Shuffled Complex Evolution Metropolis Algorithm Research Articles

Experimental Validation of Optimal Parameter and Uncertainty Estimation for Structural Systems Using a Shuffled Complex Evolution Metropolis Algorithm

The uncertainty in parameter estimation arises from structural systems’ input and output measured errors and from structural model errors. An experimental verification of the shuffled complex evolution metropolis algorithm (SCEM-UA) for identifying the optimal parameters of structural systems and estimating their uncertainty is presented. First, the estimation framework is theoretically developed. The SCEM-UA algorithm is employed to search through feasible parameters’ space and to infer the posterior distribution of the parameters automatically. The resulting posterior parameter distribution then provides the most likely estimation of parameter sets that produces the best model performance. The algorithm is subsequently validated through both numerical simulation and shaking table experiment for estimating the parameters of structural systems considering the uncertainty of available information. Finally, the proposed algorithm is extended to identify the uncertain physical parameters of a nonlinear structural system with a particle mass tuned damper (PTMD). The results demonstrate that the proposed algorithm can effectively estimate parameters with uncertainty for nonlinear structural systems, and it has a stronger anti-noise capability. Notably, the SCEM-UA method not only shows better global optimization capability compared with other heuristic optimization methods, but it also has the ability to simultaneously estimate the uncertainties associated with the posterior distributions of the structural parameters within a single optimization run.

Diagnosis of the hydrology of a small Arctic permafrost catchment using HBV conceptual rainfall-runoff model

Abstract Changes in active layer thickness (ALT) over Arctic and permafrost regions have an important impact on rainfall-runoff transformation. General warming is observed across Svalbard Archipelago and corresponds to increases in ground temperatures. Permafrost thaw and changes in ALT due to climate warming alter how water is routed and stored in catchments, and thus impact both surface and subsurface processes. The overall aim of the present study is to examine the relationships between temporal changes of active layer depth and hydrological model parameters, together with variation in the catchment response. The analysis was carried out for the small unglaciated catchment Fuglebekken, located in the vicinity of the Polish Polar Station Hornsund on Spitsbergen. For hydrological modelling, the conceptual rainfall-runoff HBV (Hydrologiska Byråns Vattenbalansavdelning) model was used. The model was calibrated and validated on runoff within subperiods. A moving window approach (3 weeks long) was applied to derive temporal variation of parameters. Model calibration, together with an estimation of parametric uncertainty, was carried out using the Shuffled Complex Evolution Metropolis algorithm. This allowed the dependence of HBV model parameters on ALT to be analysed. Also, we tested the influence of model simplification, correction of precipitation, and initial conditions on the modelling results.

Surrogate modeling-based calibration of hydrodynamic river model parameters

As opposed to other disciplines, automated calibration procedures are not common practice for full hydrodynamic river models, mainly because of the long computation times impeding the accurate assessment of parameter values. Default or text-book values are therefore often used. This paper introduces a methodology to optimize hydrodynamic model parameter values, based on the use of a surrogate conceptual model. Thanks to the spatial lumping and the explicit calculation schemes of these conceptual models, very short calculation times and a large number of simulation runs can be achieved. The surrogate model is coupled with the Shuffled Complex Evolution Metropolis algorithm of the University of Arizona (SCEM-UA) to identify the optimal parameter sets and their uncertainty. Afterwards, the optimized parameter values are transferred to the full hydrodynamic model. The methodology is demonstrated on a case study of the river Molenbeek in Belgium, using streamflow, water level and gate level observations. Results show a decrease of the hydrodynamic model residuals by about 60 percent.

Multisource hydrologic modeling uncertainty analysis using the IBUNE framework in a humid catchment

