Polarimetric radar estimators based on a constrained gamma drop size distribution model

If the shape (μ) and slope (Λ) of a three-parameter gamma distribution n(D) = N0Du exp(-ΛD) 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 Λ was derived using moments estimated from video-disdrometer measurements.

Here, the effects of DSD truncation on a μ and Λ 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.