Hillslope Runoff Through Grids of Patchy Vegetation: Predictions Using Modified Percolation Theory

Abstract

In pinon-juniper woodland sites, rapid transitions from low to high rates of hillslope runoff and erosion rates appear to occur with changes in ground cover. We use modified percolation equations, which have been used to predict rapid transitions between two states, to account for slope and to investigate scale-dependent relations for hillslope runoff. Hillslope runoff for a grid of cells is defined to be the number of runoff generating cells that actually contribute to the runoff at the bottom of the grid. We investigate how spatial pattern of runoff generating cells and grid scale effects hillslope runoff. We find that hillslope runoff increases non-linearly with percent of bare cells, crossing a threshold at intermediate values. This is similar to the behavior in general percolation theory and is important because it describes the transition between low and high levels of erosion. We also find that hillslope runoff is dependent on spatial pattern; spatial patterns are important because vegetation is aggregated in different ways at different sites. We also show that hillslope runoff is dependent on grid scale; grid scale is important because hillslopes vary in size. In general, rapid transitions are of concern because they effect the redistribution of contaminants and can deteriorate landfill covers. This preliminary study provides insight into a technique that can be useful in describing the dynamics of a transition between a low level and a high level of erosion.