Using a two-box model of the thermohaline circulation (THC) of the ocean, Stommel (1961) showed that the different response times of the ocean surface to heat and freshwater perturbations give rise to multiple equilibria of the THC with very different characteristics. This implies that forcing and other conditions do not uniquely define the state of the climate system and that perturbations beyond thresholds can trigger transitions to other equilibrium states. The model presents some fundamental concepts and demonstrates the major sources of uncertainty in simulating abrupt climate change caused by a change in the THC. Multiple equilibria, however, would not occur if all processes were linear. The nonlinearity of the Stommel model arises because the flow field of ocean water transporting heat and salt is itself a function of temperature and salinity. Nonlinearities and multiple equilibria are the fundamental concepts behind the simulation of abrupt climate change.
Simple models of the energy balance of the atmosphere exhibit multiple equilibria. The model of Sellers (1969) is a typical case: a given amount of solar irradiation allows either a cold or a warm planet in equilibrium. The nonlinearity here is introduced by a special formulation of the snow-albedo feedback, which is operative only in a particular range of temperatures. A cold earth is snowy, and snow reflects sunlight and keeps the earth cold. A warmer earth has less snow, absorbs more sunlight, and so stays warmer. Abrupt change can be triggered by variations in total solar output or other parameters that influence the radiative balance, such as snow cover.
The Lorenz models (Lorenz, 1963, 1990) provide a highly simplified description of atmospheric circulation. In addition to multiple equilibria in particular ranges of parameters, these models exhibit self-sustained oscillations and chaotic behavior. A system oscillates near one of two preferred centers; abrupt change occurs when the system switches from one mean of oscillation to the other. In a Lorenz model, these transitions occur spontaneously.
These examples suggest that abrupt climate change can occur in (at least) three fundamentally different ways:
Abrupt climate change can be the response to a rapidly varying external parameter or forcing. If one views only the atmosphere-ocean system, massive sudden discharges of freshwater from disintegrating ice sheets on land would be an example of a sudden external influence. Nonlinearity