Raindrop size distribution variability estimated using ensemble statistics

Abstract. Before radar estimates of the raindrop size distribution (DSD) can be assimilated into numerical weather prediction models, the DSD estimate must also include an uncertainty estimate. Ensemble statistics are based on using the same observations as inputs into several different models with the spread in the outputs providing an uncertainty estimate. In this study, Doppler velocity spectra from collocated vertically pointing profiling radars operating at 50 and 920 MHz were the input data for 42 different DSD retrieval models. The DSD retrieval models were perturbations of seven different DSD models (including exponential and gamma functions), two different inverse modeling methodologies (convolution or deconvolution), and three different cost functions (two spectral and one moment cost functions).

Two rain events near Darwin, Australia, were analyzed in this study producing 26 725 independent ensembles of mass-weighted mean raindrop diameter D_m and rain rate R. The mean and the standard deviation (indicated by the symbols <x> and σx) of D_m and R were estimated for each ensemble. For small ranges of <D_m> or <R>, histograms of σD_m and σR were found to be asymmetric, which prevented Gaussian statistics from being used to describe the uncertainties. Therefore, 10, 50, and 90 percentiles of σD_m and σR were used to describe the uncertainties for small intervals of <D_m> or <R>. The smallest D_m uncertainty occurred for <D_m> between 0.8 and 1.8 mm with the 90th and 50th percentiles being less than 0.15 and 0.11 mm, which correspond to relative errors of less than 20% and 15%, respectively. The uncertainty increased for smaller and larger <D_m> values. The uncertainty of R increased with <R>. While the 90th percentile uncertainty approached 0.6 mm h⁻¹ for a 2 mm h⁻¹ rain rate (30% relative error), the median uncertainty was less than 0.15 mm h⁻¹ at the same rain rate (less than 8% relative error). This study addresses retrieval error and does not attempt to quantify absolute or representativeness errors.