Model and scenarios

To model the system we used the Stormwater Management Model 5.0 (SWMM), one of the most used models in urban hydrology. The catchment is described as a set of homogeneous subcatchments, each of them modeled as a rectangular plan defined by a slope, a roughness, an area and a characteristic length (non-linear reservoir, kinematic wave; Singh, 1988), while flow-routing in the sewer system is modeled by shallow water equations (Rossmann, 2004).

This model structure involves a large set of parameters: each subcatchment is defined by characteristics of the surface (area A; imperviousness; initial losses; infiltration parameters) and of the water flow (length of the flowpath L, expressed in the model by width W: A=WxL;

slope; Manning’s coefficient); the sewer system is defined by its geometry (assumed to be known) and Manning’s coefficient. Concerning water quality, build-up and wash-off are both

9 modeled with an exponential formula (Rossmann, 2004). Each of the two processes is thus defined by two parameters per subcatchment (one coefficient and one exponent):





C

Buildup  ₁1 ^{ 2} (Equation 1)

With C₁ (kg/ha) representing the maximum buildup and C₂ (day^-1) being the time exponent.

Buildup Q

C

Washoff  ₃ ^C4 (Equation 2)

With C₃ (-) and C₄ (-) being the two wash-off parameters.

In this study, we treat sequentially water quantity and quality: in the modeling scenarios, at first the parameters pertaining to water quantity are determined, either by geographical information (GIS data) or by automatic calibration on flow-rate data. As a second step, water quality parameters are determined for the models already calibrated and validated for water quantity.

2.2.1 Water quantity scenarios

For a given model structure, an increase in the use of geographical information reduces the number of undetermined parameters requiring calibration on hydrological data. However, to include supplementary GIS data in the model, it can be necessary to increase the detail in model structure, thus increasing the number of undetermined parameters.

The different scenarios considered, ranked by increasing use of geographical information, are:

- S1: The catchment is divided in 19 homogeneous subcatchments. Their areas are known but not their imperviousness. Therefore, for each of them, widths, impervious cover and other physical parameters are undetermined.

- S2: The same as S1 but GIS data are used to estimate the impervious cover of each subcatchment.

- S3: Each “real” subcatchment is modelled as five different “model” subcatchments called Homogeneous Units (HU) depending on the nature of land cover (Petrucci et al., 2013): roofs, roofs non-connected to the sewer network, green areas, roads and

10 others. The area of each HU is calculated using GIS data. Impervious cover is fixed to 100% for roads and roofs, to 0% for green areas, and undetermined for others.

- S4: The same as S3 but the length of the surface flow path for each HU is evaluated using GIS data. For example, flow path on roads is deduced from the calculation of the mean flow path length on each HU at the scale of each subcatchment. The same approach is applied to roofs where a mean flow path length equal to 7 m is taken.

While the length depends on the type of HU, the slope of each HU remains equal to the topographical average slope of the subcatchment.

- S5: The same as S4 but with slopes calculated independently for each HU.

- S6: The same as S5 but with an explicit modelling of flow in the non represented part of the sewer network (i.e. the small collectors internal to subcatchments, linking the surfaces to the main collectors). With this purpose, a wide conduit is added between the outlet of each subcatchment and the sewer network. The length of each added conduit is estimated as the mean length of the flow path in the non-represented part of the sewer network.

In summary, there is a simple increase in geographical data passing from S1 to S2 and from S3 to S4 and to S5, while there is an increase in geographical data combined with an increase in the complexity of the model structure passing from S2 to S3 and from S5 to S6. Table 1 summarizes the calibration parameters for each scenario and the main increase in

geographical data as compared with the preceding scenario.

Table 1 - Undetermined parameters for each scenario. The last line summarizes the increase of geographical data distinguishing each scenario from the preceding one.

2.2.2 Water quality scenarios

Scenarios for water quality combine one scenario for water quantity and one scenario for water quality. Scenarios for water quality are noted Q1, Q2, Q3, Q4, Q5.

From Q1 to Q5, scenarios integrate increasing undetermined parameters as they integrate increasing variability of build up and wash off at the catchment scale:

- Q1: Build up and wash off on the catchment are modeled uniformly at the scale of the catchment with one single set of parameters.

11 - Q2: Build up and wash off only depend on land use. As three main land uses were

identified for water quantity, these are kept for water quality: green areas, roofs and roads. “Other areas” are considered as 50% roads and 50% green areas.

- Q3: Maximum build up depends on the location in the catchment: the C1 parameter is calibrated independently for each subcatchment, while C2, C3 and C4 have a unique value for the whole catchment.

- Q3: Build up and wash off completely depend on the location in the catchment. One set of 4 parameters is assigned to each subcatchment and calibrated independently.

- Q4: This scenario integrates the highest variability as water quality parameters are independently defined for each HU.

The combination between water quantity and quality scenarios are noted S_xQ_y where x and y are the indices of the quantitative and qualitative scenarios.

Table 2 – Water quality scenarios. Explanation of the symbols: “x” denotes a scenario actually considered, while “–” denotes a scenario not considered. For S1 and S2, for which land uses are not defined, Q2 and Q5 are not feasible; Q5 is applied only for two cases (S3, S4) because, as explained in section 3.2.1, a complete testing appeared unnecessary.