We have conducted surveys of the gullies that developed in a small steep watershed in the Idaho Batholith after a severe wildfire followed by intense precipitation. We measured gully extent and cross sections and used these 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 in this paper 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 which corresponds 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 two times higher than the exponents used for bedload transport in alluvial rivers, but is in the range of shear stress exponents observed in flume experiments on steep slopes and with total load equations. The concavity index of the gully profiles theoretically obtained from the area and slope exponents of the sediment transport equation agrees well with the observed profile concavity of the gullies.

Our results, although somewhat preliminary due to 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 bedload equations developed for rivers.