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.

中文翻译：

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沿覆盖有斑驳植被的山坡的浅层地表径流的阻力公式

描述表面粗糙度对流阻的影响仍然是使用Saint Venant方程（SVE）模拟浅层陆上流的首要挑战。这一挑战导致粗糙方案的泛滥，使均匀粗糙表面的特性与整体速度和阻力相关，这使得选择合适的粗糙方案变得艰巨，尤其是在异质表面上。对于水文预测，如果所得的SVE解决方案预测结果，例如径流和入渗之间的水平衡分配，山坡水文图和排放速度的不确定性小于或等于测量的不确定性，则适合采用粗糙度方案。为了评估水文预测对粗糙度方案选择的敏感性，首先在平衡流条件下将多个方案相互校准，同时在出口处施加运动波近似值。当应用于相同的坡度和流量时，此方法可得出不同粗糙度方案的参数之间的分析关系。该方法用于为一个公共表面提供五个常用粗糙度方案的参数化，并比较了多个斑驳植被山坡方案的预测。结果表明，一旦校准，在宽范围的降雨条件下，对粗糙度方案的选择的预测敏感性就很小。在操作上，结果表明，与采用的精确公式相比，参数化粗糙度方案对于预测水文模式具有更高的意义。