水文干旱多变量联合设计及水库影响评估

基于东江流域博罗站月径流数据,采用游程理论提取水文干旱事件.选用Meta-Gaussian Copula函数,统计模拟水文干旱指标的多变量联合分布.采用Kendall联合重现期和最大可能权函数,设计给定联合超越重现期的水文干旱指标组合值,并定量评估水库径流调节作用对水文干旱多变量联合特征的影响.结果表明:东江流域水文干旱历时、强度和峰值的统计优选分布均为韦布尔分布.干旱指标之间具有较高的正相关性,Meta-Gaussian Copula能够很好地模拟水文干旱指标两变量和三变量联合分布.基于任意两个变量联合设计和三变量联合设计,干旱指标设计组合值位于同频位置附近,且同一个干旱指标设计值在不同变量组合之间差别较小.水库径流调节作用对于缓解东江流域水文干旱效果明显,同一组干旱指标的多变量联合超越重现期在水库影响下明显变大.联合超越重现期越小,水库对联合设计值的影响程度越大.根据目前水库运行模式,若要满足河道内最小管理流量目标,联合超越重现期10 a一遇的干旱历时、强度和峰值依然达到了约3.89~4.04月、7.20~7.97亿m3和2.99~3.12亿m3.     

基于Copula函数的鄱阳湖水系径流丰枯遭遇多维分析

鄱阳湖流域5大水系来水变化与湖区水文极值事件有密切关系,研究径流变化特征与丰枯遭遇规律对区域防洪抗旱有重要意义.本文运用Copula函数构建了鄱阳湖水系多维径流联合分布模型,采用特枯、偏枯、平水、偏丰和特丰的径流丰枯分类,定量研究了鄱阳湖5大水系丰枯遭遇的问题,探讨了多维丰枯遭遇同步联合概率的变化特征.结果表明：鄱阳湖水系河流之间的径流具有较高的相关性,Gaussian Copula函数能较好地模拟二维至五维的径流联合分布.多条河流的丰枯遭遇随着维数的增加,丰枯组合增加,丰枯同步的联合概率明显下降,且丰枯同步的最大联合概率趋向于丰枯两端.对于相同的概率区间,非汛期径流的丰枯同步联合概率明显大于年径流和汛期径流,而年径流和汛期径流之间的丰枯同步联合概率差别较小.同处于流域北部或南部或相邻的河流之间的组合,其同步联合概率相较其他组合大,而南、北河流组合的同步联合概率相对较小.该研究可为流域水资源管理及水旱灾害预防提供科学依据.     

基于马尔科夫链模型的鄱阳湖流域水文气象干旱研究

基于气象和水文干旱的二维变量干旱状态基础上,通过一阶马尔科夫链模型对二维变量干旱状态进行频率、重现期和历时分析,建立水文气象干旱指数,从干旱灾害形成、演变和持续3方面对干旱灾害进行研究,同时预测未来6个月非水文干旱到水文干旱的概率.结果表明:(1)修河流域在干旱形成中危害大,抚河流域和修河流域在干旱演变中危害大,赣江流域和饶河流域在干旱持续中危害大;(2)鄱阳湖流域状态4(气象、水文干旱)发生的频率最高,为0.30,连续湿润或者干旱的概率最大,湿润状态(状态2)与水文干旱(状态4、状态5(气象湿润、水文干旱))的相互转移概率最低;(3)在长期干旱预测中,鄱阳湖流域从状态2转到状态4和状态5的平均概率为0.11,属最低,而状态1(气象、水文无旱)和状态3(气象干旱、水文湿润)到达状态4的概率为0.23,发生概率最大.修河流域在非水文干旱状态下未来发生气象、水文干旱状态的平均概率为0.28,是"五河"中最高的,而赣江流域在正常或者湿润状态下未来发生气象、水文干旱的概率最低,为0.18,该研究对于鄱阳湖流域水文气象干旱的抗旱减灾具有重要理论与现实意义.     

