Markovian Model of Rainfall Pattern with Application

Abstract

In this study, we model the occurrence and length of wet, medium wet and dry spells by Markov chain that best describes the rainfall pattern of Bungoma County (Western Kenya).This is achieved by Markov chain theory and estimation of probabilities of the chain by MLE. Also computed is the distribution of the length of each spells; wet, medium wet and dry from which the central moments of the rainfall pattern are computed. The model developed is applied to rainfall data from Bungoma meteorological station. A three by three transition matrix is obtained and used to predict the weather pattern. It is observed that if everything remains constant, prediction can be certain at the twelfth year as the matrix show stationarity. The three states are recurrent, non-null and a periodic hence forming an ergodic chain. Keywords: Markov chain, Wet spell, Medium wet spell, Dry spell, Prediction, Stationary distribution