Application of the generalized likelihood uncertainty estimation (GLUE) approach for assessing uncertainty in hydrological models: a review (original) (raw)
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Appraisal of the generalized likelihood uncertainty estimation (GLUE) method
Water Resources Research, 2008
1] Recent research documents that the widely accepted generalized likelihood uncertainty estimation (GLUE) method for describing forecasting precision and the impact of parameter uncertainty in rainfall/runoff watershed models fails to achieve the intended purpose when used with an informal likelihood measure. In particular, GLUE generally fails to produce intervals that capture the precision of estimated parameters, and the difference between predictions and future observations. This paper illustrates these problems with GLUE using a simple linear rainfall/runoff model so that model calibration is a linear regression problem for which exact expressions for prediction precision and parameter uncertainty are well known and understood. The simple regression example enables us to clearly and simply illustrate GLUE deficiencies. Beven and others have suggested that the choice of the likelihood measure used in a GLUE computation is subjective and may be selected to reflect the goals of the modeler. If an arbitrary likelihood is adopted that does not reasonably reflect the sampling distribution of the model errors, then GLUE generates arbitrary results without statistical validity that should not be used in scientific work. The traditional subjective likelihood measures that have been used with GLUE also fail to reflect the nonnormality, heteroscedasticity, and serial correlation among the residual errors generally found in real problems, and hence are poor metrics for even simple sensitivity analyses and model calibration. Most previous applications of GLUE only produce uncertainty intervals for the average model prediction, which by construction should not be expected to include future observations with the prescribed probability. We show how the GLUE methodology when properly implemented with a statistically valid likelihood function can provide prediction intervals for future observations which will agree with widely accepted and statistically valid analyses.
Journal of Hydrology, 2010
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… Journal of River …, 2004
The uncertainty of the GIS based rainfall runoff model LisFlood has been investigated within the Generalized Likelihood Uncertainty Estimation (GLUE) framework. Multipliers for the saturated and unsaturated hydraulic conductivity, the porosity of the upper and lower soil layer, channel and overland flow roughness and the maximum percolation from upper to lower storages have been sampled within a Monte Carlo analysis from a uniform random distribution. With each parameter set the model has been computed with input for the 1995 flood event of the river Meuse situated in France, Belgium and The Netherlands. Eight gauging stations have been used for model evaluation by the Multicomponent Mapping (M x ) method. All parameters demonstrate equifinality and no parameter set could be classified as behavioural for all the evaluation datasets. However, the results of the prediction of uncertainty percentiles on the flow are very satisfactory and encouraging. The model did further show the capability to predict the uncertainty for estimating the exceedence of threshold levels, which can be used in flood warning decision making and river basin management.
Hydrological forecasting uncertainty assessment: Incoherence of the GLUE methodology
Journal of Hydrology, 2006
The aim of the paper is to demonstrate the incoherence, in terms of Bayesian inference, of the generalized likelihood uncertainty estimation (GLUE) approach, introduced by Beven and Binley in 1992. This results into a reduced capacity of the technique to extract information, in other words to ''learn'', from observations. The paper also discusses the implications of this reduced learning capacity for parameter estimation and hydrological forecasting uncertainty assessment, which has led to the definition of the ''equifinality'' principle. The notions of coherence for learning and prediction processes as well as the value of a statistical experiment are introduced. These concepts are useful in showing that the GLUE methodology defines a statistical inference process, which is inconsistent and incoherent.
Uncertainty in hydrological modelling: A review
International Journal of Hydrology Research
Availability of hydrological data and various soft wares for developing models make easy way to answer frequently asked questions to hydrologists. A great deal of concentration has given to the development of models in the last decades. But the thorough study regarding uncertainty of simulations has not carried out in comparison with the development of models. Uncertainty in models emanates from input data, calibrated data, parameters and from the structure of models. The sources of uncertainty, cause of generation and how these can be dealt with are reviewed here. This also comprises a review about five different methods viz. Monte Carlo sampling, Bayesian approach, Generalized Likelihood Uncertainty Estimation, Bootstrap Approach and Machine learning methods which were applied in the estimation of the model and parameter uncertainty. This will indicate the comparison between the methods which were applied to measure the uncertainty of hydrological models and highlight the strength...
