Radar Polarimetry for Weather Observations

Polarization is an inherent property of electromagnetic wave (EM) that can be used to extract information about the physical properties of the medium through which the wave propagates and the scatterers that scatter electromagnetic wave in different directions. These physical properties include size, concentration, shape, orientation, and phase composition of atmospheric particles with which the wave interacts. Basic definitions of the EM attributes and different types of polarizations (linear, circular, elliptical) are presented. The scattering matrix of an individual scatterer is introduced and its elements are explicitly specified as functions of the orientation angles and scattering coefficients along the principle axes of a spheroidal scatterer. The propagation effects through the atmosphere filled with anisotropic hydrometeors are quantified via attenuation factors at orthogonal polarizations, differential attenuation, and differential phase.

Basic principles of a polarimetric Doppler radar are described in this chapter. These include formation of the transmitted EM wave by a pulsed radar, reception of the radar signal reflected from a single scatterer, and its transformation in the antenna, microwave assembly, and two receivers for orthogonally polarized components of the backscattered EM wave. Different schemes for transmission/reception (simultaneous or alternate) of the horizontally and vertically polarized EM waves are described. Derivation of the relations between electric fields, voltages, and powers associated with copolar and cross-polar components of the radar returns from a single scatterer is included as well as the definitions of the Doppler and differential phase shifts.

Scattering by an ensemble of particles is presented and the weighting in range imposed by the pulse shape and receiver filter is quantified. It is shown that the powers and correlations of the polarimetric signals are the fundamental measurands and the combination of these produces the polarimetric variables useful for interpretation of radar returns. The polarimetric radar equation is derived and the basic polarimetric variables measured in various modes of radar operation (with simultaneous or alternate transmission/reception) are defined. The effects of particles orientation are discussed in detail and analytical formulas for the angular moments which are part of closed-form solutions for various scattering quantities are presented.

Microphysical properties of hydrometeors such as size, shape, orientation, and phase composition, and distribution of these properties over an ensemble of particles determine polarimetric radar variables. In this chapter, an overview of microphysical properties of different hydrometeor types is provided. Different forms of size distributions (SD) of raindrops and ice particles are discussed, and the statistics of the key parameters of SD such as liquid or ice water content, mean volume diameter, and normalized concentration are presented. The chapter contains basic information about density of atmospheric particles and their axis ratios and orientations. Special attention is given to dielectric properties of hydrometeors including basic formulas for dielectric constant of fresh water, solid ice, dry/wet snow, graupel, and hail.

Polarimetric variables corresponding to various hydrometeor types are discussed and quantified in this chapter. Considered polarimetric variables are reflectivity factors at horizontal and vertical polarizations (Z_H and Z_V), differential reflectivity Z_DR, cross-correlation coefficient ρ_hv, total differential phase Φ_DP, specific differential phase K_DP, backscatter differential phase δ, linear depolarization ratio LDR, circular depolarization ratio CDR, specific attenuation A, and specific differential attenuation A_DP. Presented are the physical meaning of these variables and their dependencies on the primary microphysical properties of hydrometeors such as size, concentration, shape, orientation, and physical composition. These dependencies are quantified with relatively simple formulas for smaller particles using Rayleigh approximation or T-matrix simulations for hydrometeors of larger size. The overview is given for liquid- (raindrops), solid- (ice, snow), and mixed-phase (melting ice/snow) hydrometeors at the S, C, and X microwave frequency bands commonly utilized for operational polarimetric radars.

Various system and environmental effects on the quality of polarimetric measurements are discussed in this chapter. It starts with calibration of the reflectivity factor Z and differential reflectivity Z_DR. The biases in Z and Z_DR caused by attenuation/differential attenuation in rain and hail as well as wet radome are illustrated and quantified. Various techniques for attenuation/differential attenuation correction at different radar wavelengths are described, and numerous results of correction are presented. The effects of partial beam blockage on the Z, Z_DR, and ρ_hv fields are demonstrated, and ways to mitigate these are suggested. Contamination of radar signals by ground clutter is reviewed, the method used on the WSR-88D is briefly described, and potential of the polarimetric information to better identify ground clutter is suggested. Contamination of the radar variables by white noise is explained, and corrections are outlined. Progressive beam broadening with range and stronger impact of nonuniform beam filling are listed as culprits for the deterioration of polarimetric variables with range. These effects are demonstrated and approximately quantified. Depolarization by oriented ice crystals also affects the polarimetric variables, and some examples are included. Three-body scattering signature in differential reflectivity and correlation coefficient is shown and conceptually explained. Finally, statistical errors associated with computations of the polarimetric variables and spectral moments are quantified.

