Modeling Extreme Rainfall in Kaduna Using the Generalised Extreme Value Distribution (original) (raw)
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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.
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.
Applied Mathematical Sciences
Most extreme hydrological events cause severe human and material damage, such as floods and landslides. Extreme rainfall is usually defined as the maximum daily rainfall within each year. In this study, the annual maximum daily rainfalls from 1990 to 2007 are modeled for a station rainfal in Pekanbaru city. The threeparameter generalized extrem value (GEV) and generalizd Pareto (GP) distribution are considered to analized the extrem events. The paramters of these distributions are determined using L-moment method (LMOM). The goodness-offit (GOF) betwen empirical data and theorical distribution are then evaluated. The result shows that GEV provide best fit for station rainfall in Pekanbaru city. Based on the model that have been identified, the return levels of the GEV distribution for station rainfall and their 95% confidence interval are provided. In addition, the return period is also calculated based on the best model in this study, we can reasonably predict the risks associated the extreme event for various return periods. 70 Wenny Susanti et al.
Threshold Excess Analysis of Ikeja Monthly Rainfall in Nigeria
Ikeja in Lagos State was one of the major towns in Nigeria that was struck by the 2012 flooding with a devastating economic effect. However, among other major causes of this natural disaster was extreme rainfall. This paper therefore, focuses on extreme value analysis of the Ikeja monthly rainfall (January, 1980 to December, 2012 obtained from the Central Bank of Nigeria (CBN) official website. The set of data shows a very significant periodicity and strong departure from normality. The Generalized Pareto (GP) distribution was adequately fitted to the threshold excesses of the seasonally differenced rainfall data, the shape parameter ΞΎ is not significantly different from zero, and the diagnostic plots did not give any doubt on the goodness of fit of the fitted GP model. The results obtained could serve as a guide to stakeholders in weather and climatic management.
Environment and Ecology Research, 2024
Extreme rainfall events often result in destructive weather conditions, as they frequently lead to flooding. The assessment of return levels, which represent the maximum rainfall that is expected to be exceeded within a given time frame, is crucial for effective flood planning. This study aims to compare the accuracy of return level estimations using two statistical distributions: the stationary Generalized Extreme Value distribution (GEVD) and the stationary Generalized Pareto distribution (GPD). The analysis utilized daily rainfall data from Makassar city, obtained at the Hasanuddin rain gauge station, spanning the period from 1980 to 2022. Two approaches were employed to assess the accuracy of return level estimation: the block maxima (BM) approach with GEVD and the peaks over threshold (POT) approach with GPD. Return levels were estimated for return periods of 2, 3, 4, and 5 years. The root mean square error (RMSE) was used as a metric for comparing the accuracy of the two models. The findings indicate that the GPD outperforms the GEVD in predicting the return level of extreme rainfall for each return period in Makassar city. Furthermore, the study predicts the maximum rainfall expected in the following year. In 2023, based on the GEVD, the maximum rainfall is projected to exceed 144,675 mm/day with a 50% chance of occurrence, while based on the GPD, it is expected to surpass 167,320 mm/day with a 14% chance of occurrence. These predictions provide valuable insights for understanding the potential severity of extreme rainfall events and can assist in planning and managing flood risks in Makassar city.
2016
Extreme value theory (EVT) is a method developed to study extreme events. This method focuses on the behavior of the tail distribution to determine the probability of extreme values. EVT are becoming widely used in various fields of science, such as hydrology, climatology, insurance, and finance. There are two methods to identifying extreme value, Block Maxima (BM) and Peaks Over Threshold (POT). In the case of the univariate approach each methods are follow the Generalized Extreme Value distribution (GEV) and Generalized Pareto Distribution (GPD). Fawcett and Walshaw (2008) defines multivariate extreme as extreme events of a particular variable at several nearby locations (e.g. rainfall over a network of sites). One approach used is based on threshold excess models using bivariate threshold called the Bivariate Generalized Pareto Distribution (BGPD) methods. In this study it will be used BGPD methods with parameter estimation using Maximum Likelihood Estimation, which is then used ...
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.
Trends in Sciences
This paper presents an extension of the generalized extreme value (GEV) distribution, based on the T-X family of distributions: Gompertz-generated family of distributions that make the existing distribution more flexible called the Gompertz-general extreme value (Go-GEV) distribution. Some properties of the proposed distribution are introduced, and a new distribution is applied to actual data, namely rainfall in Lopburi Province, by comparing the proposed model with the traditional GEV distribution and estimating the return levels of the rainfall in Lopburi Province. Results showed that the Go-GEV was an alternative flexible distribution for extreme values that fitted with actual data and described the maximum rainfall better than the traditional GEV distribution. The probability density functions of the Go-GEV distribution had various shapes including left-skewed, right-skewed and close to symmetric. Estimation of the return levels of rainfall values in Lopburi Province by the Go-G...
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.