Extension of GPM dual-frequency iterative retrieval method with DSD-profile constraint

A new Dual-Frequency Precipitation Radar (DPR) will be included on the Global Precipitation Measurement (GPM) core satellite which will succeed the highly successful Tropical Rainfall Measuring Mission satellite launched in 1997. New dual-frequency drop-size distribution (DSD) and rain-rate estimation algorithms are being developed to take advantage of the enhanced capabilities of the DPR. It has been shown previously that a backward-iteration algorithm can be embedded within a single-loop feedback model to retrieve the rain rate. However, the single-loop model is unable to correctly estimate DSD profiles for a significant portion of global median-volume-diameter, D_o, and normalized DSD intercept parameter, N_w, combinations in rain because of a multiple-value solution space. For the remaining D_o,N_w pairs, another retrieval method is necessary. This paper proposes a dual-loop model, in which the intercept parameter, N_w, of the DSD is constrained in its vertical profile, to guide the algorithm to correct convergence. This allows an additional constraint on the DSD values estimated by the iterative algorithm and helps to retrieve correct DSD values in the regions where the iterative approach alone fails. To demonstrate feasibility of the proposed method, three test cases representative of many DSD and profile combinations are discussed. The first case is a constant vertical profile of the DSD parameters. The second case examines linear variation of the DSD parameters, and the third case examines how measurement error affects the retrieval process. In each case, the proposed constraint on the intercept parameter is implemented, and the results are discussed. Using the constraint, the dual-loop algorithm is able to retrieve reasonable values for the DSDs and rain-rate profiles and extend the convergence region of the algorithm.