This study employs the GFDL CM2.6 climate model, a high-resolution Coupled General Circulation Model (CGCM) developed by the Geophysical Fluid Dynamics Laboratory (GFDL) . CM2.6 consists of the AM2 atmosphere, LM3 land model, MOM5 ocean model, and SIS sea ice model. The atmosphere and land models have a lateral resolution of nominally 0.5° with AMS utilising 32 vertical layers. MOM5, as implemented in CM2.6, features a refined ocean resolution varying from 11 km at the equator to 4 km at high latitudes, allowing for an eddy-permitting representation of ocean dynamics . The model includes 50 vertical layers in re-scaled geopotential height (z*) coordinates, over 5500 m.

This model was selected for several reasons. demonstrated that CM2.6 realistically captures transient mesoscale eddy heat transport in the northern Atlantic, allowing a clear separation between the contributions of mean advection and eddy processes. This leads to a more accurate representation of how heat converges within the ocean interior and results in smaller temperature drifts and more stable global heat budgets over long integrations. Similarly,  showed that CM2.6 reproduces the pathways and interactions of the Northwest Atlantic circulation with much greater fidelity compared to coarser resolved climate models, yielding more realistic regional climate change projections. In the Arctic context,  found that CM2.6 provides the best agreement with observed ocean heat transport and represents inter-basin heat transport more accurately than medium- and low-resolution models from the same model suite. In summary, these findings indicate that CM2.6 offers a robust framework for investigating northern Atlantic ocean heat transport processes and their evolution under elevated CO₂ concentrations.

The model is initialized with preindustrial boundary conditions, including atmospheric CO₂ concentration of 280 ppm as well as observed present-day ocean-conditions , followed by a spin-up simulation of 100 years into quasi-equilibrium. Two experiments are performed subsequently derived from this initial simulation. In the preindustrial control run (PIC), atmospheric CO₂ concentrations are kept constant at 280 ppm for 80 years, maintaining stable preindustrial climate conditions. In the CO₂ doubling experiment (2 × CO₂), atmospheric CO₂ is increased by 1 % yr⁻¹ over a period of 70 model years, reaching a final concentration of 560 ppm. The simulation is then extended for an additional 10 years with CO₂ levels held constant, allowing the system to adjust under the increased greenhouse gas forcing . Owing to data storage limitations, we had to restrict the analysis to 20-year periods drawn from the last 20 years of each simulation. Nonetheless, this experimental design allows us to diagnose the responses to increased atmospheric CO₂ forcing.

To calculate the meridional heat transport (MHT) across a desired latitude, a net zero volume transport is required . Hence, the zero-velocity reference is utilised to estimate the geostrophic velocities. The section-averaged velocity is then subtracted from the velocity field. Similar to , we compute MHT as follows: 1MHT=ρ0Cp∫x∫zΘ(x,z)[v(x,z)-v‾]dxdz, where ρ0 is the density, which is assumed to be constant at 1025 kg m⁻³, Cp is the specific heat capacity of 4000 kJ kg⁻¹ K⁻¹, Θ is the potential temperature, v is the meridional velocity and v‾ being the mean velocity over the cross section for the full basin depth, which ensures that MHT is associated with a net zero volume transport and therefore independent of a reference temperature .

The box model used for the following analysis consists of eight boxes (Fig. ). Box 0 represents the Southern Atlantic and the connection to other ocean basins. Boxes 1, 7, and 6 represent the tropical surface waters, intermediate waters, and deep water regions, respectively. Boxes 2 and 5 cover the surface and deep waters of the northern Atlantic while boxes 3 and 4 represent the Nordic Seas. Convection is active between the surface and bottom waters of the Nordic and northern Atlantic boxes as long as the density stratification is unstable, that is if ρ2>ρ5 or ρ3>ρ4. The overturning rates, m0 and m1, are governed by the density gradients between boxes 0 and 2/5, and 2/5 and 3/4, respectively. m0 represents the AMOC, and m1 the Nordic Overturning Circulation (NOC). We use a non-linear approximation for the equation of state (EOS) analogous to  to account for the non-linear effects of the temperature on the density at temperatures close to or below zero. Furthermore, all surface boxes lose or gain heat, governed by the temperature difference between the boxes and a respective restoring temperature multiplied by the restoring rates λi. This exchange can be interpreted as heat exchange with the atmosphere. The values for the restoring rates are calculated as follows 5λi=γCpρdi. where γ is the thermal coupling constant (10 kg K⁻¹ s⁻³), Cp is the specific heat capacity (4000 J kg⁻¹ K⁻¹), ρ the density of water (1025 kg m⁻³) and di the depth of box i. The restoring temperatures are fitting parameters. Note that the model in Fig.  is only valid for positive m0 and m1 and that the arrow pointing from box 2 to box 5 flips if m1>m0. The salinity and temperature values in the box model are fitted to sea surface temperature data from the World Ocean Atlas (winter averages between 1971–2000) . The winter period was chosen because convection is active during that time. All stacked boxes add to depth of 3000 m except for boxes 3 and 4 that add to 1500 m because the Nordic Seas have a shallower average depth than the Atlantic. The regions for the Nordic Seas and the subpolar North Atlantic are shown in Fig. . Only the western Nordic Seas and the Labrador Sea are considered because this is where the main convection sites are located (Fig. ). While the Labrador Sea dominates the contributions to the North Atlantic Deep Waters , the western Nordic Seas are also known to contribute significantly to the dense overflows that feed the lower limb of the AMOC . Furthermore, most of the freshwater input in the northern Atlantic is being focused towards the Labrador Sea due to the counter clockwise rotation of the ocean currents around Greenland , which favours this region for hosing experiments. Lastly, the water in the Labrador Sea is colder, which facilitates the onset of convection in the model. In the following we will refer to these regions simply as the Nordic Seas and northern Atlantic for simplicity.

