Approximate methods for uncertainty analysis of water distribution systems

Monte Carlo simulation (MCS) has been commonly applied for uncertainty analysis of model predictions. However, when modelling a water distribution system under unsteady conditions, the computational demand of MCS is quite high even for a reasonably sized system. The aim of this study is to evaluate alternative approximation schemes and examine their ability to predict model prediction uncertainty with less computational effort. Here, MCS is compared with a point estimation method, the first-order second-moment (FOSM) method, and a quasi-MCS method, Latin hypercube sampling (LHS). Hydraulic and water quality simulations are performed using EPANET and the evaluated model outputs are nodal pressure, water age and chlorine concentration. Six input parameters, pipe diameter and roughness coefficient, nodal spatial and temporal demands and bulk and wall decay coefficients, are considered. To examine the effect of the magnitude of input uncertainty on model output, three uncertainty levels are evaluated. The study is performed for a real system with 116 pipes and 90 nodes. Results demonstrate that LHS provides very good estimates of the predicted output range for steady and unsteady conditions compared with MCS, while FOSM did well for steady conditions but poorly for some periods in the extended-period simulation for chlorine concentration.     

Assessment of the integrated urban water quality model complexity through identifiability analysis

Urban sources of water pollution have often been cited as the primary cause of poor water quality in receiving water bodies (RWB), and recently many studies have been conducted to investigate both continuous sources, such as wastewater-treatment plant (WWTP) effluents, and intermittent sources, such as combined sewer overflows (CSOs). An urban drainage system must be considered jointly, i.e., by means of an integrated approach. However, although the benefits of an integrated approach have been widely demonstrated, several aspects have prevented its wide application, such as the scarcity of field data for not only the input and output variables but also parameters that govern intermediate stages of the system, which are useful for robust calibration. These factors, along with the high complexity level of the currently adopted approaches, introduce uncertainties in the modelling process that are not always identifiable. In this study, the identifiability analysis was applied to a complex integrated catchment: the Nocella basin (Italy). This system is characterised by two main urban areas served by two WWTPs and has a small river as the RWB. The system was simulated by employing an integrated model developed in previous studies. The main goal of the study was to assess the right number of parameters that can be estimated on the basis of data-source availability. A preliminary sensitivity analysis was undertaken to reduce the model parameters to the most sensitive ones. Subsequently, the identifiability analysis was carried out by progressively considering new data sources and assessing the added value provided by each of them. In the process, several identifiability methods were compared and some new techniques were proposed for reducing subjectivity of the analysis. The study showed the potential of the identifiability analysis for selecting the most relevant parameters in the model, thus allowing for model simplification, and in assessing the impact of data sources for model reliability, thus guiding the analyst in the design of future monitoring campaigns. Further, the analysis showed some critical points in integrated urban drainage modelling, such as the interaction between water quality processes on the catchment and in the sewer, that can prevent the identifiability of some of the related parameters.     

Integrated river flow modelling: A case study

The paper presents a holistic approach to river flow modelling in which catchment rainfall-runoff, sewer hydrodynamic and river hydrodynamic models are linked together and applied to the Bradford catchment (UK). The catchment features steep gradients, flashy supercritical flow in combination with dry bed condition and is highly urbanised. Given this complexity and the paucity of data, a holistic approach was found essential, although its application proved challenging.

Most important uncertainties inherent in each sub-model were assessed individually as well as propagation effects through the integrated model. The relative contribution of uncertainty sources to the total uncertainty in river flow predictions was quantified using the concept of variance decomposition. The results show that uncertainties in model structure and rainfall input in the rainfall-runoff model were significant. However, within the river hydrodynamic model, uncertainties propagated from the rainfall-runoff model were less apparent due to additional uncertainty arising from the urban drainage system.     

