Abstract:
It is well-known that there are significant deterministic ambiguities inherent in trying to determine the particular rain rate profile which produced some given sequence of air- or space-borne radar echo powers at a single attenuating frequency. We quantify these ambiguities mathematically, and examine their effect on various proposed rain-rate profile retrieval algorithms. When the given data consist of a single radiometer measurement together with a single-look-angle single-frequency set of range-compressed echo powers, we show that several substantially different rain profiles can realistically be considered solutions. On the other hand, if the data consist of a single-look-angle two-frequency set of echo powers, the inversion problem generically has a unique solution. We note that traditional "back-of-the-envelope" arguments can be quite misleading in assessing the extent of the ambiguity, even in the simplest cases.
