Quantitative Remote Sensing of Land Surfaces  

                 Table of Contents

Preface                                                                                                                                        

ACRONYMS          

                                                                                                      

1  Introduction

 

1.1       Quantitative models in optical remote sensing..................................................... 1

1.2       Basic concepts..................................................................................................... 2

1.2.1       Digital numbers................................................................................................. 2

1.2.2       Radiance........................................................................................................... 3

1.2.3       Solid angle........................................................................................................ 3

1.2.4       Irradiance......................................................................................................... 6

1.2.5       Bidirectional reflectances and albedos............................................................ 7

1.2.6       Extraterrestrial solar irradiance...................................................................... 8

1.3       Remote sensing modeling system........................................................................ 10

1.3.1       Scene generation.............................................................................................. 11

1.3.2       Scene radiation modeling................................................................................ 13

1.3.3       Atmospheric radiative transfer modeling........................................................ 14

1.3.4       Navigation modeling....................................................................................... 14

1.3.5       Sensor modeling............................................................................................. 14

1.3.5.1     Spectral response.......................................................................................... 15

1.3.5.2     Spatial response............................................................................................ 18

1.3.6       Mapping/binning............................................................................................ 20

1.4       Summary........................................................................................................... 22

1.5       References

 

2   Atmospheric Shortwave Radiative Transfer Modeling

 

2.1       Radiative transfer equation............................................................................... 26

2.2       Surface statistical BRDF models...................................................................... 29

2.2.1       Minnaert function........................................................................................... 29

2.2.2       Lommel-Seeliger function.............................................................................. 30

2.2.3       Walthall function............................................................................................ 30

2.2.4       Staylor and Suttles function............................................................................ 31

2.2.5       Rahman function............................................................................................. 32

2.2.6       Kernel functions............................................................................................. 33

2.3       Atmospheric optical properties......................................................................... 35

2.3.1       Rayleigh scattering......................................................................................... 35

2.3.2       Mie scattering................................................................................................ 36

2.3.3       Aerosol particle size distributions................................................................. 39

2.3.4       Gas absorption............................................................................................... 46

2.3.5       Aerosol climatology...................................................................................... 51

2.4       Solving radiative transfer equations.................................................................. 51

2.4.1       Radiation field decomposition....................................................................... 52

2.4.2       Numerical solutions........................................................................................ 53

2.4.2.1     Method of successive orders of scattering..................................................... 53

2.4.2.2     Method of discrete ordinates.......................................................................... 56

2.4.3       Approximate solutions: two-stream algorithms............................................... 59

2.4.4       Representative radiative transfer solvers (software packages)....................... 63

2.5       Approximate representation for incorporating surface BRDF............................ 63

2.6       Summary............................................................................................................ 70

2.7       References

 

3   Canopy Reflectance Modeling

 

3.1       Canopy radiative transfer formulation............................................................... 76

3.1.1       Canopy configuration..................................................................................... 76

3.1.2       One-dimensional Radiative transfer formulation........................................... 80

3.1.3       Boundary conditions...................................................................................... 82

3.1.4       Hotspot effects............................................................................................... 83

3.1.5       Formulations for heterogeneous canopies...................................................... 88

3.2       Leaf optical models........................................................................................... 92

3.2.1       “Plate” models............................................................................................... 93

3.2.2       Needle leaf models........................................................................................ 97

3.2.3       Ray-tracing models....................................................................................... 97

3.2.4       Stochastic models......................................................................................... 97

3.2.5       Turbid medium models................................................................................. 99

3.3       Solving radiative transfer equations................................................................ 99

3.3.1       Approximate solutions................................................................................ 100

3.3.1.1     Models based on KM theory...................................................................... 100

3.3.1.2     Decomposition of the canopy radiation field............................................. 101

3.3.1.3     Approximation of multiple scattering......................................................... 103

3.3.2       Numerical solutions: Gauss-Seidel algorithm............................................. 110

3.4       Geometric optical models.............................................................................. 114

3.5       Computer simulation models.......................................................................... 118

3.5.1       Monte Carlo ray tracing models.................................................................. 119

3.5.1.1     Forward and reverse ray tracing................................................................ 120

3.5.1.2     Canopy scene generation............................................................................ 120

3.5.1.3     A forest ray tracing algorithm..................................................................... 121

3.5.1.4     Botanical Plant Modeling System model.................................................... 125

3.5.1.5     SPRINT model........................................................................................... 126

3.5.2       Radiosity models......................................................................................... 127

