A minimal model of the Atlantic Multidecadal Variability: its genesis and predictability

Through a box model of the subpolar North Atlantic, we examine the genesis and predictability of the Atlantic Multidecadal Variability (AMV), posited as a linear perturbation sustained by the stochastic atmosphere. Postulating a density-dependent thermohaline circulation (THC), the latter would strongly differentiate the thermal and saline damping, and facilitate a negative feedback between the two fields. This negative feedback preferentially suppresses the low-frequency thermal variance to render a broad multidecadal peak bounded by the thermal and saline damping time. We offer this “differential variance suppression” as an alternative paradigm of the AMV in place of the “damped oscillation”—the latter generally not allowed by the deterministic dynamics and in any event bears no relation to the thermal peak. With the validated dynamics, we then assess the AMV predictability based on the relative entropy—a difference of the forecast and climatological probability distributions, which decays through both error growth and dynamical damping. Since the stochastic forcing is mainly in the surface heat flux, the thermal noise grows rapidly and together with its climatological variance limited by the THC-aided thermal damping, they strongly curtail the thermal predictability. The latter may be prolonged if the initial thermal and saline anomalies are of the same sign, but even rare events of less than 1% chance of occurrence yield a predictable time that is well short of a decade; we contend therefore that the AMV is in effect unpredictable.