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1.
Studies have illustrated the performance of at-site and regional flood quantile estimators. For realistic generalized extreme value (GEV) distributions and short records, a simple index-flood quantile estimator performs better than two-parameter (2P) GEV quantile estimators with probability weighted moment (PWM) estimation using a regional shape parameter and at-site mean and L-coefficient of variation (L-CV), and full three-parameter at-site GEV/PWM quantile estimators. However, as regional heterogeneity or record lengths increase, the 2P-estimator quickly dominates. This paper generalizes the index flood procedure by employing regression with physiographic information to refine a normalized T-year flood estimator. A linear empirical Bayes estimator uses the normalized quantile regression estimator to define a prior distribution which is employed with the normalized 2P-quantile estimator. Monte Carlo simulations indicate that this empirical Bayes estimator does essentially as well as or better than the simpler normalized quantile regression estimator at sites with short records, and performs as well as or better than the 2P-estimator at sites with longer records or smaller L-CV. 相似文献
2.
Alex J. Cannon 《水文研究》2010,24(6):673-685
Parameters in a generalized extreme value (GEV) distribution are specified as a function of covariates using a conditional density network (CDN), which is a probabilistic extension of the multilayer perceptron neural network. If the covariate is time or is dependent on time, then the GEV‐CDN model can be used to perform nonlinear, nonstationary GEV analysis of hydrological or climatological time series. Owing to the flexibility of the neural network architecture, the model is capable of representing a wide range of nonstationary relationships. Model parameters are estimated by generalized maximum likelihood, an approach that is tailored to the estimation of GEV parameters from geophysical time series. Model complexity is identified using the Bayesian information criterion and the Akaike information criterion with small sample size correction. Monte Carlo simulations are used to validate GEV‐CDN performance on four simple synthetic problems. The model is then demonstrated on precipitation data from southern California, a series that exhibits nonstationarity due to interannual/interdecadal climatic variability. Copyright © 2009 Her Majesty the Queen in right of Canada. Published by John Wiley & Sons, Ltd. 相似文献
3.
Benjamin Renard Michel Lang Philippe Bois 《Stochastic Environmental Research and Risk Assessment (SERRA)》2006,21(2):97-112
Statistical analysis of extremes currently assumes that data arise from a stationary process, although such an hypothesis is not easily assessable and should therefore be considered as an uncertainty. The aim of this paper is to describe a Bayesian framework for this purpose, considering several probabilistic models (stationary, step-change and linear trend models) and four extreme values distributions (exponential, generalized Pareto, Gumbel and GEV). Prior distributions are specified by using regional prior knowledge about quantiles. Posterior distributions are used to estimate parameters, quantify the probability of models and derive a realistic frequency analysis, which takes into account estimation, distribution and stationarity uncertainties. MCMC methods are needed for this purpose, and are described in the article. Finally, an application to a POT discharge series is presented, with an analysis of both occurrence process and peak distribution. 相似文献
4.
Hongjoon Shin Taesoon Kim Sooyoung Kim Jun-Haeng Heo 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(2):183-197
In this study, the parameter estimations for the 3-parameter generalized logistic (GL) distribution are presented based on
the methods of moments (MOM), maximum likelihood (ML), and probability weighted moments (PWM). The asymptotic variances of
the MOM, ML, and PWM quantile estimators for the GL distribution are expressed as functions of the sample size, return period,
and parameters. A Monte Carlo simulation was performed to verify the derived expressions for variances and covariances between
parameters and to evaluate the applicability of the derived asymptotic variances of quantiles for the MOM, ML and PWM methods.
The simulation results generally show good agreement with the analytical results estimated from the asymptotic variances of
parameters and quantiles when the shape parameter (β) of the GL distribution is between −0.10 and 0.10 for the MOM method and between −0.25 and 0.45 for the ML and PWM methods,
respectively. In addition, the actual sample variances and the root mean square error (RMSE) of asymptotic variances of quantiles
for various sample sizes, return periods, and shape parameters were presented. In order to evaluate the applicability of the
estimation methods to real data and to compare the values of estimated parameter, quantiles, and confidence intervals based
on each parameter estimation method, the GL distribution was fitted to the 24-h annual maximum rainfall data at Pohang, Korea. 相似文献
5.
