Estimation of soil hydraulic properties and their uncertainty through the Beerkan infiltration experiment

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.     

Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling?

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.     

Response to comment by Keith Beven on “Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling?”

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.     

Estimating uncertainty associated with water stages from a single SAR image

It is the goal of remote sensing to infer information about objects or a natural process from a remote location. This invokes that uncertainty in measurement should be viewed as central to remote sensing. In this study, the uncertainty associated with water stages derived from a single SAR image for the Alzette (G.D. of Luxembourg) 2003 flood is assessed using a stepped GLUE procedure. Main uncertain input factors to the SAR processing chain for estimating water stages include geolocation accuracy, spatial filter window size, image thresholding value, DEM vertical precision and the number of river cross sections at which water stages are estimated. Initial results show that even with plausible parameter values uncertainty in water stages over the entire river reach is 2.8 m on average. Adding spatially distributed field water stages to the GLUE analysis following a one-at-a-time approach helps to considerably reduce SAR water stage uncertainty (0.6 m on average) thereby identifying appropriate value ranges for each uncertain SAR water stage processing factor. For the GLUE analysis a Nash-like efficiency criterion adapted to spatial data is proposed whereby acceptable SAR model simulations are required to outperform a simpler regression model based on the field-surveyed average river bed gradient. Weighted CDFs for all factors based on the proposed efficiency criterion allow the generation of reliable uncertainty quantile ranges and 2D maps that show the uncertainty associated with SAR-derived water stages. The stepped GLUE procedure demonstrated that not all field data collected are necessary to achieve maximum constraining. A possible efficient way to decide on relevant locations at which to sample in the field is proposed. It is also suggested that the resulting uncertainty ranges and flood extent or depth maps may be used to evaluate 1D or 2D flood inundation models in terms of water stages, depths or extents. For this, the extended GLUE approach, which copes with the presence of uncertainty in the observed data, may be adopted.     

Including prior information in the estimation of effective soil parameters in unsaturated zone modelling

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.     

Application of a data‐based mechanistic modelling (DBM) approach for predicting runoff generation in semi‐arid regions

This paper addresses the application of a data‐based mechanistic (DBM) modelling approach using transfer function models (TFMs) with non‐linear rainfall filtering to predict runoff generation from a semi‐arid catchment (795 km²) in Tanzania. With DBM modelling, time series of rainfall and streamflow were allowed to suggest an appropriate model structure compatible with the data available. The model structures were evaluated by looking at how well the model fitted the data, and how well the parameters of the model were estimated. The results indicated that a parallel model structure is appropriate with a proportion of the runoff being routed through a fast flow pathway and the remainder through a slow flow pathway. Finally, the study employed a Generalized Likelihood Uncertainty Estimation (GLUE) methodology to evaluate the parameter sensitivity and predictive uncertainty based on the feasible parameter ranges chosen from the initial analysis of recession curves and calibration of the TFM. Results showed that parameters that control the slow flow pathway are relatively more sensitive than those that control the fast flow pathway of the hydrograph. Within the GLUE framework, it was found that multiple acceptable parameter sets give a range of predictions. This was found to be an advantage, since it allows the possibility of assessing the uncertainty in predictions as conditioned on the calibration data and then using that uncertainty as part of the decision‐making process arising from any rainfall‐runoff modelling project. Copyright © 2001 John Wiley & Sons, Ltd.     

Uncertainty assessment of a process-based integrated catchment model of phosphorus

Despite the many models developed for phosphorus concentration prediction at differing spatial and temporal scales, there has been little effort to quantify uncertainty in their predictions. Model prediction uncertainty quantification is desirable, for informed decision-making in river-systems management. An uncertainty analysis of the process-based model, integrated catchment model of phosphorus (INCA-P), within the generalised likelihood uncertainty estimation (GLUE) framework is presented. The framework is applied to the Lugg catchment (1,077 km²), a River Wye tributary, on the England–Wales border. Daily discharge and monthly phosphorus (total reactive and total), for a limited number of reaches, are used to initially assess uncertainty and sensitivity of 44 model parameters, identified as being most important for discharge and phosphorus predictions. This study demonstrates that parameter homogeneity assumptions (spatial heterogeneity is treated as land use type fractional areas) can achieve higher model fits, than a previous expertly calibrated parameter set. The model is capable of reproducing the hydrology, but a threshold Nash-Sutcliffe co-efficient of determination (E or R ²) of 0.3 is not achieved when simulating observed total phosphorus (TP) data in the upland reaches or total reactive phosphorus (TRP) in any reach. Despite this, the model reproduces the general dynamics of TP and TRP, in point source dominated lower reaches. This paper discusses why this application of INCA-P fails to find any parameter sets, which simultaneously describe all observed data acceptably. The discussion focuses on uncertainty of readily available input data, and whether such process-based models should be used when there isn’t sufficient data to support the many parameters.     

A computationally efficient method for uncertainty analysis of SWAT model simulations

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.     

