Atlantic Meridional Overturning Circulation

• AMOC is a large-scale Atlantic system that transports warm, saline surface waters northward and returns colder deep waters southward, playing a key role in oceanic heat and freshwater balance.
• The circulation is analyzed through boundary-controlled components such as thermal wind, Ekman, and bottom flows that together reconstruct over 95% of the streamfunction’s spatial variability.
• AMOC stability is influenced by coupled density, salinity, and freshwater budget dynamics, with studies highlighting multiple tipping pathways and challenges in observational proxy validation.

The Atlantic Meridional Overturning Circulation (AMOC) is the large-scale Atlantic overturning system that transports warm, salty upper-ocean waters northward and returns colder, denser waters southward at depth. It is a major component of the climate system because it regulates ocean heat transport, freshwater and salinity distribution, carbon and nutrient transport, and regional climate patterns, and because a sufficiently strong weakening or collapse would have serious climatic impacts (Chen et al., 2023, Haren, 2023).

1. Structure, kinematics, and dynamical diagnostics

A standard diagnostic of AMOC is the depth-space overturning streamfunction,

$$\Psi(z;y) \equiv \int_{W(y)}^{E(y)} \int_{-H(x,y)}^{z} v(x,y,z') \, dz' \, dx,$$

where $v(x,y,z)$ is meridional velocity, $H(x,y)$ is ocean depth, and $W(y),E(y)$ are the western and eastern basin boundaries. AMOC “strength” at latitude $y$ is then

$\Psi_{\max}(y) = \max_{z} \Psi(z;y).$

This formulation underlies both observational products and model-based analyses of Atlantic overturning (Jonathan, 2022).

A low-dimensional but dynamically informative decomposition writes the meridional velocity as the sum of a depth-independent bottom contribution, a baroclinic thermal-wind contribution, and a near-surface Ekman contribution,

$$v_{N}(x,z; y) = v_{bot}(x; y) + v_{th}(x,z;y) + v_{Ekm}(x,z;y),$$

so that the reconstructed overturning becomes

$$\tilde{\Psi}(z; y) = \Psi_W(z; y) + \Psi_E(z; y) + \Psi_{bot}(z; y) + \Psi_{Ekm}(z; y).$$

In this framework, western and eastern boundary density structure constrain overturning through thermal wind, while wind stress and bottom velocity provide additional dynamically distinct components (Jonathan, 2022).

This boundary-based view is not merely formal. In a $1/4^\circ$ control simulation, the boundary-based reconstructed streamfunction explains $95.8\%$ of the spatial structure of the directly computed streamfunction, and the mean maximum overturning is relatively constant at about $v(x,y,z)$0 Sv from the South Atlantic to about $v(x,y,z)$1N even though the underlying boundary contributions vary strongly with latitude (Jonathan, 2022). A plausible implication is that AMOC is simultaneously a basin-scale circulation and a boundary-controlled dynamical object, which is why boundary monitoring remains central to observing-system design.

2. Physical drivers, density contrasts, and freshwater control

AMOC is often summarized schematically as a circulation that carries heat poleward near the surface and returns colder deep waters southward, but several papers stress that its maintenance cannot be reduced to a one-variable “thermohaline” picture. One line of argument emphasizes that the ocean is not a heat engine and that overturning requires mechanical energy input from winds and tides, with turbulent diapycnal mixing generated by internal-wave breaking providing the crucial coupling between upper-ocean buoyancy anomalies and the abyssal return circulation. In that view, deep dense-water formation is sporadic and pulsed rather than a steady primary engine, and without turbulent mixing overturning would be confined to a thin near-surface layer of roughly $v(x,y,z)$2 m (Haren, 2023).

A complementary mechanistic analysis in CESM reconstructs AMOC from a large-scale meridional density contrast. Using a thermal-wind closure with a fitted proportionality constant $v(x,y,z)$3, the reconstruction captures the mean upper-ocean overturning structure, the total weakening of roughly $v(x,y,z)$4 Sv, and the collapse transition itself. In that simulation, almost all AMOC weakening is attributed to the change in vertically averaged meridional density contrast: vertically averaged density changes cause about $v(x,y,z)$5 Sv of weakening, while changes in stratification contribute a small $v(x,y,z)$6 Sv strengthening. North Atlantic cooling offsets about $v(x,y,z)$7 of the freshening-induced AMOC weakening before tipping, and South Atlantic density changes offset about $v(x,y,z)$8 of the North Atlantic-driven weakening (Vanderborght et al., 2024).

