Thresholds, mode switching, and emergent equilibrium in geomorphic systems

Landform and landscape evolution may be convergent, whereby initial differences and irregularities are (on average) reduced and smoothed, or divergent, with increasing variation and irregularity. Convergent and divergent evolution are directly related to dynamical (in)stability. Unstable interactions among geomorphic system components tend to dominate in earlier stages of development, while stable limits often become dominant in later stages. This results in mode switching, from unstable, divergent to stable, convergent development. Divergent-to-convergent mode switches emerge from a common structure in many geomorphic systems: mutually reinforcing or competitive interrelationships among system components, and negative self-effects limiting individual components. When the interactions between components are dominant, divergent evolution occurs. As threshold limits to divergent development are approached, self-limiting effects become more important, triggering a switch to convergence. The mode shift is an emergent phenomenon, arising from basic principles of threshold modulation and gradient selection. As an example, the relationships among flow concentration, erosive force, and channel incision in fluvial systems are examined in the context of mode switching and thresholds. The commonly observed divergence in channel growth and fluvial dissection and network development, eventually transitioning to a stable, convergent configuration, is an emergent outcome of gradient selection and threshold modification, and does not imply any goal functions of balancing mass fluxes or limiting change. Copyright (c) 2013 John Wiley & Sons, Ltd.