The HadGEM3-GC3.1 coupled model used in this study forms part of the UK Met Office's contribution to the sixth phase of the Coupled Model Intercomparison Project (CMIP6) simulations . Relative to HadGEM2-AO, which was the Met Office's submission to CMIP5, the HadGEM3-GC3.1 model includes new ocean and sea ice models, new aerosol and cloud schemes, major revisions to the atmosphere dynamical core and many more updates to the parametrisation schemes. These revisions have led to marked improvements in many aspects of the simulated present-day climate. Detailed comparisons between the HadGEM3-GC3.1 model and its predecessors are given by .

HadGEM3-GC3.1 is comprised of the GA/GL7.1 atmosphere and GO6 ocean model components, coupled via OASIS-MCT coupler , in 1 h timesteps. Additionally, GA/GL7.1 implements the GLOMAP modal aerosol scheme , whereas the ocean component, based on version 3.6 of the Nucleus for European Modelling of the Ocean (NEMO) ocean model , also embeds the sea ice model GSI8.1 .

The GLOMAP (Global Model of Aerosol Processes) aerosol scheme represents a marked increase in complexity compared to the preceding aerosol scheme, CLASSIC (Coupled Large-scale Aerosol Simulator for Studies In Climate), which was used in the previous version of the climate model, HadGEM2-ES. The key difference between the two schemes is that in CLASSIC, aerosol mass is a prognostic variable, but aerosol number is a diagnostic variable, which is also based on a fixed mass distribution. Whereas in GLOMAP, both aerosol mass and number are prognostic variables . This difference means that aerosols in GLOMAP can respond to emissions, chemistry and microphysics by changing aerosol number at a given size or changing the aerosol number independently. This is important, as the same mass of aerosol distributed in different sizes can give different aerosol optical depth and hence different forcing. A further improvement to CLASSIC is that the GLOMAP aerosol scheme is capable of interactively resolving aerosol chemistry, namely, the oxidation of aerosol precursors. However, the implementation of GLOMAP for HadGEM3-GC3.1 uses only a simplified version of the chemistry scheme, and chemical oxidants are prescribed from monthly-mean climatologies instead of being interactively resolved .

The two versions of the model used throughout this study are denoted LL and MM (known as HadGEM3-GC3.1-LL and HadGEM3-GC3.1-MM, respectively). The medium-resolution (MM, N216-ORCA025) model has horizontal resolution of 60 km in the mid-latitude atmosphere and 0.25° in the ocean. The low-resolution (LL, N96-ORCA1) model has horizontal resolution of 135 km in the mid-latitude atmosphere and 1° in the ocean. The vertical resolution is the same in both LL and MM, with 85 pressure levels in the atmosphere, up to 85 km, and 75 depth levels in the ocean.

A top priority during the development of the HadGEM3-GC3.1 models was to minimise the dependence of parameters on model resolution. This has the benefit of helping to understand the effect of model resolution on important climate processes. Therefore, the MM and LL models are extremely similar and differ mainly in horizontal resolution. However, there are still some small physical differences between LL and MM, which arise mainly from the use of different parameter values to compensate for resolution-dependent processes. For example, the LL atmosphere has different parameter values to compensate for lower maximum winds and the limited resolution of gravity wave drag. There are also differences in the ocean submodels; in particular, ORCA1 includes a Gent–McWilliams parameterisation for eddy-induced fluxes, but ORCA025 does not, and ORCA1 also has a slightly lower albedo for snow on sea ice to compensate for weak Arctic sea ice bottom melt. Further details and a summary table of the differences are included in .

To investigate and isolate the influence of historical AA emissions on the North Atlantic, a set of idealised single-forcing experiments is performed. The forcing applied is realistic in spatial pattern and magnitude, but idealised in time. A perturbation of only sulphur dioxide (SO₂) emissions is introduced to otherwise pre-industrial (PI) conditions. These emissions are based on the CMIP6 historical emissions within the North Atlantic sector (i.e. North American and European emissions). The spatial pattern of the minimum (1850) and maximum (1973) SO₂ emissions is shown in Fig. a, b. The timescale of how these emissions are applied in the experiment is shown in Fig. d. The experiment begins from PI conditions, SO₂ emissions, then ramp up linearly for the first 10 years up to a maximum rate of 1700 kg s⁻¹ (defined as the 15-year mean around 1973). The maximum emission rate is then held constant for 20 years, before ramping back down to PI conditions over 10 years. The simulation ends with 10 years of constant forcing at PI conditions, running a total of 50 years.

The reason for considering only SO₂ emissions (while omitting organic carbon, black carbon and dust) is because sulphate aerosol is the primary agent of AA radiative forcing during the historical period and previous studies have found that multidecadal changes in SO₂ emissions have had the greatest influence on North Atlantic SST changes . The purpose of this set of experiments is to identify the specific mechanism linking these SO₂ emissions to the AMV, without the influence of competing sources of external forcing.

