两变量设计洪水估计的不确定性及其对水库防洪安全的影响

在两变量水文频率分析中,样本系列容量一般较小,使得水文设计值估计具有不确定性。本文基于Copula函数和Parametric Bootstrap方法,并考虑联合设计值的最可能组合模式,建立可描述两变量设计洪水估计不确定性的C-PBU(Copula-based Parametric Bootstrap Uncertainty)模型,同时提出了定量评价两变量不确定性的度量指标,分析了联合设计值估计不确定性对水库最高调洪水位的影响,并对比了不同典型洪水选取模式下的水位不确定性。以隔河岩水库为例,推求了两变量设计值估计的95%置信区域;比较了不同样本容量对不确定性的影响。结果表明:设计洪水估计和典型洪水选择具有较大的不确定性,可采用C-PBU模型推求置信区间,来考虑设计洪水估计不确定性对水库防洪安全的影响。     

泾河流域水沙联合分布特征分析及其不确定性评估

径流与泥沙是非独立的二维随机变量,若要对流域实现水沙并举的科学管理方案,开展水沙联合概率分析显得尤为必要。而在联合概率分析中,水沙样本系列容量一般较小,使得联合设计值估计具有不确定性。以泾河流域为例,本文提出基于蒙特卡洛法的两变量联合设计值不确定性量化方法。该方法基于Copula函数建立水沙联合分布模型,推求两变量联合设计值的最可能组合模式,利用蒙特卡洛抽样法分析样本不确定性对水沙联合设计值的影响,计算两变量设计值置信区间。结果表明,OR重现期为20年的情况下,联合设计值95%二元置信区间表现出较大的不确定性,对流域工程设计值的确定提出了巨大挑战,且随着重现期水平的增加,联合设计值的不确定性随之增加。     

Flood Frequency Analysis of Interconnected Rivers by Copulas

Flood frequency analysis (FFA) considering the confluence of interconnected rivers is important for hydraulic structures (such as dams or diversions) design, but it has received little attention. This study develops a copula-based method for FFA and quantile estimation considering the confluence of two interconnected rivers, along with the uncertainty estimation by a nonparametric bootstrapping algorithm. Flood probability distribution and return periods are estimated for the two rivers by mapping from bivariate to univariate peak flow quantile estimation. The methodology is applied to the case study of Qezel Ozan and Shahrud Rivers which merge to one of the largest reservoir dams in Iran: Sefidrud (Manjil) dam. According to the results from Peak flow records from Gilvan station (GPF) at Qezel Ozan River and from Loshan station (LCF) at Shahrud River, Gaussian copula with Weibull and gamma margins fits best. Also, it shows that some peak flow quantiles with the same magnitudes have a different probability of occurrences at the confluence of the rivers, and the bivariate estimation uncertainty usually plays an important role in FFA. These findings suggest the use of bivariate instead of univariate distributions to the peak flows at the confluence of interconnected rivers, in which the sampling uncertainty should be considered.

     

基于分位点回归模型的洪水概率预报方法

采用分位点回归模型分析洪水预报的不确定性, 提供洪水预报倾向值( 预报概率分布的中位数) 和 90% 置信度的预报区间成果, 实现了洪水概率预报。基于/ 精度2可靠性0 联合评价指标对分位点回归模型计算的预报倾向值 和预报区间成果进行了评估。在信江流域梅港站的应用结果表明: 基于分位点回归模型提供的倾向值定值预报结 果可进一步提升洪水预报的精度; 同时该模型提供的 90% 预报区间结果具有较高的覆盖率( 约 90% ) 且离散度较小 ( 小于 01 20) , 表明预报区间以较窄的宽度包含了绝大多数的实测值, 预报可靠性较强。     

条件期望在两变量洪水频率分析中的应用

针对现行单变量洪水频率分析计算方法无法考虑洪水要素之间的相关性这一不足,采用Copula函数构建洪水峰、量之间的二维联合分布,根据条件期望的原理,提出了一种推求两变量设计洪水的新方法。以清江隔河岩水库为例,计算了1 000 a一遇的两变量设计洪水,推求了对应的设计洪水过程线,并与单变量设计值进行了比较。结果表明,两变量设计值大于单变量设计值,两变量设计值对应的水库调洪最高水位略高于单变量设计值。由于两变量频率分析考虑了洪水峰、量之间的内在相关性,更符合水文现象的内在规律,所推求的两变量条件期望设计值组合相对于单变量设计值而言也是偏安全的。所提方法为洪水频率分析提供了一条新途径。     

