Polarimetric Radar Estimators Based on a Constrained Gamma Drop Size Distribution Model

Raindrop size distribution (DSD) retrieval from remote radar measurements or from in situ disdrometer measurements is an important area of research. If the shape ( ) and slope ( ) of a three-parameter gamma distribution n(D) N0D exp( D ) are related to one another, as recent disdrometer measurements suggest, the gamma DSD model is simplified to a two-parameter DSD, that is, a constrained gamma DSD. An empirical relation between the and was derived using moments estimated from video-disdrometer measurements. Here, the effects of DSD truncation on a and relation were analyzed. It was shown that characteristic size and variance of size of a constrained gamma DSD depend only on the shape parameter . Assuming that a constrained gamma DSD is valid, S-band polarimetric radar–based estimators for rain rate, median volume diameter, specific propagation phase, attenuation, and differential attenuation were derived. The radar-based estimators were used to obtain the spatial distribution of DSD parameters corresponding to a range–height indicator of radar measurements. Self-consistency among polarization radar measurements is used to indirectly verify constrained gamma DSD-based polarization radar estimators.