Shallow water simulation of overland flows in idealised catchments

This paper investigates the relationship between the rainfall and runoff in idealised catchments, either with or without obstacle arrays, using an extensively-validated fully-dynamic 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 S-curve 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.