Concept of equilibrium in geomorphology

When a disturbance or a change in driving force (a perturbation) is imposed on a geomorphic system, the system responds to such a change by altering one or many of its components. Discussion of responses to disturbances in the geomorphological literature tends to revolve around the concept of equilibrium. In simple terms, equilibrium is ‘a condition in which some kind of balance is maintained’, but it is a complex concept, its complexity lying in the multiplicity of equilibrium patterns and the fact that not all components of a system need be in balance at the same time for some for of equilibrium to obtain. The more recently introduced ideas of disequilibrium (moving towards a stable end state, but not yet there) and non-equilibrium (not moving towards any particular stable or steady state) add another dimension to the debate.

Static equilibrium

Static equilibrium is the condition where an object has forces acting upon it but it does not move because the forces balance.

Examples are a boulder resting on a slope and a stream that has cut down to its base level, so preventing further entrenchment.

Stable equilibrium

Stable equilibrium is the tendency of a system to return to its original state after experiencing a small perturbation, as when a sand grain at the base of a depression is rolled a little by a gust of wind but rolls back when the wind drops. Negative feedback processes may lead to the process of restoration.

Unstable equilibrium

Unstable equilibrium occurs when a small perturbation forces a system away from its old equilibrium state towards a new one. If the disturbance persists or grows, perhaps through positive feedback processes, it may lead to disequilibrium or non-equilibrium. A simple example would be a boulder perched atop a hill; a force sufficient to dislodge the boulder would lead to its rolling down slope.

Thermodynamic equilibrium

Thermodynamic equilibrium is the tendency towards maximum entropy, as demanded by the second law of thermodynamics. In geomorphology, such a tendency would lead to a continuous and gradual reduction of energy gradients (slopes) and an attendant lessening of the rates of geomorphic processes. A featureless plain would be in a state of thermodynamic equilibrium, but virtually all landscapes are far removed from such an extreme state.

Dynamic equilibrium

Dynamic equilibrium is quite a disputed term. Geomorphologists have used this concept to represent different scenarios. Currently, dynamic equilibrium is synonymous with a ‘steady state’ or with a misleading state, where the system appears to be in equilibrium but in reality is changing extremely sluggishly. Thus, the term has been a replacement for such concepts as grade. From the 1960s onward, some geomorphologists began questioning simplistic notions of equilibrium and steady state. In 1965, Alan D. Howard noted that geomorphic systems might possess thresholds that separate two rather different system economies. Schumm (1973, 1977) introduced the notions of metastable equilibrium and dynamic metastable equilibrium, showing that thresholds within a fluvial system cause a shift in its mean state. The thresholds, which may be intrinsic or extrinsic, are not part of a change continuum, but show up as dramatic changes resulting from minor shifts in system dynamics, such as caused by a small disturbance.

Metastable equilibrium

In metastable equilibrium, static states episodically shift when thresholds are crossed. It involves a stable equilibrium acted upon by some form of incremental change (a trigger mechanism) that drives the system over a threshold into a new equilibrium state. A stream, for instance, if forced away from a steady state, will adjust to the change, although the nature of the adjustment may vary in different parts of the stream and at different times. In the simplistic cause-and-effect view of landscape evolution, changes are seen as a simple response to an altered input. It shows that landscape dynamics may involve abrupt and discontinuous behaviour involving flips between quasi-stable states as system thresholds are crossed.

Dynamic meta-stable equilibrium

In dynamic meta-stable equilibrium, thresholds trigger episodic changes in states of dynamic equilibrium (dynamic equilibrium meaning here a trending mean state). So, dynamic metastable equilibrium is a combination of dynamic and meta-stable equilibria, in which large jumps across thresholds break in upon small-scale fluctuations about a moving mean. For this reason, dynamic metastable equilibrium is really a form of disequilibrium as a progressive change of the mean state occurs.