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1.
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   

2.
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   

3.
This study evaluates alternative groundwater models with different recharge and geologic components at the northern Yucca Flat area of the Death Valley Regional Flow System (DVRFS), USA. Recharge over the DVRFS has been estimated using five methods, and five geological interpretations are available at the northern Yucca Flat area. Combining the recharge and geological components together with additional modeling components that represent other hydrogeological conditions yields a total of 25 groundwater flow models. As all the models are plausible given available data and information, evaluating model uncertainty becomes inevitable. On the other hand, hydraulic parameters (e.g., hydraulic conductivity) are uncertain in each model, giving rise to parametric uncertainty. Propagation of the uncertainty in the models and model parameters through groundwater modeling causes predictive uncertainty in model predictions (e.g., hydraulic head and flow). Parametric uncertainty within each model is assessed using Monte Carlo simulation, and model uncertainty is evaluated using the model averaging method. Two model-averaging techniques (on the basis of information criteria and GLUE) are discussed. This study shows that contribution of model uncertainty to predictive uncertainty is significantly larger than that of parametric uncertainty. For the recharge and geological components, uncertainty in the geological interpretations has more significant effect on model predictions than uncertainty in the recharge estimates. In addition, weighted residuals vary more for the different geological models than for different recharge models. Most of the calibrated observations are not important for discriminating between the alternative models, because their weighted residuals vary only slightly from one model to another.  相似文献   

4.
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   

5.
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   

6.
Groundwater prediction models are subjected to various sources of uncertainty. This study introduces a hierarchical Bayesian model averaging (HBMA) method to segregate and prioritize sources of uncertainty in a hierarchical structure and conduct BMA for concentration prediction. A BMA tree of models is developed to understand the impact of individual sources of uncertainty and uncertainty propagation to model predictions. HBMA evaluates the relative importance of different modeling propositions at each level in the BMA tree of model weights. The HBMA method is applied to chloride concentration prediction for the “1,500‐foot” sand of the Baton Rouge area, Louisiana from 2005 to 2029. The groundwater head data from 1990 to 2004 is used for model calibration. Four sources of uncertainty are considered and resulted in 180 flow and transport models for concentration prediction. The results show that prediction variances of concentration from uncertain model elements are much higher than the prediction variance from uncertain model parameters. The HBMA method is able to quantify the contributions of individual sources of uncertainty to the total uncertainty.  相似文献   

7.
Keith Beven  Andrew Binley 《水文研究》2014,28(24):5897-5918
This paper reviews the use of the Generalized Likelihood Uncertainty Estimation (GLUE) methodology in the 20 years since the paper by Beven and Binley in Hydrological Processes in (1992), which is now one of the most highly cited papers in hydrology. The original conception, the on‐going controversy it has generated, the nature of different sources of uncertainty and the meaning of the GLUE prediction uncertainty bounds are discussed. The hydrological, rather than statistical, arguments about the nature of model and data errors and uncertainties that are the basis for GLUE are emphasized. The application of the Institute of Hydrology distributed model to the Gwy catchment at Plynlimon presented in the original paper is revisited, using a larger sample of models, a wider range of likelihood evaluations and new visualization techniques. It is concluded that there are good reasons to reject this model for that data set. This is a positive result in a research environment in that it requires improved models or data to be made available. In practice, there may be ethical issues of using outputs from models for which there is evidence for model rejection in decision making. Finally, some suggestions for what is needed in the next 20 years are provided. © 2013 The Authors. Hydrological Processes published by John Wiley & Sons, Ltd.  相似文献   

8.
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   

9.
This study attempts to assess the uncertainty in the hydrological impacts of climate change using a multi-model approach combining multiple emission scenarios, GCMs and conceptual rainfall-runoff models to quantify uncertainty in future impacts at the catchment scale. The uncertainties associated with hydrological models have traditionally been given less attention in impact assessments until relatively recently. In order to examine the role of hydrological model uncertainty (parameter and structural uncertainty) in climate change impact studies a multi-model approach based on the Generalised Likelihood Uncertainty Estimation (GLUE) and Bayesian Model Averaging (BMA) methods is presented. Six sets of regionalised climate scenarios derived from three GCMs, two emission scenarios, and four conceptual hydrological models were used within the GLUE framework to define the uncertainty envelop for future estimates of stream flow, while the GLUE output is also post processed using BMA, where the probability density function from each model at any given time is modelled by a gamma distribution with heteroscedastic variance. The investigation on four Irish catchments shows that the role of hydrological model uncertainty is remarkably high and should therefore be routinely considered in impact studies. Although, the GLUE and BMA approaches used here differ fundamentally in their underlying philosophy and representation of error, both methods show comparable performance in terms of ensemble spread and predictive coverage. Moreover, the median prediction for future stream flow shows progressive increases of winter discharge and progressive decreases in summer discharge over the coming century.  相似文献   

