THERMOHALINE CATASTROPHE IN A SIMPLE 4-BOX MODEL OF THE OCEAN CLIMATE

A four-box model of the ocean is examined in which a surface and deep layer of equal thickness and large volume are connected to two polar reservoirs of smaller volume. While the four reservoirs are thoroughly mixed, there is no significant mixing between them; exchange is due to flow between reservoirs with the flow out of or into the polar reservoirs driven by pressure gradients. Newtonian boundary conditions are imposed on the temperature and salinity of the surface layer and the two polar reservoirs; the deep water is forced only by flows into it from other boxes. The temperature and salinity forcing is applied with a different time scale for each variable. When the time scales are nearly equal, the system responds as a simple component fluid with a single solution for each forcing. When the salinity time scale is long compared with temperature, up to four multiple equilibria can be present for a given forcing. These equilibria are unstable to finite amplitude perturbations, and numerical solutions exhibit catastrophic transitions from one mode to another. When the deep water formation is totally inhibited as a result of a transition, the system can go into a long-term climatic oscillation, quasi-periodic in nature. The system possesses four "attractors" corresponding to deepwater formation in either, both, or neither of the two polar reservoirs.