A GPM Dual-Frequency Retrieval Algorithm: DSD Profile-Optimization Method

A new dual-frequency precipitation radar (DPR) will be included on the Global Precipitation Measurement (GPM) core satellite, which will succeed the highly successful Tropical Rainfall Measuring Mission (TRMM) satellite launched in 1997. New dual-frequency drop size distribution (DSD) and rain-rate estimation algorithms are being developed to take advantage of the enhanced capabilities of the DPR. It has been shown that the backward-iteration algorithm can be embedded within a single-loop (SL) feedback model. However, the SL model is unable to correctly estimate DSD profiles for a significant portion of global median volume diameter Do and normalized DSD intercept parameter Nw combinations in rain because of a multiple-value solution space. For the remaining Do, Nw pairs, another retrieval method is necessary. This paper proposes a supplementary profile-optimization technique to find those DSD profiles in the rain region that the SL model cannot correctly determine. The optimization method is based on a model that both Do and log(Nw) are linear vertical profiles, and that the profiles can be found using an optimization technique from the input reflectivity profiles. Using those assumptions, the optimization method finds the top and bottom Do, log(Nw) values such that a cost function related to the input-measured reflectivity is minimized. A random-restart method is used to generate random top-and-bottom DSD seed values for each optimization cycle. Example cases are shown to demonstrate the performance with and without error in the input reflectivity profiles. Limitations of the method are discussed, including its performance when the input reflectivity profiles are based on nonlinear DSD profiles and values of shape factor μ different than the algorithm assumed value.