Foreword |
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xi | |
Preface |
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xiii | |
Acknowledgments |
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xv | |
About the Author |
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xvii | |
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1 | (6) |
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1.1 Historical Development |
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1 | (3) |
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1.2 Objectives and Organization of the Book |
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4 | (3) |
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Chapter 2 Characterization of Hydrometeors |
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7 | (44) |
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2.1 Physical and Statistical Properties |
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7 | (23) |
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9 | (1) |
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2.1.1.1 Drop Size Distribution |
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10 | (6) |
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16 | (2) |
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2.1.1.3 Terminal Velocity |
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18 | (2) |
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20 | (1) |
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2.1.2.1 Snow Particle Size Distribution |
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21 | (1) |
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2.1.2.2 Snow Bulk Density |
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21 | (4) |
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25 | (4) |
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29 | (1) |
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2.1.4 Cloud Water and Ice |
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30 | (1) |
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2.2 Electromagnetic Properties |
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30 | (17) |
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2.2.1 Dielectric Constant |
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31 | (3) |
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2.2.2 Dielectric Constant for a Lossy Medium |
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34 | (1) |
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35 | (3) |
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2.2.4 Dielectric Constant for a Mixture of Two and Three Materials |
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38 | (9) |
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Appendix 2A Fitting Procedures for DSD Models: Marshall--Palmer Distribution |
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47 | (1) |
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Appendix 2B Fitting Procedures for DSD Models: Exponential Distribution |
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47 | (1) |
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Appendix 2C Fitting Procedures for DSD Models: Gamma Distribution |
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47 | (4) |
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Chapter 3 Wave Scattering by a Single Particle |
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51 | (44) |
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3.1 Wave and Electromagnetic Wave |
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51 | (8) |
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51 | (2) |
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3.1.2 Phasor Representation of Time-Harmonic Waves |
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53 | (1) |
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53 | (2) |
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3.1.4 Wave Polarization and Representation |
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55 | (2) |
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3.1.4.1 Linear Polarization |
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57 | (1) |
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3.1.4.2 Circular Polarization |
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57 | (1) |
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3.1.4.3 Elliptical Polarization |
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57 | (2) |
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3.2 Scattering Fundamentals |
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59 | (5) |
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3.2.1 Scattering Amplitude, Scattering Matrix, and Scattering Cross Sections |
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59 | (5) |
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64 | (5) |
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64 | (1) |
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3.3.2 Scattering as Dipole Radiation |
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65 | (4) |
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3.4 Mie Scattering Theory |
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69 | (4) |
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3.4.1 Conceptual Description |
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69 | (1) |
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3.4.2 Mathematical Expression and Sample Results |
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69 | (4) |
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3.5 Scattering Calculations for a Nonspherical Particle |
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73 | (9) |
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3.5.1 Basic Nonspherical Shape: Spheroid |
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74 | (1) |
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3.5.2 Rayleigh Scattering Approximation for Spheroids |
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75 | (2) |
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77 | (5) |
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3.5.4 Other Numerical Methods for Scattering Calculations |
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82 | (1) |
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3.6 Scattering for Arbitrary Orientations |
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82 | (7) |
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3.6.1 Scattering Formulation through Coordinate Transformation |
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82 | (2) |
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3.6.2 General Expression for Rayleigh Scattering |
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84 | (1) |
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3.6.3 Backscattering Matrix for a Spheroid |
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85 | (1) |
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3.6.4 Forward Scattering Alignment versus Backscattering Alignment |
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86 | (2) |
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3.6.5 Scattering Matrix by a Spheroid with Any Orientation |
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88 | (1) |
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Appendix 3A Derivation of Optical Theorem (Forward Scattering Theorem) |
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89 | (2) |
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Appendix 3B Vector Spherical Wave Harmonics |
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91 | (4) |
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Chapter 4 Scattering and Propagation in Clouds and Precipitation |
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95 | (42) |
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95 | (2) |
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4.2 Single Scattering Model |
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97 | (17) |
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4.2.1 Coherent Addition Approximation |
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97 | (1) |
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98 | (1) |
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4.2.3 Wave Intensity and Independent Scattering |
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99 | (2) |
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4.2.4 Time-Correlated Scattering |
