Mathematical–Physical Framework for Retrieval of Rain DSD Properties from Dual-Frequency Ku–Ka-Band Satellite Radar

In developing the upcoming Global Precipitation Measurement (GPM) mission, a dual-frequency Ku–Ka-band radar system will be used to measure rainfall in such a fashion that the reflectivity ratio intrinsic to the measurement will be sensitive to underlying variations in the drop size distribution (DSD) of rain. This will enable improved techniques for retrieving rain rates, which are dependent upon several key properties of the DSD. This study examines this problem by considering a three-parameter set defined by liquid water content (W), DSD effective radius (r e ), and DSD effective variance (␷ e ). Using radiative transfer simulations, this parameter set is shown to be related to a radar reflectivity factor and specific attenuation in such a fashion that details of the DSDs are immaterial under constant W, and thus effectively represent important variations in DSD that affect rain rate but with a minimal number of parameters. The analysis also examines the effectiveness of including some measure of mean Doppler fall velocity of raindrops (␷ ), given that the fundamental properties of a given precipitation situation are uniquely defined by a combination of a drop mass spectrum and drop vertical velocity spectrum. The results of this study have bearing on how future dual-frequency precipitation retrieval algorithms could be formulated to optimize the sensitivity to underlying DSD variability, a problem that has greatly upheld past progress in radar rain retrieval.