基于Copula的洞庭湖-流域-长江系统水文干旱概率分析

洞庭湖是长江中游重要的通江湖泊,水系格局复杂.近年来在气候变化和人类活动的双重影响下,江湖关系发生变化,湖泊水文干旱事件频发.基于洞庭湖、流域和长江干流水文站点的实测数据,通过标准化水位指数和标准化径流指数识别了水文干旱事件,并运用Copula函数分析了洞庭湖-流域-长江系统水文干旱的联合概率分布特征.结果表明:在年尺度上,1964—2016年间洞庭湖共发生了9次水文干旱事件,水文干旱的发生概率为14.01%,洞庭湖-流域系统、洞庭湖-长江系统的水文干旱联合概率分别为9.65%和8.58%,表明年尺度上流域来水对洞庭湖水文干旱的影响更大.在季节尺度上,洞庭湖-流域系统春季水文干旱联合概率最高,且两者同时发生水文干旱事件的次数最多,表明洞庭湖春季水文干旱与流域入湖补给减少有密切关系;而洞庭湖-长江系统,其秋季水文干旱联合概率最大,尤其自2003年以后更加极端和频发,这一方面受秋季降水减少和流域内人类活动的影响,另一方面三峡水库秋季蓄水使长江中下游干流水位降低,长江对湖泊顶托作用减弱也是重要原因之一.     

基于二次重现期的多变量洪水风险评估

由于洪水是一种具有多个特征属性的随机事件,频率分析成为洪水风险评估的一种有效手段,多变量重现期与设计值的定义与计算则是洪水频率分析中的重点和难点.本文通过构造洪水历时、洪峰与洪量的联合分布,介绍了一种新的多变量重现期定义——二次重现期,并探讨了"或"重现期、"且"重现期和二次重现期对安全与危险域识别的差异性,以及在洪水风险管理与工程设计中的合理性与可靠性.传统的"或"和"且"多变量重现期对安全与危险域的识别存在局限性,利用Kendall函数定义的二次重现期则提供了更加合理的安全与风险域识别,避免了对安全事件与危险事件的错误判定,更有利于指导洪水风险的管理.在给定的二次重现期条件下,依据出现概率最大原则推算的历时、洪峰与洪量设计值组合可以满足工程设计以较低成本承受较大风险的追求,相比于单变量设计值,考虑了洪水多个属性联合特征的多变量设计值提供了更加全面和可靠的参考信息.     

极端干旱事件中洞庭湖水面变化过程及成因

干旱是洞庭湖区长期以来面临的严重自然灾害之一,给周边人们的生产生活造成了极大的影响.针对2006和2011年洞庭湖区发生的极端干旱事件,借助遥感影像大范围、时空连续的优势,结合湖区水文气象等观测资料,从时空两方面阐释了洞庭湖在典型干旱年份水域分布及变化过程,进一步从温度、降水、径流以及蓄水量等方面对比分析不同干旱事件发生、发展过程的一致性和差异性.研究结果表明:2006年干旱大致从7月开始,至12月结束.水面淹没范围由湖心向周边扩展,到7月达到最大值,8月提前进入枯水期,减小范围主要集中在东洞庭湖外围和南洞庭湖的北边.2006年干旱属于由入湖径流减少主导的水文干旱事件;2011年的干旱则从4月开始,至11月结束,在9月以后干旱继续加重.水面淹没范围在6月急剧增大且一直到8月都维持在较高的水平,涨水期水面由中心向四周淹没,退水期水面变化范围与涨水期相反.2011年干旱是由流域降水减少引起的水文和气象干旱事件.研究结果揭示了洞庭湖区干旱成因的多样性和复杂性,对于制定科学合理的干旱灾害防范措施,减缓区域的生态环境问题等具有一定的指导和借鉴意义.     

三峡水库影响下长江中下游水文干旱演变及对气象干旱的响应

利用1960—2016年长江流域183个气象站逐月气温和降水数据以及干流3个水文站逐月径流资料, 采用标准化降水蒸散指数(SPEI)和标准化径流指数(SRI)分析三峡水库蓄水运行前后长江中下游宜昌、汉口和大通站水文干旱的多时间尺度演变以及对气象干旱的响应特征. 结果表明: (1) 三峡水库运行后下游各站冬春季旱情明显趋缓, 而秋季干旱状况略有加重; 水库蓄水后各站中旱和重旱发生频率均呈减少趋势, 其中中旱减幅明显, 而特旱发生频率则总体表现为增加趋势; (2) 三峡水库蓄水后3个站平均干旱历时的变幅相对较小, 而干旱烈度和烈度峰值的均值增幅较大; 同时, 各站短时间尺度(1和3个月) 干旱特征变量的变幅总体呈现沿程递增趋势, 而长时间尺度(6和12个月) 干旱特征变量的变幅整体表现为沿程递减趋势; (3) 水库蓄水后各站短时间尺度SRI与SPEI的相关性减小, 但相关性随时间尺度增加而迅速增强, 12个月时间尺度的相关系数达到最大并略高于蓄水前; 在年内相关性上, 蓄水后各站短时间尺度SRI与SPEI的相关系数明显减小, 冬季表现尤为突出, 而长时间尺度的相关系数则略有增加; (4) 水库影响下不同时间尺度宜昌站水文干旱滞后于气象干旱平均天数有增有减, 而汉口和大通站的滞后天数均呈显著增加趋势, 且总体表现为沿程递增趋势. 研究结果可为变化环境下水文干旱预警与水库优化调度提供参考.     

