-temporal image sequences (Merino et al. 2007; Shen et al. 2007) or multi-angles (Zhang et al. 2014). However, multi-temporal satellite images might be obtained over different periods, thus the atmosphere/surface condition or the 20 imaging scenes might be changing rapidly even over the same scene. Multi-angles, usual also obtained as multi-temporal (shorter time difference) might not have the required sence at certain time, or the sensors might not be available, and the spatial resolution of different angle images is different, the nadir image resolution is hard to match accordingly. What’s more, for all of the successful applications of multi-angle imagery, accurate registration of the multiple-view images, which at times are also multi-temporal, is a prerequisite. Both the regression-based method and the super-resolution-based method will be investigated in this study to downscale LST. 2.3 Soil moisture derivation Passive MW sensors measure the soil radiances through radiative transfer modelling or wetness indices (Njoku et al. 2003). There are mainly two ways to retrieve soil moisture from TB: the single-channel retrieval (SCR) and the multiple-channel inversion (MCI) algorithm. SCR is originally proposed by Jackson (1993) and now it is used to generate soil moisture data from Soil Moisture Operational Product System (SMOPS) (Zhan et al. 2012). MCI was proposed by Njoku and Entekhabi (1996), now it’s used for soil moisture product from AMSR-E (Njoku et al. 2003). Jackson et al. (1987) combined spatially distributed remotely sensed surface observations of soil moisture over a large area in the Texas High Plains region, United States to produce preplanting profile soil moisture maps. The conventional approach to generating the soil moisture product involved sampling the profile at selected locations 21 and then developing a contour map. Their results showed the possibility of retrieve soil moisture from passive MW sensor. Passive MW sensors have been developed for decades to retrieve soil moisture data. The most commonly used sensors are AMSR, SSM/I, Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), Scanning Multi-frequency Microwave Radiometer (SMMR) and Windsat satellite. De Jeu et al. (2003) developed soil moisture retrieval approach based on the MPDI. This method applies a forward modelling optimization procedure to solve a radiative transfer equation for soil moisture and vegetation optical depth, and no calibration required. Their methodology suggested transferable to soil moisture retrieved from the AMSR (with H polarization is and V polarization). Here, ―H‖ polarization (H) means that the electric field vector of the electromagnetic wave is oriented parallel to the earth’s surface, while ―vertical‖ polarization (V) means that a wave arrives at the interface with a vertical component. SSM/Is are boarding on the Defense Meteorological Satellites (DMS). These polar orbiting satellites have been in operation since 1987 and provide high frequencies and two polarizations. Jackson et al. (1997) used SSM/I data with atmospheric and oceanic variables to estimate SM over the southern Great Plains of the United States. The standard error of estimate was reported to be 5.14%-5.75%. TMI is a nine channel radiometer onboard TRMM satellite, began to acquire data in December 1997. Gupta et al. (2007) uses TMI 10.7 GHz TB along with NDVI to depict soil conditions, indicating the potential for drought monitoring. SMMR onboard Nimbus-7 satellite operated from 1978 to 1987. Like other MW sensors, it measured TB at five frequencies, from 6.6 GHz to 37 GHz, at both horizontal and vertical polarization. 22 Windsat is a satellite-based polarimetric microwave radiometer. It was launched in January 2003 aboard the joint DoD/Navy platform Coriolis. Li et al. (2010) demonstrated its use on retrieve soil moisture and its validation. The shortwave-infrared (SWIR) wavelength are sensitive to moisture of vegetation. Vegetation vigor and soil moisture availability have a close relation, especially in arid and semiarid areas, in many cases the satellite-derived NDVI and LST product have been used to evaluate drought condition. Sun and Kafatos (2007) indicated the negative or reverse relation between NDVI and LST may only hold during warm or growing seasons, when LST has stronger negative relationship with vegetation than TB. Therefore, NDVI and LST related drought indicesmay only be used during warm seasons, but not winter. They also suggest LST should be used instead of TB. Carlson et al. (1994) found the relationship between measured surface temperature, vegetation fraction, and soil moisture, known as the ―Universal Triangle Model‖: that temperature and NDVI are often exhibits in a triangular shape. Synergistic approaches of using microwave-optical/IR products are highly dependent on the schematic relationship of this method distribution among soil moisture, NDVI, and LST (Carlson et al. 2007). Soil moisture varies from low to high values in the triangle. SVAT model is commonly used to create the relationship between measured surface temperature, vegetation fraction, evapotranspiration and soil moisture, it can be described as following regression formula: Equation 5. The SVAT Model n n SM = a ij NDVI *(i ) T *( j ) i 0 j 0 23 The SVAT model was modified through varying parameters measured via different optical instruments since it was developed. Chauhan et al. (2003) linked LR soil moisture with the land parameters has a definite theoretical basis in the surface energy balance technique. These approaches can be simpler applied regardless of ground based meteorological measurements and have the advantage of requiring few ancillary data, but they are valid only after calibration. Piles et al. (2011) proposed to use three different spectral ranges for SM predicting. They introduced the biopolarized passive MW TB measured by Soil Moisture and Ocean Salinity (SMOS) mission in that equation: Equation 6. The enhanced SVAT model n n n SM = aijk NDVI *(i ) T *( j )TB*( k ) i 0 j 0 k 0 Where TB is required to capture at a high resolution and to reproduce changes in soil moisture due to passive MW is better to detect precipitation other than visible and infrared instrument. Through this way, soil moisture maps can be obtained by optimally merging SMOS and other coarser data (e.g., MODIS) using the downscaling algorithm. A combination observation from multi-sensors is a hot topic recently. Kim et al. (2012) developed an evaporation-based disaggregation method of microwave soil moisture product. This approach was based on a linear scaling relationship between evaporative fraction and surface soil moisture. The originality of this method relied in the representation of vegetation water stress at low resolution to derive a high-resolution soil wetness index, while previous evaporation-based methods assumed an unstressed vegetation cover. The algorithm was applied to AMSR-E level-3 soil moisture product 24 (Njoku et al. 2003) using 1 km resolution MODIS data over the SMEX04 site (75 km *50 km) in southern Arizona, and the 1 km resolution disaggregated data were evaluated at the 36 SMEX sampling sites. They also pointed out that each of the downscaling methods had essential limitations dependent on the correlation of the soil moisture with the LST and the accurate representation of the initial AMSR-E soil moisture observations. 2.4 Drought indicators Drought is particularly damaging because it occurs across a large spatial extent and lasts for a long time. The distinctions between normal, seasonal droughts and abnormal droughts are important, for example, places with Mediterranean climates, are usually concerned to be seasonal drought. A drought index would greatly improve our understanding of drought, and the severity of the effects may be the only guide to make comparisons between different drought indices. Mitigating the effects of drought can be improved by understanding the current and future status. Agricultural drought detecting is almost dependent on monitoring surface variables, which makes satellite a promising tool for studying global drought. USA has developed lots of drought monitoring systems, while it is quite limited in other countries. Currently, a detailed appreciation of past droughts is only available for North America. International effort to other regions would therefore be very valuable. Mapping the past mega droughts would assist to make predictions of the effects and adjust administrative rules. 25 While considerable progress has been made in the development of drought monitoring, there remain some issues that either by the limitation of the available data or by the accuracy of the data. Consequently, to understand droughts means to evaluate studies with entirely different aims and variables across different droughts, or in some case, different variables with same droughts. With large scale of disturbances and long duration, drought is still an unpredictable natural disaster for researchers. Multi-scale and multi-sensor drought monitoring are urgent. There are challenges require further research and developments. NASA Soil Moisture Active Passive (SMAP) (Entrkhabi et al. 2010) tries to combine passive and active MW sensor to provide a soil moisture product with a compromise spatial resolution and accuracy. Hahn et al. (2012) analyzed the Advanced SCATterometer (ASCAT) soil moisture products and the simulated soil moisture errors: the absolute calibration bias is constantly 0.22 dB all over the world. This can result further mistaken to identify droughts. Stability of the data quality needs to be sustained in time through monitoring the instrument calibration and drift correcting. For the global drought monitoring, the spatial and temporal resolution is a serious matter. The timescales and space scale will be dictated by the availability of the forcing data, though techniques for disaggregating products in both of these domains exist and are routinely applied. Lack of an appropriate scaling system in hydrological sciences, the default answer is the higher the better. To fully understand the onset, duration and impact of drought, global mapping of soil moisture, evapotranspiration (ET), LST, VIs, and drought indices are become more 26 and more demanded for international applications. Global land surface variable maps are possible to build through the use multi-sensors. It is also possible that these products could be integrated with existing drought indices to develop improved methods for monitoring and predicting drought. With global climate change, drought may increase its frequency duration, and orientation. This threatens human society with impact we poorly understand. Fully utilize the spaceborne assets - geostationary satellites, polar orbiting platforms, and multiwavelength - are needed so that proper and timely decisions can be made to modify our understanding of drought. Since there is no direct way of measuring drought, scientists use indices to define drought. Such indicators are related to teleconnection and local land-atmosphere disturbance. In this dissertation, popular drought indices will be provided for comparison proposes. Kogan et al. (1997) proposed to combine the Vegetation Condition Index (VCI) and the Temperature Condition Index (TCI) to Vegetation Health Index (VHI): VHI=a*VCI+b*TCI, where coefficient a and b are usually taken as 0.5. VCI is defined as: Equation 7. The VCI model VCI NDVI - NDVImin NDVImax NDVImin where NDVI and NDVImin are the multi yearsmaximum and minimum NDVI in a max given area for growing season. The TCI is derived from TB, and its algorithm is similar 27 to VCI except that the formula was modified to reflect the opposite to the NDVI vegetation’s response to temperature. The Center for Satellite Applications and Research (STAR) of NOAA Satellite and Information Service (NESDIS) is providing global VCI, TCI, and VHI map every week at: (http://www.star.nesdis.noaa.gov/smcd/emb/vci/VH/vh_browse.php). Wang et al. (2001) developed Vegetation Temperature Condition Index (VTCI) based on the triangular space of LST and NDVI for monitoring drought stress. It’s defined as following: Equation 8. The VTCI model VTCI LSTNDVI i.max - LSTNDVI i LSTNDVI i.max - LSTNDVI i.min ' ' where LSTNDVI i.max a b NDVIi , LSTNDVI i.min a b NDVIi , and LSTNDVI i.max and LSTNDVI i.min are the maximum and minimum land surface temperature of pixels which have same NDVI i value, respectively, LSTNDVI i denotes land surface temperature of one pixel whose NDVI value is NDVI i . a, b, a’ and b’ are coefficients. If VTCI(i) < 0.4, then area (i) is high drought area (Sun and Kafatos, 2007). Wang et al. (2004) concluded that drought information can not be described by one simple data (e.g., NDVI, Ts, etc). SM- and ET-based indicator derived from ALEXI model are considered to be one of the most comparable drought indicators (Anderson et al. 2013). The ESI derived from the ALEXI model is a drought index in which evapotranspiration anomalies are described using geostationary satellites (Anderson et al. 2011). Evaporatranspirion is retrieved via energy balance using LST time-change signals. 28 Currently, ESI maps are produced during growing season (late March to early October) at 4-km resolution over the continental United States. ESI performs similarly to short-term precipitation-based indices with a much higher resolution and without the need for precipitation data. Cloud cover can contaminate and affect results (Anderson et al. 2011). 29 CHAPTER 3 OBJECTIVE OF THIS STUDY The previous sections described the background and presented the current research results. Based on that, three objectives will be given in this chapter. 