On the Variability of Drop Size Distributions over Areas

Abstract

ast studies of the variability of drop size distributions (DSDs) have used moments of the distribution such as the mass-weighted mean drop size as proxies for the entire size distribution. In this study, however, the authors separate the total number of drops Nt from the DSD leaving the probability size distributions (PSDs); that is, DSD = Nt ? PSD. The variability of the PSDs are then considered using the frequencies of size [P(D)] values at each different drop diameter P(PD | D) over an ensemble of observations collected using a network of 21 optical disdrometers. The relative dispersions RD of P(PD | D) over all the drop diameters are used as a measure of PSD variability. An intrinsic PSD is defined as an average over one or more instruments excluding zero drop counts. It is found that variability associated with an intrinsic PSD fails to characterize its true variability over an area. It is also shown that this variability is not due to sampling limitations but rather originates for physical reasons. Furthermore, this variability increases with the expansion of the network size and with increasing drop diameter.A physical explanation is that the network acts to integrate the Fourier transform of the spatial correlation function from smaller toward larger wavelengths as the network size increases so that the contributions to the variance by all spatial wavelengths being sampled also increases. Consequently, RD and, hence, PSD variability will increase as the size of the area increases.