Modelling of Extreme maximum Rainfall using Extreme Value Theory for Tanzania (original) (raw)
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STATISTICAL MODELLING OF ANNUAL MAXIMUM RAINFALL FOR BOTSWANA USING EXTREME VALUE THEORY
IASET, 2019
The objective of this paper is to find the best-fit probability model for annual maximum rainfall data for Botswana for the period January 1901 to December 2012. The Kwiatkowski-Philips-Schmidt-Shin test of stationarity on the data shows that the time series is stationary. Based on visual inspection of the generalized quantile plot, three extreme value probability distributions are considered, belonging to the Gumbel and Frechet maximum domains of attraction: the gamma, lognormal and BurrXII. The maximum likelihood method is used to estimate the parameters of each distribution under study. The empirical CDF plots and Q-Q plots of the data show that the three models are highly competitive in terms of goodness-of-fit. Formal model assessment criteria, namely, the Anderson-Darling test and the Bayesian Information Criterion agree on the ranking of the three models: the lognormal distribution gives the best fit to the data followed closely by the gamma whilst the BurrXII distribution comes a distant third.
Modeling Extreme Rainfall in Kaduna Using the Generalised Extreme Value Distribution
Science World Journal, 2020
An important statistical distribution use in modeling such extreme events is the generalized extreme value distribution while the generalized Pareto distribution is suitable in modeling threshold excesses of extreme values. In this study, monthly rainfall data from the Nigeria Meteorological Agency in Kaduna are fitted to the generalized extreme value distribution and for a suitable threshold of 251mm, threshold excesses were fitted to the generalized Pareto distribution and a return level computed for 25, 50 and 100 years return period respectively. The threshold excesses follow the Weibull distribution and are bounded above implying that there is a finite value which the maximum above the threshold cannot exceed. For the 25, 50 and 100 years return period, a return level of 350mm, 390mm and 490mm with probability of exceedances of 0.04, 0.02 and 0.01 respectively were observed. The result further show that with the increasing level of rainfall as return period increases, there is ...
Application of Extreme Value Theory in Predicting Climate Change Induced Extreme Rainfall in Kenya
International Journal of Statistics and Probability, 2019
Climate change has brought about unprecedented new weather patterns, one of which is changes in extreme rainfall. In Kenya, heavy rains and severe flash floods have left people dead and displaced hundreds from their settlements. In order to build a resilient society and achieve sustainable development, it is paramount that adequate inference about extreme rainfall be made. To this end, this research modelled and predicted extreme rainfall events in Kenya using Extreme Value Theory for rainfall data from 1901-2016. Maximum Likelihood Estimation was used to estimate the model parameters and block maxima approach was used to fit the Generalized Extreme Value Distribution (GEVD) while the Peak Over Threshold method was used to fit the Generalized Pareto Distribution (GPD). The Gumbel distribution was found to be the optimal model from the GEVD while the Exponential distribution gave the optimal model over the threshold value. Furthermore, prediction for the return periods of 10, 20, 50 ...
An important statistical distribution use in modeling such extreme events is the generalized extreme value distribution while the generalized Pareto distribution is suitable in modeling threshold excesses of extreme values. In this study, monthly rainfall data from the Nigeria Meteorological Agency in Kaduna are fitted to the generalized extreme value distribution and for a suitable threshold of 251mm, threshold excesses were fitted to the generalized Pareto distribution and a return level computed for 25, 50 and 100 years return period respectively. The threshold excesses follow the Weibull distribution and are bounded above implying that there is a finite value which the maximum above the threshold cannot exceed. For the 25, 50 and 100 years return period, a return level of 350mm, 390mm and 490mm with probability of exceedances of 0.04, 0.02 and 0.01 respectively were observed. The result further show that with the increasing level of rainfall as return period increases, there is a high likelihood of monthly maximum rainfall increasing steadily over the years and this has great consequences on the environment. If this trend continues unchecked as a result of global warming, residents will continue to experience flood unless the government build more drainages and ensure that existing drainages are free from dirt to enhance proper channeling and free flow of water in the event of rainfall.
International Journal of Statistical Distributions and Applications
Extreme rainfall events have caused significant damage to agriculture, ecology and infrastructure, disruption of human activities, injury and loss of life. They have also significant social, economical and environmental consequences because they considerably damage urban as well as rural areas. Early detection of extreme maximum rainfall helps to implement strategies and measures, before they occur. Extreme value theory has been used widely in modelling extreme rainfall and in various disciplines, such as financial markets, insurance industry, failure cases. Climatic extremes have been analysed by using either generalized extreme value (GEV) or generalized Pareto (GP) distributions which provides evidence of the importance of modelling extreme rainfall from different regions of the world. In this paper, we focus on Peak Over Thresholds approach where the Poisson-generalized Pareto distribution is considered as the proper distribution for the study of the exceedances. This research considers also use of the generalized Pareto (GP) distribution with a Poisson model for arrivals to describe peaks over a threshold. The research used statistical techniques to fit models that used to predict extreme rainfall in Tanzania. The results indicate that the proposed Poisson-GP distribution provide a better fit to maximum monthly rainfall data. Further, the Poisson-GP models are able to estimate various return levels. Research found also a slowly increase in return levels for maximum monthly rainfall for higher return periods and further the intervals are increasingly wider as the return period is increasing.
