The NAO strange attractors

However, examining records of the fluctuations of the NAO index over more than a century, one realizes that the jumps from one value of the index to the next value of the same or different sign occur rather at random, strongly suggesting that the case study situations, although exemplary, do not actually describe two definite states of the atmosphere but two strange attractors: the system attracted by NAO+ oscillates in its vicinity until it finds a way out and goes to NAO-, oscillates in its vicinity until it finds a way out and goes back to the vicinity of NAO+- (Fig. 4).

The records show also a definite trend towards the positive NAO phase in recent decades and the increased attractiveness of the positive phase has often been attributed to a global warming effect.

One should however be attentive to the fact that, in addition to possible jumps between NAO+ and NAO- (with a possible predominance of NAO+ attributed to global warming) small deviations from the "educational" weather maps may occur as the system wanders in the vicinity of one or the other strange attractor.

Fig. 4. An educational image of trajectones jumping from one strange attractor to the other.

For instance, NAO+ conditions of the most recent winters have shown a shutdown of Labrador Sea Convection. In just two and three winters, the long-sustained cooling and freshening of LSW has been largely reversed. A comparison of Atlantic SLP anomaly pattern between the 1995-1999 period with that for 19992000 shows a slight east and northeast displacement, in the more recent period, responsible for important differences to the marine climate of the West Greenland Banks and to the convective center of the Labrador Sea.

The NAO is reminiscent of the pioneer work of Lorenz (1990) who, with the help of a severely truncated and simplified model of atmospheric dynamics, essentially, a layer of fluid heated from below, showed that for small values of the Rayleigh number (a non-dimensional measure of the temperature difference between the lower layer and the upper layer), heat was transported by conduction; for higher values of the Rayleigh number, convective cells appeared to transport heat, for still higher values of the Rayleigh number, two strange attractors appear and the system may jump from one to the other as described above.

Further increase of the Rayleigh number, however sees the strange attractors disappear and a limit cycle appear.

Could it be the same bifurcation as the one which we observed in the NAO Index in the last decades 1970-2000 and that many authors attributed to global warming?

Even if this is stretching the comparison a little far, one should remark that, in Lorenz's model, a further increase of the Rayleigh number makes away with the limit cycle and the strange attractors reappear.

Further increase of the Rayleigh number generates an intermittent succession of periodic regimes and bursts of disorder (Nihoul 2007).

In fact, although models like the Lorentz model and the NAO Index representation are helpful to guide one's intuition of possible bifurcations of the atmospheric dynamics they are far too rudimentary to describe the dynamics of the system where the number of spatial modes generated by nonlinear interactions can be the determinant factor (Nihoul 2007).

One should thus be extremely careful in interpreting the NAO Index and presumably also in looking in its variations for global warming indications.

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