Probability Distribution of Daily Rainfall Pattern over Some Selected Stations in North Western Nigeria
I. Garba *
Department of Meteorology and Climate Science, Federal University of Technology, Akure, Nigeria and Nigeria Meteorological Agency, Abuja, Nigeria.
A. Akinbobola
Department of Meteorology and Climate Science, Federal University of Technology, Akure, Nigeria.
E. C. Okogbue
Department of Meteorology and Climate Science, Federal University of Technology, Akure, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Analysis of rainfall distribution is important in studying the impact of changing weather and climate on water resources planning and management. This study assessed the performance of three different probability distribution models, namely: Generalized Extreme Value Distribution (GEV), Lognormal Distribution (LNG) and Gumbel (EV1) Distribution to describe the rainfall distribution patterns in some selected stations (Gusau, Yelwa and Sokoto) in North-Western Nigeria. Thirty years of daily rainfall data for the period of (1985-2014) for the selected stations were obtained from the archives of the Nigerian Meteorological Agency (NIMET), Abuja. The aim of the study is to determine the distribution model that best describes the distribution of daily precipitation in North-Western Nigeria and also to identify the effect of plotting position on existing models. Root mean square error (RMSE) was used to determine the efficiency of the different plotting formulae on the existing model. The model performance was evaluated based on the statistical goodness of fit test, namely Kolmogorov-Smirnov (KS) at 95% (α=0.05) significant level. The method of moment (MOM), Probability weight-moment and maximum of likelihood were used for estimating the models parameters. The result shows that the probability distribution model that best fit the data based on statistical of goodness of fit test is the EV1 followed by LNG then GEV. The EV1 model gave the smallest value of KS test for all stations except Gusau station where LNG model was the most suitable. The best plotting position formula with the entire distribution model was also observed to be the Weibull plotting position formula followed by Chegodayev, Gringoten and Hazen plotting position respectively. Hazen plotting position gave minimal errors with the EV1 and GEV probability distributions, while Weibull gave a minimal error with the LNG probability distribution for all the stations. The EV1 model was found to be the most suitable distribution for modelling the daily rainfall distribution in two out of the three stations investigated, while the LNG was observed to be only suitable for Gusau. The result of this work has provided information on rainfall probabilities as a vital tool for the design of water supply and supplemental irrigation schemes and the evaluation of alternative cropping and of soil water management plans.
Keywords: Daily rainfall, probability distribution, plotting position, generalized extreme value, Gumbel, Log-normal, goodness of fit, Sokoto, Gusau and Yelwa.