Generalized Likelihood Uncertainty Estimation Research Articles

Sensitivity and uncertainty analysis of an integrated membrane bioreactor model

AbstractSensitivity and uncertainty analysis, although can be of primarily importance in mathematical modelling approaches, are scarcely applied in the field of membrane bioreactor (MBR). An integrated mathematical model for MBR is applied with the final aim to pin down sources of uncertainty in MBR modelling. The uncertainty analysis has been performed combining global sensitivity analysis (GSA) with the generalized likelihood uncertainty estimation (GLUE). The model and methodology were applied to a University Cape Town pilot plant. Results show that the complexity of the modelled processes and the propagation effect from the influent to the effluent increase the uncertainty of the model prediction. It was found that the uncertainty of nitrogen and phosphorus model outputs increases from the first reactor-section plant to the last. Results show also that the GSA-GLUE methodology is a valid tool for uncertainty assessment for MBR modelling. Furthermore, the GSA-GLUE allows to identify the most critical p...

Impact of the numbers of observations and calibration parameters on equifinality, model performance, and output and parameter uncertainty

The level of model complexity that can be effectively supported by available information has long been a subject of many studies in hydrologic modelling. In particular, distributed parameter models tend to be regarded as overparameterized because of numerous parameters used to describe spatially heterogeneous hydrologic processes. However, it is not clear how parameters and observations influence the degree of overparameterization, equifinality of parameter values, and uncertainty. This study investigated the impact of the numbers of observations and parameters on calibration quality including equifinality among calibrated parameter values, model performance, and output/parameter uncertainty using the Soil and Water Assessment Tool model. In the experiments, the number of observations was increased by expanding the calibration period or by including measurements made at inner points of a watershed. Similarly, additional calibration parameters were included in the order of their sensitivity. Then, unique sets of parameters were calibrated with the same objective function, optimization algorithm, and stopping criteria but different numbers of observations. The calibration quality was quantified with statistics calculated based on the ‘behavioural’ parameter sets, identified using 1% and 5% cut-off thresholds in a generalized likelihood uncertainty estimation framework. The study demonstrated that equifinality, model performance, and output/parameter uncertainty were responsive to the numbers of observations and calibration parameters; however, the relationship between the numbers, equifinality, and uncertainty was not always conclusive. Model performance improved with increased numbers of calibration parameters and observations, and substantial equifinality did neither necessarily mean bad model performance nor large uncertainty in the model outputs and parameters. Copyright © 2015 John Wiley & Sons, Ltd.

Parameter identification and uncertainty analysis for simulating streamflow in a river basin of Eastern India

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

Numerical modelling of glacial lake outburst floods using physically based dam-breach models

Abstract. The instability of moraine-dammed proglacial lakes creates the potential for catastrophic glacial lake outburst floods (GLOFs) in high-mountain regions. In this research, we use a unique combination of numerical dam-breach and two-dimensional hydrodynamic modelling, employed within a generalised likelihood uncertainty estimation (GLUE) framework, to quantify predictive uncertainty in model outputs associated with a reconstruction of the Dig Tsho failure in Nepal. Monte Carlo analysis was used to sample the model parameter space, and morphological descriptors of the moraine breach were used to evaluate model performance. Multiple breach scenarios were produced by differing parameter ensembles associated with a range of breach initiation mechanisms, including overtopping waves and mechanical failure of the dam face. The material roughness coefficient was found to exert a dominant influence over model performance. The downstream routing of scenario-specific breach hydrographs revealed significant differences in the timing and extent of inundation. A GLUE-based methodology for constructing probabilistic maps of inundation extent, flow depth, and hazard is presented and provides a useful tool for communicating uncertainty in GLOF hazard assessment.

Modeling Response of Warm‐Season Turfgrass to Drought and Irrigation

When droughts occur, restrictions on outdoor water use are a frequently used tactic for reducing demand but are not always as effective as desired and can have negative impacts on homeowners and businesses. Our objective was to develop a simulation model for use in comparing irrigation strategies in terms of water usage and changes in turfgrass quality under varying levels of water restriction. Based on data from several experiments, we have developed a model for St. Augustinegrass [Stenotaphrum secundatum (Walter) Kuntze] and bermudagrass [Cynodon dactylon (L.) Pers.] that calculates a turfgrass drought index and a turfgrass quality index (TQI) on a daily basis. Turfgrass water demand is modeled as a function of TQI and reference evapotranspiration. Actual turf water uptake depends on plant‐available soil water as well as plant demand. Available soil water in the root zone is divided into two pools: an easily available pool and a less readily available pool. Turfgrass quality can increase when there is no drought stress and decline whenever drought stress exceeds a cultivar‐specific threshold. We used the generalized likelihood uncertainty estimation method to estimate five genetic coefficients for two cultivars of each species. The model was highly successful in predicting the observed values of TQI. Except for a few sample dates, simulated TQI was within the 95% confidence interval of the mean observed TQI. The model appears to respond accurately to both drought and irrigation and to capture species and cultivar differences in drought tolerance.

