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A methodology is proposed for estimating the parameters of a gamma raindrop size distribution model from radar measurements of Z h , Z dr , and K dp at S band. Previously developed algorithms by Gorgucci et al. are extended to cover low rain-rate events where both Z dr and K dp are noisy. Polarimetric data from the S-band Dual-Polarization Doppler Radar (S-Pol) during the Tropical Rainfall Measuring Mission (TRMM)/ Brazil campaign are analyzed; specifically, the gamma parameters are retrieved for samples of convective and trailing stratiform rain during the 15 February 1999 squall-line event. Histograms of N w and D o are retrieved from radar for each rain type and compared with related statistics reported in the literature. The functional behavior of N w and D o versus rain rate retrieved from radar is compared against samples of 2D-video and RD-69 disdrometer data obtained during the campaign. The time variation of N w , D o , and averaged over a 5 km 5 km area (within which a network of gauges and a profiler were situated) is shown to illustrate temporal changes associated with the gamma parameters as the squall line passed over the network. The gauge-derived areal rainfall over the network is compared against radar using the areal dp method, and the concept of an effective slope of a linear axis ratio versus diameter model is shown to significantly reduce the bias in radar-derived rainfall accumulation.

Polarization diversity radar measurements such as reflectivity factor, differential reflectivity, and differential propagation phase are extensively used in rainfall estimation. Algorithms to estimate rainfall from polarimetric radar measurements are based on a model for the raindrop shape as a function of drop diameter. Most of the current algorithms use an equilibrium shape-size model for raindrops. Variation of the prevailing mean raindrop shapes from an assumed model has a direct impact on the accuracy of radar rainfall estimates. This paper develops composite algorithms to estimate rainfall from polarimetric radar data without an a priori assumption about the specific form of mean raindrop shape-size model such as equilibrium shape model. The accuracy of rainfall estimates is evaluated in the presence of random measurement errors as well as systematic bias errors. The composite algorithms, independent of a prespecified raindrop shape model, were applied to radar parameters simulated from disdrometer data collected over 3 months, and the corresponding rainfall estimates were found to be in good agreement with disdrometer estimates. The composite algorithms were also tested with Colorado State University CHILL radar observations of the 28 July 1997 Fort Collins (Colorado) flood event. The storm total precipitation estimates based on the composite algorithms developed in this paper were in much better agreement with rain gauge estimates in comparison with conventional algorithms.

Estimation of raindrop size distribution over large spatial and temporal scales has been a long-standing goal of polarimetric radar. Algorithms to estimate the parameters of a gamma raindrop size distribution model from polarimetric radar observations of reflectivity, differential reflectivity, and specific differential phase are developed. Differential reflectivity is the most closely related measurement to a parameter of the drop size distribution, namely, the drop median diameter (D 0). The estimator for D 0 as well as other parameters are evaluated in the presence of radar measurement errors. It is shown that the drop median diameter can be estimated to an accuracy of 10%, whereas the equivalent intercept parameter can be estimated to an accuracy of 6% in the logarithmic scale. The estimators for the raindrop size distribution parameters are also evaluated using disdrometer data based simulations. The disdrometer based evaluations confirm the accuracy of the algorithms developed herein.

Abstract-The joint distribution characteristics of size and shape of raindrops directly translate into features of polarization diversity measurements in rainfall. Theoretical calculations as well as radar observations indicate that the three polarization diversity measurements, namely, reflectivity, differential reflectivity, and specific differential propagation phase, lie in a constrained space that can be approximated by a three-dimensional (3-D) surface. This feature as well as the vertical-looking observation of raindrops are used to determine biases in calibration of the radar system. A simple procedure is developed to obtain the bias in the absolute calibration from polarization diversity observation in rainfall. Simulation study as well as data analysis indicate that calibration errors can be estimated to an accuracy of 1 dB.