Constraints on the long‐term colluvial erosion law by analyzing slope‐area relationships at various tectonic uplift rates in the Siwaliks Hills (Nepal)

Abstract

The large database of topographic form and uplift rates that exists for the Siwaliks Hills (central Nepal) makes possible a thorough analysis of the long‐term erosion model. The study especially focuses on drainage areas larger than 5.10−3 km2, fixed by the database resolution, and smaller than 1 km2 above which a fluvial signature is recorded. This area range corresponds to colluvial valleys in which the dominant erosion process is likely debris flow. We evaluate a phenomenological model wherein erosion is considered to depend on drainage area and slope. We test this model by assuming that the uplift rate is in approximate equilibrium with erosion. The stream power law model, formulated by analogy to river incision and transport problems, is found to be consistent with data since an inverse power law relationship between slope and drainage area is systematically observed between 7.10−3 and ∼1 km2, with little variability on the exponent ∼−0.24. Thanks to the range of uplift rates, we obtain constraints on the slope dependency of erosion law, which appears linear and which predicts a significant erosion threshold. The linear dependence on slope in the debris‐flow zone is consistent with findings by Kirby and Whipple [2001] in the fluvial downstream zone and with the linear relationship between local relief and uplift rate documented by Hurtrez et al. [1999]. The transition between this colluvial‐channel regime and the fluvial regime appears quite sharp in contrast with recent studies, but the latter regime is not sufficiently documented to derive definite conclusions.