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1.
Yii-Chen Wu Jun-Jih Liou Yuan-Fong Su Ke-Sheng Cheng 《Stochastic Environmental Research and Risk Assessment (SERRA)》2012,26(6):873-885
Goodness-of-fit tests based on the L-moment-ratio diagram for selection of appropriate distributions for hydrological variables have had many applications in recent years. For such applications, sample-size-dependent acceptance regions need to be established in order to take into account the uncertainties induced by sample L-skewness and L-kurtosis. Acceptance regions of two-parameter distributions such as the normal and Gumbel distributions have been developed. However, many hydrological variables are better characterized by three-parameter distributions such as the Pearson type III and generalized extreme value distributions. Establishing acceptance regions for these three-parameter distributions is more complicated since their L-moment-ratio diagrams plot as curves, instead of unique points for two-parameter distributions. Through stochastic simulation we established sample-size-dependent 95% acceptance regions for the Pearson type III distribution. The proposed approach involves two key elements—the conditional distribution of population L-skewness given a sample L-skewness and the conditional distribution of sample L-kurtosis given a sample L-skewness. The established 95% acceptance regions of the Pearson type III distribution were further validated through two types of validity check, and were found to be applicable for goodness-of-fit tests for random samples of any sample size between 20 and 300 and coefficient of skewness not exceeding 3.0. 相似文献
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3.
Jun-Jih Liou Yuan-Fong Su Jie-Lun Chiang Ke-Sheng Cheng 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(2):235-251
In studies involving environmental risk assessment, Gaussian random field generators are often used to yield realizations
of a Gaussian random field, and then realizations of the non-Gaussian target random field are obtained by an inverse-normal
transformation. Such simulation process requires a set of observed data for estimation of the empirical cumulative distribution
function (ECDF) and covariance function of the random field under investigation. However, if realizations of a non-Gaussian
random field with specific probability density and covariance function are needed, such observed-data-based simulation process
will not work when no observed data are available. In this paper we present details of a gamma random field simulation approach
which does not require a set of observed data. A key element of the approach lies on the theoretical relationship between
the covariance functions of a gamma random field and its corresponding standard normal random field. Through a set of devised
simulation scenarios, the proposed technique is shown to be capable of generating realizations of the given gamma random fields. 相似文献
4.
A gamma distribution is one of the most frequently selected distribution types for hydrological frequency analysis. The bivariate gamma distribution with gamma marginals may be useful for analysing multivariate hydrological events. This study investigates the applicability of a bivariate gamma model with five parameters for describing the joint probability behavior of multivariate flood events. The parameters are proposed to be estimated from the marginal distributions by the method of moments. The joint distribution, the conditional distribution, and the associated return periods are derived from marginals. The usefulness of the model is demonstrated by representing the joint probabilistic behaviour between correlated flood peak and flood volume and between correlated flood volume and flood duration in the Madawask River basin in the province of Quebec, Canada. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
5.
Hydrological risk analysis is essential and provides useful information for dam safety management and decision-making. This study presents the application of bivariate flood frequency analysis to risk analysis of dam overtopping for Geheyan Reservoir in China. The dependence between the flood peak and volume is modelled with the copula function. A Monte Carlo procedure is conducted to generate 100,000 random flood peak-volume pairs, which are subsequently transformed to corresponding design flood hydrographs (DFHs) by amplifying the selected annual maximum flood hydrographs (AMFHs). These synthetic DFHs are routed through the reservoir to obtain the frequency curve of maximum water level and assess the risk of dam overtopping. Sensitive analysis is performed to investigate the influence of different AMFH shapes and correlation coefficients of flood peak and volume on estimated overtopping risks. The results show that synthetic DFH with AMFH shape characterized by a delayed time to peak results in higher risk, and therefore highlight the importance of including a range of possible AMFH shapes in the dam risk analysis. It is also demonstrated that the overtopping risk is increased as the correlation coefficient of flood peak and volume increases and underestimated in the independence case (i.e. traditional univariate approach), while overestimated in the full dependence case. The bivariate statistical approach based on copulas can effectively capture the actual dependence between flood peak and volume, which should be preferred in the dam risk analysis practice. 相似文献
6.
