A Sediment Transport Model for Incising Gullies on Steep Topography
We have conducted surveys of gullies that developed in a small, steep watershed in the Idaho Batholith after a severe wildfire followed by intense precipitation. We measured gully length and cross sections to estimate the volumes of sediment loss due to gully formation. These volume estimates are assumed to provide an estimate of sediment transport capacity at each survey cross section from the single gully-forming thunderstorm. Sediment transport models commonly relate transport capacity to overland flow shear stress, which is related to runoff rate, slope, and drainage area. We have estimated the runoff rate and duration associated with the gully-forming event and used the sediment volume measurements to calibrate a general physically based sediment transport equation in this steep, high shear stress environment. We find that a shear stress exponent of 3, corresponding to drainage area and slope exponents of M = 2.1 and N = 2.25, match our data. This shear stress exponent of 3 is approximately 2 times higher than those for bed load transport in alluvial rivers but is in the range of shear stress exponents derived from flume experiments on steep slopes and with total load equations. The concavity index of the gully profiles obtained theoretically from the area and slope exponents of the sediment transport equation, θc = (M − 1)/N, agrees well with the observed profile concavity of the gullies. Our results, although preliminary because of the uncertainty associated with the sediment volume estimates, suggest that for steep hillslopes such as those in our study area, a greater nonlinearity in the sediment transport function exists than that assumed in some existing hillslope erosion models which calculate sediment transport capacity using the bed load equations developed for rivers.