共查询到17条相似文献，搜索用时 203 毫秒
1.
不同水文区的丰枯遭遇概率分析属于多变量概率分布问题,涉及的水文区越多,变量的维数就越高,问题就越复杂。为找到一种简单通用的多变量（ ）水文概率问题的求解方法,以不同水文区丰枯遭遇概率分析为例,引入三维copula函数构建多变量联合概率模型,将其用于分析长江、淮河、及黄河流域的径流量的联合概率和条件概率问题。研究结果表明,当变量维数 时,由copula函数可以很容易地构建多变量概率分布模型;对一组水文数据系列,有多个不同copula函数可以选择,可采用拟合优度检验方法择优;copula函数构建的多变量概率模型,可以计算各种条件下的联合概率分布,可以分析各种不同量级水文变量的遭遇概率和条件概率;通过与多维转换为一维方法的比较,三维Frank copula函数具有更优良的拟合优度、无偏性、及有效性,且计算更简便。 相似文献
2.
受降水丰枯变化不确定性和差异性的影响,南水北调中线工程水源区与受水区降水的丰枯遭遇状态各不相同,给南水北调工程水资源调度运行带来风险。联合copula函数和贝叶斯网络理论,建立了南水北调中线工程水源区和受水区降水丰枯遭遇风险分析模型,对南水北调中线工程调水最不利的丰枯遭遇风险概率进行了研究。利用copula函数建立了水源区和受水区年降水量联合分布函数,计算条件概率,结合贝叶斯网络进行丰枯遭遇风险分析。结果表明南水北调中线4个受水区调水风险的概率均在25%以下,并对不同情景的调水风险进行了仿真分析。 相似文献
3.
研究pair-copula在干旱特性联合概率中的应用。以渭河流域咸阳站降雨资料为例,采用游程理论,选取干旱历时、干旱烈度和烈度峰值为干旱特性变量,应用Pearson线性相关系数、Spearman相关系数和Kendall秩相关系数进行相依性度量。采用4种常用的copula函数构造了12种pair-copulas,以RMSE、AIC、BIC为准则选择最优的pair-copula。运用Rosenblatt变换的Bootstrap法进行copula拟合度检验,推导3变量的联合概率分布。与3维对称、非对称阿基米德copulas和椭圆copula比较,表明pair-copula可以描述多变量水文概率分布。 相似文献
4.
以甘肃省陇西站月降水资料为例,应用9种3维Archimedean Copulas函数构造了干旱历时、干旱烈度和烈度峰值的联合概率分布,并进行了多变量的拟合优度评价,利用优选出的3维非对称型M12 Copula函数,计算联合分布的重现期以及不同组合下的条件概率与条件重现期。结果表明,M12Copula函数可以描述干旱历时、干旱烈度和烈度峰值间的联合分布。由于Copula函数能够用来构建不同边缘分布的联合分布,可以获得变量间不同组合下的重现期,因而能够更全面客观地反映干旱的特征,是描述干旱多变量分布的一种有效途径。 相似文献
5.
海河流域天然河川径流持续衰减,水文丰枯情势显著变化,亟需研究适用于非一致性水文序列的丰枯概率计算方法。基于标准化径流指数、GAMLSS模型等方法,提出一种不同等级丰枯水事件期望发生次数和期望等待时间的计算方法,研究变化环境下海河流域天然河川径流丰枯概率的演变规律。结果表明：(1)径流丰枯概率呈现出显著的枯增丰减趋势;(2)同传统的一致性分布等多类概率分布相比,以时间t为协变量的LOGNO分布拟合流域径流系列的效果最优,且基于该分布计算的期望发生次数更接近于历史实际;(3)非一致性最优模型不同情景条件下计算的流域极端枯水和极端丰水事件的期望等待时间分别为4.9～9.4 a、14.5～36.0 a,说明海河流域近期发生极端枯水的概率远大于极端丰水。 相似文献
6.