Evaluating CERES-Maize Model Using Planting Dates and Nitrogen Fertilizer in Zambia

A field experiment was conducted during the 2013/2014 season to evaluate the performance of CERES-maize model in simulating the effect of date of planting, nitrogen fertilizer and root-zone soil water profile on growth and yield of maize (Zea mays L.) at the Field Research Station of the School of Agricultural Sciences, University of Zambia, Zambia (15°23.6859'S, 28°20.226'E; 1,261 m.a.s.l). The experimental design was a split plot with three replicates, three planting dates (November 24, December 8, and December 22) assigned to main plots and two nitrogen fertilizer rates (112 and 168 kg N ha-1) assigned to sub-plot. Phenological stages and aboveground biomass were used for model evaluation and these were observed at vegetative and reproductive stages. Soil water profiles were monitored using the Diviner 2000 Probe. Planting date significantly affected grain and biomass yield at P < 0.05. The coefficients of variation for grain and biomass yield were below 12% and considered efficient. The Generalized Likelihood Uncertainty Estimation (GLUE) programme was used to estimate the genetic coefficients for the CERES-maize model. The model’s prediction of plant emergence (±1 days), time to anthesis (>= -3 <= ±1 days) and maturity (>= -4 <= 6 days) was good. Simulation of biomass (RMSE = 1135 kg/ha, d = 0.96, EF = 0.86) was reasonably accurate while leaf area index (d = 0.54, EF = -0.65) was simulated with less accuracy due to poor d-stat and forecasting efficiency. The model’s simulation of grain yield was fair (NRMSE = 21.4%) while soil root water availability demonstrated that substantial potential yield may have been lost due to water stress. The results showed that the model can be used to accurately determine optimum planting date, biomass yield and nitrogen fertilizer rates with reasonable accuracy.

Application of the generalized likelihood uncertainty estimation (GLUE) approach for assessing uncertainty in hydrological models: a review

The generalized likelihood uncertainty estimation (GLUE) technique is an innovative uncertainty method that is often employed with environmental simulation models. Over the past years, hydrological literature has seen a large increase in the number of papers dealing with uncertainty. There are now a lot of citations to their original paper which illustrates GLUE tremendous impact. GLUE’s popularity can be attributed to its simplicity and its applicability to nonlinear systems, including those for which a unique calibration is not apparent. The GLUE was introduced for use in uncertainty analysis of watershed models has now been extended well beyond rainfall-runoff watershed models. Given the widespread adoption of GLUE analyses for a broad range or problems, it is appropriate that the validity of the approach be examined with care. In this article, we present an overview of the application of GLUE for assessing uncertainty distribution in hydrological models particularly surface and subsurface hydrology and briefly describe algorithms for sampling of the prior parameter in hydrologic simulation models.

Estimating daily time series of streamflow using hydrological model calibrated based on satellite observations of river water surface width: Toward real world applications

Lacking observation data for calibration constrains applications of hydrological models to estimate daily time series of streamflow. Recent improvements in remote sensing enable detection of river water-surface width from satellite observations, making possible the tracking of streamflow from space. In this study, a method calibrating hydrological models using river width derived from remote sensing is demonstrated through application to the ungauged Irrawaddy Basin in Myanmar. Generalized likelihood uncertainty estimation (GLUE) is selected as a tool for automatic calibration and uncertainty analysis. Of 50,000 randomly generated parameter sets, 997 are identified as behavioral, based on comparing model simulation with satellite observations. The uncertainty band of streamflow simulation can span most of 10-year average monthly observed streamflow for moderate and high flow conditions. Nash–Sutcliffe efficiency is 95.7% for the simulated streamflow at the 50% quantile. These results indicate that application to the target basin is generally successful. Beyond evaluating the method in a basin lacking streamflow data, difficulties and possible solutions for applications in the real world are addressed to promote future use of the proposed method in more ungauged basins.

