Generalized Likelihood Uncertainty Estimation Procedure Research Articles

Uncertainty analysis of the HORTSYST model applied to fertigated tomatoes cultivated in a hydroponic greenhouse system

Aim of study: The objective was to perform an uncertainty analysis (UA) of the dynamic HORTSYST model applied to greenhouse grown hydroponic tomato crop. A frequentist method based on Monte Carlo simulation and the Generalized Likelihood Uncertainty Estimation (GLUE) procedure were used.Area of study: Two tomato cultivation experiments were carried out, during autumn-winter and spring-summer crop seasons, in a research greenhouse located at University of Chapingo, Chapingo, Mexico.Material and methods: The uncertainties of the HORTSYST model predictions PTI, LAI, DMP, ETc, Nup, Pup, Kup, Caup, and Mgup uptake, were calculated, by specifying the uncertainty of model parameters 10% and 20% around their nominal values. Uniform PDFs were specified for all model parameters and LHS sampling was applied. The Monte Carlo and the GLUE methods used 10,000 and 2,000 simulations, respectively. The frequentist method included the statistical measures: minimum, maximum, average values, CV, skewness, and kurtosis whilst GLUE used CI, RMSE, and scatter plots.Main results: As parameters were changed 10%, the CV, for all outputs, were lower than 15%. The smallest values were for LAI (10.75%) and DMP (11.14%) and the largest was for ETc (14.47%). For Caup (12.15%) and Pup (12.27%), the CV was lower than the one for Nup and Kup. Kurtosis and skewness values were close as expected for a normal distribution. According to GLUE, crop density was found to be the most relevant parameter given that it yielded the lowest RMSE value between the simulated and measured values.Research highlights: Acceptable fitting of HORTSYST was achieved since its predictions were inside 95% CI with the GLUE procedure.

An Approach Using a 1D Hydraulic Model, Landsat Imaging and Generalized Likelihood Uncertainty Estimation for an Approximation of Flood Discharge

Collection and investigation of flood information are essential to understand the nature of floods, but this has proved difficult in data-poor environments, or in developing or under-developed countries due to economic and technological limitations. The development of remote sensing data, GIS, and modeling techniques have, therefore, proved to be useful tools in the analysis of the nature of floods. Accordingly, this study attempts to estimate a flood discharge using the generalized likelihood uncertainty estimation (GLUE) methodology and a 1D hydraulic model, with remote sensing data and topographic data, under the assumed condition that there is no gauge station in the Missouri river, Nebraska, and Wabash River, Indiana, in the United States. The results show that the use of Landsat leads to a better discharge approximation on a large-scale reach than on a small-scale. Discharge approximation using the GLUE depended on the selection of likelihood measures. Consideration of physical conditions in study reaches could, therefore, contribute to an appropriate selection of informal likely measurements. The river discharge assessed by using Landsat image and the GLUE Methodology could be useful in supplementing flood information for flood risk management at a planning level in ungauged basins. However, it should be noted that this approach to the real-time application might be difficult due to the GLUE procedure.

조도계수와 유량의 불확실성이 홍수범람도 구축에 미치는 영향

The accuracy of flood inundation maps is determined by the uncertainty propagated from all variables involved in the overall process including input data, model parameters and modeling approaches. This study investigated the uncertainty arising from key variables (flow condition and Manning’s n) among model variables in flood inundation mapping for the Missouri River near Boonville, Missouri, USA. Methodology of this study involves the generalized likelihood uncertainty estimation (GLUE) to quantify the uncertainty bounds of flood inundation area. Uncertainty bounds in the GLUE procedure are evaluated by selecting two likelihood functions, which is two statistic (inverse of sum of squared error (1/SAE) and inverse of sum of absolute error (1/SSE)) based on an observed water surface elevation and simulated water surface elevations. The results from GLUE show that likelihood measure based on 1/SSE is more sensitive on observation than likelihood measure based on 1/SAE, and that the uncertainty propagated from two variables produces an uncertainty bound of about 2% in the inundation area compared to observed inundation. Based on the results obtained form this study, it is expected that this study will be useful to identify the characteristic of flood.

