Research by Bryan (1986) marked the beginning of realistic process modeling of the THC. This work showed that the THC in a three-dimensional ocean model can assume multiple equilibria with vastly different locations of deep-water formation. Marotzke and Willebrand (1991) found four qualitatively different equilibrium solutions in an idealized global model of the THC. Common to these models was a special formulation of the surface boundary conditions that took into account the different response characteristics of the sea surface to changes in atmosphere-ocean heat and freshwater fluxes. Multiple equilibrium solutions were reported also in a fully coupled atmosphere-ocean model (Manabe and Stouffer, 1988); thus, the result does not depend on the specific simplifications used in the ocean-only models.

Slow changes of the surface freshwater balance constitute one possible mechanism to induce abrupt change. Using an ocean-only model, Mikolajewicz and Maier-Reimer (1994) demonstrated that switches in the THC occurred if the discharge of freshwater to the Atlantic exceeded a threshold value. Other coupled models used freshwater pulses to disturb the circulation and exhibit responses that range from a large reduction (Manabe and Stouffer, 1997) to a full shutdown of the THC (Mikolajewicz et al., 1997; Schiller et al., 1997).

These models suggest that the large changes observed in the paleoclimatic records were due to rapid changes in the THC. A more systematic investigation, however, was difficult to perform with the models because of their high computational burden. Extensive parameter studies, the basis of the advancement of understanding, are hardly possible. In recent years, simplified climate models—or climate models of reduced complexity—have been developed (Stocker and Marchal, 2001). They contain limited dynamics and have high computational efficiency. This was a crucial step forward in extending the toolbox to investigate abrupt climate change. Such models are also referred to as “earth-system models of intermediate complexity.” There are three strategies for formulating such models:

1. Rigorous reduction of the governing equations of the climate system.

2. Combination of model components of differing complexity.

3. Mathematical linearization of the response of comprehensive climate models to pulse perturbations.