Development and Application of a Finite Element Distributed Rainfall Runoff Simulation Model

A deterministic model to simulate rainfall runoff from pervious and impervious surfaces is presented. With precipitation excess as input, the surface runoff model is based on a one-dimensional, variable width, kinematic wave approximation to the St Venanfs equation and Manning's equation, and was used to mathematically route overland and channel flow using the finite element method. The Galerkin's residual finite element formulation utilizing linear and quadratic one-dimensional Lagrangian elements is presented for the spatial discretization of the nonlinear kinematic runoff equations. Temporal excess rainfall discretization using linear transition over two time steps was used to eliminate abrupt discontinuities in excess rainfall intensities. The system of nonlinear equations was solved using successive substitutions employing Thomas algorithm and Gaussian elimination. The whole formulation was set up using the MapBasic and Map Info Geographical Information System. A laboratory rainfall runoff physical model was set up for observation data in order to test the numerical model. Parameters considered include, surface roughness, plane slope, constant or changing rainfall intensities. Maximum infiltration, overland flow discharge, and overland with channel flow discharge were observed for model verification. Finite element simulations have been shown to compare favourably with observed laboratory data. Linear element simulation was found to give results as accurate as the quadratic element simulation. The increased number of elements employed in the model to simulate runoff from a homogenous surface did not give any obvious added advantage. While maximum time step increment for computation is given by the Courant Criterion, it is however, always recommended that as small a time increment is to be used to eliminate any oscillatory instability. Time increment for channel flow routing was found to be always smaller when compared to lateral overland flow. Thus, the chosen time step increment for channel flow routing must be a common factor of that of lateral overland flow in order to satisfy the linear interpolation of overland outflow hydrograph as input into the channel. For laboratory scale catchments, problems of big physical elemental interface roughness differences (eg. 0.033 for bare soil surface upstream and 0.300 for grass surface downstream) can result in small wavy oscillatory at the rising limb. On the contrary, when the upstream roughness is larger then the downstream toughness, such discrepancies do not appear in the simulation. Differences in elemental interface slope (eg. 5% and 10% bare soil surfaces) can be catered for rather well in the model. A hypothetical watershed and imaginary tropical rainstorm was also studied to verify the capability of the model in larger runoff catchments. Channels, which are initially dry or with existing flows can be simulated incorporating additional rainfall. Large catchments with large physical elemental roughness and slope differences can be well simulated by the model to give typical hydrograph characteristics, without oscillations, evident in laboratory scale tests.

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