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1.
J.J. Yu 《水文科学杂志》2013,58(12):2117-2131
Abstract

A generalized likelihood uncertainty estimation (GLUE) framework coupling with artificial neural network (ANN) models in two surrogate schemes (i.e. GAE-S1 and GAE-S2) was proposed to improve the efficiency of uncertainty assessment in flood inundation modelling. The GAE-S1 scheme was to construct an ANN to approximate the relationship between model likelihoods and uncertain parameters for facilitating sample acceptance/rejection instead of running the numerical model directly; thus, it could speed up the Monte Carlo simulation in stochastic sampling. The GAE-S2 scheme was to establish independent ANN models for water depth predictions to emulate the numerical models; it could facilitate efficient uncertainty analysis without additional model runs for locations concerned under various scenarios. The results from a study case showed that both GAE-S1 and GAE-S2 had comparable performances to GLUE in terms of estimation of posterior parameters, prediction intervals of water depth, and probabilistic inundation maps, but with reduced computational requirements. The results also revealed that GAE-S1 possessed a slightly better performance in accuracy (referencing to GLUE) than GAE-S2, but a lower flexibility in application. This study shed some light on how to apply different surrogate schemes in using numerical models for uncertainty assessment, and could help decision makers in choosing cost-effective ways of conducting flood risk analysis.  相似文献   

2.
Previously we have detailed an application of the generalized likelihood uncertainty estimation (GLUE) procedure to estimate spatially distributed uncertainty in models conditioned against binary pattern data contained in flood inundation maps. This method was applied to two sites where a single consistent synoptic image of inundation extent was available to test the simulation performance of the method. In this paper, we extend this to examine the predictive performance of the method for a reach of the River Severn, west‐central England. Uniquely for this reach, consistent inundation images of two major floods have been acquired from spaceborne synthetic aperture radars, as well as a high‐resolution digital elevation model derived using laser altimetry. These data thus allow rigorous split sample testing of the previous GLUE application. To achieve this, Monte Carlo analyses of parameter uncertainty within the GLUE framework are conducted for a typical hydraulic model applied to each flood event. The best 10% of parameter sets identified in each analysis are then used to map uncertainty in flood extent predictions using the method previously proposed for both an independent validation data set and a design flood. Finally, methods for combining the likelihood information derived from each Monte Carlo ensemble are examined to determine whether this has the potential to reduce uncertainty in spatially distributed measures of flood risk for a design flood. The results show that for this reach and these events, the method previously established is able to produce sharply defined flood risk maps that compare well with observed inundation extent. More generally, we show that even single, poor‐quality inundation extent images are useful in constraining hydraulic model calibrations and that values of effective friction parameters are broadly stationary between the two events simulated, most probably reflecting their similar hydraulics. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

3.
In this paper we extend the generalized likelihood uncertainty estimation (GLUE) technique to estimate spatially distributed uncertainty in models conditioned against binary pattern data contained in flood inundation maps. Untransformed binary pattern data already have been used within GLUE to estimate domain‐averaged (zero‐dimensional) likelihoods, yet the pattern information embedded within such sources has not been used to estimate distributed uncertainty. Where pattern information has been used to map distributed uncertainty it has been transformed into a continuous function prior to use, which may introduce additional errors. To solve this problem we use here ‘raw’ binary pattern data to define a zero‐dimensional global performance measure for each simulation in a Monte Carlo ensemble. Thereafter, for each pixel of the distributed model we evaluate the probability that this pixel was inundated. This probability is then weighted by the measure of global model performance, thus taking into account how well a given parameter set performs overall. The result is a distributed uncertainty measure mapped over real space. The advantage of the approach is that it both captures distributed uncertainty and contains information on global likelihood that can be used to condition predictions of further events for which observed data are not available. The technique is applied to the problem of flood inundation prediction at two test sites representing different hydrodynamic conditions. In both cases, the method reveals the spatial structure in simulation uncertainty and simultaneously enables mapping of flood probability predicted by the model. Spatially distributed uncertainty analysis is shown to contain information over and above that available from global performance measures. Overall, the paper highlights the different types of information that may be obtained from mappings of model uncertainty over real and n‐dimensional parameter spaces. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