基于Copula函数的鄱阳湖流域极值流量遭遇频率及灾害风险

在以气温上升为主要特征的全球气候变化导致区域水循环加剧、极端气候水文事件频发的背景下,对极端水文事件,特别是水文极值遭遇频率的科学认识,对区域防洪抗旱具有重要意义.基于此,本文引入当前多变量分析中较常用的Copula函数.分析鄱阳湖流域主要支流赣江与抚河、乐安河与昌江的洪水、枯水流量联合概率特征,并对引起该流域水文极值...     

基于Copula函数的东江流域3大水库丰枯遭遇分析

东江流域在广东省政治、经济和社会中占有重要地位,域内新丰江、枫树坝和白盆珠3大水库的来水量直接影响区域生产生活供水.面对水库群联合调度新要求,本文利用Copula函数构建了3大水库入库流量的二维和三维联合分布,分析其丰枯遭遇概率,主要结论如下:(1)3大水库两两间丰枯同步的概率大于丰枯异步的概率,非汛期丰枯同步的概率大于汛期.其中,白盆珠与新丰江、枫树坝丰枯异步的概率相对较大,这为其与另两个水库丰枯互补提供了可能;(2)三维联合分布显示,3大水库丰枯同步的概率在全年、汛期和非汛期均较大,依次为42.29%、41.74%和51.99%,其中同丰和同枯的概率远大于同平的概率.枫树坝与新丰江对下游具有补偿能力的概率分别为29.81%和23.03%,不具有补偿能力的概率分别为32.75%和22.32%;(3)利用3大水库的联合分布,可获得各水库不同入库流量遭遇的概率以及特定概率下各水库入库流量的可能组合,对3大水库联合优化调度具有重要的理论与实践价值.     

我国各大流域复合高温干旱事件变化趋势与归因分析

受全球气候变化影响,复合高温干旱事件呈现增加趋势.通过构建表征复合高温干旱重现期变化的全微分方程,提出了一种复合高温干旱变化的归因方法,并利用1921～2020年月气温和月降水观测资料,分析中国夏季复合高温干旱事件时空分布特征及变化趋势,量化降水变化、气温变化和降水-气温相关关系变化这三种驱动因子在中国夏季复合高温干旱事件变化中的贡献.结果表明:近年来中国大部分地区夏季复合高温干旱事件呈现出明显的增加趋势,气温变化、降水变化、降水-气温相关关系变化对干旱高温复合事件变化的贡献依次递减.气温变化幅度最大、影响范围最广,在长江中上游地区以外的区域均导致复合事件增加,是最主要的驱动因子之一;降水变化是中国西部特别是新疆北部、青海和甘肃地区复合事件减少的重要原因;降水-气温关系则与其他驱动因子一起导致了在华南地区复合事件重现期的缩短和华东、西北部分地区复合事件重现期的增加.与此同时,降水和气温的均值趋势与离散程度的变化均可能导致复合高温干旱事件重现期的变化.     

Assessment of hydrological droughts for the Yellow River,China, using copulas

Droughts are one of the normal and recurrent climatic phenomena on Earth. However, recurring prolonged droughts have caused far‐reaching and diverse impacts because of water deficits. This study aims to investigate the hydrological droughts of the Yellow River in northern China. Since drought duration and drought severity exhibit significant correlation, a bivariate distribution is used to model the drought duration and severity jointly. However, drought duration and drought severity are often modelled by different distributions; the commonly used bivariate distributions cannot be applied. In this study, a copula is employed to construct the bivariate drought distribution. The copula is a function that links the univariate marginal distributions to form the bivariate distribution. The bivariate return periods are also established to explore the drought characteristics of the historically noticeable droughts. The results show that the return period of the drought that occurred in late 1920s to early 1930s is 105 years. The significant 1997 dry‐up phenomenon that occurred in the downstream Yellow River (resulting from the 1997–1998 drought) only has a return period of 4·4 years and is probably induced by two successive droughts and deteriorated by other factors, such as human activities. Copyright © 2007 John Wiley & Sons, Ltd.     

