Raindrop size distribution (DSD) provides fundamental information about rain microphysics. DSD information is important in accurate quantitative precipitation estimates (QPE) and microphysical parameterization in Numerical Weather Prediction (NWP) models to improve quantitative precipitation forecasts (QPF). Accurate DSD measurements have benefited from recent advancements in measurement techniques, such as video disdrometer and polarimetric radar observations. For example, the two-dimensional video disdrometer (2DVD) is capable of measuring the size, fall speed, shape and orientation of raindrops with unprecedented accuracy. Since May 2005, more than 20,000 minutes rain DSDs have been collected in Oklahoma. The dataset provides valuable prior (physical and statistical) information of rain DSDs.

Rain DSDs can also be retrieved from polarimetric radar data (PRD). PRD will be available nation-wide as the WSR-88D (Weather Surveillance Radar 88 Doppler) is upgraded with dual-polarization capability within the next five to seven years. Polarimetric radar measurements of reflectivity and differential reflectivity allow direct retrieval of rain DSDs when a two-parameter DSD model is used. However, radar measurements and the DSD model contain errors that lead to error in the retrieved DSDs. Previously, these error effects were not taken into account, and consequently, DSD retrievals have not been optimized. The Bayesian theory now offers a promising method of optimizing the use of polarimetric measurements for rain DSD retrievals. The Bayesian approach provides us with not only mean values of DSD parameters, but also their standard deviation.

In this study, we use a Bayesian approach to retrieve the rain DSD from radar reflectivity (ZH) and differential reflectivity (ZDR). A constrained gamma DSD model with two parameters is used. The statistics of the DSD parameters (slope and intercept) are obtained from the 2DVD observed DSDs which have been processed by truncated gamma moment fitting. Because DSD is the nonlinear function of DSD parameters, prior joint distribution of slope and intercept should be derived at an appropriate scale. The conditional probability model of ZH and ZDR is assumed to follow the bivariate Gaussian distribution. The standard deviations of ZH and ZDR are estimated from 2DVD data. With ZH and ZDR, the rain DSD is retrieved and the corresponding rain variables, rainfall rate, median volume diameter and total number concentration, are calculated. The comparison between retrieved rain variables and calculations from 2DVD observations demonstrates the Bayesian approach's great potential to retrieve rain DSDs and quantify their accuracy.