4.
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   

5.
The quantification of uncertainty in the simulations from complex physically based distributed hydrologic models is important for developing reliable applications. The generalized likelihood uncertainty estimation method (GLUE) is one of the most commonly used methods in the field of hydrology. The GLUE helps reduce the parametric uncertainty by deriving the probability distribution function of parameters, and help analyze the uncertainty in model output. In the GLUE, the uncertainty of model output is analyzed through Monte Carlo simulations, which require large number of model runs. This induces high computational demand for the GLUE to characterize multi-dimensional parameter space, especially in the case of complex hydrologic models with large number of parameters. While there are a lot of variants of GLUE that derive the probability distribution of parameters, none of them have addressed the computational requirement in the analysis. A method to reduce such computational requirement for GLUE is proposed in this study. It is envisaged that conditional sampling, while generating ensembles for the GLUE, can help reduce the number of model simulations. The mutual relationship between the parameters was used for conditional sampling in this study. The method is illustrated using a case study of Soil and Water Assessment Tool (SWAT) model on a watershed in the USA. The number of simulations required for the uncertainty analysis was reduced by 90 % in the proposed method compared to existing methods. The proposed method also resulted in an uncertainty reduction in terms of reduced average band width and high containing ratio.  相似文献   

6.
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.
A stochastic optimization model based on an adaptive feedback correction process and surrogate model uncertainty was proposed and applied for remediation strategy design at a dense non-aqueous phase liquids (DNAPL)-contaminated groundwater site. One hundred initial training samples were obtained using the Latin hypercube sampling method. A surrogate model of a multiphase flow simulation model was constructed based on these samples employing the self-adaptive particle swarm optimization kriging (SAPSOKRG) method. An optimization model was built, using the SAPSOKRG surrogate model as a constraint. Then, an adaptive feedback correction process was designed and applied to iteratively update the training samples, surrogate model, and optimization model. Results showed that the training samples, the surrogate model, and the optimization model were effectively ameliorated. However, the surrogate model is an approximation of the simulation model, and some degree of uncertainty exists even though the surrogate model was ameliorated. Therefore, residuals between the surrogate model and the simulation model were calculated, and an uncertainty analysis was conducted. Based on the uncertainty analysis results, a stochastic optimization model was constructed and solved to obtain optimal remediation strategies at different confidence levels (60, 70, 80, 90, 95%) and under different remediation objectives (average DNAPL removal rate ≥?70,?≥?75,?≥?80,?≥?85,?≥?90%). The optimization results demonstrated that the higher the confidence level and remediation objective, the more expensive was remediation. Therefore, decision makers can weigh remediation costs, confidence levels, and remediation objectives to make an informed choice. This also allows decision makers to determine the reliability of a selected strategy and provides a new tool for DNAPL-contaminated groundwater remediation design.  相似文献   

8.
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   

9.
Real time updating of rainfall-runoff (RR) models is traditionally performed by state-space formulation in the context of flood forecasting systems. In this paper, however, we examine applicability of generalized likelihood uncertainty estimation (GLUE) approach in real time modification of forecasts. Real time updating and parameter uncertainty analysis was conducted for Abmark catchment, a part of the great Karkheh basin in south west of Iran. A conceptual-distributed RR model, namely ModClark, was used for basin simulation, such that the basin’s hydrograph was determined by the superposition of runoff generated by individual cells in a raster-based discretization. In real time updating of RR model by GLUE method, prior and posterior likelihoods were computed using forecast errors that were obtained from the results of behavioral models and real time recorded discharges. Then, prior and posterior likelihoods were applied to modify forecast confidence limits in each time step. Calibration of parameters was performed using historical data while distribution of parameters was modified in real time based on new data records. Two scenarios of rainfall forecast including prefect-rainfall-forecast and no-rainfall-forecast were assumed in absence of a robust rainfall forecast model in the study catchment. The results demonstrated that GLUE application could offer an acceptable lead time for peak discharge forecast at the expense of high computational demand.  相似文献   

