对具有两组历史洪水的洪水系列均值计算公式的探讨

我国历次部颁的水利水电工程设计洪水计算规范，都规定采用与经验点据拟合良好的频率曲线估计洪水设计值。在利用年最大洪峰流量资料推求设计洪水计算中，洪水系列往往包含有数个历史洪水，属不连序系列，有时甚至涉及到多个调查考证期。在采用矩法进行其参数估算时，本文重新推导了具有两个不同调查考证期不连序洪水系列均值的计算公式。比较结果表明，本文推导的公式可获得理想的适线效果。     

嘉陵江凤州水文站洪水分析计算

嘉陵江属长江上游左岸一级支流,凤州水文站于1984年建立于嘉陵江凤县段龙口镇。现已有39年实测水文资料,通过对凤州水文站实测洪水资料系列进行三性审查分析,该水文站洪水资料系列代表性良好。对该站由39年实测洪水资料和1981年历史调查洪水组成的不连序洪水系列,选择独立样本法进行经验频率计算,并在频率纸上点绘经验点据,采用矩法估算初始统计参数值,选用皮尔逊Ⅲ型曲线目估适线,得出凤州水文站不同频率下的洪峰流量。     

判别洪水系列中特大值的经验方法

本文通过对黄河干支流上具有洪水特大值的测站洪峰流量频率计算成果分析,提出用连序系列模比系数与特大值模比系数关系外包线的经验公式,作为判别洪水频率计算中洪水特大值的简捷方法。     

不连序系列统计参数计算的新方法—概率权重矩法

历史洪水资料的应用可以提高洪水分析成果的精度。但历史洪水与实测洪水组成的是不连序系列样本,如何估计这类不连序系列样本的统计参数一直是人们关心的问题之一。本文导出了应用于不连序系列样本的新的参数估计方法——概率权重矩法的计算公式,并用算例说明这种方法在P-Ⅲ分布参数估计中的应用。     

几种经验频率公式适应性的分析

一、前言由于水文特征值的不确定性,在我国的洪水频率分析中,一般采用适线法,假定洪水系列服从P-Ⅲ型分布,选用目估适线或优选适线来推求统计参数,以确定洪水设计值。因此,作为适线横标的经验频率选用何种公式计     

几种水文频率曲线参数估计方法的比较

水文频率曲线参数估计多采用计算机优化适线法,然而该方法在拟合经验点据时将特大值序列与一般洪水序列等同对待,仅在数学上寻找拟合误差最小的曲线,不符合水文学中历史洪水的克-闵假定。通过对比矩法、权函数法、概率权重矩法、线性矩法、目估适线法、计算机优化适线法6种方法在柴石滩水文站水文频率的计算结果,表明:在一般洪水部分,各方法得出的结果相近,但在特大值部分,计算机优化适线法较其他方法得出的设计值大得多。在推求特大洪水设计值时应从理论上继续深入探讨,不宜简单用计算机优化适线法进行计算。     

水文频率计算中参数估计方法的统计试验研究

本文采用统计试验方法,对于P-Ⅲ型曲线分析对比了矩法、极大似然法和适线法.在适线法中分析比较了七种不同的适线准则,并着重比较了其中的平方准则φ_1和绝对值准则φ_2,同时也分析比较了各种不同的经验频率公式.另外,还研究了历史洪水的作用.大量计算结果表明:矩法所得的设计值X_p,其期望值EX_p比总体真值x_p~0偏小较多,不够安全;极大似然法虽具有较好性质,但由于P-Ⅲ曲线在C≥2时似然方程无解,因此无法普遍使用;在适线法中发现适线准则对结果的影响很大,φ_2准则配合期望值公式(简记为φ_2-W)一般能使EX_p,稍大于x_p~0,较小(与矩法接近),因此φ_2-W适线法是较好的一种估计方法,应予采用.考虑历史洪水一般使EX_p增大、σx_p降低,因此是提高计算成果质量的重要措施.给出了历史洪水折算长度的参照数值,计算了历史洪水误差的影响.并修正了计算设计洪水安全改正值用的B值图.     

不连续序系列洪水频率计算分析

设计洪水是水利工程最为重要前期工作之一。大江大河上水文站所记录的实测洪水资料是分析计算设计洪水的主要依据。分析计算设计洪水还应包括调查历史洪水,实测洪水与历史洪水共同组成的不连序系列计算出的设计洪水较为合理。文中利用工程实例对两种方法计算不连序系列的洪水频率进行分析。     

天峨水文站历史洪水首项经验频率置信区间估算

历史特大洪水加入样本系列，对提高设计洪水精度起着关键作用。但由于特大洪水的稀遇性，以及随着实测系列的延长，其经验频率又具有不确定性，给频率曲线的外延带来任意性。采用引入对首项顺序统计量置信区间估计的方法，对首位历史洪水经验频率置信区间进行估算，指导频率曲线的适点配线，对设计洪水和设计暴雨分析计算工作具有一定的实用意义。     