Asian SO₂ emissions are not considered, and only emissions from the North Atlantic sector are included in this experiment for the same reason; to simplify the situation and help isolate specific mechanisms. This is because the processes linking emissions from different regions to the North Atlantic are likely different. For example, North American and European aerosols do so predominantly through local short-wave changes , but Asian aerosols may affect the North Atlantic through complex teleconnection mechanisms such as Rossby wave train from the western North Pacific to Europe , with potentially competing effects. These atmospheric teleconnections could potentially lead to a weakening of the AMOC , but it is outside the scope of this study.

The timescale and magnitude of the idealised SO₂ emissions are chosen to simulate the multidecadal timescale of the historical SO₂ emissions. Timeseries of the historical SO₂ emissions across the North Atlantic sector are shown in Fig. c. The ramping-up and ramping-down of emissions in the idealised perturbation are designed to simulate the rapid rise and fall of emissions from the 1930s to the present day. Because the peak emissions of North America slightly lead the European emissions peak, a 15-year mean around 1973 captures the peak emissions of both regions and is therefore used as the maximum emission rate for the idealised perturbation. The idealised time series is useful for identifying key processes, because the projection of such a distinctive timeseries on different variables shows clear links between how different variables influence each other. In addition, seasonal cycles in the emissions are not considered in the single-forcing experiment; the emission ramp-up occurs at each monthly timestep of the model simulations.

This set of experiments is different to the Detection and Attribution Model Intercomparison Project (DAMIP, ) and Precipitation Driver Response Model Intercomparison Project (PDRMIP, ) experiments performed as part of CMIP6. The DAMIP experiment includes single-forcing simulations; however, global emissions are used, and the emissions follow the historical timeseries, making it more difficult to isolate specific mechanisms linking AA to North Atlantic SST changes. The PDRMIP experiment is more similar to our set of idealised experiments, including single-forcing simulations with additional regional emission simulations and idealised temporal evolution. However, the PDRMIP idealised temporal evolution is designed to test equilibrium responses instead of simulating historical changes, and the regional emissions are Europe-only or Asia-only.

A 4-member ensemble was run for 50 years for both MM and LL versions of the model. The initial conditions for each ensemble member are the same as the ones used for the CMIP6 historical simulations . The initial conditions were chosen to minimise the chance of each ensemble member starting from a similar oceanic state by considering the two leading modes of multidecadal variability: the Interdecadal Pacific Oscillation (IPO) and the Atlantic Multidecadal Variability (AMV). The MM idealised experiments were initialised with initial conditions from 1850, 1885, 1930, and 1960 of the N216 PI-control and the LL experiments from 1850, 1885, 1930 and 1970 of the N96 PI-control. These initial conditions include positive and negative phases of both the IPO and AMV . All anomalies in the following analysis are calculated by first taking the difference between each ensemble member and the time mean over their respective segment from the PI-control. This is to minimise the problem with drift in the PI control simulation. The ensemble mean anomalies are then calculated from taking a mean over the anomalies from each ensemble member.

Figure a, b shows timeseries comparison of the standard AMOC in depth space (AMOC-z, defined at a depth of 1000 m, where the mean state is at maximum) against the AMOC in density space (AMOC-sigma, at density of 27.8 and 27.6 kg m⁻³), for the two different resolutions. Both the density and depth space timeseries are defined at 45° N. The two density levels are chosen to correspond with where the mean state and where the standard deviation is largest, respectively (Fig. ). 45° N is chosen as the latitude to define the AMOC index, as it is the southern boundary of the western SPG and captures the water masses formed north of this latitude while minimising the influence of other model-dependent processes such as the southward propagation pathways of water masses .

The AMOC in depth space is not a good representation for this analysis because the same depth can contain waters of many different density classes due to the E–W density gradient at high latitudes. Indeed, the maximum AMOC-depth 45°N anomaly is 2.95 Sv in MM and 2.86 Sv in LL (Fig. a, b). There is also a larger difference between the AMOC-depth and AMOC-sigma index in MM, which is consistent with differences in the simulated AMOC structure related to model resolution. Higher resolution models tend to have a stronger E–W density gradient at high latitudes, therefore there is stronger cancellation between the light, northward flow and dense, return flow at the subpolar latitudes when represented in depth space . AMOC in density space tends to be a better representation for assessing the dynamics.

