A systems approach to GPM dual-frequency retrieval

A systems approach to the development of spaceborne dual-frequency radar retrievals is presented. The necessary integral equations governing the backscatter and forward scatter propagation of electromagnetic waves are redeveloped through the parameters of the drop-size distribution (DSD) namely the median drop diameter, D_o, and normalized intercept parameter N_w. The backward iteration algorithm using these equations is reviewed and cast in terms of a closed-loop control-system model with feedback on measured radar reflectivity values. This model is preferred over the fixed-point method because the closed-loop model calculates and iterates based on the input variables for measured reflectivity instead of using attenuation as a loop control variable. The closed-loop model is examined and analyzed in terms of sensitivity to measurement error and DSD parameters and is used to describe and develop the convergence region of the retrievals in the DSD space. The impact of the convergence region is evaluated to define the relative contribution of the methodology in a global sense. It is shown that about half the rainfall falls into the convergence zone demonstrated in this paper.