A Study of the Sampling Error in Satellite Rainfall Estimates Using Optimal Averaging of Data and a Stochastic Model

Abstract

A method of combining satellite estimates of rainfall into gridded monthly averages suitable for climatological studies is examined. Weighted averages of the satellite estimates are derived that minimize the mean squared error of the grid-box averages. A spectral model with nonlocal, scaling, diffusive behavior at small distances, tuned to tropical Atlantic (GATE) statistics, is developed to study the optimal weighting method. Using it, the effect of optimal weighting for averaging data similar to what will be provided by the Tropical Rainfall Measuring Mission (TRMM) satellite is examined. The improvement in the accuracy of the averages is found to be small except for higher-latitude grid boxes near the edges of the satellite coverage. The averages of data from a combination of TRMM and a polar orbiting instrument such as SSM/I, however, are substantially improved using the method. A simple formula for estimating sampling error for each grid box is proposed, requiring only the local rain rate and a measure of the sample volume provided by the satellite.