A stochastic model of space-time variability of mesoscale rainfall: Statistics of spatial averages

A characteristic feature of rainfall statistics is that they depend on the space and time scales over which rain data are averaged. A previously developed spectral model of rain statistics that is designed to capture this property predicts power law scaling behavior for the second moment statistics of area-averaged rain rate on the averaging length scale L as L --> 0. In the present work a more efficient method of estimating the model parameters is presented and used to fit the model to the statistics of area-averaged rain rate derived from gridded radar precipitation data from TOGA-COARE. Statistical properties of the data and the model predictions are compared over a wide range of averaging scales. An extension of the spectral model scaling relations to describe the dependence of the average fraction of grid boxes within an area containing nonzero rain (the "`rainy area fraction") on the grid scale L is also explored.