Eugene A. Sharkov
Passive Microwave Remote Sensing of the Earth
Physical Foundations
 

SPRINGER-PRAXIS BOOKS IN GEOPHYSICAL SCIENCES

Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xiii
List of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
List of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxv
List of colour plates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvii
1 Scientific and applied rationales of remote sensing study . . . . . . . . . . .1
1.1 What is meant by remote sensing? . . . . . . . . . . . . . . . . . . . .1
1.2 The wave nature and spectrum of electromagnetic radiation. . . .2
1.3 Passive and active sensing . . . . . . . . . . . . . . . . . . . . . . . . . .9
1.4 Thermal radiation: the role and sources . . . . . . . . . . . . . . . . .11
1.5 Recognition and understanding of microwave signatures . . . . . .16
1.6 Basic statements of wave electromagnetic theory . . . . . . . . . . .20
2 Random signals and fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35
2.1 Determinate and stochastic description of natural processes . . . .35
2.2 Basic characteristics of random processes . . . . . . . . . . . . . . . .37
2.2.1 Ensembles of realizations . . . . . . . . . . . . . . . . . . . . .40
2.2.2 Probability densities of random processes . . . . . . . . . .40
2.2.3 Moment functions of random processes. . . . . . . . . . . .44
2.2.4 Stationary random processes . . . . . . . . . . . . . . . . . . .45
2.2.5 Ergodic property. . . . . . . . . . . . . . . . . . . . . . . . . . .46
2.3 Fundamentals of the correlation theory of random processes . . .47
2.3.1 Basic properties of the correlation function . . . . . . . . .48
2.3.2 The correlation coef®cient. . . . . . . . . . . . . . . . . . . . .48
2.3.3 The statistical spectrum . . . . . . . . . . . . . . . . . . . . . .49
2.4 Quasi-ergodic processes. . . . . . . . . . . . . . . . . . . . . . . . . . . .53
2.5 Types of spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55
2.5.1 Rectangular low-frequency spectrum . . . . . . . . . . . . . .56
2.5.2 Gaussian spectrum . . . . . . . . . . . . . . . . . . . . . . . . .57
2.5.3 The Lorentzian spectrum . . . . . . . . . . . . . . . . . . . . .57
2.5.4 Band noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58
2.5.5 Harmonic signal . . . . . . . . . . . . . . . . . . . . . . . . . . .58
2.5.6 White noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59
2.5.7 Coloured noise . . . . . . . . . . . . . . . . . . . . . . . . . . . .59
2.6 Linear and nonlinear systems and media . . . . . . . . . . . . . . . .62
2.6.1 Low-pass filter (LPF). . . . . . . . . . . . . . . . . . . . . . . .67
2.7 Nonlinear transformations of random processes. . . . . . . . . . . .69
2.8 Measurement of noise signal intensity . . . . . . . . . . . . . . . . . .75
3 Microwave radiometers: functions,design concepts,characteristics. . . . .79
3.1 Basic types of passive microwave devices . . . . . . . . . . . . . . . .79
3.2 Basic components of a passive microwave radiometer and theirfunctions . .  . . . . . . . . . . . . . .84
3.3 The language of equivalent circuits: the antenna, radiobrightness and noise temperatures . . . . .87
3.4 Compensatory scheme of noise signal measurement . . . . . . . . .89
3.5 The ¯uctuation threshold sensitivity of radiometric systems . . . .9 3
3.6 The modulation method of noise signal measurement . . . . . . . .9 7
3.6.1 Modulation radiometer block-diagram. . . . . . . . . . . . .9 8
3.6.2 Temporal and spectral cyclograms . . . . . . . . . . . . . . .100
3.6.3 Synchronous detector. . . . . . . . . . . . . . . . . . . . . . . .102
3.6.4 Modulation reception peculiarities . . . . . . . . . . . . . . .103
3.6.5 Threshold sensitivity . . . . . . . . . . . . . . . . . . . . . . . .105
3.6.6 Null-balancing type . . . . . . . . . . . . . . . . . . . . . . . . .108
3.7 Experimental methods of threshold sensitivity measurement . . . .111
3.8 Measurement of the frequency responses of radiometric systems by Fourier spectroscopy methods . . . . . 114
3.9Basic concepts of amplifying devices . . . . . . . . . . . . . . . . . . .121
3.9.1 Detector receivers . . . . . . . . . . . . . . . . . . . . . . . . . .122
3.9.2 Direct amplification receivers. . . . . . . . . . . . . . . . . . .122
3.9.3 Superheterodyne-type receivers. . . . . . . . . . . . . . . . . .122
3.10 Limiting sensitivities of radiometric systems . . . . . . . 123
4 Thermal fluctuations and their fundamental laws . . . . . . . . . . . . . . . .127
4.1 Thermal radiation and thermal fluctuations: a historical review. .127
4.2 The fluctuation±dissipation theorem: a qualitative approach . . . .131
4.3 Thermal ¯uctuations in the electrodynamics . . . . . . . . . . . . . .135
4.4 Local thermal equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . .140
5 Emission fields and antenna systems. . . . . . . . . . . . . . . . . . . . . . . .143