Assessment of the SWMM model uncertainties within the generalized likelihood uncertainty estimation (GLUE) framework for a high-resolution urban sewershed

This research incorporates the generalized likelihood uncertainty estimation (GLUE) methodology in a high-resolution Environmental Protection Agency Storm Water Management Model (SWMM), which we developed for a highly urbanized sewershed in Syracuse, NY, to assess SWMM modelling uncertainties and estimate parameters. We addressed two issues that have long been suggested having a great impact on the GLUE uncertainty estimation: the observations used to construct the likelihood measure and the sampling approach to obtain the posterior samples of the input parameters and prediction bounds of the model output. First, on the basis of the Bayes' theorem, we compared the prediction bounds generated from the same Gaussian distribution likelihood measure conditioned on flow observations of varying magnitude. Second, we employed two sampling techniques, the sampling importance resampling (SIR) and the threshold sampling methods, to generate posterior parameter distributions and prediction bounds, based on which the sampling efficiency was compared. In addition, for a better understanding of the hydrological responses of different pervious land covers in urban areas, we developed new parameter sets in SWMM representing the hydrological properties of trees and lawns, which were estimated through the GLUE procedure. The results showed that SIR was a more effective alternative to the conventional threshold sampling method. The combined total flow and peak flow data were an efficient alternative to the intensive 5-min flow data for reducing SWMM parameter and output uncertainties. Several runoff control parameters were found to have a great effect on peak flows, including the newly introduced parameters for trees. Copyright © 2013 John Wiley & Sons, Ltd.

Uncertainty Analysis of a Dual-Continuum Model Used to Simulate Subsurface Hillslope Runoff Involving Oxygen-18 as Natural Tracer

Uncertainty Analysis of a Dual-Continuum Model Used to Simulate Subsurface Hillslope Runoff Involving Oxygen-18 as Natural TracerA one-dimensional dual-continuum model (also known as dual-permeability model) was used to simulate the lateral component of subsurface runoff and variations in the natural18O content in hillslope discharge. Model predictions were analyzed using the GLUE generalized likelihood uncertainty estimation procedure. Model sensitivity was evaluated by varying two separate triplets of parameters. The first triplet consisted of key parameters determining the preferential flow regime, i.e., the volumetric proportion of the preferential flow domain, a first-order transfer coefficient characterizing soil water exchange between the two flow domains of the dual-continuum system, and the saturated hydraulic conductivity of the preferential flow domain. The second triplet involved parameters controlling exclusively the soil hydraulic properties of the preferential flow domain, i.e., its retention curve and hydraulic conductivity function. Results of the analysis suggest high sensitivity to all parameters of the first triplet, and large differences in sensitivity to the parameters of the second triplet. The sensitivity analysis also confirmed a significant improvement in the identifiability of preferential flow parameters when18O content was added to the objective function.

Quantifying the contribution of glacier runoff to streamflow in the upper Columbia River Basin, Canada

Abstract. Glacier melt provides important contributions to streamflow in many mountainous regions. Hydrologic model calibration in glacier-fed catchments is difficult because errors in modelling snow accumulation can be offset by compensating errors in glacier melt. This problem is particularly severe in catchments with modest glacier cover, where goodness-of-fit statistics such as the Nash-Sutcliffe model efficiency may not be highly sensitive to the streamflow variance associated with glacier melt. While glacier mass balance measurements can be used to aid model calibration, they are absent for most catchments. We introduce the use of glacier volume change determined from repeated glacier mapping in a guided GLUE (generalized likelihood uncertainty estimation) procedure to calibrate a hydrologic model. This approach is applied to the Mica basin in the Canadian portion of the Columbia River Basin using the HBV-EC hydrologic model. Use of glacier volume change in the calibration procedure effectively reduced parameter uncertainty and helped to ensure that the model was accurately predicting glacier mass balance as well as streamflow. The seasonal and interannual variations in glacier melt contributions were assessed by running the calibrated model with historic glacier cover and also after converting all glacierized areas to alpine land cover in the model setup. Sensitivity of modelled streamflow to historic changes in glacier cover and to projected glacier changes for a climate warming scenario was assessed by comparing simulations using static glacier cover to simulations that accommodated dynamic changes in glacier area. Although glaciers in the Mica basin only cover 5% of the watershed, glacier ice melt contributes up to 25% and 35% of streamflow in August and September, respectively. The mean annual contribution of ice melt to total streamflow varied between 3 and 9% and averaged 6%. Glacier ice melt is particularly important during warm, dry summers following winters with low snow accumulation and early snowpack depletion. Although the sensitivity of streamflow to historic glacier area changes is small and within parameter uncertainties, our results suggest that glacier area changes have to be accounted for in future projections of late summer streamflow. Our approach provides an effective and widely applicable method to calibrate hydrologic models in glacier fed catchments, as well as to quantify the magnitude and timing of glacier melt contributions to streamflow.

