Marc B. Neumann

Uncertainty analysis in WWTP model applications: a critical discussion using an example from design.

This study focuses on uncertainty analysis of WWTP models and analyzes the issue of framing and how it affects the interpretation of uncertainty analysis results. As a case study, the prediction of uncertainty involved in model-based design of a wastewater treatment plant is studied. The Monte Carlo procedure is used for uncertainty estimation, for which the input uncertainty is quantified through expert elicitation and the sampling is performed using the Latin hypercube method. Three scenarios from engineering practice are selected to examine the issue of framing: (1) uncertainty due to stoichiometric, biokinetic and influent parameters; (2) uncertainty due to hydraulic behaviour of the plant and mass transfer parameters; (3) uncertainty due to the combination of (1) and (2). The results demonstrate that depending on the way the uncertainty analysis is framed, the estimated uncertainty of design performance criteria differs significantly. The implication for the practical applications of uncertainty analysis in the wastewater industry is profound: (i) as the uncertainty analysis results are specific to the framing used, the results must be interpreted within the context of that framing; and (ii) the framing must be crafted according to the particular purpose of uncertainty analysis/model application. Finally, it needs to be emphasised that uncertainty analysis is no doubt a powerful tool for model-based design among others, however clear guidelines for good uncertainty analysis in wastewater engineering practice are needed.

Global sensitivity analysis in wastewater treatment plant model applications: prioritizing sources of uncertainty.

This study demonstrates the usefulness of global sensitivity analysis in wastewater treatment plant (WWTP) design to prioritize sources of uncertainty and quantify their impact on performance criteria. The study, which is performed with the Benchmark Simulation Model no. 1 plant design, complements a previous paper on input uncertainty characterisation and propagation (Sin et al., 2009). A sampling-based sensitivity analysis is conducted to compute standardized regression coefficients. It was found that this method is able to decompose satisfactorily the variance of plant performance criteria (with R(2) > 0.9) for effluent concentrations, sludge production and energy demand. This high extent of linearity means that the plant performance criteria can be described as linear functions of the model inputs under the defined plant conditions. In effect, the system of coupled ordinary differential equations can be replaced by multivariate linear models, which can be used as surrogate models. The importance ranking based on the sensitivity measures demonstrates that the most influential factors involve ash content and influent inert particulate COD among others, largely responsible for the uncertainty in predicting sludge production and effluent ammonium concentration. While these results were in agreement with process knowledge, the added value is that the global sensitivity methods can quantify the contribution of the variance of significant parameters, e.g., ash content explains 70% of the variance in sludge production. Further the importance of formulating appropriate sensitivity analysis scenarios that match the purpose of the model application needs to be highlighted. Overall, the global sensitivity analysis proved a powerful tool for explaining and quantifying uncertainties as well as providing insight into devising useful ways for reducing uncertainties in the plant performance. This information can help engineers design robust WWTP plants.

Wastewater treatment modelling: dealing with uncertainties

This paper serves as a problem statement of the issues surrounding uncertainty in wastewater treatment modelling. The paper proposes a structure for identifying the sources of uncertainty introduced during each step of an engineering project concerned with model-based design or optimisation of a wastewater treatment system. It briefly references the methods currently used to evaluate prediction accuracy and uncertainty and discusses the relevance of uncertainty evaluations in model applications. The paper aims to raise awareness and initiate a comprehensive discussion among professionals on model prediction accuracy and uncertainty issues. It also aims to identify future research needs. Ultimately the goal of such a discussion would be to generate transparent and objective methods of explicitly evaluating the reliability of model results, before they are implemented in an engineering decision-making context.

