Atmospheric flows are characterized by a large number of degrees of freedom, resulting from the wide range of spatial and temporal scales at which energy enters the system and is then dissipated. This motivated Landau to describe them as the superposition of a growing number of modes with incommensurable oscillation frequencies. Ruelle-Takens later proved that flows are in general not quasi-periodic and conjectured that they could be described by a small number of degrees of freedom associated with a low dimensional strange attractor D. Nonetheless successive numerical studies showed that D for the climate (if any) would be of a very high dimension.
In this paper we compute D for daily sea-level pressure fields over the North Atlantic, obtained from the NCEP reanalysis. We then use it to retrieve some salient dynamical features of the mid-latitude circulation. Our methodology exploits the connection between the Poincaré recurrences and the extreme value theory to provide a dimension for each daily pressure field. Once averaged, this quantity gives, by definition, D. We find that D is approximately 7, pointing to the existence of a low dimensional attractor for the North Atlantic large-scale circulation. Moreover, minima of the daily dimension correspond to positive NAO-type conditions. We further demonstrate a statistical link with historical storms affecting continental Europe, suggesting a link between the extremes of the dynamical system and those of the weather. On the opposite, maxima in the dimension correspond to a blocked atmospheric flow. The intrinsic unpredictability of blocking can be interpreted as the outcome of its high dimensionality in phase space.
Low dimensional attractors may exist for several other geophysical phenomena provided that relevant spatial and time scales are selected.