BAYESIAN OPTIMAL BLENDING AND CREDIBLE INTERVAL ESTIMATION FOR SATELLITE AND GROUND RAINFALL OBSERVATIONS

Abstract

This paper introduces a Bayesian approach to blending rainfall observations from both satellite remote sensing and ground rain gauges and to estimating errors of the blended data in terms of credible interval. The Bayesian posterior estimate (BPE) approach treats one observation as prior information and uses another observation as likelihood function information and as a correction. The BPE is an alternative to the minimum mean square estimate (MMSE) approach, also known as the least square approach. The posterior estimate outputs a probability density function (PDF), while the MMSE approach yields only an estimated mean and mean square error (MSE). When a diffusive rain rate model is assumed, the sampling errors of the Tropical Rainfall Measuring Mission (TRMM) satellite and a regular array of ground rain gauges are calculated under assumptions of idealized conditions: homogenous statistical properties of the rain rate, and flush visits of TRMM approximately twice a day. The optimal blend of the TRMM and ground gauges is determined by the optimal weight for each. The weight for the rain gauges wgis a nonlinear function of the ratio of the space gap to the time gap. The error of the blended product increases as the gaps of time and space samplings expand, and the increase is almost linear when neither time gap nor space gap is small, but becomes strongly nonlinear when the space gap is very small. Our results are helpful in the design of appropriate sampling strategies for rainfall measurements.