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

摘要

This study proposes a Bayesian approach to retrieve raindrop size distributions (DSDs) and to estimate rainfall rates from radar reflectivity in horizontal polarization Z_H and differential reflectivity Z_(dr)- With this approach, the authors apply aconstrained-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 Z_H and Z_(DR) are then developed based on a T-matrix calculation of raindrop backscattering amplitude with the assumption of drop shape. The conditional PDF of Z_H and Z_(DR) 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 Z_H and Z_(DR). 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.