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Mathematical and Physical Modelling of Microwave Scattering and Polarimetric Remote Sensing. Monitoring the Earth's Environment Using Polarimetric Radar: Formulation and Potential Applications

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Radar technology is increasingly being used to monitor the environment. This monograph provides a review of polarimetric radar techniques for remote sensing.
The first four chapters cover the basics of mathematical, statistical modelling as well as physical modelling based on radiowave scattering theory. The subsequent eight chapters summarize applications of polarimetric radar monitoring for various types of earth environments, including vegetation and oceans. The last two chapters provide a summary of Western as well as former Soviet Union knowledge and the outlook.
This monograph is of value to students, scientists and engineers involved in remote sensing development and applications in particular for environmental monitoring.

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Preface Acknowledgements
TABLE OF CONTENTS
PARTI – INTRODUCTION AScope of the subject BDescription of the research program COutline of the monograph
PARTII – AN INTRODUCTION TO MATHEMATICAL AND PHYSICAL MODELLINGMICROWAVE SCATTERING AND POLARIMETRIC OF REMOTE SENSING Chapter 1: Introduction to Inverse Radar Scattering Problems 1.1Theoretical aspects 1.2Pattern recognition and evaluation parameters 1.3Conditions for implementing inverse scattering techniques 1.4Polarimetric radar 1.4.1Effects of polarization 1.4.2Effects of frequency 1.4.3Effects of angle of incidence
Chapter 2: Description of Remote Sensing by Radar Polarimetry 2.1Physical process of encodingdecoding of polarimetric data 2.1.1 Effects of propagation 2.2Physical realization of a polarimetric radar 2.2.1 Computation of the polarimetric radar received voltages 2.3Methods of measurements of polarimetric data 2.4Radar techniques for polarimetric remote sensing 2.4.1Monostatic and multistatic radars 2.4.2Multiantenna radar system for measuring field space coherence and correlation distance 2.4.3Multifrequency radar system for measuring field correlations in the frequency domain and the frequency correlation bandwidth 2.4.4Dopplerpolarimetric radar
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xiii xv
xix xix xxi
3 7 8 11 11 12 12
13 14 15 17 24 25 26
28
30 34
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Table of Contents
Chapter 3: Physical and Mathematical Modelling 3.1 Physical modelling 3.1.1Wavesurface scattering 3.1.2Wavescatterer (object) interaction 3.1.3scatteringWavemedium ( v o l u m e ) 3.1.4Effects on the polarization state of an electromagnetic wave 3.1.5System design aspects 3.2 Mathematical modelling 3.2.1the mathematical modelDescription of 3.2.2Statistical modelling of the scattered signal 3.2.3Measured statistics of scattering matrix coefficients 3.2.4Coherentincoherent scattering
Chapter 4: Summary of Available Scattering Methods 4.1 Introduction 4.1.1 Perturbation theory of scattering Small perturbations: firstorder theory Depolarization effects of scattering Higher order perturbation: modified theory M u l t i p l e scattering 4.1.2 Kirchhoff theory of scattering (short wavelength limit) M u l t i p l e scattering: depolarization 4.1.3 Other types of scattering modelling 4.2Transport theory: radiative transfer equation 4.2.1 Polarization synthesis
PARTIII – DIAGNOSTICS OF THE EARTH’S ENVIRONMENT USING POLARIMETRIC RADAR MONITORING: FORMULATION AND POTENTIAL APPLICATIONS Chapter 5: Basic Mathematical Modelling for Random Environments 5.1Introduction 5.2Space spectrum method 5.2.1General concepts and relationships 5.2.2Stochastic or ensemble averaging 5.3Solutions 5.3.1Cylinders as vegetation model 5.3.2Stochastic field equations 5.3.3Averaged stochastic equations describing scattering from extended scatterers: firstorder approximation
43 46 53 54 56 57 58 58 60 62 65
69 69 70 73 75 80 84 97 101 103 106
111 114 114 117 121 121 123
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5.4
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5.3.4 Use of field equations derived from the first approximation 5.3.5 Spatial dispersion effects: the second approximation 5.3.6 Spatial dispersion in a grass layer Conclusions and applications
