Impact of assumption of log-normal distribution on monthly rainfall estimation from TMI

Abstract

The log-normal assumption for the distribution of the rain rates used for the estimation of monthly rain totals proposed in Wilheit et al 1991 was examined. Since the log-normal assumption was originally used for the SSM/I, it is now necessary to re-evaluate the assumption for estimates from TMI, which, unlike the SSM/I, has a 10 GHz channel. The minimum chi-square estimation technique was used for the log-normal method. To check the credibility of the estimation routines, log-normally distributed synthetic data were used. Using real data from the TMI, Gaussian smoothing on the rain rates was performed to get all three channels, 10, 19 and 37 GHz, to have a common resolution so that the rain histograms could be merged into a single histogram. The log-normal estimate averaged about 5% more rainfall than the direct sum method, but this could be the result of errors in the log-normal assumption. Random error involved in TMI measurement was estimated. The result showed that the log-normal assumption contributed more random error than it removed, especially when the number of rain samples was small.