**2. Current Practice in Stormwater Quality Modelling and Its Deficiencies**

At a generic level, current stormwater models consist of two modules that operate simultaneously (see Figure 1). The rainfall-runoff module generates information about runoff during a rainfall event. The runoff quality module generates information about pollutant accumulation (build-up) on catchment surfaces during the dry weather period and subsequent wash-off via stormwater runoff [33].

The current stormwater models have been built based on either physically-based (mechanistic) or statistical (or hybrid) modelling approaches. Both approaches have strengths and deficiencies and the resulting models are likely to generate information on stormwater quantity and quality that may not be sufficiently reliable. Hence, there is no stand-alone model that can accurately replicate the entire process of stormwater pollution. For example, commonly used Stormwater Management Model (SWMM) [34,35] and Model for Urban Stormwater Improvement Conceptualisation (MUSIC) [36,37] are appropriate for planning and management decision making, but lack mathematical

formulations of complex interactions between pollutants that are accounted for in Hydrologic Simulation Program-Fortran (HSPF) [38] model. Further, only a few models such as Mike URBAN [39,40] and HSPF are capable of accounting for the processes of both, dissolved and particulate pollutants. The capabilities and limitations of different modeling tools are detailed in Table 1.

**Table 1.** Capabilities and limitations of commonly used stormwater quality modelling tools (adapted from Wijesiri [41]).


**Figure 1.** Schematic of the generic structure of current stormwater models (major deficiencies identified are in red text).

In particular, stormwater quality predictions involve various types of uncertainty (due to model structure, data, and parameters) because considerably fewer improvements have been made to the stormwater quality module, compared to the improvements made to the rainfall-runoff (quantity) module. This lack of advancement in stormwater quality modelling is because greater attention has been paid to the mitigation of stormwater quantity-related adverse impacts (e.g., flooding) rather than to improving stormwater quality for reuse [48].

The mathematical formulations included in the runoff quality module are adversely affected by the effects of climate change because the patterns of pollutant build-up and wash-off could change in response to changes in dry and wet weather periods. Therefore, the current mathematical formulations of pollutant build-up and wash-off need enhancements in order to take into consideration the effects of climate change.

Improvements to current mathematical formulations should first consider temporal and spatial patterns of pollutant build-up and wash-off under dry and wet weather conditions influenced by the regional effects of climate change. For example, several regions around the world are projected to experience longer dry periods and more frequent short duration intense rainfall, which have already become evident over the past decade [17]. Under these weather conditions, typical patterns of pollutant build-up (e.g., asymptotic increase towards an equilibrium at around 7–9 antecedent dry days) and wash-off (exponential decay) [49,50] could change as depicted in Figure 2. The pollutant load accumulated is expected to remain at the equilibrium level over a longer period of time (blue line in Figure 2) than typical dry weather events (red line in Figure 2). Consequently, the expected changes to wet weather could result in wash-off of a large amount of accumulated pollutants over a shorter period of time (blue line in Figure 2) than relatively slower wash-off that could occur during typical

rainfall events (red line in Figure 2). As such, while typical rainfall events would wash-off only a fraction of accumulated pollutants, the rainfall events influenced by climate change could wash-off almost all the accumulated pollutants from catchment surfaces. Further, lesser known effects such as first-flush phenomenon (wash-off of shock loads of pollutants at the initial portion of a rainfall event, see Figure 3) would play a greater role in influencing the quality of stormwater runoff at the catchment outlet.

**Figure 2.** Pollutant behaviour during build-up and wash-off in response to impacts of climate change (X-axis not to scale).

**Figure 3.** Hypothetical depiction of first-flush. Note: The Mass-Volume (M-V) curves show the relationship between dimensionless M and V at a given point in time (t). As such, first flush occurs when the M-V curve lies above the line of unity. M-V curve 1 shows first-flush during a typical rainfall event, while M-V curve 2 shows first flush during a rainfall event affected by climate change (adapted from Perera et al. [51]).
