Spatio-Temporal Rainfall Distribution and Markov Chain Analogue Year Stochastic Daily Rainfall Model in Ethiopia

Abstract

This paper aims at the spatiotemporal distribution of rainfall in Ethiopia and developing stochastic daily rainfall model. Particularly, in this study, we used a Markov Chain Analogue Year (MCAY) model that is, Markov Chain with Analogue year (AY) component is used to model the occurrence process of daily rainfall and the intensity or amount of rainfall on wet days is described using Weibull, Log normal, mixed exponential and Gamma distributions. The MCAY model best describes the occurrence process of daily rainfall, this is due to the AY component included in the MC to model the frequency of daily rainfall. Then, by combining the occurrence process model and amount process model, we developed Markov Chain Analogue Year Weibull model (MCAYWBM), Markov Chain Analogue Year Log normal model (MCAYLNM), Markov Chain Analogue Year mixed exponential model (MCAYMEM) and Markov Chain Analogue Year gamma model (MCAYGM). The performance of the models is assessed by taking daily rainfall data from 21 weather stations (ranging from 1 January 1984–31 December 2018). The data is obtained from Ethiopia National Meteorology Agency (ENMA). The result shows that MCAYWBM, MCAYMEM and MCAYGM performs very well in the simulation of daily rainfall process in Ethiopia and their performances are nearly the same with a slight difference between them compared to MCAYLNM. The mean absolute percentage error (MAPE) in the four models: MCAYGM, MCAYWBM, MAYMEM and MCAYLNM are 2.16%, 2.27%, 2.25% and 11.41% respectively. Hence, MCAYGM, MCAYWBM, MAYMEM models have shown an excellent performance compared to MCAYLNM. In general, the light tailed distributions: Weibull, gamma and mixed exponential distributions are appropriate probability distributions to model the intensity of daily rainfall in Ethiopia especially, when these distributions are combined with MCAYM.