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Documentation Vadose Zone Conjunctive Simulation Sleepers River Watershed Flowpath

MODFLOW-Watershed Hydrology and Transport:

Conjunctive simulation of 1-D overland flow and 2-D subsurface flow


The classic soil flume experiment of Smith (1970) [Surface Runoff] (published as Smith and Woolhiser (1971)) is simulated to confirm proper implementation of the overland flow formulation. The experiment examined laminar surface flow of a light oil (kinematic viscosity = 1.94E-4 m^2/s, about 200 times that of water) across a porous sand under both 'wet' and 'dry' initial soil conditions. The dry case is simulated here to confirm this model's ability to properly replicate the numerically difficult infiltration-excess (Hortonian) overland flow.

The soil flume measured 12.2 meters long by 5.1 centimeters thick and 1.22 meters deep and was inclined at a slope of 0.01. The oil was applied evenly across the length of the flume for 15 minutes at a rate of 0.42 cm/min. The soil in the flume was a Poudre fine sand with differing bulk densities. The soil flume's imbibition relations were determined experimentally. The distinct imbibition behavior of the light oil required the parameters for the capillary-saturation and relative permeability relations to be fit separately.


The total simulation time was 18 minutes in order to capture the recession phase of the hydrograph (figure 1). The simulated soil saturation profiles at four discrete times during the rainfall application are plotted in figure 2 with the corresponding simulation results from Smith and Woolhiser (1971). Examining the simulation results, it is immediately obvious that the timing of both the infiltration front (figure 2) and the initiation of surface runoff (figure 1) match the results of Smith and Woolhiser (1971) quite well. However, the amplitude of the runoff hydrograph peak is somewhat less than the experimental data. [Surface Runoff] This can be explained by the crude approximation of entrapped air effects used in this study that may over-estimate the available specific moisture capacity near saturation. Due to the high viscosity of the light oil, entrapped air in the soil pores prevented the soil from reaching complete saturation (Smith, 1970). This entrapped air would reduce the available storage capacity of the soil below the values defined by the capillary saturation functions used in this study. Additionally, there is some over-prediction in the lower soil layer of the soil's volumetric saturation, as the infiltration front moves down through the soil column (figure 2). This loss of water into the soil column causes the model to under-predict the surface runoff in order to maintain overall mass balance (figure 1). The model also under-estimates the timing of the receding limb of the hydrograph (figure 1), which may indicate experimental conditions such as hysteresis in the soil drainage due to the persistence of entrapped air or over-prediction by the model of the available soil water capacity. Overall the model captures the hydraulic behavior of the surface runoff hydrograph and subsurface saturation profiles quite well and illustrates the inter-connectivity of surface and subsurface hydrology.


Smith, R.E. Mathematical simulation of infiltrating watersheds. PhD dissertation, Colorado State University, Fort Collins, June 1970.

Smith, R.E. and D.A. Woolhiser, Overland flow on an infiltrating surface. Water Resour. Res., 7(4), pp. 889-913, 1971.


Thoms, R.B. Simulating fully-coupled overland flow and variably saturated subsurface flow using MODFLOW, Masters Thesis, OGI School of Science and Engineering at OHSU, 136 p., 2003.

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