Systems engineering evaluation of GPM dual-frequency retrieval algorithms

Abstract

Following the success of the Tropical Rainfall Measuring Mission (TRMM), considerable effort has been directed at the next generation of space-based precipitation radar (PR) to be launched aboard the Global Precipitation Measuring (GPM) core satellite. While the TRMM PR uses a single-frequency radar at Ku-band (13.8 GHz) to measure and map tropical precipitation, the GPM PR will employ a dual-frequency precipitation radar (DPR) at Ku and Ka-bands (13.6 and 35.6 GHz) to more accurately measure global precipitation. Systems engineering tools are used in this work to help with model and algorithm analysis. One of the retrieval algorithms being studied for use with GPM is a self-consistent, iterative, dual-frequency method that estimates drop-size-distribution (DSD) parameters, median volume diameter Do, normalized intercept parameter Nw, in each radar resolution cell or bin. From the DSD values, the rain rate in each bin is calculated. The algorithm was recast in terms of a single-loop control-system model and discovered that the single-loop method accurately retrieves the DSD values in relatively low rain-rate regions where the DSD pairs are small. When the DSD pairs are larger, the algorithm can converge properly but yield incorrect solutions. In this research, two alternative methods for DSD retrieval in those regions of incorrect convergence are presented and analyzed. The first method is a dual-loop control-system model which implicitly adds an additional system constraint on the Nw vertical profile. The second method is based on profile optimization and adds constraints on both the Do and Nw profiles and uses a non-linear optimization technique to find suitable top and bottom-bin DSD values to best fit the input reflectivity profiles. The performance of these methods is discussed in detail. It is important to know how the error in the input variables (factors) influence the output of the retrieval algorithms, and consequently which input factors are most important. Variance decomposition, a systems engineering tool based on global sensitivity analysis techniques, is used to apportion error in the output of a model to the respective input factors and allow a quantitative determination of the importance of each factor. Global sensitivity analysis performed on a TRMM-like algorithm, modelled for rainfall over both ocean and land, based on k = αZβ and R = αZb relationships, showed that at low rain rates, the error from a, b, and measured reflectivity Zm dominate. At higher rain rates, the error from the surface reference technique dominates. Sensitivity analysis performed on the GPM-profile-optimization algorithm for simulated near-vertical rainfall profiles show that the primary cause of model error is variability in the Ka-band radar signal with little variance contribution from the Ku-band signal.