A note of caution when interpreting parameters of the distribution of excesses

In climatology and hydrology, univariate Extreme Value Theory has become a powerful tool to model the distribution of extreme events. The Generalized Pareto Distribution (GPD) is routinely applied to model excesses in space or time by letting the two GPD parameters depend on appropriate covariates. Two possible pitfalls of this strategy are the modeling and the interpretation of the scale and shape GPD parameters estimates which are often and incorrectly viewed as independent variables. In this note we first recall a statistical technique that makes the GPD estimates less correlated within a Maximum Likelihood (ML) estimation approach. In a second step we propose novel reparametrizations for two method-of-moments particularly popular in hydrology: the Probability Weighted Moment (PWM) method and its generalized version (GPWM). Finally these three inference methods (ML, PWM and GPWM) are compared and discussed with respect to the issue of correlations.     

A bivariate pareto model for drought

Univariate Pareto distributions have been so widely used in hydrology. It seems however that bivariate or multivariate Pareto distributions have not yet found applications in hydrology, especially with respect to drought. In this note, a drought application is described by assuming a bivariate Pareto model for the joint distribution drought durations and drought severity in the State of Nebraska. Based on this model, exact distributions are derived for the inter arrival time, magnitude and the proportion of droughts. Estimates of 2, 5, 10, 20, 50 and 100 year return periods are derived for the three variables, drought duration, drought severity and the pairwise combinations: (drought duration, drought severity), (inter arrival time of drought, proportion of drought) and (drought duration, drought magnitude). These return period estimates could have an important role in hydrology, for example, with respect to measures of vegetation water stress for plants in water-controlled ecosystems.     

广义帕累托分布在广东重现期风速计算中的应用

利用广东省86个国家气象观测站建站以来近70a的逐月最大风速序列和近20a(1999—2018年)的逐月最大风速序列,基于POT抽样法,分别采用三参数广义帕累托分布函数对各站的重现期风速进行了概率计算,计算过程中三参数广义帕累托分布函数分别采用矩估计(MOM)、极大似然估计(MLE)、似然矩估计(LM)和概率权矩估计(PWM)等4种参数估计方法,结合表征参数估计优良性的指标:均方根误差RMSE、拟合相对偏差和显著性水平为0.05的科莫戈洛夫检验拟合适度指标K_f对拟合效果进行检验,结果表明:基于POT抽样的概率权矩估计(PWM)拟合效果最好。     

Optimal design of two-dimensional wings in ground effect using multi-objective genetic algorithm

The shape optimization of the 2-dimensional wing in ground effect (WIG) has been performed by the integration of CFD (computational fluid dynamics) and MOGA (multi-objective genetic algorithm). Because of the trade-off between the aerodynamic forces and the height stability, it is difficult to satisfy the design requirements of efficiency and stability at the same time. In this study, the lift coefficient, the lift-drag ratio and the static height stability are chosen as the objective functions to obtain the optimal wing profiles of a WIG craft. An NACA0015 airfoil is used for the baseline model; the aerodynamic characteristics of the base model are compared with that of the optimal solutions. The profile of the airfoil is constructed by four Bezier curves with fourteen control points resulting in the eighteen coordinates, which are adopted as the design variables. The optimal solutions of the multi-objective optimization are not unique but a set of the non-dominated optima: the Pareto frontiers or a Pareto set. As the results of the multi-objective optimization, the forty Pareto optima, which include high-lift, high-efficiency, and more stable airfoils on the edge of the 3-dimensional objective space, are obtained at thirty evolutions of the generation.     

Reassessment of flood frequency using historical information for the River Ouse at York,UK (1200–2000)

Abstract

The reassessment of flood risk at York, UK, is pertinent in light of major flooding in November 2000, and heightened concerns of a perceived increase in flooding nationally. Systematic flood level readings from 1877 and a wealth of documentary records dating back as far as 1263 AD give the City of York a long and rich history of flood records. This extended flood record provides an opportunity to reassess estimates of flood frequency over a time scale not normally possible within flood frequency analysis. This paper re-evaluates flood frequency at York, considering the strengths and weaknesses in estimates resulting from four contrasting methods of analysis and their corresponding data: (a) single-site analysis of gauged annual maxima; (b) pooled analysis of multi-site gauged annual maxima; (c) combined analysis of systematic annual maxima augmented with historical peaks, and (d) analysis of only the very largest peaks using a Generalized Pareto Distribution. Use of the historical information was found to yield risk estimates which were lower and considered to be more credible than those achieved using gauged records alone.

Citation Macdonald, N. & Black, A. R. (2010) Reassessment of flood frequency using historical information for the River Ouse at York, UK (1200–2000). Hydrol. Sci. J. 55(7), 1152–1162.     

利用GRNN方法分析地下管道抗震性能影响因素的敏感性

通过对地震动作用下地下管道最大轴向应力和多种影响因素的分析,基于广义回归神经网络（GRNN）建立了地下管道地震反应预测模型。在此基础之上,将正交表试验设计理论、效用函数理论与神经网络结合起来对地下管道抗震性能影响因素进行敏感性分析,并给出了敏感性分析的具体算法。最后,通过实例分析,将分析结果与用传统理论分析所得结果进行比较,结果显示,该方法不仅可靠,而且简单方便。     

基于INPGA的地下水污染治理多目标优化管理模型:Ⅱ——实例应用

简单算例研究表明改进的小生境Pareto遗传算法(INPGA)用于求解地下水系统的多目标优化管理模型时,求解过程简单,计算速度快,而且得到的Pareto解集跨度更为合理.本文以美国麻省军事保护区(Massachusetts Military Reservation,MMR)为实例,通过建立研究区复杂地下水污染治理的多目...     

Linear combinations of order statistics to estimate the position and scale parameters of the Generalized Pareto distribution

 Ad hoc techniques for estimating the position and the scale parameters of the Generalized Pareto distribution are introduced. The estimators proposed are simple linear combinations of the order statistics: they provide valuable estimates of the parameters of interest, both when the shape parameter is known and when it is unknown (this latter case being of great relevance in practical applications), and show a good performance as well when the sample size is small. The procedures are tested on simulated data, and comparisons with other techniques are shown.     

A newly-discovered GPD-GEV relationship together with comparing their models of extreme precipitation in summer

It has been theoretically proven that at a high threshold an approximate expression for a quantile of GEV （Generalized Extreme Values） distribution can be derived from GPD （Generalized Pareto Distribution）. Afterwards, a quantile of extreme rainfall events in a certain return period is found using L-moment estimation and extreme rainfall events simulated by GPD and GEV, with all aspects of their results compared. Numerical simulations show that POT （Peaks Over Threshold）-based GPD is advantageous in its simple operation and subjected to practically no effect of the sample size of the primitive series, producing steady high-precision fittings in the whole field of values （including the high-end heavy tailed）. In comparison, BM （Block Maximum）-based GEV is limited, to some extent, to the probability and quantile simulation, thereby showing that GPD is an extension of GEV, the former being of greater utility and higher significance to climate research compared to the latter.     

Multi-Objective Optimization of A Semisubmersible for Ultra-Deep Water

Semisubmersible will work well when oil exploitation goes to ultra-deep water because of its variable load capacities, and good motion performance in extreme waves. It is considered to be a main type of platform while the water depth is more than 3000 meters. This paper establishes a multi-objective optimization model of semisubmersible for ultra-deep water, and it is solved by a multi-objective genetic algorithm--NSGA-Ⅱ. The model is applied to a practical design, and Pareto results are obtained. The effectiveness of the method is verified by hydrodynamic analysis.