Boriss Siliverstovs Rainald Ötsch Claudia Kemfert Carlo C. Jaeger Armin Haas Hans Kremers 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(2):311-326
This study models maximum temperatures in Switzerland monitored in twelve locations using the generalised extreme value (GEV)
distribution. The parameters of the GEV distribution are determined within a Bayesian framework. We find that the parameters
of the underlying distribution underwent a substantial change in the beginning of the 1980s. This change is characterised
by an increase both in the level and the variability. We assess the likelihood of the heat wave of the summer 2003 using the
fitted GEV distribution by accounting for the presence of a structural break. The estimation results do suggest that the heat
wave of 2003 is not that statistically improbable if an appropriate methodology is used for dealing with nonstationarity. 相似文献
6.
Roberta-Serena Blasone Jasper A. Vrugt Henrik Madsen Dan Rosbjerg Bruce A. Robinson George A. Zyvoloski 《Advances in water resources》2008
In the last few decades hydrologists have made tremendous progress in using dynamic simulation models for the analysis and understanding of hydrologic systems. However, predictions with these models are often deterministic and as such they focus on the most probable forecast, without an explicit estimate of the associated uncertainty. This uncertainty arises from incomplete process representation, uncertainty in initial conditions, input, output and parameter error. The generalized likelihood uncertainty estimation (GLUE) framework was one of the first attempts to represent prediction uncertainty within the context of Monte Carlo (MC) analysis coupled with Bayesian estimation and propagation of uncertainty. Because of its flexibility, ease of implementation and its suitability for parallel implementation on distributed computer systems, the GLUE method has been used in a wide variety of applications. However, the MC based sampling strategy of the prior parameter space typically utilized in GLUE is not particularly efficient in finding behavioral simulations. This becomes especially problematic for high-dimensional parameter estimation problems, and in the case of complex simulation models that require significant computational time to run and produce the desired output. In this paper we improve the computational efficiency of GLUE by sampling the prior parameter space using an adaptive Markov Chain Monte Carlo scheme (the Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm). Moreover, we propose an alternative strategy to determine the value of the cutoff threshold based on the appropriate coverage of the resulting uncertainty bounds. We demonstrate the superiority of this revised GLUE method with three different conceptual watershed models of increasing complexity, using both synthetic and real-world streamflow data from two catchments with different hydrologic regimes. 相似文献
7.
Hans Van de Vyver 《水文研究》2018,32(11):1635-1647
Rainfall intensity–duration–frequency (IDF) curves are a standard tool in urban water resources engineering and management. They express how return levels of extreme rainfall intensity vary with duration. The simple scaling property of extreme rainfall intensity, with respect to duration, determines the form of IDF relationships. It is supposed that the annual maximum intensity follows the generalized extreme value (GEV) distribution. As well known, for simple scaling processes, the location parameter and scale parameter of the GEV distribution obey a power law with the same exponent. Although, the simple scaling hypothesis is commonly used as a suitable working assumption, the multiscaling approach provides a more general framework. We present a new IDF relationship that has been formulated on the basis of the multiscaling property. It turns out that the GEV parameters (location and scale) have a different scaling exponent. Next, we apply a Bayesian framework to estimate the multiscaling GEV model and to choose the most appropriate model. It is shown that the model performance increases when using the multiscaling approach. The new model for IDF curves reproduces the data very well and has a reasonable degree of complexity without overfitting on the data. 相似文献
8.
9.
Jasper A. Vrugt Cajo J. F. ter Braak Hoshin V. Gupta Bruce A. Robinson 《Stochastic Environmental Research and Risk Assessment (SERRA)》2009,23(7):1061-1062
In recent years, a strong debate has emerged in the hydrologic literature regarding what constitutes an appropriate framework
for uncertainty estimation. Particularly, there is strong disagreement whether an uncertainty framework should have its roots
within a proper statistical (Bayesian) context, or whether such a framework should be based on a different philosophy and
implement informal measures and weaker inference to summarize parameter and predictive distributions. In this paper, we compare
a formal Bayesian approach using Markov Chain Monte Carlo (MCMC) with generalized likelihood uncertainty estimation (GLUE)
for assessing uncertainty in conceptual watershed modeling. Our formal Bayesian approach is implemented using the recently
developed differential evolution adaptive metropolis (DREAM) MCMC scheme with a likelihood function that explicitly considers
model structural, input and parameter uncertainty. Our results demonstrate that DREAM and GLUE can generate very similar estimates
of total streamflow uncertainty. This suggests that formal and informal Bayesian approaches have more common ground than the
hydrologic literature and ongoing debate might suggest. The main advantage of formal approaches is, however, that they attempt
to disentangle the effect of forcing, parameter and model structural error on total predictive uncertainty. This is key to
improving hydrologic theory and to better understand and predict the flow of water through catchments. 相似文献
10.
