Tziperman, E., J. R. Toggweiler, Y. Feliks, and K. Bryan. 1994: Instability of the thermohaline circulation with respect to mixed boundary conditions: Is it really a problem for realistic models? Journal of Physical Oceanography, 24(2), 217-232.

Abstract: A global primitive equations oceanic GCM and a simple four-box model of the meridional circulation are used to examine and analyze the instability of the thermohaline circulation in an ocean model with realistic geometry and forcing conditions under mixed boundary conditions. The purpose is to determine whether this instability should occur in such realistic GCMs.

It is found that the realistic GCM solution is near the stability transition point with respect to mixed boundary conditions. This proximity to the transition point allows the model to make a transition between the unstable and stable regimes induced by a relatively minor change in the surface freshwater flux and in the interior solution. Such a change in the surface flux may be induced, for example, by changing the salinity restoring time used to obtain the steady model solution under restoring conditions. Thus, the steady solution of the global GCM under restoring conditions may be either stable or unstable upon transition to mixed boundary conditions, depending on the magnitude of the salinity restoring time used to obtain this steady solution. The mechanism by which the salinity restoring time affects the model stability is further confirmed by carefully analyzing the stability regimes of a simple four-box model. The proximity of the realistic ocean model solution to the stability transition point is used to deduce that the real ocean may also be near the stability transition point with respect to the strength of the freshwater forcing.

Finally, it is argued that the use of too short restoring times in realistic models is inconsistent with the level of errors in the data and in the model dynamics, and that this inconsistency is a possible reason for the existence of the thermohaline instability in GCMs of realistic geometry and forcing. A consistency criterion for the magnitude of the restoring times in realistic models is formulated, that should result in steady states that are also stable under mixed boundary conditions. The results presented here may be relevant to climate studies that run an ocean model under restoring conditions in order to initialize a coupled ocean-atmosphere model.