Modeling the Variability of Drop Size Distributions in Space and Time

Abstract

The information on the time variability of drop size distributions (DSDs) as seen by a disdrometer is used to illustrate the structure of uncertainty in radar estimates of precipitation. Based on this, a method to generate the space?time variability of the distributions of the size of raindrops is developed. The model generates one moment of DSDs that is conditioned on another moment of DSDs; in particular, radar reflectivity Z is used to obtain rainfall rate R. Based on the fact that two moments of the DSDs are sufficient to capture most of the DSD variability, the model can be used to calculate DSDs and other moments of interest of the DSD. A deterministic component of the precipitation field is obtained from a fixed R?Z relationship. Two different components of DSD variability are added to the deterministic precipitation field. The first represents the systematic departures from the fixed R?Z relationship that are expected from different regimes of precipitation. This is generated using a simple broken-line model. The second represents the fluctuations around the R?Z relationship for a particular regime and uses a space?time multiplicative cascade model. The temporal structure of the stochastic fluctuations is investigated using disdrometer data. Assuming Taylor hypothesis, the spatial structure of the fluctuations is obtained and a stochastic model of the spatial distribution of the DSD variability is constructed. The consistency of the model is validated using concurrent radar and disdrometer data.