Data‐based analysis of bivariate copula tail dependence for drought duration and severity

In recent decades, copula functions have been applied in bivariate drought duration and severity frequency analysis. Among several potential copulas, Clayton has been mostly used in drought analysis. In this research, we studied the influence of the tail shape of various copula functions (i.e. Gumbel, Frank, Clayton and Gaussian) on drought bivariate frequency analysis. The appropriateness of Clayton copula for the characterization of drought characteristics is also investigated. Drought data are extracted from standardized precipitation index time series for four stations in Canada (La Tuque and Grande Prairie) and Iran (Anzali and Zahedan). Both duration and severity data sets are positively skewed. Different marginal distributions were first fitted to drought duration and severity data. The gamma and exponential distributions were selected for drought duration and severity, respectively, according to the positive skewness and Kolmogorov–Smirnov test. The results of copula modelling show that the Clayton copula function is not an appropriate choice for the used data sets in the current study and does not give more drought risk information than an independent model for which the duration and severity dependence is not significant. The reason is that the dependence of two variables in the upper tail of Clayton copula is very weak and similar to the independent case, whereas the observed data in the transformed domain of cumulative density function show high association in the upper tail. Instead, the Frank and Gumbel copula functions show better performance than Clayton function for drought bivariate frequency analysis. Copyright © 2012 John Wiley & Sons, Ltd.     

Bivariate simulation using copula and its application to probabilistic pile settlement analysis

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.     

Probability of combined high sea levels and large rains in Malmö, Sweden,southern Öresund

Observations of sea level and precipitation in Malmö, Sweden in the southeastern part of the sound Öresund have been used to estimate the probabilities of local compound events of high sea level and large daily and hourly rains. There are observations of sea level and daily rains extending back to 1930. The observations of short‐term rainfall are from 1980 and onwards. Most large rainfalls come in the summer, while the highest sea levels are in the autumn and in the winter. The highest observed sea level is about 130 cm above mean sea level, and the largest daily rain is close to 100 mm. However, the highest sea level observed during a day with rainfall corresponding to the 1‐year rain is less than 60 cm. The highest sea level observed during an hour with 1‐year hourly rainfall is 30 cm. From the statistics of daily rains, hourly rains and sea level, extreme values for each of them have been computed. For events with frequency higher than one per four years the probabilities of combined events sea level – rainfall are determined directly from the observations. For more rare events, marginal distributions of sea level and rainfall are determined. Copulas and conditional probabilities are used. When the sea level exceeds 20 cm above mean sea level, daily rains exceeding 10 mm are almost independent of the sea level and so are hourly rains exceeding 5 mm. It is extremely rare that large rains occur when the sea level is very high. The combination of 1‐year rainfall and the 1‐year sea level has a return period of more than 200 years.     

大-小兴安岭接合部早—中侏罗世侵入岩SHRIMP锆石U-Pb定年及成因

大-小兴安岭接合部出露的大面积侵入岩传统认为属于华力西期。通过对3个典型岩体的解剖,获得了最新的锆石SHRIMP U-Pb年龄,花岗闪长岩形成年龄为169Ma±2Ma和177.4Ma±1.7Ma,闪长质包体为179Ma±2Ma,主量、微量元素特征表明,它们为形成于早—中侏罗世的高钾钙碱性系列I型花岗岩。各岩体和闪长质包体均具有低ISr(平均0.704668)和正εNd(t)(1.3837～3.10652)值特点,包体发育针柱状角闪石和空心磷灰石,反映岩体成因与地幔具有密切的联系。地质学、岩石学和地球化学的详细研究表明,各岩体具有壳幔混合成因,花岗质岩浆主要是从地幔中分离出的新生地壳和原有古老地壳部分熔融产生的岩浆,与来自亏损地幔岩浆相互混合形成的。通过区域动力学分析,认为本区大陆地壳生长可能经历了2个连续过程,首先是晚古生代造山期后岩石圈拆沉导致软流圈地幔上隆及幔源岩浆的底垫作用;区域上大范围三叠纪沉积记录的缺失说明此时应是北方造山带强烈的造山时期,这一机制很可能与蒙古-鄂霍次克海闭合造山有密切联系,之后岩石圈板块拆沉,并导致先存新生地壳和原有老地壳的部分熔融,形成花岗质岩浆,可能是引起本区大陆地壳生长的重要机制。     

