Statistical Analysis of Mesoscale Rainfall: Dependence of a Random Cascade Generator on Large-Scale Forcing

Abstract

Under the theory of independent and identically distributed random cascades, the probability distribution of the cascade generator determines the spatial and the ensemble properties of spatial rainfall. Three sets of radar-derived rainfall data in space and time are analyzed to estimate the probability distribution of the generator. A detailed comparison between instantaneous scans of spatial rainfall and simulated cascades using the scaling properties of the marginal moments is carried out. This comparison highlights important similarities and differences between the data and the random cascade theory. Differences are quantified and measured for the three datasets. Evidence is presented to show that the scaling properties of the rainfall can be captured to the first order by a random cascade with a single parameter. The dependence of this parameter on forcing by the large-scale meteorological conditions, as measured by the large-scale spatial average rain rate, is investigated for these three datasets. The data show that this dependence can be captured by a one-to-one function. Since the large-scale average rain rate can be diagnosed from the large-scale dynamics, this relationship demonstrates an important linkage between the large-scale atmospheric dynamics and the statistical cascade theory of mesoscale rainfall. Potential application of this research to parameterization of runoff from the land surface and regional flood frequency analysis is briefly discussed, and open problems for further research are presented.