The Atlantic’s Freshwater Budget under Climate Change in the Community Earth System Model with Strongly Eddying Oceans

We investigate the freshwater and salinity budget of the Atlantic and Arctic oceans in a strongly eddying coupled climate change simulation with the Community Earth System Model (CESM) and compare it to a simulation with a coarse ocean resolution CESM configuration, typical of CMIP6 models. Details of these budgets are important to understand the evolution of the Atlantic Meridional Overturning Circulation (AMOC) under climate change. We find that the slowdown of the AMOC in 2100 under the increasing CO2 concentrations of the RCP8.5 scenario is almost identical between both simulations. 5 Also, the surface freshwater fluxes are similar in their mean and trend under climate change in both simulations. While the basin-scale total freshwater transport is similar between the simulations, significant local differences exist. The high ocean resolution simulation exhibits significantly reduced ocean state biases, notably in the salt distribution, due to an improved circulation. Mesoscale eddies contribute considerably to the freshwater and salt transport, in particular at the boundary of the subtropical and subpolar gyres. Both simulations start in the single equilibrium AMOC regime according to a commonly 10 used AMOC stability indicator and evolve towards the multiple equilibrium regime under climate change, but only the high resolution simulation enters it due to the reduced biases in the freshwater budget.

resolution differ between the HIGH (version 1.04) and the LOW simulation (version 1.12). The newer version employs a different dynamical core in the atmosphere model (CAM5.2 versus CAM5.0) and some parameterization schemes are updated.

120
In contrast to the improvement in ocean model resolution however, halving the atmospheric grid spacing from 1 • to 0.5 • is not resolving new essential physical processes. Therefore, no significant changes are expected between the 0.5 • CAM5.0 HIGH and 1 • CAM5.2 LOW atmospheres due their resolved physics apart from coupling to different ocean boundary conditions.

Model-observation comparison
To assess the performance of the HIGH and LOW CTRL simulations we use several observational datasets which are relevant 125 for the freshwater budget and compare 30-year means of the CTRL simulations following the RCP branch-off point (years 200-229 and 500-529, see Tbl. 1). In many aspects the HIGH CTRL simulation performs better than the LOW CTRL simulation when compared to the present-day climate. Global maps of the quantities presented here for the Atlantic-Arctic and additional sea ice comparison results are included in Appendix A.
We define regions in the Atlantic that approximately correspond to the subtropical gyres (STG; sometimes specified as 130 South or North Atlantic: SA-STG and NA-STG), subpolar gyre (SPG), the Intertropical Convergence Zone (ITCZ), and the Arctic. Figure 1 shows the bounding latitudes which are at the southern end of the Atlantic basin around 34 • S, 10 • S and 10 • N generously bounding the ITCZ, 45 • N as the approximate boundary of the subtropical and subpolar gyres, and 60 • N as the boundary between the Atlantic and the Arctic. The Arctic Ocean includes Hudson Bay and is bounded on the Pacific side by the Bering Strait at 68 • N. We perform the calculations on the original model 0.1 • and 1 • grids which become distorted relative 135 to a regular latitude-longitude grid at high northern latitudes (see 60 • N line in Fig. 1).

Sea surface temperature
The sea surface temperature (SST) is important for the freshwater budget as it strongly controls evaporation. Figure 1 shows the HadISST 1990-2019 SST climatology, the bias of the CTRL simulations with respect to that climatology, and the linear SST trends of the RCP simulations. The HIGH (LOW) simulation's global mean SST is about 0.51(0.86) K too warm with a RMSE 140 of 0.99(1.39) K compared to the HadISST dataset. Some warm bias is to be expected as the simulations are subjected to constant year 2000 radiative forcing and not the transiently increasing historical forcing. In the HIGH Atlantic, with the exception of the South Atlantic near the African coast the sea surface is slightly too cold equatorward of 30 • and too warm poleward of these latitudes. The LOW SST biases are stronger with warm biases in the South Atlantic, along the North American East Coast due