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101 | (1) |
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4.2.5 PDF of Scattered Wave Fields |
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102 | (1) |
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4.2.5.1 Single-Polarization Wave Field |
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102 | (3) |
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4.2.5.2 Dual-Polarization Wave Fields |
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105 | (4) |
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4.2.6 Polarimetric Radar Variables |
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109 | (5) |
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4.3 Coherent Wave Propagation |
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114 | (7) |
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4.3.1 Concept of Effective Medium |
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114 | (1) |
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4.3.2 Scalar Wave Propagation |
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114 | (3) |
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4.3.3 Polarized Wave Propagation |
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117 | (1) |
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117 | (1) |
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4.3.3.2 Random Orientation with Zero Means |
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118 | (1) |
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4.3.3.3 General Formulation for Coherent Wave Propagation |
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119 | (2) |
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4.4 Propagation-Included Scattering |
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121 | (7) |
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4.4.1 Transmission-Included Scattering Matrix |
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122 | (2) |
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4.4.2 Propagation-Included Radar Variables |
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124 | (4) |
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Appendix 4A Monte Carlo Simulation |
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128 | (1) |
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Appendix 4B Statistics of Random Orientation Angle Terms |
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129 | (8) |
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Chapter 5 Radar Measurements and Improvement of Data Quality |
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137 | (42) |
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5.1 The Polarimetric Weather Radar System and Equation |
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137 | (4) |
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5.1.1 Fundamentals and the Polarimetric Radar Equation |
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137 | (3) |
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5.1.2 Polarization Modes of Radar Operation |
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140 | (1) |
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5.2 Regular Estimation of Polarimetric Radar Variables |
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141 | (6) |
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5.2.1 Reflectivity Estimation |
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143 | (1) |
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5.2.2 Differential Reflectivity |
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144 | (1) |
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5.2.3 Co-Polar Correlation Coefficient |
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145 | (1) |
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146 | (1) |
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5.2.5 Radial Velocity and Spectrum Width |
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146 | (1) |
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5.3 Multilag Correlation Estimators |
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147 | (10) |
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5.3.1 Concept of Multilag Correlation Estimation |
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148 | (1) |
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5.3.2 General Expressions |
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149 | (2) |
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5.3.3 Specific Estimators |
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151 | (1) |
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5.3.3.1 Two-Lag Estimator |
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151 | (1) |
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5.3.3.2 Three-Lag Estimator |
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152 | (2) |
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5.3.3.3 Four-Lag Estimator |
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154 | (1) |
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5.3.4 Performance of the Estimators |
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154 | (3) |
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157 | (13) |
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5.4.1 Background of Clutter Detection |
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159 | (1) |
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5.4.2 Definition and Property of Discriminants |
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159 | (1) |
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5.4.2.1 Power Ratio Discriminant |
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159 | (1) |
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5.4.2.2 Dual-Polarization Discriminants |
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160 | (3) |
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5.4.2.3 Dual-Scan Discriminant |
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163 | (1) |
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5.4.2.4 Dual-Pol Dual-Scan Discriminants (DPDS) |
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164 | (2) |
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5.4.3 Implementation and Evaluation of SBC Dual-Pol Clutter Detection |
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166 | (4) |
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170 | (2) |
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5.5.1 Bi-Gaussian Spectrum Model and Cost Functions |
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170 | (1) |
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5.5.2 Examples of BGMAP Fitting to Separate Weather and Clutter Spectra |
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171 | (1) |
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5.6 Spectrum-Time Estimation and Processing |
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172 | (4) |
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Appendix 5A Derivation of Cost Function for Optimal Spectral Parameter Estimation |
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176 | (1) |
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Appendix 5B NEXRAD Radar Data Access |
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177 | (2) |
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Chapter 6 Applications in Weather Observation and Quantification |
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179 | (46) |
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6.1 Observation of Polarimetric Radar Signatures |
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179 | (5) |
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6.1.1 Stratiform Precipitation |
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179 | (2) |
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6.1.2 Mesoscale Convection |
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181 | (1) |
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181 | (1) |
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181 | (3) |
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6.2 Hydrometeor Classification |
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184 | (8) |
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6.2.1 Classification Background |
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185 | (2) |
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6.2.2 Fuzzy Logic Approach |
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187 | (2) |