研究多变量干旱特性联合分布的推求方法。选择干旱历时、干旱烈度和烈度峰值为水文干旱特性变量。单变量的边际分布参数分别采用矩法、概率权重法、极大似然法和遗传算法进行计算和优化。应用检验、Kolmogorov-Smirnov等6种检验法进行单变量分布的拟合度检验。采用Pearson’s古典相关系数,Spearman秩相关系数,Kendall’s,Chi-Plots和K-Plots进行变量间的相依性度量。选择4种常用的3维Archimedean Copula函数进行干旱特性变量联合分布拟合。根据RMSE、AIC和BIC准则选择最优copula。在此基础上,采用基于Rosenblatt变换的Bootstrap法进行3维copula的拟合度检验。模型应用于渭河流域北洛河状头站径流序列,结果表明:Gumbel-Hougaard copula拟合效果最好,可以描述洛河状头站3维干旱变量的联合分布。 相似文献
7.
水文变量多特征属性的频率分析,以及各种水文事件的遭遇及联合概率分布问题需要采用多变量概率分布模型解决。总结了当前应用最广泛的几种两变量概率分布模型,对各种模型的适用性和局限性做了详细分析,并介绍了一种新的两变量概率模型——Copula函数。现有模型大都基于变量之间的线性相关关系而建立,对于非线性、非对称的随机变量难以很好地描述;大部分模型假定各变量服从相同的边际分布或对变量间的相关性有严格的限定,从而限制了其应用。Copula函数所构造的两变量概率分布模型克服了现有模型的不足,它具有任意的边际分布,可以描述变量间非线性、非对称的相关关系。作为一种用于构造灵活的多变量联合分布的工具,Copula函数在水科学领域具有广阔的应用前景。 相似文献
8.
基于Copula函数原理,利用武江流域实测水文资料,以广义GDP为洪峰洪量边缘分布,构建了流域组合变量Copula概率分布模型,分析了洪峰与洪量、洪量与洪水历时、洪峰与洪水历时的联合概率分布,绘制各种变量组合下的联合分布图及重现期等值线图,并比较了同重现期条件下,洪水单变量设计值与多维联合设计值的区别。结果表明:广义GDP分布能很好的描述洪峰、洪量边缘分布,而基于广义GDP分布和指数分布构建的两变量Copula联合概率分布模型不限定变量的边缘分布,对各种类型的水文变量联合分布拟合效果较好;能全面反映洪水各特征属性不同等级下的联合发生频率,对同一频率下联合分布推求的洪水设计值比单变量设计值偏于安全。基于Copula函数的组合变量概率分布模型描述洪峰流量、洪量、洪水历时等特征的联合分布,较为全面地反映组合特征的洪水发生的概率和重现期,进一步反映洪水风险。 相似文献
9.
Copula函数是一种灵活构造多变量联合分布和处理多变量问题的有效工具,在水文水资源领域应用广泛;随着研究的广度和深度不断推进,显示出其良好的适用性和不可替代的优越性。重点综述了近10年来Copula函数在水文事件多变量频率分析、水文事件遭遇组合分析、水文随机模拟、水文模型与预报以及其他问题中的最新应用研究进展与不足。从应用条件、参数估计、不对称性、拟合优选、尾部特性、多变量重现期选取、成果抽样误差等方面阐述了Copula函数应用需要注意的问题。展望了未来Copula函数在水文水资源领域应用中的研究重点和发展方向,为今后的研究提供借鉴和参考。 相似文献
10.
椭圆型Copulas函数在西安站干旱特征分析中的应用 总被引：5，自引：1，他引：4
本文研究了干旱发生的联合概率、条件概率和重现期等干旱特征.以陕西省西安站月降水为例,应用Meta-Gaussian Copula和Student t Copula构造了干旱历时、干旱烈度和烈度峰值的联合概率分布,并进行了多变量分布拟合优质评价及拟合检验,在此基础上计算了联合分布的重现期以及2变量和3变量情形下的条件概率与条件重现期.研究表明,Meta-Gaussian Copula可以描述干旱历时、干旱烈度和烈度峰值三者的联合分布.由于多元联合分布可以考虑到多个变量之间的不同组合,能够求得不同干旱历时、干旱烈度或烈度峰值下的条件概率和条件重现期,因而能够更加全面客观地反映干旱的特征. 相似文献
11.
