Best Fit and Selection of Probability Distribution Models for Frequency Analysis of Extreme Mean Annual Rainfall Events
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Date
2015
Journal Title
Journal ISSN
Volume Title
Publisher
Int. J. Eng. Res. Dev
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
Description
Keywords
Best-fit probability distribution function, Least sum of statistics model selection criterion (LSSMIC), Candidate model identification criterion (CMIC), Candidate probability distribution functions
Citation
Masereka, E. M., Otieno, F. A. O., Ochieng, G. M., & Snyman, J. (2015). Best fit and selection of probability distribution models for frequency analysis of extreme mean annual rainfall events. Int. J. Eng. Res. Dev, 11(4), 34-53.