The Equilibrium Concept in Geomorphology

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Annals of AAG




Equilibrium is a single word that embraces multiple concepts. The largely qualitative use of equilibrium within geomorphology has fostered imprecision and even outright error; as a result the term, for many, has degenerated to the status of a non-corrigible regulative principle. Although a few geomorphologists make precise use of equilibria terminology, their precision is invariably lost on the larger audience.

Equilibrium is associated with force in dynamics, with energy in thermodynamics (and probability by extension), and with pure numerical behavior in mathematics. In General System Theory, equilibrium is derived from thermodynamics but applied, by analogy, almost exclusively to mass. In addition, a purely geomorphic version of equilibrium (dynamic equilibrium) stems from the work of G. K. Gilbert (1876; 1877) and is based on sediment flux at the basin scale. Unfortunately, Gilbert's concept/term has been distorted by some geomorphologists in their attempt to establish linkage between equilibria concepts, especially between those relating to energy and mass.

This paper reviews and reconsiders the various equilibria concepts. An updated version of Gilbert's dynamic equilibrium based on sediment transfer proposed by Ahnert (n.d.), and termed by us “mass flux equilibrium,” holds promise. In addition, the purely mathematical concept of equilibrium outlined by Howard (1988) has considerable utility, provided union with geomorphological theory is achieved. Given the difficulty of measuring thermal energy in the field, its inefficient use in nature, and the uncertainty with which it and form can be related, thermodynamic equilibria concepts would appear, presently, to offer geomorphologists only very limited opportunities.