Surface freshwater fluxes
We compare surface freshwater fluxes to ERA-Interim precipitation minus evaporation, P − E, 1989-2010 climatology (Dee 150 et al., 2011;Trenberth et al., 2011). Figure 2 shows maps of the observed mean P − E and the bias of the two simulations, and the zonally integrated P − E fluxes. There is net evaporation in the STGs and net precipitation in the ITCZ just north of the equator (Fig. 2a) colocated with the maximum SSTs (cf. Fig. 1a) and the mid-to high-latitudes. Both simulations exhibit the same positive global precipitation biases of 0.23±1.01 mm/day (mean±RMSE; see appendix A). The P − E bias is negative almost everywhere in the HIGH Atlantic (Fig. 2b) and over large parts of the LOW Atlantic (Fig. 2c). Both simulations show 155 biases around the ITZC, most noticeably with reduced precipitation near the South American coast north of the equator. The HIGH ITCZ appears slightly rotated with a wider precipitation belt in the central equatorial Atlantic and reduced precipitation in the Northwest and Southeast. The LOW ITCZ is shifted south because the SST bias (cf. Fig. 1c) is meridionally asymmetric about the equator. Around the Gulf Stream too much water evaporates, but this is stronger and extends further north in the LOW simulation. The P − E biases around the Gulf Stream reflect the SST biases there (cf. Fig. 1c). As the surface waters 160 diverge at the equator this contributes to the saline (fresh) surface bias of the North (South) Atlantic. Both the flux per degree latitude and the meridionally integrated flux referenced to zero transport at 34 • S reveal comparable biases ( Fig. 2d) in the zonal integrals with minor differences in the ITCZ.

Salinity distribution
The circulation rearranges the salt imported from Bering Strait and the freshwater exchanged at the surface and with the 165 Mediterranean resulting in a heterogeneous distribution of salt. We use the EN4 global salinity observations averaged over 1990-2019 which is provided on a 1 × 1 • grid (Good et al., 2013). To compare to the model data, we first interpolated the EN4 data bilinearly horizontally and then linearly to the model depth coordinates for both HIGH and LOW ocean grids. Figure 3 shows the observed salinity distribution and the simulation biases of the upper 100 m, as an Atlantic zonal mean, and along a zonal transect at 34 • S. Both the HIGH (  (thin solid). Note that salinity as a mass fraction is dimensionless. simulation is significantly reduced compared the LOW simulation in all three planes. In particular, the LOW bias around 1 km 175 depth and 15-30 • N (Fig. 3f,i) can be attributed to the absence of eddies (Treguier et al., 2014). To explain several of the HIGH and LOW salinity distribution biases, we plot the barotropic streamfunction for both CTRL cases in Fig. 4. An approximation of the barotropic streamfunction Ψ has been computed as Ψ(λ, θ) = θ θ =θ S 0 z=−D u(λ, θ , z) dz dθ − Ψ 0 . Here the vertical integral of the zonal velocity u is taken over the full depth from z = −D to the surface z = 0, the merid-180 ional integral is taken from the southern boundary at Antarctica θ = θ S , and is subsequently set to 0 at the African Atlantic coast by removing a constant Ψ 0 .

Circulation and gateway transports
While the broad scale wind-driven subtropical and subpolar gyre circulation are present in both simulations, the HIGH simulation features stronger boundary currents, standing eddies, a more realistic Agulhas retroflection pathway and Gulf Stream separation point, and a stronger subpolar gyre which extends much further south along the North American coast. In the LOW 185 simulation, the inflow of Indian Ocean waters is unrealistically strong and together with the strong upper 100 m fresh bias of the Indian Ocean (supplementary Fig. A3)) contribute to the negative salinity bias of the South Atlantic (Fig. 3). In the RCP scenario the Gulf Stream in the HIGH simulation shifts northward (not shown). In the LOW simulation the subpolar gyre weakens broadly, while in the HIGH simulation only the boundary currents weaken.
North Atlantic Deep Water and close to the average salinity at 34 • S (cf. Figs. 3d/g/j). In principle, the freshwater framework has disadvantages, as the choice of the reference salinity S 0 is arbitrary and the amount of freshwater depends non-linearly on it (Schauer and Losch, 2019). However, the relevant terms relate to recirculating and eddy flows which are independent of S 0 (see App. B) and the AMOC stability criterion F ovS is framed in terms of freshwater. Only the barotropic transport depends 195 on S 0 and this component is negligible for the Atlantic freshwater transport although it contributes significantly to the total salt transport.   11 https://doi.org/10.5194/os-2020-76 Preprint. Discussion started: 18 August 2020 c Author(s) 2020. CC BY 4.0 License.