An analysis of non-normal Markovian extremal droughts

In many arid and semi-arid environments of the world, years of extended droughts are not uncommon. The occurrence of a drought can be reflected by the deficiency of the rainfall or stream flow sequences below the long-term mean value, which is generally taken as the truncation level for the identification of the droughts. The commonly available statistics for the above processes are mean, coefficient of variation and the lag-one serial correlation coefficient, and at times some indication of the probability distribution function (pdf) of the sequences. The important elements of a drought phenomenon are the longest duration and the largest severity for a desired return period, which form a basis for designing facilities to meet exigencies arising as a result of droughts. The sequences of drought variable, such as annual rainfall or stream flow, may follow normal, log-normal or gamma distributions, and may evolve in a Markovian fashion and are bound to influence extremal values of the duration and severity. The effect of the aforesaid statistical parameters on the extremal drought durations and severity have been analysed in the present paper. A formula in terms of the extremal severity and the return period ‘T’ in years has been suggested in parallel to the flood frequency formula, commonly cited in the hydrological texts. © 1998 John Wiley & Sons, Ltd.     

A framework for quantifying the impacts of climate change and human activities on hydrological drought in a semiarid basin of Northern China

Climate change and human activities are two major driving forces affecting the hydrologic cycle, which further influence the stationarity of the hydrologic regime. Hydrological drought is a substantial negative deviation from the normal hydrologic conditions affected by these two phenomena. In this study, we propose a framework for quantifying the effects of climate change and human activities on hydrological drought. First, trend analysis and change‐point test are performed to determine variations of hydrological variables. After that, the fixed runoff threshold level method (TLM) and the standardized runoff index (SRI) are used to verify whether the traditional assessment methods for hydrological drought are applicable in a changing environment. Finally, two improved drought assessment methods, the variable TLM and the SRI based on parameter transplantation are employed to quantify the impacts of climate change and human activities on hydrological drought based on the reconstructed natural runoff series obtained using the variable infiltration capacity hydrologic model. The results of a case study on the typical semiarid Laohahe basin in North China show that the stationarity of the hydrological processes in the basin is destroyed by human activities (an obvious change‐point for runoff series is identified in 1979). The traditional hydrological drought assessment methods can no longer be applied to the period of 1980–2015. In contrast, the proposed separation framework is able to quantify the contributions of climate change and human activities to hydrological drought during the above period. Their ranges of contributions to hydrological drought calculated by the variable TLM method are 20.6–41.2% and 58.8–79.4%, and the results determined by the SRI based on parameter transplantation method are 15.3–45.3% and 54.7–84.7%, respectively. It is concluded that human activities have a dominant effect on hydrological drought in the study region. The novelty of the study is twofold. First, the proposed method is demonstrated to be efficient in quantifying the effects of climate change and human activities on hydrological drought. Second, the findings of this study can be used for hydrological drought assessment and water resource management in water‐stressed regions under nonstationary conditions.     

Uncertainty and variability in bivariate modeling of hydrological droughts

There are two kinds of uncertainty factors in modeling the bivariate distribution of hydrological droughts: the alteration of predefined critical ratios for pooling droughts and excluding minor droughts and the temporal variability of univariate and/or bivariate characteristics of droughts due to the impact of human activities. Daily flow data covering a period of 56 hydrological years from two gauging stations from a humid region in South China are used. The influences of alterations of threshold values of flow and critical ratios of pooling droughts and excluding minor droughts on drought properties are analyzed. Six conventional univariate models and three Archimedean copulas are employed to fit the marginal and joint distributions of drought properties, the Kolmogorov–Smirnov and Anderson–Darling methods are used for testing the goodness-of-fit of the univariate model, and the Cramer-von Mises method based on Rosenblatt’s transform is applied for the test of the bivariate model. The change point analysis of the copula parameter of bivariate distribution of droughts is first made. Results demonstrate that both the statistical characteristics of each drought property and their bivariate joint distributions are sensitive to the critical ratio of excluding minor droughts. A model can be selected to fit the marginal distribution for drought deficit volume or maximum deficit, but it is not determined for drought duration with the lower ratios of the pooling and excluding droughts. The statistical uncertainty of drought duration makes the modeling of bivariate joint distribution of drought duration and deficit volume or of drought duration and maximum deficit undermined. Change points significantly occurred in the period from the late 1970s to the middle 1980s for a single drought property and the copula parameter of their joint distribution due to the impact of human activities. The difference between two subseries separated by the change point is remarkable in the magnitudes of drought properties and the joint return periods. A copula function can be selected to optimally fit the bivariate distribution, provided that the critical ratios of pooling and excluding droughts are great enough such as the optimal value of 0.4 in the case study. It is valuable that the modeling and designing of the bivariate joint correlation and distribution of drought properties can be performed on the subseries separated by the change point of the copula parameter.     