J. T. Shiau 《Stochastic Environmental Research and Risk Assessment (SERRA)》2003,17(1-2):42-57
Extreme hydrological events are inevitable and stochastic in nature. Characterized by multiple properties, the multivariate
distribution is a better approach to represent this complex phenomenon than the univariate frequency analysis. However, it
requires considerably more data and more sophisticated mathematical analysis. Therefore, a bivariate distribution is the most
common method for modeling these extreme events. The return periods for a bivariate distribution can be defined using either
separate single random variables or two joint random variables. In the latter case, the return periods can be defined using
one random variable equaling or exceeding a certain magnitude and/or another random variable equaling or exceeding another
magnitude or the conditional return periods of one random variable given another random variable equaling or exceeding a certain
magnitude. In this study, the bivariate extreme value distribution with the Gumbel marginal distributions is used to model
extreme flood events characterized by flood volume and flood peak. The proposed methodology is applied to the recorded daily
streamflow from Ichu of the Pachang River located in Southern Taiwan. The results show a good agreement between the theoretical
models and observed flood data.
The author wishes to thank the two anonymous reviewers for their constructive comments that improving the quality of this
work. 相似文献
7.
Estimation procedures for exchangeable Marshall copulas with hydrological application 总被引：1，自引：1，他引：0
Fabrizio Durante Ostap Okhrin 《Stochastic Environmental Research and Risk Assessment (SERRA)》2015,29(1):205-226
Complex phenomena in environmental sciences can be conveniently represented by several inter-dependent random variables. In order to describe such situations, copula-based models have been studied during the last year. In this paper, we consider a novel family of bivariate copulas, called exchangeable Marshall copulas. Such copulas describe both positive and (upper) tail association between random variables. Specifically, inference procedures for the family of exchangeable Marshall copulas are introduced, based on the estimation of their (univariate) generator. Moreover, the performance of the proposed methodologies is shown in a simulation study. Finally, an illustration describes how the proposed procedures can be useful in a hydrological application. 相似文献
8.
Modelling bivariate extreme precipitation distribution for data‐scarce regions using Gumbel–Hougaard copula with maximum entropy estimation 
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下载免费PDF全文 A new method of parameter estimation in data scarce regions is valuable for bivariate hydrological extreme frequency analysis. This paper proposes a new method of parameter estimation (maximum entropy estimation, MEE) for both Gumbel and Gumbel–Hougaard copula in situations when insufficient data are available. MEE requires only the lower and upper bounds of two hydrological variables. To test our new method, two experiments to model the joint distribution of the maximum daily precipitation at two pairs of stations on the tributaries of Heihe and Jinghe River, respectively, were performed and compared with the method of moments, correlation index estimation, and maximum likelihood estimation, which require a large amount of data. Both experiments show that for the Ye Niugou and Qilian stations, the performance of MEE is nearly identical to those of the conventional methods. For the Xifeng and Huanxian stations, MEE can capture information indicating that the maximum daily precipitation at the Xifeng and Huanxian stations has an upper tail dependence, whereas the results generated by correlation index estimation and maximum likelihood estimation are unreasonable. Moreover, MEE is proved to be generally reliable and robust by many simulations under three different situations. The Gumbel–Hougaard copula with MEE can also be applied to the bivariate frequency analysis of other extreme events in data‐scarce regions. 相似文献
9.
S. Yue 《Stochastic Environmental Research and Risk Assessment (SERRA)》2001,15(3):244-260
The open literature reveals several types of bivariate exponential distributions. Of them only the Nagao–Kadoya distribution
(Nagao and Kadoya, 1970, 1971) has a general form with marginals that are standard exponential distributions and the correlation
coefficient being 0≤ρ<1. On the basis of the principle that if a theoretical probability distribution can represent statistical
properties of sample data, then the computed probabilities from the theoretical model should provide a good fit to observed
ones, numerical experiments are executed to investigate the applicability of the Nagao–Kadoya bivariate exponential distribution
for modeling the joint distribution of two correlated random variables with exponential marginals. Results indicate that this
model is suitable for analyzing the joint distribution of two exponentially distributed variables. The procedure for the use
of this model to represent the joint statistical properties of two correlated exponentially distributed variables is also
presented. 相似文献
10.
