Quantifying the effects of three-dimensional subsurface heterogeneity on Hortonian runoff processes using a coupled numerical,stochastic approach

The impact of three-dimensional subsurface heterogeneity in the saturated hydraulic conductivity on hillslope runoff generated by excess infiltration (so-called Hortonian runoff) is examined. A fully coupled, parallel subsurface–overland flow model is used to simulate runoff from an idealized hillslope. Ensembles of correlated, Gaussian random fields of saturated hydraulic conductivity are used to create uncertainty in spatial structure. A large number of cases are simulated in a parametric manner with the variance of the hydraulic conductivity varied over orders of magnitude. These cases include rainfall rates above, equal and below the geometric mean of the hydraulic conductivity distribution. These cases are also compared to theoretical representations of runoff production based on simple assumptions regarding (1) the rainfall rate and the value of hydraulic conductivity in the surface cell using a spatially-indiscriminant approach; and (2) a percolation-theory type approach to incorporate so-called runon. Simulations to test the ergodicity of hydraulic conductivity on hillslope runoff are also performed. Results show that three-dimensional stochastic representations of the subsurface hydraulic conductivity can create shallow perching, which has an important effect on runoff behavior that is different than previous two-dimensional analyses. The simple theories are shown to be very poor predictors of the fraction of saturated area that might runoff due to excess infiltration. It is also shown that ergodicity is reached only for a large number of integral scales (∼30) and not achieved for cases where the rainfall rate is less than the geometric mean of the saturated hydraulic conductivity.     

Modeling scale-dependent runoff generation in a small semi-arid watershed accounting for rainfall intensity and water depth

Observed scale effects of runoff on hillslopes and small watersheds derive from complex interactions of time-varying rainfall rates with runoff, infiltration and macro- and microtopographic structures. A little studied aspect of scale effects is the concept of water depth-dependent infiltration. For semi-arid rangeland it has been demonstrated that mounds underneath shrubs have a high infiltrability and lower lying compacted or stony inter-shrub areas have a lower infiltrability. It is hypothesized that runoff accumulation further downslope leads to increased water depth, inundating high infiltrability areas, which increases the area-averaged infiltration rate. A model was developed that combines the concepts of water depth-dependent infiltration, partial contributing area under variable rainfall intensity, and the Green–Ampt theory for point-scale infiltration. The model was applied to rainfall simulation data and natural rainfall–runoff data from a small sub-watershed (0.4 ha) of the Walnut Gulch Experimental Watershed in the semi-arid US Southwest. Its performance to reproduce observed hydrographs was compared to that of a conventional Green–Ampt model assuming complete inundation sheet flow, with runon infiltration, which is infiltration of runoff onto pervious downstream areas. Parameters were derived from rainfall simulations and from watershed-scale calibration directly from the rainfall–runoff events. The performance of the water depth-dependent model was better than that of the conventional model on the scale of a rainfall simulator plot, but on the scale of a small watershed the performance of both model types was similar. We believe that the proposed model contributes to a less scale-dependent way of modeling runoff and erosion on the hillslope-scale.