5.1 Basic characteristics of the emission field . . . . . . . . . . . . . . . .143
5.1.1 Spectral intensity . . . . . . . . . . . . . . . . . . . . . . . . . .144
5.1.2 Spectral radiation flux . . . . . . . . . . . . . . . . . . . . . . .145
5.1.3 Spectral radiant energy density . . . . . . . . . . . . . . . . .147
5.2 Microwave antennas and their characteristics . . . . . . . . . . . . .148
5.2.1 Emission of radiowaves . . . . . . . . . . . . . . . . . . . . . .149
5.2.2 Antenna directional pattern (ADP). . . . . . . . . . . . . . .149
5.2.3 The effective surface . . . . . . . . . . . . . . . . . . . . . . . .153
5.2.4 Antenna directivity . . . . . . . . . . . . . . . . . . . . . . . . .154
5.2.5 Antenna gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . .154
5.3 Antennas and brightness temperatures . . . . . . . . . . . . . . . . . .155
5.3.1 Extended source . . . . . . . . . . . . . . . . . . . . . . . . . . .158
5.3.2 Discrete source . . . . . . . . . . . . . . . . . . . . . . . . . . . .158
5.4 The scattering coef®cient of antennas . . . . . . . . . . . . . . . . . .160
5.5 Antenna temperature of antenna with resistance loss . . . . . . . .164
5.6 Spatial-temporal dynamics in passive remote sensing . . . . . . . .166
5.7 The equation of antenna smoothing . . . . . . . . . . . . . . . . . . .169
5.8 Outdoor calibration of radiometer instruments: the method of contrasting half-spaces . . . 179
5.8.1 MCH procedure . . . . . . . . . . . . . . . . . . . . . . . . . . .190
5.8.2 Estimation of the main lobe width . . . . . . . . . . . . . . .192
5.8.3 Geometry of position of beams of multifrequency instruments . . . . . . . . . . . . . . . . . . . .193
5.9Antenna parameters of airborne microwave instruments . . . . . .193
5.10 Antenna parameters of satellite microwave instruments . . . . . . .197
6 Black-body radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .203
6.1 The ideal black-body model: historical aspects. . . . . . . . . . . . .203
6.1.1 Definition of a black body . . . . . . . . . . . . . . . . . . . .204
6.1.2 Properties of a black body . . . . . . . . . . . . . . . . . . . .204
6.1.3 Historical aspects . . . . . . . . . . . . . . . . . . . . . . . . . .206
6.2 Black-body radiation laws . . . . . . . . . . . . . . . . . . . . . . . . . .209
6.2.1 The Planck law (formula) . . . . . . . . . . . . . . . . . . . . .209
6.2.2 The Wien radiation law . . . . . . . . . . . . . . . . . . . . . .213
6.2.3 The Rayleigh-Jeans radiation law . . . . . . . . . . . . . . .213
6.2.4 The Wien displacement law. . . . . . . . . . . . . . . . . . . .214
6.2.5 The Stefan-Boltzmann law . . . . . . . . . . . . . . . . . . . .214
6.2.6 Correlation properties of black-body radiation . . . . . . .215
6.3 The Kirchhoff law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .217
6.3.1Emissive ability . . . . . . . . . . . . . . . . . . . . . . . . . . .217
6.3.2 Absorbing ability . . . . . . . . . . . . . . . . . . . . . . . . . .218
6.3.3 The Kirchhoff law forms . . . . . . . . . . . . . . . . . . . . .219
7 Grey-body radio-emission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .223
7.1 Surface reflectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .223
7.1.1 Reflection distribution function . . . . . . . . . . . . . . . . .224
7.1.2 Directional-hemispherical reflectivity . . . . . . . . . . . . . .225
7.1.3 Hemispherical reflectivity . . . . . . . . . . . . . . . . . . . . .226
7.1.4 Diffuse and specular reflection. . . . . . . . . . . . . . . . . .226
7.2 Effective radiation of reflecting surface . . . . . . . . . . . . . . . . .227
7.3 Reflection and transmission of plane waves at the plane interface boundary . . . . .233
7.4 Polarization features of radiation of a grey half-space with a smooth boundary . . . .237
7.4.1 Nadir measurements . . . . . . . . . . . . . . . . . . . . . . . .240
7.4.2 Angular measurements . . . . . . . . . . . . . . . . . . . . . . .241
7.5 Features of emission of a two-layer structure in the monochromatic approximation . . . .245
7.6 Properties of quasi-coherence in thermal emission and the limits of its applicability . . .253
7.7 Thermal emission of multi-layered non-isothermal media . . . . . .258
7.7.1 Physical substance of the problem . . . . . . . . . . . . . . .259
7.7.2 Thermal emission of non-isothermal media with arbitrary parameters. . . . . . . . . . . . . 261
7.7.3 Limiting cases of general theory. . . . . . . . . . . . . . . . .264
7.7.4 Conditions for the method's feasibility . . . . . . . . . . . .267
7.7.5 Spectral characteristics of thermal emission for some stratified media. . . . . . . . . . . . . . . . . .268
8 Dielectric and emissive properties of terrestrial surfaces . . . . . . . . . . .277
8.1 Frequency dispersion of the electromagnetic properties of dielectrics. . . . . . . . . . . . . . . . . . . . . . . . .277