10.
With the recent development of distributed hydrological models, the use of multi‐site observed data to evaluate model performance is becoming more common. Distributed hydrological model have many advantages, and at the same time, it also faces the challenge to calibrate over‐do parameters. As a typical distributed hydrological model, problems also exist in Soil and Water Assessment Tool (SWAT) parameter calibration. In the paper, four different uncertainty approaches – Particle Swarm Optimization (PSO) techniques, Generalized Likelihood Uncertainty Estimation (GLUE), Sequential Uncertainty Fitting algorithm (SUFI‐2) and Parameter Solution (PARASOL) – are taken to a comparative study with the SWAT model applied in Peace River Basin, central Florida. In our study, the observed river discharge data used in SWAT model calibration were collected from the three gauging stations at the main tributary of the Peace River. Behind these approaches, there is a shared philosophy; all methods seek out many parameter set to fit the uncertainties due to the non‐uniqueness in model parameter evaluation. On the basis of the statistical results of four uncertainty methods, difficulty level of each method, the number of runs and theoretical basis, the reasons that affected the accuracy of simulation were analysed and compared. Furthermore, for the four uncertainty method with SWAT model in the study area, the pairwise correlation between parameters and the distributions of model fit summary statistics computed from the sampling over the behavioural parameter and the entire model calibration parameter feasible spaces were identified and examined. It provided additional insight into the relative identifiability of the four uncertainty methods Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

11.
Uncertainty is inherent in modelling studies. However, the quantification of uncertainties associated with a model is a challenging task, and hence, such studies are somewhat limited. As distributed or semi‐distributed hydrological models are being increasingly used these days to simulate hydrological processes, it is vital that these models should be equipped with robust calibration and uncertainty analysis techniques. The goal of the present study was to calibrate and validate the Soil and Water Assessment Tool (SWAT) model for simulating streamflow in a river basin of Eastern India, and to evaluate the performance of salient optimization techniques in quantifying uncertainties. The SWAT model for the study basin was developed and calibrated using Parameter Solution (ParaSol), Sequential Uncertainty Fitting Algorithm (SUFI‐2) and Generalized Likelihood Uncertainty Estimation (GLUE) optimization techniques. The daily observed streamflow data from 1998 to 2003 were used for model calibration, and those for 2004–2005 were used for model validation. Modelling results indicated that all the three techniques invariably yield better results for the monthly time step than for the daily time step during both calibration and validation. The model performances for the daily streamflow simulation using ParaSol and SUFI‐2 during calibration are reasonably good with a Nash–Sutcliffe efficiency and mean absolute error (MAE) of 0.88 and 9.70 m3/s for ParaSol, and 0.86 and 10.07 m3/s for SUFI‐2, respectively. The simulation results of GLUE revealed that the model simulates daily streamflow during calibration with the highest accuracy in the case of GLUE (R2 = 0.88, MAE = 9.56 m3/s and root mean square error = 19.70 m3/s). The results of uncertainty analyses by SUFI‐2 and GLUE were compared in terms of parameter uncertainty. It was found that SUFI‐2 is capable of estimating uncertainties in complex hydrological models like SWAT, but it warrants sound knowledge of the parameters and their effects on the model output. On the other hand, GLUE predicts more reliable uncertainty ranges (R‐factor = 0.52 for daily calibration and 0.48 for validation) compared to SUFI‐2 (R‐factor = 0.59 for daily calibration and 0.55 for validation), though it is computationally demanding. Although both SUFI‐2 and GLUE appear to be promising techniques for the uncertainty analysis of modelling results, more and more studies in this direction are required under varying agro‐climatic conditions for assessing their generic capability. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

