ocean-only models is what the effect of the atmosphere is on the variability. Coupling the atmosphere to the ocean in tropical models tends to induce instabilities that were not present in models of either the atmosphere or the ocean. Whether the atmosphere is stabilizing or destabilizing for the variability exhibited in ocean-only models must await detailed simulations with coupled atmosphere-ocean models.
The authors are indebted to Michael Winton and Fenglin Yin for very helpful discussions, to Michael Ghil for a detailed reading of the first draft of this paper, and to Ed Harrison and Steve Hankin of NOAA/PMEL for the use of FERRET, a diagnostics and graphics program that was used extensively in this research. This work was supported as part of the Atlantic Climate Change Program by a grant from the NOAA/Office of Global Programs to the University of Washington Experimental Climate Forecast Center. David McDermott was also supported as a Graduate Fellow for Global Change by the Department of Energy, and part of this research was performed using the resources located at the Advanced Computing Laboratory of Los Alamos National Laboratory.
University of California, Los Angeles
I very much enjoyed this paper. However, it needs to be put into the broader context of the other papers on decade-to-century variability in the ocean's thermohaline circulation (THC) presented at this workshop. There is considerable activity going on in this area, and we will get together a small Climate System Modeling Program (CSMP) workshop at UCLA in October 1993 to clarify some of the issues further.
My view of the scientific method is that we proceed from detection of phenomena via understanding to simulation, and eventually on to prediction. There are some shortcuts, such as statistical predictions that try to circumvent understanding and simulation, but we have full confidence only when all the stages of this progression have been visited.
Now, this gradual approach to the entire cognitive process also implies that there should be a gradual approach to one particular step, which is the understanding of the models. So I would just like to refer you to a couple of relevant figures that are halfway between Dr. Bryan's 'toy' model and Dr. Sarachik's complex one (Figures 9, 14, and 16 of Quon and Ghil, 1992), and talk about the issue of multiple equilibria in such simple models, as touched upon by Claes Rooth.
It has been observed in a number of THC models of different complexity that, under symmetric forcing with respect to the equator, you can have either two-cell symmetric circulation or one-cell pole-to-pole circulation. My illustrations show that essentially you can have all the intermediate steps. In other words, you can go from the symmetric circulation to the completely antisymmetric one gradually. Actually, this is a more realistic approach to the Atlantic's THC, as presented in McDermott and Sarachik's Figure 1 (see also Figure 1 of Ghil et al., 1987). There is North Atlantic Deep Water (NADW) reaching into the high southern latitudes, but there is Antarctic Bottom Water (AABW) spreading under it past the equator. So while the Quon and Ghil (1992) model is only two-dimensional, it manages to capture this asymmetry (see Figure 9 there), with one cell (NADW) dominating the other (AABW) without suppressing the latter entirely.
The linear stability analysis for this highly resolved, albeit two-dimensional, model yields a regime diagram (Figure 14 of Quon and Ghil). This diagram demonstrates that increasing either the imposed pole-to-equator temperature gradient at the surface or the salinity flux across the boundary will produce a gradual transition between two-cell symmetric circulations and completely antisymmetric circulations. A gradual increase of the measure of asymmetry is thus possible. Mathematically, this gradual increase is captured by a pitchfork bifurcation (Figure 16 in Quon and Ghil).
Now, Dr. Sarachik started with symmetric forcing and then also imposed slightly asymmetric forcing. Actually, when these mixed boundary conditions were enforced, in one case the response of his model was to switch to another steady state; in the other case, it went to oscillatory behavior.
To conclude, I believe that oscillations shown by some of these ocean THC models or coupled atmosphere-ocean GCMs have something to do with the spectral peaks detected in global and local temperature series (e.g., Ghil and Vautard, 1991; also Cook et al., 1995, and Keeling and Whorf, 1995, both in this volume). We need to identify certain oscillations in the models with what we think we observe, since confronting models with observations is the name of the game in the physical sciences.