Extreme Value Modelling of Rainfall Using Poisson-generalized Pareto Distribution: A Case Study Tanzania (original) (raw)
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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 ...
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.
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.
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 ...
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.
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.
Modelling of Extreme maximum Rainfall using Extreme Value Theory for Tanzania
2016
A series of rainfall data over 31 years in the period 1961-2014 and 1984-2014 recorded at fourteen different stations in Tanzania is modelled using Extreme Value Theory. In order to reduce destruction and loss of life and property, it is necessary to make proper inference about extreme rainfall. The main goal of this study was to determine the best fitting distribution to the extreme daily rainfall based for each station, while considering b o t h s t a t i o n a r y and non-stationary processes. The model parameters were estimated and predicted the extreme rainfall return periods and their confidence intervals. The evidences of non-stationary for Dar es Salaam region and stationary for the remaining stat ions were found. The model fit suggest that, the Gumbel distribution provides the most appropriate model for the annual maximums of daily rainfall and the Exponential distribution gives the reasonable model for the daily rainfall data over the threshold value of 99\% for all statio...
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...