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1.
Abstract

Heavy rainfall events often occur in southern French Mediterranean regions during the autumn, leading to catastrophic flood events. A non-stationary peaks-over-threshold (POT) model with climatic covariates for these heavy rainfall events is developed herein. A regional sample of events exceeding the threshold of 100 mm/d is built using daily precipitation data recorded at 44 stations over the period 1958–2008. The POT model combines a Poisson distribution for the occurrence and a generalized Pareto distribution for the magnitude of the heavy rainfall events. The selected covariates are the seasonal occurrence of southern circulation patterns for the Poisson distribution parameter, and monthly air temperature for the generalized Pareto distribution scale parameter. According to the deviance test, the non-stationary model provides a better fit to the data than a classical stationary model. Such a model incorporating climatic covariates instead of time allows one to re-evaluate the risk of extreme precipitation on a monthly and seasonal basis, and can also be used with climate model outputs to produce future scenarios. Existing scenarios of the future changes projected for the covariates included in the model are tested to evaluate the possible future changes on extreme precipitation quantiles in the study area.

Editor Z.W. Kundzewicz; Associate editor K. Hamed

Citation Tramblay, Y., Neppel, L., Carreau, J., and Najib, K., 2013. Non-stationary frequency analysis of heavy rainfall events in southern France. Hydrological Sciences Journal, 58 (2), 280–294.  相似文献   

2.
极值理论在地震危险性分析中有着重要应用, 发震震级超过某一阈值的超出量分布可以近似为广义帕累托分布. 基于广义帕累托分布给出了若干地震活动性参数的估计公式, 包括强震震级分布、 地震复发周期和重现水平、 期望重现震级、 地震危险性概率和潜在震级上限等; 以云南地区震级资料为基础数据, 讨论了阈值选取、 模型拟合诊断和参数估计; 在此基础上计算了该地区的地震活动性参数. 结果表明, 广义帕累托分布较好地刻画了强震震级分布, 通过超阈值(POT)模型计算的复发周期与实际复发间隔统计基本一致, 高分位数估计在一定阈值范围内表现稳定, 为工程抗震中潜在震级上限的确定提供了一种途径.   相似文献   

3.
Abstract

Abstract A new theoretically-based distribution in frequency analysis is proposed. The extended three-parameter Burr XII distribution includes the generalized Pareto distribution, which is used to model the exceedences over threshold; log-logistic distribution, which is also advocated in flood frequency analysis; and Weibull distribution, which is a part of the generalized extreme value distribution used to model annual maxima as special cases. The extended Burr distribution is flexible to approximate extreme value distribution. Note that both the generalized Pareto and generalized extreme value distributions are limiting results in modelling the exceedences over threshold and block extremes, respectively. From a modelling perspective, generalization might be necessary in order to obtain a better fit. The extended three-parameter Burr XII distribution is therefore a meaningful candidate distribution in the frequency analysis. Maximum likelihood estimation for this distribution is investigated in the paper. The use of the extended three-parameter Burr XII distribution is demonstrated using data from China.  相似文献   

4.
Goodness-of-fit tests based on the L-moment-ratio diagram for selection of appropriate distributions for hydrological variables have had many applications in recent years. For such applications, sample-size-dependent acceptance regions need to be established in order to take into account the uncertainties induced by sample L-skewness and L-kurtosis. Acceptance regions of two-parameter distributions such as the normal and Gumbel distributions have been developed. However, many hydrological variables are better characterized by three-parameter distributions such as the Pearson type III and generalized extreme value distributions. Establishing acceptance regions for these three-parameter distributions is more complicated since their L-moment-ratio diagrams plot as curves, instead of unique points for two-parameter distributions. Through stochastic simulation we established sample-size-dependent 95% acceptance regions for the Pearson type III distribution. The proposed approach involves two key elements—the conditional distribution of population L-skewness given a sample L-skewness and the conditional distribution of sample L-kurtosis given a sample L-skewness. The established 95% acceptance regions of the Pearson type III distribution were further validated through two types of validity check, and were found to be applicable for goodness-of-fit tests for random samples of any sample size between 20 and 300 and coefficient of skewness not exceeding 3.0.  相似文献   