3.1 Synergistic study on MW and TIR LST Synergistic studies on MW and TIR LSTs have been conducting ever since the advantage and viability are noticed (Chapter 2.1.3). The merits and disadvantages of the two sensors are discussed in the previous chapter. Thermal instruments like MODIS and GOES can provide high quality LST products under clear sky conditions (Wan and Dozier 1997; Sun and Pinker 2003; Sun et al. 2012), and passive microwave (e.g., AMSR-E and AMSR-2) can provide LST under cloudy conditions. Utilizing the MW and TIR sensors will make up the inconvenience of each other, and provide a new near all weather LST product. It is also a difficult issue to match the LST observations spatially and temporally from two sensors. AMSR-E and MODIS sensors are onboard the same EOS Aqua satellite, so the LST integration of these two sensors gained lots of attentions. However, the algorithms are not matured enough to be implement for a new LST product, and the missing gaps still require effort to fill. 30 Due to different local condition, in ALEXI model, Two Source Energy Balance Model (TSEB) is applied twice during the morning of Atmospheric Boundary Layer (ABL) model growth phase (1 to 1.5h after sunrises and local noon). The GOES-based retrievals of LST are currently implemented with a gap-filling algorithm to estimate evaportranspiration (ET) at spatial resolutions of 4~10 km scales twice a day (Anderson et al. 2007a) with the requirement of clear-sky conditions during the time interval of obtaining. In the meaning time, MW sensors, such as the polar orbiting satellite sensor AMSR-2 onboard JAXA's GCOM-W1 spacecraft is currently operating. Both AMSR-E and AMSR-2 can provide LST twice a day (the equator crossing time 1:30 pm and 1:30 am) under all weather conditions and hence can fill the gaps due to clouds. Since ALEXI model uses two morning LSTs from GOES as an input, the relation between the two morning LSTs and the two day/night (ascending /descending) LSTs from AMSR-2 needs to be developed. To do so, the ALEXI model with the new derived LST can provide output even under cloudy conditions when there is no valid GOES TIR data. One of the objectives in the dissertation is to develop new models for surface temperature under near all weather conditions (except the rain) by integrating MW and optical data. To produce a mature system for LST integration, AMSR-E data will be calibrated, and models between AMSR-E TB to MODIS LST will be established. To meet the demands of applications in ALEXI model, AMSR-2 LSTs TB will be used to build models for converting GOES LSTs to AMSR-2 LSTs. Gap-filling algorithms will be also investigated to implement the consistent LST observations. Intensiveand 31 comprehensive analysis will be conducted for the TIR-MW surface temperature retrieval methods and evaluation against the collected in-situ data. 3.2 Derivation of HR LST Fine resolution sensors should be applied for surface monitoring, and downscaling approaches that merge information from lower spatial resolution to higher spatial resolution is crucial to estimate surface parameters. In this dissertation, different downscaling algorithms will be explored based on different requirements. The existing LST downscale methods usually require the simultaneous observations and ancillary data. These limitations make HR WM LSTs hard to contribute for analysis. For example, ALEXI model require two morning LSTs as input, while there are no other HR data available as GOES observations at the sametime. Unless the regression models are built to link another period of observations, the LST is difficult to be downscaled using the existing method. After the LST is retrieved through integrating MW and TIR satellite images, AMSR-E 25 km (or 5 km after GWR-based gap-filling) LST in 2008 and AMSR-2 10 km LST in 2015 can be obtained. In this dissertation, AMSR-E LST is going to be downscaled to 1 km spatial resolution, and AMSR-2 LST is to be downscaled to 1 km as well as 4 km (the same spatial resolution as the current ALEXI input). New methods will be developed to retrieve LST at the required fine resolution without auxiliary data or any concurrent observations. The new derived HR LSTs are compared with fine resolution satellite data as well as the ground-based SurfRad data. 32 The results illustrate the possibility of using Super-Resolution-Retrieval (SRR) method to derive HR LST. Therefore, the new 1-km spatial resolution LSTs could be implemented to ALEXI model to estimate new ETs. 3.3 Application of HR LST The application could be deployed with the HR LST. In this dissertation, HR LSTs will input soil moisture models, and soil moisture anomalies will be utilized for drought analysis. Result will be compared with other drought indices. With the consistent HR LSTs, the surface models that predict the drought condition could be updated daily. The surface drought situation in both regional and the continental United States will be analyzed using the HR soil moisture anomalies. California is the most populous and leading agricultural state of the United States, where its large agricultural areas are in arid zones. It differs from other places: (1) majority of precipitation supply is in the north, while majority of demand is in the south; (2) runoff is the greatest in winter/spring, while demand is the greatest in summer; (3) California has the highest demand for groundwater, but has little regulation. California has experienced severe drought conditions in recent years. Drought mitigation policies were often made through crisis management rather than preplanned projects. Thus a comparative study on California drought would provide scientific guidance to drought mitigation actions. Based on the USDM classifications, three typical drought conditions were considered for California drought analysis: Extreme drought in 2007 and 2013, Severe drought in 2004 and 2009, and Normal drought in 2005 and 2006. The drought 33 condition in the continental United States could also be analyzed based on HR soil moisture anomalies, and compared with other drought indices. 3.4 Hypothesis The drought occurred in 2012 over Northern American, especially Central Great Plains were the most severe since 1895 (Hoerling et al. 2014). This event developed rapidly so-called ―flash drought.‖ The normal precipitation in the early year made it is hard for drought prediction on a long-term. However, the short-term drought monitoring is possible for this event. In this dissertation, daily HR drought maps are going to derive and would be used in the case study of 2012 drought to test the two hypotheses: Null (H0): SRR can not contribute to improving the spatial resolution of LST and soil moisture, and further, the high spatial and temporal resolution soil moisture anomaly maps are not beneficial for drought analyses. Alternative (H1): SRR can contribute to improving the spatial resolution of LST and soil moisture and further, the high spatial and temporal resolution soil moisture anomaly maps are beneficial for drought analyses. 34 CHAPTER 4 METHODOLOGY FOR LST INTEGRATION 4.1 Merging LSTs from MW and TIR data 4.1.1 Data In this section, statistic models between TIR LST and MW brightness temperature (TB) will be built with the auxiliary data. Ancillary data include satellite and solar geometry (to make sure MW and Infrared have the same observing time), cloud mask product (the TIR product is to be selected only under cloud-free condition), NDVI (its relation to LST can give the overview of surface), topography (runoff is highly related to the topographic position, slope aspect, and steepness), and land cover (different land cover will influence the hydrological processes differently). This does not necessarily imply that all the variables should be assembled into this model. The Corrected Akaike Information Criterion (AICC) is used to evaluate different parameters and define a basis for model selection.We use the year 2007 dataset to built the model for integrating AMSR-E and MODIS LST, the year 2013 dataset to built the model for integrating AMSR-2 and GOES LST. The models would be evaluated by the year 2008 and 2015 for integrating AMSR-E and MODIS LST, and integrating AMSR-2 and GOES LST, correspondingly. 35 4.1.1.1 Microwave data AMSR-E for the Earth Observing System (EOS) is a dual-polarized passive microwave radiometer onboard Aqua that operates at frequencies of 6.9 GHz, 10.7 GHz, 18.7 GHz, 23.8 GHz, 36.5 GHz, and 89.0 GHz (Kawanishi et al. 2003). AMSR-E has approximately 75 43, 51 29, 27 16, 32 18, 14 8, and 6 4 km spatial resolution at 6.9 GHz, 10.65 GHz, 18.7 GHz, 23.8 GHz, 36.5GHz, and 89.0 GHz, correspondingly. The low frequencies can be oversampled into a 25-km (McCabe et al. 2005). It can provide MW TB twice a day (The equator crossing time 1:30 pm ascending and 1:30 am descending). AMSR-E sensor failed in October 2011, the AMSR-2 onboard the GCOM-W1 satellite was launched in May 2012 as a replacement for AMSR-E. AMSR-2 onboard the GCOM-W1 satellite is to measure the microwave emission from the surface or atmosphere of the Earth. It has seven frequencies with vertical and horizontal polarizations – an additional frequency at 7.3 GHz compared with AMSR-E. AMSR-2 has approximately 62 35, 62 35, 42 24,22 14, 19 11,12 7, and 5 3 km spatial resolution at 6.9 GHz, 7.3GHz, 10.65 GHz, 18.7 GHz, 23.8 GHz, 36.5GHz, and 89.0 GHz, correspondingly. The low frequencies can be oversampled into a 10 km (Japan Aerospace Exploration Agency, 2013). Same as AMSR-E sensor, It can acquire a set of daytime andnighttime MW data twice a day (The equator crossing time 1:30 pm ascending and 1:30 am descending). 4.1.1.2 Thermal Infrared Data 36 MODIS will be used to compare with AMSR-E databefore 2011, and GOES will be used since 2013 to compare with AMSR-2. The MODIS sensors are onboard NASA's Aqua and Terra satellites that have near-polar orbits. Image acquisition on Aqua is about 01:30 a.m/p.m. and on Terra is 10:30 a.m/p.m. local time. The LST data are available from the USGS Land Processes Distributed Active Archive Center (https://lpdaac.usgs.gov/). Daily MODIS/Aqua and MODIS/Terra LST L3 Global at 0.05Deg CMG product (Short name: MYD11C1 and MOD11C1) will be used in this chapter. Such product is derived from TIR bands 31 (10.78–11.28 µm) and 32 (11.77–12.27 µm) (Wan and Dozier, 1996). The MODIS surface products used here are the daily Aqua LST product (MYD11C1) in version 5, and the yearly LC product (MCD12Q1) in version 5.1. The spatial resolutions of these surface products are 5 km, and 0.5 km, respectively. Only good quality LST data with accuracy of less than 1K are selected (cloud-free). GOES Imager is onboard GOES system, a geostationary satellites network, with two TIR channels(10.2–11.2 and 11.5–12.5 µm). GOES mainly monitors the land surface of Northern America and Southern America. Its TIR imaging can provide daily 10-kmresolution LST data covering the continental United States using the algorithms developed by Sun and Pinker (2003) and Sun et al. (2013). 4.1.2 Algorithms for retrieving LST from passive microwave data 37 4.1.2.1 The single-channel algorithm The 36.5 GHz is considered to be the most appropriate MW channel for temperature retrieval (Holmes et al. 2008) in many studies, but often invalid in wet seasons due to the scattering effect of rain droplets (Gao et al. 2008). Equation 9. The single channel algorithm Where β1and β2 are regression coefficients. 4.1.2.2 The four-channel algorithm Mao et al. (2007a, b) thought: (1)T36.5V is the primary channel to retrieve LST; (2) The brightness temperature difference at the 36.5GHz and 23.8GHz channels in vertical polarization (T36.5V– T23.5V) is utilized to attenuate the influence of atmospheric water vapor; (3) T36.5V– T18.7Hcan compensate for the influence of surface water; and (4) T89V can decrease the average influence of atmosphere.Based on that, LST can be derived as: Equation 10. The four-channel LST model Where Tb refers to brightness temperature, the subscripts refer to frequencies in GHz at different bands, C0, C1…C4 are regression coefficients. 4.1.2.3 The five-channel algorithm We utilize five channels at 6.9, 18.7, 23.5, 36.5, and 89 GHz in both vertical and horizontal polarizations, since we use optical sensor to calibrate microwave sensor, the time for the two types of sensor may be different, so we especially add the time of microwave sensor as a parameter. 38 Equation 11. Five-channel LST model LST A0 +A1* (T6.9V-a1T6.9H) + A2*(T36.5V–a2T36.5H) + A3* (T23.5V–a3T23.5H) + A4* (T18.7V–a4 T18.7H) +A5* (T89V–a5T89H)+A6*UTC Where T refers to brightness temperature, the subscripts refer to frequencies in GHz at different bands, UTC is the UTC time of the microwave sensor, A0, A1…A6, a0, a1…a5 are regression coefficients. 