Best Fit and Selection of Probability Distribution Models for Frequency Analysis of Extreme Mean Annual Rainfall Events

Abstract

Frequency analysis of extreme low mean annual rainfall events is important to water resource planners at catchment level because mean annual rainfall is an important parameter in determining mean annual runoff. Mean annual runoff is an important input in determining surface water available for water resource infrastructure development. In order to carry out frequency analysis of extreme low mean annual rainfall events, it is necessary to identify the best fit probability distribution models (PDMs) for the frequency analysis. The primary objective of the study was to develop two model identification criteria. The first criterion was developed to identify candidate probability distribution models from which the best fit probability distribution models were identified. The second criterion was applied to select the best fit probability distribution models from the candidate models. The secondary objectives were: to apply the developed criteria to identify the candidate and best fit probability distribution models and carry out frequency analysis of extreme low mean annual rainfall events in the Sabie river catchment which is one of water deficit catchments in South Africa. Although not directly correlated, mean annual rainfall determines mean annual runoff at catchment level. Therefore frequency analysis of mean annual rainfall events is important part of estimating mean annual runoff events at catchment level. From estimated annual runoff figures water resource available at catchment level can be estimated. This makes mean annual rainfall modeling important for water resource planning and management at catchment level. The two model identification criteria which were developed are: Candidate Model Identification Criterion (CMIC) and Least Sum of Statistics Model Identification Criterion (LSSMIC). CMIC and LSSMIC were applied to identify candidate models and best fit models for frequency analysis of distribution of extreme low mean annual rainfall events of the 8 rainfall zones in the Sabie river catchment. The mean annual rainfall data for the period 1920-2004 obtained from the Water Research Commission of South Africa was used in this study. Points below threshold method (PBTM) was applied to obtain the samples of extreme low mean annual rainfall events from each of the 8 rainfall zones. The long term mean of 85 years of each of the 8 rainfall zones was chosen as the threshold. The identification of the best-fit models for frequency analysis of extreme low mean annual rainfall events in each of the 8 rainfall zones was carried out in 2 stages. Stage 1 was the application of CMIC to identify candidate models. Stage 2 was the application of LSSMIC to identify the best fit models from the candidate models. The performance of CMIC and LSSMIC was assessed by application of Probability-Probability (P-P) plots. Although P-P plot results cannot be considered completely conclusive, CMIC and LSSMIC criteria make useful tools as model selection method for frequency analysis of extreme mean annual rainfall events. The results from the application of CMIC and LSSMIC showed that the best fit models for frequency analysis of extreme low mean annual rainfall events in the Sabie river catchment are; Log Pearson 3, Generalised Logistic and Extreme Generalised Value.