A heuristic dynamical model of the North Atlantic Oscillation with a Lorenz-type chaotic attractor

Despite observational evidence of a distinct regime behaviour in the low-frequency variability of the North Atlantic Oscillation (NAO), the theoretical support for the existence of separate NAO regimes has been limited. Although NAO-like regimes have been detected in numerical models of varying complexity, the role of forcings and feedbacks originated by diabatic processes in the specific geographical setting of the North Atlantic region has not been explicitly advocated as a source of regime behaviour for the NAO. In this study, we develop a minimal theoretical model of the interactions between zonal flow (and associated temperature gradient), planetary waves and surface heat fluxes in the North Atlantic, guided by results from observational diagnostics. Using re-analysis data, we show that interactions between an equivalent barotropic NAO anomaly and climatological stationary waves with a baroclinic structure and a larger meridional scale generate a positive feedback between the NAO-like wave and the strength of the zonal flow. On the other hand, an increased zonal wind generates stronger surface heat fluxes which damp both the zonal and the wave components of the NAO-like anomaly. Using these observational results to guide the choice of empirical parameters, we construct a 3-variable model which is formally equivalent to the Lorenz (J Atmos Sci 20:130-141, 1963) chaotic model for Rayleigh-Benard convection, and possesses two regimes originated by oscillations around two weakly unstable stationary states. From a physical point of view, the two regimes correspond to opposite phases of a near-resonant planetary wave which occur when the zonal flow is either below (negative NAO) or above (positive NAO) the value corresponding to zero phase speed. Finally, we expand the model to a five-variable system by splitting the zonal-mean wind into its barotropic (i.e. height independent) and thermal component, and including a variable representing the area-averaged amplitude of high-frequency baroclinic eddies. Following earlier studies, we assume that high-frequency eddy activity grows by extracting available potential energy from the zonal-mean temperature gradient and decays by feeding kinetic energy into the barotropic component of the zonal wind. The extended model still displays a chaotic, two-regime behaviour, with additional sub-seasonal variability driven by the energy exchanges associated with high-frequency eddy amplification and decay.