基于Copulas函数的二维干旱变量联合分布 总被引：1，自引：1，他引：0
通过构建干旱变量的联合分布揭示干旱演变规律,可作为干旱分析的重要手段。基于8种单参数族的Copulas函数进行新疆乌鲁木齐和石河子气象站二维干旱变量的联合分布。经拟合优度评价:Frank Copula对干旱历时和干旱烈度、干旱历时和烈度峰值的拟合度最好;Clayton Copula对于干旱烈度和烈度峰值的拟合效果最好。二维变量联合超越概率值随单变量值的减小而增大;单变量的重现期介于二维变量联合重现期与同现重现期之间。表明Copulas函数能够描述二维干旱特征变量的联合分布。 相似文献
12.
The effects of rainfall and the El Niño Southern Oscillation (ENSO) on groundwater in a semi-arid basin of India were analyzed using Archimedean copulas considering 17 years of data for monsoon rainfall, post-monsoon groundwater level (PMGL) and ENSO Index. The evaluated dependence among these hydro-climatic variables revealed that PMGL-Rainfall and PMGL-ENSO Index pairs have significant dependence. Hence, these pairs were used for modeling dependence by employing four types of Archimedean copulas: Ali-Mikhail-Haq, Clayton, Gumbel-Hougaard, and Frank. For the copula modeling, the results of probability distributions fitting to these hydro-climatic variables indicated that the PMGL and rainfall time series are best represented by Weibull and lognormal distributions, respectively, while the non-parametric kernel-based normal distribution is the most suitable for the ENSO Index. Further, the PMGL-Rainfall pair is best modeled by the Clayton copula, and the PMGL-ENSO Index pair is best modeled by the Frank copula. The Clayton copula-based conditional probability of PMGL being less than or equal to its average value at a given mean rainfall is above 70% for 33% of the study area. In contrast, the spatial variation of the Frank copula-based probability of PMGL being less than or equal to its average value is 35–40% in 23% of the study area during El Niño phase, while it is below 15% in 35% of the area during the La Niña phase. This copula-based methodology can be applied under data-scarce conditions for exploring the impacts of rainfall and ENSO on groundwater at basin scales. 相似文献
13.
三峡工程的运行对鄱阳湖防洪形势存在潜在影响。以三峡-鄱阳湖系统为典型,采用基于copula理论的多维联合分布函数,建立三峡工程运行前长江-鄱阳湖-"五河"(赣江、抚河、信江、饶河、修河)系统中水文要素之间的联合概率分布及条件概率分布,并假设该条件分布关系在三峡工程运行前后保持不变;估计三峡工程运行后长江水文要素的概率分布,结合前面的条件概率分布,可以得到三峡工程运行后研究变量的概率分布;对比分析前后概率分布的变化,即可从统计角度评价三峡水库运行对鄱阳湖水文情势的影响。研究表明:三峡工程运行对鄱阳湖水位有一定影响;5、6月份三峡预泄,将增高鄱阳湖水位,其中,平均水位的增幅大于最高水位增幅,低水增幅大于高水增幅;三峡预泄影响下,湖区圩堤堤前水位没有超过原有堤防设计水位,没有降低湖区圩堤的防洪标准。 相似文献
14.