4.1.2.4 The five-channel algorithm with auxiliary data In addition to five bands, we add auxiliary data, elevation, NDVI, and land cover relevant to LST, to the above model: Equation 12. Five-channel LST model with auxiliary data LST = B0 +B1* (T6.9V-b1T6.9H) + B2*(T36.5V–b2T36.5H) +B3* (T23.5V–b3T23.5H) +B4* (T18.7V–b4T18.7H) +B5* (T89V–b5T89H) + B6*UTC+B7*DEM + B8*LC+ B9*NDVI Where all the symbols are the same as those in Eq.11, DEM is digital elevation model (DEM), and LC is for Land Cover, and B0, B1…B8, b0, b1…b5 are regression coefficients. NDVI is extracted from MODIS 16-days NDVI composite (short name: MYD13C1) with a resolution of 0.05° (Huete et al. 1999).Elevation data is derived from National Elevation Dataset (NED) data (Gesch et al. 2002) at a resolution of 100 meters.Land Cover is the MODIS land cover Climate Modeling Grid (CMG) product (Short Name: MCD12C1) providing the dominant land cover types at a spatial resolution of 0.05°. Not all the bands are useful in this study, AICC is used to select the first six valuable parameters. The MW also has the issue of rain cloud. Identify the rain condition is necessary for this study, and viable research indicate the scattering signatures of rain could 39 besimply obtained by comparing a low-frequency measurement with a high-frequency measurement (Ferraro et al. 1998). Methods like applying a simple threshold on one brightness temperature (TB) band or a combination of TB bands. Ferraro et al. (1994) is to use the TB at 22V and 85V GHz. Grody (1991) uses a combination of TB at 19, 22, 85 GHz.These method are easy to use in warm season and remains confusion other scattering surfaces (Ferraro et al. 1998). Follow Grody (1991) and Ferraro et al. (1997), the simple method is used in this dissertation over the land to make the rain judgment, and rain is likely to be found when the global threshold (Grody, 1991): Equation 13. The judge of rain existence The specificprocedure is as follows: (1) Regularize the data: spatial and temporal match the data; (2) Eliminate the bad data. TIR data that has error > 1K, under cloud conditions. MW data under raining condition based on Eq. 13. (3) Separate the data into four seasons, spring(from March 1st to May31st), summer (from June 1st to August 31st), autumn (from September 1st to November 30th), and winter (the whole month of January, February, and December), (4) Apply AICc to choose the parameters, select the data for each season, each situation. When choosing the variables, lowest AICc value, highest adjusted R2 are selected. We noticed that six of them would enough to make p-value to near-zero, and adjusted R2 be the highest. In order not to increase the complexity as well as cause the over-fitting issue, we choose six channels, and each significance is showing in Table 2. It 40 can be seen that different channels play a diverse role in deriving different microwave LSTs. Table 2. The channel selection for different microwave LSTs. Channels MW LST T6.9Vb1T6.9H Spring T36.5Vb2T36.5H T23.5V– b3T23.5H T18.7V– b4T18.7H T89V– b5T89H ⑤ ① ② UTC DEM LC NDVI ④ ⑥ ③ ⑤ ⑥ ② ⑥ ③ ⑥ ④ AMSR-E Summer ④ ③ ① Autumn ④ ② ① ⑤ Winter ⑤ ① ② ③ Spring ③ ② ⑥ ① ⑤ ④ Summer ② ③ ⑥ ① ④ ⑤ Autumn ③ ① ⑥ ② ③ ② ⑤ ① ⑤ ① ② ⑥ ③ ④ ① ② ④ ⑥ ⑤ ① ⑤ ③ ④ ② ④ Ascending LST AMSR-E Descending ⑤ ④ LST Winter ⑥ Spring ④ AMSR-2 Summer ③ Autumn ② ③ ④ Winter ② ⑥ ① Spring ⑤ ③ ① ③ ① ② ① ② ③ ④ ① ② ③ ④ Ascending ⑥ LST ⑤ ⑥ AMSR-2 Summer ④ ⑥ ⑤ Descending Autumn ⑥ ⑤ LST Winter 41 ⑥ ⑤ Table 3. Different AMSR-2 Ascending LST retrieving models in autumn and analyses. Adj-R2 P-Value AICC The single channel algorithm 0.53 1.77e-1 3.67e4 The four channel algorithm 0.68 2.71e-2 2.01e4 The five channel algorithm 0.72 1.50e-16 1.70e4 The five channel algorithm with auxiliary 0.74 2.40e-19 1.65e4 The algorithm with all parameters* 0.74 4.74e-16 1.68e4 Model * : All the available parameter are included in this method. I.e., are the parameters(nine in total) in Table 2. To better understand the variables that are selected in LST derivation, an example of MW LST (AMSR-2 Ascending autumn LST) is analysed based on the different channel/ models (Table 3). Overfitting is likely to happen when more than six or all the variables (the last row in Table 3) are selected. And the five channel algorithm with auxiliary data could provide the smallest AICc value and the highest Adjusted R2 (Table 3, fourth row). 4.2 Regression Tree algorithm The traditional linear regression is a global model that uses a single formula to predict the entire data-space. The LST to be derived has dependent features (e.g., different TB bands) that behave in complicated, nonlinear ways. The Regression Tree (RT) can construct a flexible and robust analytical method for identifying the relationships between complex environmental data (Breiman et al. 1984). RT technique builds the tree structure, and each tree leave is corresponding to a linear regression model. This method is used here to automatically train the coefficients from matched 42 observations. It is to integrate all the possible candidate predictors, such as AMSR-2 descending TB bands T23.5V-b3T23.5H, T18.7V-b4T18.7H, T89V-b5T89H, UTC, LC, NDVI for winter LST retrieval, to determine the threshold values for different conditions, and give accuracy estimates. Models T36.5V-b2T36.5H T23.5V–b3T23.5H T18.7V–b4T18.7H T89V–b5T89H LC NDVI 1 2.97 123.46 -1.6 14.62 0.006 -0.85 2 2.35 117.34 -1.28 18.42 0.004 -0.43 43.44 0.2 -10.07 … ... … 407 1.66 65.58 -1.08 Figure 2. An example: part of the RT structure and regression models from AMSR-E and MODIS descending LST M5P training for autumn 2007. 43 There are viable RT approaches, for example, M5P, Random Tree, and Reduced Error Pruning Error, and etc. M5P (Quinlan, 1992) is a decision tree with the possibility of linear regression functions at the nodes. Bhattacharya et al. (2005) presents M5 tree is the suitable for a particular domain of input space – it split the data-space into sub-spaces and construct a local specialized linear regression model for each area (separate-andconquer technique).Compared with other RT algorithms, the leaves of the M5P tree structure consist of multivariate linear regression models (Sun et al. 2011). Thus, it is possible to model local LST linearity within the data similarly to piecewise linear functions. The M5P RT algorithm is adopted to train LST from different combinations of channels (Table 2). Figure 2 shows an example of (part of) RT structure for training AMSR-E and MODIS descending LST in autumn 2007. In this case, it uses a set of independent variables (T36.5V-b2T36.5H, T23.5V-b3T23.5H, T18.7V-b4T18.7H, T89V-b5T89H, LC, NDVI) to recursively split AMSR-E descending LSTs into different subsets that maximize the reduction in the residual sum of squares. 4.3 GWR-based gap-filling algorithm LST is a fast changing variable, and it can not be simply replaced by the observations from previous days. Instead, we first assume that each gap pixel relies on its connectingneighbour horizontally, vertically and diagonally. The value of the gap pixel thus can be interpolated by its surroundings: from up and down, from left and right 44 (Figure 3). Since some TIR LSTs can be avaliable inside the MW passing gaps, and partially fill the gaps, and can also help reduce the errors of the interpolation. 1 2 3 4 5 6 Figure 3. The regular process of gap-filling algorithm. However, such regular gap-filling method can not catch the observations when there is a big gap (Figure 4e). So we propose a gap-filling method based on the GWR. Beside that, the spatial resolution can be also downscaled same as the TIR observations. The traditional GWR algrithm has been used is to interpolates the regression coefficients and residual (Duan et al. 2016). To fill the gaps between the observations, bi-cubic interpolation is also applied among the observations. This process require two auxiliary data: NDVI data and elevation. The daily NDVI data is derived from MODIS/AQUA 0.05 degree grid surface reflectance product (short name: MYD09CMG) (Vermote et al. 2010). Elevation data is obtained from National Elevation Dataset (NED) data (Gesch et al. 2002) at a resolution of 100 meters, and downsampled via bi-cubic interpolation to 5 km as well as 25 km. Here we take AMSR-E and MODIS as an example, the specific procedures are as follows: 45 (1) Apply the regular gap-filling algorithm to both MODIS LST and AMSR-E LST, so that gap-free observations can be obtained preliminarily. (2) Aggregate NDVI and NED to microwave resolution (25 km for AMSR-E) in terms of pixel averaging. NDVI5km and NED5km denote the auxiliary variables at the MODIS pixel resolution, whereas NDVI25km and NED25kmrepresent the aggregated auxiliary variables at the AMSR-E pixel resolution. (3) Establish the non-stationary relationship between AMSR-E 25km LST with the same spatial resolution auxiliary data, that is: Equation 14. The non-stationary relationship between AMSR-E and MODIS with auxiliary data LST25km = a025km (x,y)*MLST25km + a125km(x,y)*NDVI25km + a225km(x,y)*NED25km + ϵ25km (4) Estimate the regression coefficients via Gaussian distance weighting a0 (x,y), a1 (x,y), a2 (x,y), and the error term ϵ at coarse microwave resolution. (5) Bi-cubic interpolation is used to interpolate the regression coefficients and the residual at coarse microwave resolution into MODIS 5km resolution a05km (x,y), a15km(x,y), a25km(x,y), and error term ϵ5km. (6) The final downscaled LST at 5 km resolution can be calculated using the auxiliary variables (NDVI and NED) at 5 km resolution in conjunction with the regression coefficients and the residual at 5km resolution: Equation 15. 5km LST downscaled based on GWR LST5km = a05km (x,y)*MLST5km + a15km(x,y)*NDVI5km + a25km(x,y)*NED5km + ϵ5km 46 (b) (a) Figure 4. (a) Cloud free MODIS LST, (b) the combined LST based on MODIS and AMSR-E data, (c) LST from the selected region (Figure 4a, inside the purple square) of MODIS observations, (d) the regular gap-filling method apply for (c), (e) LST from the selected region (Figure 4b, inside the purple square) of the combined observation, (f) the regular gap-filling method apply for (e), (h) the GWR-based filling algorithm applied to fill the gaps of the purple square, during nighttime/descending pass on December 15, 2008. Figure 4 gives an example of the GWR-based gap-filling algorithm output when there is enough valid TIR observations (Figure 4a) and MW observations (Figure 4b). Figure 4f shows the result using regular gap-filling algorithms, and the error is quite large within big gaps. Figure 4h is the result after applying GWR-based gap-filling algorithm. Figure 5 gives an example of the GWR-based gap-filling algorithm output when there is not enough valid TIR observations (Figure 5a) and MW observations (Figure 5b). The GWR-based interpolation (Figure 5d) outperforms the regular gap filling method (Figure 5c). One disadvantage is that this process takes a long time to implement, thus we 47 cut the images into small size to run this algorithm in practical use. The more MODIS observations it has inside the MW gap, the more accurate LST can be obtained. As shown in Figure 5, if there are not enough TIR and/or MW observations, the accuracy will be limited (Figure 5c). Note in Figure 5, the results are zooming in for comprehensive studies, so the values are also derived outside this range. If there is not enough valid data in wide gaps inside the merged TIR and MW image, the results come from interpolation, this method has the limitation to fill LST observations. (a) (b) (c) (d) Figure 5. (a) MODIS LST from the selected region (Figure 4a, inside the red square) of MODIS observations, (b) AMSR-E LST from the selected region (Figure 4b, inside the red square) of the combined observation, (c) the regular method to fill gaps of (b), (d) the GWR-based filling algorithm applied to fill the gaps of (b), during nighttime/descending pass on December 15, 2008. 4.4 Results from AMSR-E to MODIS calibration 48 MODIS LST data were aggregated to 25 km, the same resolution as the AMSR-E. Only high quality LST data with standard deviation less than 1 K are used for training the coefficients in equations (9)-(12). The above algorithms were then applied to the AMSR-E observations. The LST retrieved from the AMSR-E are comparedwith the MODIS LST product. Correlation coefficients, the Mean Absolute Errors (MAE) and Root Mean Square Error (RMSE) in relative to MODIS LST products are used to evaluate the retrieval results of the models. 4.4.1 Implementation of the single-channel algorithm Table 4. LST derived from AMSR-E with the single-channel algorithm vs. MODIS LST in daytime Correlation coefficient Mean absolute error Root mean squared error Total Number of Instances Spring 0.89 4.82 6.23 7644 Summer 0.64 4.79 6.59 10323 Autumn 0.62 4.46 6.33 13403 Winter 0.82 4.26 5.69 9919 The implementation results for single channel algorithm are listed in Tables 4 and 5. Table 4 is about the daytime results with the AMSR-E ascending data, and Table 5 is about the night results with the AMSR-E descending data, we can see the average MAE are about 4.5 K with the single frequency (band). Night time MABs are about 4 K and 49 show a little bit better than day time. This may be because the influence of the soil water and atmosphere during night time is less than those during thedaytime. The results using only one frequency (band) indicate a RMSE of about 6 K and average absolute error of about 4.5 K, which may be too big to meet our application requirements. Table 5. LST derived from AMSR-E the single-channel algorithm vs. MODIS LST in nighttime Correlation coefficient Mean absolute error Root mean squared error Total Number of Instances Spring 0.80 4.85 6.35 7792 Summer 0.73 3.38 4.54 9973 Autumn 0.58 3.80 4.93 12785 Winter 0.72 4.12 5.70 9664 4.4.2 Implementation of the four-channel algorithm The four-channel algorithm proposed by Mao et al. (2007a) is also implemented to the real AMSR-E data and compared with the MODIS LST product. The results are similar to those from Mao et al. (2005, 2007a). The MAE is about 2–3 K and RMSE error is about 3-4 K during daytime (Table 6) and MAEis about 2 K and RMS error is about 2.5 K during night time (Table 7) in relative to the MODIS LST product. 50 Table 6. LST derived from the AMSR-E with the four-channel algorithm vs. MODIS LST during daytime Correlation coefficient Mean absolute error Root mean squared error Total Number of Instances Spring 0.90 3.41 4.51 300831 Summer 0.88 3.69 4.84 537915 Autumn 0.91 3.01 4.03 591495 Winter 0.94 2.30 3.08 205511 Table 7. LST derived from the AMSR-E with the four-channel algorithm vs. MODIS LST during nighttime Correlation coefficient Mean absolute error Root mean squared error Total Number of Instances Spring 0.89 2.11 2.81 81194 Summer 0.93 1.81 2.43 245781 Autumn 0.93 1.80 2.38 292023 Winter 0.89 1.90 2.54 56626 4.4.3 Implementation of the new proposed five-channel algorithm As shown in Tables 8 and 9, the new proposed five-channel algorithm as represented by Eq. 11 by using 6.9, 18.7, 23.5, 36.5, and 89 GHz in both vertical and horizontal polarizations only shows some improvements to four-channel algorithm (Tables 6 and 7) during autumn nighttime, but no improvements during daytime. This indicates proper predictors should be selected before constructing the model, the channels should not be considered as the more the better. 