A drought frequency formula

Abstract

The important elements of a drought phenomenon are the longest duration and the largest severity for a desired return period. These elements form a basis for designing water storage systems to cope with droughts. At times, a third element, drought intensity, is also used and is defined as the ratio of severity to duration. The commonly available statistics for the causative drought variables such as annual rainfall or runoff sequences are the mean, the coefficient of variation and the lag one serial correlation coefficient, and occasionally some indication of the probability distribution function (pdf) of the sequences. The extremal values of the duration and severity are modelled in the present paper using information on the aforesaid parameters at the truncation level equal to the mean of the drought sequence, which is generally taken as the truncation level in the analysis of droughts. The drought severity has been modelled as the product of the duration and intensity with the assumption of independence between them. An estimate of drought intensity has been realized from the concept of the truncated normal distribution of the standardized form of the drought sequences in the normalized domain. A formula in terms of the extremal severity and the T-year return period has been suggested similar to the flood frequency formulae, commonly cited in hydrological texts.     

Developing a large‐scale water‐balance approach to seasonal forecasting: application to the 2012 drought in Britain

Seasonal hydrological forecasts, or outlooks, can potentially provide water managers with estimates of river flows and water resources for a lead time of several months ahead. An experimental modelling tool for national hydrological outlooks has been developed which combines a hydrological model estimate of sub‐surface water storage across Britain with a range of seasonal rainfall forecasts to provide estimates of area‐wide hydrological conditions up to a few months ahead. The link is made between a deficit in sub‐surface water storage and a requirement for additional rainfall over subsequent months to enable sub‐surface water storage and river flow to return to mean monthly values. The new scheme is assessed over a recent period which includes the termination of the drought that affected much of Britain in the first few months of 2012. An illustration is provided of its use to obtain return‐period estimates of the ‘rainfall required’ to ease drought conditions; these are well in excess of 200 years for several regions of the country, for termination within a month of 1 April 2012, and still exceed 40 years for termination within three months. National maps of sub‐surface water storage anomaly show for the first time the current spatial variability of drought severity. They can also be used to provide an indication of how a drought situation might develop in the next few months given a range of possible future rainfall scenarios. © 2013 CEH/Crown and John Wiley & Sons, Ltd.     

Application of copulas for derivation of drought severity–duration–frequency curves

This study presents copula‐based multivariate probabilistic approach to model severity–duration–frequency (S‐D‐F) relationship of drought events in western Rajasthan, India. Drought occurrences are analysed using standardized precipitation index computed on monthly mean areal precipitation, aggregated at a time scale of 6 months. After testing with a series of probability density functions, the drought variable severity is found to be better represented with log‐normal distribution, whereas duration is well fitted with exponential distribution. Four different classes of bivariate copulas – Archimedean, extreme value, Plackett, and elliptical families are evaluated for modelling joint distribution of drought characteristics. It is observed that the extreme value copula – Gumbel–Hougaard copula – performed better as compared with other classes of copulas, based on results of various statistical tests and upper tail dependence coefficient. The joint distribution obtained from best performing copula is then employed to determine conditional return period and to derive drought severity‐duration‐frequency (S‐D‐F) curves for the study region. The results of the study suggests that the copula method can be used effectively to derive the drought S‐D‐F curves, which can be helpful in planning and adopting suitable drought mitigation strategies in drought‐prone areas. Copyright © 2011 John Wiley & Sons, Ltd.     

Copula models for frequency analysis what can be learned from a Bayesian perspective?

Large spring floods in the Québec region exhibit correlated peakflow, duration and volume. Consequently, traditional univariate hydrological frequency analyses must be complemented by multivariate probabilistic assessment to provide a meaningful design flood level as requested in hydrological engineering (based on return period evaluation of a single quantity of interest). In this paper we study 47 years of a peak/volume dataset for the Romaine River with a parametric copula model. The margins are modeled with a normal or gamma distribution and the dependence is depicted through a parametric family of copulas (Arch 12 or Arch 14). Parameter joint inference and model selection are performed under the Bayesian paradigm. This approach enlightens specific features of interest for hydrological engineering: (i) cross correlation between margin parameters are stronger than expected , (ii) marginal distributions cannot be forgotten in the model selection process and (iii) special attention must be addressed to model validation as far as extreme values are of concern.