*2.2. 1D*/*2D Coupled Approaches for Urban Pluvial Modelling*

Urban areas have a complex topography and contain small-scale elements such as streets and buildings that are usually not taken into account in standard river floodplain studies [12]. Therefore, a higher resolution is required to represent features at the city scale, although this may lead to larger computational time, notwithstanding the fact that urban model areas are generally smaller than a river floodplain. For all of these reasons, urban, pluvial flooding requires a different modeling approach than the one used for fluvial flooding [12].

During the last two decades, several authors have published papers about the need to develop and use urban stormwater models (USMs) based on coupled approaches (the modeling of the surface and sewer flows at the same time by 1D/1D or 1D/2D models) to represent adequately urban flood caused by surcharged sewers [13–16] and carry out realistic flood risk assessments [17].

Although the choice between using a 1D or a 2D surface overland flow model (to be coupled to a 1D sewer model) determines the accuracy of results and the computational time required to obtain them, when the flow overtops street curbs and does not remain within the street profile, using a 2D model is crucial [12,18].

In 1D/2D USMs, the underground sewer network is represented by a 1D sewer model while the surface flow is computed using a 2D model. The 2D model reproduces the urban surface topography and is essential to achieve a more realistic simulation of the flow spreading across complex urban surfaces, with results such as flow depths and velocities anywhere in the urban model area [12].

USM can be semi-distributed (SD) or fully distributed (FD). SD models, commonly applied in urban stormwater modeling, are based on subcatchment units where rainfall is applied, while runoff is estimated and routed according to specific hydrological losses and rainfall–runoff transformation methods. FD models, which are generally more detailed and theoretically more realistic, are based on the two-dimensional (2D) discretization of the overland surface, where runoff volumes are estimated and directly routed by the 2D overland flow module [19]. Both kinds of approaches can be followed to create 1D/2D coupled models that are able to simulate, at the same time, the behavior of the sewer system and the urban surfaces and their mutual interaction in case of pluvial flooding events (Figure 5). Finally, hybrid models (H) can account for runoff produced by rainfall which is directly applied from subcatchment units formed by building areas (roofs, terraces and courtyards) and directly conveyed into the sewer systems; for the other impervious (streets, sidewalks, squares, etc.) and pervious (parks and natural areas) urban surfaces, the 2D overland flow model computes and routes the runoff produced by the rainfall directly applied to these surfaces [20]. These approaches are represented in Figure 5.

**Figure 5.** Scheme of semi-distributed (SD) (**a**), fully-distributed (FD) (**b**) and hybrid (H) (**c**) 1D/2D coupled urban stormwater model (USM) approaches (adapted from [19]). In brown, subcatchment units are represented, while blue lines and arrows indicate the pathway of the runoff from the source (subcatchment units or discretized 2D surface) to the sewer system.

The amount of runoff entering the underground sewer network is limited by the hydraulic efficiency of surface drainage structures (inlets, transversal grates, etc.) [21–23] and their state of maintenance and clogging [23,24], although these aspects are often neglected in urban drainage models [19]. Generally, SD models apply all the runoff estimated in a given subcatchment directly into the selected computational node of the sewer system, without accounting for the hydraulic capacity of surface drainage capacity. With this assumption, this kind of model only considers the flooding that occurs when the sewer system surcharges and neglects urban floods produced by the

poor capacity of inlet systems [19]. On the contrary, FD modelling packages, such as Infoworks ICM (Integrated Catchment Modeling) software [25], can take into account the hydraulic performance of surface drainage systems connecting network nodes with the 2D overland surface mesh by weirs, orifices and other experimental equations [20,21].