51 Table 8. LST derived from the AMSR-E with the new proposed five-channel algorithm vs. MODIS LST during daytime Correlation coefficient Mean absolute error Root mean squared error Total Number of Instances Spring 0.89 3.37 4.50 234761 summer 0.88 3.57 4.75 5000333 autumn 0.90 2.95 3.97 533948 winter 0.93 2.32 3.11 144937 Table 9.LST derived from the AMSR-E with the new proposed five-channel algorithm vs. MODIS LST during night time Correlation coefficient Mean absolute error Root mean squared error Total Number of Instances Spring 0.89 2.25 3.03 139793 summer 0.91 1.88 2.56 255269 autumn 0.94 1.84 2.45 253139 winter 0.87 2.55 3.39 105963 4.4.4 Implementation of the new proposed five-channel algorithm with auxiliary data If we add some auxiliary data such as topography or digital elevation model (DEM)and land cover (LC) data to the five-channel algorithm, as shown in Tables 10 and 11, the five-channel algorithm show further improvements during both daytime and nighttime. If we use regression tree (RT) method, then the algorithm can be further significantly improved. The mean errors or accuracies can be reduced from about 2-3 K with linear regression (L) to less than 1 K with RT and RMS errors can be reduced from 52 3-4 K with linear regression (L) to less than 1 K with RTand the correlations can be increasedto 0.99 from about 0.90 for linear regression. Table 10. LST derived from AMSR-E ascending data with the new proposed five-channel and auxiliary data, compared with MODIS LST product during daytime, 2007. Seasons Spring Summer Methods Correlation coefficient Mean absolute error Root mean squared error L 0.92 2.95 3.95 RT 0.99 0.16 0.83 L 0.90 3.32 4.38 RT 0.99 0.7 0.84 Total Number of Instances 215184 348823 L 0.92 2.92 3.98 Autumn RT 0.99 0.7 0.78 341448 Winter L RT 0.95 0.99 2.25 0.63 2.99 0.46 168043 Table 11. LST derived from AMSR-E descending data with the new proposed five-channel and auxiliary data, compared with MODIS LST product during nighttime, 2007. Seasons Spring Summer Autumn Winter Methods Correlation coefficient Mean absolute error Root mean squared error L 0.90 2.25 3.02 RT 0.99 0.33 0.43 L 0.94 1.80 2.55 RT 0.99 0.41 0.52 L 0.94 1.73 2.44 RT 0.99 0.46 0.57 L 0.92 2.02 3.35 RT 0.99 0.39 0.64 53 Total Number of Instances 139793 255269 253139 105963 4.5 Results from AMSR-2 to GOES calibration This five-channel algorithm with axillary data is also used to train the AMSR-2 ascending LST with the GOES 1.5h before noon LST (Table 12) for 2013. AMSR-2 descending LST with the GOES 1.5h after sunrise LST (Table 13). Table 12. LST derived from AMSR-2 Ascending data with new proposed five-channel and auxiliary data, compared with the GOES 1.5h before noon LST, 2013. Seasons Spring Summer Autumn Winter Methods Correlation coefficient Mean absolute error Root mean squared error L 0.93 2.96 3.83 RT 0.985 1.18 1.64 L 0.91 3.22 4.14 RT 0.981 1.21 1.70 L 0.92 2.88 3.70 RT 0.990 1.048 1.44 L 0.92 2.54 3.29 RT 0.990 0.912 1.27 Total Number of Instances 382965 757026 897344 203571 The results are highly improved with RT method.During daytime, the MBEs are about 2-3 K with the linear regression (L) method, and 1-1.5 K with the regression tree (RT) method and the RMS errors are about 3-4 K from the linear regression and about 1.5 K from the RT method, and correlation coefficients are about 0.9-0.95 from linear regression and about 0.99 from the RT method. During nighttime (Table 13), the mean accuracies are about 2.5 K and RMS errors are about 3 K from the linear regression, and MBEs are reduced to about 1K, and RMS errors are reduced to about 1-1.5 K from the RT method. 54 Table 13. LST derived from AMSR-2 descending data with the new proposed five-channel with auxiliary data, compared with the GOES 1.5h after sunrise LST, 2013. Seasons Spring Summer Autumn Winter Methods Correlation coefficient Mean absolute error Root mean squared error L 0.84 2.63 3.38 RT 0.982 0.881 1.25 L 0.84 2.33 3.07 RT 0.977 0.815 1.17 L 0.87 2.18 2.87 RT 0.986 0.841 1.16 L 0.82 2.83 3.86 RT 0.982 0.902 1.29 55 Total Number of Instances 159725 550810 613528 195493 CHAPTER 5 DERIVATION OF HIGH-RESOLUTION LST 5.1 The regression-based LST downscaling algorithms The regression method includes stationary and non-stationary based LST downscaling algorithms. The TsHARP technique is a popular LST stationary downscaling approach that has been studied even recently. The GWR is a favorite nonstationary approach. LST data derived from microwave (AMSR-E 25 km) will be downscaled to fine spatial resolution as MODIS at 1 km, with the help of MODIS LST along with other selected auxiliary data. The procedure to implement the TsHARP is: (1) select a subset of pixels from a finer image where NDVI is uniform, (2) aggregate the NDVI to develop a coarser resolution pixel that matches with TIR pixels, (3) develop a statistical relationship between coarser resolution NDVI and TIR, (4) use the resulting statistical relationship to estimate TIR at both coarser and finer resolutions using respective NDVI values, and (5) finally, add the difference between the observed and predicted TIR at the coarser resolution to the finer resolution TIR image. The last step is expected to account for divergence of the retrieved temperatures from the observed temperature due to factors other than percent cover such as spatial variability in soil water. Greater accuracy with this downscaling method can be achieved by developing several NDVI classes differentiating soil from crop cover and further differentiating land cover type. 56 However, all these regression-based downscaling algorithms need the existence of another concurrent HR image, as well as other correlated auxiliary data are crucial in all these downscaling algorithms. These limitations make microwave LSTs hard to contribute for further detailed analysis. Thus, the Super Resolution Reconstruction (SRR) is introduced to reduce the inconvenience of downscaling LSTs in the next section. 5.2 The SRR-based LST downscaling algorithms The Multi-Images Super-Resolution (MISR) is a classical solution that deals with image sequences from the same scene (often caused by shifts), and HR details are usually recovered by subpixel realignments. The fundamental point underneath this method is that several images from the same area can often be obtained in satellite applications. Firstly, this approach is under the assumption that subpixel shifts from each other are different, i.e., it will notfunctionif the input images are identical. Secondly, multiple LR images should be available from the same scene, i.e., these observations shall have no significant changes. Two primary methods - Maximum Likelihood Estimator (ML) and the Projection Onto Convex Sets (POCS)- are applied to downscale LSTs in this section. The Single-Image Super-Resolution (SISR) mainly include three types: (1) interpolation-based SISR. This methodology has been extensively studied. Usually, this approach cannot recover the lost or degraded high-frequency components during the LR sampling process (Park et al. 2003), and creates blurry or over-smoothed edges for the reconstructed HR image. (2) Reconstruction-based SISR. The prior knowledge of an observation model is required to mapthe HR image to the LR images. This method is 57 numerically limited to a scaling factor of two (Park et al. 2003). (3) Database-drivenbased SISR. It learns the correspondence between HR and LR image patches from a database, and reconstruct HR image based on such correspondence. This idea is adopted in this dissertation, and further details will be stated. Let and denote the sequence of high resolution and low resolution images, respectively. The commonly used image model is given as: Equation 16. Image model Where Z is a down-sampling operator, B is a blurring function, M is a motion factor, and N is an additive noise. Subscript j,k stands for the image frame number, t is the total frame number of images, and 1 j, k t. Shen et al. (2007) also considered the photometric effects of zenith angle and atmosphere by adding a linear system with gain and offset of the photometric parameters into Eq.17. Let A be the degradation factors. The classic image restoration model (Eq.17) can simplify as: Equation 17. Simplified Image model The resolution enhancement is thus becomes the solution of defining A. 5.2.1 The multi-images SRR 5.2.1.1 The POCS-based SRR The POCS methodis an alternative iterative approachto incorporating prior knowledge about the solutioninto the reconstruction process. Let 58 be a closed convex set that satisfy a certain property. The POCS is to use prior knowledges to constrain the solution, and to found an intersection convex set by alternating projections. Such process can be described as: Equation 18. POCS process Where projects each is an initial point, and to the convex sets is the projection operator that (Park et al. 2003). The prior knowledge R can add into this equation to define the convex sets and projection algorithm. The key of the POCS method is to solve a constrained optimization problem (Shen et al. 2014). With the geographically corrected data, assuming that denotes the observed k-th LR images. The estimated LR image is regarded as the image degenerated from the HR image through the degrading function h: Equation 19. LR images from the degrading of HR images h is also called Point Spread Function (PSF) – due to undersampling of LR images, and we assume that the degrading processes via Gaussian blurring with blurring level (standard deviation) σ. w is the PSF radius. Define positive constant. as a threshold that represents the observation confidence, c is a is the ideal HR images. This procedure can be described as (Trussell et al. 1984): If the residual same; if is in the threshold range, then is outside the threshold range, will remain the will be increased or decreased to reach the near-zero. During this process, a constant threshold is used to constrain the convergence 59 speed of the iterative process. The projection of an arbitrary onto can be given as: Equation 20. The projectiona LR image A new projector is determined in each restriction step and the successive convex sets will converge to an intersection point to get the final solution (Aguena et al. 2006). POCS utilizes the dominant spatial domain observation model. 5.2.1.2 The ML-based SRR The likelihood is the reverse process of possibilities. Maximum Likelihood (ML) is to find the most likely solution for the observations by maximizing the conditional Probability Density Function (PDF) of the . Assuming that the LR LST images x are uniform, and data are geographically corrected (no motion estimation is required), the ML-SR reconstruction can be simplified as: Equation 21. ML reconstruction xML argmin y x Ax 2 The pseudo-inverse result with respect to x and equating to zero gives: Equation 22. The pseudo-inverse result of ML xML AT A 1 AT y Irani and Peleg (1991) proposed a simplified algorithm that iteratively minimizing simulation errors convolved with a Back Projection Function (BPF). To start, estimate an initial solution for the desired HR image via a simple interpolation. Most of the studies 60 take the average of upscaled LR images . We noticed that when choosing the latest LST observations as the initial image(aiming to downscale the latest LSTs) the ring effect will make the image too blur and noisy. So for a LR image set { frame }, image are averaged to set as the initial image: Equation 23. The initial image of ML method y0 The error between and Ax n will be corrected by back-projecting to until it meeting the pre-defined requirement. Equation 24. Each estimation with the BPF function where is the back-projection kernel, pixel influenced by HR pixel, and is the upsampling operator, k is a LR is the simulated k-th LR frame from the current HR estimation. The solution of BPF depends on the initialization and the choice of backprojection kernel. It affects how much the error for LR image will contribute to the next HR guess. In this study, assuming that the effect is a Gaussian random processing, thus given an estimate of the super-resolved image , the total probability of an observed LR image (k 1,…,t, t is the total number of LR images) is: Equation 25. The total probability of an observed LR image The choice of standard deviation is imperative, that higher would cause smoother edges. The result of HR LST derived from ML method will be provided in Chapter 7. 61 5.2.2 The single-image SRR Prior information is required so that a single image could be reconstructed. Such prior information is available either in the explicit form of an energy functional defined on the imageclass, or in the implicit form of example images leading to example-based super-resolution. In this session, we will explore the SRR algorithms with external and internal database. External database driven SR maps HR images learned from a large database of LR-HR image pairs, which we called example-base method in this study. Internal database driven SR maps HR images by exploiting similarities within the images, which we called self-similarity-based method. 5.2.2.1 Example-based SRR Freeman et al. (2002) are one of the first scientists to propose example-based SRR approaches. Such approaches are patch-based, and each patch pair is connected through image model (Eq.18). The patterns between HR and LR can be learned from patchexamples, and a statistical model that aims to find patch reoccurrence is applied onto the single LR image to predict HR image. Ever since example-base SISR has been proposed and tested, more related studies have been taking place (e.g., Kim et al. 2009), with a primary focus on natural images. Nasrollahi et al. (2014) reported the database that were built for satellite and aerial imagery (Said et al. 2009). To obtain the HR LST, a specific database for LST image patches should be created, along with alleviating the data complexity and a simple prediction function. 