Risk and uncertainty analysis for dam overtopping – Case study: The Doroudzan Dam,Iran

There is a growing tendency to assess the safety levels of existing dams by using mathematical and statistical methods. In this study, the application of risk and uncertainty analysis to dam overtopping is presented for Doroudzan Reservoir located at the south part of Iran. The main objective of the overtopping analysis of dams is estimating the height of water in the reservoir under various inflows and comparing the computed results with the dam crest elevation. Hence, the main steps of this study include univariate flood frequency analysis of annual maximum inflows to estimate the peak flows in various return periods, generate inflow hydrographs based on the estimated peak flows, and route the hydrographs through the reservoir to compute the maximum height of the water in reservoir. In this study, the spillway discharge coefficient, quantile of peak flows, and initial water surface level are subject to uncertainty, and the Monte-Carlo simulation (MCS) and Latin hypercube sampling (LHS) are applied to perform the uncertainty analysis. In addition to inflows, the effect of different wind speeds on the probability of overtopping has been considered. The results demonstrated that both increasing water level and wind speed have significant impact on the risk of overflowing.     

Reliability analysis for reservoir water supply due to uncertainties in hydrological factors,rainfall-runoff routing and operating rule curves

This study aims at developing a reliability-analysis model (RA_WS_RES) to quantify the effect of variations in uncertainties factors regarding the reservoir inflow and outflow at various 10-day periods on the reliability of water supply from the reservoir. The uncertainty factors considered are classified into three types: the hydrological factors (rainfall, baseflow, and initial water level of the reservoir), the reservoir operation rules for the water-allocation model (RIBASIM), and the parameters of rainfall-runoff model (i.e. Sacramento Soil Moisture Accounting, SAC-SMA). In the proposed RA_WS_RES model, the reliability of the water supply attributed to the uncertainty factors considered can be quantified by collaborating the multivariate Monte Carlo simulation (MMCS) methods and uncertainty-risk (advanced first order and second moment, AFOSM) analysis. Shihmen Reservoir watershed in Northern Taiwan is selected as the study area and four associated demand nodes are regarded as the study nodes; the hourly rainfall data from 1987 to 2014 and other hydrological data (i.e. rainfall, baseflow, and initial water level of the reservoir) as well as the operation rule curves are adopted in the model development and application. The results from the numerical experiences indicate that among the uncertainty factors concerned, the average rainfall depth at the current 10-day period and the range between the lower and critical levels are more sensitive to the estimation of water supply from Shihmen Reservoir. Additionally, the impact of variation in baseflow on the reliability of the water supply from Shihmen Reservoir should be taken into account, especially in the dry season. In addition to rainfall and baseflow, the initial water level should be an important source for the water supply, and its effect gradually reduces with the 10-day period. Furthermore, the reliability of water supply is obviously impacted by the uncertainty in the range between the lower and critical rule level, especially in the dry season, due to its range being adversely related with the water supply. Eventually, the proposed RA_WS_RES model can effectively and reasonably quantify the reliability of water supply attributed to variations in uncertainty factors at different 10-day period under the consideration of climate change.     

基于联系数集对势置信区间估计的旱灾风险分析模型

针对现有集对势方法难以进一步挖掘联系数中不确定性变化信息问题,提出将三元联系数减法集对势看作一个服从正态分布的随机变量,采用95%置信水平下置信区间的长度来反映不确定性大小,建立了基于联系数集对势置信区间估计的旱灾风险分析模型。以宿州市为例对构建的模型进行了验证,评价结果与现有的减法集对势、半偏减法集对势方法相一致,说明基于联系数集对势置信区间估计的旱灾风险分析模型合理有效;该模型得到的评价结果不是一个数值,而是一置信概率区间,提供了关于评价结果可靠性方面的信息,能够反映在多种不确定因素综合影响下的旱灾风险实际情况,在水资源保护系统不确定性分析评价中具有应用前景。     

