Abstract
Abstract In this paper, the delta function is introduced to describe the observed rainfall-rate distribution including the mixture of discrete and continuous parts. Thus the observed rainfall-rate distribution can be expressed as a simple mathematical formula. Also the probability density function (pdf) of frontal rainfall in the region of the United Kingdom is investigated. It is found that the pdf during the period of 26 January–25 February 1990 can be fitted well by the lognormal distribution, and there is a linear correlation between the mean and the standard deviation of rainfall-rate pdf during this period. The GARP Atlantic Tropical Experiment (GATE) data for pixel sizes of 4.0 and 40.0 km are also analyzed in this paper. It is also found that both mean and standard deviation decrease with the increment of the observing pixel size. Based on the rainfall-rate distribution formula; the research results of Kedem et al. regarding modeling the rain-rate pdf as lognormal, gamma, and inverse Gaussian; the...
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