Modeling Landforms as Self‐Organized, Hierarchical Dynamical Systems

Landforms result from self-organization, by which local nonlinear, dissipative interactions between the fast- and small-scale constituents of a system give rise to emergence of a larger-scale, slower evolving form. Landscapes are ordered in a temporal hierarchy in which a range of levels characterized by discrete, separated time scales are connected by self-organization but do not dynamically interact. The relationship between these two hypotheses and their implications for modeling are explored here using three properties of self-organized systems: emergence of order, in which the number of variables decreases; time-scale separation, in which the time scale characterizing the reaction to perturbations increases; and dynamical asymmetry, in which dynamics of the self-organized form becomes abstracted and slaves the constituent dynamics. These three properties of self-organization form the basis of a new modeling methodology, hierarchical modeling. Models are constructed at levels in a hierarchy corresponding to emergent, self-organized forms, patterns or behaviors of the landscape. Hierarchical modeling is compared theoretically to two more traditional, end-member methodologies employed in geomorphology: reductionism, which uses detailed dynamics at the fundamental scale, and universality, which treats the slowly varying dynamics or steady state common amongst diverse systems. Hierarchical modeling incorporates the acquisition of physical insight into model construction across a range of temporal scales, whereas insight is required only at the scale of fundamental constituents for reductionism and at the longest scales for universality. Hierarchical modeling potentially provides improved predictability because the resulting models contain neither too many variables and processes (as in reductionism), which can lead to numerical and conceptual errors, nor too few variables and processes (as in universality), which permits only a partial representation of the dynamics of a landscape. These general arguments are illustrated by consideration of bedforms, hillslopes, rivers, patterned ground and the nearshore.