Freshwater-budget analyses show why South Atlantic conditions matter. At $v(x,y,z)$9S, the equivalent freshwater import by the overturning circulation is

$H(x,y)$0

while the azonal or gyre-related component is

$H(x,y)$1

If $H(x,y)$2, the overturning exports salt from the Atlantic basin and the salt-advection feedback is negative; if $H(x,y)$3, the overturning imports salt and a weakening AMOC reduces that salt import, freshens the basin, and promotes further weakening. The South Atlantic zonal salinity contrast directly affects $H(x,y)$4, and through freshwater-budget compensation it shifts $H(x,y)$5, thereby altering whether the system is in a single stable “ON” state or a multiple-equilibria regime (Cimatoribus et al., 2011).

In CESM, the analogous South Atlantic stability indicator is the overturning freshwater transport at $H(x,y)$6S, $H(x,y)$7. A negative sign indicates a destabilising salt-advection feedback. The sign change of $H(x,y)$8 from positive to negative around year $H(x,y)$9 marks the transition from a weakly stabilizing to a destabilizing overturning background state, after which the salt-advection feedback becomes the dominant driver of collapse (Vanderborght et al., 2024). This suggests that AMOC stability is set by coupled density, salinity, and freshwater-transport structure across the basin rather than by northern sinking alone.

3. Multistability, tipping, and transition pathways

AMOC is widely treated as a multistable system with vigorous “ON” and weak or collapsed “OFF” regimes, but the geometry of that multistability differs across models. In a physically derived five-box model calibrated to FAMOUS, the loss of stability of the “ON” state is caused not by a simple saddle-node but by a subcritical Hopf bifurcation. Before that local instability, a homoclinic basin bifurcation shrinks the basin of attraction of the strong state, so tipping can occur through finite perturbations or rapid forcing changes even while the “ON” equilibrium still exists (1901.10111).

This distinction matters for nonautonomous climate change. The same conceptual framework shows rate-induced thresholds: the AMOC can tip for perturbations that do not cross the bifurcation, because rapid forcing can move the state outside the shrinking basin of attraction. Related work on a four-dimensional conceptual model combines a Stommel-type salt-advection feedback with a Welander-type smooth convective-adjustment mechanism and finds up to four coexisting overturning states, together with periodic and chaotic regimes in which a millennial oscillation is modulated by faster decadal-to-centennial variability arising from episodic shutdowns of subpolar convection (Bailie et al., 12 Mar 2026). A plausible implication is that “threshold” language is often too coarse unless the underlying basin geometry and forcing rate are specified.

Higher-dimensional dynamical-systems analyses strengthen this point. In a primitive-equation ocean GCM, an unstable AMOC “Melancholia” or edge state has been explicitly constructed on the basin boundary between vigorous and collapsed regimes. It is intermediate in upper-ocean properties but has a deep Atlantic that is fresher and colder than both stable regimes, and it has higher dynamic enthalpy than either stable state, exceeding the OFF state by $W(y),E(y)$0 J and the ON state by $W(y),E(y)$1 J (Lohmann et al., 2024). In PlaSim-LSG, the strong attractor and the edge state collide in a boundary crisis between $W(y),E(y)$2 and $W(y),E(y)$3 ppm, after which long chaotic transients are organized by a ghost state and ensemble trajectories split under identical forcing (Börner et al., 28 Apr 2025).

Noise-induced transitions add another layer. In a stochastic five-box World Ocean model, the most probable AMOC-collapse path starts with a temporary strengthening of the AMOC and then an immediate drop within a couple of years due to a short but relatively strong freshwater pulse, whereas recovery is a slow process requiring gradual North Atlantic salinification over about $W(y),E(y)$4 years (Soons et al., 2023). This suggests that bifurcation-induced collapse, noise-induced collapse, and rate-induced collapse need not have the same precursor structure.