《Advances in water resources》2007,30(4):1053-1055
The recent paper by Loaiciga and Leipnik [Loaiciga HA, Leipnik RB. Correlated gamma variables in the analysis of microbial densities in water. Adv Water Resour 2005;28:329–35] introduced a novel bivariate gamma distribution and studied its ratio distribution with application to hydrological sciences. In this note, we derive the corresponding distributions of the sum and the product. We also derive a powerful mixture representation of the bivariate gamma distribution unnoticed by Loaiciga and Leipnik. 相似文献
11.
Abstract In the bivariate analysis of hydrological events, such as rainfall storms or flood hydrographs, the choice of an appropriate return period for structure design leads to infinite combinations of values of the related random variables (e.g. peak and volume in the analysis of floods). These combinations are generally not equivalent, from a practical point of view. In this paper, a methodology is proposed to identify a subset of the critical combinations set that includes a fixed and arbitrarily chosen percentage in probability of the events, on the basis of their probability of occurrence. Therefore, several combinations can be selected within the subset, taking into account the specific characteristic of the design problem, in order to evaluate the effects of different hydrological loads on a structure. The proposed method is applicable to any type of bivariate distribution, thus providing a simple but effective rule to narrow down the infinite possible choices for the hydrological design variables. In order to illustrate how the proposed methodology can be easily used in practice, it is applied to a study case in the context of bivariate flood frequency analysis. Editor Z.W. Kundzewicz; Associate editor Sheng Yue Citation Volpi, E. and Fiori, A., 2012. Design event selection in bivariate hydrological frequency analysis. Hydrological Sciences Journal, 57 (8), 1506–1515. 相似文献
12.
在准确揭示水文过程变化特性的基础上开展中长期(月尺度及以上)水文预报,是掌握未来水文情势和演变规律,以及研究解决实际水文水资源问题的重要基础.水文时间序列预报方法是揭示未来水文情势和演变规律的重要技术手段.本文首先梳理了目前常用的各类水文序列预报方法,分析讨论了各方法的基本原理和主要缺陷.然后,通过综合分析相关研究成果,总结得到关于水文序列预报方法的4点重要认识:序列预报前应进行序列分解;序列中确定成分和随机成分应分别建模预报;序列预报结果需要估计不确定性;模型集成效果常常优于单个模型效果.最后,提出一个水文时间序列概率预报方法的通用架构.利用该通用架构能够克服常规模型或方法的缺陷,进行物理成因分析的基础上,针对水文序列中不同特性的确定成分和随机成分别进行分析,既可得到准确的确定性预报结果,又可对预报结果的不确定性进行定量评估,并可提高最终预报结果的合理性和可靠性. 相似文献
13.
针对目前研究蒸散发时间尺度转换方面的不足,构建了月蒸散发时间尺度转换模型,对淮河史灌河流域黄泥庄小流域1982-1987年月蒸散发能力进行逐栅格解集,并与改进后的AFFDEF分布式水文模型耦合进行日径流过程模拟.结果显示:解集产生的日蒸散发能力随时间在平均值附近波动变化,能很好地体现日蒸发量的时间变异特点;模拟的日径流过程的精度较高,平均Nash效率系数在80%以上,径流深相对误差都在10%以内,平均泊松相关系数为0.912,模拟流量过程曲线与实测值匹配的较好;经与采用平均解集模式的模拟结果对比发现,耦合蒸散发时间尺度转换模型后的模拟精度与前者大体相当,部分指标略优于前者.蒸散发时间尺度转换模型解集产生的日蒸散发量序列能够反映日蒸发量的时间变异特点,更能满足区域日降雨径流过程模拟的需要,可为解决资料匮乏区域水文模拟提供一个新途径. 相似文献
14.
Random variable simulation has been applied to many applications in hydrological modelling, flood risk analysis, environmental impact assessment, etc. However, computer codes for simulation of distributions commonly used in hydrological frequency analysis are not available in most software libraries. This paper presents a frequency‐factor‐based method for random number generation of five distributions (normal, log–normal, extreme‐value type I, Pearson type III and log‐Pearson type III) commonly used in hydrological frequency analysis. The proposed method is shown to produce random numbers of desired distributions through three means of validation: (1) graphical comparison of cumulative distribution functions (CDFs) and empirical CDFs derived from generated data; (2) properties of estimated parameters; (3) type I error of goodness‐of‐fit test. An advantage of the method is that it does not require CDF inversion, and frequency factors of the five commonly used distributions involves only the standard normal deviate. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
15.
