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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 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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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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Edward A. Brandes, Guifu Zhang, and J. Vivekanandan

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Recently, two physically based algorithms, the “beta” (β) method and the “constrained-gamma” method, have been proposed for retrieving the governing parameters of the gamma drop size distribution (DSD) from polarimetric radar measurements. The β method treats the drop axis ratio as a variable and computes drop shape and DSD parameters from radar reflectivity (Z), differential reflectivity (Z DR), and specific differential phase (K DP). The constrained-gamma method assumes that the axis ratio relation is fixed and computes DSD parameters from reflectivity, differential reflectivity, and an empirical relation between the DSD slope and shape parameters. In this paper, the two approaches are evaluated by comparing retrieved rain DSD parameters with disdrometer observations and examining derived fields for consistency. Error effects on the β method retrievals are analyzed. The β approach is found to be sensitive to errors in K DP and to be inconsistent with observations. Large retrieved β values are found to associate with large retrieved DSD shape parameters and small median drop diameters. The constrained-gamma DSD method provides reasonable rain DSD retrievals that agree better with disdrometer observations.

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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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Lesya Borowska, Guifu Zhang, and Dusan S. Zrnić

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When spectral moments in the azimuth are spaced by less than a beamwidth, it is called oversampling. Superresolution is a type of oversampling that refers to sampling at half a beamwidth on the national network of Doppler weather radars [Weather Surveillance Radar-1988 Doppler (WSR-88D)]. Such close spacing is desirable because it extends the range at which small severe weather features, such as tornadoes or microbursts, can be resolved. This study examines oversampling for phased array radars. The goal of the study is to preserve the same effective beamwidth as on the WSR-88D while obtaining smaller spectral moment estimate errors at the same or faster volume update times. To that effect, a weighted average of autocorrelations of radar signals from three consecutive radials is proposed. Errors in three spectral moments obtained from these autocorrelations are evaluated theoretically. Methodologies on how to choose weights that preserve the desirable effective beamwidth are presented. The results are demonstrated on the fields of spectral moments obtained with the National Weather Radar Testbed (NWRT), a phased array weather radar at NOAA’s National Severe Storms Laboratory (NSSL).

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Edward A. Brandes, Guifu Zhang, and J. Vivekanandan
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Edward A. Brandes, Guifu Zhang, and J. Vivekanandan

Abstract

Polarimetric radar measurements are used to retrieve properties of raindrop distributions. The procedure assumes that drops are represented by a gamma distribution and retrieves the governing parameters from an empirical relation between the distribution shape and slope parameters and measurements of radar reflectivity and differential reflectivity. Retrieved physical characteristics of the drop size distribution (DSD) were generally well matched with disdrometer observations. The method is applied to select storms to demonstrate utility. Broad DSDs were determined for the core (high reflectivity) regions of thunderstorms. Largest drop median volume diameters were at the leading edge of the storm core and were displaced slightly downwind from updrafts. Rainy downdrafts exhibited what are believed to be equilibrium DSDs in which breakup and accretion are roughly in balance. DSDs for stratiform precipitation were dominated by relatively large drops. Median volume diameters at the ground were closely related to the intensity of an overlying bright band. The radar measurements suggest that, although DSDs in stratiform rain were also broad and nearly constant in the rain layer, they were not at equilibrium but were merely steady. DSD invariance is attributed to small total drop numbers, which result in few collisions.

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Edward A. Brandes, Guifu Zhang, and J. Vivekanandan

Abstract

A method for estimating the governing parameters of gamma drop size distributions (DSDs) and associated rainfall rates from polarimetric radar measurements at the S band is examined. The technique uses radar reflectivity at horizontal polarization, differential reflectivity, and an empirical constraining relationship between the DSD shape factor and slope parameter. Retrieved DSD parameters show good agreement with disdrometer observations. Retrieved rainfall estimates are insensitive to drop climatological regime. Comparison with fixed-form power-law estimators reveals that the constrained-gamma method outperforms reflectivity estimators and is roughly equivalent to radar reflectivity–differential reflectivity estimators optimized for local DSDs.

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