5.
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6.
An important problem in frequency analysis is the selection of an appropriate probability distribution for a given sample data. This selection is generally based on goodness-of-fit tests. The goodness-of-fit method is an effective means of examining how well a sample data agrees with an assumed probability distribution as its population. However, the goodness of fit test based on empirical distribution functions gives equal weight to differences between empirical and theoretical distribution functions corresponding to all observations. To overcome this drawback, the modified Anderson–Darling test was suggested by Ahmad et al. (1988b). In this study, the critical values of the modified Anderson–Darling test statistics are revised using simulation experiments with extensions of the shape parameters for the GEV and GLO distributions, and a power study is performed to test the performance of the modified Anderson–Darling test. The results of the power study show that the modified Anderson–Darling test is more powerful than traditional tests such as the χ2, Kolmogorov–Smirnov, and Cramer von Mises tests. In addition, to compare the results of these goodness-of-fit tests, the modified Anderson–Darling test is applied to the annual maximum rainfall data in Korea.  相似文献   

7.
A peaks over threshold (POT) method of analysing daily rainfall values is developed using a Poisson process of occurrences and a generalised Pareto distribution (GPD) for the exceedances. The parameters of the GPD are estimated by the method of probability weighted moments (PWM) and a method of combining the individual estimates to define a regional curve is proposed.  相似文献   

8.
Many investigators have attempted to define the threshold of landslide failure, that is, the level of the selected climatic variable above which a rainfall-induced landslide occurs. Intensity–duration (I–d) relationships are the most common type of empirical thresholds proposed in the literature for predicting landslide occurrence induced by rainfall. Recent studies propose the use of the kinetic power per unit volume of rainfall (J m−2 mm−1) to quantify the threshold of landslides induced by rainfall. In this paper, the relationship between rainfall duration and kinetic power corresponding to landslides triggered by rain was used to propose a new approach to define the threshold for predicting landslide occurrence. In particular, for the first time, a kinetic power per unit volume of rainfall–duration relationship is proposed for defining the minimum threshold needed for landslide failure. This new method can be applied using commonly used relationship for estimating the kinetic power per unit volume of rainfall and a new equation based on the measured raindrop size distribution. The applicability of this last method was tested using the data of rainfall intensity, duration and median volume diameter for 51 landslides in Taiwan. For the 51 landslides, the comparison between the measured pairs' kinetic power–duration and all selected relationships demonstrated that the equation based on the measured raindrop size distribution is the best method to define the landslide occurrence threshold, as it is both a process-oriented approach and is characterized by the best statistical performance. This last method has also the advantage to allow the forecasting of landslide hazard before the end of the rainfall event, since the rainfall kinetic power threshold value can be exceeded for a time interval less than the event duration.  相似文献   

9.
Abstract

This paper describes a stochastic rainfall model which has been developed to generate synthetic sequences of hourly rainfalls at a point. The model has been calibrated using data from Farnborough in Hampshire, England. This rainfall data series was divided into wet and dry spells; analysis of the durations of these spells suggests that they may be represented by exponential and generalized Pareto distributions respectively. The total volume of rainfall in wet spells was adequately fitted by a conditional gamma distribution. Random sampling from a beta distribution, defining the average shape of all rainfall profiles, is used in the model to obtain the rainfall profile for a given wet spell. Results obtained from the model compare favourably with observed monthly and annual rainfall totals and with annual maximum frequency distributions of 1, 2, 6, 12, 24 and 48 hours duration at Farnborough. The model has a total of 22 parameters, some of which are specific to winter or summer seasons.  相似文献   

10.
Regional frequency analysis based on L-moments was applied to assess the spatial extent of meteorological droughts in tandem with their return periods in Zambia. Weather station monthly rainfall data were screened to form homogeneous sub-regions-, validated by a homogeneity criterion and fitted by a generalized extreme value distribution using goodness-of-fit test statistics. Predictor equations at regional scale for L-moment ratios and mean annual precipitation were developed to generate spatial maps of meteorological drought recurrences. The 80% of normal rainfall level and two thresholds of 60% and 70% were synonymous with moderate and severe droughts, respectively. Droughts were more severe in the south than in the north of Zambia. The return periods for severe and moderate droughts showed an overlapping pattern in their occurrence at many locations, indicating that in certain years droughts can affect the entire country. The extreme south of Zambia is the most prone to drought.  相似文献   