Hydrologic cycle is a complex system associated with both certain and uncertain constituents. The propagation of confidence bounds from different uncertainty sources to model output is of great significance for hydrologic modeling. In this paper, we applied the integrated bayesian uncertainty estimator to quantify the effects of parameter, input and model structure uncertainty on hydrologic modeling progressively. Two hydrologic models (Xinanjiang model and TOPMODEL) were applied to a humid catchment under three scenarios. Case I: the shuffled complex evolution metropolis (SCEM-UA) algorithm was conducted to determine the posterior parameter distribution of hydrologic models and analyze the corresponding forecast uncertainty. Case II: input uncertainty was also considered by assuming rain depth bias follows a normal distribution, and integrated with SCEM-UA. Case III: Simulations from two models were combined by the Bayesian model averaging to fully quantify multisource uncertainty effects. Results suggested that, from Case I to II, the containing ratio (percentage of observed streamflow enveloped by 95% confidence interval) obviously increased by an average magnitude of 10% for the study period 2000–2006. Besides, it also found that the width of 95% confidence interval became wider and narrower for Xinanjiang model and TOPMODEL, respectively, from Case I to II. This may indicate that the uncertainty of TOPMODEL results was more remarkable than Xinanjiang model in Case I. By combining results from two models, model structure uncertainty was also considered in Case III. The accuracy of uncertainty bounds further improved with the containing ratio of 95% confidence interval >95%. In addition, the optimized deterministic results from the uncertainty analysis showed that the average Nash–Sutcliffe coefficient increased continually from Case I to II and III (0.82, 0.84 and 0.90, respectively) for the study period. The analysis demonstrated the improvement of modeling accuracy when extra uncertainty sources were also quantified, and this finding also proved the applicability of IBUNE framework in hydrologic modeling.

Colloid-Facilitated Plutonium Transport in Fractured Tuffaceous Rock.

Colloids have the potential to enhance the mobility of strongly sorbing radionuclide contaminants in groundwater at underground nuclear test sites. This study presents an experimental and numerical investigation of colloid-facilitated plutonium transport in fractured porous media to identify plutonium reactive transport processes. The transport parameters for dispersion, diffusion, sorption, and filtration are estimated with inverse modeling by minimizing the least-squares objective function of multicomponent concentration data from multiple transport experiments with the shuffled complex evolution metropolis algorithm. Capitalizing on an unplanned experimental artifact that led to colloid formation, we adopt a stepwise strategy to first interpret the data from each experiment separately and then to incorporate multiple experiments simultaneously to identify a suite of plutonium-colloid transport processes. Nonequilibrium or kinetic attachment and detachment of plutonium-colloid in fractures were clearly demonstrated and captured in the inverted modeling parameters along with estimates of the source plutonium fraction that formed plutonium-colloids. The results from this study provide valuable insights for understanding the transport mechanisms and environmental impacts of plutonium in groundwater aquifers.

Optimization of Power System Scheduling Based on Shuffled Complex Evolution Metropolis Algorithm

Due to the world’s increasingly serious energy crisis, shortage of resources, and environmental degradation, traditional power system analysis and scheduling optimization methods have faced new challenges. This article examines the features of optimal scheduling of power system containing cascade hydropower, and establishes a scheduling model based on the Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm. This model takes the cost of power generation, emission of gaseous pollutants, and the characteristics of the generators fully into account. Constraints on the changes in thermoelectric generator power output were added to the set of constraint conditions, reducing the impact of thermal power fluctuations on the power system. Here, the SCEM-UA algorithm was used to solve the problem of optimal power system scheduling and render the model capable of global optimization searches. Analyses of simulated cases have demonstrated that the SCEM-UA algorithm can resolve the conflict between convergence speed and global search capability, increasing the global search capability of the model.

Recharge estimation and soil moisture dynamics in a Mediterranean, semi-arid karst region

Abstract. Knowledge of soil moisture dynamics in the unsaturated soil zone provides valuable information on the temporal and spatial variability of groundwater recharge. This is especially true for the Mediterranean region, where a substantial fraction of long-term groundwater recharge is expected to occur during high magnitude precipitation events of above-average wet winters. To elucidate process understanding of infiltration processes during these extreme events, a monitoring network of precipitation gauges, meteorological stations, and soil moisture plots was installed in an area with a steep climatic gradient in the Jordan Valley region. In three soil moisture plots, Hydrus-1D was used to simulate water movement in the unsaturated soil zone with soil hydraulic parameters estimated by the Shuffled Complex Evolution Metropolis algorithm. To generalize our results, we modified soil depth and rainfall input to simulate the effect of the pronounced climatic gradient and soil depth variability on percolation fluxes and applied the calibrated model to a time series with 62 years of meteorological data. Soil moisture measurements showed a pronounced seasonality and suggested rapid infiltration during heavy rainstorms. Hydrus-1D successfully simulated short and long-term soil moisture patterns, with the majority of simulated deep percolation occurring during a few intensive rainfall events. Temperature drops in a nearby groundwater well were observed synchronously with simulated percolation pulses, indicating rapid groundwater recharge mechanisms. The 62-year model run yielded annual percolation fluxes of up to 66% of precipitation depths during wet years and of 0% during dry years. Furthermore, a dependence of recharge on the temporal rainfall distribution could be shown. Strong correlations between depth of recharge and soil depth were also observed.

