An urban drainage stormwater quality model: Model development and uncertainty quantification

Summary

The evaluation of urban stormwater quality is of relevant importance for urban drainage, and mathematical models may be of great interest in this respect. To date, several detailed mathematical models are available to predict stormwater quantity–quality characteristics in urban drainage systems. However, only a few models take sewer sediments into account, considering their cohesive-like properties that influence the build-up process of the pollutant load. Furthermore, the model data requirements, especially for the quality aspects, are extensive, which limit their applicability and affect model results with large uncertainty. Uncertainty analysis provides a measure or index regarding the significance and the accuracy of the results obtained by mathematical modelling and is therefore of high interest. Nevertheless, only few studies have been carried out in the urban drainage field, and very few deal with water quality issues. One of the main reasons for this lack of research is the computational burden required by detailed models that preserve this analysis and generally require several Monte Carlo simulation runs. A possible to this problem may be the adoption of simplified parsimonious models that generally require shorter computational times. In this context, this paper presents a parsimonious conceptual model for the evaluation of the pollutant load in-sewers. The model contains two modules: a hydrological and hydraulic module that calculates the hydrographs at the inlet and at the outlet of the sewer system, and a solid transfer module that calculates the pollutographs. The cohesive properties of sewer sediments were carefully considered. Further, the effectiveness of the innovative sewer sediment modelling approach has been verified by taking into account the uncertainty assessed according to the GLUE methodology. The model has been tested using experimental quantity–quality data gathered in two Italian catchments, Fossolo (Bologna) and Parco d’Orlèans (Palermo).

Introduction

Several studies since the 1960s have shown that the contribution of stormwater pollutants must be considered in order to correctly implement an environmental preservation method for a receiving water body (Sartor et al., 1974, Novotny et al., 1985). The management of urban stormwater pollution represents a big task due to the extreme spatial–temporal variability of the stormwater quality–quantity characteristics and the high uncertainty in their evaluation (Beck, 1987, Willems, 2000, Willems, 2004, Ashley et al., 2005).

During the last decade, the importance of sediment control and the management of sewer systems have gained attention. The presence of sediment deposits in combined sewer collectors has been recognised as one of the main causes of hydraulic and environmental problems, such as the reduction of the design flow capacity and first flush pollution (Ashley et al., 1994, Arthur and Ashley, 1998, Butler et al., 2003). The erosion of deposited in-pipe sediments discharged from overflows during storm events have been attributed as the main pollutant sources (up to 80% of the pollutant loads) (Ahyerre and Chebbo, 2002, Ashley et al., 1992). These observations emphasise the desirability of having the ability to control in-sewer sedimentation processes as a method for reducing the subsequent pollutant releases from combined sewer systems (Banasiak et al., 2005). For this to be possible, proper design relationships that can reliably predict sedimentation zones and subsequent erosion rates need to be formulated (Banasiak et al., 2005). However, most commercial sewer flow quality models currently available typically use simple approaches (Zug et al., 1998, Bouteligier et al., 2002a, Bouteligier et al., 2002b). Furthermore, very few of those models deal in any way with in-sewer deposition and erosion (Bouteligier et al., 2002a, Bouteligier et al., 2002b, Banasiak et al., 2005). Indeed, as pointed out by Bouteligier et al., 2002a, Bouteligier et al., 2002b, sediment transport equations that are applied in commercial modelling software packages such as Storm Water Management Model (SWMM, Huber, 2001) or HydroWorks/InfoWorks CS (Wallingford Software Ltd., 1995) are based on sediment transport equations that were developed for open channel flow (e.g., natural rivers) and non-cohesive sediment particles, while assuming steady uniform flow. Some commercial models such as MOSQITO (Bertand-Krajewski et al., 1993) or MouseTrap/Mike Urban (Crabtree et al., 1995) take sewer sediment cohesion into account in an indirect way. For example, to take sewer sediment cohesion into account, MOSQITO considers deposits separated in two layers: an upper one, composed of non-cohesive easily eroded sediments, with a significant organic matter fraction, and a lower layer, composed of consolidated deposits with a significant mineral fraction. When the whole active layer is eroded, portions of the storage layer are allowed to pass into the active layer if the flow shear stress is greater than a critical value. MouseTrap/Mike Urban represents the cohesion properties of the sewer sediments in a different manner. The thresholds for the onset of erosion are taken to be the values of applied shear stress at which the sediment types have been observed to erode (Crabtree et al., 1995). Current modelling approaches ignore physical processes such as consolidation and generally do not consider any chemical and biological processes. As pointed out by Banasiak et al. (2005), the improvement of knowledge related to sewer processes, such as deposition in dry weather, followed by erosion and transport in storm events, will address key weaknesses of current sewer modelling and is essential for better management of sewer sediments (Ashley et al., 2000). The aforementioned oversimplification and lack of model interaction between hydraulic regimes and deposited and eroding sediments have led to poor simulation of sediment transport rates and, as a consequence, low end-user confidence characterised by high uncertainty (Jack et al., 1996, Margetts, 2000, Skipworth et al., 2000). Indeed, one of the areas in-sewer solids research that needs more attention was identified by Ashley et al. (2005), as the estimation of uncertainty in model results (Schellart et al., 2008). A measure or index regarding the significance as well as the accuracy of the results obtained by mathematical modelling is necessary. In this regard, uncertainty analysis can provide useful hints as well as information regarding the best model approach to be used with respect to its significance and degree of reliability. Furthermore, the evaluation of parameter uncertainties is necessary to estimate their impact on model performance and for their calibration (Beck, 1987). More specifically, uncertainty and sensitivity analysis can offer valid tools for characterising the uncertainty associated with a model. In any case, sensitivity analysis may aid in understanding the contribution of the various sources of uncertainty to the model output uncertainty and system performance, in general. Thus, uncertainty is a measure of the ‘goodness’ of a result; without such a measure, it is difficult to judge the fitness of the value as a basis for making decisions related to scientific excellence. The uncertainty of a model can be stated by giving a range (or a band) of values that are likely to bracket the true value of a specific simulated variable: lower uncertainty is connected with stricter uncertainty bands; larger bands are caused by high uncertainty models.

