Figure 3.3 (also see Plate 6) shows that the steady states of the two-box model can be calculated analytically and the dependence of the flux q (a measure of the strength of the THC) on the freshwater flux H can be examined. In the standard case (weak diffusion, lower curve), the THC is strongest (value arbitrarily set to 1) when the freshwater flux H vanishes. With higher H, the THC weakens. If H = 0.3, no steady-state solution with q > 0 is possible. However, for H > 0.1, there is a second stable equilibrium, a reverse mode of the THC, with q < 0. This flow pattern strengthens as H increases. For a certain parameter range, here 0.1 < H < 0.3, three equilibria are possible; it is readily shown that the middle one (on the dotted part of the curve) is not a stable solution. In that range of H, the model exhibits hysteresis.
The presence of hysteresis is strongly dependent on model parameters. This is shown for a case in which the effect of the horizontal mixing due to gyre transports is increased (strong diffusion). Hysteresis disappears (upper curve); and for progressively increasing freshwater forcing, the THC smoothly approaches zero and—again smoothly—turns into the reverse mode for H = 0.56. For any given freshwater forcing, there is a unique and stable THC. The presence of multiple equilibria of the THC therefore depends strongly on the model formulation, parameterization of processes, and choice of parameter values.
and complexity, clearly are among the major unsolved problems in climate dynamics. Results that depend crucially on a specific shape of the hysteresis are likely not to be robust findings at this stage.
Whether the nonlinearities giving rise to abrupt change in the simplified models are an artifact of the simplifications or carry over to more complex and realistic systems needs to be investigated. Only more comprehensive and more complete climate models can make a convincing case that the assumptions underlying the nonlinearities in these simple models bear sufficient realism.
Earlier, three fundamental ways of causing abrupt climate change were presented; all have been simulated with coupled GCMs. The first category