Assessing the Uncertainty of the Xinanjiang Rainfall-Runoff Model: Effect of the Likelihood Function Choice on the GLUE Method

In this paper, the generalized likelihood uncertainty estimation (GLUE) methodology, which is widely applied in the field of hydrology, is used for testing and predictive uncertainty estimation in the application of the Xinanjiang rainfall-runoff (XAJ-RR) model for estimating monthly stream flow (Nangao reservoir) catchment in China. However, one of the drawbacks of using the GLUE method is the definition of the likelihood function, which reflects the behavior of the hydrological model. Although there are different formulations of likelihood functions in the literature, most previous research focused on the application of the GLUE method with the likelihood function of Nash-Sutcliffe (NS) efficiency. In this respect, to illustrate the impact of the selection of likelihood functions on the results of the GLUE method, the authors adopted four likelihood functions: NS, normalized absolute error (NAE), index of agreement (IoA), and Chiew and McMahon (CM). The main findings of the study are that (1) the parameter uncertainty is more sensitive to the choice of the likelihood functions than the uncertainty in the model prediction by the GLUE method; (2) the parameters of the XAJ-RR model with NS had less uncertainty compared to those of NAE, IoA, and CM; (3) the uncertainty bounds showed slight differences from various likelihood functions; and (4) the computational efficiency of the GLUE method based on likelihood function IoA was much better because the IoA likelihood function corresponded to narrower uncertainty bounds, higher bracketing of observations, and the best maximum value of likelihood functions. Thus, this study confirms the importance of the likelihood function selection in the application of GLUE to the uncertainty assessment of the XAJ-RR model.

Uncertainty Evaluation of a Groundwater Conceptual Model by Using a Multimodel Averaging Method

ABSTRACTA groundwater field is a complex and open system. Groundwater simulation and prediction often deviated from true values, which is attributed to the uncertainty of groundwater modeling. The conceptual model (model struture) is one of the main sources of groundwater modeling uncertianty. In this study, the mean Euclidean distance (MED) between model simulations and observations is proposed to assess the integrated likelihood value of a conceptual model in Bayesian model averaging (BMA). Moreover, this proposed BMA method is compared with the traditional generalized likelihood uncertainty estimation (GLUE) BMA method by a synthetical groundwater model, and the characteristics of these two BMA methods are summarized.

Uncertainty in a monthly water balance model using the generalized likelihood uncertainty estimation methodology

Hydrological models are simplified representations of natural processes and subject to errors. Uncertainty bounds are a commonly used way to assess the impact of an input or model architecture uncertainty in model outputs. Different sets of parameters could have equally robust goodness-of-fit indicators, which is known as Equifinality. We assessed the outputs from a lumped conceptual hydrological model to an agricultural watershed in central Chile under strong interannual variability (coefficient of variability of 25%) by using the Equifinality concept and uncertainty bounds. The simulation period ran from January 1999 to December 2006. Equifinality and uncertainty bounds from GLUE methodology (Generalized Likelihood Uncertainty Estimation) were used to identify parameter sets as potential representations of the system. The aim of this paper is to exploit the use of uncertainty bounds to differentiate behavioural parameter sets in a simple hydrological model. Then, we analyze the presence of equifinality in order to improve the identification of relevant hydrological processes. The water balance model for Chillan River exhibits, at a first stage, equifinality. However, it was possible to narrow the range for the parameters and eventually identify a set of parameters representing the behaviour of the watershed (a behavioural model) in agreement with observational and soft data (calculation of areal precipitation over the watershed using an isohyetal map). The mean width of the uncertainty bound around the predicted runoff for the simulation period decreased from 50 to 20 m3s−1 after fixing the parameter controlling the areal precipitation over the watershed. This decrement is equivalent to decreasing the ratio between simulated and observed discharge from 5.2 to 2.5. Despite the criticisms against the GLUE methodology, such as the lack of statistical formality, it is identified as a useful tool assisting the modeller with the identification of critical parameters.

Uncertainty in Future High Flows in Qiantang River Basin, China

AbstractUncertainties in high flows originating from greenhouse gas emissions scenarios, hydrological model structures, and their parameters for the Jinhua River basin, China, were assessed. The baseline (1961–90) and future (2011–40) climates for A1B, A2, and B2 scenarios were downscaled from the general circulation model (GCM) using the Providing Regional Climates for Impacts Studies (PRECIS) regional climate model with a spatial resolution of 50 km × 50 km. Bias-correction methods were applied to the PRECIS-derived temperature and precipitation. The bias-corrected precipitation and temperature were used as inputs for three hydrological models [modèle du Génie Rural à 4 paramètres Journalier (GR4J), Hydrologiska Byråns Vattenbalansavdelning (HBV), and Xinanjiang] to simulate high flows. The parameter uncertainty was considered and quantified in the hydrological model calibration by means of the generalized likelihood uncertainty estimation (GLUE) method for each hydrological model for the three emissions scenarios. It was found that, compared with the high flows in the baseline period, the high flows in the future tended to decrease under scenarios A1B, A2, and B2. The largest uncertainty was observed in HBV, and GR4J had the smallest uncertainty. It was found that the major source of uncertainty in this study was from parameters, followed by the uncertainties from the hydrological model structure, and the emissions scenarios have the smallest uncertainty contribution to high flows in this study.

