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Analytical Solutions To Runoff On Hillslopes With Curvature: Numerical And Laboratory Verification
Hydrological Processes ( IF 2.8 ) Pub Date : 2020-09-20 , DOI: 10.1002/hyp.13879
Dana Ariel Lapides 1 , Cy David 1 , Anneliese Sytsma 2 , David Dralle 3 , Sally Thompson 4, 5
Affiliation  

Predicting the behavior of overland flow with analytical solutions to the kinematic wave equation is appealing due to its relative ease of implementation. Such simple solutions, however, have largely been constrained to applications on simple planar hillslopes. This study presents analytical solutions to the kinematic wave equation for hillslopes with modest topographic curvature that causes divergence or convergence of runoff flowpaths. The solution averages flow depths along changing hillslope contours whose lengths vary according hillslope width function, and results in a one‐dimensional approximation to the two‐dimensional flow field. The solutions are tested against both two‐dimensional numerical solutions to the kinematic wave equation (in ParFlow) and against experiments that use rainfall simulation on machined hillslopes with defined curvature properties. Excellent agreement between numerical, experimental and analytical solutions is found for hillslopes with mild to moderate curvature. The solutions show that curvature drives large changes in maximum flow rate q peak and time of concentration t c , predictions frequently used in engineering hydrologic design and analysis.

中文翻译:

具有曲率的山坡径流的分析解决方案:数值和实验室验证

使用运动学波动方程的解析解来预测地表流的行为很有吸引力,因为它相对容易实现。然而,这种简单的解决方案在很大程度上仅限于在简单的平面山坡上的应用。本研究提出了具有适度地形曲率的山坡运动波动方程的解析解,这些坡度会导致径流流动路径的发散或收敛。该解决方案沿变化的山坡轮廓平均流动深度,其长度根据山坡宽度函数而变化,并导致二维流场的一维近似。这些解决方案针对运动学波动方程(在 ParFlow 中)的二维数值解和在具有定义曲率特性的机加工山坡上使用降雨模拟的实验进行了测试。对于轻度至中度曲率的山坡,在数值、实验和解析解之间找到了极好的一致性。解表明曲率驱动最大流速 q peak 和浓度时间 tc 的大变化,这些预测经常用于工程水文设计和分析。
更新日期:2020-09-20
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