Climatologically tuned reflectivity-rain rate relations and links to area-time integrals

TLDR: In this article, an effort is made to determine relationships between reflectivity (Z) and rain rate (R) which are tuned to the local climatology, where the relation is tuned so that the probability distribution of reflectivity, P(Z), replicates that of R over some predetermined space-time climatic domain.

Abstract: An effort is made to determine relationships between reflectivity (Z) and rain rate (R) which are tuned to the local climatology. The development of such relations was motivated by the need to understand the role of precipitation in controlling general circulation and in affecting such phenomena as ENSO. Attention is given to methods of deriving such relations and how they are linked to area integral rainfall measurements. In essence, the relation is tuned so that the probability distribution of reflectivity, P(Z), replicates that of R over some predetermined space-time climatic domain. Thus, the accurate measurement of the average R over any smaller domain depends on how closely the sampled P(Z) approximates the climatic P(Z). The probability matching method used is a modification of the approach of Calheiros and Zawadzki (1987) and Rosenfeld (1980). The technique is applied to data from Germany and the eastern tropical Atlantic (GATE).