A non-critical hillslope model: Evidence and topographic implications

Abstract

Hillslopes constitute the majority of a drainage basin space, and they, together with channelized streams and mountain glaciations, form the most representative exogenic agents sculpting the diverse landforms of the Earth's surface. It is well acknowledged that the hillslope evolution is dominated by a diffusion mechanism. A prominent progress in the last two decades is the proposed non-linearity in hillslope process, suggesting a non-linear relationship between the hillslope transport flux and the hillslope gradient. Existing non-linear hillslope models, by introducing a critical hillslope gradient, are successful in accounting for catastrophic processes, e.g., landslides. However, the present analytical descriptions of hillslope morphology remain complex in mathematical forms, hindering straightforward practical implementation. In this study, we develop a non-critical hillslope model based on the generic hillslope transport equation, which has the advantages of a simple mathematical form and easy practical application. The new hillslope model is compatible with the existing linear and non-linear hillslope models and is capable of emulating topographic evolution under arbitrary hillslope gradients. Using the non-critical hillslope model, we explore the characteristics of steady-state hillslope morphology, its identification, and the general transient response to tectonic uplift by numerical modeling. The proposed non-critical hillslope model is validated and supported by high-resolution topography in southern Tibet and wide basin erosional data compiled from published studies, supporting that the non-linear behavior of hillslopes is universal and might not be unique to steep hillslopes. The non-critical hillslope model provides a new prospective framework for modeling hillslope and landform evolution.