Box 3.3 Multiple Equilibria and Model Parameters
FIGURE 3.3 Steady-state solutions of the two-box model as a function of the atmosphere-ocean freshwater flux H. Depending on the strength of the horizontal mixing (diffusion) the model exhibits multiple eqilibria for a limited range of freshwater fluxes (bottom curve) or, alternatively, a unique solution (top curve). (See plate 6 for more detail.)
exhibits a permanent change in the THC (Manabe and Stouffer, 1988). This aspect has been associated with the quantitatively different vertical mixing in these models (Manabe and Stouffer, 1999).
The simple box model above demonstrates that the shape and position of the hysteresis in parameter space depend strongly on the model setup and on values of model parameters. Uncertainties in the parameters translate directly into uncertainties in the hysteresis and therefore uncertainties in the likely response of a system to a perturbation. Investigations using simplified models indicate that mixing schemes and values of mixing parameters are crucial in determining the shape of the hysteresis (Knutti and Stocker, 2000; Schmittner and Weaver, 2001). Unfortunately, mixing in the ocean is not well simulated in current-generation climate models, because of poorly parameterized small-scale processes and insufficient resolution. The location of the present, past, and future states of the climate system on the hysteresis curve, and its shape