12.
Multi-model averaging is currently receiving a surge of attention in the atmospheric, hydrologic, and statistical literature to explicitly handle conceptual model uncertainty in the analysis of environmental systems and derive predictive distributions of model output. Such density forecasts are necessary to help analyze which parts of the model are well resolved, and which parts are subject to considerable uncertainty. Yet, accurate point predictors are still desired in many practical applications. In this paper, we compare a suite of different model averaging techniques by their ability to improve forecast accuracy of environmental systems. We compare equal weights averaging (EWA), Bates-Granger model averaging (BGA), averaging using Akaike’s information criterion (AICA), and Bayes’ Information Criterion (BICA), Bayesian model averaging (BMA), Mallows model averaging (MMA), and Granger-Ramanathan averaging (GRA) for two different hydrologic systems involving water flow through a 1950 km2 watershed and 5 m deep vadose zone. Averaging methods with weights restricted to the multi-dimensional simplex (positive weights summing up to one) are shown to have considerably larger forecast errors than approaches with unconstrained weights. Whereas various sophisticated model averaging approaches have recently emerged in the literature, our results convincingly demonstrate the advantages of GRA for hydrologic applications. This method achieves similar performance as MMA and BMA, but is much simpler to implement and use, and computationally much less demanding.  相似文献   

13.
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   

14.
Maximum likelihood Bayesian averaging of uncertain model predictions   总被引：13，自引：2，他引：11  
  相似文献   

15.
Pump‐and‐treat systems can prevent the migration of groundwater contaminants and candidate systems are typically evaluated with groundwater models. Such models should be rigorously assessed to determine predictive capabilities and numerous tools and techniques for model assessment are available. While various assessment methodologies (e.g., model calibration, uncertainty analysis, and Bayesian inference) are well‐established for groundwater modeling, this paper calls attention to an alternative assessment technique known as screening‐level sensitivity analysis (SLSA). SLSA can quickly quantify first‐order (i.e., main effects) measures of parameter influence in connection with various model outputs. Subsequent comparisons of parameter influence with respect to calibration vs. prediction outputs can suggest gaps in model structure and/or data. Thus, while SLSA has received little attention in the context of groundwater modeling and remedial system design, it can nonetheless serve as a useful and computationally efficient tool for preliminary model assessment. To illustrate the use of SLSA in the context of designing groundwater remediation systems, four SLSA techniques were applied to a hypothetical, yet realistic, pump‐and‐treat case study to determine the relative influence of six hydraulic conductivity parameters. Considered methods were: Taguchi design‐of‐experiments (TDOE); Monte Carlo statistical independence (MCSI) tests; average composite scaled sensitivities (ACSS); and elementary effects sensitivity analysis (EESA). In terms of performance, the various methods identified the same parameters as being the most influential for a given simulation output. Furthermore, results indicate that the background hydraulic conductivity is important for predicting system performance, but calibration outputs are insensitive to this parameter (KBK). The observed insensitivity is attributed to a nonphysical specified‐head boundary condition used in the model formulation which effectively “staples” head values located within the conductivity zone. Thus, potential strategies for improving model predictive capabilities include additional data collection targeting the KBK parameter and/or revision of model structure to reduce the influence of the specified head boundary.  相似文献   

16.
Within hydrology performance criteria such as the Nash–Sutcliffe efficiency have been used to condition the parameter space of a model. Their use is motivated by the fact that the stochastic error series between a model output and corresponding observations is the result of the composite effect of multiple error sources which cannot be described, even in form, a priori. This paper formalises the use of such performance criteria within a Bayesian framework, such as Generalised Likelihood Uncertainty Estimation (GLUE), by introducing the concept of Informal Likelihoods. Informal Likelihoods are used to characterise desirable features in the relationship between the model output and corresponding observed data. A number of common performance criteria are considered as Informal Likelihoods. Analytical results and a simulation indicate all of the performance criteria considered as Informal Likelihoods in this paper have one or more properties which may be considered undesirable, but may perform no less well in conditioning model parameters than formal likelihoods for which the assumptions are only mildly incorrect.  相似文献   

