Statistical Methods for Space-time Averaged Rain Rate Estimation Applied to the Dual-Frequency Precipitation Radar

Statistical methods for the estimation of space-time averaged rain rates have been shown to be accurate if the set of rain measurements on which the methods are applied is sufficiently large. For satellite-borne weather radars that operate at Ku-band and above, the methods offer the potential of reasonably accurate estimates of mean rain rate over large areas and time scales even when the estimates at higher rain rates are corrupted or undetectable because of signal attenuation.

The two types of statistical methods that are investigated are the fractional-area and the multiple threshold approaches. For the first method, we consider the relationship between the fractional area above a rain rate threshold, R_th, and the sample mean rain rate where the rain rates used to compute the sample mean are based on radar reflectivities that have been corrected for attenuation at each field of view. This fractional area-mean rain rate (FrA-RR) relationship can be view as a function of the threshold R_th as well as a parameter zeta, which is a proxy variable for path attenuation that is used to filter out attenuated data. One of the primary questions to be addressed is the strength of the FrA-RR relationship as a function of R_th and zeta at Ku- and Ka-band frequencies.

Recognizing that the fractional area at R_th is closely related to the cumulative distribution function of the rain rate at R_th, FrA(R_th) can be computed at multiple R_th values to yield an estimate for the cumulative distribution function for the space-time averaged rain rate. As in the fractional-area method, thresholding by zeta serves the role in eliminating from the distribution rain rate estimates that are affected by attenuation.

In this paper, we look into the application of these methods to data taken by the dual-frequency precipitation radar (DPR) on board the GPM satellite. The DPR provides 3 types of data which consist of the Ku-band data over a wide swath (245 km) and two kinds of Ka-band data which include those data spatially coincident with the Ku-band in the inner swath (125 km, KaMS) and the higher-sensitivity Ka-band interleaved data (KaHS) also in the inner swath. Among the questions to be addressed are whether the statistical methods can be applied with the same accuracy to the Ka-band as they are to the Ku-band data, the role of zeta in filtering the data, the space-time region that is needed to achieve accurate mean rain rates and the difference in the performance of the methods when applied to the Ku, KaMS and KaHS data.