A Bayesian Method for Upsizing Single Disdrometer Drop Size Counts for Rain Physics Studies and Areal Applications

Abstract

A time or spatial series of drop counts is but one realization of a multiple stochastic process. In this paper, a method is presented that extracts more of the information contained in the time series of 1-min Joss-Waldvogel disdrometer counts in rain than a simple analysis of the magnitudes of the counts would provide. This is done by greatly increasing the size of a data set using a Bayesian analysis of drop count measurements in 17 size bins. Using the empirical copula statistical technique of probability density function transformations, a 1391-min time series of drop counts was expanded to the equivalent of 40 000 min. This dramatic increase in sample size permits a deeper characterization of the rain. Using this single disdrometer, it also allows one to translate these counts into a 200 × 200 grid filled at each point with drop size distributions of mean drop concentrations consistent with the observed statistical properties of the rain. Such a field can be used for remote sensing studies of the effect of partial beam filling and for algorithm development. Moreover, since there is nothing unique to this set of drop counts, this approach can be applied to any other set of count data, including snow and clouds.