Methodological approaches for numerical integration of culverts in 2D surface models in urban flood analysis

Urban flood response at road crossings hinges on how short conveyance structures are represented. In our study, each location in the watercourse is not modelled as a bridge per se but alternatively represented as (i) oDEM - a terrain opening that preserves open-channel through-routing; (ii) Culvert - an explicit 1D element transferring flow between inlet and outlet via head-loss formulations; or (iii) Sewer - a short 1D sewer network element (using SWMM) coupled to the surface. As a control, (iv) cDEM enforces overtopping-only exchange to emulate hydraulically ineffective bridge passages. We provide a scenario-controlled, side-by-side benchmark of these four approaches across five sites and three precipitation types (Euler-II 30-year, Euler-II 100-year, and a duration-matched 100-year block event), comparing discharge timing, maximum water depths, flooded area, and end-of-run water balances. Across scenarios, oDEM and Culvert preserve longitudinal connectivity, yielding broader-but-shallower upstream extents and higher boundary outflow, whereas cDEM and Sewer promote upstream storage and compact, deeper ponds. Our contribution is a controlled comparison that clarifies when each representation is fit-for-purpose: for short crossings, the Culvert representation emerges as a practical baseline that captures inlet/outlet losses and pressurised/free-surface transitions, while Sewer may over-retain heads where surface–sewer coupling footprints are restrictive. oDEM and cDEM can be read as bounding models - oDEM as an optimistic high-connectivity envelope, cDEM as a conservative overtopping-only envelope—to bracket plausible responses where calibration data are scarce.