Doppler Radar and Weather Observations

1st Edition - January 1, 1984
Author: Richard J. Doviak
Language: English
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 1 4 9 1 6 - 7

Doppler Radar and Weather Observations deals with the use of Doppler radar to make observations of a variety of weather phenomena such as tornado vortices, hurricanes, and… Read more

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Doppler Radar and Weather Observations deals with the use of Doppler radar to make observations of a variety of weather phenomena such as tornado vortices, hurricanes, and lightning channels. Topics covered include electromagnetic waves and propagation; weather echo signals; Doppler spectra of weather echoes; and meteorological radar signal processing. Rain and turbulence measurements are also considered, along with observations of winds, storms, and related phenomena. Comprised of 11 chapters, this book begins with an introduction to weather radar principles and how the radar parameters and signal characteristics relate to the target's meteorological properties. The effect of the atmosphere on the path of the signal is then examined, together with techniques used in extracting a target's properties from its echoes. The radar signal path from the transmitter, through the antenna, along the beam to the target, and on its return to the receiver is also discussed. Subsequent chapters explore the discrete Fourier transform and its application to weather echo signals; the weather Doppler spectrum and the signal processing methods used to derive its principal moments; range and Doppler velocity ambiguities as they pertain to distributed targets; and the limitations imposed by antenna sidelobes, ground clutter, signal decorrelation, and power. A comprehensive treatment of pulse compression and the Doppler processing of frequency modulated signals is given. This monograph should be of value to oceanographers, meteorologists, atmospheric scientists, and radar engineers, as well as students and researchers interested in Doppler radar principles.

