The thermohaline circulation (THC) of the Atlantic Ocean — the overturning that carries warm, saline upper water northward and returns cold deep water southward — may possess more than one stable equilibrium. In the standard coupled ocean-atmosphere model of the Geophysical Fluid Dynamics Laboratory (GFDL), Manabe and Stouffer (1999) found two stable equilibria (an active mode, and a weak 'reverse' mode), but showed that the reverse mode loses stability in a version of the same model with a much larger vertical subgrid-scale diffusion coefficient, implying a critical diffusivity above which bistability disappears. Because tracer observations indicated that the real ocean's thermocline diffusivity (about 0.1-0.2 cm² s⁻¹) is smaller than the model's, they inferred — but could not establish — that the real ocean is in the bistable regime. What later literature made of that question is as follows. Subsequent work confirmed that mixing strongly conditions THC stability, but found the dependence to be model- and basin-dependent, in some ocean models even of opposite sign, so that no universal critical diffusivity has been determined; observed mixing is now far better constrained but spatially heterogeneous; and state-of-the-art coupled models remain divided over whether a weakened overturning recovers after freshwater forcing is removed. Reviews through 2019-2026 conclude that the present Atlantic overturning may be close to a multiple-equilibria regime but that its position relative to stability thresholds is not known. The problem is therefore open: to determine, quantitatively and in a model-independent way, whether the observed ocean's diapycnal mixing places the Atlantic overturning in a bistable regime, and to disentangle why comprehensive models disagree.

Background

The Atlantic branch of the thermohaline circulation (THC) — now usually called the Atlantic Meridional Overturning Circulation (AMOC) — is the overturning in which warm, saline near-surface water flows northward in the Atlantic, cools and sinks in the Nordic and Labrador seas to form North Atlantic Deep Water (NADW, the sinking branch's water-mass product), and returns southward at depth. The circulation is density-driven, depending on both temperature ('thermo') and salinity ('haline'), and its possible instability has been a central concern of climate dynamics since box-model studies in the 1960s showed that two qualitatively different circulation regimes can both be stable under the same forcing (Stommel, 1961; a 'box model' is a severely idealized model in which the ocean is reduced to a few well-mixed reservoirs). The key mechanism is the salt-advection feedback: the overturning carries salty water northward, that salinity makes high-latitude surface water denser and sustains sinking; if the circulation weakens, less salt arrives, sinking weakens further, and the circulation can collapse toward a second equilibrium with deep water formed near the Antarctic instead — the 'reverse' or 'off' mode.

A coupled ocean-atmosphere general circulation model (GCM) simulates atmosphere, ocean, land, and sea ice simultaneously; early coupled GCMs required 'flux adjustment' — prescribed, time-independent corrections to the surface heat and freshwater fluxes — to keep simulated surface temperature and salinity near observed values. With such a model, Manabe and Stouffer (1988) obtained two stable equilibria corresponding to Stommel's two regimes. The 1999 Tellus A paper examined here (Manabe and Stouffer, 1999) showed that the two modes persist when seasonal variation of sunlight is included, but disappear in a version of the same model given a much larger coefficient of vertical subgrid-scale diffusion — the 'large vertical diffusion' (LVD) version. Subgrid-scale diffusion is the parameterized small-scale turbulent mixing that exchanges water properties; 'diapycnal' diffusion acts across surfaces of constant density (roughly vertically, in the stratified ocean), and it is what converts the deep cold reservoir upward and thereby sustains the overturning. A larger diapycnal diffusivity generally strengthens the overturning and, in this model, removes the second equilibrium: the paper concludes that 'there is a critical value of diffusivity above which two stable equilibria do not exist.' The model's standard profile (Bryan and Lewis, 1979) rises from 0.3 to 1.3 cm² s⁻¹ (3×10⁻⁵ to 1.3×10⁻⁴ m² s⁻¹) below the thermocline, whereas tracer-based observations — transient-tracer invasions and the deliberate open-ocean tracer release of Ledwell, Watson and Law — put the thermocline value at 0.1-0.2 cm² s⁻¹ (1-2×10⁻⁵ m² s⁻¹). Because the observed value lies below the model's, the authors inferred that the real ocean likely does possess the reverse mode. Other models behaved oppositely: in the coupled model of the Max Planck Institute for Meteorology (MPI; Schiller, Mikolajewicz and Voss, 1997) the collapsed circulation recovered once freshwater input stopped, and a global ocean model coupled to a simplified model atmosphere had, under slowly varying freshwater forcing, earlier displayed the associated bifurcation structure (Rahmstorf, 1995). The standard probe of such behavior is 'hosing' — prescribing an excess of freshwater over the North Atlantic — and 'hysteresis': the property that the circulation's state depends on its forcing history, so that increasing and then decreasing the hosing traces different branches, with an intermediate range where both strong and weak overturning are stable.

The paper's concluding section left five linked open items: the numerical value of the critical diapycnal diffusivity is unknown, so observational mixing estimates cannot be mapped onto stability regimes; the effective diapycnal and isopycnal (along-density-surface) eddy diffusion of the real ocean — and, for models, the implicit numerical diffusion generated by their advection schemes — is insufficiently constrained; intermodel differences have several confounded candidate causes and need controlled intercomparisons; the experiments should be repeated at much higher resolution with better bottom topography; and paleoceanographic evidence about North Atlantic ventilation during the Younger Dryas — the abrupt cold event about 12,700 years ago near the end of the last deglaciation, long attributed to a THC collapse — is ambiguous between a transient weakening and a longer-lived reversed state. Together these items pose one question: is the real ocean's Atlantic overturning, given its actual mixing, in the two-equilibria regime or not?

Problem Statement

Determine whether the real ocean's Atlantic overturning lies within a bistable (multiple-equilibria) regime, and specifically whether that regime is controlled by effective diapycnal mixing at magnitudes compatible with observations. Concretely: (i) establish, in realistic coupled ocean-atmosphere models, how the existence, width, and location of the bistable regime depends on the effective diapycnal diffusivity, meaning the sum of the explicitly parameterized mixing and the implicit numerical diffusion of the model's advection scheme, including whether a well-defined critical value exists at all, given that later studies found the dependence to be model- and basin-dependent and in some ocean-only models of opposite sign to the original coupled result; (ii) map observationally constrained mixing rates (deliberate tracer-release experiments, and microstructure and fine-structure compilations — measurements of small-scale temperature, salinity, and velocity fluctuations and of internal-wave strain, from which turbulent diffusivity is inferred) onto the diagnosed stability regimes, with quantified uncertainty; (iii) disentangle the intermodel disagreement in overturning bistability among comprehensive models — explicit diffusivity, numerical diffusion from advection schemes, resolution, wind-stress patterns, flux adjustment, and feedbacks such as salinity advection and the Antarctic Intermediate Water reverse cell — through controlled intercomparisons at the highest resolution feasible; and (iv) test the inferred stability regime against paleoceanographic evidence for North Atlantic ventilation during events such as the Younger Dryas. Items (i)-(iv) are all required. The target admits either of two outcomes: a defensible, uncertainty-quantified determination of whether the present-day Atlantic overturning is, or is not, within a bistable regime as far as its mixing environment is concerned, or a demonstration that no model-independent critical-diffusivity characterization exists, together with an established and validated replacement stability diagnostic.

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