A Class of Single- and Dual-Frequency Algorithms for Rain-Rate Profiling from a Spaceborne Radar. Pad I: Principle and Tests from Numerical Simulations

Abstract

A class of single- and dual-frequency algorithms that can be used to infer rain-rate profile from a downward-looking spaceborne radar operating at attenuating frequencies is presented. These algorithms rely on use of power-law relations between the radar reflectivity factor Z and the specific attenuation coefficient k. First, they provide estimates of attenuation-related parameters such as the range-profiled specific attenuation coefficient or partial range-averaged specific attenuation coefficients. Then, the corresponding rain rate R range profile can be derived by using a relevant R-k relationship. Profiling may be performed either from the radar or from the surface. The basic purpose of the various algorithms is to correct for several types of range-free scaling errors that may alleviate, for example, requirements on radar calibration and/or storm modeling (cloud, melting layer). Corrections are performed by using an additional measurement of the surface echo, an additional hypothesis (such as uniformity of rain rate versus range near the surface) for the case of single-freqnency algorithms, or by exploiting the correlation between the two attenuation coefficients at both frequencies for the case of dual-frequency algorithm. The present paper (Part I) describes the basic formalism of both single- and dual-frequency algorithms using a unified mathematical framework. Tests of their performances for rain-rate profile retrieval versus range are presented using numerical simulators of spaceborne radar data for the frequency pair (13.75, 24) GHz. Results point out the interest of a dual-frequency radar for future space missions. Validation tests using real data from airborne radar measurements will be presented in a future paper (Part II).