Estimation of mean rain rate - Application to satellite observations

A method for the estimation of the mean area average rain rate from dependent data is developed and applied to the GARP Atlantic Tropical Experiment data. The method consists of fitting a mixed distribution, containing an atom at zero, by minimum chi-square in combination with certain time-space sampling designs. In modeling the continuous component of the mixed distribution, it is shown that the lognormal distribution provides a very close fit for the nonzero area average rainrates. A comparison with the gamma distribution shows that the lognormal distribution is a better choice as expressed by the minimum chi-square criterion. Some of the time-space sampling designs correspond to satellite sampling. The results indicate that a satellite visiting an area of about 350 x 350 sq km in the tropics approximately every 10 hours over a period can provide a rather close estimate for the mean area average rain rate.