62 During the training phase, 5000 available images of MODIS 5 km LST (cloud pixels < 10%, size N*N) are chosen from different region and time for 2007 to 2008. We degrade each of the images to make the corresponding LR datasets (size M*M, where N = 2,3,4,5*M). Note that N = 2*M means we blur and subsample half of HR pixels from each dimension, thus the final pixels of LR will be a quarter of HR pixels. The factor represents the desired scale, should remain the same in one database. Followed by Freeman et al. (2002), assume that HR-LR image patches are independent, normalize image patches to increase the efficiency of the training set. (a) (b) (c) (d) Figure 6. An example of training data. (a) The MODIS 5-km LSTs observations; (b) the selected region for HR version of image; (c) bicubic spline interpolation for the full coverage HR image; (d) LR version of the image. The bicubic spline interpolation is applied on LR images, and only the differences between HR and LR images will be stored in the database. Also we filtered out the lowest frequency components since the more necessary prediction details are the highest spatial frequency components in this case (Freeman et al. 2002). Figure 6 gives an example of training imagery: select a region that cloud pixels < 10% (Figure 6b) from one MODIS 5km cloud free LST observation (Figure 6a), fill the empty gap by bicubic spline 63 interpolation to get a full coverage HR image (Figure 6c), and then obtain LR image (Figure 6d) by the nearest downsampling from Figure 6c. While predicting the HR LST, we perform the nearest interpolation on the LR, and then this LR patch will be compared with LR patches in the database. When matches are found, we generate a set of candidate estimates. Similar as Freeman et al. (2002), Markov network is used to probabilistically model the spatial relationships between the patches. Based on learning, we can get the matrix of transition probability probability between HR patches, as well as the matrix of transition between HR and LR patches. To a given LR image y, scan it with a small window (of size M), so that the corresponding position in the Markov network for each patch as well as the relation between high patches could be found, then we add the highfrequency component to make the final estimation. The probability of HR patch can be given as: Equation 26. The probability of HR patches where C is a normalization constant, is the observed HR patche at node i, is the observed LR patche at node j. NS(i) stands for the 8-connected neighbors of the pixel location i. and are specified as: Equation 27. The matrix of transition probability between HR patches Equation 28. The transition probability matrix between HR and LR patches 64 is a noise parameter, is used here to is to weight the costs (Kim et al. 2009). >1 favors a strong edge over small edges; <1 will cause smoother edges. Belief Propagation is used to find the best solution of Eq. 24 from the candidate set. Four times iterations of the algorithm are used, which is sufficient according to Freeman et al. (2002). Sufficiency and predictability are the key success factors for this method (Nasrollahi et al. 2014). With this specific built LST database, the possibility of finding similar training data in the database is highly enhanced. 5.2.2.2 Self-similarity-based SRR Example-based methods assume that the missing high resolution detail can be learned and inferred from the low-resolution image and a representative training set. To do so, a large and representative database of HR-LR image pairs as well as the mapping methods are the two key factors to achieve. Such method has the disadvantages: (1) the requirement of large and various dataset. (2) The database might not be able to full cover the missing high-frequency details. (3) the rich image structural information is not exploited. (4) various learning algorithms might cause uncertainties (Yang et al. 2011). Glanser et al. (2009) combined the example-based SR and self-similarity by exploiting the patch recurrence within and across image scales without the external database. Nature images have self-similarity, which means that HR and LR patches in a single image tend to redundantly recur within the image at varying scales (Glanser et al. 2009). A possible way to avoid the use of training images has been proposed in (Huang et al. 2015) where they found patch recurrence in a single image with pixel re-alignment similar to the 65 example-based super resolution. This method is to build an internal training set from the image pyramid of itself. So in this session, we also generates image patch pairs of one single frame instead of training extrinsic set of images. To build the image pyramid, similar to Eq.19, with the input LR image , Equation 29. The image pyramid where we used here is a Gauss kernel with blurring level σ, downsampling operator, here we used bi-cubic intepoltation. Upsampling the is, is the , that . The original LR is also upsampled then we can get LR images sequences { image sequences { }. Note that } and the corresponding HR has the same size as the same HR-LR image patches as the example-based method. 66 Thus, we can get CHAPTER 6 APPLICATIONS 6.1 Soil moisture derivation 6.1.1 Variables input to SM models A comprehensive data set is collected and processed in this study for derivinghigh resolution satellite soil moisture estimates and evaluating drought conditions in the study area. These data include: A. Land Skin temperature (LST) obtained from NASA Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) 8-days composite data (short name: MYD11C2) with a resolution of about 5-km (Wan et al. 1996). B. Normalized Difference Vegetation Index (NDVI) extracted from MODIS 16days NDVI composite (short name: MYD13C1) with a resolution of 0.05° (Huete et al. 1999). C. Precipitation that is the accumulated rainfall at daily and weekly scales obtained from the multi-satellite data for 0.25°× 0.25° grids and 3-hourly time periods of the TRMM Multi-satellite Precipitation Analysis (TMPA) project (Huffman et al. 2007). D. Elevation data derived from National Elevation Dataset (NED) data (Gesch et al. 2002) at a resolution of 100 meters. 67 E. Land Cover that is the MODIS land cover Climate Modeling Grid (CMG) product (Short Name: MCD12C1) providing the dominant land cover types at a spatial resolution of 0.05°. F. Soil Texture data that is obtained from the Food and Agriculture Organization / United Nations Educational, Scientific and Cultural Organization (FAO/UNESCO) soil map (Henkel 2015; Batjes 1997), with a resolution of about 0.0833°. G. Soil Moisture that is obtained from the Soil Moisture Operational Product System (SMOPS) of NOAA-NESDIS that merges soil moisture retrievals from microwave satellite sensors such as the Advanced Scatterometers (ASCAT) on MetOp-A and B, Soil Moisture and Ocean Salinity of European Space Agency, WindSat of Naval Research Lab based on the Single Channel Algorithm (Zhan et al. 2011; Jackson 1993).In this study, the soil moisture data from is served as the out of sample training data to build its relationship with other land parameters. 6.1.2 Temporal compositing and spatial resampling The datasets used in this study were obtained at different temporal and spatial resolutions. In order to compare with the USDM drought condition maps, all the datasets have been resampled or interpolated into uniform weekly (7 days) temporal and 0.0833° (about 12-km) spatial resolutions. Land Cover data has been sampled via the nearest neighbor assignment due to its discrete value. The bicubic interpolation assignment (Keys 1981) was used to re-scale the other datasets, assuming that each point value changes consistently during observations. 6.1.3 Models for HR soil moisture estimates 68 The hydrological condition of agricultural drought is closely linked to soil moisture (Bolten et al. 2010), which is dependent on precipitation, water infiltration and soil water holding capacity. 6.1.2.1 The Universal Triangle Model A close relationship exists between vegetation vigor and soil moisture availability, especially in arid and semiarid areas, thus in many casessatellite-derived NDVI and LST products have been used to evaluate drought condition. As to the SVAT model (Eq. 3), Chauhan et al. (2003) argued that the second or third order polynomial gives a better representation of the data since a single polynomial represents a wide range of surface climate conditions and land surface types. Thus the Triangle Model can be described as: Equation 30. The Universal Triangle Model SM T a0 a1 NDVI * a2 NDVI * a3 LST * a4 LST * 2 2 2 a5 NDVI * LST * a6 NDVI * LST * 2 2 a7 NDVI * LST * a8 NDVI *2 LST * Where NDVI * NDVI NDVI min NDVI max NDVI min , LST * LST LSTmin LSTmax LSTmin , subscripts max and min refer to the maximum and minimum values. Parameters a0, a1, …, a8 are regression coefficients.For California, and the values are 0.04, 0.01, 0.29, -0.17, -0.07, 0.31, -0.19, 0.21, 0.01, respectively. NDVI * LST * and NDVI * 6.1.2.2 2 are more significant in this model. The Basic Model Sun and Kafatos (2007) indicated the negative or reverse relation between NDVI and LST can only hold during warm or growing seasons, therefore, NDVI and LST 69 related drought indices may only be used during warm seasons, but not winter. Chauhan et al. (2003) added surface albedo into Eq. 30 to strengthen the relationship between soil moisture and measurable land surface parameters. Nevertheless, California or Contiguous United States, where surface types vary significantly, even a combination of NDVI, LST or albedo is not enough to fully describe its surface condition. Soil moisture is also highly related to precipitation (the land water balance equation indicates the change of soil moisture is highly related to precipitation), soil texture (physical properties such as dielectric constant can affect water content in soil), topography (runoff is highly related to the topographic position, slope aspect, and steepness), and land cover (different land cover will influence the hydrological processes differently). Thus it’s desirable to combine and integrate all these datasets to build a soil moisture model. This does not necessarily imply that all the variables should be assembled into this model. AICC is used to evaluate different parameters and form a basis for model selection (Hurvich et al. 1993). Conclusively, the basic regression model is built as: Equation 31. The basic soil moisture regression model SM B b0 b1Rain b2 DEM b3VI b4 Sand b5 Poro b6VI 2 b7T b8 LC Where SMB is the daily soil moisture, other parameters including Rain, DEM, VI, T, LC are all daily data listed in Table 14. Sand and Poro data are described in the previous section about data selection. b0, b1, …, b8 are regression coefficients. Thevalues are 0.36, 0.19, -0.20, -0.07, -0.18, 0.12, 0.22, 0.15, 0.02 for California region, respectively. Elevation, NDVI * 2 2 ( VI ), and daily precipitation (Rain) are more significant in this model. 70 Table 14. Different soil moisture models and the AICC values over California. Adj-R2 P-Value AICC +T+VI+VI2+T2+VI*T 0.3564 2.00e-16 -1.09e4 +Rain 0.3643 1.00e-16 -1.10e4 +Rain+DEM 0.4771 1.05e-16 -1.15e4 +Rain+DEM+N 0.5171 7.36e-8 -1.26e4 +Rain+DEM+N+Sand 0.5486 1.00e-16 -1.31e4 +Rain+DEM+N+Sand+Poro 0.5691 3.69e-16 -1.34e4 +Rain+DEM+N+Sand+Poro+VI2 0.5659 2.35e-16 -1.35e4 +Rain+DEM+N+Sand+Poro+VI2+T 0.5775 5.55e-05 -1.35e4 +Rain+DEM+N+Sand+Poro+VI2+T+LC 0.5889 4.74e-15 -1.36e4 +Rain+DEM+N+Sand+Poro+VI2+T+LC+T2 0.5990 6.15e-2 -1.36e4 +Rain+DEM+N+Sand+Poro+VI2+T+LC+T2+VI*T 0.5990 6.67e-1 -1.35e4 Model In this table, ―Rain‖ represents precipitation, ―DEM‖ represents elevation, ―VI‖ represents NDVI, ―T‖ represents LST, ―Poro‖ represents porosity and ―LC‖ represents land type. 6.1.2.3 The Refined Model Time series analysis of the USDM weekly drought conditions over California from 2003 to 2014 is presented in Figure 7a. The black line in Figure 7b is the corresponding normalized monthly accumulated precipitation derived from TRMM. Drought condition cannot be directly reflected by temporal precipitation because drought is caused by inadequate precipitation during some period of time, usually more than a season. 71 (a) (b) Figure 7. (a) USDM weekly drought condition map. (b) Normalized Monthly accumulated precipitation over California (32 - 42°N, 114 - 125 °W) retrieved from TRMM, and normalized monthly accumulated precipitation seasonal decomposition by Loess (blue line), from Jan 2003 to Dec 2014. Detecting the real trend and seasonal components of time series enables the identification of different types of changes. Discerning systematic changes in the seasonal pattern is essential for accurately assessing drought responses to precipitation changes. The LOESS (LOWESS or LOcally Weighted Scatterplot Smoothing) is a flexible and ideal method to model non-linear processes or provide a smoothing parameter value and the degree of the local polynomial (Koster et al. 1996; Ek et al. 2003). The basic concept of this approach is to build up a function that describes the deterministic part of the 72 variation in the data, point by point by fitting simple models to localized subsets of the data with a weight matrix. LOESS is applied to describe the nonlinear trends of precipitation (The blue line in Figure 7b). It shows that precipitation has an accumulating and lagging effect on drought condition. For example, the trend of precipitation is decreasing in 2006 (Figure 7b), yet the USDM marked this year as normalconditions (Figure 7a) due to sufficient accumulated rainfall in previous period. Large region of California has a Mediterranean climate, where rain season is in winter and spring, from late October through March. It is found that the accumulated precipitation from the last year’s warm season to the current time can describe the drought conditions better than the daily precipitation, thus the daily precipitation in the basic model may be replaced by the accumulated precipitation. Based on this fact, we refined the basic model by replacing the precipitation component in Eq.31 with the accumulated rainfall for the whole year starting from last year’s warm season. The modified basic model is referenced as the ―refined model‖, and it can be described as: Equation 32. The refined soil moisture regression model SM R c0 c1 DEM c2VI c3 Sand c4 Poro c5VI 2 c6T c7 LC c8 * Ac _ Pr Where Ac_Pr is for accumulated precipitationstarting from last year since April until the requested day.c0, …. c8 are the regression coefficients. The values are 0.10, 0.21, -0.04, -0.15, 0.09, 0.19, 0.12, 0.01, 0.28 respectively for California. The parameters have similar coefficients as the basic model, while the accumulated precipitation (Ac_Pr) is the most significant input in this model. 