Nonlinear dynamics and the evolution of relief

Theories of landscape evolution, and available field evidence, suggest that topographic relief may increase, decrease, or remain relatively constant over time. The trend depends on the relative balance between endogenic and exogenic forces and/or the spatial scale. A straightforward mathematical argument shows that when relief generally decreases over time, or remains constant, landscape evolution is stable and non-chaotic. Chaotic, unstable topographic evolution produces divergence, where initial elevation differences (and subsequent perturbations) generally increase over time. This leads to, or at least towards, a conceptual model of landscape evolution. This model, based on nonlinear dynamical systems (NDS) theory, recognizes 10 modes — five stable and five chaotic — of topographic evolution. Together, these modes can accommodate existing theories and models of landscape evolution. No mode can persist indefinitely over geologic time, implying that landscapes inevitably undergo phases of increasing and decreasing relief (these phases may be quite long). Because the model can accommodate any observed trend in relief evolution, it is not falsifiable and is, therefore, not proposed as a theory. The NDS model does have implications with respect to the preservation of planar surfaces; the next step is to develop a testable hypothesis.