Gamma Drop Size Distribution Assumptions in Bulk Model Parameterizations and Radar Polarimetry and Their Impact on Polarimetric Radar Moments

Abstract

A suitable formulation of the rain drop size distribution (DSD) is a prerequisite for a successful assimilation of radar polarimetric information on rain into a numerical weather prediction model. Popular DSD parameterizations in two-moment bulk microphysics schemes use relations between the so-called mean-mass diameter and the DSD shape parameter ?, in order to prevent overly strong size sorting in the models. In radar polarimetry constrained-gamma DSDs with empirical relations between the shape and scale parameter are commonly used. This study compares the different DSD formulations and highlights the differences. Synthetic polarimetric radar observations for X band (9.39 GHz) and S band (3 GHz) were calculated from the different DSDs using the T-matrix method. Depending on the constraint that is assumed for the DSDs, the polarimetric moments exhibit quite different dependencies on the mean diameter, which are particularly striking for differential reflectivity ZDR. To successfully assimilate observed polarimetric moments into atmospheric models, formulations?possibly more flexible than those investigated in this study?have to be found that sufficiently represent microphysical processes and at the same time are consistent with empirical relations derived from disdrometer and radar polarimetric measurements.