8.1.1 Dispersive properties . . . . . . . . . . . . . . . . . . . . . . . .278
8.1.2 The Kronig-Kramers relations. . . . . . . . . . . . . . . . . .281
8.2 Physical mechanisms of the polarization of dielectrics . . . . . . . .282
8.3 Relaxation polarization models. . . . . . . . . . . . . . . . . . . . . . .288
8.3.1 The Debye model . . . . . . . . . . . . . . . . . . . . . . . . . .289
8.3.2 Models of multiplicity of relaxation times . . . . . . . . . .293
8.3.3 The Cole-Cole model . . . . . . . . . . . . . . . . . . . . . . .296
8.3.4 The Davidson-Cole model . . . . . . . . . . . . . . . . . . . .297
8.3.5 The Havriliak-Negami model . . . . . . . . . . . . . . . . . .297
8.4 Dielectric properties of freshwater. . . . . . . . . . . . . . . . . . . . .298
8.4.1 The structure of water . . . . . . . . . . . . . . . . . . . . . . .299
8.4.2 The experimental data processing technique . . . . . . . . .302
8.4.3 Empirical models . . . . . . . . . . . . . . . . . . . . . . . . . .307
8.4.4 The analysis of the "0t and St parameters . . . . . . .310
8.4.5 Analysis of parameter "It . . . . . . . . . . . . . . . . . . .311
8.5 Dielectric properties of salt water . . . . . . . . . . . . . . . . . . . . .314
8.5.1 Electrolyte structure . . . . . . . . . . . . . . . . . . . . . . . .315
8.5.2 The experimental data processing technique . . . . . . . . .318
8.5.3 Spectral dependences of strong electrolytes. . . . . . . . . .319
8.5.4 The C-C diagrams for strong electrolytes. . . . . . . . . . .323
8.5.5 The C-C model parameters for strong electrolytes . . . . .325
8.5.6 Dielectric properties of polyelectrolytes . . . . . . . . . . . .328
8.6 Spectral and temperature characteristics of the emissive properties of water basins . . . . . . .329
8.6.1 Requirements for SSS observations. . . . . . . . . . . . . . .335
8.7 Emissive properties of ice surfaces . . . . . . . . . . . . . . . . . . . .336
8.8 Radiation properties of the terrestrial surfaces. . . . . . . . . . . . .341
8.8.1 Primitive models . . . . . . . . . . . . . . . . . . . . . . . . . . .341
8.8.2 Rocks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .343
8.8.3 Soils. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .344
8.8.4 Tilled soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .353
8.8.5 Vegetation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .354
9 Foundations of radiative transfer theory . . . . . . . . . . . . . . . . . . . . .357
9.1 Radiative transfer theory phenomenology . . . . . . . . . . . . . . . .357
9.1.1 RTT applicability conditions . . . . . . . . . . . . . . . . . . .359
9.2 Energy transformation by a volume element . . . . . . . . . . . . . .360
9.2.1 The act of absorption . . . . . . . . . . . . . . . . . . . . . . .360
9.2.2 The act of emission . . . . . . . . . . . . . . . . . . . . . . . . .361
9.2.3 The act of scattering . . . . . . . . . . . . . . . . . . . . . . . .362
9.3 The radiative transfer equation. . . . . . . . . . . . . . . . . . . . . . .365
9.4 Special cases of the radiative transfer equation . . . . . . . . . . . .367
9.4.1 A purely scattering medium . . . . . . . . . . . . . . . . . . .367
9.4.2 The absorbing and emitting medium. . . . . . . . . . . . . .368
9.4.3 Transparent medium . . . . . . . . . . . . . . . . . . . . . . . .369
9.4.4 The `cold' layer approximation . . . . . . . . . . . . . . . . .369
9.5 Equation of radiative transfer for the plane layer case . . . . . . .370
9.6 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .375
9.6.1 The transparent boundaries. . . . . . . . . . . . . . . . . . . .375
9.6.2 The black boundaries . . . . . . . . . . . . . . . . . . . . . . .375
9.6.3 Mirror-reflecting and black boundaries . . . . . . . . . . . .376
9.7 Radiative transfer in the emitting and absorbing medium . . . . .376
9.8 Features of radiation of a half-space with the semi-transparent atmosphere. . . . . . . . . . 378