11.
The development of an optimal scheme for evaluation of maximal water discharges is discussed, including adequate probability distribution laws, an effective procedure for their approximation based on observational data, and reliable goodness-of-fit tests for analytical and empirical distributions. One-dimensional probability distribution laws are systematized. Promising distributions were identified, including generalized distribution of extreme values, lognormal distribution, Pearson type V power distribution, and GPD, for evaluating maximal discharges. The available methods for approximating analytical curves, including the up-to-date method of L-moments are considered. Parameter estimation algorithm based on L-moment method for Pearson type III distribution is considered. Pearson type III distribution, lognormal distribution, GEV, and GPD are compared in the approximation of maximal water discharges in rivers of Austria, Siberia, Far East, and the Hawaiian Islands.  相似文献   

12.
In this paper, the goodness-of-fit test based on a convex combination of Akaike and Bayesian information criteria is used to explain the features of interoccurrence times of earthquakes. By analyzing the seismic catalog of Iran for different tectonic settings, we have found that the probability distributions of time intervals between successive earthquakes can be described by the generalized normal distribution. This indicates that the sequence of successive earthquakes is not a Poisson process. It is found that by decreasing the threshold magnitude, the interoccurrence time distribution changes from the generalized normal distribution to the gamma distribution in some seismotectonic regions. As a new insight, the probability distribution of time intervals between earthquakes is described as a mixture distribution via the expectation-maximization algorithm.  相似文献   

13.
Abstract

There is increasing concern that flood risk will be exacerbated in Antalya, Turkey as a result of global-warming-induced, more frequent and intensive, heavy rainfalls. In this paper, first, trends in extreme rainfall indices in the Antalya region were analysed using daily rainfall data. All stations in the study area showed statistically significant increasing trends for at least one extreme rainfall index. Extreme rainfall datasets for current (1970–1989) and future periods (2080–2099) were then constructed for frequency analysis using the peaks-over-threshold method. Frequency analysis of extreme rainfall data was performed using generalized Pareto distribution for current and future periods in order to estimate rainfall intensities for various return periods. Rainfall intensities for the future period were found to increase by up to 23% more than the current period. This study contributed to better understanding of climate change effects on extreme rainfalls in Antalya, Turkey.  相似文献   

14.
Goodness-of-fit tests for the spatial spectral density   总被引：1，自引：1，他引：0  
Detection and modeling the spatial correlation is an important issue in spatial data analysis. We extend in this work two different goodness-of-fit testing techniques for the spatial spectral density. The first approach is based on a smoothed version of the ratio between the periodogram and a parametric estimator of the spectral density. The second one is a generalized likelihood ratio test statistic, based on the log-periodogram representation as the response variable in a regression model. As a particular case, we provide tests for independence. Asymptotic normal distribution of both statistics is obtained, under the null hypothesis. For the application in practice, a resampling procedure for calibrating these tests is also given. The performance of the method is checked by a simulation study. Application to real data is also provided.  相似文献   

15.
This study uses the method of peaks over threshold (P.O.T.) to estimate the flood flow quantiles for a number of hydrometric stations in the province of New Brunswick, Canada. The peak values exceeding the base level (threshold), or `exceedances', are fitted by a generalized Pareto distribution. It is known that under the assumption of Poisson process arrival for flood exceedances, the P.O.T. model leads to a generalized extreme value distribution (GEV) for yearly maximum discharge values. The P.O.T. model can then be applied to calculate the quantiles X T corresponding to different return periods T, in years. A regionalization of floods in New Brunswick, which consists of dividing the province into `homogeneous regions', is performed using the method of the `region of influence'. The 100-year flood is subsequently estimated using a regionally estimated value of the shape parameter of the generalized Pareto distribution and a regression of the 100-year flood on the drainage area. The jackknife sampling method is then used to contrast the regional results with the values estimated at site. The variability of these results is presented in box-plot form. Received: June 1, 1997  相似文献   

16.
This study uses the method of peaks over threshold (P.O.T.) to estimate the flood flow quantiles for a number of hydrometric stations in the province of New Brunswick, Canada. The peak values exceeding the base level (threshold), or `exceedances', are fitted by a generalized Pareto distribution. It is known that under the assumption of Poisson process arrival for flood exceedances, the P.O.T. model leads to a generalized extreme value distribution (GEV) for yearly maximum discharge values. The P.O.T. model can then be applied to calculate the quantiles X T corresponding to different return periods T, in years. A regionalization of floods in New Brunswick, which consists of dividing the province into `homogeneous regions', is performed using the method of the `region of influence'. The 100-year flood is subsequently estimated using a regionally estimated value of the shape parameter of the generalized Pareto distribution and a regression of the 100-year flood on the drainage area. The jackknife sampling method is then used to contrast the regional results with the values estimated at site. The variability of these results is presented in box-plot form. Received: June 1, 1997  相似文献   