We also implement a diffusion process between the tropical surface and intermediate waters to regulate the temperature in box 7. The full model equations for positive m0 and m1, as well as m0>m1, can be found in Appendix A. For the convection parameter ci 6ci=≫m0,if water column is unstable0,otherwise applies. The exact value of c is not critical, as long as it is large enough to guarantee that the surface box and deep water box are sufficiently mixed. The parameters Ks, Kn, and Knn are constant and take into account the gyre transport between the respective boxes. The values of Ks and Kn are 3.4 Sv respectively, and were estimated using the results of . The value of Knn was chosen to be 1 Sv.

η determines the rate of diffusion. η, f1, k0, k1 and the restoring temperatures are fitted by minimizing the loss function 7l=1.78∑k(Tk-T‾k)2+7.98∑k(Sk-S‾k)2+(m0-m0‾)2+(m1-m1‾)2+10(c1-c1‾)2 where k is the box number and the overlined letters are the present day values according to WOA23 data and, in case of AMOC (m0, 17 Sv) and NOC (m1, 6 Sv), current meter observations . The last term is added to guarantee convection in the Nordic Seas. The weights for the salinity and temperature differences are the values of α and β (in orders of magnitude of 10-4) in the linear EOS, because a difference in salinity impacts the density scaling with β, while the impact of a temperature difference scales with α. While these hyperparameters could potentially be tuned, this choice already yields satisfactory results. We divide by 8 to average over the 8 boxes.

A value of 0.07 Sv for f2 is chosen according to . They mention 20–30 mSv precipitation in the northern Atlantic region and about 40 mSv of freshwater influx from Arctic Sea Ice, Greenland Ice Sheet and the Canadian Arctic Archipelago combined. f3 is chosen to be smaller than but in the same order of magnitude as f2 since in the model freshwater is transported directly from the northern Atlantic into the Nordic Seas. The data is averaged from 0–100 m for the surface layers and from 100 m to a maximum depth of 3000 m/1500 m, according to the depth of the boxes.

The same data was used to calculate the order of magnitude of the increase in f2 per year. An approximate increase rate of 0.75 mSv yr⁻¹ was obtained from  for the influx from the Arctic Sea Ice, Greenland Ice Sheet and the Canadian Arctic Archipelago (calculated between 2000 and 2020). The net precipitation increased by a factor of three in about 25 years , so about 8 % yr⁻¹. Multiplying this with the 20–30 mSv measured by  one gets a crude estimate of the increase which is 2 mSv yr⁻¹. Prior to the global warming and hosing experiments, the model was spun up for 3000 years to achieve equilibrium. The beginning of the experiments is designated as model year 2000, aligning with the period of the fitting data.

Comparing the CM2.6 preindustrial control (PIC) and 2 × CO₂ simulations, we find a reduction of -0.09 PW in MHT into the subpolar North Atlantic and the Labrador Sea following a doubling of atmospheric CO₂. In contrast to this reduced MHT into the subpolar North Atlantic, there is an increase of 0.07 PW into the Nordic Seas over the same period. A heat budget analysis further reveals that in 2 × CO₂, this divergence in MHT is balanced by a substantial reduction in surface heat flux (SHF; defined as positive entering into the ocean) of -0.16 PW (SHF_2×CO2 - SHF_PIC) over the subpolar North Atlantic. A detailed presentation of the CM2.6 heat budget results is given in Table .

In the previous section it was shown that the increased heat transport into the Nordic Seas in 2 × CO₂ simulations with GFDL CM2.6 is associated with a strengthening of Nordic Overturning. In the following, we will use our box model to conceptually explore the possible reasons behind this increase by doing hosing and global warming experiments under the assumption that both, AMOC and NOC, are driven by density gradients. We compared different hosing rates ranging from 2 to 4 mSv yr⁻¹ and global warming scenarios from 0.1 to 0.4 °C per decade. We combined each hosing rate with each global warming scenario. The results are shown in Fig. . The warming was imposed on the restoring temperatures T*.

