Channel propagation, branching and self-similarity in circular-domain landscape evolution models

Abstract

Earth's surface topography exists in a long-term dynamic feedback system with climate and geologic processes, the implications of which extend from landslides to agriculture to carbon cycling. High-order models have been constructed to understand the intricacies of the landscape evolution system, but sacrifice mechanistic, process-level understanding of the characteristic feedbacks and nonlinearities. Here, we study a minimalist landscape evolution model (LEM) that is able to isolate and capture the core modes of topographic variability. We characterize the behavior of this LEM on circular domains under a range of conditions to improve both quantitative and qualitative understanding of soil diffusion, channel inception, and landscape self-similarity. Our results serve as a critical first step in quantifying the length scales over which transitions between different landscape behaviors occur, and highlight the need for further study of the effects of boundary conditions and parameter choice on modeled topography.