Prediction of annual rainfall pattern using Hidden Markov Model (HMM) in Jos, Plateau State, Nigeria

Abstract

A Hidden Markov Model (HMM) is a double stochastic process in which one of the stochastic processes is an underlying Markov chain, the other stochastic process is an observable stochastic process. Hidden Markov model is very influential in stochastic world because of its uniqueness, double stochastic nature and independence assumption between consecutive observations. A hidden Markov model to predict annual rainfall pattern has been presented in this paper. The model is developed to provide necessary information for the farmers, agronomists, water resource management scientists and policy makers to enable them plan for the uncertainty of annual rainfall. The model classified annual rainfall amount into three states, each with eight possible observations. The parameters of the model were estimated from the annual rainfall data of Jos, Plateau state, Nigeria for the period of 39 years (1977-2015). After which, the model was trained using Baum-Welch algorithm to attend maximum likelihood. The model is designed such that, if given any of the three rainfall states and its observation in the present year, it is possible to make quantitative prediction on how rainfall will be in the following year and in the subsequent years. The test HMM1 was able to make prediction with 75% accuracy in state and 50% accuracy in observations. The accuracy level of the model shows that, it is dependable and therefore, information from the model could be used as a guide to the farmers, agronomists, water resources management scientists and the government to plan strategies for crop production in the region.

Keywords: Markov model, Hidden Markov model, Transition probability, Observation probability, Crop Production, Annual Rainfall