3.5.2.1     Generating the 3D scene............................................................................. 128

3.5.2.2     Calculate the emission for all surfaces in the scene.................................... 129

3.5.2.3     Computing the view factors......................................................................... 129

3.5.2.4     Solving the radiosity equation..................................................................... 131

3.5.2.5     Rendering the scene for a given viewpoint and calculating BRF................. 131

3.5.2.6     Applications................................................................................................ 132

3.6       Summary.......................................................................................................... 133

3.7       References

4   Soil and snow reflectance Modeling

 

4.1       Single scattering properties of snow and soil.................................................. 143

4.1.1       Optical properties of snow........................................................................... 143

4.1.2       Optical properties of soils............................................................................ 145

4.2       Multiple scattering solutions for angular reflectance from snow and soil........ 147

4.2.1       Approximate solutions.................................................................................. 148

4.2.1.1     snow............................................................................................................ 148

4.2.1.2     Soil.............................................................................................................. 154

4.2.2       Numerical solutions...................................................................................... 160

4.3       Geometric optical modeling............................................................................. 161

4.4       Inversion of snow parameters.......................................................................... 163

4.5       Practical issues................................................................................................ 165

4.5.1       Snow and soil surface roughness.................................................................. 166

4.5.2       Mixed snow pixels....................................................................................... 167

4.5.3       Thin snow vs. dirty snow............................................................................. 167

4.5.4       Soil inversion with ancillary information.................................................... 169

4.5.5       Soil sensible depth...................................................................................... 169

4.5.6       Soil moisture conditions.............................................................................. 169

4.6       Summary.......................................................................................................... 171

4.7       References

 

5   Satellite Sensor Radiometric Calibration

 

5.1       Background...................................................................................................... 177

5.2       Post-launch calibration methods...................................................................... 179

5.2.1       Ocean........................................................................................................... 180

5.2.2       Deserts......................................................................................................... 181

5.2.3       Clouds.......................................................................................................... 181

5.2.4       Others.......................................................................................................... 181

5.3       Calibration coefficients for Landsat TM and AVHRR reflective bands......... 182

5.3.1       Landsat TM................................................................................................. 182

5.3.1.1     Absolute calibration of the reflective bands.............................................. 182

5.3.1.2     Relative calibration of the thermal-IR band............................................... 186

5.3.2       NOAA AVHRR.......................................................................................... 187

5.3.2.1     NOAA7..................................................................................................... 189

5.3.2.2     NOAA9.................................................................................................... 189

5.3.2.3     NOAA 11................................................................................................. 190

5.3.2.4     NOAA 14................................................................................................. 190

5.3.2.5     NOAA-15................................................................................................. 191

5.3.2.6     NOAA-16................................................................................................ 192

5.4       Summary....................................................................................................... 193

5.5       References

 

6   Atmospheric Correction

 

6.1       Introduction.................................................................................................. 195

6.2       Methods for correcting single viewing-angle imagery................................ 196

6.2.1       Invariant-object methods.......................................................................... 196

6.2.2       Histogram matching methods................................................................... 198

6.2.3       Dark-object methods................................................................................ 199

6.2.4       Contrast reduction methods...................................................................... 201

6.2.5       Cluster matching method.......................................................................... 201

6.2.5.1     Estimation of aerosol optical depth........................................................ 202

6.2.5.2     Surface adjacency effects....................................................................... 204

6.2.5.3     Correction examples.............................................................................. 209

6.3       Methods for correcting multiangular observations..................................... 211

6.3.1       Estimating aerosol optical depth from MISR data................................... 211

6.3.2       Retrieval of surface directional reflectance from MISR data................. 213

6.3.2.1     HDRF and BHR..................................................................................... 213

6.3.2.2     Retrieve BRF and DHR......................................................................... 215

6.4       Methods for estimating total column water vapor content......................... 216

6.4.1       Overview of various techniques............................................................. 217

6.4.2       Differential absorption technique............................................................ 219

6.4.3       Split-window algorithms......................................................................... 222

6.4.4       Unit conversions...................................................................................... 224

6.5       Summary...................................................................................................... 224

6.6       References

 

7   Topographic Correction Methods

 

7.1       Introduction................................................................................................ 230