17.
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   

18.
In the last few years, the use of mathematical models in WasteWater Treatment Plant (WWTP) processes has become a common way to predict WWTP behaviour. However, mathematical models generally demand advanced input for their implementation that must be evaluated by an extensive data-gathering campaign, which cannot always be carried out. This fact, together with the intrinsic complexity of the model structure, leads to model results that may be very uncertain. Quantification of the uncertainty is imperative. However, despite the importance of uncertainty quantification, only few studies have been carried out in the wastewater treatment field, and those studies only included a few of the sources of model uncertainty. Seeking the development of the area, the paper presents the uncertainty assessment of a mathematical model simulating biological nitrogen and phosphorus removal. The uncertainty assessment was conducted according to the Generalised Likelihood Uncertainty Estimation (GLUE) methodology that has been scarcely applied in wastewater field. The model was based on activated-sludge models 1 (ASM) and 2 (ASM2). Different approaches can be used for uncertainty analysis. The GLUE methodology requires a large number of Monte Carlo simulations in which a random sampling of individual parameters drawn from probability distributions is used to determine a set of parameter values. Using this approach, model reliability was evaluated based on its capacity to globally limit the uncertainty. The method was applied to a large full-scale WWTP for which quantity and quality data was gathered. The analysis enabled to gain useful insights for WWTP modelling identifying the crucial aspects where higher uncertainty rely and where therefore, more efforts should be provided in terms of both data gathering and modelling practises.  相似文献   

19.
Characterization of groundwater contaminant source using Bayesian method   总被引：2，自引：1，他引：1  
Contaminant source identification in groundwater system is critical for remediation strategy implementation, including gathering further samples and analysis, as well as implementing and evaluating different remediation plans. Such problem is usually solved with the aid of groundwater modeling with lots of uncertainty, e.g. existing uncertainty in hydraulic conductivity, measurement variance and the model structure error. Monte Carlo simulation of flow model allows the input uncertainty onto the model predictions of concentration measurements at monitoring sites. Bayesian approach provides the advantage to update estimation. This paper presents an application of a dynamic framework coupling with a three dimensional groundwater modeling scheme in contamination source identification of groundwater. Markov Chain Monte Carlo (MCMC) is being applied to infer the possible location and magnitude of contamination source. Uncertainty existing in heterogonous hydraulic conductivity field is explicitly considered in evaluating the likelihood function. Unlike other inverse-problem approaches to provide single but maybe untrue solution, the MCMC algorithm provides probability distributions over estimated parameters. Results from this algorithm offer a probabilistic inference of the location and concentration of released contamination. The convergence analysis of MCMC reveals the effectiveness of the proposed algorithm. Further investigation to extend this study is also discussed.  相似文献   

20.
Despite the abundance of existing hydrological models, there is no single model that has been identified as performing consistently over the range of possible catchment types and catchment conditions. An attractive alternative to selecting a single model is to combine the results from several different hydrological models, thereby providing a more appropriate representation of model uncertainty than is the case otherwise. Methods based on Bayesian statistical techniques provide an ideal means to compare and combine competing models, as they explicitly account for model uncertainty. Bayesian model averaging is one such alternative that combines individual models by weighting models proportional to their respective posterior probability of selection. However, the necessity of having fixed weights for each model over the entire length of the simulation period means that the relative usefulness of different models at different times is not considered. The hierarchical mixtures of experts (HME) framework is an appealing extension of the model averaging framework that allows the individual model weights to be estimated dynamically. Consequently, a model more capable at simulating low flow characteristics attains a higher weight (probability) when such conditions are likely, switching over to a lower weight when catchment storage increases. In this way, different models apply in different hydrological states, with the probability of selecting each model being allowed to depend on relevant antecedent condition characteristics. HME models provide additional flexibility compared with simple combinations of models, by allowing the way that model predictions are combined to depend on predictor variables. Thus, for hydrological models, the ‘switch’ from one model to another can depend on the existing catchment condition. This new modelling framework is applied using a simple conceptual model to 10 selected Australian catchments. The study regions are chosen to vary considerably in terms of size, yield and location. Results from this application are compared with the alternative where a single fixed model structure is applied. Comparison of the model simulations using the maximum log‐likelihood and the Nash‐Sutcliffe coefficient of efficiency show that more variance in streamflow was explained by the HME model, compared with the conceptual model alone for each of the catchments investigated. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

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