In density space, both indices at 27.8 and 27.6 kg m⁻³ capture a larger increase in MM (Fig. a, b). Although the magnitude of the AMOC-sigma anomalies and the inter-model differences are much more pronounced with the 27.8 kg m⁻³ index. The 27.8 kg m⁻³ index has a maximum anomaly of 7.89 Sv in MM and 5.24 Sv in LL, which is an increase of 52 % and 42 % over the maximum AMOC-sigma strength at 45° N in the PI control mean state for the MM and LL models, respectively. Whereas, the 27.6 kg m⁻³ index has maximum anomaly of 4.09 and 2.94 Sv in MM and LL respectively, corresponding to an increase of 30 % and 26 % from the maximum PI control mean. As shown in the previous section, the AMOC tends to shift to a higher density class as it strengthens, and we are interested in the difference in the AMOC response between the two resolutions, therefore we will use the AMOC strength at the denser level of 27.8 kg m⁻³ as the AMOC-sigma index hereafter.

The combined effect of air-sea exchanges of heat and freshwater on sea water density (i.e. surface density flux) can be written as a function of the net surface heat (Q) and freshwater (F) fluxes as follows: 1f=-αCpQ-βS1-SF where α and β are the (positive) thermal expansion and haline contraction coefficients, Cp is the specific heat capacity of seawater, and S is the sea surface salinity . The sign convention used here is that positive (red in Fig. ) denotes an increase in sea surface density and negative (blue in Fig. ) denote a more buoyant sea surface.

Figure  shows the evolution of annual mean surface density flux anomalies. Additionally, extended late winter (January–February–March–April, JFMA) ocean surface density 27.6 and 27.8 kg m⁻³ are highlighted by the blue and black contour lines as these density levels correspond to the maximum AMOC-sigma mean in the PI control and location of the largest AMOC-sigma anomalies in the idealised experiment respectively. The regions bounded by these contour lines indicate where these isopycnals outcrop to the surface, and therefore, the regions where surface forcing is directly driving the AMOC lower limb. The JFMA period is chosen because this is when the ocean surface is at its densest, therefore it is the period at which isopycnals of the densest water classes outcrop at the surface and water mass transformation occurs. Note that the surface density shown is the ensemble mean, not anomalies with respect to the PI control. This is because the absolute values of density are important for identifying specific density classes, not the relative changes. Figure  focuses only on the initial 19-years, to minimise the influence of the feedback from ocean circulation changes as the strengthening of AMOC and associated heat transport can also impact on the surface fluxes and water mass transformation.

In both LL and MM, two key regions are highlighted where the 27.6 kg m⁻³ density level consistently outcrops (i.e. blue contour lines, Fig. ). These are the western SPNA (WSPNA) region and the Arctic region, which includes the GIN and Barents Seas. Note that the location and size of the two regions do not appear to change much with the varying levels of SO₂ emissions. The WSPNA outcropping region is larger in MM, spanning across much of both the LS and Irminger Seas (IS). Whereas, in LL, the WSPNA outcropping region is smaller and does not extend as far into the LS and IS. Additionally, the surface is denser in MM, with denser waters of 27.8 kg m⁻³ outcropping in the central LS, which does not occur in LL. In the Arctic, the regions of outcropping are more comparable between the two models (Fig. ). The Arctic surface is very dense in both LL and MM, with the 27.8 kg m⁻³ level outcropping across the whole of the Barents Sea and much of the eastern GIN Seas.

Where key isopycnals outcrop in the WSPNA region, the surface density flux anomalies are generally positive in both LL and MM, which indicates that surface density fluxes here are responsible for driving the AMOC (Fig. ). In the central SPNA, the large surface density flux anomalies are likely related to oceanic feedback, i.e. strengthening of the AMOC leads to a delayed warming of the SST, which then leads to more heat flux out of the ocean.

The relationship between surface density flux and the isopycnal outcropping region is different further north in the Barents and Kara Seas (Fig. ). Although the surface of the Barents and Kara Seas is more dense than the SPNA with widespread outcropping of the 27.8 kg m⁻³ isopycnal, the surface density fluxes are generally negative. These negative surface flux anomalies are likely related to the growth of sea ice (Fig. ), inhibiting heat flux into the atmosphere (Fig. ), suggesting that deep water formation in the Barents and Kara Seas is likely not important for the aerosol-forced AMOC strengthening.

A further question here is the relative importance of surface heat versus surface freshwater fluxes in driving the overall surface density flux, as this can help narrow down the possible processes involved. The decomposition of surface density flux into its thermal and haline components, i.e. the two terms on the right-hand side of Eq. (), is included in Fig.  in Appendix B. The thermal component dominates the total surface density fluxes throughout the whole simulation in both LL and MM. The haline component is an order of magnitude smaller than the thermal component. This result rules out many potential mechanisms involving freshwater fluxes, such as precipitation changes and sea-ice driven surface salinity changes, which have been proposed in previous studies, e.g. .

