Radar–Rain Gauge Comparisons under Observational Uncertainties

Abstract

A simple, analytically tractable model of the radar–rain gauge rainfall observational process, including measurement errors, is presented. The model is applied to study properties of different reflectivity–rainfall (Z–R) relationships estimated from radar and rain gauge data. Three common Z–R adjustment schemes are considered: direct and reverse nonlinear regression, and the probability matching method. The three techniques result in quite different formulas for the estimated Z–R relationships. All three also are different from the intrinsic Z–R of the model and depend strongly on the assumed observational uncertainties. The results explain, to a degree, the diversity of Z–R relationships encountered in the literature. They also suggest that development of new tools that account for the uncertainties is necessary to separate the observational and natural causes of the Z–R variability.