Modelling discharge from a coastal watershed in southeast Sweden using an integrated framework

AbstractThe field hydrology model DRAINMOD integrated with Arc Hydro in geographical information system (GIS) framework (Arc Hydro–DRAINMOD) was used to simulate the hydrological response of a coastal watershed in southeast Sweden. Arc Hydro–DRAINMOD uses a distributed approach to route water from each field edge to the watershed outlet. In the framework the Arc Hydro data model was used to describe the stream network in the watershed and to connect the individual simulated DRAINMOD‐field outflow time series from each plot using Arc Hydro schema‐links features, which were summed at Arc Hydro schema‐nodes features along the stream network to generate the stream network flow. Hydrology data collected during six periods between 2003 and 2008 were used to test Arc Hydro–DRAINMOD and its performance was evaluated by considering uncertainties in model inputs using generalized likelihood uncertainty estimation (GLUE). The GLUE estimates obtained (uncertainty bands 5% and 95%) agreed satisfactorily with measured monthly discharges. The percentage of time in which the observed discharges were bracketed by the uncertainty bands was 88% in calibration periods and 75% in validation periods. Although monthly time step simulations showed good agreement with observed discharges during the two main discharge events in spring, the contradictory daily time step results indicate that the watershed response simulations on a daily basis need to be improved. The uncertainty analysis showed that in periods of higher discharge, such as spring periods, the uncertainty in prediction was higher. It is important to note that these uncertainty estimations using the GLUE procedure include the uncertainties in measured discharge values, model inputs, boundary conditions and model structures. It was estimated that stream baseflow represented 42% of the total watershed discharge, but further research is needed to confirm this. These results show that the new Arc Hydro–DRAINMOD framework is applicable for predicting discharge from artificially drained watersheds in southeast Sweden. Copyright © 2010 John Wiley & Sons, Ltd.

Uncertainty assessment of forest road modeling with the Distributed Hydrology Soil Vegetation Model (DHSVM)

We used a generalized likelihood uncertainty estimation procedure with the Distributed Hydrology Soil Vegetation Model (DHSVM) for two streamflow and 11 road ditchflow locations. We observed considerable uncertainty in DHSVM simulations of forest road and stream runoff. The accuracy of simulations decreased as the size of the area modeled decreased. For streamflow, 44% of attempted model structures exceeded a 0.5 Nash–Sutcliffe efficiency threshold for a 630 ha catchment; 12% of attempted model structures exceeded a 0.5 Nash–Sutcliffe efficiency threshold for a 55 ha catchment. DHSVM simulations produced behavioral model structures for only six of the 11 road ditchflow sites (<10 ha). Cumulative distribution functions of parameter values did not indicate specific parameter ranges of parameter values across all locations, indicating that parameter values in DHSVM are influenced by their interaction with other parameters. The sensitivity of parameters and the range of that sensitivity varied across simulations of road ditchflow and streamflow. DHSVM simulations for two streamflow locations varied outside the uncertainty bounds for 10%–22% of storm volumes and 12%–22% of peak flows, respectively. Twenty-eight percent to 52% of storm volumes and 28%–48% of peak flows were outside the uncertainty bounds for the six road ditchflow locations.

Stochastic transfer function model applied to combined reservoir management and flow routing

The paper presents an application of a Stochastic Transfer Function (STF) approach and a nonlinear transformation of model variables to combined reservoir management and flow routing on the Upper Narew River, northeast Poland. The management objective is to reach the required flow conditions in the reaches of an ecologically valuable river. A 1-D distributed flow routing model was designed for the study. However, both optimization methods and reservoir management analysis require numerous model realizations which are computationally very expensive. A much more efficient solution consists of the application of a simplified STF simulator of river flow, which is calibrated on historical data and simulated flows via a distributed model for those parts of the river where observations are not available. The model is stochastic, enabling the derivation of a simulator prediction uncertainty in a straightforward manner. The optimal control policy obtained is tested on a fully distributed model. Obviously, the simulator's predictive uncertainty is larger than the uncertainty of the original distributed model. Therefore, in this application the original model is used to derive probability maps of inundation extent at high- and low-flow conditions under optimized reservoir discharges, following the Generalized Likelihood Uncertainty Estimation procedure. The main advantage of using the simulator lies in the much shorter computation times required by the water management optimization problem, which would be very difficult to solve with a distributed model used for flow routing. Additionally, the simulator may be used for the estimation of probability maps of inundation extent in the case where a distributed flow routing model cannot be run in a Monte Carlo set-up. Citation Romanowicz, R. J., Kiczko, A. & Napiórkowski, J. J. (2010) Stochastic transfer function model applied to combined reservoir management and flow routing. Hydrol. Sci. J. 55(1), 27–40.

