Best-Fit Probability Distribution Model for Annual Monthly Maximum Rainfall in Calabar City, Nigeria

Abstract

The choice of a suitable model that could predict the possibility of occurrence of rainfall event of a specified magnitude depends mainly on the characteristics of rainfall data at a particular site. This study was aimed at determining the best-fit probability distribution model for annual maximum monthly rainfall. Fifty years rainfall data (1969-2018) obtained from Nigerian Meteorological Agency (NIMET), Calabar, were collated to form an annual series ranked in a decreasing order of magnitude. The data were then evaluated with 6 probability distributions namely; Normal, Log-Normal, Pearson Type III, Log-Pearson Type III, Gumbel Extreme Value Type I and Log-Gumbel probability distributions. The best-fit probability distribution model at the study area was selected based on the results of 4 goodness of fit tests namely; Mean Absolute Deviation Index (MADI), Chi-Squared ) test, Root Mean Square Error (RMSE) and Relative Root Mean Square Error (RRMSE). The performance of the 6 distributions were ranked and the total scores of 8, 23, 16, 12, 21 and 4 were allocated to Normal, Log-Normal, Pearson Type III, Log-Pearson Type III, Gumbel Extreme Value Type I and Log-Gumbel probability distributions, respectively. The results indicate that the best-fit probability distribution model was Log-Normal, which was used to predict rainfall values of 566.8, 664.0, 721.6, 788.1, 834.4, 878.4, 920.7, 974.8 and 1014.4 mm for different return periods of 2, 5, 10, 25, 50, 100, 200, 500 and 1000 years, respectively. It is, therefore, recommended that Log-Normal distribution is the preferred model for frequency analysis of rainfall data for the planning and design of hydraulic structures in the study area. This is necessary for effective flood prevention and mitigation interventions.