This paper presents a numerical model suitable for a broad range of surface flow problems such as overland flow, wetting and drying processes, varying flow conditions and shock waves. It is based on solution of two-dimensional fully dynamic shallow water equations using a cell-centred finite-volume method. Numerical fluxes are computed with a Harten, Lax and van Leer approximate Riemann solver with a contact wave restored. The scheme is second-order accurate in space, and a total variation diminishing method is used to avoid spurious oscillations in the solution. For extending the model to rainfall-runoff applications, infiltration is considered as a constant runoff coefficient and by the Green-Ampt model. The model is implemented in the Hydroinformatics Modelling System, an object-oriented framework that enables the implementation and simulation of single and multiple processes in different spatial and temporal resolutions, as well as their interactions. The capabilities of the model are shown by comparison with analytical solutions and experimental data of a flash flood and a surface runoff experiment. Finally, a real rainfall-runoff event in a small alpine catchment is investigated. Overall, good agreement of numerical and analytical results, as well as measurements, has been obtained. A area of the considered cell m 2 À Á C Chézy coefficient s m À1=6 À Á c concentration (À) D diffusion coefficient m 2 s À1 À Á d water depth (m) ε vegetation drag related coefficient η water elevation above datum: η ¼ z B þ d (m) f flux vector g standard gravity 9:81 m s À2 À Á Γ boundary of control volume (m) I cumulative infiltration (m) i infiltration rate m s À1 À Á K average residence time (s) k index of a face of the considered cell l k length of face k (m) m c contaminant source/sink term s À1 À Á m w water source/sink term m s À1 À Á n k normal vector pointing outwards of face k n Manning coefficient (s m À1=3 ) n time step index ∇ del operator: ∇ ¼ @ @x , @ @y T ν t turbulent kinematic viscosity m 2 s À1 À Á Ψ runoff coefficient (-) Q discharge m 3 s À1 À Á q vector of conserved flow variables r rainfall intensity m s À1 À Á ρ density of water kg m À3 À Á S storage (m 3 ) s source vector t time (s) Δt time step (s) u velocity component in x-direction m s À1 À Á v velocity component in y-direction m s À1 À Á v velocity vector V w specific soil water volume (m) x X coordinate (m) y Y coordinate (m) z B bottom elevation above datum (m) Ω control volume (m 2 )

Hinkelmann, R. (2016). Urban flood modeling using shallow water equations with depth-dependent anisotropic porosity. Journal of Hydrology, 541, 1165Hydrology, 541, -1184Hydrology, 541, . https://doi.org/10.1016Hydrology, 541, /j.jhydrol.2016 Özgen, I.; Zhao, J.; Liang, D.; Hinkelmann, R.Urban flood modeling using shallow water equations with depth-dependent anisotropic porosity The shallow water model with anisotropic porosity conceptually takes into account the unresolved subgrid-scale features, e.g. microtopography or buildings. This enables computationally efficient simulations that can be run on coarser grids, whereas reasonable accuracy is maintained via the introduction of porosity. This article presents a novel numerical model for the depth-averaged equations with anisotropic porosity. The porosity is calculated using the probability mass function of the subgrid-scale features in each cell and updated in each time step. The model is tested in a one-dimensional theoretical benchmark before being evaluated against measurements and high-resolution predictions in three case studies: a dam-break over a triangular bottom sill, a dam-break through an idealized city and a rainfall-runoff event in an idealized urban catchment. The physical processes could be approximated relatively well with the anisotropic porosity shallow water model. The computational resolution influences the porosities calculated at the cell edges and therefore has a large influence on the quality of the solution. The computational time decreased significantly, on average three orders of magnitude, in comparison to the classical high-resolution shallow water model simulation.

This paper derives a novel formulation of the depth-averaged shallow water equations with anisotropic porosity for computational efficiency reasons. The aim is to run simulations on coarser grids while maintaining an acceptable accuracy through the introduction of porosity terms, which account for subgrid-scale effects. The porosity is divided into volumetric and areal porosities, which are assigned to the cell volume and the cell edges, respectively. The former represents the volume in the cell available to flow and the latter represents the area available to flow over an edge, hence introducing anisotropy. The porosity terms are variable in time in dependence of the water elevation in the cell and the cumulative distribution function of the unresolved bottom elevation. The main novelty of the equations is the formulation of the porosities which enables full inundation of the cell. The applicability of the equations is verified in five computational examples, dealing with dam break and rainfall-runoff simulations. Overall, good agreement between the model results and a high-resolution reference simulation has been achieved. The computational time decreased significantly: on average three orders of magnitude.

This paper investigates the relationship between the rainfall and runoff in idealised catchments, either with or without obstacle arrays, using an extensively-validated fullydynamic shallow water model. This two-dimensional hydrodynamic model allows a direct transformation of the spatially distributed rainfall into the flow hydrograph at the catchment outlet. The model was first verified by reproducing the analytical and experimental results in both one-dimensional and two-dimensional situations. Then, dimensional analyses were exploited in deriving the dimensionless S-curve, which is able to generically depict the relationship between the rainfall and runoff. For a frictionless plane catchment, with or without an obstacle array, the dimensionless Scurve seems to be insensitive to the rainfall intensity, catchment area and slope, especially in the early steep-rising section of the curve. Finally, the model was used to study the hydrological response of an idealised catchment covered with buildings, which were represented as an obstacle array. The influences of the building array size and layout on the catchment response were presented in terms of the dimensionless time at which the catchment outflow reaches 50% of the equilibrium value.

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