Retrieval of Raindrop Size Distribution from Simulated Dual-Frequency Radar Measurements

As part of NASA's precipitation measurement mission, the performance of raindrop size distribution (DSD) retrieval algorithm from simulated dual-frequency radar measurements has been tested employing disdrometer observations collected at different climatic regimes of the world. Reflectivities at 13.6 GHz and 35 GHz frequencies were calculated from disdrometric measurements through Mie scattering for 20? C with an assumption of spherical raindrops as they appear when observed at vertical cross-section. Integral rainfall parameters of rain rate, liquid water content, and mean mass diameter were also calculated from disdrometric measurements. A three parameter gamma function in the form of N(D) = N0 Dm exp (-õD), where N0 , õ, and m are intercept, slope, and shape parameters, respectively, was adopted for the retrieval of the DSD. Unfortunately, there is no analytical solution for the parameters of the gamma distribution and therefore we seek numerical solutions for a fixed shape parameter. At a given shape parameter, the ratio of two reflectivity measurements (DFR = Z13.6/Z35) had three different regions where no, one, and two solutions were available for slope parameter. The intercept parameter, which is not a function of DFR, was then solved for using either reflectivity. Integral rainfall parameters were recalculated from gamma fitted distributions for a range of shape parameters. Best shape parameter was then determined for the lowest bias and mean absolute error between observed and retrieved integral rainfall parameters. A relationship between the best shape parameter and 13.6 GHz reflectivity was then derived for each climate regime. In this study, we tested the performance of gamma function in retrieving the DSD from dual frequency radar measurements such the one on board upcoming Global Precipitation Measurement mission. We consider that the radar is well-calibrated and the attenuation correction has been successfully applied.