Revista Brasileira de Ciências Ambientais, 2021
Extreme rain events can cause social and economic impacts in various sectors. Knowing the risk of occurrences of extreme events is fundamental for the establishment of mitigation measures and for risk management. The analysis of frequencies of historical series of observed rain through theoretical probability distributions is the most commonly used method. The generalized extreme value (GEV) and Gumbel probability distributions stand out among those applied to estimate the maximum daily rainfall. The indication of the best distribution depends on characteristics of the data series used to adjust parameters and criteria used for selection. This study compares GEV and Gumbel distributions and analyzes different criteria used to select the best distribution. We used 224 series of annual maximums of rainfall stations in Santa Catarina (Brazil), with sizes between 12 and 90 years and asymmetry coefficient ranging from -0.277 to 3.917. We used the Anderson–Darling, Kolmogorov-Smirnov (KS)...
Estimating the exceedance probability of extreme rainfalls up to the probable maximum precipitation
Journal of Hydrology, 2016
The Akosombo dam is a major source of electric energy in Ghana. Considering the current increase in the demand for electricity in the country, where such an increase in demand implies more pressure on the dam, it is of key interest to study the tail behaviour of the water levels of the dam. Such a study is important because the level of water in the dam determines the amount of electricity generated. The study employed the Univariate Extreme Value Theory to model the monthly maximum and minimum water levels of the dam. The Generalized Extreme Value Distribution was fitted to the data and the Maximum likelihood estimation method was employed to estimate the model parameters. The study indicated that, the water levels cannot fall below 226.00ft which is the critical water level of the Akosombo dam. It further showed that, the lowest ever level of water the dam can attain is 226.69ft and the highest 279.07ft. The study also found that, though the water cannot fall below the critical level, there was evidence of its falling below the minimum operation head.
Modelling extreme rainfall with Block Maxima and Peak-Over Threshold methods in Rwanda
Research Square (Research Square), 2022
In this study two fundamental approaches of extreme value theory (EVT) were applied on the extreme precipitation incidents over twelve synoptic stations of Rwanda: the Block Maxima (BM) and the Peak-Over Threshold (POT). Annual maximum rainfall series (AMS) and partial duration rainfall series (PDS) higher than a selected threshold were fitted respectively to the Generalized Extreme Value (GEV) distribution and the Generalized Pareto (GP) distribution at each station. Four methods were used for the estimation of the parameters of the GEV and the GP distributions: the Maximum Likelihood Estimation (MLE) method, the L-Moments Estimation (LME) method, the Bayesian Estimation (BAYE) method and the Generalized Maximum Likelihood Estimation (GMLE) method. The performances of those methods were analyzed and compared for best fitting the data based on goodness-of-fit tests. It was found that in general, those methods are suitable for the two distributions at the sites considered in Rwanda with slight differences in estimated return levels and their confidence intervals. However, the MLE and LME methods perform better than the other methods for the GEV distributions whereas for the GP distribution it is the BAYE method. Return levels of extreme rainfalls with their 95% confidence intervals were computed for return periods of 10, 20, 50, 75, 100, 150 and 200 years. It was found that using the selected parameterization methods, the GP distribution presents higher return levels than GEV distribution for all stations Those methods can therefore be recommended as best parametric methods for estimating extreme rainfall in Rwanda using EVT.
Extreme Value Modeling and Prediction of Extreme Rainfall: A Case Study of Penang
2010
This paper aims to study the suitability of modeling and predicting extreme rainfall events using only ten years of data. Fitting monthly and half-yearly maximum daily rainfall values to the Generalized Extreme Value (GEV) distribution and fitting rainfall values which exceed a certain threshold to the Generalized Pareto (GP) distribution are used. The parameters are estimated and the tests for stationarity and seasonality are performed. Result shows monthly and half-yearly maximum converges to the GEV distribution and declustering improves the fit to the GP distribution. Return levels estimated using monthly maximum is higher than half-yearly maximum, while return levels from GEV is higher than GP. The return level estimated shows rainfall amount will exceed the maximum rainfall observed in the ten years rainfall data in five years time.
The analysis of 27 years rainfall data of Kumulur region was conducted using two types of probability distributions, viz Gumbel distribution and generalised extreme value distribution. The method of L-moments was used for the analysis. Annual one day maximum and 2, 3,4, 5 and 7 consecutive days maximum rainfall data for 27 years was analysed and the return levels for 2, 5, 10 and 25-years were calculated using the proposed probability distribution functions. Chisquare test was conducted for comparison of the observed and expected return levels obtained using both the distributions. The statistical analysis revealed that, the annual maxima rainfall data for one day maxima and consecutive days maxima of Kumulur region fits best with the generalised extreme value distribution.