Identification of uncertainty in low flow frequency analysis using Bayesian MCMC method 总被引：1，自引：0，他引：1
This study employs the Bayesian Markov Chain Monte Carlo (MCMC) method with the Metropolis–Hastings algorithm and maximum likelihood estimation (MLE) using a quadratic approximation of the likelihood function for the evaluation of uncertainties in low flow frequency analysis using a two‐parameter Weibull distribution. The two types of prior distributions, a non‐data‐based distribution and a data‐based distribution using regional information collected from neighbouring stations, are used to establish a posterior distribution. Eight case studies using the synthetic data with a sample size of 100, generated from two‐parameter Weibull distribution, are performed to compare with results of analysis using MLE and Bayesian MCMC. Also, Bayesian MCMC and MLE are applied to 36 years of gauged data to validate the efficiency of the developed scheme. These examples illustrate the advantages of Bayesian MCMC and the limitations of MLE based on a quadratic approximation. From the point of view of uncertainty analysis, Bayesian MCMC is more effective than MLE using a quadratic approximation when the sample size is small. In particular, Bayesian MCMC method is more attractive than MLE based on a quadratic approximation because the sample size of low flow at the site of interest is mostly not enough to perform the low flow frequency analysis. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
11.
Zhongmin Liang Wenjuan Chang Binquan Li 《Stochastic Environmental Research and Risk Assessment (SERRA)》2012,26(5):721-730
The specific objective of the paper is to propose a new flood frequency analysis method considering uncertainty of both probability distribution selection (model uncertainty) and uncertainty of parameter estimation (parameter uncertainty). Based on Bayesian theory sampling distribution of quantiles or design floods coupling these two kinds of uncertainties is derived, not only point estimator but also confidence interval of the quantiles can be provided. Markov Chain Monte Carlo is adopted in order to overcome difficulties to compute the integrals in estimating the sampling distribution. As an example, the proposed method is applied for flood frequency analysis at a gauge in Huai River, China. It has been shown that the approach considering only model uncertainty or parameter uncertainty could not fully account for uncertainties in quantile estimations, instead, method coupling these two uncertainties should be employed. Furthermore, the proposed Bayesian-based method provides not only various quantile estimators, but also quantitative assessment on uncertainties of flood frequency analysis. 相似文献
12.
AbstractFlood frequency analysis (FFA) is essential for water resources management. Long flow records improve the precision of estimated quantiles; however, in some cases, sample size in one location is not sufficient to achieve a reliable estimate of the statistical parameters and thus, regional FFA is commonly used to decrease the uncertainty in the prediction. In this paper, the bias of several commonly used parameter estimators, including L-moment, probability weighted moment and maximum likelihood estimation, applied to the general extreme value (GEV) distribution is evaluated using a Monte Carlo simulation. Two bias compensation approaches: compensation based on the shape parameter, and compensation using three GEV parameters, are proposed based on the analysis and the models are then applied to streamflow records in southern Alberta. Compensation efficiency varies among estimators and between compensation approaches. The results overall suggest that compensation of the bias due to the estimator and short sample size would significantly improve the accuracy of the quantile estimation. In addition, at-site FFA is able to provide reliable estimation based on short data, when accounting for the bias in the estimator appropriately.
Editor D. Koutsoyiannis; Associate editor Sheng Yue 相似文献
13.
Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling? 总被引：1，自引：0，他引：1
Jasper A. Vrugt Cajo J. F. ter Braak Hoshin V. Gupta Bruce A. Robinson 《Stochastic Environmental Research and Risk Assessment (SERRA)》2009,23(7):1011-1026
In recent years, a strong debate has emerged in the hydrologic literature regarding what constitutes an appropriate framework for uncertainty estimation. Particularly, there is strong disagreement whether an uncertainty framework should have its roots within a proper statistical (Bayesian) context, or whether such a framework should be based on a different philosophy and implement informal measures and weaker inference to summarize parameter and predictive distributions. In this paper, we compare a formal Bayesian approach using Markov Chain Monte Carlo (MCMC) with generalized likelihood uncertainty estimation (GLUE) for assessing uncertainty in conceptual watershed modeling. Our formal Bayesian approach is implemented using the recently developed differential evolution adaptive metropolis (DREAM) MCMC scheme with a likelihood function that explicitly considers model structural, input and parameter uncertainty. Our results demonstrate that DREAM and GLUE can generate very similar estimates of total streamflow uncertainty. This suggests that formal and informal Bayesian approaches have more common ground than the hydrologic literature and ongoing debate might suggest. The main advantage of formal approaches is, however, that they attempt to disentangle the effect of forcing, parameter and model structural error on total predictive uncertainty. This is key to improving hydrologic theory and to better understand and predict the flow of water through catchments. 相似文献
14.