4. Observations, proxies, and monitoring strategies

A persistent difficulty in AMOC research is that direct, continuous in situ measurements extend back only to about 2004, so longer-term inference relies on proxies rather than direct overturning observations (Chen et al., 2023). This has made observational methodology a central source of disagreement.

One major debate concerns early warning signals from historical proxy records. A focused rebuttal of Boers (2021) argues that the reported early warning signals are largely false alarms generated by increasing observational coverage through time. In EN4 $W(y),E(y)$5 fields, early decades had extremely sparse observations, so climatological infill suppressed variance; as coverage improved, variance rose mechanically even if underlying climate variability did not. Chen and Tung further show that climate models without early warning signals can be made to yield apparent signals when subsampled according to historical observational coverage, and they argue that two subpolar salinity proxies used in the tipping narrative have their signs reversed (Chen et al., 2023). Their conclusion is not that AMOC collapse is impossible in principle, but that those particular observational records do not robustly support a pending collapse.

A related criticism targets SST-based collapse estimators more generally. One argument is that a particular estimator of sea-surface temperature may be mathematically robust yet still “lack physical insight of the drivers of the AMOC,” because physical processes such as stratification changes, internal-wave pathways, boundary mixing, and turbulent diapycnal exchange can alter SST independently of actual approach to collapse. In that view, salinity, density gradients or stratification, and turbulence intensity are more physically tied to overturning than SST alone (Haren, 2023).

At the same time, some monitoring frameworks exploit spatial structure rather than single indices. In FAMOUS hosing experiments, a Pearson Correlation Climate Network built from the Atlantic MOC field yields an early warning indicator based on the kurtosis of the degree distribution, $W(y),E(y)$6, which crosses the control maximum at year $W(y),E(y)$7, giving a lead time of $W(y),E(y)$8 years before the collapse time $W(y),E(y)$9 years. Single-section monitoring performs poorly, but multi-section arrays spanning both hemispheres remain effective; in that study, sections near $y$0S and $y$1N are especially important (Feng et al., 2014). Boundary-monitoring theory provides an independent rationale: sparse boundary density profiles can reconstruct the overturning well, and the eastern boundary density structure is sufficiently simple that practical monitoring may require relatively few profiles (Jonathan, 2022).

A more recent surface-current approach identifies an “Atlantic Convergence-Divergence Mode” (ACDM) from Atlantic surface-current directional data and proposes it as a physically grounded proxy for interannual AMOC variability. Its annual index $y$2 correlates with RAPID-MOCHA AMOC observations at $y$3, and it captures a pronounced regime shift around 2009 (Huang et al., 13 Apr 2026). This suggests that basin-scale surface-current organization may complement density- and transport-based observing systems.

5. Contemporary assessments of weakening and future collapse risk

Recent assessments diverge sharply on what present observations and model trajectories imply. One line of work infers a relatively vulnerable AMOC. Combining targeted CESM simulations, CMIP6 models, observations, and reanalysis, one study estimates a critical threshold of about $y$4 global mean surface warming relative to pre-industrial, with a $y$5–$y$6 confidence interval of $y$7 to $y$8. In that framework, AMOC tipping is more likely than not under SSP2-4.5 and very likely under SSP5-8.5 within the 21st century, even though the fully collapsed state often emerges only after 2100 (Westen et al., 2024).

Another line of work argues that such threshold statements are strongly path dependent. In CESM experiments initialized from a vulnerable AMOC state, a slow CO$y$9 increase of $\Psi_{\max}(y) = \max_{z} \Psi(z;y).$0 ppm yr$\Psi_{\max}(y) = \max_{z} \Psi(z;y).$1 keeps the AMOC stable up to about $\Psi_{\max}(y) = \max_{z} \Psi(z;y).$2C global mean surface temperature anomaly, whereas RCP4.5 and RCP8.5 from the same state produce collapse onset around $\Psi_{\max}(y) = \max_{z} \Psi(z;y).$3C and $\Psi_{\max}(y) = \max_{z} \Psi(z;y).$4C, respectively (Westen et al., 10 Feb 2026). The proposed mechanism is that slow forcing permits coherent adjustment of surface and interior density structure, enhanced evaporation, reduced sea-ice extent, and continued water-mass transformation, whereas faster forcing causes the surface ocean to outrun the interior and closes the adiabatic pathways required to sustain overturning.

