Evaluation of the GPM Scheme for Handling Drop Size Distributions

 

Williams et al. (JAMC, 2014, pp. 1282-1296) described a new approach to handling drop-size distributions (DSDs) for use with the Global Precipitation Measurement (GPM) dual-frequency radar system. Novel features include a generic form of the DSD function n(D) with no requirement to specify a mathematical form such as gamma or lognormal; use of the standard deviation σ_m of the drop mass distribution as one of the three parameters (the other two being a normalized concentration coefficient N_w and the mass-weighted mean diameter D_m); and a statistically robust scheme for finding an empirical relationship between σ_m and D_m so that the two radar measurements are sufficient to determine the needed DSD characteristics.

This poster will present an evaluation of their approach, in two parts. The first part is a mathematical analysis showing that the approach is in essence another moment method for estimating DSD parameters from disdrometer data. As such, it is subject to the biases and errors inherent in all moment methods (as illustrated in our earlier papers). It uses the third, fourth and fifth moments of the disdrometer-sampled DSDs, so on that score it is not a particularly good moment method. When the form of the DSD function is specified, it is inferior (like all moment methods) to the maximum likelihood technique for fitting parameters to sampled data. The second part of this work is a series of sampling simulations to illustrate the biases and errors involved in applying the Williams et al. scheme to gamma DSDs. The scheme tends to underestimate the width σ_m of the distribution, and consequently to overestimate the gamma shape parameter - with large RMS errors. As previously shown, it also underestimates D_m and overestimates N_w. Comparison with maximum likelihood estimates shows the degree of improvement in the estimates that could be obtained.

In application to the GPM situation, the lack of a requirement to specify the form of the DSD function can be an asset that may help to counterbalance the difficulty with biases and errors in the parameter estimates. Nevertheless, users of the Williams et al. approach should be cognizant of the biases and errors that can occur. The simulations presented here are not configured to deal with their method for finding relationships between the DSD parameters.