Resolving structural errors in a spatially distributed hydrologic model using ensemble Kalman filter state updates

Abstract. In hydrological modeling, model structures are developed in an iterative cycle as more and different types of measurements become available and our understanding of the hillslope or watershed improves. However, with increasing complexity of the model, it becomes more and more difficult to detect which parts of the model are deficient, or which processes should also be incorporated into the model during the next development step. In this study, we first compare two methods (the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA) and the Simultaneous parameter Optimization and Data Assimilation algorithm (SODA)) to calibrate a purposely deficient 3-D hillslope-scale model to error-free, artificially generated measurements. We use a multi-objective approach based on distributed pressure head at the soil–bedrock interface and hillslope-scale discharge and water balance. For these idealized circumstances, SODA's usefulness as a diagnostic methodology is demonstrated by its ability to identify the timing and location of processes that are missing in the model. We show that SODA's state updates provide information that could readily be incorporated into an improved model structure, and that this type of information cannot be gained from parameter estimation methods such as SCEM-UA. We then expand on the SODA result by performing yet another calibration, in which we investigate whether SODA's state updating patterns are still capable of providing insight into model structure deficiencies when there are fewer measurements, which are moreover subject to measurement noise. We conclude that SODA can help guide the discussion between experimentalists and modelers by providing accurate and detailed information on how to improve spatially distributed hydrologic models.

Comparison of three global optimization algorithms for calibration of the Xinanjiang model parameters

The Xinanjiang model, a conceptual rainfall-runoff (CRR) model with distributed parameters, has been successfully and widely applied to flood forecasting of large basins in humid and semi-humid regions of China. With an increasing demand for timely and accurate forecasts in hydrology, how to obtain more appropriate parameters for CRR models has long been an important topic. These models have a large number of parameters which cannot be directly obtained from measurable quantities of catchments characteristics. In this study, three different optimization methods are used to calibrate the Xinanjiang streamflow model: genetic algorithm (GA), shuffled complex evolution of the University of Arizona (SCE-UA) and the recently developed shuffled complex evolution Metropolis algorithm of the University of Arizona (SCEM-UA), using streamflow data of the Shuangpai Reservoir in China. Two different time steps of 1 and 3 hr are used in the analysis. The results indicate that the SCEM-UA algorithm can infer the most probable parameter set and furnish useful information about the nature of the response surface in the vicinity of the optimum. Moreover, there is larger uncertainty for 1 hr forecasting than for 3 hr forecasting. This is significant in assessing risks in likely applications of Xinanjiang models.

Uncertainty assessment and optimization of hydrological model with the Shuffled Complex Evolution Metropolis algorithm: an application to artificial neural network rainfall-runoff model

Assessment of parameter and predictive uncertainty of hydrologic models is an essential part in the field of hydrology. However, during the past decades, research related to hydrologic model uncertainty is mostly done with conceptual models. As is accepted that uncertainty in model predictions arises from measurement errors associated with the system input and output, from model structural errors and from problems with parameter estimation. Unfortunately, non-conceptual models, such as black-box models, also suffer from these problems. In this paper, we take the artificial neural network (ANN) rainfall-runoff model as an example, and the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA) is employed to analysis the parameter and predictive uncertainty of this model. Furthermore, based on the results of uncertainty assessment, we finally arrive at a simpler incomplete-connection artificial neural network (ICANN) model as well as with better performance compared to original ANN rainfall-runoff model. These results not only indicate that SCEM-UA can be a useful tool for uncertainty analysis of ANN model, but also prove that uncertainty does exist in ANN rainfall-runoff model. Additionally, in some way, it presents that the ICANN model is with smaller uncertainty than the original ANN model.