Preface

Acknowledgments

List of Symbols

1 Introduction

References

2 Electromagnetic Waves and Propagation

2.1 Waves

2.2 Propagation Paths

2.2.1 Refractive Index of Air

2.2.2 Refractivity N

2.2.3 Spherically Stratified Atmospheres

References

3 Principles of Radar

3.1 The Doppler Radar (Transmitting Aspects)

3.1.1 The Electromagnetic Beam

3.1.2 Antenna Gain

3.2 The Target

3.2.1 Scattering Cross Section

3.2.2 Doppler Shift

3.3 Attenuation

3.3.1 Attenuation by Rain

3.3.2 Attenuation by Cloud Droplets

3.3.3 Snow Attenuation Rate

3.3.4 Gaseous Attenuation Rate

3.4 The Doppler Radar (Receiving Aspects)

3.4.1 The Radar Equation

3.4.2 The Received Waveform (In-Phase and Quadrature Components)

3.5 Practical Considerations

3.5.1 System Noise Temperature

3.5.2 Bandwidth

3.5.3 Filtered Waveform

3.5.4 Signal-to-Noise Ratio; Matched Filters

3.6 Ambiguities

References

4 Weather Echo Signals

4.1 The Echo Sample

4.2 Signal Statistics

4.3 The Weather Radar Equation

4.3.1 The Range Weighting Function

4.3.2 Resolution Volume

4.3.3 Reflectivity Factors

4.4 Signal-to-Noise Ratio for Distributed Targets

4.5 Correlation of Echo Samples along the Range Time Axis

References

5 Doppler Spectra of Weather Echoes

5.1 Spectral Analysis of Weather Signals

5.1.1 Discrete Fourier Transform

5.1.2 Convolution and Correlation

5.1.3 Power Spectrum of Random Sequences

5.1.4 Bias, Variance, and the Window Effect

5.1.5 Expressing Spectral Estimates in Terms of the True Spectrum

5.1.6 Variance of the Periodogram

5.2 Doppler Weather Spectrum and Its Relation to Reflectivity and Radial Velocity Fields

5.3 Velocity Spectrum Width, Shear, and Turbulence

References

6 Meteorological Radar Signal Processing

6.1 Spectral Moments

6.2 Radar Signal Processing

6.3 Echo Sample Intensity Estimation

6.3.1 Sample Time Averaging

6.3.2 Range Time Averaging

6.4 Mean Frequency Estimators

6.4.1 Autocovariance Processing: The Pulse Pair Processor

6.4.2 Spectral Processing

6.5 Estimators of the Spectrum Width

6.5.1 Autocovariance Processing

6.5.2 Spectral Processing

6.6 Minimum Variance Bounds

6.7 Performance on Data

References

7 Considerations in the Observation of Weather

7.1 Range Ambiguities

7.1.1 Probability of Obscuration by a Single Cell

7.1.2 Obscuration by a Squall Line

7.2 Velocity Ambiguities

7.3 Echo Coherency

7.4 Techniques to Extend the Unambiguous Range and Velocity and to Reduce the Loss of Information from Overlaid Echoes

7.4.1 Phase Diversity

7.4.2 Spaced Pairs with Polarization Coding

7.4.3 Staggering the PRT to Increase the Unambiguous Velocity

7.4.4 Interlaced Sampling

7.4.5 Correcting Aliased Velocities

7.5 Methods to Decrease the Acquisition Time

7.5.1 Frequency Diversity

7.5.2 Random Signal Transmission

7.6 Effective Antenna Pattern of a Scanning Radar

7.7 Antenna Side Lobes

7.8 Ground Clutter and Its Suppression

7.9 Spectral Artifacts

7.9.1 Quantization and Saturation Noise

7.9.2 Amplitude and Phase Imbalance

7.9.3 Phase Jitter

7.10 Detection of Weakly Scattering Weather Targets

7.10.1 Pulse Compression

7.10.2 Complementary Codes

7.10.3 FM cw Doppler Radar

References

8 Rain Measurements

8.1 Drop Size Distributions

8.1.1 Cloud Drop Distributions

8.1.2 Raindrop Size Distributions

8.2 Terminal Velocity of Drops

8.3 Rainfall Rate, Reflectivity, Attenuation, and Liquid Water Content

8.3.1 Liquid Water Content

8.3.2 Reflectivity Factor Z

8.3.3 Rainfall Rate

8.3.4 Attenuation Rate K

8.4 Single-Parameter Measurement to Estimate the Rainfall Rate

8.4.1 R,Z Relations

8.4.2 Attenuation Method

8.5 Dual Parameter Measurement to Estimate the Rainfall Rate

8.5.1 Rain Parameter Diagram

8.5.2 Dual Wavelength Method

8.5.3 Dual Polarization

8.5.4 Rain Gauge and Radar

8.6 Distribution of Hydrometeors from Doppler Spectra

8.7 Summary

References

9 Observations of Winds, Storms, and Related Phenomena

9.1 Thunderstorm Structure

9.2 Observations with Two Doppler Radars

9.2.1 Reconstruction of Wind Fields

9.2.2 Observation of Tornadic Storms

9.2.3 Errors in Synthesized Wind Fields

9.3 Linear Wind Measurements with a Single Doppler Radar

9.3.1 Least Squares Fitting of the Wind Field

9.3.2 Analysis on a Circular Arc

9.3.3 Analysis on a Complete Circle

9.3.4 Analysis on Sections of a Conical Surface

9.3.5 Analysis within a Volume: The VVP Method

9.3.6 Prestorm Observations

9.4 Nonlinear Wind

9.4.1 Vertical Wind

9.4.2 Waves

9.5 Weather Phenomena Observed with a Single Doppler Radar

9.5.1 Vortices

9.5.2 Severe Storms

9.5.3 Doppler Spectra of Tornados

9.5.4 Downdrafts

9.5.5 Gust Fronts

9.5.6 Lightning

9.5.7 Hurricanes

References

10 Measurement of Turbulence

10.1 Statistical Theory of Turbulence

10.1.1 Turbulence Spectra and the Correlation Function

10.1.2 Structure Functions (Locally Homogeneous Fields)

10.1.3 Structure and Correlation Functions from Similarity Assumptions

10.1.4 Chandrasekhar's Theory

10.2 Spatial Spectra of Point and Average Velocities

10.2.1 Filtering by the Resolution Volume

10.2.2 Variance of Point and Average Velocities

10.2.3 Turbulence Parameters from a Single Radar

10.2.4 Turbulence Parameters from Two Doppler Radars

10.3 Doppler Spectrum Width and Eddy Dissipation Rate

10.4 Doppler Spectrum Width in Severe Thunderstorms

References

11 Echoes from the Precipitation-Free Turbulent Troposphere

11.1 Reflection, Refraction, and Scatter: Coherence

11.2 Formulation of the Wave Equation for Inhomogeneous and Turbulent Media

11.3 Solution for Fields Scattered by Irregularities

11.4 Fraunhofer Scatter

11.4.1 Discussion and Examples

11.4.2 Expected Scattered Power Density

11.5 Fresnel Scattering

11.5.1 Correlation Length Shorter Than the Fresnel Length

11.5.2 Correlation Length Comparable to or Larger Than the Fresnel Length

11.5.3 Backscattering from Anisotropie Irregularities

11.6 Structure Constant of the Refractive Index

11.6.1 Dependence of the Structure Constant on the Height

11.6.2 Inertial Subrange

11.6.3 Criteria for Measurement of the Velocity of Refractive Index Irregularities

11.7 Observations of Clear-Air Reflectivity

11.8 Observations of Wind, Waves, and Turbulence in Clear Air

11.8.1 Wind Profiling

11.8.2 Kinematic Structure of the Convective Boundary Layer

References

Appendix A Geometric Relations for Rays in the Troposphere

A.1 Integral Solutions for Ray Path in a Spherically Stratified Medium

A.2 Relating a Target's Apparent Range and Elevation Angle to Its True Height and Great Circle Distance

References

Appendix B Correlation between Echo Samples as a Function of Sample Time

Appendix C Correlation of Echoes from Spaced Resolution Volumes

C.1 Echo Sample Correlation versus Range Difference cδτs/2

C.2 Correlation of Echoes from Azimuthally Spaced Resolution Volumes

Appendix D Geometric Optics Approximation to the Wave Equation

Appendix E Derivation of Green's Function

Reference

Index