Uncertainty-based calibration and prediction with a stormwater surface accumulation-washoff model based on coverage of sampled Zn, Cu, Pb and Cd field data

Abstract

A dynamic conceptual and lumped accumulation wash-off model (SEWSYS) is uncertainty-calibrated with Zn, Cu, Pb and Cd field data from an intensive, detailed monitoring campaign. We use the generalized linear uncertainty estimation (GLUE) technique in combination with the Metropolis algorithm, which allows identifying a range of behavioral model parameter sets. The small catchment size and nearness of the rain gauge justified excluding the hydrological model parameters from the uncertainty assessment. Uniform, closed prior distributions were heuristically specified for the dry and wet removal parameters, which allowed using an open not specified uniform prior for the dry deposition parameter. We used an exponential likelihood function based on the sum of squared errors between observed and simulated event masses and adjusted a scaling factor to cover 95% of the observations within the empirical 95% model prediction bounds. A positive correlation between the dry deposition and the dry (wind) removal rates was revealed as well as a negative correlation between the wet removal (wash-off) rate and the ratio between the dry deposition and wind removal rates, which determines the maximum pool of accumulated metal available on the conceptual catchment surface. Forward Monte Carlo analysis based on the posterior parameter sets covered 95% of the observed event mean concentrations, and 95% prediction quantiles for site mean concentrations were estimated to 470 μg/l ±20% for Zn, 295 μg/l ±40% for Cu, 20 μg/l ±80% for Pb and 0.6 μg/l ±35% for Cd. This uncertainty-based calibration procedure adequately describes the prediction uncertainty conditioned on the used model and data, but seasonal and site-to-site variation is not considered, i.e. predicting metal concentrations in stormwater runoff from gauged as well as ungauged catchments with the SEWSYS model is generally more uncertain than the indicated numbers.

Introduction

Heavy metal pollution originating from stormwater runoff from paved surfaces is among the most significant sources to poor environmental quality of urban water courses (e.g. Christensen et al., 2006, Eriksson et al., 2007, Karlaviciene et al., 2009, Kayhanian et al., 2008). Heavy metals are of particular interest in stormwater runoff due to their toxicity, ubiquitous feature, and the fact that metals cannot be biologically transformed. Monitoring generally reveals high variability of metal concentrations from site to site, from event to event and within events, due to the multitude of diffuse urban sources of metal pollution (Lützhøft et al., 2009, Chon et al., 2010) and the complexity of the processes leading to accumulation on urban surfaces as well as release and transport during rainfall-runoff (Bertrand-Krawjewski, 2007). This makes it difficult to model and thus to predict heavy metal concentrations and loads accurately, which is needed as part of the efforts to limit urban emissions of heavy metals to surface waters as required by the European Water Framework Directive (European Union, 2000, European Union, 2008).

Several conceptual computer models have been developed for analysing water quality problems related to stormwater runoff (e.g. Achleitner and Rauch, 2005, Calabro, 2001; Obropta and Kardos, 2007, Ruan, 1999, Wong et al., 2002). If appropriately applied, these constitute tools for enhancing further understanding, for predicting flow and water quality in urban drainage systems and receiving waters and thereby for decision support in relation to implementation of monitoring programmes or pollution mitigation strategies. Past applications of such models have however focused on macro pollutants such as nutrients and organic matter characterised as COD or BOD, and only very few have focused on heavy metals and other priority substances.

In a conceptual model the mechanistic details are simplified by considering empirical relationships. Thus, the parameters of a conceptual model need to be adjusted by comparing simulations with measured data, i.e. a calibration of the model has to be performed. As pointed out by e.g. Freer et al. (1996), the gain of finding solely one "optimally calibrated" solution is limited, because there will be many others that are almost equally good and if a second period of data is considered, then the rankings of these will change and the best solutions found for the first period will not be the best for the second. Parameter estimates are thus associated with uncertainty, which will influence the predictive ability of the model; this is true for many environmental systems in which observations to support model calibration often are relatively sparse, and in particular to the case of urban stormwater runoff quality where the dynamics exceed those of most other environmental systems.

Early work on uncertainty in relation to urban drainage modelling was based on simple first order analysis or forward Monte Carlo simulation based on assumed uncertainties in input and parameters (e.g. Arnbjerg-Nielsen and Harremoës, 1996, Daebel and Gujer, 2005, Hansen et al., 2005, Harremoës et al., 2005, Lei and Schilling, 1996). Currently, literature tends to concentrate on general water quality parameters (TSS, organic matter, nutrients) where large uncertainties exist (e.g. Willems, 2006) and methods to condition model predictions on observed data are being applied and evaluated (e.g. Dotto et al., 2010, Dotto et al., 2011, Freni et al., 2008, Freni et al., 2009, Freni and Mannina, 2010, Kleidorfer et al., 2009, Thorndahl et al., 2008), however mostly without explicitly quantifying the uncertainty in relation to how well the model predictions are able to cover the available observations.

The objective of the current work is to analyse the uncertainty related with model predictions of heavy metal loads in stormwater runoff, which is considered more uncertain than modelling of general water quality parameters. The results are derived conditional on (i) a pre-defined dynamic conceptual stormwater rainfall-runoff accumulation-washoff model, (ii) a fixed set of results from a field sampling campaign, and (iii) a desire to cover 95% of the observations with the 95% empirical prediction bounds. The applied model is a re-formulation of SEWSYS^® that was developed for simulation of water flow and quality in urban drainage systems (Ahlman and Svensson, 2002). The experimental data include monitored rain intensities and stormwater flow as well as intra-event flow-proportional concentration measurements of copper (Cu), zinc (Zn), lead (Pb) and cadmium (Cd). The uncertainty was assessed for predictions of the event mean concentrations (EMCs) and the site mean concentrations (SMCs), as these are important variables in determining the total pollutant load from the area, as well as for communicating the results and comparing them with other studies.