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 (μ) and slope (A) of a three-parameter gamma distribution n(D) = N₀D^μ exp(-AD) 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 μ and A was derived using moments estimated from video-disdrometer measurements. Here, the effects of DSD truncation on a μ and A relation were analyzed. It was shown that characteristic size and variance of size of a constrained gamma DSD depend only on the shape parameter μ. 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.