Multiple perspectives of resilience: A holistic approach to resilience assessment using cognitive maps in practitioner engagement.

Resilience has become a regulatory concept influencing investment decisions in the water and wastewater sector. However, current assessments predominantly focus on technical resilience and on engineering solutions. Here we propose an alternative, more holistic approach that captures multiple perspectives of resilience by eliciting and comparing cognitive maps of diverse agents both from within as well as external to a wastewater utility. We use Fuzzy Cognitive Mapping as a practical tool to elicit subjective views on resilience mechanisms and illustrate the methodology in co-production with professionals from the wastewater sector in the Belfast area (Northern Ireland). We find that the proposed participatory process facilitates a more "reflective", "inclusive" and "integrated" assessment than current approaches. Screening for risks and vulnerabilities using this new approach can foster an integrated system perspective by (i) systematically identifying connections between (sub)systems which are normally assessed separately, (ii) detecting feedbacks between system components which may reveal unintended consequences of resilience interventions and by (iii) obtaining a wider portfolio of potential interventions to increase overall resilience. We conclude that the suggested approach may be useful for strategic planning purposes within a utility and for improving cross-departmental communication among both internal and external agents.

Stochastic diffusion models to describe the evolution of annual heatwave statistics: A three-factor model with risk calculations.

In view of risk assessments this paper proposes a stochastic diffusion model to characterise statistics of extreme events when climate- or environmental variables surpass critical thresholds. The proposed three-factor model captures trend and volatility of such statistics and could prove valuable for climate and environmental impact analysis in many systems such as human health, agriculture or ecology. The model supports decisions in view of lowering risks to acceptable levels. We illustrate the development of the model for heatwave impacts on human health in the context of climate change. We propose a generic model composed of three random processes characterising annual statistics of heatwaves: a Poisson process characterising the number of heatwaves, a Gamma process characterising mean duration and a truncated Gaussian process capturing mean excess temperature of heatwave days. Additionally, potential correlations between the three processes are taken into account. The model is calibrated with data obtained from a regional climate model for two cities in Spain. The suitability of the model for probabilistic analysis is tested with Monte Carlo simulations. We assess the time-dependent probability distributions of heatwave-related mortality and demonstrate how to obtain relevant risk metrics such as the 95th percentile and the average of the 5% of worst cases (ES (95%)).

Valuing deaths or years of life lost? Economic benefits of avoided mortality from early heat warning systems.

The study aims to explore the main drivers influencing the economic appraisal of heat warning systems by integrating epidemiological modelling and benefit-cost analysis. To shed insights on heat wave mortality valuation, we consider three valuation schemes: (i) a traditional one, where the value of a statistical life (VSL) is applied to both displaced and premature mortality; (ii) an intermediate one, with VSL applied for premature mortality and value of a life year (VOLY) for displaced mortality; and (iii) a conservative one, where both premature and displaced mortality are quantified in terms of loss of life expectancy, and then valued using the VOLY approach. When applying these three schemes to Madrid (Spain), we obtain a benefit-cost ratio varying from 12 to 3700. We find that the choice of the valuation scheme has the largest influence, whereas other parameters such as attributable risk, displaced mortality ratio, or the comprehensiveness and effectiveness of the heat warning system are less influential. The results raise the question of which is the most appropriate approach to value mortality in the context of heat waves, given that the lower bound estimate for the benefit-cost ratio (option iii using VOLY) is up to two orders of magnitude lower than the value based on the traditional VSL approach (option i). The choice of the valuation methodology has significant implications for public health authorities at the local and regional scale, which becomes highly relevant for locations where the application of the VOLY approach could lead to benefit-cost ratios significantly lower than 1. We propose that specific metrics for premature and displaced VOLYs should be developed for the context of heat waves. Until such values are available, we suggest testing the economic viability of heat warning systems under the three proposed valuation schemes (i-iii) and using values for VOLY commonly applied in air pollution as the health end points are similar. Lastly, periodical reassessment of heat alert plans should be performed by public health authorities to monitor their long-term viability and cost-effectiveness.

Adaptation in hindsight: dynamics and drivers shaping urban wastewater systems.