Quantification and relative comparison of different types of uncertainties in sewer water quality modeling

Quantifiable sources of uncertainty have been identified for a case study of integrated modeling of a sewer system with a more downstream wastewater treatment plant and storage sedimentation tank. The different sources were classified in model input and model-structure-related uncertainties. They were quantified and propagated towards the uncertainty in the event-based prediction of sewer emissions (flow, and physico-chemical water quality concentrations and loads). Based on the concept of variance decomposition, the total prediction uncertainty was split into the contributions of the various uncertainty sources and the different submodels. Although the results strongly depend on the water quality variable considered, it is in most general terms concluded that the uncertainty contribution by the water quality submodels is an order of magnitude higher than that for the flow submodels. Future model improvement should therefore mainly focus on water quality data collection, which would reduce current problems of spurious model calibration and verification, but also of knowledge gaps in in-sewer processes.     

Understanding data requirements for trihalomethane formation modelling in water supply systems

Tighter regulatory standards for trihalomethanes in drinking water have been introduced in many countries in response to improved epidemiological evidence. This has led to the need to model better the THM concentrations in water distribution systems in order to manage efficiently economic, chemical and microbiological factors. THM modelling is a challenging process given the complex chemistry and dependence on river catchment, water treatment works and distribution system characteristics. It is demonstrated that a good understanding of the system from raw water to tap is needed if cost effective models of appropriate fidelity are to be produced. For appropriate systems models can incorporate, through empirical relationships, raw water quality variations based on river flow predictions, aspects of unit process management decision making variables as well as distribution system characteristics. In many systems model fidelity and hence efficient management is constrained by a lack of knowledge of system response.     

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.     

Managing Agricultural Pollution Using a Linked Geographical Information System and Non-Point Source Pollution Model

This study documents the development of a link between a geographical information system (GIS) and a non-point source pollution model. The GIS ARC/INFO was linked to the agricultural non-point source pollution model and ORACLE data sources. Application of the system is demonstrated using the Bedford-Ouse catchment as a suitable case study. Water quality impacts are predicted from source data describing topography, soils, land use and river network. The model results were in agreement with observed nitrate concentrations at the catchment outlet, and more appropriate data sources are considered to be the main priority for improving model predictive ability. Management scenarios were established to assess the impact of changing agricultural management practices on predicted water quality. The approach has significant potential for the management of agricultural pollution in the UK.     

Comparison of different uncertainty techniques in urban stormwater quantity and quality modelling

Urban drainage models are important tools used by both practitioners and scientists in the field of stormwater management. These models are often conceptual and usually require calibration using local datasets. The quantification of the uncertainty associated with the models is a must, although it is rarely practiced. The International Working Group on Data and Models, which works under the IWA/IAHR Joint Committee on Urban Drainage, has been working on the development of a framework for defining and assessing uncertainties in the field of urban drainage modelling. A part of that work is the assessment and comparison of different techniques generally used in the uncertainty assessment of the parameters of water models. This paper compares a number of these techniques: the Generalized Likelihood Uncertainty Estimation (GLUE), the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA), an approach based on a multi-objective auto-calibration (a multialgorithm, genetically adaptive multi-objective method, AMALGAM) and a Bayesian approach based on a simplified Markov Chain Monte Carlo method (implemented in the software MICA). To allow a meaningful comparison among the different uncertainty techniques, common criteria have been set for the likelihood formulation, defining the number of simulations, and the measure of uncertainty bounds. Moreover, all the uncertainty techniques were implemented for the same case study, in which the same stormwater quantity and quality model was used alongside the same dataset. The comparison results for a well-posed rainfall/runoff model showed that the four methods provide similar probability distributions of model parameters, and model prediction intervals. For ill-posed water quality model the differences between the results were much wider; and the paper provides the specific advantages and disadvantages of each method. In relation to computational efficiency (i.e. number of iterations required to generate the probability distribution of parameters), it was found that SCEM-UA and AMALGAM produce results quicker than GLUE in terms of required number of simulations. However, GLUE requires the lowest modelling skills and is easy to implement. All non-Bayesian methods have problems with the way they accept behavioural parameter sets, e.g. GLUE, SCEM-UA and AMALGAM have subjective acceptance thresholds, while MICA has usually problem with its hypothesis on normality of residuals. It is concluded that modellers should select the method which is most suitable for the system they are modelling (e.g. complexity of the model’s structure including the number of parameters), their skill/knowledge level, the available information, and the purpose of their study.     