Influence of likelihood function choice for estimating crop model parameters using the generalized likelihood uncertainty estimation method

Proper estimation of model parameters is required for ensuring accurate model predictions and good model-based decisions. The generalized likelihood uncertainty estimation (GLUE) method is a Bayesian Monte Carlo parameter estimation technique that makes use of a likelihood function to measure the closeness-of-fit of modeled and observed data. Various likelihood functions and methods of combining likelihood values have been used in previous studies. This research was conducted to determine the effects of using previously reported likelihood functions in a GLUE procedure for estimating parameters in a widely-used crop simulation model. A factorial computer experiment was conducted with synthetic measurement data to compare four likelihood functions and three methods of combining likelihood values using the CERES-Maize model of the Decision Support System for Agrotechnology Transfer (DSSAT). The procedure used an arbitrarily-selected parameter set as the known “true parameter set” and the CERES-Maize model to generate true output values. Then synthetic observations of crop variables were randomly generated (four replicates) by using the simulated true output values (dry yield, anthesis date, maturity date, leaf nitrogen concentration, soil nitrate concentration, and soil moisture) and adding a random observation error based on the variances of corresponding field measurements. The environmental conditions were obtained from a sweet corn ( Zea mays L.) experiment conducted in 2005 in northern Florida. Results showed that the method of combining likelihood values had a strong influence on parameter estimates. The combination method based on the product of the likelihoods associated with each set of observations reduced the uncertainties in posterior distributions of parameter estimates most significantly. It was also found that the likelihood function based on Gaussian probability density function was the best among those tested. This combination accurately estimated the true parameter values, suggesting that it can be used when estimating CERES-Maize model parameters for real experiments.

Applying GLUE for Estimating CERES-Maize Genetic and Soil Parameters for Sweet Corn Production

Sweet corn (Zea mays L.) is one of the five most valuable vegetable crops in Florida. The application of nitrogen fertilizer is necessary for farmers to reliably produce sweet corn. The use of crop simulation models can facilitate the evaluation of management practices that are profitable with minimal unwanted impacts on the environment. Before using such models in decision making, it is necessary to specify model parameters and understand the uncertainties associated with simulating variables that are needed for decision making. The generalized likelihood uncertainty estimation (GLUE) method was used to estimate genotype and soil parameters of the CERES-Maize model of the Decision Support System for Agrotechnology Transfer (DSSAT). The uncertainties in predictions for sweet corn production in northern Florida were evaluated using the existing field corn genotype coefficient and soil parameter database contained within DSSAT and field data collected during a series of experiments carried out in 2005 and 2006. Genotype coefficients (P1, P5, and PHINT) and soil parameters (SLDR, SLRO, SDUL, SLLL, and SSAT) were generated using a multivariate normal distribution that preserved the correlations between parameters. The soil parameter SLPF was not correlated with other parameters and was generated with a uniform distribution. After parameters were estimated, the CERES-Maize model correctly predicted the dry matter yields, anthesis dates, and harvest dates. The mean values of these variables were close to those measured in the field, with an average relative error of 4.4% and 2.4% for the data sets of 2005 and 2006, respectively. The calibrated CERES-Maize model simulated the temporal trend of leaf TKN concentration accurately during the early stage of the growth season, but underestimated the leaf TKN concentrations during the latter half of the season. The GLUE procedure accurately estimated soil parameters (SLLL, SDUL, and SSAT) when compared to independent measurements made in the laboratory, with an average absolute relative error of about 8.5%. The simulated time series of soil water content adequately simulated the observed soil water changes during both growth seasons for every layer. However, there were some large differences between simulated and observed soil nitrate contents. In a relevant further study, the average absolute relative error between model-predicted and field-estimated amounts of potential nitrogen leaching was 15.3%, which is much better than some reported comparable studies of nitrogen leaching modeling. In the posterior distribution of estimated parameters, the uncertainties in parameters were substantially reduced, with CV values mostly lower than 10%. The average CV value of the parameters was reduced from 27.2% in the prior distribution to 4.6% in the posterior distribution. In general, the results of this study showed that the CERES-Maize model was capable of simulating sweet corn production in northern Florida and the associated soil water content. The model can also simulate potential nitrogen leaching with acceptable accuracy. We suggest that the model can now be used to compare different management practices relative to productivity and potential nitrogen leaching outcomes.

Influence of errors in radar rainfall estimates on hydrological modeling prediction uncertainty

This study aims to assess the impact of a class of radar rainfall errors on prediction uncertainty of a conceptual water balance model. Uncertainty assessment is carried out by means of the Generalized Likelihood Uncertainty Estimation procedure (GLUE). The effects of model input and structural error are separated, and the potential for compensating errors between them is investigated. It is shown that the radar rainfall bias term operates in a multiplicative sense on the model structural uncertainty, by either magnifying or reducing it according to the sign of the bias. The results show also that adjustment of radar rainfall, aimed to remove local biases and to reduce random errors, allows ensuring that a larger percentage of the observed flows are enclosed by the uncertainty bounds, with respect to nonadjusted radar input. However, this is obtained at the price of increasing the wideness of the uncertainty bounds. This effect is emphasized with increasing the radar beam elevation. As a second step, the issue of the impact of radar rainfall estimation error on model parameter distribution and parameter transferability across sites under the radar umbrella is examined. Radar data at different radar beam elevations are used to simulate radar estimation errors at different distances from the radar site and to analyze the impact of these errors on prediction uncertainty. The results show that distortion of parameter distribution due to radar error may be considerable and that adjustment of radar rainfall estimates improves the regionalization potential of radar‐based precipitation estimates (at least for ranges less than 70 km).

Uncertainties in DRAINMOD predictions of subsurface drain flow for an Indiana silt loam using the GLUE methodology

AbstractGood modelling practice requires the incorporation of uncertainty analysis into hydrologic/water quality models. The generalized likelihood uncertainty estimation procedure was used to evaluate the uncertainty in DRAINMOD predictions of daily, monthly, and yearly subsurface drain flow. A variance‐based sensitivity analysis technique, the extended Fourier amplitude sensitivity test, was used to identify the main sources of prediction uncertainty. The analysis was conducted for the experimental drainage field at the Southeast Purdue Agricultural Center in Indiana. Six years of data were used and the uncertainties in eight model parameters were considered to analyse how uncertainties in input parameters propagate to model outputs. The width of 90% confidence interval bands of drain flow ranged from 0 to 0·6 cm day−1 for daily predictions, from 0 to 3·1 cm month−1 for the monthly predictions, and from 7·6 to 12·4 cm year−1 for yearly predictions. Annual drain flow predicted by DRAINMOD fell well within the 90% confidence bounds. Model results were most sensitive to the vertical saturated hydraulic conductivity of the restrictive layer and the lateral hydraulic conductivity of the deepest soil layer, followed by the lateral hydraulic conductivity of the top soil layer and surface micro‐storage. Parameter interactions also contributed to the prediction uncertainty. Copyright © 2006 John Wiley & Sons, Ltd.

An Improved Dual‐Permeability Model of Water Flow and Solute Transport in the Vadose Zone

We introduce an improved, one‐dimensional, non‐steady‐state dual‐permeability model (MACRO 5.1). The model simulates water flow and solute transport in the vadose zone of structured soils by coupling a high‐conductivity–low porosity macropore domain to a low‐conductivity–high porosity domain representing the soil matrix. Mass exchange between the domains is approximated by first‐order expressions. The numerical solutions are briefly described, focusing on the dual‐permeability formulation. The solution method for water flow in macropores was verified by comparing simulation results with analytical solutions for a “kinematic wave”. The model was tested against high time‐resolution measurements of water flow and nonreactive (Cl−) solute transport in transient microlysimeter experiments. The objective was to test the identifiability of four key model parameters determining the degree of preferential flow using the generalized likelihood uncertainty estimation (GLUE) procedure. The parameters were chosen either because they are difficult or impossible to measure directly or because they were considered sensitive on the basis of earlier experience with the model. The measurements, indicating strong preferential flow, were adequately reproduced by the model simulations (overall model efficiency = 0.62). The GLUE procedure conditioned the saturated matrix hydraulic conductivity, the macroporosity, and the mass exchange coefficient (diffusion pathlength), indicating that these parameters would be identifiable in inverse modeling approaches based on microlysimeter experiments. The conditioning of the kinematic exponent was poor, which was attributed primarily to correlation with the macroporosity.

