Prediction of Weekly Rainfall Both in Discrete and Continuous Time Using Markov Model

Abstract

In this chapter, a Markov model to study weekly rainfall both in discrete and continuous time is presented. The model predicts and analyzes weekly rainfall pattern of  Makurdi, Nigeria using rainfall data of  eleven years(2005-2015). After some successful iterations of the discrete time Markov model, its stabilizes to equilibrium probabilities, revealing that   in the  long-run  22% of the weeks during rainy season in Makurdi, will  experience No rainfall, 50% will experience Low rainfall, 25% will experience Moderate rainfall and 2% will experience High rainfall. For the continuous time Markov model, It was observed that, if it is in 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 respectively 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 model 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. With the combined results of the discrete and continuous time Markov model, the rainfall pattern of the study area is better understood. These results are important information to the residents of Markudi and environmental management scientists  for effective planning and viable crop production.