Improved Coupled Z-R and k-R Relations and the Resulting Ambiguities in the Determination of the Vertical Distribution of Rain from the Radar Backscatter and the Integrated Attenuation

Several algorithms to calculate a rain-rate profile from a single-frequency air-or spaceborne radar backscatter profile and a given path-integrated attenuation have been proposed. The accuracy of any such algorithm is limited by the ambiguities between the (multiple) exact solutions, which depend on the variability of the parameters in the Z-R and k-R relations used. In this study, coupled Z-R and k-R relations are derived based on the drop size distribution. It is then shown that, because of the coupling, the relative difference between the multiple mutually ambiguous rain-rate profiles solving the problem must remain acceptably low, provided the available path-integrated attenuation value is known to within 0.5 dB.