In urban drainage modelling, uncertainty analysis is of undoubted necessity. However, uncertainty analysis in urban water-quality modelling is still in its infancy and only few studies have been carried out. Therefore, several methodological aspects still need to be experienced and clarified especially regarding water quality modelling. The use of the Bayesian approach for uncertainty analysis has been stimulated by its rigorous theoretical framework and by the possibility of evaluating the impact of new knowledge on the modelling predictions. Nevertheless, the Bayesian approach relies on some restrictive hypotheses that are not present in less formal methods like the Generalised Likelihood Uncertainty Estimation (GLUE). One crucial point in the application of Bayesian method is the formulation of a likelihood function that is conditioned by the hypotheses made regarding model residuals. Statistical transformations, such as the use of Box–Cox equation, are generally used to ensure the homoscedasticity of residuals. However, this practice may affect the reliability of the analysis leading to a wrong uncertainty estimation. The present paper aims to explore the influence of the Box–Cox equation for environmental water quality models. To this end, five cases were considered one of which was the “real” residuals distributions (i.e. drawn from available data). The analysis was applied to the Nocella experimental catchment (Italy) which is an agricultural and semi-urbanised basin where two sewer systems, two wastewater treatment plants and a river reach were monitored during both dry and wet weather periods. The results show that the uncertainty estimation is greatly affected by residual transformation and a wrong assumption may also affect the evaluation of model uncertainty. The use of less formal methods always provide an overestimation of modelling uncertainty with respect to Bayesian method but such effect is reduced if a wrong assumption is made regarding the residuals distribution. If residuals are not normally distributed, the uncertainty is over-estimated if Box–Cox transformation is not applied or non-calibrated parameter is used. 相似文献
15.
16.
A Bayesian hierarchical spatio-temporal model for extreme rainfall in Extremadura (Spain) 总被引：1，自引：1，他引：0
A statistical study was made of the temporal trend in extreme rainfall in the region of Extremadura (Spain) during the period 1961–2009. A hierarchical spatio-temporal Bayesian model with a GEV parameterization of the extreme data was employed. The Bayesian model was implemented in a Markov chain Monte Carlo framework that allows the posterior distribution of the parameters that intervene in the model to be estimated. The results show a decrease of extreme rainfall in winter and spring and a slight increase in autumn. The uncertainty in the trend parameters obtained with the hierarchical approach is much smaller than the uncertainties obtained from the GEV model applied locally. Also found was a negative relationship between the NAO index and the extreme rainfall in Extremadura during winter. An increase was observed in the intensity of the NAO index in winter and spring, and a slight decrease in autumn. 相似文献
17.
叠前反演的目的是基于弹性波理论从地震数据中获得地层参数的可靠估计,进而用于描述地层的流体和岩性特征.然而叠前反演问题都是高维的和非适定的,并且容易受各种噪声和采集过程中不确定因素的影响,因此,为了获得稳定可靠的解必需对反演过程加以合理的约束.本文提出了一种基于非线性二次规划的叠前三参数反演方法.首先基于贝叶斯参数估计理论,假设似然函数服从高斯分布,并使待反演的参数服从于改进的Cauchy分布,从而提高了反演结果的分辨率;其次用协方差矩阵来描述参数间的相关程度,进一步提高了反演结果的稳定性;最后将问题转化为一个非线性二次规划的求解问题,并在多种约束下得到问题的解.仿真实验和实际应用皆已表明,本文提出的反演方法运算速度快捷,既使在信噪比很低的情况下也可获得较好的反演结果,为储层的进一步识别提供更多的物性参数. 相似文献
18.
