Stability of the Dual-Frequency Radar Equations and a New Method Applied to the GPM’s Dual-Frequency Precipitation Radar (DPR) Data

A new algorithm is proposed, which estimates two parameters of the particle size distribution (PSD) at each range bin from the global precipitation measurement’s (GPM’s) dual-frequency precipitation radar (DPR) data. The equation that expresses the relationship of the PSD parameters between adjacent range bins is derived. By including the attenuation effect within the bin in the discretized equation, the new algorithm alleviates the double-solution problem when attenuation within the bin is sufficiently large. The stability of the solutions to the equation depends on the value of the mean diameter
$D_{m}$
and its gradient with respect to the range in the case of liquid precipitation. There is a critical diameter above which the backward processing of the equation provides a stable or moderately diverging solution, unlike the forward processing that often gives unstable solutions. To provide a set of initial conditions without using the surface reference technique (SRT) in the backward processing, an initialization method using the Hitschfeld–Bordan (HB) attenuation correction method is proposed and tested. The proposed algorithm may provide a tool for investigating the assumptions used in various algorithms.