Simulation of the distributed rainfall-runoff process

Abstract

A deterministic model to simulate rainfall runoff from pervious and impervious surfaces is presented. The surface runoff model is based on an established one-dimensional, variable width, kinematics wave approximation to the Saint Venant equations and Manning equation, 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 delimitation of the nonlinear kinematics runoff equations. 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 MapInfo Geographical Information System. A laboratory rainfall runoff physical model was set up to test the numerical model. Parameters considered include, surface roughness, plane slope, constant or changing rainfall intensities. Linear element simulation was found to give results as accurate as the quadratic element simulation. Increasing the number of elements to simulate runoff from a homogenous surface did not give any added advantage. Whilst the Courant Criterion gives maximum time step increment for computation, it is however recommended that as small a time increment 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, smaller upstream plane and larger downstream plane roughness, 0.033 for bare soil surface upstream and 0.300 for grass surface downstream, respectively, can result in small oscillatory disturbances at the rising limb. Such discrepancy does not occur when upstream roughness is larger then downstream roughness. Differences in elemental interface slope can be catered for rather well in the model. A hypothetical watershed and imaginary tropical rainstorm was also studied to verify the stability 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, without oscillations that are evident in laboratory scale tests.