AMOC
210 Figure 5 shows the meridional overturning streamfunction of the CTRL mean state (colors) together with the RCP trends (contours) in both HIGH and LOW simulations. The maximum of ψ is located just below 1 km depth for both simulations around 35 • N, but the LOW upper cells stretches further north consistent with its STG that extends too far north (cf. Fig. 4). The

Surface freshwater fluxes
The Atlantic is a net evaporative basin and Fig. 6 shows maps of the total surface freshwater flux, F surf , and its major 225 contributing components: precipitation P and evaporation E. In addition, F surf comprises runoff from land R and ice, as well as sea ice melt and brine rejection which, from here on, are all defined as positive freshwater fluxes into the ocean. Precipitation occurs mainly in the ITCZ region, with stronger maxima in the HIGH simulation over the Gulf Stream, and in the midlatitude storm tracks. In the HIGH (LOW) CTRL simulation between 34 • S and 60 • N there is a net freshwater loss of 0.88 (0.93) Sv.
Evaporation is strongly tied to SSTs ( Fig. 1) with most occurring in the subtropical gyres and at the above zonal-average SSTs    Despite different volume fluxes at Bering Strait, the freshwater inflow is about the same between the simulations because of 250 the stronger fresh bias of the LOW simulation (cf. Tbl. 2, vertical lines in Fig. 7, Fig. 3). The Arctic is a net precipitative basin, in part due to its extensive catchment area, resulting in even more freshwater entering the Atlantic at 60 • N. In the subpolar gyre and the ITCZ, i.e. in latitudes of net precipitation, freshwater diverges, while net evaporation in the subtropical gyres results in freshwater convergence by the oceanic transport. Under the RCP forcing scenario, the total freshwater flow is more southward because more freshwater enters at 60 • N primarily due to increased net precipitation (including runoff) in the The gyre transport trends consist both of a gyre strength signal (Fig. 4) and one due to the salinity azonality trend (Fig. 8).
In the HIGH simulation the F az trends are the largest contribution to the total southward freshwater trends. In fact, between 275 20-40 • N the HIGH F az trend is so negative due to the strong salinification along the North American Atlantic coast (Fig. 8), that the F ov trend becomes slightly positive. This occurs also around 5-20 • S in the HIGH simulation where F az switch signs under forcing. These negative F az trends are much weaker in the LOW simulation so that the overturning component trend remains latitudinally coherent in its sign.
Eddy transports of freshwater and salt are not associated with volume fluxes as they are due to correlations between salinity 280 and flow anomalies, which we define with a cutoff timescale of one year, i.e. including the seasonal cycle. A detailed analysis of the eddy salt transports revealed that they are associated with two distinct mechanisms (Treguier et al., 2012). First, at the equatorward edges of the STGs seasonal variations in surface salinity and wind driven circulation cause eddy transports.
Second, at the boundary between the subtropical and subpolar gyres baroclinic mesoscale eddies are responsible for eddy transports. As expected, in the diffusive LOW simulation the eddy transports are negligible outside tropical seasonal variability, 285 but in the HIGH simulation, the eddy freshwater transports F eddy contribute significantly and bring freshwater polewards in the low latitudes and equatorwards around the Gulf Stream and its extension. The eddy transports thus move freshwater generally down-gradient, which is parameterized in the LOW simulation by the Gent-McWilliams scheme as a diffusive salt flux (Gent and McWilliams, 1990 (Fig. 4) and the meridional salinity gradient increases (Fig. 8). In the absence of eddy transports in LOW 45 • N there is a divergence of freshwater around 40-45 • N which is absent in the HIGH simulation. This LOW freshwater divergence contributes to the salinity bias (cf. Fig. 3f). In our RCP climate change scenario, the Atlantic's salinity changes significantly as surface freshwater fluxes and transport 295 convergences change, even though these salt storage changes are small compared to the fluxes and their changes. Figure 8 shows Currents (see Fig. 6 ). While the subpolar gyre freshens uniformly in LOW, this is only the case for the eastern HIGH SPG while it is positive in the East and West Greenland as well as Labrador Currents bringing salt into the subpolar gyre. This is the result of advection of salinifying waters from the central Arctic north of Greenland and Svalbard. While the Arctic surface layer between Bering Strait and the North Pole becomes fresher in both simulations due to enhanced net precipitation including runoff, the subsurface salinifies strongly in the HIGH simulation enhancing stratification.