The Influence of Objective Function and Acceptability Threshold on Uncertainty Assessment of an Urban Drainage Hydraulic Model with Generalized Likelihood Uncertainty Estimation Methodology

Urban drainage model is an important computer-aided tool in stormwater management and drainage planning and designing. A popular urban drainage hydraulic model, stormwater management model (SWMM), was applied in a pump lifting combined sewer system for a high-intensity urban catchment located in Shanghai, China. Uncertainty of SWMM water quantity parameters was assessed with generalized likelihood uncertainty estimation (GLUE) methodology. The sensitivity of parameters was discussed and compared based on the results of uncertainty analysis. To discuss the influence of the acceptability threshold on model parameter sensitivity and the margin of uncertainty band, the GLUE approach was applied several times varying acceptability threshold. The results indicated that a higher acceptability threshold value is contributed to achieve a stricter verification with a high confidence level, and the uncertainty analysis significant level can be featured by the value of acceptability threshold. The selection of acceptability threshold value can be regarded as a tradeoff process. Both reducing the low efficient simulation and reducing computation cost should be considered for the selection of acceptability threshold. Moreover, the GLUE approach was applied several times varying different objective functions with corresponding acceptability thresholds. The results indicated that some parameters may be sensitive to a specific objective function, and other parameters may be sensitive to another objective function. Some parameters cannot easily identified when a single objective function was used within the GLUE approach, and a multiple-objective function combined different objective functions requirements, may be a alternative approach to reduce the model prediction uncertainty.

The comparative study of multi‐site uncertainty evaluation method based on SWAT model

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

Uncertainty assessment of water quality modeling for a small-scale urban catchment using the GLUE methodology: a case study in Shanghai, China.

There is often great uncertainty in water quality modeling for urban drainage systems because water quality variation in systems is complex and affected by many factors. The stormwater management model (SWMM) was applied to a small-scale urban catchment with a simple and well-maintained stormwater drainage system without illicit connections. This was done to assess uncertainty in build-up and wash-off modeling of pollutants within the generalized likelihood uncertainty estimation (GLUE) methodology, based on a well-calibrated water quantity model. The results indicated great uncertainty of water quality modeling within the GLUE methodology. Comparison of uncertainties in various pollutant build-up and wash-off models that were available in SWMM indicated that those uncertainties varied slightly. This may be a consequence of the specific characteristics of rainfall events and experimental sites used in the study. The uncertainty analysis of water quality parameters in SWMM is conducive to effectively evaluating model reliability, and provides an experience base for similar research and applications.

Inferring the Shape of Fractures and Hydraulic Properties of the Coal Seam Using Inverse Modeling on Pumping Test Results – Broke, NSW, Australia

Coal seam gas or coal bed methane production is becoming a significant industry in Australia. The area around the Broke township (located in the north-west of the Sydney Basin) has had coal seam gas exploration activities over the last decade. One methodology of well stimulation, hydraulic fracturing, has the potential to cause some environmental problems. The Broke region includes 4 aquifers (3 confined and semi-confined), more than 3 major coal seams (3 gas bearing) and has been covered by variety of different sedimentary rocks of Permian age. The groundwater system, with the gas bearing deposits is the function of conductivity and storativity (K and S) of the coal seam and geometry of properties of the fractures. The required data to investigate the hydraulic properties in the fractured zone includes; corehole data to assessment the geology and underground system, micro-seismic data to infer the fracture properties, pumping tests results, and monitoring wells data to evaluate the hydraulic properties of the coal seams. This paper investigates the shape of drawdown curves, resulting from the hydraulic pumping tests at Broke performed to determine the hydraulic and fracture properties, such as length, width, conductivity of fractures, and the proportion of the water and gas contained in the targeted coal seam. In order to reduce data uncertainty and increase the reliability of the hydraulic property estimation the Generalized Likelihood Uncertainty Estimation (GLUE) will be applied. Finally, with investigation of the shape (length and width) and conductivity of the fractures, the best monitoring method to ensure public safety of provide assurances that if problems occur the monitoring system will provide early warning for this study area will be determined.