Chapter 6: Review of Vegetation Models 6.1Introduction 6.2Biometrical characteristics of vegetation 6.3Electrophysical characteristics of vegetation 6.4vegetationElectrodynamic model of 6.4.1 Homogeneous and cylindrical model 6.4.2 Disk model 6.4.3 Threedimensional model 6.4.4 Model using transport theory 6.5vegetation from radarDetermination of biometrical characteristics of remote sensing data 6.6vegetationClassification of 6.7Conclusions and applications
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139 141 145 152
155 155 159 162 162 169 173 176
179 180 181
Chapter 7: Electrodynamic and Physical Characteristics of the Earth’s Surfaces 7.1Introduction183 7.2Complex permittivity184 7.3Dielectric and physical parameters185 7.3.1 Dielectric permittivity and moisture185 7.3.2 Dielectric permittivity and medium density188 7.3.3 Dielectric permittivity and salinity192 7.3.4 Dielectric permittivity and temperature197 7.4 Interrelations between dielectric and physical characteristics199 7.4.1Water199 7.4.2Ice201 7.4.3 Snow204 7.4.4Soil205 7.4.5 Vegetation207 7.5 Conclusions and applications208
Chapter 8: Reflection of Electromagnetic Waves from NonUniform Layered Structures 8.1Introduction211 8.2Deterministic approach211 8.2.1 Multilayered structure with an exponential permittivity profile211
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8.2.2 Layer with exponential permittivity profile 8.2.3 Single layer with a polynomial permittivity profile 8.3Stochastic case of three layers with flat boundaries 8.3.1 Integral equation approach 8.3.2 Reflection from layers with constant average permittivity 8.3.3 Reflection from a surface as volume scattering 8.4 Conclusions and applications
Chapter 9: Radiowave Reflection from Structures with Internal Ruptures 9.1Introduction 9.2Reflection from a symmetrical wedgeshaped fracture 9.2.1 Vertical probing 9.2.2 Probing at low grazing angles 9.2.3 Restrictions 9.3fractureReflection from an asymmetric wedgeshaped 9.4Reflection from a pit with spherical form 9.5Reflection from a rectangular pit with finite depth 9.6Antenna pattern and fracture f i l l i n g effects 9.7Combined model 9.7.1 Computation of the reflection coefficient 9.8Conclusions and applications
Chapter 10: Scattering of Waves by a Layer with a Rough Boundary 10.1Introduction 10.2 Initial equations and solutions 10.2.1 Firstorder approximation 10.2.2 Secondorder approximation 10.2.3 Scattering diagram 10.3 Model parameters of an ensemble of codirectional cylinders 10.3.1 Radar backscattering matrix of a vegetationearth twolayer system 10.3.2 Radar polarization effects 10.4 Conclusions and applications
226 233 238 238 243 255 258
261 261 267 268 269 270 271 276 277 278 279 285
287 287 291 295 296 302 302 303 305
Chapter 11: Polarimetric Methods for Measuring Permittivity Characteristics of the Earth’s Surface 11.1Introduction309 11.2 Determination of the complex permittivity310 11.3 The KLLsphere316 11.4 Conclusions and applications320
Table of Contents
Chapter 12: Implementing Solutions to Inverse Scattering Problems: Signal Processing and Applications 12.1Introduction 12.2Radar imaging 12.2.1 Processing 12.2.2 Examples of classification 12.3Synthetic Aperture Radar (SAR) 12.4Radar altimeter 12.5Troposphericscatter radar 12.6Atmospheric monitoring with polarimetry 12.6.1 Precipitation 12.6.2 Turbulence
PART IV: CONCLUDING REMARKS Chapter 13: Review of Potential Applications of Radar Polarimetry 13.1Introduction 13.2Results of polarimetric remote sensing 13.3Comparisonreview of the inverse scattering models analyzed
Chapter 14: Historical Development of Radar Polarimetry in Russia 14.1Introduction 14.2radiowavespolarization of General theory of 14.3The polarization theory of the radar targets 14.4Polarization selection 14.5Development of algorithms for the reception of polarized signals 14.6Polarization modulation 14.7scattered and reflected radiowaves forThe polarization analysis of studying the environment 14.8radarpolarimetry in remote sensing systemsApplications of Appendix A Appendix B Appendix C Appendix D Appendix E Appendix F References
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361 362 363 364 365 367
368 369 373 377 381 383 385 387 389
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