Polarimetric characteristics of hydrometeors reflect ongoing microphysical processes in clouds and precipitation. The chapter describes basic microphysical processes and their influence on the evolution of hydrometeors and associated polarimetric radar variables. Some processes have unique polarimetric signatures or “fingerprints,” and examples of these are given here. The examined microphysical processes involve liquid cloud drops, raindrops, mixed-phase particles, and ice particles. Rain processes include condensation, evaporation, coalescence, breakup, and size sorting. Ice and mixed-phase processes include depositional growth, sublimation, riming, aggregation, freezing/refreezing, and melting.

Overview of polarimetric measurements in deep convective storms is presented in this chapter. General characteristics of the spatial distributions of polarimetric radar variables in mesoscale convective systems (MCSs), hailstorms, and supercell tornadic storms are examined. Spatial pattern of the polarimetric variables in the MCSs is consistent with the accepted conceptual model. Combinations of polarimetric variables that correspond uniquely to locations within storms where specific scatterer types reside are identified and named “polarimetric signatures.” Prominent among these is the column of differential reflectivity indicative of convective updraft and preferred location for hail formation. The bottom of the column of specific differential phase is identified as location of precipitation-laden downdraft. Other important signatures associated with tornadic storms and discussed in this chapter are tornado debris signature (TDS), Z_DR arc, and midlevel “rings” of enhanced Z_DR and depressed ρ_hv. Examples of polarimetric variables in hailstorms are illustrated and related to the kinematic and microphysical features within these storms. Observations of large hail are presented, and comparisons between measurements at C and S band are made. Examples of tornado debris signatures observed with S-, C-, and X-band radars are also included. Modeling of the polarimetric characteristics of these deep convective storms is the subject of the last section, and examples from the literature are used to illustrate the inferred polarimetric signatures and compare these with observations.

Automatic classification of radar returns using the polarimetric variables and environmental conditions is presented in this chapter. General principles of classification are reviewed with emphasis on the fuzzy logic method. Then, the hydrometeor classification algorithm operational on WSR-88D network is described, and other classification algorithms are discussed. The method for melting layer detection as an important part of the most classification schemes is described in detail. A section of the chapter is devoted to detection of hail and estimation of its size together with some verification. Also presented is automated detection of tornado debris signatures in the context of tornado detection, and tracks of detections are plotted along the damage paths of several tornadoes. Automatic detection of convective updrafts is based on the columns of differential reflectivity, and examples are included. A separate section is devoted to classification specifically tailored for winter precipitation. This implies combined use of the polarimetric data and numerical weather prediction model output. Finally, classification of radar returns other than from hydrometeors is described. Specifically, polarimetric methods to identify land and sea clutter, biological scatterers, chaff, smoke plumes, dust storms, and volcanic ash are presented.

Quantitative precipitation estimation (QPE) is the subject of this chapter. A summary of various radar rainfall relations and their sensitivity to variability of drop-size distributions (DSD) at S, C, and X bands is presented. Emphasized is the algorithm based on the specific attenuation A. Various advantages of the R (A) methodology are discussed including its low sensitivity to the DSD variability and its immunity to radar miscalibration, partial beam blockage, and wet radome. The impact of contamination by hail and bright band on the performance of radar rainfall estimators is examined, and methods for mitigation of such contamination are suggested.

Large-scale validation of various QPE techniques is overviewed with the focus on the performance of the rainfall estimation algorithms which were tested on the US WSR-88D network of operational radars.

The problem of radar measurement of snow is addressed in the last section of the chapter. The challenges with reflectivity-based estimates of snow water equivalent rate are described, and possible polarimetric methodologies for snow measurements are outlined.

The retrieval of the mixing ratios for different hydrometeor types (or water and ice contents), median or mean volume diameter, and particle number concentration is the thrust of this chapter. These retrieved parameters of the bulk hydrometeor properties are suitable for assimilation into storm-scale numerical weather prediction models. The chapter starts with estimation of the liquid water content and the parameters of the drop size distribution in pure rain. Then polarimetric retrievals in ice and snow follow. Specifically, the methods for estimating the ice water content and the snow size distribution parameters are introduced. This is followed by discussion of measurement errors and validation of the retrievals in the case of mesoscale convective system. The chapter concludes with an example of the ice retrieval in a typical tropical cyclone.