This rate sensitivity complicates claims of an imminent observationally detectable collapse. Chen and Tung’s critique maintains that currently available proxy evidence does not provide credible evidence for a pending AMOC collapse (Chen et al., 2023), whereas the surface-current analysis of ACDM argues that a pronounced regime shift in 2009 reflects a nonlinear, step-like weakening of AMOC and a basin-scale reorganization of Atlantic surface currents (Huang et al., 13 Apr 2026). These positions are not logically identical: one rejects a specific early-warning interpretation of proxy variance, while the other emphasizes a recent nonlinear circulation shift at interannual timescales. Together they indicate that present-day AMOC diagnosis remains contested not because AMOC is climatically unimportant, but because the inferential chain from sparse observations to basin-scale stability is still uncertain.

6. Resilience, intervention, and unresolved problems

AMOC resilience has increasingly been framed probabilistically rather than purely in terms of bifurcation points. A rare-event framework defines resilience through both “resistance to change” and “ability to return,” using an observable that distinguishes the background AMOC-on region $\Psi_{\max}(y) = \max_{z} \Psi(z;y).$5 from an undesirable region $\Psi_{\max}(y) = \max_{z} \Psi(z;y).$6. In a conceptual AMOC model, the score function

$\Psi_{\max}(y) = \max_{z} \Psi(z;y).$7

is used with Adaptive Multilevel Splitting to estimate level-crossing probabilities, return probabilities, and mean first-passage times, leading to a resilience functional

$\Psi_{\max}(y) = \max_{z} \Psi(z;y).$8

In that setting resilience decreases approximately linearly with increasing freshwater forcing, is strongly reduced by larger noise, and supports a conditional safe operating space defined in terms of collapse probability conditioned on observed weakening (Jacques-Dumas et al., 2024).

Intervention studies remain exploratory but have begun to appear. In CLIMBER-X, an artificial closure of the Bering Strait can increase the AMOC safe carbon budget, but only if the AMOC is still sufficiently strong at the time of closure. The reported threshold is an equilibrium AMOC under OBS of $\Psi_{\max}(y) = \max_{z} \Psi(z;y).$9 Sv, equivalent to a reduction of $$v_{N}(x,z; y) = v_{bot}(x; y) + v_{th}(x,z;y) + v_{Ekm}(x,z;y),$$0 from pre-industrial strength; below that threshold, closure helps and can add up to $$v_{N}(x,z; y) = v_{bot}(x; y) + v_{th}(x,z;y) + v_{Ekm}(x,z;y),$$1 PgC to the safe carbon budget, whereas for a weaker AMOC the same intervention reduces resilience (Soons et al., 27 Aug 2025). The paper explicitly treats this as a theoretical proof of concept rather than a policy-ready proposal.

Several unresolved problems cut across the literature. One is proxy validity: basin-wide AMOC proxies are often weakly validated and can disagree in sign or spatial coherence (Chen et al., 2023). Another is structural uncertainty in modern climate models, especially the interpretation of $$v_{N}(x,z; y) = v_{bot}(x; y) + v_{th}(x,z;y) + v_{Ekm}(x,z;y),$$2: if many CMIP-class models have a positive $$v_{N}(x,z; y) = v_{bot}(x; y) + v_{th}(x,z;y) + v_{Ekm}(x,z;y),$$3 bias, their AMOC may be too stable, implying underestimated collapse risk under climate change (Vanderborght et al., 2024). A further issue is phase-space complexity. Edge states, ghost states, stochastic instantons, and rate-induced thresholds all indicate that AMOC cannot be fully characterized by a single equilibrium branch or a single warming threshold (Börner et al., 28 Apr 2025, Soons et al., 2023). This suggests that future progress will depend on combining boundary and section observations, process-based freshwater and density budgets, rare-event methods, and fully coupled dynamical-systems analysis.