Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling     

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   

Indices for assessing the prediction bounds of hydrological models and application by generalised likelihood uncertainty estimation / Indices pour évaluer les bornes de prévision de modèles hydrologiques et mise en œuvre pour une estimation d'incertitude par vraisemblance généralisée     

《水文科学杂志》2013,58(5):852-871

Abstract

To reflect the uncertainties of a hydrological model in simulating and forecasting observed discharges according to rainfall inputs, the estimated result for each time step should not be just a point estimate (a single numerical value), but should be expressed as a prediction interval, i.e. a band defined by the prediction bounds of a particular confidence level α. How best to assess the quality of the prediction bounds thus becomes very important for understanding the modelling uncertainty in a comprehensive and objective way. This paper focuses on seven indices for characterizing the prediction bounds from different perspectives. For the three case-study catchments presented, these indices are calculated for the prediction bounds generated by the generalized likelihood uncertainty estimation (GLUE) method for various threshold values. In addition, the relationships among these indices are investigated, particularly that of the containing ratio (CR) to the other indices. In this context, three main findings are obtained for the prediction bounds estimated by GLUE. Firstly, both the average band-width and the average relative band-width are seen to have very strong linear correlations with the CR index. Secondly, a high CR value, a narrow band-width, and a high degree of symmetry with respect to the observed hydrograph, all of which are clearly desirable properties of the prediction bounds estimated by the uncertainty assessment methods, cannot all be achieved simultaneously. Thirdly, for the prediction bounds considered, the higher CR values and the higher degrees of symmetry with respect to the observed hydrograph are found to be associated with both the larger band-widths and the larger deviation amplitudes. It is recommended that a set of different indices, such as those considered in this study, be employed for assessing and comparing the prediction bounds in a more comprehensive and objective way.  相似文献   

Comparison of parameter uncertainty analysis techniques for a TOPMODEL application     

Binquan?LiEmail authorView author&#;s OrcID profile  Zhongmin?Liang  Yingqing?He  Lin?Hu  Weimin?Zhao  Kumud?Acharya 《Stochastic Environmental Research and Risk Assessment (SERRA)》2017,31(5):1045-1059

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   

Quantification of parametric uncertainty of ANN models with GLUE method for different streamflow dynamics   总被引：2，自引：1，他引：1  

Hakan?TongalEmail authorView author&#;s OrcID profile  Martijn?J.?Booij 《Stochastic Environmental Research and Risk Assessment (SERRA)》2017,31(4):993-1010

This study describes the parametric uncertainty of artificial neural networks (ANNs) by employing the generalized likelihood uncertainty estimation (GLUE) method. The ANNs are used to forecast daily streamflow for three sub-basins of the Rhine Basin (East Alpine, Main, and Mosel) having different hydrological and climatological characteristics. We have obtained prior parameter distributions from 5000 ANNs in the training period to capture the parametric uncertainty and subsequently 125,000 correlated parameter sets were generated. These parameter sets were used to quantify the uncertainty in the forecasted streamflow in the testing period using three uncertainty measures: percentage of coverage, average relative length, and average asymmetry degree. The results indicated that the highest uncertainty was obtained for the Mosel sub-basin and the lowest for the East Alpine sub-basin mainly due to hydro-climatic differences between these basins. The prediction results and uncertainty estimates of the proposed methodology were compared to the direct ensemble and bootstrap methods. The GLUE method successfully captured the observed discharges with the generated prediction intervals, especially the peak flows. It was also illustrated that uncertainty bands are sensitive to the selection of the threshold value for the Nash–Sutcliffe efficiency measure used in the GLUE method by employing the Wilcoxon–Mann–Whitney test.  相似文献   

Including prior information in the estimation of effective soil parameters in unsaturated zone modelling   总被引：2，自引：0，他引：2  