17.
Abstract

Statistical analysis of extremes is often used for predicting the higher return-period events. In this paper, the trimmed L-moments with one smallest value trimmed—TL-moments (1,0)—are introduced as an alternative way to estimate floods for high return periods. The TL-moments (1,0) have an ability to reduce the undesirable influence that a small value in the statistical sample might have on a large return period. The main objective of this study is to derive the TL-moments (1,0) for the generalized Pareto (GPA) distribution. The performance of the TL-moments (1,0) was compared with L-moments through Monte Carlo simulation based on the streamflow data of northern Peninsular Malaysia. The result shows that, for some cases, the use of TL-moments (1,0) is a better option as compared to L-moments in modelling those series.

Citation Ahmad, U.N., Shabri, A. & Zakaria, Z.A. (2011) Trimmed L-moments (1,0) for the generalized Pareto distribution. Hydrol.Sci. J. 56(6), 1053–1060.  相似文献   

18.
In the hydrologic analysis of extreme events such as precipitation or floods, the data can generally be divided into two types: partial duration series and annual maximum series. Partial duration series analysis is a robust method to analyze hydrologic extremes, but the adaptive choice of an optimal threshold is challenging. The main goal of this paper was to determine the best method for choosing optimal thresholds. Ten semi-parametric tail index estimators were applied to find the optimal threshold of a 24-h duration precipitation period using data from the Korean Meteorological Administration. The mean square errors of the 10 estimators were calculated to determine the optimal threshold using a semi-parametric bootstrap method. A modified generalized Jackknife estimator determined the best performance in this study among the 10 estimators evaluated with regard to estimating the mean square error of the shape estimator for the generalized Pareto distribution.  相似文献   

19.
A water harvesting system for research purposes has been established in the Lisan Peninsula of the Dead Sea in the middle of the Jordan Rift Valley, where no authorized guideline is available for designing water harvesting systems. Rainfall and runoff, which occurred as flash floods, were observed at the downstream end of a gorge with a 1.12 km2 barren catchment area from October 2014 through July 2019. Due to the extremely arid environment, runoff from the catchment is ephemeral, and the flash flood events can be clearly distinguishable from each other. Thirteen flash flood events with a total runoff volume of more than 100 m3 were successfully recorded during the five rainy seasons. Pearson and Spearman correlations between duration, total rainfall depths at two points, total runoff volume, maximum runoff discharge, bulk runoff coefficient, total variation in runoff discharge and maximum variation in runoff discharge of each flash flood event were examined, revealing no straightforward relationship between rainfall and runoff. The performance of the conventional SCS runoff curve number method was also deficient in reproducing any rainfall–runoff relationship. Therefore, probability distribution fitting was performed for each random variable, focusing on the lognormal distribution with three parameters and the generalized extreme value distribution. The maximum goodness-of-fit estimation turns out to be a more rational and efficient method in obtaining the parameter values of those probability distributions rather than the standard maximum likelihood estimation, which has known disadvantages. Results support the design of the water harvesting system and provide quantitative information for designing and operating similar systems in the future.  相似文献   

20.
Abstract

Statistical analysis of extreme events is often carried out to predict large return period events. In this paper, the use of partial L-moments (PL-moments) for estimating hydrological extremes from censored data is compared to that of simple L-moments. Expressions of parameter estimation are derived to fit the generalized logistic (GLO) distribution based on the PL-moments approach. Monte Carlo analysis is used to examine the sampling properties of PL-moments in fitting the GLO distribution to both GLO and non-GLO samples. Finally, both PL-moments and L-moments are used to fit the GLO distribution to 37 annual maximum rainfall series of raingauge station Kampung Lui (3118102) in Selangor, Malaysia, and it is found that analysis of censored rainfall samples of PL-moments would improve the estimation of large return period events.

Editor D. Koutsoyiannis; Associate editor K. Hamed

Citation Zakaria, Z.A., Shabri, A. and Ahmad, U.N., 2012. Estimation of the generalized logistic distribution of extreme events using partial L-moments. Hydrological Sciences Journal, 57 (3), 424–432.  相似文献   

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