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Qing Cao and Guifu Zhang

Abstract

There have been debates and differences of opinion over the validity of using drop size distribution (DSD) models to characterize precipitation microphysics and to retrieve DSD parameters from multiparameter radar measurements. In this paper, simulated and observed rain DSDs are used to evaluate moment estimators. Seven estimators for gamma DSD parameters are evaluated in terms of the biases and fractional errors of five integral parameters: radar reflectivity (ZH), differential reflectivity (Z DR), rainfall rate (R), mean volume diameter (Dm), and total number concentration (NT). It is shown that middle-moment estimators such as M234 (using the second-third-fourth moments) produce smaller errors than lower- and higher-moment estimators if the DSD follows the gamma distribution. However, if there are model errors, the performance of M234 degrades. Even though the DSD parameters can be biased in moment estimators, integral parameters are usually not. Maximum likelihood (ML) and L-moment (LM) estimators perform similarly to low-moment estimators such as M012. They are sensitive to both model error and the measurement errors of the low ends of DSDs. The overall differences among M234, M246, and M346 are not substantial for the five evaluated parameters. This study also shows that the discrepancy between the radar and disdrometer observations cannot be reduced by using these estimators. In addition, the previously found constrained-gamma model is shown not to be exclusively determined by error effects. Rather, it is equivalent to the mean function of normalized DSDs derived through Testud’s approach, and linked to precipitation microphysics.

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Guifu Zhang and Richard J. Doviak

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The theory of spaced-antenna interferometry (SAI) is formulated to detect and locate deterministic objects and reflectivity inhomogeneities embedded within the phased-array weather radar’s resolution volume V 6 and to improve weather radar performance. An analogy is made between monopulse tracking and SAI. The cross-correlation function and its power spectrum are derived based on wave scattering by a large deterministic object and clusters of randomly distributed precipitation particles. It is shown that nonuniform beam filling leads to an effective narrower beam and an increase in cross-correlation coefficient at zero lag. Hence, an individual object or a subvolume inhomogeneity can be detected and located by SAI. This capability further enhances the potential applications of phased-array weather radar used as a multimission system.

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Guifu Zhang and Richard J. Doviak

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The theory of measuring crossbeam wind, shear, and turbulence within the radar’s resolution volume V6 is described. Spaced-antenna weather radar interferometry is formulated for such measurements using phased-array weather radar. The formulation for a spaced-antenna interferometer (SAI) includes shear of the mean wind, allows turbulence to be anisotropic, and allows receiving beams to have elliptical cross sections. Auto- and cross-correlation functions are derived based on wave scattering by randomly distributed particles. Antenna separation, mean wind, shear, and turbulence all contribute to signal decorrelation. Crossbeam wind cannot be separated from shear, and thus crossbeam wind measurements are biased by shear. It is shown that SAI measures an apparent crossbeam wind (i.e., the angular shear of the radial wind component). Whereas the apparent crossbeam wind and turbulence within V6 cannot be separated using monostatic Doppler techniques, angular shear and turbulence can be separated using the SAI.

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Petar Bukovčić, Dušan Zrnić, and Guifu Zhang

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Observations and analysis of an ice–liquid phase precipitation event, collected with an S-band polarimetric KOUN radar and a two-dimensional video disdrometer (2DVD) in central Oklahoma on 20 January 2007, are presented. Using the disdrometer measurements, precipitation is classified either as ice pellets or rain/freezing rain. The disdrometer observations showed fast-falling and slow-falling particles of similar size. The vast majority (>99%) were fast falling with observed velocities close to those of raindrops with similar sizes. In contrast to the smaller particles (<1 mm in diameter), bigger ice pellets (>1.5 mm) were relatively easy to distinguish because their shapes differ from the raindrops. The ice pellets were challenging to detect by looking at conventional polarimetric radar data because of the localized and patchy nature of the ice phase and their occurrence close to the ground. Previously published findings referred to cases in which ice pellet areas were centered on the radar location and showed a ringlike structure of enhanced differential reflectivity Z DR and reduced copolar correlation coefficient ρ hv and horizontal reflectivity Z H in PPI images. In this study, a new, unconventional way of looking at polarimetric radar data is introduced: slanted vertical profiles (SVPs) at low (0°–1°) radar elevations. From the analysis of the localized and patchy structures using SVPs, the polarimetric refreezing signature, reflected in local enhancement in Z DR and reduction in Z H and ρ hv, became much more evident. Model simulations of sequential drop freezing using Marshall–Palmer DSDs along with the observations suggest that preferential freezing of small drops may be responsible for the refreezing polarimetric signature, as suggested in previous studies.