Comparison of different uncertainty techniques in urban stormwater quantity and quality modelling

Urban drainage models are important tools used by both practitioners and scientists in the field of stormwater management. These models are often conceptual and usually require calibration using local datasets. The quantification of the uncertainty associated with the models is a must, although it is rarely practiced. The International Working Group on Data and Models, which works under the IWA/IAHR Joint Committee on Urban Drainage, has been working on the development of a framework for defining and assessing uncertainties in the field of urban drainage modelling. A part of that work is the assessment and comparison of different techniques generally used in the uncertainty assessment of the parameters of water models. This paper compares a number of these techniques: the Generalized Likelihood Uncertainty Estimation (GLUE), the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA), an approach based on a multi-objective auto-calibration (a multialgorithm, genetically adaptive multi-objective method, AMALGAM) and a Bayesian approach based on a simplified Markov Chain Monte Carlo method (implemented in the software MICA). To allow a meaningful comparison among the different uncertainty techniques, common criteria have been set for the likelihood formulation, defining the number of simulations, and the measure of uncertainty bounds. Moreover, all the uncertainty techniques were implemented for the same case study, in which the same stormwater quantity and quality model was used alongside the same dataset. The comparison results for a well-posed rainfall/runoff model showed that the four methods provide similar probability distributions of model parameters, and model prediction intervals. For ill-posed water quality model the differences between the results were much wider; and the paper provides the specific advantages and disadvantages of each method. In relation to computational efficiency (i.e. number of iterations required to generate the probability distribution of parameters), it was found that SCEM-UA and AMALGAM produce results quicker than GLUE in terms of required number of simulations. However, GLUE requires the lowest modelling skills and is easy to implement. All non-Bayesian methods have problems with the way they accept behavioural parameter sets, e.g. GLUE, SCEM-UA and AMALGAM have subjective acceptance thresholds, while MICA has usually problem with its hypothesis on normality of residuals. It is concluded that modellers should select the method which is most suitable for the system they are modelling (e.g. complexity of the model’s structure including the number of parameters), their skill/knowledge level, the available information, and the purpose of their study.

Uncertainty assessment of hydrologic and climate forecast models in Northeastern Brazil

AbstractSeasonal streamflow forecasts based on climate information can guide water managers toward superior reservoir operations, leading to improved water resources management efficiency. Uncertainty, however, is always present in seasonal streamflow forecasts, affecting the forecast value. Thus, a forecast should not be considered complete without a description of its uncertainty, which is critical for climate risk and water resources management. This study investigates the uncertainties of a seasonal streamflow forecast system for Northeastern Brazil based on climate precipitation forecasts and hydrologic modeling. These two sources of uncertainty are treated independently and then compared in order to guide future investments in the forecast system. Sea surface temperature is considered to be the primary source of uncertainty for the seasonal precipitation forecasts, based upon a 10‐member climate model ensemble. Parameter uncertainty is considered to be the only source of uncertainty for the hydrologic model. Estimation of parameter uncertainty is estimated by the Shuffled Complex Evolution Metropolis algorithm, which employs a Markov Chain Monte Carlo scheme to provide the posterior distribution of the parameters and form uncertainty bounds on streamflow forecasts. Results indicate that uncertainties associated with the climate forecast are much larger than those from parameter estimation in the hydrologic model. Although model structure has not been considered in the evaluation of hydrologic uncertainties, this study indicates that future efforts to address the predominant source of uncertainty should focus on the climate prediction models. Copyright © 2011 John Wiley & Sons, Ltd.

Catchment responses to plausible parameters and input data under equifinality in distributed rainfall‐runoff modeling

AbstractIn a hydrological simulation using a complex model, equifinality is likely to occur in many different ways, due to various sources associated with the model structure, parameter as well as data uncertainties involved in modeling process. This study aims to demonstrate the equifinality problem in streamflow prediction with a distributed rainfall‐runoff model and also investigate the effect of parameter and input uncertainties on an internal catchment response in time and space under the equifinality condition. For this objective, several experiments were carried out step by step as follows. First, we estimated plausible parameter sets, which lead to similarly good objective function values, using the shuffled complex evolution metropolis (SCEM‐UA) algorithm and also generated plausible input scenarios with different spatial patterns from radar rainfall field, which showed minimum runoff errors. Then, we adopted a computational tracer method based on a time‐space accounting scheme, combined with a distributed model for analyzing how a catchment behaves under a given equifinality condition by parameter and input uncertainties. It was found that the global responses of a catchment to the predefined equifinality factors were very similar; all simulated hydrographs were almost identical in spite of the different model parameter values and different spatial patterns of rainfall data. On the other hand, the internal catchment responses, tracked by the computational tracer method, were sensitive to plausible scenarios. The results of the internal catchment behavior show that the distributed rainfall‐runoff model has multiple alternative flow pathways, providing identical hydrographs in time and space when the rainfall over the catchment transforms into runoff. Our approach can be used to understand catchment responses to various uncertainty sources by visualizing the spatiotemporal runoff generation process at the watershed scale. Copyright © 2011 John Wiley & Sons, Ltd.

