Sampling Issues in Estimating Radar Variables from Disdrometer Data

There is a long history of calculating radar variables and inferring raindrop size distribution functions from raindrop size data. In statistical terms, the usual process is the inference of characteristics of populations (the drops aloft) from measurements on samples collected at the ground (the disdrometer data). The typical procedure is just to collect the data, calculate some things, and proceed from there; questions about the uncertainties and possible biases in the results are seldom raised.

However, sampling issues are ubiquitous in using observations of raindrop size distributions to estimate bulk quantities such as rainfall rate R, radar reflectivity factor Z, specific differential phase Kdp or differential reflectivity Zdr. Sampling variability problems range from skewness in the estimates of such quantities (most of the estimates are too low and a few are too high) to mathematical correlations among the estimated variables that can mimic physical relationships among the quantities. Even if the drop size distributions are reasonably homogeneous over the sampled volumes of the atmosphere, samples comprising large numbers of drops are required to obtain good estimates of those variables. However, the samples provided by available disdrometers are often not large enough, especially in light rainfall situations, to give satisfactory results.

This paper explores the effects of raindrop sample sizes on the biases and errors in estimates of radar variables (conventional and polarimetric) from disdrometer data. Simulated sampling from known drop size distributions with known values of the radar variables provides estimates of those variables, and the associated biases and errors in those estimates, for samples of different sizes. Those biases and errors diminish as the sample sizes increase, but can remain significant even for samples of many hundreds of drops. An interesting finding is the strong relationship between the estimates of the polarimetric variables and the size of the largest drop in the sample; this relationship is evident until the samples get fairly large.