J Mertens  H Madsen  D Jacques 《Journal of Hydrology》2004,294(4):251-269

In this paper we propose a methodology to include prior information in the estimation of effective soil parameters for modelling the soil moisture content in the unsaturated zone. Laboratory measurements on undisturbed soil cores were used to estimate the moisture retention curve and hydraulic conductivity curve parameters. The soil moisture content was measured at 25 locations along three transects and at three different depths (surface, 30 and 60 cm) on an 80×20 m hillslope for the year 2001. Soil cores were collected in 84 locations situated in three profile pits along the hillslope. For the estimation of the effective soil hydraulic parameters the joint probability distribution of measured parameter values was used as prior information. A two-horizon single column 1D MIKE SHE model based on Richards' equation was set-up for nine soil moisture measurement locations along the middle transect of the hillslope. The goal of the model is to simulate the soil moisture profile at each location. The shuffled complex evolution (SCE) algorithm has been applied to estimate effective model parameters using either wide parameter ranges, referred to as the ‘no-prior’ case, or the joint probability distribution of measured parameter values as prior information (‘prior’ case). When the prior information is incorporated in the SCE optimisation the goodness-of-fit of the model predictions is only slightly worse compared to when no-prior information is incorporated. However, the effective parameter estimates are more realistic when the prior information is incorporated. For both the no-prior and prior case the generalised likelihood uncertainty estimation procedure (GLUE) was subsequently used to estimate the uncertainty bounds (UB) on the model predictions. When incorporating the prior information more parameter sets were accepted for the estimation of the predictive uncertainty and the parameter values were more realistic. Moreover, UB better enclosed the observations. Thus, incorporating prior information in GLUE reduces the amount of model evaluations needed to obtain sufficient behavioural parameter sets. The results indicate the importance of prior information in the SCE and GLUE parameter estimation strategies.  相似文献   

A computationally efficient method for uncertainty analysis of SWAT model simulations     

P.?Athira  C.?Nanda  K.?P.?SudheerEmail author 《Stochastic Environmental Research and Risk Assessment (SERRA)》2018,32(6):1479-1492

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   

Advancing understanding in data-limited conditions: estimating contributions to streamflow across Tanzania’s rapidly developing Kilombero Valley     

Alexander J. Koutsouris  Steve W. Lyon 《水文科学杂志》2018,63(2):197-209

Large seasonal variability in precipitation patterns may help overcome data limitations and difficult conditions when characterizing hydrological flow pathways. We used a limited amount of weekly water chemistry as well as stable water isotope data to perform end-member mixing analysis (EMMA) in a generalized likelihood uncertainty estimation (GLUE) framework in a sub-catchment of the Kilombero Valley, Tanzania. While there were considerable uncertainties related to the characterization and mixing of end-members, some robust estimates could be made on contributions to seasonal streamflow variability. For example, there is a low connectivity between the deep groundwater and the stream system throughout the year. Also, a considerable wetting-up period is required before overland flow occurs. Thus, in spite of large uncertainties, our results highlight how improved system understanding of hydrological flows can be obtained even when working in difficult environments.  相似文献   

The role of hydrological modelling uncertainties in climate change impact assessments of Irish river catchments   总被引：5，自引：0，他引：5  

Satish Bastola  Conor MurphyJohn Sweeney 《Advances in water resources》2011,34(5):562-576

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   

The comparison of sensitivity analysis of hydrological uncertainty estimates by GLUE and Bayesian method under the impact of precipitation errors     

Lu Li  Chong-Yu Xu 《Stochastic Environmental Research and Risk Assessment (SERRA)》2014,28(3):491-504

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   

GLUE: 20 years on          下载免费PDF全文

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   

Calibration of hydrological models in ungauged basins based on satellite radar altimetry observations of river water level     

Wenchao Sun  Hiroshi Ishidaira  Satish Bastola 《水文研究》2012,26(23):3524-3537

This paper proposes a new orientation to address the problem of hydrological model calibration in ungauged basin. Satellite radar altimetric observations of river water level at basin outlet are used to calibrate the model, as a surrogate of streamflow data. To shift the calibration objective, the hydrological model is coupled with a hydraulic model describing the relation between streamflow and water stage. The methodology is illustrated by a case study in the Upper Mississippi Basin using TOPEX/Poseidon (T/P) satellite data. The generalized likelihood uncertainty estimation (GLUE) is employed for model calibration and uncertainty analysis. We found that even without any streamflow information for regulating model behavior, the calibrated hydrological model can make fairly reasonable streamflow estimation. In order to illustrate the degree of additional uncertainty associated with shifting calibration objective and identifying its sources, the posterior distributions of hydrological parameters derived from calibration based on T/P data, streamflow data and T/P data with fixed hydraulic parameters are compared. The results show that the main source is the model parameter uncertainty. And the contribution of remote sensing data uncertainty is minor. Furthermore, the influence of removing high error satellite observations on streamflow estimation is also examined. Under the precondition of sufficient temporal coverage of calibration data, such data screening can eliminate some unrealistic parameter sets from the behavioral group. The study contributes to improve streamflow estimation in ungauged basin and evaluate the value of remote sensing in hydrological modeling. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