10.
This research incorporates the generalized likelihood uncertainty estimation (GLUE) methodology in a high‐resolution Environmental Protection Agency Storm Water Management Model (SWMM), which we developed for a highly urbanized sewershed in Syracuse, NY, to assess SWMM modelling uncertainties and estimate parameters. We addressed two issues that have long been suggested having a great impact on the GLUE uncertainty estimation: the observations used to construct the likelihood measure and the sampling approach to obtain the posterior samples of the input parameters and prediction bounds of the model output. First, on the basis of the Bayes' theorem, we compared the prediction bounds generated from the same Gaussian distribution likelihood measure conditioned on flow observations of varying magnitude. Second, we employed two sampling techniques, the sampling importance resampling (SIR) and the threshold sampling methods, to generate posterior parameter distributions and prediction bounds, based on which the sampling efficiency was compared. In addition, for a better understanding of the hydrological responses of different pervious land covers in urban areas, we developed new parameter sets in SWMM representing the hydrological properties of trees and lawns, which were estimated through the GLUE procedure. The results showed that SIR was a more effective alternative to the conventional threshold sampling method. The combined total flow and peak flow data were an efficient alternative to the intensive 5‐min flow data for reducing SWMM parameter and output uncertainties. Several runoff control parameters were found to have a great effect on peak flows, including the newly introduced parameters for trees. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

11.
Joint Monte Carlo and possibilistic simulation for flood damage assessment   总被引：7，自引：5，他引：2  
A joint Monte Carlo and fuzzy possibilistic simulation (MC-FPS) approach was proposed for flood risk assessment. Monte Carlo simulation was used to evaluate parameter uncertainties associated with inundation modeling, and fuzzy vertex analysis was applied for promulgating human-induced uncertainty in flood damage estimation. A study case was selected to show how to apply the proposed method. The results indicate that the outputs from MC-FPS would present as fuzzy flood damage estimate and probabilistic-possibilistic damage contour maps. The stochastic uncertainty in the flood inundation model and fuzziness in the depth-damage functions derivation would cause similar levels of influence on the final flood damage estimate. Under the worst scenario (i.e. a combined probabilistic and possibilistic uncertainty), the estimated flood damage could be 2.4 times higher than that computed from conventional deterministic approach; considering only the pure stochastic effect, the flood loss would be 1.4 times higher. It was also indicated that uncertainty in the flood inundation modeling has a major influence on the standard deviation of the simulated damage, and that in the damage-depth function has more notable impact on the mean of the fitted distributions. Through applying MC-FPS, rich information could be derived under various α-cut levels and cumulative probabilities, and it forms an important basis for supporting rational decision making for flood risk management under complex uncertainties.  相似文献   

12.
The Beerkan method based on in situ single‐ring water infiltration experiments along with the relevant specific Beerkan estimation of soil transfer parameters (BEST) algorithm is attractive for simple soil hydraulic characterization. However, the BEST algorithm may lead to erroneous or null values for the saturated hydraulic conductivity and sorptivity especially when there are only few infiltration data points under the transient flow state, either for sandy soil or soils in wet conditions. This study developed an alternative algorithm for analysis of the Beerkan infiltration experiment referred to as BEST‐generalized likelihood uncertainty estimation (GLUE). The proposed method estimates the scale parameters of van Genuchten water retention and Brooks–Corey hydraulic conductivity functions through the GLUE methodology. The GLUE method is a Bayesian Monte Carlo parameter estimation technique that makes use of a likelihood function to measure the goodness‐of‐fit between modelled and observed data. The results showed that using a combination of three different likelihood measurements based on observed transient flow, steady‐state flow and experimental steady‐state infiltration rate made the BEST‐GLUE procedure capable of performing an efficient inverse analysis of Beerkan infiltration experiments. Therefore, it is more applicable for a wider range of soils with contrasting texture, structure, and initial and saturated water content. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