9.8.1 Brightness contrast . . . . . . . . . . . . . . . . . . . . . . . . .379
9.8.2 Angular measurements . . . . . . . . . . . . . . . . . . . . . . .380
9.8.3 The oblique section method . . . . . . . . . . . . . . . . . . .381
9.9 Radiative transfer in the emitting, absorbing and scattering medium . . . . . . . . . . . . . . .383
9.10 Radiation of the inhomogeneous and non-isothermal half-space .............385
9.11 Approximate methods for solution of the complete transfer equation . . . . . . . . . . . . . 388
9.11.1 The spherical harmonics method . . . . . . . . . . . . . . . .389
9.11.2 The Gaussian quadratures method . . . . . . . . . . . . . . .391
9.11.3 Approximate formulas . . . . . . . . . . . . . . . . . . . . . . .394
10 Electromagnetic properties of disperse media . . . . . . . . . . . . . . . . . .397
10.1 Electromagnetic properties of secluded particles . . . . . . . . . . . .397
10.1.1 The scattering cross-section and the scattering amplitude........398
10.1.2 The absorption cross-section . . . . . . . . . . . . . . . . . . .400
10.1.3 The extinction cross-section. . . . . . . . . . . . . . . . . . . .401
10.1.4 The single scattering albedo . . . . . . . . . . . . . . . . . . .401
10.1.5 The scattering indicatrix . . . . . . . . . . . . . . . . . . . . . .401
10.1.6 The optical theorem . . . . . . . . . . . . . . . . . . . . . . . .402
10.1.7 Integral presentations of scattering amplitude and absorption cross-section . . . . . . . . . . . . . .403
10.2 Basic concepts of Mie theory . . . . . . . . . . . . . . . . . . . . . . . .404
10.2.1 Parameters of the Mie theory . . . . . . . . . . . . . . . . . .405
10.3 Rayleigh scattering features . . . . . . . . . . . . . . . . . . . . . . . . .409
10.3.1 Metal particles . . . . . . . . . . . . . . . . . . . . . . . . . . . .412
10.3.2 Soft particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . .412
10.3.3 Water particles . . . . . . . . . . . . . . . . . . . . . . . . . . . .413
10.4 Features of scattering properties of aqueous particles . . . . . . . .414
10.5 Electromagnetic properties of polydisperse media . . . . . . . . . . .416
10.5.1 The density function . . . . . . . . . . . . . . . . . . . . . . . .418
10.5.2 The volume density of particles . . . . . . . . . . . . . . . . .418
10.5.3 The integral distribution function . . . . . . . . . . . . . . . .419
10.5.4 The relative density function . . . . . . . . . . . . . . . . . . .419
10.5.5 The density sampling probability . . . . . . . . . . . . . . . .419
10.5.6 The total mass and the relative volume concentration of water . . . . . . . . . . . .420
10.5.7 Radar reflectivity . . . . . . . . . . . . . . . . . . . . . . . . . .421
10.5.8 Rainfall rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . .421
10.5.9Natural polydisperse media . . . . . . . . . . . . . . . . . . . .422
10.5.10 Analytical forms of the density function . . . . . . . . . . .423
10.5.11 Parameters of attenuation and scattering of a polydisperse medium. . . . . . . .425
10.6 Features of radiative transfer in dense media . . . . . . . . . . . . .428
10.6.1 Disperse medium and its characteristics . . . . . . . . . . . .430
10.6.2 Experimental technique . . . . . . . . . . . . . . . . . . . . . .433
10.6.3 Average values of electrodynamical characteristics . . . . .433
10.6.4 Fluctuation mode of extinction . . . . . . . . . . . . . . . . .435
11 Selective radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .443
11.1 Mechanisms of selective radiation . . . . . . . . . . . . . . . . . . . . .443
11.2 The detailed equilibrium principle . . . . . . . . . . . . . . . . . . . . .446
11.3 The photon model and the transfer equation for quantum systems .............448
11.4 Mechanisms of broadening of spectral lines . . . . . . . . . . . . . .450
11.5 Radiation transmission through a gas layer . . . . . . . . . . . . . .
462