基流分割对城市雨洪模拟不确定性分析的影响

为了探究基流分割对城市雨洪模拟的影响,以济南市主城区流域为例构建SWMM模型,采用2005—2010年7场基流分割前后的实测洪水资料校验模型,应用GLUE方法,以均方根误差为似然评判依据对模拟结果进行不确定性分析,探讨了基流分割前后流量数据对模拟结果不确定性的影响。结果表明:各场次暴雨基流占洪峰流量的比例均值为13.38%,对洪水模拟效果影响较大;GLUE方法能够有效提取高精度参数集,相比于原始流量序列,应用基流分割后流量作为校验模型依据,流量过程90%置信区间覆盖率增大100%,平均偏移幅度和平均对称度分别减小42.60%和87.19%。通过基流分割可有效降低流量数据作为模型校验数据导致的模拟结果不确定性,提升洪水预报性能,获取更精确对称的流量预报区间。     

Integrated modelling under uncertainty in watershed-level assessment and management.

Uncertainty in water quality model predictions is inevitably high due to natural stochasticity, model uncertainty, and parameter uncertainty. An integrated modelling system (modified-BASINS) under uncertainty is described and demonstrated for use in receiving-water quality prediction and watershed management. A Monte Carlo simulation was used to investigate the effect of various uncertainty types on output prediction. Without pollution control measures in the watershed, the concentrations of total nitrogen (T-N) and total phosphorus (T-P) in the Hwaong Reservoir, considering three uncertainty types, would be less than about 4.4 and 0.23 mg L(-1), respectively, in 2012, with 90% confidence. The effects of two watershed management practices, wastewater treatment plants (WWTP) and constructed wetlands (WETLAND), were evaluated. The combined scenario (WWTP + WETLAND) was the most effective at improving reservoir water quality, bringing concentrations of T-N and T-P in the Hwaong Reservoir to less than 3.4 and 0.14 mg L(-1), 24 and 41% improvements, respectively, with 90% confidence. Overall, the Monte Carlo simulation in the integrated modelling system was practical for estimating uncertainty and reliable in water quality prediction. The approach described here may allow decisions to be made based on the probability and level of risk, and its application is recommended.     

基于广义极值分布和Metropolis-Hastings抽样算法的贝叶斯MCMC洪水频率分析方法

广义极值（GEV）分布是国内外洪水频率分析建模中广泛应用的一种概率分布。本文将水文频率分布线型的未知参数看作随机变量，通过基于Metropolis-Hastings抽样算法的贝叶斯MCMC方法估计GEV分布参数和设计时段洪量的后验分布，并据此进行极值洪水的频率分析。汉江流域丹江口水库年最大1日（3日、5日、7日）洪量频率分析的结果表明了本方法的有效性和实用性。主要结论包括：基于Metropolis-Hastings抽样的MCMC模拟在GEV分布参数的贝叶斯估计计算中行之有效；由于利用了与似然函数渐近性质无关的先验信息，贝叶斯估计方法得到的高分位数设计洪量的后验分布比经典统计方法得到的设计洪量能包含更多的信息，从而能表达由于参数不确定性而引起的预测不确定性。该方法能显著地通过分位数图、PPCC法、均方根误差法、K-S法等多种拟合优度检验方法，拟合效果不亚于其他常用的经典统计方法。     

Optimal Design of Water Distribution Networks Considering Fuzzy Randomness of Demands Using Cross Entropy Optimization

This paper presents cross entropy (CE) optimization for optimal design of water distribution networks (WDN) under demand uncertainty. In design of WDNs, it is desired to achieve a minimum cost WDN that provides higher reliability in meeting the demands. To achieve these goals, an optimization model is formulated for design of WDNs with an objective of minimizing the total cost of WDN subject to meeting the nodal demands at a specified system reliability, mass conservation and other physical constraints. The uncertainty in future water demands is modeled using the theory of fuzzy random variable (FRV). The water demand at each node is assumed to be following a normal distribution with a fuzzy mean, and 10 % (or 20 %) of the fuzzy mean as its standard deviation. The water demand is represented as a triangular fuzzy number with the random demand as its kernel, and the interval of ±5 % (or ±10 %) variation of the random demand as its support for two scenarios. The fuzzy random system reliability (R) of WDNs is defined on the basis of necessity measure to assess system performance under fuzzy random demands and crisp head requirements. The latin hypercube sampling method is adopted for sampling of uncertain demands. The methodology is applied to two WDNs, and optimization models are solved through cross entropy optimization for different levels of reliability, and generated tradeoffs between the cost and R. On comparing the solutions obtained with the proposed methodology with earlier reported solutions, it is noted that the proposed method is very effective in producing robust optimal solutions. On analyzing the tradeoffs between reliability and costs, the results show that negligence of uncertainty can lead to under design of the WDNs, and the cost increases steeply at higher levels of reliability. The results of the two case studies demonstrate that the presented CE based methodology is effective for fuzzy-probabilistic design of WDNs.     

