The length‐slope factor in the universal soil loss equation (USLE) is a purely empirical relationship that was derived from an extensive data base. A physically based length‐slope factor was independently derived in this paper by using unit stream power theory to describe the erosion processes associated with sheet and rill flow on hill‐slopes. It was shown that the two length‐slope factors are equivalent. Therefore, the USLE length‐slope factor is a measure of the sediment transport capacity of runoff from the landscape, but fails to fully account for the hydrological processes that affect runoff and erosion. The strength of the theoretically derived length‐slope factor is that it explicitly accounts for the dual phenomena of catchment convergence and rilling. The empirically derived factor can not account for changes in either surface flow or erosion processes, nor slope geometry, and this may explain why the values derived for other factors in the USLE, especially soil erodibilities, have been found to be inconsistent.

Theoretical equations for calculating the unit stream power of both sheet and rill flow were developed and used to predict the sediment transport capacity of such flows. Independent data sets from three sources representing both finely aggregated clay soils and coarse textured nonaggregated soils, sheet, rill, and composite sheet rill flow systems, and a range of slopes were used to test the utility of the method. The results were very good and demonstrated the simplicity and robustness of the method. For shallow overland flow the best results were obtained when the critical unit stream power at incipient sediment motion was treated as a constant value that was independent of slope. The results also suggest that a unique value of critical unit stream power for rill initiation exists that is independent of soil type. For noncohesive loams or fine sands and finely aggregated clay soils the sediment transport capacity can be accurately predicted from a knowledge of the physical characteristics of the soil or bed material alone. For aggregated clay soils this requires information on the aggregate size distribution and the effects of soil particle size differentiation as flow rates and unit stream powers increase with the transition from sheet to rill flow.

After dry summers or drought, eucalypt forest soils at two sites in southeastern Australia developed hydrophobic or non-wetting surface characteristics that reduced infiltration, measured using a sprinkling infiltrometer. At one site the development of hydrophobic conditions caused the rainfall to runoff conversion efficiency of a forested catchment to increase from 5 per cent to 15 per cent. Under non-hydrophobic conditions at this site, grassland always generated more runoff than forest. However, one major rainfall-runoff was recorded at a time of highly hydrophobic forest soil conditions and this storm generated greater runoff on the forested catchment than the grassland catchment.At the second site forest soils have naturally highly conductive surface layers because of a dense network of macropores and pathways for preferential flow. Hydrophobic conditions produced by drought caused soil water movement to be confined to only a few of the larger macropores exposed to surface ponded'water. Even so, infiltration rates remained relatively high so that the impacts of hydrophobic soils were not translated into increased catchment runoff as at the first site.

A digital model for discretizing three-dimensional terrain into small irregularly shaped polygons or elements based on contour lines and their orthogonals is described. From this subdivision the model estimates a number of topographic attributes for each element including the total upslope contributing area, element area, slope, and aspect. This form of discretization of a catchment produces natural units for problems involving water flow as either a surface or subsurface flow phenomenon. The model therefore has wide potential application for representing the three-dimensionality of natural terrain and water flow processes in the fields of hydrology, sedimentology, and geomorphology. Three example applications are presented and discussed. They are the prediction of zones of surface saturation, the prediction of the distribution of potential daily solar radiation, and the prediction of zones of erosion and deposition in a catchment.

No abstract