Application of a Threshold Method to Airborne–Spaceborne Attenuating-Wavelength Radars for the Estimation of Space–Time Rain-Rate Statistics

Abstract

A method is proposed for estimating the area-average rain-rate distribution from attenuating-wavelength spaceborne or airborne radar data. Because highly attenuated radar returns yield unreliable estimates of the rain rate, these are eliminated by means of a proxy variable, Q, derived from the apparent radar reflectivity factors and a power law relating the attenuation coefficient and the reflectivity factor. In determining the probability distribution function of areawide rain rates, the elimination of attenuated measurements at high rain rates and the loss of data at light rain rates, because of low signal-to-noise ratios, leads to truncation of the distribution at the low and high ends. To estimate it over all rain rates, a lognormal distribution is assumed, the parameters of which are obtained from a nonlinear least squares fit to the truncated distribution. Implementation of this type of threshold method depends on the method used in estimating the high-resolution rain-rate estimates (e.g., either the standard Z?R or the Hitschfeld?Bordan estimate) and on the type of rain-rate estimate (either point or path averaged). To test the method, measured drop size distributions are used to characterize the rain along the radar beam. Comparisons with the standard single-threshold method or with the sample mean, taken over the high-resolution estimates, show that the present method usually provides more accurate determinations of the area-averaged rain rate if the values of the threshold parameter, QT, are chosen in the range from 0.2 to 0.4.