The physically based distributed hydrological models are ideal for hydrological simulations; however most of such models do not use the basic equations pertaining to mass, energy and momentum conservation, to represent the physics of the process. This is plausibly due to the lack of complete understanding of the hydrological process. The soil and water assessment tool (SWAT) is one such widely accepted semi-distributed, conceptual hydrological model used for water resources planning. However, the over-parameterization, difficulty in its calibration process and the uncertainty associated with predictions make its applications skeptical. This study considers assessing the predictive uncertainty associated with distributed hydrological models. The existing methods for uncertainty estimation demand high computational time and therefore make them challenging to apply on complex hydrological models. The proposed approach employs the concepts of generalized likelihood uncertainty estimation (GLUE) in an iterative procedure by starting with an assumed prior probability distribution of parameters, and by using mutual information (MI) index for sampling the behavioral parameter set. The distributions are conditioned on the observed information through successive cycles of simulations. During each cycle of simulation, MI is used in conjunction with Markov Chain Monte Carlo procedure to sample the parameter sets so as to increase the number of behavioral sets, which in turn helps reduce the number of cycles/simulations for the analysis. The method is demonstrated through a case study of SWAT model in Illinois River basin in the USA. A comparison of the proposed method with GLUE indicates that the computational requirement of uncertainty analysis is considerably reduced in the proposed approach. It is also noted that the model prediction band, derived using the proposed method, is more effective compared to that derived using the other methods considered in this study. 相似文献
16.
In this study, a fuzzy‐based simulation method (FBSM) is developed for modelling hydrological processes associated with vague information through coupling fuzzy vertex analysis technique with distributed hydrological model. The FBSM can handle uncertainties existed as fuzzy sets in the hydrological modelling systems, and solutions under an associated number of α‐cut levels can be generated by solving 2n deterministic models. The lower reach of the Tarim River Basin in China is selected as a study case for demonstrating applicability of the proposed method. The developed model is calibrated and validated against observed groundwater elevation for four wells during the period 2000–2001, and generally performed acceptable for model Nash–Sutcliffe coefficient (R2) and correlation coefficient (R). The R2 is approximately over 0·65 and the correlation coefficient is higher than 0·90. Based on the technique of fuzzy simulation, the uncertainties of two parameters (KH and LC) are reflected under different α‐cut levels. The results indicate that, under a lower degree of plausibility, the interval between the lower and upper bounds of the groundwater elevation is wider; conversely, a higher degree of plausibility would lead to a narrow interval. The main effect of KH is more significant than the effect of LC at most well sites. The proposed method is useful for studying hydrological processes within a system containing multiple factors with uncertainties and providing support for identifying proper water resources management strategies. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
17.
D. R. Helwade A. Subramanyam 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(2):271-281
In this paper, a certain bivariate exponential distribution is used for the spatial prediction. The unobserved random variable
is predicted by the projection onto the space of all linear combinations of the powers, up to degree m, of the observed random variables plus the constant 1. We obtain a solution by assuming that all the bivariate distributions
follow Gumbel’s type III or logistic form of bivariate exponential. The method is implemented on two data sets and the results
are presented. The predictions are compared with the original values through Mean Structural Similarity (MSSIM) index of Wang
et al. (IEEE Trans Image Process 13(4):600–612, 2004). Using the MSSIM index the proposed method is also compared with Ordinary Kriging and with Simple Kriging after normal score
transform. 相似文献
18.
Spatial rainfall amounts accumulated over short to medium periods of time, say a few days, tend to have a probabilistic structure with very distinctive features. Some of these that are specially relevant for the purpose of spatial modeling are the presence of mixed sampling distributions, right skewed distributions conditional on rainfall occurrence, and a complex spatial association structure. The goal of this work is to construct a family for the bivariate distributions of spatial rainfall fields that incorporates these distinctive features. It is based on the separate modeling of spatial occurrence of rainfall and the spatial distribution of positive rainfalls. The main properties of the bivariate distributions are derived, and some properties of the random field realizations are illustrated through simulation. Some limitations of the proposed model are also discussed. 相似文献
19.
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. 相似文献
20.
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. 相似文献