异地海域年极值风暴增水同现规律的探讨

以塘沽和龙口海洋观测站20年极值增水值为样本，基于二维冈贝尔逻辑分布模式，探讨了不同海域风暴潮增水极值的联合分布规律。通过对二维分布的联合概率密度、条件概率密度和同现概率的计算，给出了相应的工程设计参数，供有关部门在防潮规划时参考。     

南四湖流域暴雨分布特征及可能日最大降水量计算

利用南四湖流域11县市1971～2007年的暴雨资料,分析南四湖流域首次和末次暴雨的开始和结束时间以及暴雨的时空分布特征,发现南四湖流域暴雨的时空分布差异较大,但日降水极值的概率分布却有一定规律,呈Λ(x)型渐进分布。利用耿贝尔分布计算南四湖流域多年一遇的日最大降水量极值,计算的未来10年、20年、40年的日最大降水量与历史上10年、20年、40年的日最大降水量重现期基本一致,对未来50～200年的估算值也具有一定的参考价值。     

On seasonal approach to flood frequency modelling. Part I: Two‐component distribution revisited

The annual peak flow series of the Polish rivers are mixtures of summer and winter flows. In the Part I of a sequence of two papers, theoretical aspects of applicability of seasonal approach to flood frequency analysis (FFA) in Poland are discussed. A testing procedure is introduced for the seasonal model and the data overall fitness. Conditions for objective comparative assessment of accuracy of annual maxima (AM) and seasonal maxima (SM) approaches to FFA are formulated and finally Gumbel (EV1) distribution is chosen as seasonal distribution for detailed investigation. Sampling properties of AM quantile x(F) estimates are analysed and compared for the SM and AM models for equal seasonal variances. For this purpose, four estimation methods were used, employing both asymptotic approach and sampling experiments. Superiority of the SM over AM approach is stated evident in the upper quantile range, particularly for the case of no seasonal variation in the parameters of Gumbel distribution. In order to learn whether the standard two‐ and three‐parameter flood frequency distributions can be used to model the samples generated from the Two‐Component Extreme Value 1 (TCEV1) distribution, the shape of TCEV1 probability density function (PDF) has been tested in terms of bi‐modality. Then the use of upper quantile estimate obtained from the dominant season of extreme floods (DEFS) as AM upper quantile estimate is studied and respective systematic error is assessed. The second part of the paper deals with advantages and disadvantages of SM and AM approach when applied to real flow data of Polish rivers. Copyright © 2011 John Wiley & Sons, Ltd.     

基于Clayton Copula函数的二维Gumbel模型及其在海洋平台设计中的应用

根据Gumbel分布和Clayton Copula函数构造出二维Gumbel Clayton Copula分布,根据渤海海域某观测站测得的1970—1993年年最大波高及风速,具体介绍该二维Gumbel模型在海洋工程设计中的使用方法。通过导管架平台基底剪力计算表明,使用该二维Gumbel模型所得的50a一遇剪力值降低了37%,对于边际油田,可以降低荷载设计标准,从而减少海洋工程的投资费用。     

重庆地面最低气温年极值的渐近分布及参数估计

利用重庆 1951-1996 年间 46 年地面气温年极小值的记录,采用韦伯分布和耿贝尔分布分别进行拟合试验.通过统计推断和对比,找出重庆地面最低气温年极值遵循的最佳渐近分布--韦伯分布.     

Depth distribution of interrill overland flow and the formation of rills

A Gumbel distribution for maxima is proposed as a model for the depths of interrill overland flow. The model is tested against three sets of field measurements of interrill overland flow depths obtained on shrubland and grassland hillslopes at Walnut Gulch Experimental Watershed, southern Arizona. The model is found to be a satisfactory fit to 81 of the 90 measured distributions. The shape δ and location λ parameters of all fitted distributions are strongly correlated with discharge. However, whereas a common relationship exists between discharge and δ for all depth distributions, the relationships with λ vary systematically downslope. Using the Gumbel distribution as a model for the distribution of overland flow depths, a probabilistic model for the initiation of rills is developed, drawing upon the previous work of Nearing. As an illustration of this approach, we apply this model to the shrubland and grassland hillslopes at Walnut Gulch. It is concluded that the presence of rills on the shrubland, but not on the grassland, is due to the greater runoff coefficient for the shrubland and/or the greater propensity of the shrubland for soil disturbance compared with the grassland. Finally, a generalized conceptual model for rill initiation is proposed. This model takes account of the depth distribution of overland flow, the probability of flow shear stress in excess of local soil shear strength, the spatial variability in soil shear strength and the diffusive effect of soil detachment by raindrops. Copyright © 2005 John Wiley & Sons, Ltd.     

A new unbiased plotting position formula for Gumbel distribution

The probability plots (graphical approach) are used to fit the probability distribution to given series, to identify the outliers and to assess goodness of fit. The graphical approach requires probability of exceedence or non exceedence of various events. This is obtained through the use of plotting position formula. In literature many plotting position formulae have been reported. All of the many existing formulae provide different results particularly at the tails of the distribution and hence there is need of unbiased plotting position formulae for different distributions. Expression for the largest expected order statistics is found in a simple form. Using exact plotting position from Gumbel order statistics a new unbiased plotting position formula has been developed for the Gumbel distribution. The developed formula better approximates the exact plotting positions as compared to other existing formulae.     

Mixture distributions - an alternative approach for estimating maximum magnitude earthquake occurrence

Summary. Gumbel's theory of extreme value has been employed in the statistical forecasting of maximum-magnitude earthquake occurrence. The basic working hypothesis behind this method assumes that observations follow either Gumbel type I or type III asymptotic distributions. In certain cases, however, it is found that neither type of distribution fits the data well enough to produce accurate parameter-estimates, particularly in the larger earthquake range. This article proposes an alternative approach based on finite-mixture distributions whereby a more realistic prediction of upper earthquake magnitudes (at given return periods) is expected using a combined analysis of both Gumbel types I and III extremal distributions.     

A comparison of two bivariate extreme value distributions

There are two distinct bivariate extreme value distributions constructed from Gumbel marginals, namely Gumbel mixed (GM) model and Gumbel logistic (GL) model. These two models have completely different structures and their dependence ranges are different. The product-moment correlation coefficient for the former is [0,2/3] and the latter is [0,1]. It is natural to ask which one is more appropriate for representing the joint probabilistic behavior of two correlated Gumbel-distributed variables. This study compares these two models by numerical experiments. The comparison is based on that: (i) if the two distribution models are identical, then the joint probability and the joint return period computed by the GM model should be the same as those by the GL model; and (ii) if a selected distribution is the true distribution from which sample data are drawn, then the probabilities computed by the theoretical model should provide a good fit to empirical ones. Comparison results indicate that in the range of correlation coefficient [0,2/3], both models provide identical joint probabilities and joint return periods, and both indicate a good fit to empirical probabilities; while for (2/3,1), only the Gumbel logistic model can be used.     

A note on asymptotic approximations of distributions for maxima of wave crests

The distribution of maxima during a given time interval is of interest in many applications in risk analysis. Within the framework of stationary Gaussian processes, several theoretical results considering asymptotics from different aspects have been derived for this distribution. In this note, we review results from the theory and study the accuracy of these approximations by exemplifying with a model for wave heights from oceanography. It turns out that for high values and the time periods normally encountered for buoy measurements, care should be taken in use of approximation based on the Gumbel distribution.