Intrinsic Ambiguities in the Retrieval of Rain Rates from Radar Returns at Attenuating Wavelengths

Abstract

It is well known that there are significant deterministic ambiguities inherent in trying to determine the particular rain-rate profile that produced some given sequence of air- or spaceborne radar echo powers at a single attenuating frequency. For different combinations of radar data, formulas for the mutually ambiguous solutions are derived and the resulting ambiguities are quantified mathematically. When the given data consist of a single radiometer measurement together with a single-frequency set of range-gated echo powers, it is shown that several substantially different rain profiles can still realistically be considered solutions. On the other hand, if the data consist of a two-frequency set of echo powers, it is proven that the inversion problem generically has a unique solution.