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

Observations of raindrop size distributions (DSDs) have validated the use of three-parameter distribution functions in representing the observed spectra. However, dual-frequency radar measurements are limited to retrieving two independent parameters of the DSD, thus requiring a constraint on a three-parameter distribution. In this study, disdrometer observations from a variety of climate regions are employed to develop constraints on the gamma distribution that are optimized for dual-frequency radar rainfall retrievals. These observations are composited by reflectivity, and then gamma parameters are fit to the composites. The results show considerable variability in shape parameter between regions and within a region at different reflectivities. Most notable is that oceanic regions exhibit maxima in shape parameter at 13.6-GHz reflectivities between 40 and 50 dBZ, in contrast to continental regions. The shape parameter and slope parameter of all composite DSDs are poorly correlated. Thus, constraints of a constant shape parameter or shape parameter–slope parameter relationship are inadequate to represent the observed variability. However, the shape and slope parameters are highly correlated at a given reflectivity. Constraints of a fixed shape parameter and relationships between a shape parameter m and slope parameter Λ, both of which are given as functions of 13.6-GHz reflectivity, are applied to retrieve rain rate, liquid water content, and mean mass diameter from the composites. The m–Λ relationships perform best at high reflectivity (dBZ13.6 > 35), whereas the fixed shape parameter generally results in lower error at medium and low reflectivities (dBZ13.6 < 35). All calculations have been made under the assumption that the reflectivity measurements have been corrected for attenuation.