A dimensional analysis‐based model for the prediction of nitrogen concentrations in Laborec River,Slovakia

During the past decades, several models that predict the concentration profiles after a discharge of pollutants in a river have been developed. A model that predicts nitrogen concentrations in a river has been developed and is presented in this paper. The developed model that determines nitrogen concentrations in a water stream is based on a dimensional analysis. Fundamentals of the modelling of the pollutant predictions in a water stream consist of a derivation of function dependency from expressed non‐dimension arguments. Non‐dimension arguments are stated from variables, which influence the occurrence of pollutants. The model for the prediction of nitrogen concentrations in water streams has been developed for the Laborec River (eastern Slovakia). The differences between the nitrogen concentrations predicted from developed models and measured concentrations in the river are also discussed here.     

Uncertainty in urban stormwater quality modelling: the effect of acceptability threshold in the GLUE methodology

Uncertainty analysis in integrated urban drainage modelling is of growing importance in the field of water quality. However, only few studies deal with uncertainty quantification in urban drainage modelling; furthermore, the few existing studies mainly focus on quantitative sewer flow modelling rather than uncertainty in water quality aspects. In this context, the generalised likelihood uncertainty estimation (GLUE) methodology was applied for the evaluation of the uncertainty of an integrated urban drainage model and some of its subjective hypotheses have been explored. More specifically, the influence of the subjective choice of the acceptability threshold has been detected in order to gain insights regarding its effect on the model results. The model has been applied to the Savena case study (Bologna, Italy) where water quality and quantity data were available. The model results show a strong influence of the acceptability threshold selection and confirm the importance of modeller's experience in the application of GLUE uncertainty analysis.     

The management of urban surface water drainage in England and Wales

Partly in response to the UK flooding events of 2007, a number of reports have recently been produced addressing the legislative, administrative, institutional and structural practices that are required to improve urban surface water management and hence reduce future flooding incidents and associated pollution impacts. This paper addresses the principal barriers to progress that have been identified and how these are likely to be overcome. Improved and integrated organisational structures, process and procedures are required and relationships between flood risk management and water quality need to be addressed at regional, area and local levels as well as legislative clarification on surface water discharges. Nontechnical aspects will need to be supported by new modelling approaches for flood risk prediction at both local and catchment scale with effective communication systems and tools being developed and implemented for full and effective stakeholder participation.     

An analytical model for solute mixing in surcharged manholes

A mathematical model has been developed to describe solute mixing in surcharged manholes using the submerged jet theory. The model has been applied for straight-through flow manholes and for manholes with a difference in the level of the inlet and outlet pipes. The model is applicable to dissolved substances, i.e. the model has not been validated for high sediment concentrations (above 1 g/l) and care should be taken in such cases. Simulation results from the new model are compared with laboratory measurements and are further compared to conventional modelling techniques currently available in commercial software specially developed for modelling the water quality in sewers. The results prove that the new model produces considerably better results compared to the traditional assumption of full mixing in a manhole. The new model compares well to the laboratory measurements and hence improves the accuracy of modelling soluble pollutant transport in sewers. The applicability of the new modelling approach is discussed and further studies are recommended.     

Eutrophication research of West Lake,Hangzhou, China: modeling under uncertainty

The models such as the eutrophication ecosystem model of West Lake, Hangzhou (EEM), are always used to make policy decisions for eutrophication management. Thus it is important to know the uncertainty in the model predictions due to the combined effects of uncertainty in the full set of input variables, and the individual input parameters whose variations have the greatest effect on variations in model predictions. In this study, randomized methods based on Monte Carlo technique have been developed and applied to the model (EEM). The technique consists of parameter sensitivity analysis, randomly sampling from underlying probability distributions and multivariate regression analysis. With this technique, model uncertainties during modeling are clarified and their propagation evaluated. Results show that among the five input parameters selected for uncertainty analysis, the settling rate of algae SVS and water temperature TEM have the largest contribution to model prediction uncertainty of the model outputs (PC, PS and PHYT).     

