Polarimetric Doppler Weather Radar:

This work provides a detailed introduction to the principles of Doppler and polarimetric radar, focusing in particular on their use in the analysis of weather systems. The authors first discuss underlying topics such as electromagnetic scattering, polarization, and wave propagation. They then detail the engineering aspects of pulsed Doppler polarimetric radar, before examining key applications in meteorology and remote sensing. The book is aimed at graduate students of electrical engineering and atmospheric science as well as practitioners involved in the applications of polarimetric radar.

Preface

xi

Acknowledgments

xiv

Notation

xv

1 Electromagnetic concepts useful for radar applications

1

(44)

1.1 Review of Maxwell's equations and potentials

1

(5)

1.2 Integral representation for scattering by a dielectric particle

6

(4)

1.3 Rayleigh scattering by a dielectric sphere

10

(4)

1.4 Scattering, bistatic, and radar cross sections

14

(4)

1.5 Absorption and extinction cross sections

18

(1)

1.6 Clausius-Mosotti equation and Maxwell-Garnet mixing formula

19

(3)

1.7 Faraday's law and non-relativistic Doppler shift

22

(7)

1.8 Moving dielectric spheres: coherent and incoherent summation

29

(3)

1.9 Moving dielectric sphere under plane wave incidence

32

(6)

1.10 Coherent forward scattering by a slab of dielectric spheres

38

(5)

Notes

43

(2)

2 Scattering matrix

45

(44)

2.1 The forward scatter and back scatter alignment conventions

45

(5)

2.2 Reciprocity theorem

50

(2)

2.3 Scattering matrix for sphere and spheroid in the Rayleigh-Gans approximation

52

(23)

2.4 Mie solution

75

(8)

2.5 Mie coefficients in powers of k0a: low frequency approximation

83

(2)

2.6 Numerical scattering methods for non-spherical particles

85

(3)

Notes

88

(1)

3 Wave, antenna, and radar polarization

89

(71)

3.1 Polarization state of a plane wave

89

(9)

3.2 Basics of antenna radiation and reception

98

(6)

3.3 Dual-polarized antennas: linear polarization basis

104

(3)

3.4 Radar range equation for a single particle: linear polarization basis

107

(1)

3.5 Change of polarization basis: linear to circular basis

108

(5)

3.6 Radar range equation: circular basis

113

(4)

3.7 Bilinear form of the voltage equation

117

(2)

3.8 Polarization synthesis and characteristic polarizations

119

(7)

3.9 Partially polarized waves: coherency matrix and Stokes' vector

126

(3)

3.10 Ensemble-averaged Mueller matrix

129

(4)

3.11 Time-averaged Mueller and covariance matrices

133

(5)

3.12 Some implications of symmetry in scattering

138

(4)

3.13 Covariance matrix in circular basis

142

(9)

3.14 Relation between linear and circular radar observables

151

(7)

Notes

158

(2)

4 Dual-polarized wave propagation in precipitation media

160

(51)

4.1 Coherent wave propagation

161

(10)

4.2 Oguchi's solution

171

(5)

4.3 Radar range equation with transmission matrix: linear polarization basis

176

(8)

4.4 Radar range equation with transmission matrix: circular polarization basis

184

(8)

4.5 Transmission-modified covariance matrix

192

(7)

4.6 Relation between linear and circular radar observables in the presence of propagation effects

199

(5)

4.7 Measurements in a "hybrid" basis

204

(5)

Notes

209

(2)

5 Doppler radar signal theory and spectral estimation

211

(83)

5.1 Review of signals and systems

211

(6)

5.2 Received signal from precipitation

217

(5)

5.3 Mean power of the received signal

222

(11)

5.4 Coherency matrix measurements

233

(2)

5.5 Autocorrelation of the received signal

235

(8)

5.6 Spaced-time, spaced-frequency coherency function

243

(3)

5.7 Sampling the received signal

246

(11)

5.8 Noise in radar systems

257

(5)

5.9 Statistical properties of the received signal

262

(9)

5.10 Estimation of mean power

271

(3)

5.11 Doppler spectrum (or power spectral density) and estimate of mean velocity

274

(13)

5.12 Example of received signal statistics and spectral estimation

287

(6)

Notes

293

(1)

6 Dual-polarized radar systems and signal processing algorithms

294

(84)

6.1 General system aspects

294

(23)

6.2 Antenna performance characteristics

317

(15)

6.3 Radar calibration

332

(10)

6.4 Estimation of the covariance matrix

342

(11)

6.5 Variance of the estimates of the covariance matrix elements

353

(15)

6.6 Estimation of specific differential phase (Kdp)

368

(8)

Notes

376

(2)

7 The polarimetric basis for characterizing precipitation

378

(156)

7.1 Rain

379

(47)

7.2 Convective precipitation

426

(47)

7.3 Stratiform precipitation

473

(17)

7.4 The estimation of attenuation and differential attenuation in rain using Φdp

490

(23)

7.5 Hydrometeor classification

513

(19)

Notes

532

(2)

8 Radar rainfall estimation

534

(36)

8.1 Physically based parametric rain rate estimation algorithms

534

(10)

8.2 Physically based parametric rainwater content algorithms

544

(1)

8.3 Error structure and practical issues related to rain rate algorithms using Zh, Zdr, and Kdp

545

(9)

8.4 Statistical procedures for rainfall estimation

554

(5)

8.5 Neural-network-based radar estimation of rainfall

559

(8)

8.6 Some general comments on radar rainfall estimation

567

(2)

Notes

569

(1)

Appendices

570

(37)

1 Review of electrostatics

570

(15)

2 Review of vector spherical harmonics and multipole expansion of the electromagnetic field

585

(6)

3 T-matrix method

591

(4)

4 Solution for the transmission matrix

595

(4)

5 Formulas for variance computation of autocorrelation functions, their magnitude, and phase, and for estimators in the periodic block pulsing scheme

599

(8)

References

607

(22)

Index

629

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Polarimetric Doppler Weather Radar: Principles and Applications

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Table of Contents

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