Uncertainty analysis of flood inundation modelling using GLUE with surrogate models in stochastic sampling   总被引：1，自引：0，他引：1       下载免费PDF全文

J. J. Yu  X. S. Qin  O. Larsen 《水文研究》2015,29(6):1267-1279

A generalized likelihood uncertainty estimation (GLUE) method incorporating moving least squares (MLS) with entropy for stochastic sampling (denoted as GLUE‐MLS‐E) was proposed for uncertainty analysis of flood inundation modelling. The MLS with entropy (MLS‐E) was established according to the pairs of parameters/likelihoods generated from a limited number of direct model executions. It was then applied to approximate the model evaluation to facilitate the target sample acceptance of GLUE during the Monte‐Carlo‐based stochastic simulation process. The results from a case study showed that the proposed GLUE‐MLS‐E method had a comparable performance as GLUE in terms of posterior parameter estimation and predicted confidence intervals; however, it could significantly reduce the computational cost. A comparison to other surrogate models, including MLS, quadratic response surface and artificial neural networks (ANN), revealed that the MLS‐E outperformed others in light of both the predicted confidence interval and the most likely value of water depths. ANN was shown to be a viable alternative, which performed slightly poorer than MLS‐E. The proposed surrogate method in stochastic sampling is of practical significance in computationally expensive problems like flood risk analysis, real‐time forecasting, and simulation‐based engineering design, and has a general applicability in many other numerical simulation fields that requires extensive efforts in uncertainty assessment. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

Estimation of soil hydraulic properties and their uncertainty through the Beerkan infiltration experiment          下载免费PDF全文

Saeed Ghavidelfar  Asaad Y. Shamseldin  Bruce W. Melville 《水文研究》2015,29(17):3699-3713

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   

Assessing uncertainties in a conceptual water balance model using Bayesian methodology / Estimation bayésienne des incertitudes au sein d’une modélisation conceptuelle de bilan hydrologique     

《水文科学杂志》2013,58(1)

Abstract

Abstract The aim of this study was to estimate the uncertainties in the streamflow simulated by a rainfall–runoff model. Two sources of uncertainties in hydrological modelling were considered: the uncertainties in model parameters and those in model structure. The uncertainties were calculated by Bayesian statistics, and the Metropolis-Hastings algorithm was used to simulate the posterior parameter distribution. The parameter uncertainty calculated by the Metropolis-Hastings algorithm was compared to maximum likelihood estimates which assume that both the parameters and model residuals are normally distributed. The study was performed using the model WASMOD on 25 basins in central Sweden. Confidence intervals in the simulated discharge due to the parameter uncertainty and the total uncertainty were calculated. The results indicate that (a) the Metropolis-Hastings algorithm and the maximum likelihood method give almost identical estimates concerning the parameter uncertainty, and (b) the uncertainties in the simulated streamflow due to the parameter uncertainty are less important than uncertainties originating from other sources for this simple model with fewer parameters.  相似文献   

Climate models and hydrological parameter uncertainties in climate change impacts on monthly runoff and daily flow duration curve of a Mediterranean catchment     

Haykel Sellami  Sihem Benabdallah  Isabelle La Jeunesse  Marnik Vanclooster 《水文科学杂志》2013,58(8):1415-1429

ABSTRACT

Climate models and hydrological parameter uncertainties were quantified and compared while assessing climate change impacts on monthly runoff and daily flow duration curve (FDC) in a Mediterranean catchment. Simulations of the Soil and Water Assessment Tool (SWAT) model using an ensemble of behavioural parameter sets derived from the Generalized Likelihood Uncertainty Estimation (GLUE) method were approximated by feed-forward artificial neural networks (FF-NN). Then, outputs of climate models were used as inputs to the FF-NN models. Subsequently, projected changes in runoff and FDC were calculated and their associated uncertainty was partitioned into climate model and hydrological parameter uncertainties. Runoff and daily discharge of the Chiba catchment were expected to decrease in response to drier and warmer climatic conditions in the 2050s. For both hydrological indicators, uncertainty magnitude increased when moving from dry to wet periods. The decomposition of uncertainty demonstrated that climate model uncertainty dominated hydrological parameter uncertainty in wet periods, whereas in dry periods hydrological parametric uncertainty became more important.