Simulation of the Kenyan longest dry and wet spells and the largest rain-sums using a Markov model

Abstract

In general, the dry and wet spells during a rainy season tend to persist and can be modelled using a Markov (order 1) process. The stochastic behaviour of the longest dry and wet spells can be predicted using the theory of runs, Poisson probability density function of the occurrence of spells, geometric distribution of the length of spells and the Weibull distribution of total rain over a wet spell (designated as rain-sum). The entire analysis can be carried out using only five parameters, namely, the probability of any day being a dry day (q), the probability of a dry day followed by the previous dry day (qq), the probability of a wet day followed by the previous wet day (pp), the mean (μ) and variance (σ2) of the daily rainfall sequences during a rainy season. The aforesaid modelling technique adequately simulated the length of the longest dry and wet spells, and the largest rain-sums for Kabete (semihumid) and Kibwezi (semiarid) in Kenya, East Africa. Rainfall in Kenya is generally characterized by a bimodal distribution with the short rains during November-December and long rains in March-May. A major application of the longest dry spell analysis is to predict extended drought durations during the growing season which forms a basis for planning the crop production strategies. The largest rain-sum analysis forms one criterion of designing rainwater catchment systems. The graphical comparison of cumulative distribution function of the simulated longest dry and wet spells with observed ones provides a powerful way of affirming the Markov persistence as against a customary chi-square test involving transitional probability matrices.