Theoretical Investigation of the Atlantic Multidecadal Oscillation

A weakly damped mode of variability, corresponding to the oceanic signature of the Atlantic multidecadal oscillation (AMO) was found through the linear stability analysis of a realistic ocean general circulation model. A simple two-level model was proposed to rationalize both its period and damping rate. This model is extended here to three levels to investigate how the mode can draw energy from the mean flow, as found in various ocean and coupled models. A linear stability analysis in this three-level model shows that the positive growth rate of the oscillatory mode depends on the zonally averaged isopycnal slope. This mode corresponds to a westward propagation of density anomalies in the pycnocline, typical of large-scale baroclinic Rossby waves. The most unstable mode corresponds to the largest scale one (at least for low isopycnal slope). The mode can be described in four phases composing a full oscillation cycle: 1) basin-scale warming of the North Atlantic (AMO positive phase), 2) decrease in upper-ocean poleward transport [hence a reduction of the Atlantic meridional overturning circulation (AMOC)], 3) basin-scale cooling (negative AMO), and 4) AMOC intensification. A criterion is developed to test, in oceanic datasets or numerical models, whether this multidecadal oscillation is an unstable oceanic internal mode of variability or if it is stable and externally forced. Consistent with the classical theory of baroclinic instability, this criterion depends on the vertical structure of the mode. If the upper pycnocline signature is in advance of the deeper pycnocline signature with respect to the westward propagation, the mode is unstable and could be described as an oceanic internal mode of variability