Comparative Study of Three Updating Procedures for Real-Time Flood Forecasting

Accurate real-time flood forecasting is essential for flood control and warning system, reservoir operation and other relevant water resources management activities. The objective of this study is to investigate and compare the capability of three updating procedures, namely autoregressive (AR) model, recursive least-squares (RLS) model and hydrologic uncertainty processor (HUP) in the real-time flood forecasting. The Baiyunshan reservoir basin located in southern China was selected as a case study. These three procedures were employed to update outputs of the established Xinanjiang flood forecasting model. The Nash-Sutcliffe efficiency (NSE) and Relative Error (RE) are used as model evaluation criteria. It is found that all of these three updating procedures significantly improve the accuracy of Xinanjiang model when operating in real-time forecasting mode. Comparison results also indicated that the HUP performed better than the AR and RLS models, while RLS model was slightly superior to AR model. In addition, the HUP implemented in the probabilistic form can quantify the uncertainty of the actual discharge to be forecasted and provide a posterior distribution as well as interval estimation, which offer more useful information than two other deterministic updating procedures. Thus, the HUP updating procedure is more promising and recommended for real-time flood forecasting in practice.     

大渡河流域超阈值降雨样本模拟及不确定性分析

大渡河流域地形十分复杂,流域内气候随高程变化差异较大。通过超阈值模型模拟大渡河流域范围内9个雨量站的逐日降水资料序列,利用极大似然估计法计算模型参数,采用概率图、分位数图、重现水平图、密度函数图4种较直观的诊断图形对模型的合理性进行了全面评估,并借助轮廓似然方法估计模型关键参数及设计强降雨的置信区间。研究结果表明,各站点超阈值降雨样本均服从Pareto分布,可以选择GPD模型作为大渡河流域强降雨统计推断的分布函数类型,轮廓似然法能反映重现期长短对设计降雨置信区间的影响。可为大渡河流域降雨不确定性的定量评估及梯级水库群洪水预报提供依据。     

基于多步预报模型的径流中长期预测研究

针对径流中长期预报模型中广泛存在的不确定性问题,在以往研究的基础上,建立了基于最近邻回归预测的径流中长期多步概率预报模型。介绍了该模型的计算方法和重要参数的选取方法,并应用于实例预报工作中。结果表明,该模型在4个月的预报期内,具有较高的概率预报精度。同时,该模型概念清晰,避免了参数不确定性,不仅能够提供常规的确定性预报结果,而且能够给出在不同置信水平下的预报置信区间,便于量化预报风险,为最优决策的制定提供依据。     

A Superposed Model for the Pipe Failure Assessment of Water Distribution Networks and Uncertainty Analysis: A Case Study

Pipe failure often occurs in water distribution networks (WDNs) and results in high levels of water loss and socio-economic damage. Physical-based, statistical and data-driven models have been developed to estimate pipe failure rates (failures per km of pipe per year) to efficiently manage water losses from WDNs and to ensure safe operations. Due to the complexities of pipe failure patterns, we develop a superposed statistical model to depict the relationship between pipe failure rate and pipe age. The model’s level of uncertainty was then quantified by simulating pipe failures as Poisson numbers. Part of Beijing’s WDN is taken as a study case, and pipe failure data for a 4-year period, as well as pipe properties, are collected to develop the pipe failure model. The case study results show that the pipe failure rates vary with time in a non-monotonic manner and that the proposed model captures pipe failure behaviour with an R² value of 0.95. A 95% confidence interval of modelled pipe failures for each pipe age group is used to describe the uncertainty level of the model. We find that 88% of the observations fall under the 95% confidence interval. The established model could be applied to prioritize pipes with higher failure rates to optimize pipe replacement/rehabilitation strategies. Our uncertainty analysis of this model can help utility managers understand the model’s reliability and formulate reasonable WDN management plans.     

