Polarimetric Radar Rain Estimation through Retrieval of Drop Size Distribution Using a Bayesian Approach

Abstract

Abstract This study proposes a Bayesian approach to retrieve raindrop size distributions (DSDs) and to estimate rainfall rates from radar reflectivity in horizontal polarization ZH and differential reflectivity ZDR. With this approach, the authors apply a constrained-gamma model with an updated constraining relation to retrieve DSD parameters. Long-term DSD measurements made in central Oklahoma by the two-dimensional video disdrometer (2DVD) are first used to construct a prior probability density function (PDF) of DSD parameters, which are estimated using truncated gamma fits to the second, fourth, and sixth moments of the distributions. The forward models of ZH and ZDR are then developed based on a T-matrix calculation of raindrop backscattering amplitude with the assumption of drop shape. The conditional PDF of ZH and ZDR is assumed to be a bivariate normal function with appropriate standard deviations. The Bayesian algorithm has a good performance according to the evaluation with simulated ZH and ZDR. The algorithm is also tested on S-band radar data for a mesoscale convective system that passed over central Oklahoma on 13 May 2005. Retrievals of rainfall rates and 1-h rain accumulations are compared with in situ measurements from one 2DVD and six Oklahoma Mesonet rain gauges, located at distances of 28–54 km from Norman, Oklahoma. Results show that the rain estimates from the retrieval agree well with the in situ measurements, demonstrating the validity of the Bayesian retrieval algorithm.