用随机模型分析三峡年输沙量

矩法估算水文实测系列的统计参数存在抽样误差，随机模型可估算抽样误差，应用水文随机模拟方法，对三峡工程设计主要依据水文站屏山，寸滩，宜昌年输沙量进行随机模拟，估计了均值的抽样误差，并用均方误估计，累积平均和滑动平均等３种方法对随机模拟结果作了分析比较，结果表明，上述３站多年平均输沙量较稳定，以宜昌站多年平均输沙量５．３亿ｔ作为三峡工程泥沙设计的基本数值是合理的。     

混合分布在非一致性水文频率分析中的应用

传统水文频率分析方法的前提条件是水文极值系列需满足一致性要求,然而由于气候变化和人类活动的影响,使得水文资料的非一致性问题越来越突出,导致现行水文频率分析方法的应用受到挑战。根据重建的淮河流域1470年-1999年共530年夏季面平均降雨量长系列数据,进行分析,通过假设检验表明系列在1534年、1724年和1923年发生跳跃性变异,因而将系列划分为4个子平稳系列;采用现行频率分析方法估计每个子系列的概率分布函数,再根据混合分布概念由各子系列的概率分布构建一个综合的概率分布函数,作为非一致性降雨系列总体分布的估计。在此基础上,计算了给定设计标准下的设计值,并与基于大样本(530年)计算的经验设计值进行了对比,结果表明混合分布模型对观测系列具有较好的拟合效果。     

The Analysis and Improvement of the Fuzzy Weighted Optimum Curve-Fitting Method of Pearson – Type III Distribution

In the optimum curve-fitting method, due to the dissimilar purposes, the discrepant accuracy and positions of the experience points, the importance of the points should be different. For the limited sample size of the hydrologic sequence, there are sampling errors in the parameter estimation. In order to focus on the important points and reduce the errors effectively, the weight has been introduced in the optimum curve-fitting method. The existing weighted optimum curve-fitting methods are analyzed and studied. The Fuzzy Weighted Optimum Curve-fitting Method (FWOCM), which are the limited nomograph length and the determination of the membership degree function without the premise of a large sample. In order to solve the problems, the improvement of the method should be conducted. A new membership degree function is deducted and demonstrated on the premise that the hydrologic sequence is a large sample. The Monte Carlo statistical test optimum curve-fitting method is used to extend the nomograph to the entire frequency range. The improved FWOCMs are tested by the ideal data and the real data. In order to evaluate the performances of the improved FWOCMs, the selected excellent method and the improved percentage method are introduced to analyze the relative errors. The results show that the extension of the nomograph and the new membership degree function to a certain extent weakens the impact of the shorter hydrologic sequence on the curve-fitting. It indicates that the effect of the improved optimum curve-fitting methods is satisfying and can be used in the engineering practice.     

P—Ⅲ分布求矩适线法MATLAB实现与北海海域设计波高估计

介绍了P—Ⅲ分布求解参数的一种方法——求矩适线法。在一定的误差限内对样本的变差系数CU和均值x进行调整,然后调试偏态系数CS与CU之间的关系,并且按照绝对值准则挑选出一组最适合这组数据的参数值。并且给出了MATLAB的具体实现方法。最后介绍了P—Ⅲ分布求矩适线法在工程上的应用的一个例子,并且与P—Ⅲ分布矩法和极大似然法求参数进行了比较,求矩适线法求解参数,绝对值残差和最小,对数据拟合效果比较好。给出了北海海域的设计波高,为相关海洋工程的设计提供参考。     

Semi-parametric Estimation for Selecting Optimal Threshold of Extreme Rainfall Events

The two primary approaches of extreme events analysis are annual maximum series (AMS), which fits Generalized Extreme Value (GEV) distribution to the yearly peaks of events in the observation period, and partial duration series (PDS), which fits Generalized Pareto (GP) distribution to the peaks of events that exceed a given threshold. The PDS is able to reduce sampling uncertainty and is more useful in dealing with extreme values and asymmetries in the tails, but the optimal threshold is required. The objective of this study is to compare and determine the best method for selecting the optimal threshold of PDS using the hourly, 12-h and 24-h aggregated data of rainfall time series in Peninsular Malaysia. The choice of the threshold, or the number of largest order statistics, can be estimated by the parameters of extreme events. In this study, thirteen semi-parametric estimators are considered and applied to estimate the shape parameter or extreme value index (EVI). A semi-parametric bootstrap is then used to estimate the mean square error (MSE) of the estimator at each threshold and the optimal threshold is selected based on the smallest MSE. Based on the smallest MSE, the majority of stations and data durations favor the Adapted Hill estimator, followed by the QQ, Hill and Moment Ratio 1 estimators. Therefore, this study proves that the application of different estimators on real data may result in different optimal values of threshold and the choice of the best method is very much data-dependent.     