The AMOC exhibits a non-linear response to freshwater hosing (Fig. a, c, e). The hosing rate determines the steepness of the trajectory while the imposed warming initiates earlier convection shutdown due to decreasing surface buoyancy. Under 2 mSv yr⁻¹ of hosing and 0.1 °C per decade warming, convection ceases around year 2155 followed by a steep AMOC decline and final shutdown around 2170. For a warming rate of 0.4 °C per decade, however, convection already stops around 2130 – several decades earlier.

The increase in NOC as a response to a weakening AMOC is clearly visible in the box model and limited to about 1 Sv over 100 years (Fig. f), equivalent to a rate of 0.1 Sv per decade. This order of magnitude agrees well with climate model projections . Even though the hosing still appears to be the dominant factor, the warming steepens the NOC's trajectory, due to the temperature difference between the northern Atlantic and the Nordic Seas. Warming impacts the density in the northern Atlantic more than in the Nordic Seas because of the temperature-dependent thermal expansion coefficient in the equation of state, causing a nonlinear response of density to temperature changes. This increases the density gradient between the two ocean basins.

Due to the weakening of the AMOC, more freshwater accumulates in the northern Atlantic, decreasing the surface density and continuing to steepen the density gradient between the Nordic Seas and the northern Atlantic. The contributions of AMOC weakening and freshwater hosing to the freshening are initially comparable. However, as the hosing intensifies, the AMOC contribution eventually levels off, because the growing salinity contrast between the North Atlantic and the tropics begins to compensate for the weakened circulation (Fig. ). The freshening increases exchange between the northern Atlantic and Nordic Seas, causing the NOC to increase. This anticorrelation only breaks down when convection in the northern Atlantic shuts off because the freshwater at the surface layer can no longer be mixed downward at a sufficient rate. This causes more freshwater to be transported into the Nordic Seas via gyre transport and increased NOC, shutting down Nordic Sea convection in turn. This marks the crossing of the NOC's tipping point, which is followed by a steep decline in overturning strength. Additionally, we find that the decline of the AMOC is mitigated by an increase in NOC, as more cold, dense water is supplied to the northern Atlantic, counteracting the decrease in density.

To decompose the response of AMOC and NOC to the combined forcing, we conducted experiments with isolated global warming and hosing scenarios (Fig. ). Under isolated global warming the AMOC initially stays stable, while the NOC shows an accelerating increase until 2050 after which the rate of increase stays constant. The temperature difference between the northern Atlantic and the Southern Ocean is not as large as between the northern Atlantic and Nordic Seas, which explains the weak change in AMOC strength, since the thermal expansion coefficient is similar in both boxes.

Under hosing, the AMOC decreases steeply, while the NOC shows an increase in the short-term response due to the same mechanisms explained above, and then begins to decline around 2050 until convection shuts off and both currents cease. The decrease in NOC under isolated hosing, is explained by the continuous freshwater transport into the Nordic Seas via gyre transport and increased NOC which weakens the density gradient between the subpolar North Atlantic and Nordic Seas.

These results imply a short-term and long-term response under combined forcing: The short-term response of the current system is characterised by a negative feedback loop: Hosing weakens the AMOC by decreasing the water density in the northern Atlantic. This, in turn, increases the NOC and thus the transport of cold, dense water into the northern Atlantic which mitigates the AMOC's decline, but does not prevent it.

In the long term, warming delays the decline of the NOC (Fig. b), but accelerates the breakdown of convection (Fig. ) which causes an earlier AMOC shut-down. For very high hosing rates, the distances between the break-off points begin to diminish. This is because the accumulation of freshwater is so strong that it outweighs the effect of increasing temperature (Fig. ).

In order to compare with the box model results, we analyse density changes between the two forcing scenarios in CM2.6. The results in Fig. support the findings of the box model by illustrating how the density gradients between the northern Atlantic and the Nordic Seas strengthen under elevated CO₂ concentrations. The subpolar North Atlantic exhibits a pronounced density decrease, while the Nordic Seas show a localized density increase, particularly along the Greenland–Scotland Ridge and the western Nordic Seas. This pattern indicates that warming and freshening in the subpolar North Atlantic under increased CO₂ reduce surface density there, whereas the Nordic Seas experience comparatively smaller density reductions or even densification, consistent with the nonlinear thermal response in the equation of state discussed earlier. The resulting enhanced meridional density gradient aligns with the box model mechanism, where a weakening AMOC and surface buoyancy changes drive increased Nordic Overturning (NOC). A latitude–depth cross-section of the red box in Fig. a, further highlights this contrast: the upper ocean in the subpolar North Atlantic becomes significantly lighter, while the intermediate and deep layers toward the Nordic Seas show minor density increases, pointing to shoaling of isopycnals in the subpolar region and deepening in the Nordic Seas. Together, these patterns confirm that under increased CO₂, density-driven contrasts between the two basins intensify, as the box model predicts.