Compositional Bayesian indicator estimation 总被引：1，自引：1，他引：0
Carolina Guardiola-Albert Eulogio Pardo-Ig��zquiza 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(6):835-849
Indicator kriging is widely used for mapping spatial binary variables and for estimating the global and local spatial distributions
of variables in geosciences. For continuous random variables, indicator kriging gives an estimate of the cumulative distribution
function, for a given threshold, which is then the estimate of a probability. Like any other kriging procedure, indicator
kriging provides an estimation variance that, although not often used in applications, should be taken into account as it
assesses the uncertainty of the estimate. An alternative approach to indicator estimation is proposed in this paper. In this
alternative approach the complete probability density function of the indicator estimate is evaluated. The procedure is described
in a Bayesian framework, using a multivariate Gaussian likelihood and an a priori distribution which are both combined according
to Bayes theorem in order to obtain a posterior distribution for the indicator estimate. From this posterior distribution,
point estimates, interval estimates and uncertainty measures can be obtained. Among the point estimates, the median of the
posterior distribution is the maximum entropy estimate because there is a fifty-fifty chance of the unknown value of the estimate
being larger or smaller than the median; that is, there is maximum uncertainty in the choice between two alternatives. Thus
in some sense, the latter is an indicator estimator, alternative to the kriging estimator, that includes its own uncertainty.
On the other hand, the mode of the posterior distribution estimator, assuming a uniform prior, is coincidental with the simple
kriging estimator. Additionally, because the indicator estimate can be considered as a two-part composition which domain of
definition is the simplex, the method is extended to compositional Bayesian indicator estimation. Bayesian indicator estimation
and compositional Bayesian indicator estimation are illustrated with an environmental case study in which the probability
of the content of a geochemical element in soil being over a particular threshold is of interest. The computer codes and its
user guides are public domain and freely available. 相似文献
19.
Parameter uncertainty in hydrologic modeling is crucial to the flood simulation and forecasting. The Bayesian approach allows one to estimate parameters according to prior expert knowledge as well as observational data about model parameter values. This study assesses the performance of two popular uncertainty analysis (UA) techniques, i.e., generalized likelihood uncertainty estimation (GLUE) and Bayesian method implemented with the Markov chain Monte Carlo sampling algorithm, in evaluating model parameter uncertainty in flood simulations. These two methods were applied to the semi-distributed Topographic hydrologic model (TOPMODEL) that includes five parameters. A case study was carried out for a small humid catchment in the southeastern China. The performance assessment of the GLUE and Bayesian methods were conducted with advanced tools suited for probabilistic simulations of continuous variables such as streamflow. Graphical tools and scalar metrics were used to test several attributes of the simulation quality of selected flood events: deterministic accuracy and the accuracy of 95 % prediction probability uncertainty band (95PPU). Sensitivity analysis was conducted to identify sensitive parameters that largely affect the model output results. Subsequently, the GLUE and Bayesian methods were used to analyze the uncertainty of sensitive parameters and further to produce their posterior distributions. Based on their posterior parameter samples, TOPMODEL’s simulations and the corresponding UA results were conducted. Results show that the form of exponential decline in conductivity and the overland flow routing velocity were sensitive parameters in TOPMODEL in our case. Small changes in these two parameters would lead to large differences in flood simulation results. Results also suggest that, for both UA techniques, most of streamflow observations were bracketed by 95PPU with the containing ratio value larger than 80 %. In comparison, GLUE gave narrower prediction uncertainty bands than the Bayesian method. It was found that the mode estimates of parameter posterior distributions are suitable to result in better performance of deterministic outputs than the 50 % percentiles for both the GLUE and Bayesian analyses. In addition, the simulation results calibrated with Rosenbrock optimization algorithm show a better agreement with the observations than the UA’s 50 % percentiles but slightly worse than the hydrographs from the mode estimates. The results clearly emphasize the importance of using model uncertainty diagnostic approaches in flood simulations. 相似文献
20.
Philyong Yoon Tae-Woong Kim Chulsang Yoo 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(5):1143-1153
Extreme rainfalls in South Korea result mainly from convective storms and typhoon storms during the summer. A proper way for dealing with the extreme rainfalls in hydrologic design is to consider the statistical characteristics of the annual maximum rainfall from two different storms when determining design rainfalls. Therefore, this study introduced a mixed generalized extreme value (GEV) distribution to estimate the rainfall quantile for 57 gauge stations across South Korea and compared the rainfall quantiles with those from conventional rainfall frequency analysis using a single GEV distribution. Overall, these results show that the mixed GEV distribution allows probability behavior to be taken into account during rainfall frequency analysis through the process of parameter estimation. The resulting rainfall quantile estimates were found to be significantly smaller than those determined using a single GEV distribution. The difference of rainfall quantiles was found to be closely correlated with the occurrence probability of typhoon and the distribution parameters. 相似文献