On development and comparative study of two Markov models of rainfall in the dry zone of Sri Lanka

Abstract

Being closer to the equator, the most important climatic element for agricultural production in Sri Lanka is rainfall which is erratic and highly unpredictable in nature, especially in the dry zone. This study attempts to model the weekly rainfall climatology of dry zone using Markov processes as the driving mechanism based on the 51 years of past data. The weekly occurrence of rainfall was modelled by two-state first and second order Markov chains while the amount of rainfall on a rainy week was approximated by taking random variates from the best fitted right skewed probability distribution out of Gamma, Weibull, Log-Normal and Exponential distributions. The parameters of the both models namely, elements of transition matrices, and scale and shape parameters of the desired distribution, were determined using weekly data. Both first and second Markov chains performed similarly in terms of modelling weekly rainfall occurrence and amount of rainfall if rain occurred. Use of second order Markov chain did not enhance the representativeness of the simulated data to the observed data in spite of being penalised for its large number of computations. Weekly rainfall data generated with the first-order Markov chain model preserve the statistical and seasonal characteristics that exist in the historical records.