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