Instability and chaos in hillslope evolution

Abstract

Instability - the failure of particular landforms or process-response relationships to persist in the face of environmental change - has been widely observed in geomorphic phenomena. This is often manifested as a symptotic instability, which implies exponential divergence of system states away from an equilibrium following a change or perturbation. Asymptotic instability may indicate chaos - complexity which can arise from the nonlinear dynamics of completely deterministic phenomena. A mass balance model of hillslope evolution, the explicit basis for Ahnert's slope evolution model and the conceptual basis for all comprehensive slope evolution models, is examined with regard to its stability and the possibility of chaotic behavior. The mass balance is unstable. The analysis suggests that chaotic behavior is possible in the evolution of slope regolith cover. Chaos, which occurs at high rates of debris removal relative to weathering rates, implies that spatial and temporal complexity in landscape evolution can occur independently of environmental heterogeneity and stochastic forcings. -from Author