A Markov-Weibull rain-sum model for designing rain water catchment systems

Abstract

Rain-sum, defined as the sum of the total rain over a wet spell during a rainy season, forms a sequence which has the potential to provide the statistics for designing a rainwater catchment system. The probability density function (pdf) of the rain-sum coupled with the Poisson law of occurrence of wet spells are used as building blocks to generate the cumulative distribution function (cdf) of the largest rain-sum. This cdf can form the basis for estimating system design parameters. This study revealed that the rain-sum for kenyan environments (semi-arid and semi-humid) tends to obey Weibull distribution, while successive occurrences of wet days obey the Markov law of persistence. The process of estimating the cdf of the largest rain-sum not only provides statistics for the design of rainwater catchment systems, but also provides an alternative for identifying the pdf of the rain-sum and dependence structure in the occurrence of wet days.