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6.2.3 Classification Results from PRD |
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189 | (3) |
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6.3 Quantitative Precipitation Estimation |
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192 | (8) |
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6.3.1 Radar Rain Estimators |
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193 | (1) |
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6.3.2 Polarimetric Radar Rain Estimators |
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194 | (4) |
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6.3.3 Rain Estimation Results |
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198 | (1) |
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6.3.4 Estimation Errors and Practical Issues |
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199 | (1) |
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200 | (11) |
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6.4.1 Selection of Measurements and DSD Model |
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201 | (2) |
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6.4.2 Retrieval Procedure |
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203 | (2) |
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6.4.3 Application of DSD Retrieval in Parameterization of Rain Microphysics |
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205 | (6) |
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6.5 Attenuation Correction |
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211 | (6) |
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212 | (1) |
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212 | (2) |
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214 | (1) |
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6.5.1.3 Self-Consistent with Constraint Method |
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215 | (1) |
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6.5.1.4 Dual-Frequency Method |
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216 | (1) |
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217 | (1) |
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Appendix 6A Rain Estimation Based on Bayes' Theorem |
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217 | (4) |
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Appendix 6B Equivalence among Constrained Gamma DSD Models |
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221 | (4) |
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Chapter 7 Advanced Methods and Optimal Retrievals |
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225 | (28) |
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7.1 Simultaneous Attenuation Correction and DSD Retrieval |
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225 | (4) |
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7.1.1 Analogy between Dual-Polarization and Dual-Frequency Radar Techniques |
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225 | (1) |
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7.1.2 Formulation: Integral Equation Method |
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226 | (2) |
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7.1.3 Example of a Simultaneous Retrieval |
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228 | (1) |
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7.2 Statistical Retrieval of Rain DSDs |
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229 | (7) |
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7.2.1 Statistical Retrieval Method: Bayesian Approach |
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229 | (1) |
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7.2.2 Prior Distribution of DSD Parameters |
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230 | (1) |
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7.2.3 The Forward Conditional Distribution |
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230 | (2) |
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7.2.4 Results and Evaluation |
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232 | (4) |
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7.3 Variational Retrieval |
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236 | (8) |
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7.3.1 Formulation of Variational Retrieval |
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236 | (1) |
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7.3.1.1 General Formulation |
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236 | (1) |
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7.3.1.2 Formulation for DSD Retrieval fromPRD |
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237 | (1) |
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7.3.2 Forward Observation Operator and Iteration Procedure |
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238 | (2) |
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240 | (4) |
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7.4 Optimal Retrieval through DA |
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244 | (9) |
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244 | (1) |
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7.4.2 Observation Operators and Errors |
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245 | (1) |
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7.4.3 Model Microphysics Uncertainty |
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246 | (4) |
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7.4.4 Expectation for Future PRD DA |
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250 | (3) |
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Chapter 8 Phased Array Radar Polarimetry |
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253 | (30) |
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8.1 Background and Challenges |
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253 | (6) |
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8.2 Formulation for Planar Polarimetric Phased Array Radar |
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259 | (11) |
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259 | (3) |
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8.2.2 Backscattering Matrix |
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262 | (1) |
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8.2.3 Scattering Matrix Corrections |
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263 | (1) |
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8.2.3.1 Alternate Transmission |
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263 | (1) |
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8.2.3.2 Simultaneous Transmission |
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264 | (1) |
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8.2.4 Correction to Polarimetric Variables |
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264 | (1) |
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8.2.4.1 Reflectivity Factor |
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265 | (1) |
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8.2.4.2 Differential Reflectivity |
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265 | (3) |
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8.2.4.3 Correlation Coefficient |
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268 | (1) |
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8.2.4.4 Linear Depolarization Ratio |
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269 | (1) |
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8.3 Cylindrical Polarimetric Phased Array Radar |
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270 | (8) |
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8.3.1 CPPAR Concept and Formulation |
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271 | (4) |
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8.3.2 Sample Calculation of CPPAR Patterns |
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275 | (2) |
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277 | (1) |
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Appendix 8A PPAR Formulation for Aperture and Patch Elements |
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278 | (5) |
References |
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283 | (14) |
Index |
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297 | |