11.6 Microwave radiative transfer in the terrestrial atmosphere . . . . .467
11.6.1 Atmospheric models . . . . . . . . . . . . . . . . . . . . . . . .468
11.6.2 Strati®ed atmosphere radiation . . . . . . . . . . . . . . . . .468
11.6.3 Molecular oxygen . . . . . . . . . . . . . . . . . . . . . . . . . .470
11.6.4 Atmospheric water vapour . . . . . . . . . . . . . . . . . . . .
474
11.6.5 Absorption of microwaves in the terrestrial atmosphere ....476
12 Radiative properties of the terrestrial `surface - atmosphere' system . . .479
12.1 Radiation of the homogeneous ocean-atmosphere system . . . . .479
12.1.1 The basis model . . . . . . . . . . . . . . . . . . . . . . . . . . .479
12.1.2 Integral parameters . . . . . . . . . . . . . . . . . . . . . . . . .484
12.1.3 Temperature profiles . . . . . . . . . . . . . . . . . . . . . . . .486
12.2 Microwave remote sensing of cloud fields. . . . . . . . . . . . . . . .488
12.2.1 Cloud classification schemes -  the contribution of
microwave radiometry . . . . . . . . . . . . . . . . . . . . . . .488
12.2.2 Microwave remote sensing of rainfalls. . . . . . . . . . . . .492
12.3 Microwave remote sensing of surface oceanic heat flux fields . . .495
12.3.1 Radiothermal spectroscopy of the ocean-atmosphere transition layer . . . . . . . . . . . . 498
12.4 Microwave remote sensing of the oceanic surface. . . . . . . . . . .501
12.4.1 Rough sea surface. . . . . . . . . . . . . . . . . . . . . . . . . .502
12.4.2 Sea wave breaking fields. . . . . . . . . . . . . . . . . . . . . .507
12.5 Microwave remote sensing of catastrophic oil spills on the sea surface . . . . . . . . . . . 511
12.5.1 Investigation techniques and processing of the results. . .512
12.5.2 Analysis of radar mapping data. . . . . . . . . . . . . . . . .516
12.5.3 Radiothermal measurement data analysis . . . . . . . . . . .517
12.5.4 Joint analysis of radar and radiothermal images . . . . . .521
12.5.5 Radio-spectroscopic observations . . . . . . . . . . . . . . . .522
13 Inversion problems for passive microwave measurements . . . . . . . . . . .525
13.1 Features of microwave measurements . . . . . . . . . . . . . . . . . .525
13.2 Basic categories of inversion procedures for microwave sensing. ..526
13.2.1 Statistical techniques . . . . . . . . . . . . . . . . . . . . . . . .527
13.2.2 Forward model inversion . . . . . . . . . . . . . . . . . . . . .527
13.2.3 Explicit inverse . . . . . . . . . . . . . . . . . . . . . . . . . . . .529
13.2.4 Other techniques. . . . . . . . . . . . . . . . . . . . . . . . . . .530
14 Passive microwave space missions . . . . . . . . . . . . . . . . . . . . . . . . .531
14.1 Elements of microwave radiometry history . . . . . . . . . . . . . . .531
14.2 Ongoing missions and tendencies of their development . . . . . . .536
14.2.1 DMSP mission . . . . . . . . . . . . . . . . . . . . . . . . . . . .536
14.2.2 TRMM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .538
14.2.3 Aqua mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . .539
14.2.4 ADEOS-II mission . . . . . . . . . . . . . . . . . . . . . . . . .542
14.3 Future passive microwave space missions . . . . . . . . . . . . . . . .544
14.3.1 MTVZA-OK mission. . . . . . . . . . . . . . . . . . . . . . . .544
14.3.2 CLOUDS mission . . . . . . . . . . . . . . . . . . . . . . . . . .546
14.3.3 MEGHA-TROPIQUES mission . . . . . . . . . . . . . . . . .548
14.3.4 NPOESS program. . . . . . . . . . . . . . . . . . . . . . . . . .552
14.3.5 OSIRIS concept . . . . . . . . . . . . . . . . . . . . . . . . . . .554
Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .557
Appendix A - The International System of Units (SI units) . . . . . . . . . . .559
Appendix B - Fundamental theorems and correlations of Fourier spectrum analysis. . . . . . .565
References and bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .569
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .611