Bayesian Uncertainty Assessment Research Articles

A fast and effective parameterization of water quality models

Water quality (WQ) models parameterization remains a challenging task, as these models are typically characterized by a high number of parameters. The objective of this study was to present a solution to the WQ parameterization problem by the use of a fast sensitivity analysis (SA) method and a manual calibration. For this purpose, we applied the simple screening LH-OAT method to the conceptual WQ model of the River Dender, Belgium. To evaluate the effectiveness of LH-OAT to identify the influential parameters, the advanced PAWN method was applied. A manual calibration was done using the influential parameters.LH-OAT provided a parameter ranking that was very similar to the one of PAWN but in a much more efficient way. The Bayesian uncertainty assessment showed the effectiveness of the LH-OAT results. To conclude, a fast screening method is preferred over an advanced SA method to identify the influential parameters for the calibration.

Uncertainty Assessment in the Quantification of Risk Rates of Occupational Accidents

Occupational risk rates per hour of exposure have been quantified for 63 occupational accident types for the Dutch working population. Data were obtained from the analysis of more than 9,000 accidents that occurred over a period of six years in the Netherlands and resulted in three types of reportable consequences under Dutch law: (a) fatal injury, (b) permanent injury, and (c) serious recoverable injury requiring at least one day of hospitalization. A Bayesian uncertainty assessment on the value of the risk rates has been performed. Annual risks for each of the 63 occupational accident types have been calculated, including the variability in the annual exposure of the working population to the corresponding hazards. The suitability of three risk measures-individual risk rates, individual annual risk, and number of accidents-is examined and discussed.

The importance of hydrological uncertainty assessment methods in climate change impact studies

Abstract. Climate change impact assessments have become more and more popular in hydrology since the middle 1980s with a recent boost after the publication of the IPCC AR4 report. From hundreds of impact studies a quasi-standard methodology has emerged, to a large extent shaped by the growing public demand for predicting how water resources management or flood protection should change in the coming decades. The "standard" workflow relies on a model cascade from global circulation model (GCM) predictions for selected IPCC scenarios to future catchment hydrology. Uncertainty is present at each level and propagates through the model cascade. There is an emerging consensus between many studies on the relative importance of the different uncertainty sources. The prevailing perception is that GCM uncertainty dominates hydrological impact studies. Our hypothesis was that the relative importance of climatic and hydrologic uncertainty is (among other factors) heavily influenced by the uncertainty assessment method. To test this we carried out a climate change impact assessment and estimated the relative importance of the uncertainty sources. The study was performed on two small catchments in the Swiss Plateau with a lumped conceptual rainfall runoff model. In the climatic part we applied the standard ensemble approach to quantify uncertainty but in hydrology we used formal Bayesian uncertainty assessment with two different likelihood functions. One was a time series error model that was able to deal with the complicated statistical properties of hydrological model residuals. The second was an approximate likelihood function for the flow quantiles. The results showed that the expected climatic impact on flow quantiles was small compared to prediction uncertainty. The choice of uncertainty assessment method actually determined what sources of uncertainty could be identified at all. This demonstrated that one could arrive at rather different conclusions about the causes behind predictive uncertainty for the same hydrological model and calibration data when considering different objective functions for calibration.

Bayesian uncertainty assessment of a semi-distributed integrated catchment model of phosphorus transport

Process-based models of nutrient transport are often used as tools for management of eutrophic waters, as decision makers need to judge the potential effects of alternative remediation measures, under current conditions and with future land use and climate change. All modelling exercises entail uncertainty arising from various sources, such as the input data, selection of parameter values and the choice of model itself. Here we perform Bayesian uncertainty assessment of an integrated catchment model of phosphorus (INCA-P). We use an auto-calibration procedure and an algorithm for including parametric uncertainty to simulate phosphorus transport in a Norwegian lowland river basin. Two future scenarios were defined to exemplify the importance of parametric uncertainty in generating predictions. While a worst case scenario yielded a robust prediction of increased loading of phosphorus, a best case scenario only gave rise to a reduction in load with probability 0.78, highlighting the importance of taking parametric uncertainty into account in process-based catchment scale modelling of possible remediation scenarios. Estimates of uncertainty can be included in information provided to decision makers, thus making a stronger scientific basis for sound decisions to manage water resources.

Bayesian uncertainty assessment of flood predictions in ungauged urban basins for conceptual rainfall-runoff models

Abstract. Urbanization and the resulting land-use change strongly affect the water cycle and runoff-processes in watersheds. Unfortunately, small urban watersheds, which are most affected by urban sprawl, are mostly ungauged. This makes it intrinsically difficult to assess the consequences of urbanization. Most of all, it is unclear how to reliably assess the predictive uncertainty given the structural deficits of the applied models. In this study, we therefore investigate the uncertainty of flood predictions in ungauged urban basins from structurally uncertain rainfall-runoff models. To this end, we suggest a procedure to explicitly account for input uncertainty and model structure deficits using Bayesian statistics with a continuous-time autoregressive error model. In addition, we propose a concise procedure to derive prior parameter distributions from base data and successfully apply the methodology to an urban catchment in Warsaw, Poland. Based on our results, we are able to demonstrate that the autoregressive error model greatly helps to meet the statistical assumptions and to compute reliable prediction intervals. In our study, we found that predicted peak flows were up to 7 times higher than observations. This was reduced to 5 times with Bayesian updating, using only few discharge measurements. In addition, our analysis suggests that imprecise rainfall information and model structure deficits contribute mostly to the total prediction uncertainty. In the future, flood predictions in ungauged basins will become more important due to ongoing urbanization as well as anthropogenic and climatic changes. Thus, providing reliable measures of uncertainty is crucial to support decision making.

Assessing the impacts of parameter uncertainty for computationally expensive groundwater models

Computational requirements often limit the assessment of uncertainty in complex environmental models. Monte Carlo–based techniques such as generalized likelihood uncertainty estimation (GLUE) and Bayesian uncertainty assessment are limited in applicability because of their heavy computational demands. This paper presents a computationally efficient method that combines automatic calibration using function‐approximation‐based global optimization with importance weighting for assessing parametric uncertainty in model outputs for computationally expensive models. We call this method automatic calibration and uncertainty assessment using response surfaces (ACUARS). The bias introduced during optimization because of oversampling of high goodness of fit regions of the parameter space is corrected using a multidimensional cell‐declustering technique. The proposed method is applied to two hypothetical examples in enhanced bioremediation of chlorinated ethenes in groundwater that differ in computational requirements and the number of parameters that were calibrated. The results from the simpler example in which uncertainty of three model parameters in model outputs was considered showed that for a given acceptability threshold and a given number of permissible model simulations, ACUARS finds many more representative parameter sets than GLUE. GLUE produced only half the number of acceptable parameter sets for uncertainty assessment, even after 10 times as many simulations as ACUARS was performed for GLUE. Further, the median output of ACUARS predicted the true value of the outputs more closely than GLUE. For a more complicated numerical example, where noisy data were used for calibration of seven model parameters, GLUE required 2400 simulations to find 31 acceptable parameter sets, while ACUARS found 46 acceptable parameter sets in only 300 simulations for a moderately stringent threshold. This enabled a more accurate estimate of uncertainty by providing closer estimates of the true outputs.

Bayesian uncertainty assessment in multicompartment deterministic simulation models for environmental risk assessment

AbstractWe use a special case of Bayesian melding to make inference from deterministic models while accounting for uncertainty in the inputs to the model. The method uses all available information, based on both data and expert knowledge, and extends current methods of ‘uncertainty analysis’ by updating models using available data. We extend the methodology for use with sequential multicompartment models. We present an application of these methods to deterministic models for concentration of polychlorinated biphenyl (PCB) in soil and vegetables. The results are posterior distributions of concentration in soil and vegetables which account for all available evidence and uncertainty. Model uncertainty is not considered. Copyright © 2003 John Wiley & Sons, Ltd.

Sensitivity analysis, Monte Carlo risk analysis, and Bayesian uncertainty assessment.

Standard statistical methods understate the uncertainty one should attach to effect estimates obtained from observational data. Among the methods used to address this problem are sensitivity analysis, Monte Carlo risk analysis (MCRA), and Bayesian uncertainty assessment. Estimates from MCRAs have been presented as if they were valid frequentist or Bayesian results, but examples show that they need not be either in actual applications. It is concluded that both sensitivity analyses and MCRA should begin with the same type of prior specification effort as Bayesian analysis.