Estimation of Monthly Rainfall over Oceans from Truncated Rain-Rate Samples: Application to SSM/I Data

Abstract

A physical?statistical monthly rainfall retrieval algorithm has been developed using multichannel brightness temperatures from the Special Sensor Microwave/Imager (SSM/I). Since an emission-based retrieval algorithm gives the most physically direct estimation of rainfall over oceans, instantaneous rain rates are retrieved using brightness temperature?rain rate (T?R) relationships derived from a radiative transfer model. The retrieved rain rates, however, are only reliable and useful over a portion of a whole dynamic range of rain rate due to limitations of the emission-based algorithm. When monthly rainfall in a 5° ? 5° box is estimated, the instantaneous rain-rate samples are actually truncated. The method used in this study assumes that monthly rainfall intensity in a 5° ? 5° box has a mixed lognormal distribution. Thus, the contribution of the rain rates outside of the dynamic range can be estimated by extrapolation. Coefficients of the mixed lognormal distribution are determined by fitting the truncated rain-rate samples to the lognormal form using a maximum likelihood estimate method. The beamfilling error is corrected by a multiplicative factor generated from simulation studies. Comparison between the monthly rainfall estimated from the SSM/I and Pacific atoll data indicates that the algorithm works very well in tropical areas. Although this algorithm is tested on SSM/I data, it is also suited for the Tropical Rainfall Measuring Mission data, which should have a larger dynamic range with 10.7-GHz channels added.