6.2 Drought analyses 73 6.2.1 SM anomaly calculation Soil moisture changes slowly, therefore cannot catch the fast change of drought conditions. Soil moisture anomaly is more appropriate to describe drought conditions than the absolute soil moisture (Reichle et al. 2005). To match with the UM drought maps temporally, daily soil moisture were averaged into weekly.Soil moisture anomaly maps are obtained by the difference between weekly soil moisture and the long-term average soil moisture based on the equation: Equation 33. Soil moisture anomalies SM _ Anomaly SM SM Where the average soil moisture SM for each pixel is calculated for 11 years from January 1 2003 to December 31 2014. Negative soil moisture anomalies stand for the observed data are lower than the averaged data, and indicate dry conditions. 6.2.2 Comparison with traditional indices and model outputs The temporal correlation coefficients are computed between the outputs of the three models and the USDM drought classifications at weekly scales during the growing season from April to October of each year. The VTCI (Eq. 6) and VHI (Eq. 5 is the VCI) have been adopted for monitoring the spatial extent and magnitude of drought (Wan et al. 2004; Bokusheva et al. 2016). Here NDVI and LST from MODIS 8-day composite data (See 6.1) during cloud-free periods were used to construct VTCI. VHI is obtained from the Center for Satellite Applications and Research (STAR) of NOAA Satellite and Information Service (NESDIS). 74 North American Land Data Assimilation System – Phase 2 (NLDAS-2) utilizes the real-time and forcing data sets (Cosgrove et al. 2003) to execute Land Surface Models (LSMs) such as Mosaic (Koster et al. 1996), Noah (Ek et al. 2003), and the Variable Infiltration Capacity (VIC) model (Liang et al.1996). NLDAS can provide high quality soil moisture fields (Mitchell et al. 2004) and has been used as one of the drought monitoring indicators in the United States (Anderson et al. 2013). In this dissertation, the weekly anomalies of soil moisture content (total column) from three LSMs are used for comparison. 75 CHAPTER 7 RESULTS 7.1 Integrated LSTs Since RT method shows significant improvement over the traditional linear regression method, the rules and regression models obtained from the RT machine learning or training are therefore applied to real AMSR-E and AMSR-2 observations. Figure 8 and Figure 9 show examples of MODIS LST product (a), LST derived from the AMSR-E observation (b), blended AMSR-E LST and MODIS LST, in which LSTs are obtained from MODIS product under clear conditions, while under cloudy conditions, LST are derived from the AMSR-E measurements (c); there are still some gaps there due to different satellite passes, so we applied a gap filling algorithm to fill the gaps as shown in (d). We can see optical sensors, like MODIS, can only obtain LST under clearsky conditions, there may still exist a lot of areas without data, while microwave like AMSRE can fill the gaps due to clouds, and give a complete picture. Figure 10 and Figure 11 demonstrate GOES LST product (a), LST derived from AMSR-2 (b), the blended GOES and AMSR-2 LST (c), where there is some cloud contamination in GOES LST; integrated GOES and AMSR-2 LST with pass gaps filled(d). 76 77 Figure 8. (a)Cloud free MODIS LST, (b) the derived AMSR-E LST based on Five-channel algorithm,(c) the combined LST based on MODIS and AMSR-E, (d) the integrated LST from MODIS and AMSR-E, during daytime on December 5, 2008. 78 Figure 9. (a)Cloud free MODIS LST , (b) the derived AMSR-E LST, (c) the combined LST based on MODIS under clear sky and AMSR-E under clouds, (d)the integrated LST from MODIS and AMSR-E, during nighttime on June 2, 2008. 79 Figure 10. (a) Cloud free GOES LST at 1.5h before noon, (b) the AMSR-2 Ascending LST, (c) GOES and AMSR-2 combined LST, and (d) the integrated LST from GOES and AMSR-2 on October 22, 2015. 80 Figure 11. (a) Cloud free GOES LST at 1.5 h after sunrise, (b) the AMSR-2 descending LST, (c) the GOES and AMSR-2 combined LST, and (d) the integrated LST from GOES and AMSR-2 on August 3, 2015. 7.2 HR LST derivation 7.2.1 Regression-based derivation It shows in Figure 12 that GWR outperformed TsHARP method, and the overall results are similar as original MODIS LST observations. The auxiliary NDVI and elevation data used in all regression methods were described in section 4.4. AMSR-E has a full coverage over the scene (Figure 12b) while MODIS (Figure 12a) has no valid data in some area due to the cloud influence. The results produced from traditional TsHARP and GWR methods are shown in Figure 12c and Figure 12d, correspondingly. Apply the method we proposed in section 4.4. – the GWR-based gap-filling algorithm – the result is shown in Figure 12e. The traditional GWR downscaling method did not interpolate the LST observations beforehand. I.e., step (1) is missing in the traditional GWR algorithms. This new GWR-based gap-filling algorithm is able to provide a gap-free LST observations. (a) (b) (c) (d) (e) Figure 12. Spatial distribution of (a) MODIS LST, (b) AMSR-E LST, (c) TsHARP, (d) traditional GWR downscaled LST, and (e)the GWR Gap-filling algorithm downscaled LST for the image at the same time (Oct 2, 2008). 81 As discussed before, in order to get rid of the concurrent HR observations as well as other correlated auxiliary data, SRR is more suitable in downscaling LSTs. And the results will provide in the following section. 7.2.2 MISR-based derivation In this MISR-based downscaling process, only two LST observations will be used due to the fast changes of LST observations even in a short time period.The LST observations are derived previously from the WM and TIR integrated LSTs. Two case are shown in Figure 13 to demonstrate the results from POCS and ML methods, where we want to retirevel the LST of the latest observation(1: 30 pm, February 14, 2008). Since only two images are given to reconstruct HR LST, POCS and ML downscaling level are quite limited. As mentioned before, due to the ringing effect, we averaged the images as the initial plane. Figure 13a is the target LST image - latest AMSR-E onbroad Aqua around 1: 30 p.m. Figure 13b1 is the previous day of AMSR-E LST at the same time (around 1: 30 p.m. LST). Itcan be seem that if the two observations are similar (LST observations has little changes), both ML and POCS can be used to downscale LST (Figure 13c1-d1). Figure 13b2 is the same day of AMSR-E around 10: 30 a.m. LST, retrieved from AMSR-E LST onbroad Terra. In this case, the two LST observations (three hours between two observations on same day) change a lot, ML can not present the situtaion for the current LST, more over, it gives a result more like a temperature between the two observation (Figure 13c2). POCS, under the same situation, can exhibit better results (Figure 13d2).The ringing effects of POCS is neglected in this dissertation, since other 82 scientists have been working on it and made great results (Nasonov et al. 2009). Many studies are to integrate the spatial and frequency domain to decrease the edge oscillation phenomena (Shen et al. 2014; Tekalp et al. 1992). This might due to the sorting method in POCS, which we put the current LST, thus the result is more likely to be the really current LST. As for the Gaussian kernal, the standard deviation is set to 400 to obtain a smoother edge. Over all, such methods might be useful in slow-changing satellite images, like land cover. (b) (c) (d) (c2) (d2) + (a) (b2) + Figure 13. Spatial distribution of (a) AMSR-E around 1: 30 p.m. LST, (b1) previous day of AMSR-E around 1: 30 p.m. LST, (c1) ML downscaled LST retrieval based on (a) and (b1), (d1) POCS downscaled LST retrieval based on (a) and (b1); (b2) same day of AMSR-E around 10: 30 a.m. LST, (c2) ML downscaled LST retrieval based on (a) and (b2), (d2) POCS downscaled LST retrieval based on (a) and (b2). Date: February 14, 2008. 83 7.2.3 SISR-based derivation (a) (b) Figure 14.Spatial distribution of downscaled LST from different SISR methods: (a) Example-based method (b) Self-similarity method. Date: 1:30 p.m., February 14, 2008. To compare with the MISR-based LST downscaling method, Figure 14 provides the same HR LSTs derived from the Example-based method (Figure 14a) and the Selfsimilarity method (Figure 14b) in previous example (Figure 13). Figure 14a is the orginal image, with a coarse resolution 25 km, the SISR were applied seperately to get HR LST at the resolution 1km. The standard deviation is also set to 400. When the latest LST is aimed to retrival (1: 30 pm, February 14, 2008), example-based SRR and self-similaritybased SRR can perform better. Given by another example in Figure 15,where the aimed LST is 1.5h before noon. GWR can not applied because there is no concurrentHR satellite obeservations. But withthe SISRmethod, the LST can be downscale to 1 km. Since the example-based 84 dataset is we built on our own, comparing with other database, we are not hypercritical about the edges, and specifically focus on LST, which makes the results visually match. (a) (b) (c) Figure 15. An example for different SR methods: (a) Original LR image (10 km). (b) Example-based method (c) Self-similarity based method. LST data is 1.5h AMSR-2 LST before noon for August 9, 2015. Figure 16. An example: The final HR AMSR-E LST compared with MODIS LST during daytime on December 8, 2008 Given the orginal MODIS LST observations (Figure 16a) and GOES 1.5h after sunrise LST (Figure 17a), the gap-free LST at the 1-km spatial resolution observations can be retrievaled (Figure 16b-c and figure 17b-c). This result supports the alternative 85 hypothesis (H1) in Chapter 3.4, that is, SRR can help to improve the spatial resolution of LST and soil moisture. Figure 17. The final HR AMSR-2 LST compared with GOES 1.5h after sunrise LST on March 29, 2015 7.3 Soil moisture With the continuous daily LSTs input, soil moisture can be retrieved from the refined model (Eq. 32). Soil moisure alone is not easy to be observed the virsual changes. Soil moisure anomaly can demonstrate the drought condition better than soil moisure itself. Soil moisure anomaly and soil moisture percentiles are calculated over continental US. And soil moisure anomaly and soil moisure percentiles showed a correct trend for drought situation. 7.4 Drought analyses and case study 7.4.1 Drought in California This study is carried out for California State (the latitude and longitude of capital city Sacramento is about 38.6° N, 121.5° W). California has experienced the most severe drought conditions in the past years. In this section, the drought conditions in California 86 are analyzed using soil moisture anomalies derived from integration of optical and microwave satellite observations along with auxiliary land surface variables. The landscape of the state includes mountain regions, forests, farmlands, grasslands and barren. Urban or built-up areas and surface water each account for less than 5% of California. Sierra Nevada is located in the interior of California and stretches along almost the entire state from north to south; its snowpack is a key component of the hydrologic cycle in California (Mote 2006). The study area has diverse soil types and land resources. Northwestern California is covered by forest, while southeastern California is arid with barren land or scrublands. Southern California gets about half of its water from Colorado River. The large geographic center of California (Central Valley) is a flat and broad agricultural land. The leading commodity like nuts, dairy, and fruits consume 80% of California water, most of them from massive water projects (NASS, 2014). Drought conditions based on soil moisture anomalies are compared with the USDM classification from 2003 to 2014. Three typical drought conditions were considered: extreme drought in 2007 and 2013, severe drought in 2004 and 2009, and normal drought in 2005 and 2006. The top panel in Figure 18 shows the weekly USDM drought cases for six different years. The universal trianglemodel (Figure 18, the seventhpanel) is quite limited to identify the drought conditions, showing less drought in southern California in July of 2009 and June of 2004, but more severe drought in April of 2005 than those from the USDM. The mountain region (Sierra Nevada) demonstrated a wet condition with slight changes. Its western side, on the other hand, was almost dry 87 throughout all the six different years. And it fails to identify the relatively dry surface condition in 2013. Meanwhile, the basic model (Figure 18, the eighth panel) enhances the performance of triangle model, and shows relatively closer agreement with the USDM patterns. For example, 2005 is considered to be ―wetter‖ comparing with the triangle model. Thisbasic modelspatially demonstratesmore severe drought conditions in 2007 and 2013, moderate drought conditions in 2009 and 2004, and relatively normal years in 2006 and 2005. However, it can barely tell the temporal variations of drought conditions, and misjudged the wet condition in the Northwestern region. Overall, VTCI is hard to differentiate severe drought condition from normal year (Figure 18, the second panel). VHI and North American Land Data Assimilation System (NLDAS) soil moisture outputare indicators input USDM drought classes, thus the match with the USDM observations. The refined model (Figure 18, bottom panel) – or the modified basic model with the input of accumulated precipitation - shows similar drought patterns to those from the USDM classifications. Given the situation that a normal condition week ended on June 22 2004 on the northwest of California, a dry condition was classified based on the basic model (Figure 18, third panel), while the refined model considers the condition as ―wet‖ (Figure 18, fourth panel) due to the additional input. 88 Figure 18. Drought condition from different indicators. From top to bottom: USDM classification, VTCI, VHI, model output, soil moisture anomalies based on “Triangle Model”, basic model output, and the refined model. Anomaly of Soil moisture content. ∆ equals to 0.02 (unit: m3m-3), γ equals to 60 (unit: kg/m2). 