7.2       Cosine correction algorithms...................................................................... 232

7.3       IPW method................................................................................................. 233

7.4       Shadowing function algorithm..................................................................... 236

7.5       DEM data and generation............................................................................ 241

7.6       Summary...................................................................................................... 242

7.7       References

 

8   Estimation of Land Surface Biophysical Variables

 

8.1       Statistical methods.................................................................................... 246

8.1.1       Multispectral vegetation indices............................................................ 246

8.1.1.1     Soil-line concept.................................................................................. 248

8.1.1.2     Normalized Difference vegetation Index (NDVI)................................ 248

8.1.1.3     Simple ratio (SR)................................................................................. 250

8.1.1.4     Soil Adjusted Vegetation Index (SAVI)............................................... 251

8.1.1.5     Global Environment Monitoring Index (GEMI)................................... 255

8.1.1.6     Soil and atmospherically resistant vegetation index (SARVI)............. 255

8.1.1.7     Aerosol free vegetation index (AFRI)................................................. 256

8.1.1.8     Tasseled Cap transformation............................................................... 258

8.1.1.9     FPAR index......................................................................................... 259

8.1.1.10  Comparisons and applications.............................................................. 263

8.1.2       Hyperspectral vegetation indices.......................................................... 270

8.1.2.1     Chlorophyll absorption ratio index (CARI)......................................... 271

8.1.2.2     triangular vegetation index (TVI)......................................................... 272

8.1.2.3     BNC and BNA..................................................................................... 272

8.1.2.4     Indices based on the red edge reflectance characteristics.................... 273

8.1.2.5     Indices based on spectral continuum measures.................................... 280

8.1.2.6     Photochemical reflectance index (PRI)................................................ 280

8.1.2.7     Structure independent pigment index (SIPI)......................................... 280

8.1.2.8     Indices for estimating leaf moisture content......................................... 280

8.1.3       Spatial signatures and applications....................................................... 281

8.1.4       An operational statistical method......................................................... 285

8.1.4.1     NDVI correction.................................................................................. 285

8.1.4.2     FPAR & LAI calculations.................................................................... 286

8.2       Optimization inversion method................................................................. 287

8.3       Generic Algorithm (GA)........................................................................... 289

8.4       Table look-up methods.............................................................................. 290

8.5       Hybrid inversion methods......................................................................... 292

8.5.1       Neural network........................................................................................ 293

8.5.2       Projection pursuit..................................................................................... 294

8.5.3       Regression tree ....................................................................................... 295

8.6       Comparisons of different inversion methods............................................... 298

8.7       Summary...................................................................................................... 299

8.8       References

 

9   Estimation of Surface Radiation Budget: I.  Broadband Albedo

 

9.1       Introduction................................................................................................. 308

9.2       Broadband albedo characteristics............................................................... 312

9.3       Narrowband to broadband conversion........................................................ 316

9.3.1       ALI........................................................................................................... 319

9.3.2       ASTER.................................................................................................... 319

9.3.3       AVHRR (Advanced Very High Resolution Radiometer)......................... 320

9.3.4       GOES....................................................................................................... 322

9.3.5       LANDSAT TM/ETM+............................................................................ 322

9.3.6       MISR....................................................................................................... 323

9.3.7       MODIS.................................................................................................... 324

9.3.8       POLDER.................................................................................................. 325

9.3.9       VEGETATION........................................................................................ 326

9.4       Direct estimation of surface broadband albedos......................................... 326

9.4.1       Methodology............................................................................................ 327

9.4.1.1     Radiative transfer simulations................................................................ 328

9.4.1.2     Statistical algorithms.............................................................................. 329

9.4.2       Case studies............................................................................................. 329

9.5       Diurnal cycle modeling............................................................................... 330

9.6       Summary...................................................................................................... 336

9.7       References

 

10 Estimation of Surface Radiation Budget (II): Longwave

 

10.1     Introduction.................................................................................................. 343

