Modeling rain-driven overland flow: empirical versus analytical friction terms in the shallow water approximation

Modeling and simulating overland flow fed by rainfall is a common issue in watershed surface hydrology. Modelers have to choose among various friction models when defining their simulation framework. The purpose of this work is to compare the simulation quality for the Manning, Darcy-Weisbach, and Poiseuille friction models on the simple case of a constant rain on a thin experimental flume. Results show that the usual friction law of Manning is not suitable for this type of flow. The Poiseuille friction model gave the best results both on the flux at the outlet and the velocity and depth profile along the flume. The Darcy-Weisbach model shows good results for laminar flow. Additional testing should be carried out for turbulent cases.