城市地表水体径流污染模拟分析:以苍海湖为例

在我国城市持续推进绿色发展理念的背景下,为科学支撑海绵城市规划编制工作,以梧州市苍海湖为研究实例,结合国内外相关研究经验和属地化的测量参数,应用InfoWorks ICM构建研究区水量水质数学模型。设计旱季和雨季两种模拟情景,分别对苍海湖汇水区内的污染物径流冲刷效应和湖体内污染物迁移扩散规律进行模拟分析,计算不同设计情景下地表污染物随雨水径流进入苍海湖及在湖内扩散的演进过程,并基于计算结果为苍海湖水动力条件改善、湖泊水质保护等提出工程指引建议,以期为水量水质数学模型在海绵城市规划中的应用提供参考。     

Identifying key sources of uncertainty in the modelling of greenhouse gas emissions from wastewater treatment

This study investigates sources of uncertainty in the modelling of greenhouse gas emissions from wastewater treatment, through the use of local and global sensitivity analysis tools, and contributes to an in-depth understanding of wastewater treatment modelling by revealing critical parameters and parameter interactions. One-factor-at-a-time sensitivity analysis is used to screen model parameters and identify those with significant individual effects on three performance indicators: total greenhouse gas emissions, effluent quality and operational cost. Sobol's method enables identification of parameters with significant higher order effects and of particular parameter pairs to which model outputs are sensitive. Use of a variance-based global sensitivity analysis tool to investigate parameter interactions enables identification of important parameters not revealed in one-factor-at-a-time sensitivity analysis. These interaction effects have not been considered in previous studies and thus provide a better understanding wastewater treatment plant model characterisation. It was found that uncertainty in modelled nitrous oxide emissions is the primary contributor to uncertainty in total greenhouse gas emissions, due largely to the interaction effects of three nitrogen conversion modelling parameters. The higher order effects of these parameters are also shown to be a key source of uncertainty in effluent quality.     

Modelling of recharge and pollutant fluxes to urban groundwaters

Urban groundwater resources are of considerable importance to the long-term viability of many cities world-wide, yet prediction of the quantity and quality of recharge is only rarely attempted at anything other than a very basic level. This paper describes the development of UGIf, a simple model written within a GIS, designed to provide estimates of spatially distributed recharge and recharge water quality in unconfined but covered aquifers. The following processes (with their calculation method indicated) are included: runoff and interception (curve number method); evapotranspiration (Penman-Grindley); interflow (empirical index approach); volatilization (Henry's law); sorption (distribution coefficient); and degradation (first order decay). The input data required are: meteorological data, landuse/cover map with event mean concentration attributes, geological maps with hydraulic and geochemical attributes, and topographic and water table elevation data in grid form. Standard outputs include distributions of: surface runoff, infiltration, potential recharge, ground level slope, interflow, actual recharge, pollutant fluxes in surface runoff, travel times of each pollutant through the unsaturated zone, and the pollutant fluxes and concentrations at the water table. The process of validation has commenced with a study of the Triassic Sandstone aquifer underlying Birmingham, UK. UGIf predicts a similar average recharge rate for the aquifer as previous groundwater flow modelling studies, but with significantly more spatial detail: in particular the results indicate that recharge through paved areas may be more important than previously thought. The results also highlight the need for more knowledge/data on the following: runoff estimation; interflow (including the effects of lateral flow and channelling on flow times and therefore chemistry); evapotranspiration in paved areas; the nature of unsaturated zone flow below paved areas; and the role of the pipe network. Although considerably more verification is needed, UGIf shows promise for use: in providing input for regional groundwater solute transport models; in identifying gaps in knowledge and data; in determining which processes are the most important influences on urban groundwater quantity and quality; in evaluating existing recharge models; in planning, for example in investigation of the effects of landuse or climate change; and in assessing groundwater vulnerability.     