305
The zonal gradient of the salinity trends of the upper 1000 m in Fig. 8 is generally westward equatorward of 45 • and more pronounced in the HIGH simulation. This leads to more azonal northward salt and southward freshwater transport by the North Atlantic subtropical gyre and where the southward Angola Current carries runoff from tropical Africa southward.
South of 25 • S the trend enhances the existing zonal salinity gradient resulting in strengthened azonal transport components (Fig. 7). The azonality at 34 • S is opposed by surface freshwater flux trends at this latitude. This is more strongly so in the 310 LOW simulation compared to the HIGH simulation (Fig. 6) where it leads to a weaker enhancement of the azonal transport components.

Freshwater budget
In order to gain insight into regional changes, we evaluate the freshwater budget over several regions of the Atlantic and Arctic, which is formulated as where the change in freshwater storage over time dW / dt over a region is a consequence of the freshwater convergence across the lateral volume boundaries F ∇ , surface fluxes F surf , and a residual mixing term F mix that captures subgridscale diffusion (including eddy parametrizations) and errors introduced by our choice of the reference salinity S 0 = 35. The freshwater content W of a volume V of ocean water is defined relative to the reference salinity asW = −1/S 0 (S−S 0 ) dV . Similarly, freshwater 320 transport across a surface is defined as F = − S−S0 S0 u ⊥ dA where u ⊥ is the velocity perpendicular to the durface element dA. Surface freshwater fluxes, F surf , are implemented as virtual salt fluxes, F S surf , in the POP2 model and we calculate this flux as F surf = −F S surf /S 0 . Figure 9 presents the freshwater and salt budget terms for each of the regions and the Atlantic from 34 • S to 60 • N as a whole. there. Both the ITCZ and the subpolar gyre gain freshwater through surface fluxes. Here the freshwater transport divergence is much smaller in magnitude compared to the STG freshwater convergences both due the smaller areas and flux densities (cf. Figs. 1 and 6i/j) and the STGs dominate the signal of the whole Atlantic from 34 • S to 60 • N. The freshwater reservoir tendency 330 term, dW/ dt, is small compared to the other terms. However, for example for the whole Atlantic between 34 • S and 60 • N, the tendency term is crucial in closing the budget as the trends of the transport convergence, −∇F tot , are smaller than the opposing trends in the surface fluxes. Full depth regionally integrated salt content trends are very similar between the simulations with largest salt content increase in the NA-STG (cf. Figs. 9a and 8). The mixing term is negligible in the HIGH simulation and sizable in the LOW simulation as it includes the parameterized diffusion by eddy fluxes which act down-gradient, thus adding 335 freshwater to the saltier, evaporative STGs.
The detailed plot (9b) contains the major surface freshwater flux terms as well as the meridional transport components. As discussed with the surface flux maps (Fig. 6), both the means of the CTRL simulations (bars) and the RCP trends (arrows) are similar between the simulations given that the exact numbers depend on the choice of bounding latitude. South of 45 • N, all chosen regions experience more evaporation than precipitation (Fig. 6), but in the ITCZ there is net freshwater flux into In steady state, the oceanic freshwater convergence compensates the surface fluxes. The barotropic and hence total salt transports is southward everywhere due to the import through Bering Strait which is larger in the HIGH simulation, while the barotropic freshwater transport term sign and magnitude depends on the choice of S 0 (Schauer and Losch, 2019). The magnitude of these regional convergences shown in red in Fig. 9a and as vertical bars on the bottom axis in Fig. 9b is generally smaller for the LOW simulation compared to the HIGH simulation. The HIGH and LOW decomposition differences into over-350 turning and azonal convergence offset each other in the STGs, the ITCZ, and the Atlantic as a whole, resulting in the same sign of the total transport convergence. Only in the SPG does the sign of the total convergence differ as the overturning convergence is stronger and the azonal divergence is weaker in the HIGH simulation and the mixing term captures the parametrized eddy transports in the LOW simulation. The extreme strengthening of the HIGH eddy transport at 45 • N is related to the northward shift of the Gulf Stream under forcing (cf. Fig. 7). The trends in the overturning and azonal convergence trends offset each 355 other (except in the HIGH NA-STG with its strong growth in eddy convergence) indicating a change in the azonality of the salinity distribution (cf. Fig. 8).