Comparison of sensitivity analysis methods for pollutant degradation modelling: A case study from drinking water treatment

Five sensitivity analysis methods based on derivatives, screening, regression, variance decomposition and entropy are introduced, applied and compared for a model predicting micropollutant degradation in drinking water treatment. The sensitivity analysis objectives considered are factors prioritisation (detecting important factors), factors fixing (detecting non-influential factors) and factors mapping (detecting which factors are responsible for causing pollutant limit exceedances). It is shown how the applicability of methods changes in view of increasing interactions between model factors and increasing non-linearity between the model output and the model factors. A high correlation is observed between the indices obtained for the objectives factors prioritisation and factors mapping due to the positive skewness of the probability distributions of the predicted residual pollutant concentrations. The entropy-based method which uses the Kullback-Leibler divergence is found to be particularly suited when assessing pollutant limit exceedances.

Applying global sensitivity analysis to the modelling of flow and water quality in sewers.

While several approaches for global sensitivity analysis (GSA) have been proposed in literature, only few applications exist in urban drainage modelling. This contribution discusses two GSA methods applied to a sewer flow and sewer water quality model: Standardised Regression Coefficients (SRCs) using Monte-Carlo simulation as well as the Morris Screening method. For selected model variables we evaluate how the sensitivities are influenced by the choice of the rainfall event. The aims are to i) compare both methods concerning the similarity of results and their applicability, ii) discuss the implications for factor fixing (identifying non-influential parameters) and factor prioritisation (identifying important parameters) and iii) rank the important parameters for the investigated model. It was shown that both methods lead to similar results for the hydraulic model. Parameter interactions and non-linearity were identified for the water quality model and the parameter ranking differs between the methods. For the investigated model the results allow a sound choice of output variables and rainfall events in view of detailed uncertainty analysis or model calibration. We advocate the simultaneous use of both methods for a first model assessment as they allow answering both factor fixing and factor prioritisation at low computational cost.

Global sensitivity analysis for model-based prediction of oxidative micropollutant transformation during drinking water treatment

This study quantifies the uncertainty involved in predicting micropollutant oxidation during drinking water ozonation in a pilot plant reactor. The analysis is conducted for geosmin, methyl tert-butyl ether (MTBE), isopropylmethoxypyrazine (IPMP), bezafibrate, beta-cyclocitral and ciprofloxazin. These compounds are representative for a wide range of substances with second order rate constants between 0.1 and 1.9x10(4)M(-1)s(-1) for the reaction with ozone and between 2x10(9) and 8x10(9)M(-1)s(-1) for the reaction with OH-radicals. Uncertainty ranges are derived for second order rate constants, hydraulic parameters, flow- and ozone concentration data, and water characteristic parameters. The uncertain model factors are propagated via Monte Carlo simulation and the resulting probability distributions of the relative residual micropollutant concentrations are assessed. The importance of factors in determining model output variance is quantified using Extended Fourier Amplitude Sensitivity Testing (Extended-FAST). For substances that react slowly with ozone (MTBE, IPMP, geosmin) the water characteristic R(ct)-value (ratio of ozone- to OH-radical concentration) is the most influential factor explaining 80% of the output variance. In the case of bezafibrate the R(ct)-value and the second order rate constant for the reaction with ozone each contribute about 30% to the output variance. For beta-cyclocitral and ciprofloxazin (fast reacting with ozone) the second order rate constant for the reaction with ozone and the hydraulic model structure become the dominating sources of uncertainty.

Biological nitrogen and phosphorus removal in membrane bioreactors: model development and parameter estimation

Membrane bioreactors (MBR) are being increasingly used for wastewater treatment. Mathematical modeling of MBR systems plays a key role in order to better explain their characteristics. Several MBR models have been presented in the literature focusing on different aspects: biological models, models which include soluble microbial products (SMP), physical models able to describe the membrane fouling and integrated models which couple the SMP models with the physical models. However, only a few integrated models have been developed which take into account the relationships between membrane fouling and biological processes. With respect to biological phosphorus removal in MBR systems, due to the complexity of the process, practical use of the models is still limited. There is a vast knowledge (and consequently vast amount of data) on nutrient removal for conventional-activated sludge systems but only limited information on phosphorus removal for MBRs. Calibration of these complex integrated models still remains the main bottleneck to their employment. The paper presents an integrated mathematical model able to simultaneously describe biological phosphorus removal, SMP formation/degradation and physical processes which also include the removal of organic matter. The model has been calibrated with data collected in a UCT-MBR pilot plant, located at the Palermo wastewater treatment plant, applying a modified version of a recently developed calibration protocol. The calibrated model provides acceptable correspondence with experimental data and can be considered a useful tool for MBR design and operation.