Although we have shown that surface freshwater fluxes do not appear to play a big role in dense water formation, it does not mean that the salinity-controlled portion of density changes is unimportant for the overall AMOC response. The northward transport of salty water as the AMOC strengthens () or the southward transport of density anomalies in the Arctic () may also play a role in changing the ocean density. The question of whether AMOC differences are related to differences in how density anomalies propagate around the North Atlantic basin will be explored in a later Sect. .

The previous section defined an appropriate AMOC-sigma index and showed that the SPNA is the key region of surface density flux. Figure c, d shows a comparison between the AMOC-sigma 45° N index and the timeseries of area-averaged SPNA surface density flux alongside its decomposition into contributions from the western portion (which includes the Labrador Sea only) and the eastern portion (includes the Irminger Sea and eastern SPNA), separated at Cape Farewell (regions shown by black box and dashed grey line in Fig. ). Both models show a similar relationship between the AMOC-sigma strength and the total SPNA density flux (i.e. a similar amount of volume flux (Sv) per unit of density flux (kg m⁻² s⁻¹)). This agreement between the two models is consistent with previous studies showing that SPNA surface fluxes can strongly predict AMOC variability . The stronger AMOC response in MM is also consistent with the larger density flux anomalies in the SPNA. In LL, the maximum density fluxes lag AMOC from year 30, which could be due to feedback from the AMOC strengthening, where increased northward heat transport also increases the SPNA SST and hence the surface heat loss and density fluxes.

The differences between the models are largely explained by differences in the western part of SPNA (Fig. c, d). The trend of surface density flux is positive in MM, but negative in LL. In contrast, the trend and magnitude of the eastern portion are more comparable between the two models. The higher maximum density flux in MM is likely related to an AMOC feedback, where the stronger AMOC response in MM results in stronger northward ocean heat flux and hence enhanced surface heat loss and stronger density flux.

What appears to explain the differences in both the size of isopycnal outcropping regions and the Labrador Sea surface density flux is the very regional difference in the sea ice response. Figure  shows the spatial pattern of the surface density flux plotted alongside the boreal winter (DJF) sea ice concentration with the 27.6 and 27.8 kg m⁻³ isopycnals overlaid as contours. Only the 5-year mean for years 24–28 is shown for brevity, the result described below holds true for any particular years. The overall pattern of surface density flux is largely similar in MM and LL except for the western and northermost side of the Labrador Sea. In MM, weakly positive surface density fluxes over the Labrador Sea are accompanied by minimal sea ice growth and widespread isopycnal outcropping of both the 27.6 and 27.8 kg m⁻³ density levels. In LL, surface density flux anomalies in the northernmost region of the Labrador Sea are strongly negative and are collocated with large positive anomalies in sea ice concentration. Sea ice growth will inhibit heat loss to the atmosphere, which results in reduced surface cooling and therefore negative density flux anomalies. Furthermore, the reduced surface density fluxes over this region also likely result in a more buoyant sea surface, which is consistent with the reduced area of isopycnal outcropping.

The inter-model differences in sea ice response also appear to be consistent with differences in the model's mean states in the PI-control simulations. Figure  shows the mean state of winter sea ice concentration (DJF SIC) and annual mean SST in MM minus LL. In the mean state of MM, there is less LS sea ice but more sea ice in the GIN and Barents Seas. Where there is more sea ice in the mean state, there is also colder SST, which creates conditions conducive to sea ice growth. These mean state differences are consistent with the stronger LS sea ice growth in LL and stronger GIN and Barents Sea sea ice growth in MM. Although the sea ice differences in the GIN and Barents Seas are likely unimportant for the AMOC response to the aerosol forcing in these two models because anomalous surface density fluxes in the Arctic do not appear to play an important role for reasons discussed in Sect. .

In summary, inter-model differences in LS sea ice response appears to control the magnitude and trend of SPNA surface density fluxes, and the size of isopycnal outcropping in the SPNA. The stronger sea ice growth in LL inhibits heat loss to the atmosphere and weakens surface density fluxes while also limiting the region of isopycnal outcropping. These two factors mean the total water mass transformation is weaker in LL, and likely explain why the AMOC response is weaker in the LL model despite a stronger overall aerosol-forced hemispheric energy imbalance. Furthermore, the differences in the sea ice response are consistent with the differences in the sea ice and SST mean states between the two models. showed that these mean state differences in SST and sea ice are related to the position of the Gulf Stream and North Atlantic Current, and the associated heat transport, which is more realistic in MM. A separate study found that these Labrador Sea biases also explain the disagreement between the observed and simulated overturning along the OSNAP (Overturning in the Subpolar North Atlantic Program) line in the HadGEM3-GC3.1 models .