Resistance Formulations in Shallow Overland Flow Along a Hillslope Covered With Patchy Vegetation

Describing the effects of surface roughness on flow resistance remains a first-order challenge for modeling shallow overland flow using the Saint Venant equations (SVE). This challenge has resulted in a proliferation of roughness schemes relating the properties of a uniform rough surface to bulk velocity and resistance, making selection of an appropriate roughness scheme daunting-especially on heterogeneous surfaces. For hydrological predictions, a roughness scheme is appropriate if the resulting SVE solutions predict outcomes such as water balance partitioning between runoff and infiltration, the hillslope hydrograph, and the discharge velocity with uncertainties that are less than or comparable to uncertainty in measurements. To assess the sensitivity of hydrological predictions to the choice of a roughness scheme, multiple schemes are first calibrated to each other under equilibrium flow conditions while imposing the kinematic wave approximation at the outlet. This approach yields analytical relations between the parameters of different roughness schemes when applied to the same hillslope and discharge. The approach is used to provide a parameterization of five commonly used roughness schemes for a common surface, and the predictions of the schemes for multiple patchily vegetated hillslopes are compared. The results suggest that, once calibrated, there is minimal prediction sensitivity to the choice of roughness scheme across a wide range of rainfall conditions. Operationally, the results demonstrate that parameterizing a roughness schemes is of higher significance for predicting hydrological patterns than the precise formulation employed.