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Analytical solutions to runoff on hillslopes with curvature: numerical and laboratory verification
  • +2
  • Dana Lapides,
  • Cy David,
  • Anneliese Sytsma,
  • David Dralle,
  • Sally Thompson
Dana Lapides
University of California Berkeley
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Cy David
University of California Berkeley
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Anneliese Sytsma
University of California Berkeley
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David Dralle
Sacramento State University
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Sally Thompson
University of Western Australia
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Abstract

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 in all cases. The solutions show that curvature drives large changes in maximum flow rate qmax and time of concentration tc, predictions frequently used in engineering hydrologic design and analysis.

Peer review status:ACCEPTED

14 Apr 2020Submitted to Hydrological Processes
17 Apr 2020Submission Checks Completed
17 Apr 2020Assigned to Editor
17 Apr 2020Reviewer(s) Assigned
01 Jul 2020Review(s) Completed, Editorial Evaluation Pending
01 Jul 2020Editorial Decision: Revise Major
24 Jul 20201st Revision Received
25 Jul 2020Reviewer(s) Assigned
25 Jul 2020Submission Checks Completed
25 Jul 2020Assigned to Editor
26 Jul 2020Review(s) Completed, Editorial Evaluation Pending
26 Jul 2020Editorial Decision: Accept