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Youngsun Jung, Ming Xue, and Guifu Zhang

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A new general polarimetric radar simulator for nonhydrostatic numerical weather prediction (NWP) models has been developed based on rigorous scattering calculations using the T-matrix method for reflectivity, differential reflectivity, specific differential phase, and copolar cross-correlation coefficient. A continuous melting process accounts for the entire spectrum of varying density and dielectric constants. This simulator is able to simulate polarimetric radar measurements at weather radar frequency bands and can take as input the prognostic variables of high-resolution NWP model simulations using one-, two-, and three-moment microphysics schemes. The simulator was applied at 10.7-cm wavelength to a model-simulated supercell storm using a double-moment (two moment) bulk microphysics scheme to examine its ability to simulate polarimetric signatures reported in observational studies. The simulated fields exhibited realistic polarimetric signatures that include Z DR and K DP columns, Z DR arc, midlevel Z DR and ρ rings, hail signature, and K DP foot in terms of their general location, shape, and strength. The authors compared the simulation with one employing a single-moment (SM) microphysics scheme and found that certain signatures, such as Z DR arc, midlevel Z DR, and ρ rings, cannot be reproduced with the latter. It is believed to be primarily caused by the limitation of the SM scheme in simulating the shift of the particle size distribution toward larger/smaller diameters, independent of mixing ratio. These results suggest that two- or higher-moment microphysics schemes should be used to adequately describe certain important microphysical processes. They also demonstrate the utility of a well-designed radar simulator for validating numerical models. In addition, the simulator can also serve as a training tool for forecasters to recognize polarimetric signatures that can be reproduced by advanced NWP models.

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Guifu Zhang, Juanzhen Sun, and Edward A. Brandes

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Disdrometer observations indicate that the raindrop size distribution (DSD) can be represented by a constrained-gamma (CG) distribution model. The model is used to retrieve DSDs from polarization radar measurements of reflectivity and differential reflectivity and to characterize rain microphysics and physical processes such as evaporation, accretion, and precipitation. The CG model parameterization is simplified to a single parameter for application in single-moment numerical models. This simplified parameterization is applied in the Variational Doppler Radar Analysis System (VDRAS) using Kessler-type parameterizations for model initialization and forecasting. Results are compared to those for the Marshall–Palmer (MP) DSD model. It is found that the simplified CG model parameterization better preserves the stratiform rain and produces better forecasts than the MP model parameterization.

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Youngsun Jung, Guifu Zhang, and Ming Xue

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A radar simulator for polarimetric radar variables, including reflectivities at horizontal and vertical polarizations, the differential reflectivity, and the specific differential phase, has been developed. This simulator serves as a test bed for developing and testing forward observation operators of polarimetric radar variables that are needed when directly assimilating these variables into storm-scale numerical weather prediction (NWP) models, using either variational or ensemble-based assimilation methods. The simulator takes as input the results of high-resolution NWP model simulations with ice microphysics and produces simulated polarimetric radar data that may also contain simulated errors. It is developed based on calculations of electromagnetic wave propagation and scattering at the S band of wavelength 10.7 cm in a hydrometeor-containing atmosphere. The T-matrix method is used for the scattering calculation of raindrops and the Rayleigh scattering approximation is applied to snow and hail particles. The polarimetric variables are expressed as functions of the hydrometeor mixing ratios as well as their corresponding drop size distribution parameters and densities. The presence of wet snow and wet hail in the melting layer is accounted for by using a new, relatively simple melting model that defines the water fraction in the melting snow or hail. The effect of varying density due to the melting snow or hail is also included. Vertical cross sections and profiles of the polarimetric variables for a simulated mature multicellular squall-line system and a supercell storm show that polarimetric signatures of the bright band in the stratiform region and those associated with deep convection are well captured by the simulator.

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Mohammad-Hossein Golbon-Haghighi and Guifu Zhang

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A novel 3D discriminant function is introduced as part of a ground clutter detection algorithm for improving weather radar observations. The 3D discriminant function utilizes the phase fluctuations of the received signals for horizontal and vertical polarizations and the dual-scan cross-correlation coefficient. An optimal decision based on the 3D discriminant function is made using a simple Bayesian classifier to distinguish clutter from weather signals. For convenience of use, a multivariate Gaussian mixture model is used to represent the probability density functions of discriminant functions. The model parameters are estimated based on the maximum likelihood using the expectation–maximization (ML-EM) method. The performance improvements are demonstrated by applying the proposed detection algorithm to radar data collected by the polarimetric Norman, Oklahoma (KOUN), weather radar. This algorithm is compared to other clutter detection algorithms and the results indicate that, using the proposed detection algorithm, a better probability of detection can be achieved.

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Edward A. Brandes, Guifu Zhang, and Juanzhen Sun

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Polarimetric radar measurements are used to retrieve drop size distributions (DSD) in subtropical thunderstorms. Retrievals are made with the single-moment exponential drop size model of Marshall and Palmer driven by radar reflectivity measurements and with a two-parameter constrained-gamma drop size model that utilizes reflectivity and differential reflectivity. Results are compared with disdrometer observations. Retrievals with the constrained-gamma DSD model gave better representation of total drop concentration, liquid water content, and drop median volume diameter and better described their natural variability. The Marshall–Palmer DSD model, with a fixed intercept parameter, tended to underestimate the total drop concentration in storm cores and to overestimate significantly the concentration in stratiform regions. Rainwater contents in strong convection were underestimated by a factor of 2–3, and drop median volume diameters in stratiform rain were underestimated by 0.5 mm. To determine possible DSD model impacts on numerical forecasts, evaporation and accretion rates were computed using Kessler-type parameterizations. Rates based on the Marshall–Palmer DSD model were lower by a factor of 2–3 in strong convection and were higher by about a factor of 2 in stratiform rain than those based on the constrained-gamma model. The study demonstrates the potential of polarimetric radar measurements for improving the understanding of precipitation processes and microphysics parameterization in numerical forecast models.

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