Despite the relevance of uncertainty analysis, only few studies have been carried out in the urban drainage field, and very few deal with water quality issues (among others, Gaume et al., 1998, Willems, 2000, Willems, 2008, Kanso et al., 2005, Mannina, 2005, Korving and Clemens, 2005, Mannina et al., 2006, Lindblom et al., 2007, Refsgaard et al., 2007, Schellart et al., 2008, Thorndahl et al., 2008, Thorndahl and Willems, 2008). The main reasons that prevent the application of uncertainty analysis by means of detailed models are:

• Computational burden required to solve the model algorithms that may be prohibitive for carrying out long-term simulations of the entire system. More specifically, the bottle-neck from the computational point of view is the hydraulic equations, which describe flow propagation in-sewer pipes, i.e., the Saint–Venant equations (Meirlaen et al., 2002). Because such equations are non-linear partial differential equations, the solutions are often time consuming. These equations require complex numerical algorithms to solve, making the models slow and thus difficult to use for optimisation studies.

• Limited knowledge about the system geometry (pipe dimensions, junctions, etc.).

• Lack of distributed field data for the whole catchment. Indeed, generally concentrations at the catchment’s outlet are available. This fact leads to identifiability issues (Freni et al., 2009a, Freni et al., 2009b) that hamper a reliable assessment of model parameters. Due to limited field data, the modeller is generally forced to use the same values of model parameters for the whole catchment. As a matter of a fact, the modeller generally neglects possible variations in model parameters with respect to catchment location.

• Limited information about sewer sediment in terms of both composition and height in the pipes.

As already drawn by other authors (among others Willems, 2000, Willems, 2008, Willems, 2009, Meirlaen et al., 2002, Willems and Berlamont, 2002, Mannina and Viviani, 2010), a possible solution may be adoption of parsimonious models (i.e., the simplest approach that fits the purpose of the application (Harremoës and Madsen, 1999)) that generally require shorter computational times. Parsimonious models that provide a lower level of parameterization, a low degree of auto-correlation between parameters and possible compensation effects among parameters are required (Beck, 1999, Willems, 2008, Willems, 2006, Kanso et al., 2005, Bertrand-Krajewski, 2007).

In this context, a mathematical model for the assessment of pollutant loads during storm events is presented. The objectives were: (i) to set up a useful tool to effectively simulate the quantity and quality phenomena that play a central role in the generation of the pollutants, focusing on sewer sediments modelling; (ii) to perform a preliminary sensitivity analysis aimed at identifying the most sensitive model parameters to be calibrated; (iii) to calibrate such a model on the basis of field data; (iv) to perform a Monte Carlo simulation to estimate model uncertainty by means of the Generalised Likelihood Uncertainty Estimator (GLUE) methodology (Beven and Binley, 1992a, Beven and Binley, 1992b). The model takes into account the sewer sediment cohesive-like properties, while trying to overcome the inappropriate transport rate relationships, characteristic of most current models developed mainly in fluvial environments (Englund and Hansen, 1967, Ackers and White, 1973, Van Rijn, 1984). Indeed, current methods assume that in-sewer sediments are granular and that particle characteristics are inorganic and uniform in nature (Banasiak et al., 2005). These models, therefore, neglect several important aspects in the in-sewer sediment cycle. Concerning the uncertainty analysis, the GLUE method has been extensively used for simultaneous calibration and uncertainty assessment, especially for hydrologic models (Lamb et al., 1998, Freer et al., 2004, McMichael et al., 2006, Xionga and O’Connor, 2008). However, the GLUE methodology has, as far as the authors know, rarely been applied for the uncertainty assessment of sewer sediment modelling. The GLUE, compared to other methods, is easy to implement and allows a flexible definition of the so-called likelihood function used to separate behavioural and non-behavioural solutions. The likelihood function can include several variables, a feature that is particularly valuable for assessment of integrated, distributed models that operate with multi-variable, multi-site and multi-response criteria.

The model aims to be as accurate and reliable as possible while at the same time requiring a limited number of parameters for its implementation. The goal is to create a reliable tool for the estimation of the water quality characteristics during a storm event in order to prevent the detrimental Combined Sewer Overflow (CSO) discharges from affecting the receiving water body.