Abstract
We modelled the mean annual rainfall for data recorded in Zimbabwe from 1901 to 2009. Extreme value theory was used to estimate the probabilities of meteorological droughts. Droughts can be viewed as extreme events which go beyond and/or below normal rainfall occurrences, such as exceptionally low mean annual rainfall. The duality between the distribution of the minima and maxima was exploited and used to fit the generalised extreme value distribution (GEVD) to the data and hence find probabilities of extreme low levels of mean annual rainfall. The augmented Dickey Fuller test confirmed that rainfall data were stationary, while the normal quantile-quantile plot indicated that rainfall data deviated from the normality assumption at both ends of the tails of the distribution. The maximum likelihood estimation method and the Bayesian approach were used to find the parameters of the GEVD. The Kolmogorov–Smirnov and Anderson–Darling goodnessof- fit tests showed that the Weibull class of distributions was a good fit to the minima mean annual rainfall using the maximum likelihood estimation method. The mean return period estimate of a meteorological drought using the threshold value of mean annual rainfall of 473 mm was 8 years. This implies that if in the year there is a meteorological drought then another drought of the same intensity or greater is expected after 8 years. It is expected that the use of Bayesian inference may better quantify the level of uncertainty associated with the GEVD parameter estimates than with the maximum likelihood estimation method. The Markov chain Monte Carlo algorithm for the GEVD was applied to construct the model parameter estimates using the Bayesian approach. These findings are significant because results based on non-informative priors (Bayesian method) and the maximum likelihood method approach are expected to be similar.
Highlights
Extreme low rainfall attributed to global warming, rare, is a natural phenomenon that affects people’s socio-economic activities worldwide
Droughts can be viewed as extreme events outside of the normal rainfall occurrences, such as exceptionally lower amounts of mean annual rainfall.[2]
The extreme value theorem provides a theoretical framework to model the distribution of extreme events and the three-parameter generalised extreme value distribution (GEVD) was recommended for meteorology frequency analysis.[17]
Summary
Extreme low rainfall attributed to global warming, rare, is a natural phenomenon that affects people’s socio-economic activities worldwide. Extreme droughts occur from time to time in Zimbabwe, and impact negatively on the country’s economic performance. The drought of rainfall season year 1991/1992 was one of the worst in the recorded history of Zimbabwe. Its impact was felt even in the insurance industry which received high claims for crop failure.[1] Droughts can be viewed as extreme events outside of the normal rainfall occurrences, such as exceptionally lower amounts of mean annual rainfall.[2] In Zimbabwe, at least 50% of the gross domestic product is derived from rain-fed agriculture.[3] With more low technology indigenous farmers entering commercial agriculture through the accelerated land-reform programme, modelling and prediction of extreme low annual rainfall and the associated probabilities of drought become more relevant
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