Spatio-Temporal Multi-Criteria Optimization of Reservoir Water Quality Monitoring Network Using Value of Information and Transinformation Entropy

Identifying optimal Water Quality Monitoring Stations (WQMS) with high values of information on the entire reservoir status, instead of all potential WQMS would significantly reduce the monitoring network expenditure while providing adequate spatial coverage. This study presented a new methodology for spatio-temporal multi-criteria optimization of reservoir WQMS based on Value of Information (VOI), Transinformation Entropy (TE), Non-dominated Sorting Genetic Algorithm II (NSGA-II), Preference Ranking Organization METHod for Enrichment Evaluation (PROMETHEE), and IRanian Water Quality Index (IRWQI). Although, all mentioned methods and concepts are well-known and have been used in water resources management, but their integration into a specific application for spatio-temporal multi-criteria optimization of reservoir WQMS is definitely an innovation and a contribution to improvement of WQMS design. More specifically, maximizing VOI as a decision-makers’ design criteria for optimization of WQMS, and considering spatial and temporal variations of water quality at different reservoir depths are new innovations in this research. The multi-objective optimization model was based on three objectives: 1) minimizing costs; 2) maximizing VOI; and 3) minimizing TE (redundant information). Considering these objectives, the NSGA-II multi-objective optimization method was used to find Pareto-optimal solutions. The most preferable solution was then determined using PROMETHEE multi-criteria decision making method. The proposed methodology was applied to Karkheh Reservoir with more than 5 billion cubic meter capacity and 60 km length that is one of the largest reservoirs in Southwestern Iran, however, the proposed approach has the ability to be generalized for any generic reservoir. Considering equal weights for criteria, PROMETHEE method resulted in 6 optimized WQMS out of 60 potential ones and a period of 25 days for optimal sampling interval. The optimized monitoring stations were mainly located at deep parts where most water quality variations are expected to occur. To show sensitivity of the model to different weights, 4 scenarios with various relative weights were evaluated in the PROMETHEE method. Results indicated that by increasing the weight of the second criterion (maximizing VOI), the number of optimized WQMS increased and the sampling interval decreased.     

基于GLUE的新安江模型参数不确定性分析及应用

结合新安江模型在东洋河流域的应用,提出了基于GLUE方法的新安江模型参数不确定性分析。采用GLUE算法抽样结果对东洋河流域进行不确定性预报,选用水文模拟中常用的确定性系数作为似然判据,通过设定0.7为阀值,得到的90%置信区间的流量过程,实例研究表明,以该结果进行不确定预报是可行的。     

比估计法在节水工程节水量计算中的应用

在大规模的节水工程中，用简单抽样方法抽取典型灌区，然后在典型灌区进行实地的精确观测和研究计算。运用统计方法中较复杂的非线性估计中的比估计，计算各个中间值并对中间值进行处理分析。通过辅助函数，寻求最优权系数，从而得到均方差最小的估计值，并求出置信区间。从而完成对整体总和的最优估计，以及量化这种估计的偏离概率。     

Uncertainty Analysis of Flood Control Design Under Multiple Floods

Hydraulic engineerings built on tributaries at the confluence of main and branch streams are significant to river management and runoff regulation. The Flood Control Design Level (FCDL) calculations for these works are directly influenced by tributary floods and supporting effects from the mainstream. However, the determination of design level under main and tributary floods has not been well investigated. To address this issue, the authors proposed a Copula-based approach to analyze the design level under multiple runoff discharge with a case study of the Guiping Shipping Hub(GPSH). The proposed method is compared with the conventional multivariate hydrological elements analysis approach, and the sampling uncertainty is also studied. The results showed that the joint distribution of main and tributary floods is well modeled by Clayton Copula, with PE3s as the best-fit marginal distributions. Furthermore, the different roles of main and branch fluxes in design level calculation can be identified by the offered Flood Control return period(FCRP). And the design levels conducted by the FCRP can avoid the situation over-or-under performed by the OR or AND RP. Moreover, flood combinations uncertainty analysis indicates that the uncertainty of the joint design combinations decreases with the increase of sample size n but increases with the rise of the design T. Finally, the 95% confidence interval and standard deviation of the design level calculated by FCRP are smaller than that of OR RP, which means the FCRP can reduce uncertainty under multiple floods. These results suggest that the proposed FCRP provides an appropriate approach for determining the design level under combined fluxes and serves as a reference for engineering practice.