Modelling the fate of faecal indicators in a coastal basin

The paper describes a modelling study of near-shore coastal waters, undertaken to assess the impact of various bacterial input loads on the receiving waters in a coastal basin in the UK. Total and faecal coliforms, used as the indicators for bathing water quality under the European Union (EU) Bathing Water Directive, were numerically modelled using a 2D depth integrated hydro-environmental model. Details are given of the governing equations and solution methods used in the numerical model, together with a discussion of the recent development in faecal bacterial indicator modelling. Details are also given of a field data collection exercise, which involved initially collecting existing information on effluent input loads and followed by an intensive field survey. Using the water quality model, the mortality rate of the pathogen bacteria was investigated. Three methods were used to represent the relationship between the decay rate and the level of solar radiation including: a constant decay rate, day- and night-time decay rates and a solar radiation related time varying decay rate. Relatively close agreement between model predicted and measured total and faecal coliform concentration distributions were obtained for different day- and night-time decay rates and time varying decay rates. No significant differences were found in the optimum decay rates for total and faecal coliform levels. Finally, the impact of the individual inputs on the bathing water quality of the basin was also statistically and numerically investigated. Results showed that the River Irvine was the most significant input during high river flows, and that under these conditions the bathing waters were likely to fail to comply with the European Union Bathing Water Directive. For base river flow conditions the Meadowhead effluent input was found to be critical for both total and faecal coliform level predictions.     

Is the future blue-green? A review of the current model predictions of how climate change could affect pelagic freshwater cyanobacteria

There is increasing evidence that recent changes in climate have had an effect on lake phytoplankton communities and it has been suggested that it is likely that Cyanobacteria will increase in relative abundance under the predicted future climate. However, testing such a qualitative prediction is challenging and usually requires some form of numerical computer model. Therefore, the lake modelling literature was reviewed for studies that examined the impact of climate change upon Cyanobacteria. These studies, taken collectively, generally show an increase in relative Cyanobacteria abundance with increasing water temperature, decreased flushing rate and increased nutrient loads. Furthermore, they suggest that whilst the direct effects of climate change on the lakes can change the timing of bloom events and Cyanobacteria abundance, the amount of phytoplankton biomass produced over a year is not enhanced directly by these changes. Also, warmer waters in the spring increased nutrient consumption by the phytoplankton community which in some lakes caused nitrogen limitation later in the year to the advantage of some nitrogen-fixing Cyanobacteria. Finally, it is also possible that an increase in Cyanobacteria dominance of the phytoplankton biomass will lead to poorer energy flow to higher trophic levels due to their relatively poor edibility for zooplankton.     

The impact of new developments on river water quality from an integrated system modelling perspective

New housing areas are a ubiquitous feature of modern life in the developing and developed world alike built in response to rising social, demographic and economic pressures. Inevitably, these new developments will have an impact on the environment around them. Empirical evidence confirms the close relationship between urbanisation and ambient water quality. However, what is lacking so far is a detailed and more generalised analysis of environmental impact at a relatively small scale. The aim of this paper is to quantify the impact of new developments on river water quality within an integrated system modelling perspective. To conduct the impact analyses, an existing integrated urban wastewater model was used to predict water flow and quality in the sewer system, treatment plant and receiving water body. The impact on combined sewer overflow (CSO) discharges, treatment plant effluent, and within the river at various reaches is analysed by ‘locating’ a new development on a semi-hypothetical urban catchment. River water quality is used as feedback to constrain the scale of the new development within different thresholds in compliance with water quality standards. Further, the regional sensitivity analysis (RSA) method is applied to reveal the parameters with the greatest impact on water quality. These analyses will help to inform town planners and water specialists who advise them, how to minimise the impact of such developments given the specific context.