General probability-matched relations between radar reflectivity and rain rate

An improved method for transforming radar-observed reflectivities Ze into rain rate R is presented. The method is based on a formulation of a Ze-R function constrained such that (1) the radar-retrieved pdf of R and all of its moments are identical to those determined from the gauges over a sufficiently large domain, and (2) the fraction of the time that it is raining above a low but still has an accurately measurable rain intensity is identical for both the radar and for simultaneous measurements of collocated gauges on average. Data measured by a 1.65-deg beamwidth C-band radar and 22 gauges located in the vicinity of Darwin, Australia, are used. The resultant Ze-R functions show a strong range dependence, especially for the rain regimes characterized by strong reflectivity gradients and substantial attenuation. The application of these novel Ze-R functions to the radar data produces excellent matches to the gauge measurements without any systematic bias.