Comparison of parameter uncertainty analysis techniques for a TOPMODEL application

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.     

Equifinality and uncertainty in physically based soil erosion models: application of the GLUE methodology to WEPP–the Water Erosion Prediction Project–for sites in the UK and USA

Despite the wealth of soil erosion models available for the prediction of both runoff and soil loss at a variety of scales, little quantification is made of uncertainty and error associated with model output. This in part reflects the need to produce unequivocal or optimal results for the end user, which will often be an unrealistic goal. This paper presents a conceptually simple methodology, Generalized Likelihood Uncertainty Estimation (GLUE), for assessing the degree of uncertainty surrounding output from a physically based soil erosion model, the Water Erosion Prediction Project (WEPP). The ability not only to be explicit about model error but also to evaluate future improvements in parameter estimation, observed data or scientific understanding is demonstrated. This approach is applied to two sets of soil loss/runoff plot replicates, one in the UK and one in the USA. Although it is demonstrated that observations can be largely captured within uncertainty bounds, results indicate that these uncertainty bounds are often wide, reflecting the need to qualify results that derive from ‘optimum’ parameter sets, and to accept the concept of equifinality within soil erosion models. Attention is brought to the problem of under‐prediction of large events/over‐prediction of small events, as an area where model improvements could be made, specifically in the case of relatively dry years. Finally it is proposed that such a technique of model evaluation be employed more widely within the discipline so as to aid the interpretation and understanding of complex model output. Copyright © 2000 John Wiley & Sons, Ltd.     

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

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.     

Numerical investigation of the impact of uncertainties in satellite rainfall estimation and land surface model parameters on simulation of soil moisture

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.     

Uncertainty assessment of a model for biological nitrogen and phosphorus removal: Application to a large wastewater treatment plant

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.     

A method to reduce the computational requirement while assessing uncertainty of complex hydrological models

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.     

Implications of model uncertainty for the mapping of hillslope‐scale soil erosion predictions

An integrated modelling approach (MIRSED) which utilizes the process‐based soil erosion model WEPP (Water Erosion Prediction Project) is presented for the assessment of hillslope‐scale soil erosion at five sites throughout England and Wales. The methodology draws upon previous uncertainty analysis of the WEPP hillslope soil erosion model by the authors to qualify model results within an uncertainty framework. A method for incorporating model uncertainty from a range of sources is discussed as a first step towards using and learning from results produced through the GLUE (Generalized Likelihood Uncertainty Estimation) technique. Results are presented and compared to available observed data, which illustrate that levels of uncertainty are significant and must be taken into account if a meaningful understanding of output from models such as WEPP is to be achieved. Furthermore, the collection of quality, observed data is underlined for two reasons: as an essential tool in the development of soil erosion modelling and also to allow further constraint of model uncertainty. Copyright © 2001 John Wiley & Sons, Ltd.     

Evaluation of the hydrology of the IBIS land surface model in a semi‐arid catchment

This paper evaluates the Integrated BIosphere Simulator (IBIS) land surface model using daily soil moisture data over a 3‐year period (2005–2007) at a semi‐arid site in southeastern Australia, the Stanley catchment, using the Monte Carlo generalized likelihood uncertainty estimation (GLUE) approach. The model was satisfactorily calibrated for both the surface 30 cm and full profile 90 cm. However, full‐profile calibration was not as good as that for the surface, which results from some deficiencies in the evapotranspiration component in IBIS. Relatively small differences in simulated soil moisture were associated with large discrepancies in the predictions of surface runoff, drainage and evapotranspiration. We conclude that while land surface schemes may be effective at simulating heat fluxes, they may be ineffective for prediction of hydrology unless the soil moisture is accurately estimated. Sensitivity analyses indicated that the soil moisture simulations were most sensitive to soil parameters, and the wilting point was the most identifiable parameter. Significant interactions existed between three soils parameters: porosity, saturated hydraulic conductivity and Campbell ‘b’ exponent, so they could not be identified independent of each other. There were no significant differences in parameter sensitivity and interaction for different hydroclimatic years. Even though the data record contained a very dry year and another year with a very large rainfall event, this indicated that the soil model could be calibrated without the data needing to explore the extreme range of dry and wet conditions. IBIS was much less sensitive to vegetation parameters. The leaf area index (LAI) could affect the mean of daily soil moisture time series when LAI < 1, while the variance of the soil moisture time series was sensitive to LAI > 1. IBIS was insensitive to the Jackson rooting parameter, suggesting that the effect of the rooting depth distribution on predictions of hydrology was insignificant. Copyright © 2014 John Wiley & Sons, Ltd.     

Assessment of flood forecasting lead time based on generalized likelihood uncertainty estimation approach

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.     

The role of hydrological modelling uncertainties in climate change impact assessments of Irish river catchments

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.     

GLUE: 20 years on

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.     

Assessing the uncertainty in distributed model predictions using observed binary pattern information within GLUE

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.