Variance-based sensitivity analysis for wastewater treatment plant modelling.

Global sensitivity analysis (GSA) is a valuable tool to support the use of mathematical models that characterise technical or natural systems. In the field of wastewater modelling, most of the recent applications of GSA use either regression-based methods, which require close to linear relationships between the model outputs and model factors, or screening methods, which only yield qualitative results. However, due to the characteristics of membrane bioreactors (MBR) (non-linear kinetics, complexity, etc.) there is an interest to adequately quantify the effects of non-linearity and interactions. This can be achieved with variance-based sensitivity analysis methods. In this paper, the Extended Fourier Amplitude Sensitivity Testing (Extended-FAST) method is applied to an integrated activated sludge model (ASM2d) for an MBR system including microbial product formation and physical separation processes. Twenty-one model outputs located throughout the different sections of the bioreactor and 79 model factors are considered. Significant interactions among the model factors are found. Contrary to previous GSA studies for ASM models, we find the relationship between variables and factors to be non-linear and non-additive. By analysing the pattern of the variance decomposition along the plant, the model factors having the highest variance contributions were identified. This study demonstrates the usefulness of variance-based methods in membrane bioreactor modelling where, due to the presence of membranes and different operating conditions than those typically found in conventional activated sludge systems, several highly non-linear effects are present. Further, the obtained results highlight the relevant role played by the modelling approach for MBR taking into account simultaneously biological and physical processes.

Likelihood of climate change pathways under uncertainty on fossil fuel resource availability

Uncertainties concerning fossil fuel resource availability have traditionally been deemphasized in climate change research as global baseline emission scenarios (i.e., scenarios that do not consider additional climate policies) have been built on the assumption of abundant fossil fuel resources for the 21st century. However, current estimates are subject to critical uncertainties and an emerging body of literature is providing revised estimates. Here we consider the entire range of revised estimates, applying an integrated assessment model to perform a likelihood analysis of climate change pathways. Our results show that, by the end of the century, the two highest emission pathways from the IPCC, the Representative Concentration Pathways RCP6 and RCP8.5, where the baseline scenarios currently lie, have probabilities of being surpassed of 42% and 12%, respectively. In terms of temperature change, the probability of exceeding the 2 °C level by 2100 remains very high (88%), confirming the need for urgent climate action. Coal resource uncertainty determines the uncertainty about the emission and radiative forcing pathways due to the poor quality of data. We also find that the depletion of fossil fuels is likely to occur during the second half of the century accelerating the transition to renewable energy sources in baseline scenarios. Accordingly, more investments may be required to enable the energy transition, while the additional mitigation measures would in turn necessitate a lower effort than currently estimated. Hence, the integrated analysis of resource availability and climate change is essential to obtain internally consistent climate pathways.

Ecosystem-based management of a Mediterranean urban wastewater system: A sensitivity analysis of the operational degrees of freedom

Urban wastewater systems discharge organic matter, nutrients and other pollutants (including toxic substances) to receiving waters, even after removing more than 90% of incoming pollutants from human activities. Understanding their interactions with the receiving water bodies is essential for the implementation of ecosystem-based management strategies. Using mathematical modeling and sensitivity analysis we quantified how 19 operational variables of an urban wastewater system affect river water quality. The mathematical model of the Congost system (in the Besòs catchment, Spain) characterizes the dynamic interactions between sewers, storage tanks, wastewater treatment plants and the river. The sensitivity analysis shows that the use of storage tanks for peak shaving and the use of a connection between two neighboring wastewater treatment plants are the most important factors influencing river water quality. We study how the sensitivity of the water quality variables towards changes in the operational variables varies along the river due to discharge locations and river self-purification processes. We demonstrate how to use the approach to identify interactions and how to discard non-influential operational variables.