Physical Basis of the Length‐slope Factor in the Universal Soil Loss Equation

TLDR

The USLE length‑slope factor is a purely empirical relationship derived from an extensive database. The study aims to derive a physically based length‑slope factor using unit stream power theory. The derivation employs unit stream power theory to model erosion from sheet and rill flow on hill‑slopes. Both the empirically derived and the physically based length‑slope factors are equivalent, yet the latter more accurately represents sediment transport capacity by incorporating catchment convergence and rilling, though it still does not fully account for hydrological processes that influence runoff and erosion, which may explain inconsistencies in other USLE factors.

Abstract

Abstract 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.