Development and Sensitivity Analysis of a Fully Kinetic Model of Sequential Reductive Dechlorination in Groundwater

A fully kinetic biogeochemical model of sequential reductive dechlorination (SERD) occurring in conjunction with lactate and propionate fermentation, iron reduction, sulfate reduction, and methanogenesis was developed. Production and consumption of molecular hydrogen (H(2)) by microorganisms have been modeled using modified Michaelis-Menten kinetics and has been implemented in the geochemical code PHREEQC. The model have been calibrated using a Shuffled Complex Evolution Metropolis algorithm to observations of chlorinated solvents, organic acids, and H(2) concentrations in laboratory batch experiments of complete trichloroethene (TCE) degradation in natural sediments. Global sensitivity analysis was performed using the Morris method and Sobol sensitivity indices to identify the most influential model parameters. Results show that the sulfate concentration and fermentation kinetics are the most important factors influencing SERD. The sensitivity analysis also suggests that it is not possible to simplify the model description if all system behaviors are to be well described.

Trade-offs and responsiveness of the single-layer urban canopy parametrization in WRF: An offline evaluation using the MOSCEM optimization algorithm and field observations

For an increasing number of applications, mesoscale modelling systems now aim to better represent urban areas. The complexity of processes resolved by urban parametrization schemes varies with the application. The concept of fitness-for-purpose is therefore critical for both the choice of parametrizations and the way in which the scheme should be evaluated. A systematic and objective model response analysis procedure (Multiobjective Shuffled Complex Evolution Metropolis (MOSCEM) algorithm) is used to assess the fitness of the single-layer urban canopy parametrization implemented in the Weather Research and Forecasting (WRF) model. The scheme is evaluated regarding its ability to simulate observed surface energy fluxes and the sensitivity to input parameters. Recent amendments are described, focussing on features which improve its applicability to numerical weather prediction, such as a reduced and physically more meaningful list of input parameters. The study shows a high sensitivity of the scheme to parameters characterizing roof properties in contrast to a low response to road-related ones. Problems in partitioning of energy between turbulent sensible and latent heat fluxes are also emphasized. Some initial guidelines to prioritize efforts to obtain urban land-cover class characteristics in WRF are provided. Copyright © 2010 Royal Meteorological Society and Crown Copyright.

Probabilistic prediction of urban water consumption using the SCEM-UA algorithm

Prediction of urban water consumption can help to improve the performance of water distribution systems. Despite the obvious presence of uncertainty in measurements and in assumed model types/structures, most of the existing water consumption prediction models are developed and used in a deterministic context. Methods for more realistic assessment of parameter and model prediction uncertainties have begun to appear in literature only recently. A novel application of the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA) for the calibration of a water consumption prediction model is proposed here. The model is applied to a case study of the city of Catania (Italy) with the aim to predict daily water consumption. The SCEM-UA algorithm is used to calibrate the parameters of the artificial neural network based prediction model and in turn to determine the associated parameter and model prediction uncertainties. The results obtained using the SCEM-UA ANN approach were compared to the corresponding results obtained using other predictive models developed recently by the authors of the paper. When compared to the these models, the SCEM-UA ANN based water consumption prediction model shows similar predictive capability but also the ability to identify simultaneously the prediction uncertainty bounds associated with the posterior distribution of the parameter estimates.