Journal of Hydrology, 2010
Conceptual hydrological model Uncertainty Bayesian method GLUE s u m m a r y Quantification of uncertainty of hydrological models has attracted much attention in hydrologic research in recent years. Many methods for quantification of uncertainty have been reported in the literature, of which GLUE and formal Bayesian method are the two most popular methods. There have been many discussions in the literature concerning differences between these two methods in theory (mathematics) and results, and this paper focuses on the computational efficiency and differences in their results, but not on philosophies and mathematical rigor that both methods rely on. By assessing parameter and modeling uncertainty of a simple conceptual water balance model (WASMOD) with the use of GLUE and formal Bayesian method, the paper evaluates differences in the results of the two methods and discusses the reasons for these differences. The main findings of the study are that: (1) the parameter posterior distributions generated by the Bayesian method are slightly less scattered than those by the GLUE method; (2) using a higher threshold value (>0.8) GLUE results in very similar estimates of parameter and model uncertainty as does the Bayesian method; and (3) GLUE is sensitive to the threshold value used to select behavioral parameter sets and lower threshold values resulting in a wider uncertainty interval of the posterior distribution of parameters, and a wider confidence interval of model uncertainty. More study is needed to generalize the findings of the present study.
Journal of Water Supply: Research and Technology—AQUA, 2013
This study is designed to consider the uncertainty in the kinematic runoff and erosion model named KINEROS2. The Generalized Likelihood Uncertainty Estimation (GLUE) method was used for assessing the uncertainty associated with model predictions, which assumes that due to the limitations in model structure, data and calibration scheme, many different parameter sets can make acceptable simulations. GLUE is a Bayesian approach based on the Monte Carlo method for model calibration and uncertainty analysis. The assessment was performed in the Zayanderood River basin located in Central Iran. To make an accurate calibration, five runoff events were selected from three different gauging stations for the purpose. Statistical evaluations for streamflow prediction indicate that there is good agreement between the measured and simulated flows with Nash-Sutcliffe values of efficiency of 0.85 and 0.79 for calibration and validation periods respectively.
An Approach to Uncertainty Identification in Hydrological Modeling
PROCEEDINGS OF HYDRAULIC ENGINEERING, 2005
We propose a methodology to identify prediction uncertainty through recognizing and quantifying the different uncertainty sources in a hydrologic model. Statistical second moment is used as a measure of uncertainty; also an index which originated from Nash coefficient of efficiency named Model Structure Indicating Index (MSII) is proposed to quantify model structure uncertainty. The results show that MSII can well reflect the goodness of model structure, while a larger value of MSII indicating a poorer structure of hydrologic model. The index can be used as a tool for implementing model quantitative comparison (selection).
Stochastic Environmental Research and Risk Assessment, 2014
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.
Development Of A Repository For Hydrologic Model Uncertainty Data
2014
Hydrologic processes are complex and when modeling them using a deterministic or stochastic approach one invariably introduces errors because of simplifications and assumptions made. However, not all assumptions and simplifications in the approach chosen produce the amount of errors; in fact the impact of deviations from the truth on a final output set of variables varies greatly. In addition, not every catchment behaves alike adding another layer of complexity to the modeling effort. Hence, every approach exhibits a degree of uncertainty in their results. While this uncertainty can be examined systematically in this technical note we focus on the development of a repository for modeling uncertainty data. We store information about the model used (lumped, semi distributed, fully distributed), the objective function (Nash Sutcliff, Root Mean Square Error, ...) used to calculate the fitness of an approach, a Pareto best parameter combination, and also some statistical values that arri...