AMOC stability indicators
The freshwater import (export) by the AMOC constitutes a negative (positive) feedback. The freshwater convergence by the overturning circulation Σ = F ovS − F ovN , where F ovS /F ovN are located at 34 • S/60 • N, has been suggested as an indicator for 360 an AMOC multiple equilibrium regime (Dijkstra, 2007;Huisman et al., 2010). Figure 10 shows the evolution of these indicators together with the azonal freshwater transport at 34 • S, F azS , for both CTRL and RCP simulations. Both the HIGH and LOW CTRL simulation initially equilibrate with increasing F ovS values. At the point where the RCP simulations are branched off, F ovS appears to have reached an equilibrium as the concurrent CTRL time series are statistically stationary. Despite a very similar overturning strength, the LOW CTRL F ovS values are significantly higher due to the stronger vertical salt bias (Fig.   365 3). Non-eddying CMIP5 models have a positive bias in the F ovS sign and may hence be too stable; much of this bias is a result of the salinity bias with fresh surface anomalies south of 20 • N and salty anomalies elsewhere in the Atlantic (Mecking et al., 2017). Artificially replacing the CMIP5 model salinities by observed values as in (Mecking et al., 2017), reduces F ovS to negative values. The CTRL azonal component F azS equilibrates faster than the overturning component as it relates to the shallower transport by the wind-driven STGs. The total freshwater transport at 60 • N is almost identical between the simulations 370 and consists predominantly of the azonal component (cf. Figs. 7, 9), but the exact azonal vs. overturning decomposition differs such that the LOW F ovN magnitude is larger than the HIGH F ovN magnitude, resulting in a larger offset in Σ.
In response to the RCP forcing, the F ovS values decrease because the salinity trends offset the fresh bias near the surface (cf. Figs. 3 and 8) with the HIGH F ovS trend being stronger at -0.14 Sv/century compared to the LOW trend at -0.10 Sv/century.
The Σ value is also plotted in Fig. 10 as well and its trend is evidently dominated by F ovS while F ovN barely changes under   forcing (Fig. 7). The azonal gyre component F azS also evolves in response to the forcing (cf. Fig. 8) and is connected to F ovS through the overall freshwater budget . Its change compensates the change in F ovS completely in the HIGH simulation and only half of it in the LOW simulation. Both F ovS and Σ indicate a shift into the multiple equilibrium regime under the RCP forcing in the HIGH but not the LOW simulation.

380
We compared the Atlantic freshwater budget between strongly eddying (HIGH) and coarse resolution (LOW) simulations with the CESM under a present day control forcing (CTRL) and a climate change scenario with increasing greenhouse gases (RCP).
Previous studies have analysed the Atlantic freshwater budget's present day state with strongly eddying ocean models (Treguier et al., 2012) or investigated the freshwater budget under climate change but with coarse resolution ocean models (Drijfhout et al., 2011), but this is the first analysis of the freshwater budget under climate change investigating the effect of strongly 385 eddying oceans. Apart from the ocean horizontal resolution in the CESM, also the atmosphere model component version and resolution differ. However, the mean surface freshwater fluxes are comparable where ocean biases are comparable and the forced hydrological cycle response is similar between the HIGH and LOW simulation (Fig. 6). In validating the simulations, uncertainty in observations, particularly in the different P − E products (Fig. 2), must be acknowledged (Trenberth et al., simulation (Jüling et al., 2020). This could potentially influence the results (Jüling et al., 2020), but the magnitude of the response to the strong RCP forcing is very large compared to this internal variability.
Increasing the resolution of the ocean component enables more realistic simulation of currents, eddies and overflows, and the circulation features such as the Gulf Stream separation or the Agulhas retroflection are better represented in the HIGH simulation (Fig. 4). We find that many ocean biases are reduced in the HIGH simulation compared to the LOW simulation.

395
Although the HIGH ocean presents a more realistic boundary condition to the atmosphere with more energy at smaller spatial and temporal scales (Kirtman et al., 2012), the atmosphere freshwater flux CTRL mean and RCP trends are similar between the two model setups (cf. Figs. 2d,6,and 9). The large scale hydrological cycle strengthens similarly with generally warming surface temperatures, the exception being the cooling NA-SPG (Fig. 6). Also the AMOC weakens similarly (Fig. 5) in both RCP simulations, such that any differences in the simulated responses are likely due to the different ocean model resolution.

