Thesis (M.Sc. (Statistics)) -- University of Limpopo, 2020 / Several studies indicated a growing trend in terms of frequency and severity
of extreme events. Extreme rainfall could cause disasters that lead to loss of
property and life. The aim of the study was to model the monthly rainfall
variability in selected provinces of South Africa using extreme value distributions.
This study investigated the best-fit probability distributions in the
five provinces of South Africa. Five probability distributions: gamma, Gumbel,
log-normal, Pareto and Weibull, were fitted and the best was selected
from the five distributions for each province. Parameters of these distributions
were estimated by the method of maximum likelihood estimators. Based
on the Akaike information criteria (AIC) and Bayesian information criteria
(BIC), the Weibull distribution was found to be the best-fit probability distribution
for Eastern Cape, KwaZulu-Natal, Limpopo and Mpumalanga, while
in Gauteng the best-fit probability distribution was found to be the gamma
distribution. Monthly rainfall trends detected using the Mann–Kendall test
revealed significant monotonic decreasing long-term trend for Eastern Cape,
Gauteng and KwaZulu-Natal, and insignificant monotonic decreasing longterm
trends for Limpopo and Mpumalanga. Non-stationary generalised extreme
value distribution (GEVD) and non-stationary generalized Pareto distribution
(GPD) were applied to model monthly rainfall data. The deviance
statistic and likelihood ratio test (LRT) were used to select the most appropriate
model. Model fitting supported stationary GEVD model for Eastern Cape,
Gauteng and KwaZulu-Natal. On the other hand, model fitting supported
non-stationary GEVD models for maximum monthly rainfall with nonlinear
quadratic trend in the location parameter and a linear trend in the scale parameter
for Limpopo, while in Mpumalanga the non-stationary GEVD model,
which has a nonlinear quadratic trend in the scale parameter and no variation
in the location parameter fitted well to the maximum monthly rainfall data.
Results from the non-stationary GPD models showed that inclusion of the time
covariate in our models was not significant for Eastern Cape, hence the bestfit
model was the stationary GPD model. Furthermore, the non-stationary
GPD model with a linear trend in the scale parameter provided the best-fit
for KwaZulu-Natal and Mpumalanga, while in Gauteng and Limpopo the nonstationary
GPD model with a nonlinear quadratic trend in the scale parameter
fitted well to the monthly rainfall data. Lastly, GPD with time-varying
thresholds was applied to model monthly rainfall excesses, where a penalised
regression cubic smoothing spline was used as a time-varying threshold and
the GPD model was fitted to cluster maxima. The estimate of the shape parameter
showed that the Weibull family of distributions is appropriate in modelling
the upper tail of the distribution for Limpopo and Mpumalanga, while for Eastern
Cape, Gauteng and KwaZulu-Natal, the exponential family of distributions
was found to be appropriate in modelling the upper tail of the distribution. The
dissertation contributes positively to the body of knowledge in extreme value
theory application to rainfall data and makes recommendations to the government
agencies on the long-term rainfall variability and their negative impact
on the economy.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:ul/oai:ulspace.ul.ac.za:10386/3457 |
| Date | January 2021 |
| Creators | Masingi, Vusi Ntiyiso. |
| Contributors | Maposa, D., Lesaoana, M. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | xvi, 138 leaves |
| Relation |
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