Well-planned urban infrastructure should meet critical loads during its design lifetime. In order to proceed with design, engineers are forced to make numerous assumptions with very little supporting information about the development of various drivers. For the wastewater sector, these drivers include the future amount and composition of the generated wastewater, effluent requirements, technologies, prices of inputs such as energy or chemicals, and the value of outputs produced such as nutrients for fertilizer use. When planning wastewater systems, there is a lack of methods to address discrepancies between the timescales at which fundamental changes in these drivers can occur, and the long physical life expectancy of infrastructure (on the order of 25-80 years). To explore these discrepancies, we take a hindsight perspective of the long-term development of wastewater infrastructure and assess the stability of assumptions made during previous designs. Repeatedly we find that the drivers influencing wastewater loads, environmental requirements or technological innovation can change at smaller timescales than the infrastructure design lifetime, often in less than a decade. Our analysis shows that i) built infrastructure is continuously confronted with challenges it was not conceived for, ii) significant adaptation occurs during a structure's lifetime, and iii) "muddling-through" is the pre-dominant strategy for adaptive management. As a consequence, we argue, there is a need to explore robust design strategies which require the systematic use of scenario planning methods and instruments to increase operational, structural, managerial, institutional and financial flexibility. Hindsight studies, such as this one, may inform the development of robust design strategies and assist in the transition to more explicit forms of adaptive management for urban infrastructures.

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.

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.

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.

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.

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.

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.

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 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.

Underestimation of uncertainty in statistical regression of environmental models: influence of model structure uncertainty.

As the quality of sensors increases, systematic discrepancies between measurements and model outputs become more apparent Applying regression type analysis in these cases leads to autocorrelated residuals, biased parameter estimates, and underestimation of uncertainty. This paper examines how parameter estimates are affected by model structure uncertainty for an application from wastewater treatment. A Monod model is fitted to synthetic data generated by a reference system exhibiting predefined Tessier kinetics and a known error process. A range of methods are suggested to test if the resulting residuals fulfill the IID (independent and identically distributed)-requirement visual examination of time series, autocorrelation, and partial autocorrelation functions, the Jarque-Bera normality test, the Runs test for independence, and the BDS test for IID. The tests are shown to perform well at low measurement noise but not at higher levels of noise where transferring the parameter estimates gained from a batch system leads to erroneous estimation of steady state concentrations in a completely stirred tank reactor. Additional diagnostics are suggested which include second order autocorrelation functions of the residuals in the case of a single experiment and examination of moving averages of residuals in the case of multiple experiments.

Sources of parameter uncertainty in predicting treatment performance: the case of preozonation in drinking water engineering.

This study investigates the factors that determine parameter uncertainty when applying predefined, existing models to predict the performance of a full scale treatment system from environmental engineering. The analysis is performed for ozonation of surface water, a technology applied in drinking water treatment for disinfection and oxidation of micropollutants. The pseudo first order rate constant of ozone decay k(O3) is characterized as a time dependent parameter and estimated from data obtained from three experimental setups representing upscaling stages in engineering design. To obtain meaningful uncertainty estimates, various factors need to be acknowledged: uncertainty about the model structure, uncertainty of other model parameters, uncertainty due to non-representative sampling, and errors in chemical analysis. It is concluded that an on-site automated sequencing batch reactor is best suited for estimating kinetics during operation of the full scale system. Furthermore, the transferability of information in upscaling from laboratory experiments to the full scale system is found to be critical. Although uncertainty analysis enhances the understanding of the system, it is also shown to be a subjective process depending on the knowledge and assumptions of the modeler and the availability and quality of data.

Uncertainty in prediction of disinfection performance.

Predicting the disinfection performance of a full-scale reactor in drinking water treatment is associated with considerable uncertainty. In view of quantitative risk analysis, this study assesses the uncertainty involved in predicting inactivation of Cryptosporidium parvum oocysts for an ozone reactor treating lake water. A micromodel is suggested which quantifies inactivation by stochastic sampling from density distributions of ozone exposure and lethal ozone dose. The ozone exposure distribution is computed with a tank in series model that is derived from tracer data and measurements of flow, ozone concentration and ozone decay. The distribution of lethal ozone doses is computed with a delayed Chick-Watson model which was calibrated by Sivaganesan and Marinas [2005. Development of a Ct equation taking into consideration the effect of Lot variability on the inactivation of Cryptosporidium parvum oocysts with ozone. Water Res. 39(11), 2429-2437] utilizing a large number of inactivation studies. Parameter uncertainty is propagated with Monte Carlo simulation and the probability of attaining given inactivation levels is assessed. Regional sensitivity analysis based on variance decomposition ranks the influence of parameters in determining the variance of the model result. The lethal dose model turns out to be responsible for over 90% of the output variance. The entire analysis is re-run for three exemplary scenarios to assess the robustness of the results in view of changing inputs, differing operational parameters or revised assumptions about the appropriate model. We argue that the suggested micromodel is a versatile approach for characterization of disinfection reactors. The scheme developed for uncertainty assessment is optimal for model diagnostics and effectively supports the management of uncertainty.