| Abstract: | Overland flows on hillslopes due to rainfall excess are numerically simulated with a simplified strip microtopography which has one single straight rill, and comparisons are made between predictions of a dynamic wave model (DWM) and a kinematic wave model (KWM). Overland flow on the strip is treated as one-dimensional and interrill flow is not simulated. The DWM is based on the Saint-Venant equation, and the KWM is derived using the Chezy formula. A numerical scheme is developed which solves the non-linear DWM equations in a similar way to that of solving the KWM equations, i.e.on the basis of the method of characteristics. This scheme greatly reduces the complexity of the solution procedure and therefore allows the use of DWM in process-based catchment models involving a large number of topographical elements, i.e., hillslopes. Simulation result shows that. in terms of the predicted flow velocity V and depth h, the kinematic.wave model is an accurate approximation to the dynamic one for broad sheet overland flows resulted from normal rainfall excess rates (1-3 mm/min). However. for small rill width, e.g. B<20cm. or if the rainfal excess rate is extremely large (e.g.. 20 mm/min). differences of V and h between the two models will be significant. In general, the KWM tends to underestimate rill flow depth but overestimate its velocity, especially for small rill width. though it does give the same steady discharge per unit width, q =V h, as that predicted by DWM for steady rainfall excess rate. At the rising stage of the hydrograph, KWM predicts higher unit width discharge q, which leads to overestimation of rill detachment as a stream power function method is used. |
