Modeling depth distributions of overland flows

Hydrological and erosion models use water depth to estimate routing velocity and resultant erosion at each spatial element. Yet the shear stress distribution imposed on the soil surface and any resulting flow detachment and rill incision is controlled by the full probability distribution of depths of overland flow. Terrestrial Laser Scanning (TLS) is used in conjunction with simple field-flume experiments to provide high-resolution measures of overland flow depth-distributions for three semi-arid hillslope transects with differing soil properties. A two-parameter gamma distribution is proposed as the optimum model for depths of both interrill and rill flows. The shape and scale parameters are shown to vary consistently with distance downslope reflecting the morphological signature of runoff processes. The scale parameter is related to the general increase of depths with discharge (P < 0.0001) as flows gradually concentrate; the shape parameter is more related to the soil surface roughness and potentially provides a control on the rate of depth, but also velocity increase with discharge. Such interactions between surface roughness and overland flows are of crucial importance for flow hydraulics and modeling sediment transport.