Dian‐Qing Li Xiao‐Song Tang Kok‐Kwang Phoon Yi‐Feng Chen Chuang‐Bing Zhou 《国际地质力学数值与分析法杂志》2013,37(6):597-617
This paper aims to propose a procedure for modeling the joint probability distribution of bivariate uncertain data with a nonlinear dependence structure. First, the concept of dependence measures is briefly introduced. Then, both the Akaike Information Criterion and the Bayesian Information Criterion are adopted for identifying the best‐fit copula. Thereafter, simulation of copulas and bivariate distributions based on Monte Carlo simulation are presented. Practical application for serviceability limit state reliability analysis of piles is conducted. Finally, four load–test datasets of load–displacement curves of piles are used to illustrate the proposed procedure. The results indicate that the proposed copula‐based procedure can model and simulate the bivariate probability distribution of two curve‐fitting parameters underlying the load–displacement models of piles in a more general way. The simulated load–displacement curves using the proposed procedure are found to be in good agreement with the measured results. In most cases, the Gaussian copula, often adopted out of expedience without proper validation, is not the best‐fit copula for modeling the dependence structure underlying two curve‐fitting parameters. The conditional probability density functions obtained from the Gaussian copula differ considerably from those obtained from the best‐fit copula. The probabilities of failure associated with the Gaussian copula are significantly smaller than the reference solutions, which are very unconservative for pile safety assessment. If the strong negative correlation between the two curve‐fitting parameters is ignored, the scatter in the measured load–displacement curves cannot be simulated properly, and the probabilities of failure will be highly overestimated. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
15.
Xing Zheng Wu 《Computational Geosciences》2013,17(5):739-755
In probabilistic slope stability analysis, the influence of cross correlation of the soil strength parameters, cohesion and internal friction angle, on the reliability index has not been investigated fully. In this paper, an expedient technique is presented for probabilistic slope stability analysis that involves sampling a series of combinations of soil strength parameters through a copula as input to an existing conventional deterministic slope stability program. The approach organises the individual marginal probability density distributions of componential shear strength as a bivariate joint distribution by the copula function to characterise the dependence between shear strengths. The technique can be used to generate an arbitrarily large sample of soil strength parameters. Examples are provided to illustrate the use of the copula-based sampling method to estimate the reliability index of given slopes, and the computed results are compared with the first-order reliability method, considering the correlated random variables. A sensitivity study was conducted to assess the influence of correlational measurements on the reliability index. The approach is simple and can be applied in practice with little effort beyond what is necessary in a conventional analysis. 相似文献
16.
The flood characteristics, namely, peak, duration and volume provide important information for the design of hydraulic structures, water resources planning, reservoir management and flood hazard mapping. Flood is a complex phenomenon defined by strongly correlated characteristics such as peak, duration and volume. Therefore, it is necessary to study the simultaneous, multivariate, probabilistic behaviour of flood characteristics. Traditional multivariate parametric distributions have widely been applied for hydrological applications. However, this approach has some drawbacks such as the dependence structure between the variables, which depends on the marginal distributions or the flood variables that have the same type of marginal distributions. Copulas are applied to overcome the restriction of traditional bivariate frequency analysis by choosing the marginals from different families of the probability distribution for flood variables. The most important step in the modelling process using copula is the selection of copula function which is the best fit for the data sample. The choice of copula may significantly impact the bivariate quantiles. Indeed, this study indicates that there is a huge difference in the joint return period estimation using the families of extreme value copulas and no upper tail copulas (Frank, Clayton and Gaussian) if there exists asymptotic dependence in the flood characteristics. This study suggests that the copula function should be selected based on the dependence structure of the variables. From the results, it is observed that the result from tail dependence test is very useful in selecting the appropriate copula for modelling the joint dependence structure of flood variables. The extreme value copulas with upper tail dependence have proved that they are appropriate models for the dependence structure of the flood characteristics and Frank, Clayton and Gaussian copulas are the appropriate copula models in case of variables which are diagnosed as asymptotic independence. 相似文献
17.
A geotechnical problem that involves several spatially correlated parameters can be best described using multivariate cross-correlated random fields. The joint distribution of these random variables cannot be uniquely defined using their marginal distributions and correlation coefficients alone. This paper presents a generic methodology for generating multivariate cross-correlated random fields. The joint distribution is rigorously established using a copula function that describes the dependence structure among the individual variables. The cross-correlated random fields are generated through Cholesky decomposition and conditional sampling based on the joint distribution. The random fields are verified regarding the anisotropic scales of fluctuation and copula parameters. 相似文献