89 While in most cases soil moisture anomalies from the refined model agree with the USDM classification, the Southeast part of California is more likely to be classified into dry condition due to its insufficient precipitation and land surface type (barren land). This place imports about 80% of water from Colorado River, thus it has been highly impacted by anthropogenic activities. Compared with the USDM classifications, the refined model can tell whether the drought condition is relieving or getting worse, yet it emphasizes the persistent-effect of drought condition. For example, there was enough precipitation in 2005 (Figure 18, bottom panel) to make 2006 a wet year. The refined model noticed this change but still consider more water supplies are required for central California to reach the ―wet point‖. Figure 19 shows the temporal correlation coefficients between the soil moisture anomaly output from the three models and the USDM drought classes, where greener color indicates a better match between the two classifications. The statistical metrics of Averaged Temporal Correlation Coefficients are also showing above each figure. In general, the refined model outputs have higher correlation with the USDM drought classifications. 90 Figure 19. The temporal correlation coefficient maps between the USDM drought classifications and the triangle model (top panel), the basic model (middle panel), the refined model (bottom) outputs. 7.4.2 Drought in contiguous U.S. Figure 20 gives the example of drought condition using different indicators over contiguous U.S., same as the previous result, drought condition can be detected by the soil moisture anomalies. The percentile of soil moisture can not easily catch the visual changes, so soil moisture anomalies percentile is used instead. The Refined soil moisture provide an easy method for monitoring surface condition. It presents the drought condition from 2004 to 2010 (7 years), the surface wetness matches with the observations from USDM. VHI and ESI are good indicators, and NLDAS output are visually alike. 91 Figure 20. Contiguous U.S. Drought condition from different indicators. From top to bottom: the USDM classification, VTCI, VHI, ESI, NLDAS model output, soil moisture anomalies based on the refined model, and the soil moisture percentile based on the refined model. 7.4.3 Continuous drought monitoring 92 Figure 21. An example of weekly USDM observation compared with daily SM anomalies. First column: weekly USDM observations. Soil moisture anomalies observations in the continuous 8 days (from June 3 to June 10) (Second column) based on previous LST and (Third column) based on the new derived Example-based LST. ∆ equals to 0.02 (unit: m3m-3). 93 USDM as well as other drought indicators can provide a weekly drought monitoring, while the new algorithm can provide soil moisture anomalies observations on a daily basis. The previous LST product that input the soil moisture model is lack of observations due to cloud influence, and made the observation ofsoil moisture anomalies with gaps(second column, white area is lack of observation, thus consider the surface condition is normal). With the example-based LST (ExB LST, figure 21, third column), the soil moisture anomalies can be given continuously and gap-free. It matches with USDM drought conditions, as well as catching the flash changes. 7.4.4 Case study: drought in 2012 Figure 22. Main Drought area in 2012. Flash drought frequently occur in central and eastern United States (Lorenz et al. 2017). The 2012 drought over Northern American has the worst surface condition since the 1930s Dust Bowl (Grigg et al. 2014). The drought started in 2011, extended rapidly in 94 2012 (especially in June and July according to USDM classifications), and continued in 2013. This event is pervasive in the central regions of the United States due to the absence of rainfall in the growing season. The rapid soil moisture loss led this event as ―flash drought‖ (Otkin et al. 2016). Unlike the common drought that is caused by external forcing like SST (Chapter 1.3.2), this event was a result of natural weather variations, with little warnings could be found in traditional drought metrics or climate model simulations (Hoerling et al. 2014). It suggests that the current drought monitoring should enhance its temporal resolution. USDM classifications reported the distribution of this drought event on a weekly basis. In this dissertation, the soil moisture anomalies are calculated on a daily basis to compare with the USDM drought classification. Figure 22 shows the main area for 2012 drought, i.e., the following twelve states are selected: Texas, Colorado, Kanas, New Mexico, Nebraska, Oklahoma, Wyoming, South Dakota, Iowa, Missouri, Arkansas, Louisiana. Figure 23a is the USDM weekly drought condition map over the twelve states (Figure 22) in 2012. Figure 23b is the average soil moisture anomalies over the twelve states. The drought condition could be monitored from the soil moisture anomalies on a daily basis using the system this dissertation built. Among these severe dry regions, states such as Iowa, Nebraska, Texas account for a large amount of corn yield in the United States. Corn losses were the most substantial among crops in 2012. USDA expected the U.S. corn yield to be 166.0 bushels per acre and production of 14.79 billion bushels; after-drought, the loss was more than a quarter 95 (Rippey 2015). The National Centers for Environmental Information (NCEI) estimates the largely agricultural losses to be $30 billion (Rippey 2015). (a) (b) Figure 23. (a) USDM weekly drought condition map over the twelve states in 2012. (b) The average soil moisture anomalies over the twelve states. 96 (a) (b) (c) Figure 24. (a) The USDM classification (b) soil moisture anomalies based on the refined model in Texas, and (c) the 1-km resolution soil moisture anomalies (drought conditions) on the west Texas. Date: May 8, 2012. ∆ equals to 0.02 (unit: m3m-3) The drought condition at the coarser or finer resolution scale might be dramatically different (Figure 24), and same results have been found in other studies 97 (Duncan et al. 2015). Resolution plays a critical role in water management, thus further influence drought occurrence and mitigation. With the HR drought risk maps, changes in water demand and supply could be better observed and adjusted for stakeholders. Figure 25. 2012 Corn Future historical prices. The figure obtained from TDAmeritrade. This study answers the hypothesis in Chapter 3.4, that is, the high spatial and temporal resolution soil moisture anomaly maps are beneficial for drought analyses. For example, the high spatial resolution drought maps might help farmers to coordinate their irrigation. Figure 25 is the 2012 corn price for the Future market, providing evidence that the drought condition (Figure 23b) could influence the market. The spatial distribution of drought condition is not further shown here. The previous examples of SM anomalies (e.g., Figure 21) demonstrate the advantages for stakeholders. 98 CHAPTER 8 EVALUATIONS 8.1 Validation of the integrated LST against SurfRad observations Validation effort is conducted by comparing retrieval LSTs against in situmeasurements from SurfRad. The in-situ LST measurements are matched with the retrieved LSTs at the same time over the same location. The SurfRad network has been operatingsince 1995 in the United States. It provides high quality in-situ measurements of upwelling and downwelling longwave radiations, along with other meteorological parameters (Augustine et al. 2000). It continuously monitors components of the surfaceradiation budget. In this dissertation, six sites are selected to evaluate the integrated LST separately. Brief information about this six SurfRad stations (e.g., site location, associated surface type) is presented in Table 15. Table 15. SurfRad sites for algorithm validation Site No. Site Location Lat (N)/Lon(W) Surface Type* 1 Bondville, IL 40.05/88.37 Crop Land 2 Fort Peck, MT 48.31/105.10 Close Shrublands 3 Goodwin Creek, MS 34.25/89.87 Deciduous Forest 4 Boulder, CO 40.13/105.24 Crop Land 5 Sioux Falls, SD 43.73/96.62 Grass Land 99 6 Pennsylvania State University, PA 40.72/77.93 Mixed Forest *IGBP surface types. SurfRad observed surface longwave radiation (upwelling and downwelling radiative fluxes) could be converted to skin temperature according to the StefanBoltzmann law: Equation 34. LST conversion from SurfRad observations 1 F (1 b ) F 4 Ts b Where F↑ is the upwelling longwave radiation, F↓is the surface downwelling longwave radiation, is the surface broadband emissivity, and σ is the Stefan-Boltzmann constant (σ 5.67× 10-8 Wm-2 K-4). The broadband emissivity ε in Eq. 34is estimated from the MODIS spectral emissivity using the narrowband to broadband conversion method (Wang et al. 2005). The Surface Reflectance Daily L3 Global 0.05Deg CMG (Short Name: MYD09CMG) is used here to as the daily emissivity data. Only the highest quality data were selected. If the data is not available, then the nearest data were selected. Equation 35. Approximate emissivity b 0.2122 29 + 0.3859 31 + 0.4029 32 Where , , and are the spectral emissivityof MODIS bands 29, 31 and 32, respectively. The total uncertainty of this method is approximately 0.005 (Jin and Liang 2006). 100 The in-situ LST measurements should spatially and temporally match with the retrieved LST observations. The LST pixel that is spatially closest to each SurfRad site is selected. Since the new derived LSTs are to implement the missing observations of TIR sensors, the observation time should be the same as TIR LSTs. Thus the viewing time can also be obtained from the original MODIS/GOES LST product. SurfRad time segment that is closest to the integrated LSTproduct in the time series would be selected to derive the corresponding LST. These consistent observations are able to provide 5-km spatial resolution LSTs to compare with SurfRad, so the accuracy is limited within 5-km of SurfRad observations. The temporal resolution of the SurfRad observation is about one minute (three minutes in 2007 and 2008), so the time could be matched up quite precisely. The integrated AMSR-E and MODIS LST model was built based on the dataset from year 2007. Other years besides 2007 could be test, in this dissertation; we present the integrated LSTs for the year 2008 by applying such model. The integrated AMSR-2 and GOES LST model was built based on the dataset from the year 2013. And in this dissertation, we present the integrated LSTs for the year 2015 by applying such model. These integrated LSTs are called AMSR-E LST and AMSR-2 LST for convenience, correspondingly. The validation results against the SurfRad ground observations are presented in Figure 26 for MODIS and AMSR-E in the year of 2008 and Figure 29 for GOES and AMSR-2 in the year of 2015. Since the TIR sensors are sensitive under cloudy conditions, MODIS/GOES LSTs are taken into account when under clear conditions. 101 (b) MODIS Descending LST V.S. SurfRad LST (a) MODIS Ascending LST V.S. SurfRad LST (c) AMSR-E Ascending LST V.S. SurfRad LST (d) AMSR-E Descending LST V.S. SurfRad LST Figure 26. Scatter plots of MODIS and AMSR-E LST against the SurfRad Observations in 2008. The Bias refers to Mean Bias Error (MBE) or accuracy calculated as Eq. 36, Std is the Standard Deviation based on Eq.37, R means Pearson Correlation Coefficient, N stands for Sample Number. The black diagonal refers to 1:1 line, the pink line is for least square fit line. 102 Figure 27. Scatterplots of the comparison of LST from AMSR-E ascending /daytime retrievals and groundbased measurements at six SurfRad sites in 2008. To give a statistical analysis of the result, Mean Bias Error (MBE) and the Standard Deviation (StD) are calculated as: Equation 36. Mean Bias Error 103 Equation 37. Standard Deviation For MODIS LST product, the MBE or accuracy is -2.48 K during daytime and 0.47 K during nighttime, and the Correlation Coefficient (R) is 0.978 during daytime (ascending pass) and 0.968 during nighttime (descending pass). For LST derived from the AMSR-E data, the accuracy is 0.42 K during daytime and -1.56 K during nighttime; the correlation is about 0.97 for the ascending and 0.93 for the descending data. The StD of AMSR-E LST is about 1 K higher than the MODIS LST, which requires the system error correlation and other enhancement in the future. The ascending and descending AMSR-E LSTs observations are also compared with the six SurfRad station separately and exhibited in Figure 27 and Figure 28. It can be seen that the Table Mountain/Boulder in Colorado State and Fort Peck in Montana State could employ the system error correlation to enhance their accuracy. This new LST is likely to exaggerate the temperature in daytime and cut down the temperature during nighttime in these two sites. The overall observations from each station are positive correlated with the observations. 