Application of Markov Model in Continuous Time for the Analysis and Prediction of Weekly Rainfall Pattern

Abstract

A stochastic process whose future state depends on the present state and not on the past state is a Markov chain. This principle was used to formulate a four state stochastic model in continuous time. The model is developed to analyze and predict weekly rainfall pattern of Makurdi in continuous time to enable the inhabitants to plan for the uncertainty of rainfall. The parameters of the model were estimated from weekly rainfall amount of Makurdi, Benue state, Nigeria for a period of eleven years(2005-2015). It was observed that if it is no rainfall state in a given week, it would take at most 49%,27% and 16% of the time to make a transition to low rainfall , moderate rainfall, and high rainfall in the far future. Thus given the rainfall in a week, it is possible to determine quantitatively the probability of finding weekly rainfall in other states in the following week and in the long run. The transition probability matrix, also reveals that , a week of high rainfall cannot be followed by another week of high rainfall , a week of high rainfall cannot be followed by a week of no rainfall and a week of moderate rainfall cannot precede a week of high rainfall. These results are important information to the residents of Makurdi and environmental management scientists to plan for the uncertainty of rainfall, for effective and viable production.