13.
The input uncertainty is as significant as model error, which affects the parameter estimation, yields bias and misleading results. This study performed a comprehensive comparison and evaluation of uncertainty estimates according to the impact of precipitation errors by GLUE and Bayesian methods using the Metropolis Hasting algorithm in a validated conceptual hydrological model (WASMOD). It aims to explain the sensitivity and differences between the GLUE and Bayesian method applied to hydrological model under precipitation errors with constant multiplier parameter and random multiplier parameter. The 95 % confidence interval of monthly discharge in low flow, medium flow and high flow were selected for comparison. Four indices, i.e. the average relative interval length, the percentage of observations bracketed by the confidence interval, the percentage of observations bracketed by the unit confidence interval and the continuous rank probability score (CRPS) were used in this study for sensitivity analysis under model input error via GLUE and Bayesian methods. It was found that (1) the posterior distributions derived by the Bayesian method are narrower and sharper than those obtained by the GLUE under precipitation errors, but the differences are quite small; (2) Bayesian method performs more sensitive in uncertainty estimates of discharge than GLUE according to the impact of precipitation errors; (3) GLUE and Bayesian methods are more sensitive in uncertainty estimate of high flow than the other flows by the impact of precipitation errors; and (4) under the impact of precipitation, the results of CRPS for low and medium flows are quite stable from both GLUE and Bayesian method while it is sensitive for high flow by Bayesian method.  相似文献   

14.
In flood risk management, the divergent concept of resilience of a flood defense system cannot be fully defined quantitatively by one indicator and multiple indicators need to be considered simultaneously. In this paper, a multi-objective optimization (MOO) design framework is developed to determine the optimal protection level of a levee system based on different resilience indicators that depend on the probabilistic features of the flood damage cost arising under the uncertain nature of rainfalls. An evolutionary-based MOO algorithm is used to find a set of non-dominated solutions, known as Pareto optimal solutions for the optimal protection level. The objective functions, specifically resilience indicators of severity, variability and graduality, that account for the uncertainty of rainfall can be evaluated by stochastic sampling of rainfall amount together with the model simulations of incurred flood damage estimation for the levee system. However, these model simulations which usually require detailed flood inundation simulation are computationally demanding. This hinders the wide application of MOO in flood risk management and is circumvented here via a surrogate flood damage modeling technique that is integrated into the MOO algorithm. The proposed optimal design framework is applied to a levee system in a central basin of flood-prone Jakarta, Indonesia. The results suggest that the proposed framework enables the application of MOO with resilience objectives for flood defense system design under uncertainty and solves the decision making problems efficiently by drastically reducing the required computational time.  相似文献   

15.
Flood risk assessment is customarily performed using a design flood. Observed past flows are used to derive a flood frequency curve which forms the basis for a construction of a design flood. The simulation of a distributed model with the 1‐in‐T year design flood as an input gives information on the possible inundation areas, which are used to derive flood risk maps. The procedure is usually performed in a deterministic fashion, and its extension to take into account the design flood‐and flow routing model uncertainties is computer time consuming. In this study we propose a different approach to flood risk assessment which consists of the direct simulation of a distributed flow routing model for an observed series of annual maximum flows and the derivation of maps of probability of inundation of the desired return period directly from the obtained simulations of water levels at the model cross sections through an application of the Flood Level Frequency Analysis. The hydraulic model and water level quantile uncertainties are jointly taken into account in the flood risk uncertainty evaluation using the Generalized Likelihood Uncertainty Estimation (GLUE) approach. An additional advantage of the proposed approach lies in smaller uncertainty of inundation predictions for long return periods compared to the standard approach. The approach is illustrated using a design flood level and a steady‐state solution of a hydraulic model to derive maps of inundation probabilities. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