10.2     Monochromatic Radiative transfer formulation and solutions..................... 344

10.2.1     Thermal-IR radiative transfer equation.................................................... 344

10.2.2     Approximations and numerical solutions................................................. 345

10.3     Line-by-line methods................................................................................... 350

10.3.1     Line shapes.............................................................................................. 350

10.3.2     Spectral sampling.................................................................................... 353

10.3.3     Continuum absorption.............................................................................. 354

10.3.4     Calculation of transmittance and radiance............................................... 355

10.4     Band models............................................................................................... 356

10.4.1.1       Elsasser model................................................................................... 357

10.4.1.2       Statistical model................................................................................. 358

10.5     Correlated k-distribution methods............................................................... 359

10.6     Atmospheric correction methods................................................................. 363

10.7     Split-window algorithm for estimating LST............................................... 365

10.7.1     Theoretical Derivation............................................................................. 366

10.7.2     Representative algorithms........................................................................ 369

10.7.3     Emissivity specification........................................................................... 372

10.8     Multispectral algorithms for separating temperature and emissivity........... 374

10.8.1     Reference channel method....................................................................... 375

10.8.2     ADE method............................................................................................ 375

10.8.3     Temperature independent spectral indices (TISI).................................... 377

10.8.4     The MODIS day and night algorithm........................................................ 378

10.8.5     The ASTER algorithm............................................................................. 379

10.8.6     An optimization algorithm........................................................................ 381

10.9         Computing broadband emissivity............................................................ 384

10.10       Surface energy balance modeling............................................................ 386

10.11       Summary.................................................................................................. 389

10.12       References

 

11 Four-Dimensional (4D) Data Assimilation

 

11.1     Introduction................................................................................................. 396

11.2     Assimilation algorithms.............................................................................. 397

11.2.1     Background.............................................................................................. 397

11.2.2     The method of successive correction....................................................... 399

11.2.3     Optimal interpolation............................................................................... 403

11.2.4     Variational analysis algorithms................................................................ 405

11.2.4.1       3D variational analysis....................................................................... 405

11.2.4.2       4D variational analysis....................................................................... 407

11.2.5     Physically-Space Statistical Analysis Scheme......................................... 409

11.2.6     Extended Kalman Filter (EKF)................................................................ 410

11.3     Minimization algorithms............................................................................. 412

11.3.1     Steepest descent method.......................................................................... 413

11.3.2     Conjugate-gradient methods..................................................................... 413

11.3.3     Newton-Raphson method......................................................................... 414

11.3.4     Quasi-Newton methods............................................................................ 416

11.4     Data assimilation in hydrology.................................................................... 418

11.5     Data assimilationdata with crop growth models......................................... 420

11.5.1     Background.............................................................................................. 420

11.5.2     Case studies............................................................................................. 422

11.6     Summary...................................................................................................... 424

11.7     References

 

12 Validation and Spatial Scaling

 

12.1     Rationale of validation................................................................................ 429

12.2     Validation methodology.............................................................................. 430

12.2.1     Direct correlative measurements............................................................. 430

12.2.1.1       Instrumentation and measurement techniques...................................... 431

12.2.1.2       Spatial sampling design...................................................................... 436

12.2.1.3       Observation networks......................................................................... 440

12.2.2     Inter-comparisons of algorithms and products......................................... 443

12.2.3     NASA EOS Validation Program.............................................................. 445

12.3     Spatial scaling techniques........................................................................... 446

12.3.1     Upscaling methods................................................................................... 446

12.3.2     Downscaling methods.............................................................................. 450

12.3.2.1       Linear unmixing methods.................................................................... 450

12.3.2.2       Methods for generating continuous fields........................................... 452

12.3.2.3       Decomposition of NDVI temporal profiles........................................ 454

             12.3.2.4      Multiresolution data fusion …………...…………………….456

12.3.2.5       Methods for statistical downscaling GCM outputs............................. 461

12.4     Summary..................................................................................................... 463

12.5     References

13 Applications

 

13.1     Methodologies for integrating remote sensing with ecological models....... 469

13.2     Agricultural Applications........................................................................... 476

13.2.1     Remote sensing and precision agriculture................................................ 476

13.2.2     Examples of decision supports in agriculture.......................................... 480

13.2.3     Drought monitoring.................................................................................. 483

13.2.4     Crop yield estimation............................................................................... 491

13.3     “Urban Heat island” effects......................................................................... 499

13.4     Carbon cycle studies................................................................................... 501

13.4.1     Background.............................................................................................. 501

13.4.2     “Bottom-up” approach............................................................................. 503

13.4.3     Case demonstrations................................................................................ 506

13.5     Land-atmosphere interaction....................................................................... 509

13.6     Summary...................................................................................................... 512

13.7     References