400
The mean and trend of the ocean freshwater and salt transport, its convergence, and its decomposition differ between the HIGH and LOW simulations, especially in regions of strong eddy activity (cf. Figs. 7 and 9).
By comparing the CTRL simulations against observations relevant to the freshwater budget, we find that the HIGH simulation's biases are notably reduced compared to the LOW simulation. In particular, we diagnosed reduced biases of SST (Figs. 1 and A1), the precipitation minus evaporation fluxes (Figs. 2 and A2), the 3D Atlantic salinity distribution (Figs. 3 and A3).

405
Two phenomena contribute to the strong meridional surface salinity bias gradient of the LOW simulation that also plagues other coarse resolution models (Mecking et al., 2017): first an unrealistically large import of too fresh surface waters from the Southwest Indian Ocean into the South Atlantic (cf. Figs. 4 and A3), and second the southward shift of the ITCZ due to a more asymmetric Atlantic meridional SST bias (cf. Figs. 1 and 2).
Despite similar atmospheric changes and AMOC slowdown, there are many notable differences between the HIGH and LOW 410 simulations. Forced circulation changes differ in that the HIGH Gulf Stream moves north and the SPG circulation strength trends show a dipole pattern as opposed to a large-scale weakening in the LOW simulation. Also, Arctic surface freshwater fluxes change differently and the sea ice response may be underestimated due to low-biased heat transport into the Arctic in the LOW simulation (Fig. 9). The large-scale structure of the F tot transport is similar and so is the forced response, with the exception of the STG-SPG boundary around 45 • N where the LOW simulation shows no trends in any transport component, 415 but the HIGH simulation exhibits a large negative F tot trend, due in equal parts to the eddy and overturning components.
The decomposition between overturning and azonal components differs between HIGH and LOW as the azonality of both the salinity and velocity fields differ. Eddy fluxes are significant at the northern and southern boundaries of the STGs (Treguier et al., 2012(Treguier et al., , 2014. The evolution of the AMOC under climate change is of great interest and based on our results, and that of others, simulating 420 strongly eddying oceans does not appear to systematically influence that response (Gent, 2018;Hirschi et al., 2020). The CTRL AMOC strength and reduction under the RCP scenario are almost identical between the simulations with a reduction of ∼ 5 Sv from 18 Sv which compares well with the observed AMOC strength at the RAPID array at 26.5 • N of 17.0 Sv (Smeed et al., 2018). The reduced heat transport by the AMOC into the subpolar gyre constitutes a positive atmospheric feedback AMOC feedback and it can lead to multiple equilibria if the overturning circulation exports freshwater from the Atlantic basin. A weakened AMOC would export less freshwater which would ultimately further suppress deep water formation in the North Atlantic and vice versa. As it is not possible to prove the existence of multiple AMOC equilibria with modern coupled climate models due to the high dimensionality and the prohibitive computational cost of equilibrating the ocean circulation after millennia, it is desirable to use scalar indicators based on simpler models. The import of freshwater to the Atlantic by the 430 overturning circulation F ovS can hence provide further insight into the question of AMOC stability if atmospheric feedbacks are negligible (Huisman et al., 2010). Observations suggest a negative F ovS between -0.28 and 0.05 Sv at present (Weijer et al., 2019). Due to their salinity bias at 34 • S, both HIGH and LOW CTRL simulations import freshwater into the Atlantic, but this bias is significantly stronger in the LOW simulation ( Figs. 3 and 10). This bias, from which all coarse resolution CMIP5 models suffer (Mecking et al., 2017;Gent, 2018), is countered by salinification of the surface under radiative forcing decreasing the 435 F ovS value which indicates decreasing stability.
The ocean mean state as well as the forced response are different with higher resolution, but from our two RCP simulations we cannot discern any systematic effect on AMOC response to climate change as it is a large-scale flow feature and the correct simulation of the sinking regions is likely more important (Hirschi et al., 2020). Yet due to the reduced salinity biases in particular at 34 • S in the HIGH simulation, the indicator of the multiple equilibrium regime F ovS suggest that the 440 salt-advection feedback can destabilize the AMOC in the 21st century. However, the HIGH freshwater overturning transport response is meridionally incoherent and hence freshwater may not be simply advected northward with the AMOC. As the transport decomposition is further complicated by an eddy term, it is questionable whether the simple indicator is useful for quantifying the salt-advection feedback and it may have to be adapted. In the absence of eddy terms and changes in the salt reservoirs, the overturning and azonal components must balance which was used by de Vries (2005) to change the sign of F ovS .