16.
In this paper a new procedure to derive flood hazard maps incorporating uncertainty concepts is presented. The layout of the procedure can be resumed as follows: (1) stochastic input of flood hydrograph modelled through a direct Monte-Carlo simulation based on flood recorded data. Generation of flood peaks and flow volumes has been obtained via copulas, which describe and model the correlation between these two variables independently of the marginal laws involved. The shape of hydrograph has been generated on the basis of a historical significant flood events, via cluster analysis; (2) modelling of flood propagation using a hyperbolic finite element model based on the DSV equations; (3) definition of global hazard indexes based on hydro-dynamic variables (i.e., water depth and flow velocities). The GLUE methodology has been applied in order to account for parameter uncertainty. The procedure has been tested on a flood prone area located in the southern part of Sicily, Italy. Three hazard maps have been obtained and then compared.  相似文献   

17.
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   

18.
This study aims at evaluating the uncertainty in the prediction of soil moisture (1D, vertical column) from an offline land surface model (LSM) forced by hydro-meteorological and radiation data. We focus on two types of uncertainty: an input error due to satellite rainfall retrieval uncertainty, and, LSM soil-parametric error. The study is facilitated by in situ and remotely sensed data-driven (precipitation, radiation, soil moisture) simulation experiments comprising a LSM and stochastic models for error characterization. The parametric uncertainty is represented by the generalized likelihood uncertainty estimation (GLUE) technique, which models the parameter non-uniqueness against direct observations. Half-hourly infra-red (IR) sensor retrievals were used as satellite rainfall estimates. The IR rain retrieval uncertainty is characterized on the basis of a satellite rainfall error model (SREM). The combined uncertainty (i.e., SREM + GLUE) is compared with the partial assessment of uncertainty. It is found that precipitation (IR) error alone may explain moderate to low proportion of the soil moisture simulation uncertainty, depending on the level of model accuracy—50–60% for high model accuracy, and 20–30% for low model accuracy. Comparisons on the basis of two different sites also yielded an increase (50–100%) in soil moisture prediction uncertainty for the more vegetated site. This study exemplified the need for detailed investigations of the rainfall retrieval-modeling parameter error interaction within a comprehensive space-time stochastic framework for achieving optimal integration of satellite rain retrievals in land data assimilation systems.  相似文献   

19.
J. Yazdi 《水文科学杂志》2017,62(10):1669-1682
The configuration of check dams and their numbers throughout a basin are important factors for reducing floods in downstream reaches of rivers. In this paper, a stochastic model based on surrogate modelling and Monte Carlo simulation, linked to an evolutionary optimization tool, is developed to assign the optimal sites and number of check dams on a stream network. To handle uncertainty of rainfall variables and their correlation structures, the copula method is employed and an artificial neural network (ANN) is used to emulate the computationally expensive hydrological model, HEC-HMS, within the optimization routines. The prepared modelling framework is applied to a mountainous basin to determine the arrangement of check dams in its sub-basins. The experimental results show that optimal strategies can reduce the expected value of peak flood discharges by up to 50%, with significantly lower costs or number of check dams, relative to a traditional approach with a large number of check dams in sub-basins, presenting a maximum of 21% efficiency.  相似文献   

20.
The estimation of flood frequency is vital for the flood control strategies and hydraulic structure design. Generating synthetic flood events according to statistical properties of observations is one of plausible methods to analyze the flood frequency. Due to the statistical dependence among the flood event variables (i.e. the flood peak, volume and duration), a multidimensional joint probability estimation is required. Recently, the copula method is widely used for multivariable dependent structure construction, however, the copula family should be chosen before application and the choice process is sometimes rather subjective. The entropy copula, a new copula family, employed in this research proposed a way to avoid the relatively subjective process by combining the theories of copula and entropy. The analysis shows the effectiveness of the entropy copula for probabilistic modelling the flood events of two hydrological gauges, and a comparison of accuracy with the popular copulas was made. The Gibbs sampling technique was applied for trivariate flood events simulation in order to mitigate the calculation difficulties of extending to three dimension directly. The simulation results indicate that the entropy copula is a simple and effective copula family for trivariate flood simulation.  相似文献   

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