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.

Constraining dynamic TOPMODEL responses for imprecise water table information using fuzzy rule based performance measures

Dynamic TOPMODEL is applied to the Maimai M8 catchment (3.8 ha), New Zealand using rainfall–runoff and water table information in model calibration. Different parametric representations of hillslope and valley bottom landscape units (LU's) were used to improve the spatial representation of the model structure. The continuous time series water table information is obtained from tensiometric observations from both near stream (NS) and hillslope ( P5) locations having different responses to rainfall events. For each location, and within an area equivalent to an effective model gridscale (25 m 2), a number of tensiometer readings at different depths were available (11 for the NS site and nine for the P5 site). Using this information a distribution of water table elevations for each time step at each location was calculated. The distribution of water table elevations was used to derive fuzzy estimates of the water table depth for the whole time series that includes the temporal variability of the uncertainty in the observations. These data were used to constrain the spatial representation of the model having previously conditioned the model using the rainfall–runoff data. Model conditioning was assessed using the Generalised Likelihood Uncertainty Estimation procedure. Results show that many combinations of parameter values for the two LU's were able to simulate the rainfall–runoff data. Further constraining of the model responses using the fuzzy water table elevations at both locations considerably reduced the number of behavioural parameter sets. An evaluation of the distributions of behavioural parameter sets showed that improvements to the model structure for the two LU's were required, especially for simulations of the response at the hillslope location.

Data assimilation and uncertainty analysis of environmental assessment problems—an application of Stochastic Transfer Function and Generalised Likelihood Uncertainty Estimation techniques

Abstract Stochastic Transfer Function (STF) and Generalised Likelihood Uncertainty Estimation (GLUE) techniques are outlined and applied to an environmental problem concerned with marine dose assessment. The goal of both methods in this application is the estimation and prediction of the environmental variables, together with their associated probability distributions. In particular, they are used to estimate the amount of radionuclides transferred to marine biota from a given source: the British Nuclear Fuel Ltd (BNFL) repository plant in Sellafield, UK. The complexity of the processes involved, together with the large dispersion and scarcity of observations regarding radionuclide concentrations in the marine environment, require efficient data assimilation techniques. In this regard, the basic STF methods search for identifiable, linear model structures that capture the maximum amount of information contained in the data with a minimal parameterisation. They can be extended for on-line use, based on recursively updated Bayesian estimation and, although applicable to only constant or time-variable parameter (non-stationary) linear systems in the form used in this paper, they have the potential for application to non-linear systems using recently developed State Dependent Parameter (SDP) non-linear STF models. The GLUE based-methods, on the other hand, formulate the problem of estimation using a more general Bayesian approach, usually without prior statistical identification of the model structure. As a result, they are applicable to almost any linear or non-linear stochastic model, although they are much less efficient both computationally and in their use of the information contained in the observations. As expected in this particular environmental application, it is shown that the STF methods give much narrower confidence limits for the estimates due to their more efficient use of the information contained in the data. Exploiting Monte Carlo Simulation (MCS) analysis, the GLUE technique is used to estimate how the errors involved in the STF model structure and observations influence the model outputs and errors. The discussion on updating information originating from different locations using GLUE procedure is also given. A final aim of the paper is to use the results obtained in this particular example to explore the differences between the GLUE and STF approaches.

Modelling uncertainty in estimates of recharge to a shallow coastal aquifer

Due to the difficulty of field characterization, one is often forced to employ hydrological models in order to determine estimates of aquifer recharge. A Geographical Information System (GIS) and Digital Elevation Model (DEM) may provide the basic support for such hydrological models. Unfortunately, despite the availability of these tools, the values of many parameters within distributed models remain uncertain for application to real world problems. Using the Bisagno basin (100 km2) in the Liguria region of Italy, the role of model parameter uncertainty on estimates of recharge to the Bisagno Aquifer is demonstrated. Uncertainty estimation is achieved through Monte Carlo simulations with the aid of the Generalised Likelihood Uncertainty Estimation procedure of Beven & Binley (1992).