变化环境下西江北江枯水流量联合分布分析

基于Clayton copula和Kendall分布函数分析广东西江马口站和北江三水站枯水流量的联合分布及其风险概率。根据两站流量之间的时空关联与变异,以1959-2010年西江马口站历年连续7日平均最小流量和对应期间的北江三水站枯水流量为样本,分别计算1959-1985年和1986-2010年两个时段(分别称为样本A和样本B)的西江北江枯水流量联合分布的"或"重现期、"且"重现期和二次重现期及其最可能的设计分位数。结果表明:①样本B中马口站的枯水流量设计值小于样本A相应重现期设计值,三水站则显著增大;②1985年后西江和北江枯水流量同频率遭遇的可能性较前期明显减小;③二次重现期所对应的累积频率代表了特定设计频率情况下西江和北江枯水流量遭遇的风险率;④由更严谨的二次重现期计算的马口站枯水流量最大可能设计值Q_7d,T=20a、Q_7d,T=10a和Q_7d,T=2a设计值或更适合分别作为西江三角洲供水规划、生态需水和调水压咸设计参考值。     

Joint frequency analysis and uncertainty estimation of coupled rainfall–runoff series relying on historical and simulated data

ABSTRACT

Joint frequency analysis and quantile estimation of extreme rainfall and runoff (ERR) are crucial for hydrological engineering designs. The joint quantile estimation of the historical ERR events is subject to uncertainty due to the errors that exist with flow height measurements. This study is motivated by the interest in introducing the advantages of using Hydrologic Simulation Program-Fortran (HSPF) simulations to reduce the uncertainties of the joint ERR quantile estimations in Taleghan watershed. Bivariate ERR quantile estimation was first applied on P_AMS-Q_SIM pairs and the results were compared against the historical rainfall–runoff data (P_AMS-Q_obs). Student’s t and Frank copulas with respectively Gaussian-P3 and Gaussian-LN3 marginal distributions well suited to fit the P_AMS-Q_obs and P_AMS-Q_SIM pairs. Results revealed that confidence regions (CRs) around the p levels become wider for P_AMS-Q_obs compared to P_AMS-Q_SIM, indicating the lower sampling uncertainties of HSPF simulations compared to the historical observations for bivariate ERR frequency analysis.     

An improved nonstationary model for flood frequency analysis and its implication for the Three Gorges Dam,China

This study proposes an improved nonstationary model for flood frequency analysis by investigating the relationship between flood peak and flood volume, using the Three Gorges Dam (TGD), China, for verification. First, the generalized additive model for location, scale and shape (GAMLSS) is used as the prior distribution. Then, under Bayesian theory, the prior distribution is updated using the conditional distribution, which is derived from the copula function. The results show that the improvement of the proposed model is significant compared with the GAMLSS-based prior distribution. Meanwhile, selection of a suitable prior distribution has a significant effect on the results of the improvement. For applications to the TGD, the nonstationary model can obviously increase the engineering management benefits and reduce the perceived risks of large floods. This study provides guidance for the dynamic management of hydraulic engineering under nonstationary conditions.     

Probabilistic disaggregation of a spatial portfolio of exposure for natural hazard risk assessment

In natural hazard risk assessment situations are encountered where information on the portfolio of exposure is only available in a spatially aggregated form, hindering a precise risk assessment. Recourse might be found in the spatial disaggregation of the portfolio of exposure to the resolution of the hazard model. Given the uncertainty inherent to any disaggregation, it is argued that the disaggregation should be performed probabilistically. In this paper, a methodology for probabilistic disaggregation of spatially aggregated values is presented. The methodology is exemplified with the disaggregation of a portfolio of buildings in two communes in Switzerland and the results are compared to sample observations. The relevance of probabilistic disaggregation uncertainty in natural hazard risk assessment is illustrated with the example of a simple flood risk assessment.     

基于三维copula函数的多水文区丰枯遭遇分析

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(n≥3)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n≥3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。     

基于Copula函数的川西南地区连旱危险度分析

利用川西南地区1960—2010年逐日降水资料,结合降水距平百分率干旱指标,基于Copula函数,构造川西南地区季节间连旱的危险度评估模型,对各站春夏连旱、夏秋连旱、秋冬连旱及冬春连旱的危险度特征进行分析。结果表明：Clayton Copula函数可用于季度间连旱模型的建立。通过各站的危险度评估模型得出,川西南地区遭遇春夏连旱的危险度最低,其中乐山市低至452%;而遭遇冬春连旱的危险度最高,攀枝花市高达2899%。针对各站点而言,攀枝花市遭遇各种连旱的危险度最高,而乐山市遭遇各种连旱的危险度最低。对同一种连旱而言,各站遭遇不同强度连旱的危险度特征也有所差异。总体而言,当相邻季节均为重旱时,各站的连旱的危险度最小;当两季节均为偏旱强度时,各站的连旱的危险度最高。