Surface Runoff in Watershed Modeling—Turbulent or Laminar Flows?

Determination of overland sheet flow depths, velocities and celerities across the hillslope in watershed modeling is important towards estimation of surface storage, travel times to streams and soil detachment rates. It requires careful characterization of the flow processes. Similarly, determination of the temporal variation of hillslope-riparian-stream hydrologic connectivity requires estimation of the shallow subsurface soil hydraulic conductivity and soil-water retention (i.e., drainable porosities) parameters. Field rainfall and runoff simulation studies provide considerable information and insight into these processes; in particular, that sheet flows are likely laminar and that shallow hydraulic conductivities and storage can be determined from the plot studies. Here, using a 1 m by 2 m long runoff simulation flume, we found that for overland flow rates per unit width of roughly 30–60 mm2/s and bedslopes of 10%–66% with varying sand roughness depths that all flow depths were predicted by laminar flow equations alone and that equivalent Manning’s n values were depth dependent and quite small relative to those used in watershed modeling studies. Even for overland flow rates greater than those typically measured or modeled and using Manning’s n values of 0.30–0.35, often assumed in physical watershed model applications for relatively smooth surface conditions, the laminar flow velocities were 4–5 times greater, while the laminar flow depths were 4–5 times smaller. This observation suggests that travel times, surface storage volumes and surface shear stresses associated with erosion across the landscape would be poorly predicted using turbulent flow assumptions. Filling the flume with fine sand and conducting runoff studies, we were unable to produce sheet flow, but found that subsurface flows were onflow rate, soil depth and slope dependent and drainable porosities were only soil depth and slope dependent. Moreover, both the sand hydraulic conductivity and drainable porosities could be readily determined from measured capillary pressure displacement pressure head and assumption of pore-size distributions (i.e., Brooks-Corey lambda values of 2–3).