104 Figure 28. Scatterplots of the comparison of LST from AMSR-E descending /nighttime retrievals and groundbased measurements at six SurfRad sites in 2008. For the GOES LST product, accuracy is -2.1 K and correlation is 0.96 for the time at 1.5 hours after the sunrise(Figure 29a); and the accuracy is -0.94 K and correlation is 0.93 for the time at 1.5 hours before the noon time (Figure 29b). For LSTs derived from the AMSR-2 observations, accuracy is 0.45 K and correlation is 0.95 for the ascending 105 data (Figure 29c); and the accuracy is about -0.04 K, and correlation is 0.93 for the descending data (Figure 29d). (a) GOES 1.5h before noon LST V.S. SurfRad LST (b) GOES 1.5h after sunrise LST V.S. SurfRad LST (c) AMSR-2 Ascending LST V.S. SurfRad LST (d) AMSR-2 Descending LST V.S. SurfRad LST Figure 29. Scatter plots of GOES LST product and the retrieved AMSR-2 LST vs. SurfRad observations in 2015 during daytime and nighttime. The Bias refers to Mean Bias Error (MBE) or accuracy calculated as Eq. 36, Std is the Standard Deviation based on Eq.37, R means Pearson Correlation Coefficient, N stands for Sample Number. The black diagonal refers to 1:1 line, the pink line is for least square fit line. 106 Figure 30. Scatterplots of the comparison of LST from AMSR-2 ascending /daytime retrievals and ground-based measurements at six SurfRad sites in 2015. In general, LST from thermal measurements such as MODIS and GOES have higher correlations and are still better than those from microwave sensors such as AMSRE and AMSR-2. Therefore, for clear sky conditions, we still use thermal IR data, only under cloudy conditions, we use microwave data. The ascending and descending AMSR-2 LSTs observations are also compared with the six SurfRad station separately and exhibited in Figure 30 and Figure 31. In 107 daytime, this new LST observation is like to underestimate the temperature of Goodwin Creek (deciduous forest). In both daytime and nighttime, the temperature in Boulder and Fort Peckare likely to be exaggerated. The overall observations show positive correlations between the observations. Figure 31. Scatterplots of the comparison of LST from AMSR-2 descending /nighttime retrievals and groundbased measurements at six SurfRad sites in 2015. 108 8.2 Validation of the GWR-based gap-filled LST To validate the GWR gap-filling algorithm, the MODIS/ Terra LST is used. Terra equator descending passing time is 10:30 a.m., which is about the same time as GOES 1.5h before local noon observations. The LSTs that are derived through gap-fillings are selected to compare with the available Terra observations at the same time. Figure 32. An comparison between gap-filling LST and Terra LST. (a) Cloud free GOES LST at 1.5h before noon, (b) the AMSR-2 ascending LST, (c) GOES and AMSR-2 combined LST, (d) the integrated LST from GOES and AMSR-2, (e)Terra descending LST, (f) the difference between images based retrieval on June 18, 2015. Samples are selected if there are available Terra observations (Figure 32e) at the same missing area in Figure 32c. Figure 32d is the final LST image after GWR-based gap-filling. The difference of the final LST in the gap region of figure 32c is compared with Terra LST. As shown in Figure 32f, positive value stands for the final LST is larger 109 than Terra observations, and vice versa. The histogram of the difference between gapfilling LSTs and Terra LSTs is given as Figure 33. Figure 33. The histogram of the difference between gap-filling LSTs and Terra LSTs in figure 32f. Figure 34. A sample set for comparing the gap-filling LSTs with MODIS/TERRA at 1-km for 2015. The Bias refers to Mean Bias Error (MBE) or accuracy calculated as Eq. 36, Std is the Standard Derivation based on Eq.37, R means Pearson Correlation Coefficient, N stands for Sample Number. The black diagonal refers to 1:1 line, the pink line is the least square fit line. We randomly reduce the observations 500 times and compare it with the valid (cloud free) Terra LST of 2015. Overall the LST retrieved from the gap-filling algorithms 110 agree with the same time Terra observations. The accuracy is 0.12 K the Correlation Coefficient (R) is 0.95, and the StD is about 4 K (Figure 34). 8.3 Downscaled results 8.3.1 Comparison with fine-resolution satellite data (a) (b) Figure 35. A sample set HR LST compared with MODIS at 1-km for 2008, based on (a) example-based SRR, (b) self-similarity SRR. The Bias refers to Mean Bias Error (MBE) or accuracy calculated as Eq. 36, Std is the Standard Deviation based on Eq.37, R means Pearson Correlation Coefficient, N stands for Sample Number. The black diagonal refers to 1:1 line, the pink line is for least square fit line. Figure 35 gives the scatter plot of HR LSTs downscaled by SISR method with the same resolution as MODIS (1 km). The results from MISR method are not discussed here since these methods have limitations on monitoring LSTs. Due to too many samples available in a whole year, we randomly reduce the observations 10000 times, then compare it with the valid (cloud free) MODIS 1 km LST. For HR LSTs, accuracy is 0.36 K and correlation is 0.97 when derived from the Example-based method; and the 111 accuracy is about -0.06 K, and correlation is 0.96 when obtained from the Self-similaritybased method. It seems that Example-base SRR is a little better than Self-similarity-based SRR. The overall correlation coefficient is quite high. However, the limitations of microwave LST make the high uncertainties: the StD is 3.2 K and 3.7 K, correspondingly. 8.3.2 Evaluation against the SurfRad observations (a) Example-based AMSR-E LST V.S. SurfRad LST (b) Self-similarity-based AMSR-E LST V.S. SurfRad LST Figure 36. Scatter plots of the AMSR-E LST vs. SurfRad observations in 2008 during daytime/ascending (a) LSTs retrieved from Example-Based SRR and (b) LSTs retrieved from Self-Similarity-Based SRR. The Bias refers to Mean Bias Error (MBE) or accuracy calculated as Eq. 36, Std is the Standard Deviation based on Eq.37, R means Pearson Correlation Coefficient, N stands for Sample Number. The black diagonal refers to 1:1 line, the pink line is for least square fit line. The LSTs (1-km) obtained from the proposed Example-based and Self-similaritybased algorithm are validated against the ground observations. Figure 36 is for the AMSR-E LSTs comparing with Surfrad LSTs in 2008 and Figure 37 is for the AMSR-2 LSTs comparing with Surfrad LSTs in 2015. For LST derived from the example-based method, the accuracy is -0.32 K for AMSR-E and 0.27 K for AMSR-2, the correlation is 112 0.95 for both AMSR-E and AMSR-2; for LST derived from the self-similarity-based method, the accuracy is 1.52 K for AMSR-E and 0.38 K for AMSR-2, the correlation is 0.93 for AMSR-E and 0.94 for AMSR-2.The example-based method is better than the self-similarity-based method. The results also indicate that in general, microwave LSTs have the uncertainty about 4~5 K. This might due to the limitations inherited from original MW LSTs. Thus the MW LST enhanced algorithms should be further investigated. (a) Example-basedAMSR-2 LST V.S. SurfRad LST (b) Self-similarity-basedAMS2-E LST V.S. SurfRad LST Figure 37. Scatter plots of the AMSR-2 LST vs. SurfRad observations in 2015 during daytime (a) LSTs obtained from Example-Based SRR and (b) LSTs obtained from Self-Similarity-Based SRR. The Bias refers to Mean Bias Error (MBE) or accuracy calculated as Eq. 36, Std is the Standard Deviation based on Eq.37, R means Pearson Correlation Coefficient, N stands for Sample Number. The black diagonal refers to 1:1 line, the pink line is for least square fit line. 8.4 Validation of the soil moisture against SCAN observations The validation of soil moisture over continental U.S. is conducted by using the Soil Climate Analysis Network (SCAN) soil moisture monitoring stations (Schaefer et al. 113 2007). The SCAN networks have a sparse density. The SCAN data can be obtained from the National Agricultural Statistics Service (NASS), USDA on an hourly basis. The measurements for this dissertation are the top 2 in (5 cm) soil moisture at the available SCAN sites of 2008. Four available sites are selected to evaluate the soil moisture measurements. Brief information about this four SCAN stations (e.g., site location, associated surface type) is presented in Table 16. Table 16. Scan sites for algorithm validation Site No. Scan 2031 Scan 2006 Scan 2011 Scan 2049 Site Location Lat (N)/Lon(-W) Ames, IA 42.02/ -93.73 Bushland, TX 35.17/ -102.10 Geneva, NY 42.88/ -77.03 PowderMill, MD 39.02/ -76.85 Surface Type Grass Land Open Shrublands Closed Shrublands Grass Land Figure 38 is scatter plots of soil moisture retrievals from the refined model compare with SCAN sites in 2008. The accuracy is -0.04 m3/m3 and the correlation is 0.66. 114 Figure 38. Scatter plots of soil moisture retrievals from the refined model compare with SCAN sites. 115 CHAPTER 9 CONCLUSION AND DISCUSSIONS This dissertation presents the consistent HR LST retrieval methods, as well as its application in soil moisture analysis and drought detection. A new five-channel with axillary data algorithmis proposed to derive the new MW LST. The supervised machine learning technique was applied to determine the stratification of regression coefficients under different conditions. The regression coefficients for the proposed five-channel algorithm derived from the training were used to real AMSR-E and AMSR-2 observations and validated against the ground observations. To obtain a consistent LST observation, a GWR-based gap-filling algorithm is introduced. We maximized the information from MW and TIR sensors, and avoided the onefold LST value in the gap brought from the regular gap-filling algorithm. For LST derived from the AMSR-E data, the accuracy is 0.42 K during daytime and 1.56 K during nighttime; the correlation is about 0.97 for the ascending and 0.92 for the descending data. For LSTs derived from the AMSR-2 observations, the accuracy is 0.47 K and correlation is 0.95 for the ascending data and the accuracy is about -0.04 K, and correlation is 0.92 for the descending data. The results also indicate that in general, LST from thermal IR measurements such as MODIS and GOES have higher correlations and are still better than those from MW sensors such as AMSR-E and AMSR-2. Compared with previous algorithms, (1) the selection of variables shows improvements even by linear regression method; when the RT is applied, the results 116 shows high positive correlation with the TIR observations. (2) A continuous LST observation is obtained under near all weather conditions. Different downscaling approaches are conducted for enhancing the spatial resolution of LST observations. Each method is developed according to the specific LST downscaling requirement, and the limitations of different methods are discussed. Among the regression-based downscaling algorithms, the non-stationary can outperform the stationary approach. However, like other existing methodologies, the regression-based methods require the simultaneous observations along with ancillary data. To keep away from these limitations, we explored SRR process to reconstruct the HR LSTs for the first time. MISR techniques should only be applied when the two LST observations have minor changes. SISR uses a single image, and it is preferred to apply for LST sharpening. In this study, it is the first time a specific LST database and reconstruction model was constructed and applied. The use of the LST database allowed the incorporation of highfrequency information to reconstruct HR images. And this methodology could be also used for other variables, soil moisture, for example. It can conclude that the adaptation of the super-resolution techniques to data fusion gives a larger flexibility in the choice of the obtained results. In MISR method, there would be issues when LST changes too fast, and the ringing effect should be further eliminated. For SISR methods, one of the big challenges is that they are sensitive to the noise, which might cause the LST pixel exaggerated or underestimated. Also, the example-based method requires large and high-quality training dataset, and such dataset could be further improved. In this dissertation, AMSR-E 25km 117 LST (as well as AMSR-2 10 km LST) are downscaled to 1 km spatial resolution without auxiliary data and concurrent observations. The new derived HR LSTs are compared with fine resolution satellite data as well as the ground-based SurfRad data.The visual comparison of the spatial distribution for the downscaled LST indicates that SRR-based method has a practice usage, and the evaluations against in-situ observations prove its viability of deriving HR LST. The further application with the new consistent HR LST is investigated to estimate soil moisture at high spatial resolution and to evaluate drought conditions in both continental United States, California State and 2012 central United States. It is found the universal Triangle Model barely agreed with the USDM drought classifications. With the auxiliary data such as precipitation, topography, soil texture, and surface types, the results produced improvements. We further applied the LOWESS model based on time series analysis, and found precipitation had some kind of accumulated and lagging effects on soil moisture. Therefore we proposed to use accumulated precipitation starting from last year’s warm season, instead of real time daily precipitation, referenced as the Refined Model. The drought conditions identified by the Refined Model show the closest agreement with the USDM classifications. Compared with the previous drought index, the new implement soil moisture anomalies can map on a daily basis and without gaps, so that a continuous surface dry/wet condition is able to be monitored from satellite sensing. We test the hypothesis, that SRR can contribute to improving the spatial resolution of LST and soil moisture and further, the high spatial and temporal resolution 118 soil moisture anomaly maps are beneficial for drought analyses. A credible drought map at fine-scale resolution is crucial for early warning, mitigation, and management adaptation; the current drought maps usually have a coarse resolution, and this cause uncertainties and limitations for appropriate mitigation strategies (Duncan et al. 2015). The fine resolution surface condition shall improve end user applications. In the future, the SRR approaches should enhance the accuracy, and to apply it on different remote sensing data. Rain condition should be further investigated. 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Sensors, 15(6), 13406-13423. 134 BIOGRAPHY Yu Li received her Bachelor of Science in Signal and Information Processing from Chengdu University of Information Technology, China in 2009. She received her Master of Science in Signal and Information Processing for Atmosphere Sounding from Institute of Atmospheric Physics, Chinese Academy of Sciences and Chengdu University of Information Technology in 2012. She was a visiting scientist at Department of Meteorology and Climate Science, San José State University for two years. 135

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