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Empirical power-law relations between the equivalent radar reflectivity factor Ze and the slope parameter of the gamma function Λ (i.e., Λ = c; used to describe ice hydrometeor size distributions) are derived. The Λ parameter can also be considered as a size parameter since it is proportional to the inverse of the hydrometeor characteristic size, which is an important geophysical parameter describing the entire distribution. Two datasets from two-dimensional microphysical probes, collected during aircraft flights in subtropical and midlatitude regions, were used to obtain Λ by fitting measured size distributions. Reflectivity for different radar frequencies was calculated from microphysical probe data by using nonspherical-particle models. The derived relations have exponent d values that are approximately from −0.35 to −0.40, and the prefactors c are approximately between 30 and 55 (Λ: cm−1; Ze: mm6 m−3). There is a tendency for d and c to decrease when radar frequency increases from Ku band (~14...

Empirical Relations between Size Parameters of Ice Hydrometeor Populations and Radar Reflectivity