5. Conclusion

 

We have described and analysed a simple atmosphere-ocean model which supports growing coupled modes and exhibits decadal oscillations in SST, air pressure, and oceanic streamfunction. Moreover, the growth rate and form of the coupled modes have aspects in common with observations of natural variability in the North Atlantic, the North Pacific and the Antarctic Circumpolar Wave. The `clock' of the coupled model is provided by oceanic baroclinic Rossby waves (in this manner, it resembles the model of Latif and Barnett (1994). Undulations of the sub-surface thermal field, associated with the westward-propagating baroclinic Rossby waves, exposed to the surface by wintertime mixed-layer deepening, induce SST anomalies which change the diabatic heating rates of the atmosphere and hence its circulation. The resulting anomalous winds blow over the ocean and exert a stress on it: in the growing mode, this anomalous windstress acts to amplify sub-surface undulations, leading to larger deep thermal anomalies and magnified SST anomalies, resulting in a positive feedback.

We find that the vertical structure of the atmospheric response to thermal forcing is central to the coupling mechanism. In order to support a growing mode the response must be equivalent barotropic, with highs above warm water. If the doppler-shifted atmospheric Rossby wave speed is sufficiently slow, so that the time it takes to cross an SST anomaly is long compared to the thermal equilibration timescale, $(\vert\nu\vert /\Gamma \ll 1)$, then thermal equilibration will occur and coupled modes grow rapidly enough to maintain themselves against dissipative processes.

Two approaches to the specification of SST were considered. In the first, SST was tied to subsurface thermal anomalies associated with vertical undulations in isotherms. In the second SST was determined by horizontal circulation across a specified large-scale meridional SST gradient. Both `recipes' yield growing modes with very similar structure. The former model exhibits more rapid growth for the parameters chosen in this study, and (at least for the parameters chosen here) the limit where entrainment completely dominates SST provides an excellent, simpler approximation to the full dispersion relation. Air-sea heat flux, the third important influence on SST, acts to reduce the growth rate, but does not affect the fastest-growing mode at all, because that mode has negligible air-sea temperature difference. The coupling mechanism is most active during periods of rapid entrainment (winter); the mode may become less strongly coupled and therefore ``dormant'' during the summer, though subsurface Rossby waves will continue to propagate during dormancy.

Comparisons of such a simple model with observations must be rather tentative. There is evidence that the response of the atmophere to SST anomalies on internnual timescales is equivalent barotropic with highs over warm surface anomalies -- see, for example, Kushnir (1994). Moreover, we find that the structure and growth rate of the fastest growing coupled mode is broadly consistent with what is known of the spatial scale, and low-frequency variability of the North Atlantic Oscillation. Our mode will be much more strongly coupled in the winter, in agreement with Hurrell & Van Loon's (1997) and others' observation that the NAO is strongest and shows greatest persistence in winter. There are also some aspects that resemble the Antarctic Circumpolar Wave, although observed air-sea phase relationships appear to differ from this model's predictions.

However, in relating this simple model to phenomema in the atmosphere and ocean, one must proceed with care. The coupling parameters $\alpha$ and r are poorly known, the true barotropic and baroclinic modes of the atmosphere are complicated pressure-weighted averages of vertical quantities rather than the simple two-level sum and difference used here, and quasi-geostrophy and the $\beta$-plane approximation give only qualitative guidance on such large scales, particularly near resonance. Any of the these factors could significantly change the numerical values of $\mu$, $\nu$ and $\Gamma$.

Our use of a two-level QG atmosphere can easily be criticized. In nature the response of the atmosphere is sensitive to the upper boundary conditions (a rigid lid was assumed here, which may overemphasize the downstream stationary-wave response by prohibiting upward transmission of wave energy) and the vertical profile of heating (which is trivial in a 2-layer model). Our model may also be suspect near resonance, as other dynamics may become important.

Of even more importance, perhaps, are the lack of zonal asymmetries in our model. The model ocean has no meridional boundaries (there are no land masses!) and the mean flow of the atmosphere is not purely zonal. However, nearly-stationary atmospheric waves also exist in non-uniform flows. For example, Marshall & Molteni (1993) seek ``neutral vectors'' of the free atmosphere, and find free, almost-stationary waves that can co-exist with climatological winds. Moreover they strongly resemble EOF's of the low-frequency variability and have an uncanny resemblance to observed low-fequency variability patterns like the NAO. In the real atmosphere, these neutral vectors may take the place of the linear nearly-stationary Rossby waves that can efficiently couple with the ocean in this model.

We christen this growth mechanism a ``candle instability'' by analogy with a burning candle. The candle's flame feeds on the energy in the molten wax while melting more wax, ensuring a constant fuel supply, in the same way that our atmospheric model feeds on the SST anomalies, while driving a circulation which replenishes those anomalies. The candle flame and our growing mode's atmosphere also react similarly to strong atmospheric advection.