Uncertainty based analysis of the impact of watershed phosphorus load on reservoir phosphorus concentration

Summary In many regions of the world that depend on surface reservoirs as a source of water supply, eutrophication is a major water quality problem. Developing simulation models to evaluate the impact of watershed nutrient loads on the reservoir’s water quality is an essential step in eutrophication management. In this regard, analysis of model uncertainty gives an opportunity to assess the reliability and the margin of safety of the model predictions for Total Maximum Daily Load (TMDL) from the watershed nutrient load. In this study, a computational procedure has been proposed for the analysis of the model uncertainties in simulation of watershed phosphorous load and reservoir phosphorous concentration. Data from the Aharchai watershed which is located upstream of the Satarkhan reservoir in the northwestern part of Iran, is used as the study area to test the effectiveness of the proposed methodology. The Soil and Water Assessment Tools (SWAT) is utilized for assessment of watershed phosphorus load as the main agent resulting in the reservoir eutrophication in the region. The most effective parameters in model performance are identified by a global sensitivity analysis technique named modified Fourier Amplitude Sensitivity Test (FAST) which can incorporate parameter interdependencies. The Generalized Likelihood Uncertainty Estimation (GLUE) technique is also applied to set up behavioral ranges of the parameters that are relevant to the actual observations. Finally, the cumulative weighted-likelihood distribution functions (CWLDF) are derived for outputs of the SWAT. They are used jointly for estimation of results uncertainty limits using the Copula method. To assess the effectiveness of applying Best Management Practices (BMPs) in the watershed, two scenarios of with and without BMPs application are tested. The results showed the effectiveness of the proposed model in uncertainty estimation of watershed phosphorus load and reservoir phosphorus concentration as well as the effectiveness of BMPs in reducing P loads from the watershed.

A Review On Accuracy and Uncertainty of Spatial Data and Analyses with special reference to Urban and Hydrological Modelling

Abstract. Data quality for GIS processing and analysis is becoming an increased concern due to the accelerated application of GIS technology for problem solving and decision making roles. Uncertainty in the geographic representation of the real world arises as these representations are incomplete. Identification of the sources of these uncertainties and the ways in which they operate in GIS based representations become crucial in any spatial data representation and geospatial analysis applied to any field of application. This paper reviews the articles on the various components of spatial data quality and various uncertainties inherent in them and special focus is paid to two fields of application such as Urban Simulation and Hydrological Modelling. Urban growth is a complicated process involving the spatio-temporal changes of all socio-economic and physical components at different scales. Cellular Automata (CA) model is one of the simulation models, which randomly selects potential cells for urbanisation and the transition rules evaluate the properties of the cell and its neighbour. Uncertainty arising from CA modelling is assessed mainly using sensitivity analysis including Monte Carlo simulation method. Likewise, the importance of hydrological uncertainty analysis has been emphasized in recent years and there is an urgent need to incorporate uncertainty estimation into water resources assessment procedures. The Soil and Water Assessment Tool (SWAT) is a continuous time watershed model to evaluate various impacts of land use management and climate on hydrology and water quality. Hydrological model uncertainties using SWAT model are dealt primarily by Generalized Likelihood Uncertainty Estimation (GLUE) method.

A fast simplified model for predicting river flood inundation probabilities in poorly gauged areas

The capability of a simple kinematic-storage model (KSM) is analysed to be used as a tool for a Decision Support System for the evaluation of probability inundation maps in near real time in poorly gauged areas. KSM simulates the floodplain as a storage and assumes no exchange of momentum with the channel. For the in-bank flow, the storage is modified through a coefficient for taking the variations of channel cross sections into account. The generalized likelihood uncertainty estimation approach is used for addressing the probability flood maps along with their associated uncertainties. The model is tested on two river reaches along the Tiber River in Central Italy where observed inundation maps are available for two recent flood events. Despite the inherent uncertainties present in the input data and in the model structure, the results show that the model reproduces reasonably well, in terms of both precision and accuracy, the observed inundated areas. Tests were performed at different digital elevation model resolutions, showing a small effect of the geometry on the maximum performance obtained. The very low computational times, the parsimony of the model and its low sensitivity to the quality of the geometry representation of the channel and the floodplain makes KSM very appealing for flood forecasting and early warning system applications in poorly gauged and inaccessible areas. Copyright © 2014 John Wiley & Sons, Ltd.

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.