Comparison of Three Multiobjective Optimization Algorithms for Inverse Modeling of Vadose Zone Hydraulic Properties

Inverse modeling has become increasingly popular for estimating effective hydraulic properties across a range of spatial scales. In recent years, many different algorithms have been developed to solve complex multiobjective optimization problems. In this study, we compared the efficiency of the Nondominated Sorting Genetic Algorithm (NSGA‐II), the Multiobjective Shuffled Complex Evolution Metropolis algorithm (MOSCEM‐UA), and AMALGAM, a multialgorithm genetically adaptive search method for multiobjective estimation of soil hydraulic parameters. In our analyses, we implemented the HYDRUS‐1D model and used observed pressure head data at three different depths from the Spydia experimental field site in New Zealand. Our optimization problem was posed in a multiobjective context by simultaneously using three complementary RMSE criteria at each depth. We analyzed the trade‐off between these criteria and the adherent Pareto uncertainty. The results demonstrate that all three algorithms were able to find a good approximation of the Pareto set of solutions, but differed in the rate of convergence to this distribution. Small differences in performance of the various algorithms were observed because of the relative high dimension of the optimization problem in combination with the presence of multiple local optimal solutions within the three‐objective search space. The Pareto parameter sets yielded satisfactory results when simulating the transient tensiometric pressure at predetermined observation points in the investigated vadose zone profile. The overall best parameter set was found by AMALGAM with RMSE values of 0.14, 0.11, and 0.17 m at the 0.4‐, 1.0‐, and 2.6‐m depths, respectively. In contrast, the fit errors were substantially higher at these respective depths, with RMSE values ranging from 0.87 to 1.49 m, when using soil hydraulic parameters derived from laboratory analysis of small vadose zone cores.

A New Approach to Estimate Soil Hydraulic Parameters Using Only Soil Water Retention Data

Traditional approaches for estimating soil hydraulic parameters (such as the RETC code) perform well when experimental data for both the retention curve and hydraulic conductivity function are available; however, unsaturated hydraulic conductivity data are often unavailable. The objective of this work was to develop an approach to estimate robust soil hydraulic parameters from water retention curve data alone. The proposed approach, called the Multiobjective Retention Curve Estimator (MORE), is based on the Multiobjective Shuffled Complex Evolution Metropolis (MOSCEM‐UA) algorithm and estimates an optimal parameter set by simultaneously minimizing two objective functions each representing water content and relative unsaturated hydraulic conductivity residuals. To address the lack of observed unsaturated hydraulic conductivity data, MORE transforms both predicted and observed water contents into the hydraulic conductivity space using a pore‐size distribution model (e.g., the Mualem model) and also optimizes the soil hydraulic parameters in this fictitious space. We applied MORE to two cases. In the first case, MORE was used to estimate soil parameters using only retention curve data for 12 random soils selected from the UNSODA database. While the soil hydraulic parameters estimated using RETC and MORE fit the retention curve similarly, the MORE approach consistently decreased the error in fitting unsaturated hydraulic conductivities by as much as 5% compared with RETC. The second case involved using the parameters fitted using the MORE and RETC approaches to model a field‐scale experiment. Compared with RETC, the error in predicted water contents decreased by 25% using parameters predicted by MORE. The MORE approach was shown to fit robust soil hydraulic parameters; however, the approach is relatively slower and more time consuming than RETC.

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.

Multiple batch extraction test to estimate contaminant release parameters using a Bayesian approach

Industrial activities produce vast amounts of weakly contaminated materials which are commonly reused as filling materials on natural ground. There is a strong demand to define guidelines for the application of these materials, to estimate the leaching potential of contaminants from the materials, and to assess the potential hazard for groundwater pollution. We present a multiple batch experiment, where measurements of liquid-phase concentrations at varying liquid/solid ratios are used to estimate the total mass of contaminant that can be extracted from a contaminated material with a mild extractant like water. Furthermore, the experiment yields estimates of the isotherm describing the partitioning of the contaminant between the solid and liquid phases, and a concentration that might be expected under soil hydraulic conditions representative for the field situation. Model parameters are estimated from liquid-phase concentrations within a Bayesian framework by applying the Shuffled Complex Evolution Metropolis Algorithm (SCEM-UA), an efficient Markov Chain Monte Carlo sampler. A sensitivity analysis and inversions of synthetically generated data corrupted with noise show the general suitability of the proposed method. An uncertainty analysis for model parameters and model predictions shows the expected accuracy of the estimates. An application to concentration measurements obtained from a multiple batch extraction test illustrates the applicability of the approach for a real situation.