龙虎水文站设站年限分析

通过抽样误差检验法、产汇流参数检验法及设计洪水检验法对龙虎水文站的设站年限进行分析。结果表明:抽样误差检验法的设站年限为30 a;产汇流参数检验法的设站年限为20 a;设计洪水检验法的设站年限为10 a。据此判断,龙虎站设站年限为30 a,已达到设站年限,为站网规划调整提供了科学依据。     

Concept of Equivalent Reliability for Estimating the Design Flood under Non-stationary Conditions

Stationary hydrological frequency analysis (SHFA) has been commonly employed for estimating the design flood in most countries. Fundamental to applying SHFA is the assumption that the data series is stationary. In theory it is not applicable if the series is non-stationary. In this paper, we propose a concept of Equivalent Reliability (ER) to estimate the design flood under non-stationary conditions, which considers the impact of design life period of an engineering on design flood. ER implies that regardless of environmental changes, the design reliability of engineering under non-stationary conditions should be identical with the planned design reliability specified at the stage of the engineering planning. ER is expected to solve two key questions: (i) to estimate the design flood with a given return period for an engineering to be constructed, and (ii) to adjust the original design flood of an already constructed engineering to obtain a new design flood for making the engineering adapt to the changing conditions. Two experiments are provided to demonstrate how to employ ER to solve the above two questions. In addition, an example of annual peak flow series was also used to illustrate ER. Results show that the design life poses a considerable impact on the estimation of design flood and the uncertainty of parameter estimations leads to a non-negligible uncertainty on the estimation of design flood. Overall, ER can be a potential method for estimation of design flood under non-stationary conditions.     

变化环境下水文设计值计算方法研究综述

系统总结了国内外在变化环境下单、多变量水文设计值计算及计算成果不确定性评估三方面的研究成果,重点评述了基于水文极值系列重构、分布函数加权综合和变参数概率分布模型3类单变量水文设计值计算方法,分析了考虑边缘分布非一致性和结构参数非一致性的变参数联合分布函数模型,指出一致性条件下多变量重现期和设计值计算方法无法应用于非一致性条件下的多变量情景。提出了变化环境下水文设计值计算领域需进一步深入研究的问题,包括已建工程设计洪水复核调整、多变量情形下组合设计值计算、计算成果可靠性评估等。     

红水河与清水河干、支流洪水遭遇分析

以红水河与清水河汇合口迁江镇河段为例,通过分析干流红水河与支流清水河洪水的组合情况,推算受干流红水河顶托影响的支流清水河河口段设计洪水位。河段设计洪水水面线是堤防设计的主要依据,对于有干支流洪水相互顶托的河段,需分析其洪水组合和遭遇规律,进行不同组合情况的水面线推算,以外包线作为设计的依据。     

Real-time flood forecasting of Huai River with flood diversion and retarding areas

A combination of the rainfall-runoff module of the Xin’anjiang model, the Muskingum routing method, the water stage simulating hydrologic method, the diffusion wave nonlinear water stage method, and the real-time error correction method is applied to the real-time flood forecasting and regulation of the Huai River with flood diversion and retarding areas. The Xin’anjiang model is used to forecast the flood discharge hydrograph of the upstream and tributary. The flood routing of the main channel and flood diversion areas is based on the Muskingum method. The water stage of the downstream boundary condition is calculated with the water stage simulating hydrologic method and the water stages of each cross section are calculated from downstream to upstream with the diffusion wave nonlinear water stage method. The input flood discharge hydrograph from the main channel to the flood diversion area is estimated with the fixed split ratio of the main channel discharge. The flood flow inside the flood retarding area is calculated as a reservoir with the water balance method. The faded-memory forgetting factor least square of error series is used as the real-time error correction method for forecasting discharge and water stage. As an example, the combined models were applied to flood forecasting and regulation of the upper reaches of the Huai River above Lutaizi during the 2007 flood season. The forecast achieves a high accuracy and the results show that the combined models provide a scientific way of flood forecasting and regulation for a complex watershed with flood diversion and retarding areas.     

Estimation of discharge and its distribution in compound channels简

Results of research into a compound channel having width ratio(?)in excess of 11 are presented in the form of boundary shear distributions across the compound cross section.New relationship is derived between the percentage of shear carried by the flood plains(%)fp S and the percentage of area occupied by the flood plains(%)fp A.The equation so derived is taken as the basis to develop a new methodology to predict the stage discharge relationship specifically for wide compound channels using Darcy’s friction factor(f)for the main channel and flood plain regions.The methodology also is used for compound channels with smaller width ratios by applying the appropriate relation for%fp S derived earlier by different researchers and seems to work well.Next,as a corollary to the methodology,separate formulae are proposed to estimate flow distribution in main channel and flood plain regions.The proposed method and its corollary are tested for their validity against well-published small-scale data series of previous researchers along with some large-scale data series from EPSRC-FCF(A-Series)compound channel experiments and very good agreement is observed between the measured values and predicted values for total flow as well as zonal distribution of flow.The methodology is also applied to some compound river section data published in literature and is found to serve well the purpose of predicting flow in real world application.This new method gives the least RMS value of error for discharge prediction compared with some other well-known methods used for estimating stage-discharge relation in compound channels by considering all data sets.