Laboratory Methods in Surface Hydrology: Using Engineered Surfaces to Verify Analytical Solutions for Overland Flow on Complex Surfaces

Abstract:

The development of inexpensive laboratory and data processing methods in hydrology has great potential to provide insight into basic hydrologic processes. Scale models provide a highly-controlled environment in which flow processes are still fully complex, and the errors inherent to laboratory experiments are systematically different than those inherent to numerical simulation, allowing for independent verification of models. In this study, laboratory methods are used to examine one of the most common problems in hydrologic science and engineering—the prediction of overland flow. This study presents analytical solutions to the kinematic wave equations for hillslopes with modest curvature, causing divergence or convergence of runoff flowpaths. The solution approach involves approximating the two-dimensional flow field with a one-dimensional, contour-average streamline, an approximation requiring validation. In the absence of an analytical solution for fully complex flow against which to test the new results, this study complements two-dimensional numerical solutions to the kinematic wave equation (in ParFlow) with an independent method of validation: laboratory experiments on machined hillslopes of known geometry. We present a routine for selecting an optimal smoothing method that enables analysis of noisy datasets from low-budget laboratory experiments. In both laboratory and numerical cases, there is excellent agreement with the theoretical solutions for hillslopes of mild to moderate curvature, indicating that curvature creates large changes in maximum flow rate and time of equilibrium. Cost-efficient scale experiments may greatly facilitate validation of hydrologic models.