445
By changing the azonality of the freshwater surface fluxes at 34 • S and hence the gyre transport, Cimatoribus et al. (2012) was able to collapse the AMOC without any further changes, suggesting that also this component of the transport must be taken into account when assessing the stability. Furthermore, any interpretation of the F ovS in short strongly eddy simulations should be undertaken with care. Figure 10 shows that the HIGH CTRL simulation switches sign from negative to positive F ovS only after 150 years as the ocean equilibrates.

450
To conclude, the changes in the Atlantic freshwater and salt budgets due to global warming are fairly robust to the resolution improvement from a diffusive to a strongly eddying ocean in CESM. This strengthens trust in using the current generation of coupled climate models (CMIP5, CMIP6) and their AMOC change projections, which are computationally significantly cheaper to perform. On the other hand, the biases in the present-day state are strongly reduced in the strongly eddying ocean version of CESM and hence indicate that better parameterizations are needed in the CMIP5/CMIP6 models to reduce these equator with large-scale cold biases only in the Northern Hemisphere subtropical gyres and the southern edge of the NA-SPG.

B1 Freshwater budget
We define freshwater fluxes in the ocean relative to a reference salinity of S 0 = 35 in units of 1 Sv = 10 6 m 3 s −1 . The freshwater flux budget of an arbitrary full depth ocean volume is given by Eq.
(1) which we repeat here for a self-contained presentation of the budget calculations: S − S 0 dV is the freshwater content of the volume V . The first term on the right hand side, F ∇ , is due to the advection of freshwater gradients across the vertical boundary b, which is full depth and encloses the volume V : The second term is the freshwater flux at the surface comprising precipitation P , evaporation E, runoff from land R and ice I, as well as sea ice melt M and brine rejection B which are all defined as positive freshwater fluxes into the ocean: The last term, F mix , captures diffusion (including eddy parametrizations), errors introduced by the time averaging of the output and the choice of the reference salinity S 0 and is calculated as a residual: Furthermore, we ignore changes in sea surface height in the calculation ofW such that these small effects are included in 480 F mix .
To ascertain whether a perturbation in the overturning is amplified or damped through the salt advection feedback, the freshwater transport due to the overturning is evaluated at the southern boundary (F ovS ). In general, the advective term can be divided into a barotropic component F bt , an overturning component F ov , an azonal component due to the gyre circulation F az , and an eddy component F eddy such that: where F ∇ is evaluated between the Southern and Northern boundaries, θ S/N . The hat notationq of an arbitrary quantity q denotes the section average,q = q dx dz/ dx dz. In case q = v,v is the barotropic velocity and v * = v −v is the baroclinic velocity. Angled brackets q = q dx/ dx denote zonal averaging, while primed quantities q = q − q are deviations from zonal means.
In specific case of the Atlantic-Arctic freshwater budget, the oceanic advection term can be decomposed into advective where u is the zonal velocity.
Note that sometimes F ov is defined to include the barotropic component (e.g. de Vries (2005)): Equations (B6) and (B10) are equal if the reference salinity is equal to the section average, S 0 =Ŝ, and the barotropic transport is zero, F bt = 0.
Due to the volume-conserving, virtual salt flux formulation of the ocean model, the barotropic meridional volume transport throughout the Atlantic equals that through Bering Strait ( Table 2). The barotropic freshwater transport thus depends only on 505 the section average salinity which is so close to the reference salinity, S 0 ≈Ŝ, that F bt is negligibly small compared to the other transport components and hence not shown.

B2 Eddy-mean decomposition
To calculate the eddy terms, we use the eddy-mean decomposition of the total flux: where the overbar x denotes a time average, which we choose to be annual, and primed quantities x denote eddy terms.
Neither the total nor the eddy freshwater transport terms, v [S − S 0 ] and − 1 S0 v [S − S 0 ] , are part of the model output. However, the total salt transport vS is, so that one can calculate the eddy salt transport: The freshwater eddy transport is linearly related to the eddy salt transport and the total freshwater flux is thus: