Regional imprints of changes in the Atlantic Meridional Overturning Circulation in the eddy-rich ocean model VIKING20X

Abstract. A hierarchy of global 1/4∘ (ORCA025) and Atlantic Ocean 1/20∘ nested (VIKING20X) ocean–sea-ice models is described. It is shown that the eddy-rich configurations performed in hindcasts of the past 50–60 years under CORE and JRA55-do atmospheric forcings realistically simulate the large-scale horizontal circulation, the distribution of the mesoscale, overflow and convective processes, and the representation of regional current systems in the North and South Atlantic. The representation of the Atlantic Meridional Overturning Circulation (AMOC), and in particular the long-term temporal evolution, strongly depends on numerical choices for the application of freshwater fluxes. The interannual variability of the AMOC instead is highly correlated among the model experiments and also with observations, including the 2010 minimum observed by RAPID at 26.5∘ N. This points to a dominant role of the wind forcing.
The ability of the model to represent
regional observations in western boundary current (WBC) systems at 53∘ N, 26.5∘ N and 11∘ S is explored. The question is investigated of whether WBC systems are able to represent the AMOC, and in particular whether these WBC systems exhibit similar temporal evolution to that of the zonally integrated AMOC. Apart from the basin-scale measurements at 26.5∘ N, it is shown that in particular the outflow of North Atlantic Deepwater at 53∘ N is a good indicator of the subpolar AMOC trend during the recent decades, once provided in density coordinates. The good reproduction of observed AMOC and WBC trends in the most reasonable simulations indicate that the eddy-rich VIKING20X is capable of representing realistic forcing-related and ocean-intrinsic trends.


. Domain and resolution (in km) of the VIKING20X configuration. The nest area is marked by increased resolution ranging from 5 to 3 km embedded into a global ORCA025 host grid (for both grids every 60th grid line is shown in x and y direction). geopotential z-levels with layer thicknesses from 6 m at the surface gradually increasing to ∼250 m in the deepest layers. 125 Bottom topography is represented by partially filled cells with a minimum layer thickness of 25 m allowing for an improved representation of the bathymetry (Barnier et al., 2006) and to adequately represent flow over the dynamically relevant f /H contours (f being the Coriolis Parameter and H the water depth). Together with a momentum advection scheme in vector form with applied Hollingsworth correction (Hollingsworth et al., 1983), conserving both energy and enstrophy (EEN, Arakawa and Hsu, 1990), this leads to an good representation of the large-scale, horizontal flow field (Barnier et al., 2006). For 130 tracer advection, a 2-step flux corrected transport, total variance dissipation scheme (TVD, Zalesak, 1979) is used, ensuring positive-definite values. Momentum diffusion is given along geopotential surfaces in a bi-Laplacian form with a viscosity of 15×10 10 m 4 s −1 . Tracer diffusion is along iso-neutral surfaces in Laplacian form with an eddy diffusivity of 300 m 2 s −1 . Fast external gravity waves are damped applying a filtered free surface formulation (Roullet and Madec, 2000) in a linearised form to ensure a volume conservative ocean. Horizontal sidewall boundary conditions are formulated as free-slip everywhere except 135 for a region around Cape Desolation where no-slip is applied to improve the representation of West Greenland Current eddies . A quadratic bottom friction term is applied as vertical boundary condition. In the upper ocean, a turbulent kinetic energy (TKE) mixed layer model (Blanke and Delecluse, 1993) diagnoses the depth of the mixed layer and increases vertical mixing for unstable water columns. This includes the representation of deep convection in formation regions of deep and bottom waters.

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VIKING20X consists of a global ORCA025 host grid and a nest covering the Atlantic Ocean from 33.5 • S to ∼65 • N (Owing to the tripolar grid, the northernmost latitude varies, with a maximum of 69.3 • N and a mean of 65.1 • N) at a nominal horizontal resolution of 1/20 • . Both grids are connected through a two-way nesting capability, using AGRIF with a grid refinement factor of 5 (Fig. 1). Due to its mandatory rectangular shape on the host grid, the nest reaches into the Pacific Ocean to 100 • W and Table 1. Experiments with forcing and integration period. Also provided are internal names used to identify the specific experiments. For the initialisation, 'Spinup' refers to an experiment covering the period 1980 to 2009 under CORE forcing, 'Rest' to an initialisation with temperatures and salinities of WOA13 and velocities at rest. VIKING20X-JRA-short was restarted from the end state of year 1979 of VIKING20X-CORE. SSSR is the sea surface salinity restoring timescale in m yr −1 , FWB is a potentially used freshwater budget correction.
Experiments are grouped according to their initialisation and application of freshwater fluxes. follows the OMIP-2 protocol (Griffies et al., 2016) and started from rest and an initialisation of temperature and salinities of the World Ocean Atlas 2013 (WOA13, Locarnini et al., 2013;Zweng et al., 2013). It also differs in respect to the sea surface salinity (SSS) restoring and the balance of the freshwater budget (see below). For comparison, the two long-term experiments were accompanied by experiments in ORCA025: ORCA025-JRA and ORCA025-JRA-strong following VIKING20X-JRAlong, and ORCA025-JRA-OMIP following VIKING20X-JRA-OMIP. 220 To reduce model drifts due to missing feedbacks from the atmosphere, a SSS restoring towards the initial climatological field is applied in most VIKING20X experiments with a piston velocity of 50 m 4.1 yr −1 (12.2 m yr −1 ) leading to a restoring timescale of 183 days for the uppermost 6-m grid cell. In sea-ice covered areas as well as where runoff enters the ocean, restoring is suppressed. Furthermore, at the river mouths vertical mixing in the upper 10 m of the water column is enhanced.
ORCA025-JRA-strong, ORCA025-JRA-OMIP and VIKING20X-JRA-OMIP instead used a stronger piston velocity of 50 m 225 yr −1 (timescale of 44 days) and a freshwater budget correction that globally balances the freshwater fluxes to zero at any host timestep. In all experiments under JRA55-do forcing restoring is also suppressed in an 80 km wide band around Greenland to allow for a free spread of the enhanced fresh water input to the ocean from melting ice-sheets.
For comparison, in particular to assess potential restrictions due to the location of the southern boundary in VIKING20X,  Schwarzkopf et al. (2019). In contrast to VIKING20X-JRA-long, the SSS restoring in INALT20-JRA-long is stronger (50 m yr −1 ), and the restoring also applies around Greenland. INALT20-JRA-long is initialized with the ocean state of a spin-up integration in INALT20 under CORE forcing from 1980-2009. The lateral boundary condition in INALT20-JRA-long is no-slip in the nest and free-slip on the host grid without any special treatment at Cape Desolation.
It is important to acknowledge that the integration history of eddy-rich models is often less systematic as one would like to have for a systematic evaluation, often aiming at the 'best' experiment under demanding computational costs. The use of accompanying experiments with ORCA025 helps to isolate individual choices, such as the SSS restoring parameter by comparing ORCA025-JRA and ORCA025-JRA-strong. The latest experiment (VIKING20X-JRA-OMIP), also differing in 240 the initialisation, is following the recent OMIP-2 protocol (Tsujino et al., 2020) and was completed during the writing of this manuscript. ORCA025-JRA-OMIP was already performed over a subsequently following second cycle through the JRA55-do forcing.

Basin-wide Circulation
We start the analyses with an evaluation of the basin-scale circulation. In contrast to the horizontal circulation, for which 245 satellite altimetry provides a good estimate, there is no ground-truth for the general structure of the AMOC. Utilising the longest available observational time series by the RAPID Programme for an evaluation of the AMOC strength and evolution, we compare the different evolution of the experiments.
The broad patterns of the mean sea surface height (SSH) are similar in all experiments (Fig. A1), reflecting a robust representation of the upper-layer circulation in the subtropical and subpolar gyres, the equatorial circulation, and the South Atlantic-250 Indian Ocean supergyre. For the path of the North Atlantic Current and the separation of the subtropical and subpolar gyres, VIKING20X shows a major improvement compared to ORCA025. The impact of resolution becomes even more apparent in the patterns of the SSH variability (Fig. 2). Gauged by the observational account provided by AVISO, the VIKING20X experiments show a much improved solution compared to ORCA025, applying both to the magnitude and to the horizontal patterns of the mesoscale variability at the western boundary and along open-ocean currents such as the Azores Current at around 35 • N.

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Prominent differences particularly concern the more realistic separation of the Gulf Stream near Cape Hatteras and the course of the North Atlantic Current in its northward turn into the Northwest Corner in VIKING20X compared to ORCA025.The latter represents an improvement also to its precursor version (VIKING20) that simulated a Northwest Corner extending too far north into the southern Labrador Sea (Breckenfelder et al., 2017).
More than the horizontal circulation, being in large parts already determined by the grid resolution and the wind field, 260 the vertical overturning circulation strongly depends on both wind and thermohaline driving mechanisms. This does not only involve the applied atmospheric forcing itself but also details of its application such as SSS restoring and its impact on the freshwater budget at higher latitudes (Behrens et al., 2013). The AMOC, represented by the streamfunction derived from    with a longer history tend to simulate a weaker AMOC, pointing to a spin-down effect (see below). This in particular applies to VIKING20X-JRA-short that starts from a relatively high level of VIKING20X-CORE, thus simulates (over the same time period) a 3-4 Sv higher AMOC compared to VIKING20X-JRA-long under the same numerical conditions.
The RAPID data allow a more detailed evaluation of the depth structure. Figure 4a shows vertical profiles of the AMOC 280 at 26.5 • N; its vertical derivative represents the meridional transport per unit depth, thus providing a direct account of the northward and southward branches of the AMOC (Fig. 4b). Regarding the total strength of the NADW cell, all model results are lower than the observations (see also Table 2). Closer inspection shows that the differences mostly concern the representation of the deepest portion of the southward flow, i.e., the transport of lower NADW below ∼3200 m, whereas the upper part (1000-3000 m) appears reasonably well represented. The deficit in the range of lower NADW has been recognised as a longstanding, 285 persistent issue in ocean and climate models (Fox-Kemper et al., 2019), and can largely be attributed to a loss of the highdensity source waters from the Nordic Seas, e.g., by spurious mixing in the outflows across the Greenland-Scotland ridge system (Legg et al., 2006). The deficit is most pronounced in ORCA025; the representation is improved in VIKING20X, but there is still a gap by about 500 m in the reversal from southward NADW to northward AABW flow ( Figure 4b). It remains unclear if this is a result of a too weak representation of the densest NADW, e.g. through spurious entrainment into the overflow, 290 or by a too strong modelled AABW cell. It could also be influenced by the choice of the reference level used for the RAPID array (Sinha et al., 2018), noting that the representation of AABW is not its major aim. Figure 5a shows that the AMOC differs not only in mean strength but also exhibits pronounced differences in its temporal evolution over multi-decadal time scales. The CORE-based experiment (VIKING20X-CORE) produces an increasing AMOC with a maximum in the mid-1990s, and a decline and stabilisation thereafter. This maximum corresponds well to the reported    Table 2) is underestimated by 10-20% with only little resolution dependency. However, the interannual variability 310 of VIKING20X is higher than that of ORCA025, but still underestimates the observations by more than 30%. We also notice that the high variability of the latter may include errors from measurements and the processing of the different AMOC components from RAPID data.
An important aspect for the long-term evolution of the AMOC is freshwater fluxes provided by the atmospheric forcings and the numerical details of its application. This is demonstrated by also considering the ORCA025 sensitivity experiments: While a clear attribution of the AMOC trends to either physical drivers (i.e., atmospheric forcing and runoff) or spurious model drift is not possible at this stage, we can use the range of solutions with their diverging trends to assess their manifestation in regional current systems, and thereby explore if and how regional observational arrays may be capable in depicting the longterm evolution and variability of the AMOC. An important part of the analysis is the formation and spreading of deepwater 340 masses. From a number of observational and modelling studies, Lozier (2010) concluded that NADW only partly follows a coherent Deep Western Boundary Current (DWBC) as explained by classical theory (Stommel, 1958). In several parts of the Atlantic Ocean deviations into the interior, recirculations and disruptions by deep mesoscale eddies play an important role in the spreading.

Subpolar North Atlantic
The subpolar North Atlantic is a key region for the AMOC. It receives surface water masses from the subtropics and overflow water from the Nordic Seas. Here, the different components of the NADW are formed through exchange with the atmosphere and mixing processes. They directly maintain the strength of the AMOC and modulate its variability.

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The densest component of the NADW is formed in the Nordic Seas: through heat loss to the atmosphere and sea-ice formation, dense water is formed and, by convection, builds a large reservoir at depth between Greenland, Iceland and Norway.
It then spills over the Greenland-Scotland Ridge into the subpolar North Atlantic. Two narrow passages, the Denmark Strait between Greenland and Iceland with a sill depth of 650 m and the Faroe Bank Channel between the Faroe Islands and Scotland with a sill depth of 850 m, funnel this exchange. Figure 8 and Table 3 show density and transport through both passages. reported σ 0 =28.05-28.07 (Harden et al., 2016;Hansen et al., 2016), which can also be due to the limited vertical resolution not resolving the bottom boundary layer.
Except for a strong weakening trend in ORCA025-JRA and a spindown in the first decades of ORCA025-JRA-OMIP, transports do not show a long-term trend, and are quite stable. This is probably a result of the continuous supply of dense water north of the sills and hydraulic control limiting the transport to its given value (Käse et al., 2003). More important than The distribution of long-term mean annual maximum mixed layer depth (MLD a , Fig. 9a-c) shows that the spatial patterns of    in VIKING20X-JRA-short, VIKING20X-JRA-OMIP, and ORCA025-JRA-OMIP see Fig. 9), the AMOC only represents the 430 one in the 1990s (Fig. 5).
One important key location picking up the different constituents and timescales of subpolar gyre variability and deepwater formation is the observational array off Labrador at 53 • N (Zantopp et al., 2017). The DWBC at this location is seen as an index for the subpolar AMOC and for the overall AMOC on decadal and longer timescales due to the increasing meridional coherence Bingham et al., 2007;Wunsch and Heimbach, 2013;Buckley and Marshall, 2016, see also discussion).  to experiments with the predecessor VIKING20, they produce a stronger surface maximum, a weaker deep velocity maximum and a stronger recirculation than in observations (Handmann et al., 2018). In the ORCA025 experiments the boundary current appears too wide with a split surface maximum and no deep boundary current core, the latter pointing to a too strong erosion of lower NADW on its way around the Irminger and Labrador Seas. Both, the ORCA025-JRA and the VIKING20X-JRA-short are   features the too zonal path of the North Atlantic Current common for lower resolution models. This is a typical behaviour even at 1/12 • resolution as demonstrated by Chassignet and Xu (2017).

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In the subtropical North Atlantic, the southward flow of NADW is again concentrated along the western boundary (Fig. 7). It aligns with the northward flowing surface branch of the Antilles Current (Fig. 13), which is complemented by the flow through the Florida Strait. The characteristics of the AMOC introduced in the subpolar and subarctic regions, but also details of the bathymetry south of it, have an imprint in the current structure at the western boundary. In ORCA025 the flow of NADW clearly lacks the denser part of the NADW because of the inability to maintain the overflow at this resolution, while in VIKING20X 480 the DWBC reaches much deeper. This is also reflected in the integral measures of the AMOC (Figs. 3 and 4). The surface branch instead depends on the representation of the Bahamas Islands and the Bahamas Bank. In VIKING20X the Antilles Current is variable, eddies are crossing the section at 26.5 • N northwestward, providing a prolonged maximum of eddy kinetic energy (EKE) (Fig. 13a). ORCA025 has a much weaker and stable surface transport, with even southward transport directly at the surface.

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An important component of the RAPID observational array (and motivation for the choice of its particular latitude) are the long-term measurements of the transport through the Florida Strait obtained from voltage differences with telephone cables (e.g., Meinen et al., 2010). Table 6 demonstrates that Florida Current transports agrees well with the observations within 1-2.6 Sv for VIKING20X-CORE, VIKING20X-JRA-short and VIKING20X-JRA-OMIP. The transport is weaker in Figure 14. Time series of the transport through Florida Strait from experiments (interannually filtered) and from cable measurements (orange) given as yearly averages for years with data coverage > 70%.  correlation with the observations. Also, some experiments (e.g. VIKING20X-CORE and VIKING20X-JRA-OMIP) showed a correlation of ∼0.75 between the Florida Current and the AMOC, while others (in particular VIKING20X-JRA-long, but also 495 the experiments in ORCA025) did not. This demonstrates that the Florida Current is not just a WBC closure in form of net (wind-related) Sverdrup changes from the interior but is rather regionally influenced from the flow through the Caribbean Sea and through regional atmospheric forcing (Lee and Williams, 1988;DiNezio et al., 2009;Hirschi et al., 2019).

Surprisingly, all VIKING20X experiments (including VIKING20X-CORE) show a declining trend that starts in the 1990s
which is not reflected in the latter part of the observations. The VIKING20X experiments forced by JRA55-do simulated a 500 decline of the Florida Current of ∼0.1 Sv per year over the RAPID period 2004-2018, which is about 27-43% of the AMOC in the same period (here not shown).

Tropical Atlantic
From the subtropical North Atlantic towards the tropics, the NADW transport is concentrated along the western boundary (Fig.   7). Between 10 • N and 10 • S, offshore recirculation patterns appear more prominently than at other latitudes. Figure 15 (similar 505 to Fig. 7 but here as a snapshot) indicates a connection with North Brazil Current rings (Kirchner et al., 2009) that are spun off from the reflection of the North Brazil Undercurrent (NBUC) and drift northwestward, as suggested by eddy kinetic energy  Angola since 2013. Rühs et al. (2015) show that the NBUC transport can be used as an indicator for the upper branch of the AMOC if the horizontal wind-driven circulation is also accounted for. In addition to the northward return flow associated 520 with the AMOC, the NBUC also carries most of the equatorward flow related to the South Atlantic Subtropical Cell (Schott et al., 2004). Figure 16 shows that the general structure of the WBC system is visible in all experiments. The NBUC with its subsurface maximum and the DWBC below already exist in ORCA025-JRA. The eddy-rich configurations better represent the elongated subsurface core of the NBUC and the wider, eddying (cf. Fig. 15a) DWBC, merging with a recirculation pattern offshore of the (deeper part of the) NBUC. The representation of the water masses (here indicated by the density lines) appears 525 quite well. Model transports are usually within the standard deviations of the observational estimates based on the moorings, but are generally too weak at low resolution and by 1/3 (NBUC) and 2/3 (DWBC) too strong for VIKING20X-CORE (Table   7).
It is interesting to note and a guidance for future model-observation comparisons that even for a (with 12 ship-based observations) well-covered section a detailed temporal selection of model output can be important depending on the variability 530 of the system in question (Schwarzkopf, 2016). While the values deducted from the moorings show a good agreement with the ship sections for the NBUC, those for the DWBC are off by more than 10 Sv (Table 7). This is due to the fact that the ship-based estimate is biased by intra-seasonal variability (Hummels et al., 2015), with ship sections often conducted during times of maximum southward flow that often only lasts for a few days (Fig. 17e, especially during 2000(Fig. 17e, especially during -2004. It is important to emphasise that the simulations capture the strong variability and confirm the apparent discrepancy between the long-term 535 and the subsampled values. Figure 17a shows the temporal evolution of the AMOC at 11 • S. In contrast to the one at 26.5 • N (Fig. 5a), it shows a minimum in the late 1960s which is in particular the case in VIKING20X-JRA-OMIP that started one decade earlier from rest. In the following decades, the experiments (apart from VIKING20X-JRA-long) simulate an increase into the 1990s with a decline thereafter.

Subtropical South Atlantic
Entering the subtropical South Atlantic brings us closer to the southern boundary of VIKING20X's high-resolution nest. In the following we explore the ability of the nested configuration to simulate the mesoscale circulation in the Agulhas Current system and the Brazil-Malvinas confluence and if the host model is capable in correctly simulating the transports at the SAMOC 550 observations which are placed just outside the nested area. For comparison we use INALT20 (Schwarzkopf et al., 2019), a configuration that is in large parts (in particular resolution and atmospheric forcing) similar to VIKING20X, but with an eddy-rich nest reaching into the Southern Ocean and into the western Indian Ocean. Figure 18 confirms the general ability of VIKING20X to simulate parts of the mesoscale in the vicinity of the southern nest boundary. It is logical that the variability in the Brazil-Malvinas confluence in VIKING20X-JRA-short is lower and rather 555 comparable to ORCA025-JRA ( Fig. 18a and b), given the fact that this latitudes are only represented on the host grid at  Table 7 for details of the definitions) are given in (d) and (e) together with mooring based (orange curves; thick monthly, thin 2.5-day averages) and ship based observations (purple dots) 1/4 • resolution. In addition to the mesoscale signal Schwarzkopf et al. (2019) demonstrated that the correct representation of the confluence region has consequences for the structure and transport of the Malvinas Current. The picture is similar for the path of Agulhas rings. Here, the formation process in the retroflection of the Agulhas Current south of Africa is outside the VIKING20X nest. Since Agulhas rings are generally represented in ORCA025 (Schwarzkopf et al., 2019), they also enter 560 the nest. The difference compared to a configuration fully resolving the Agulhas Current dynamics (and observations) is that ORCA025 simulates too regular Agulhas rings. This results in too regular pathways into the South Atlantic (cf. Fig. 18b and d).
The AMOC at 34.5 • S shows the same evolution as the one in the North Atlantic, with a maximum in 1990s (  It is intriguing that the DWBC trend at 53 • N is able to capture the of the AMOC trend calculated in density coordinates within 10-15% (Table 9). This correspondence even holds for the stronger trends in VIKING20X-JRA-short. This agreement confirms the high potential of WBC measurements at 53 • N (Fischer et al., 2004;Zantopp et al., 2017;Handmann et al., 2018) to truly monitor changes of the AMOC in the subpolar North Atlantic .

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For the transport through the Florida Strait and its agreement with AMOC changes at 26.5 • N, we get a different picture: In VIKING20X-JRA-short and VIKING20X-JRA-long, the decline of the Florida Current is about 75-80% of the decline of the AMOC; in contrast to VIKING20X-JRA-OMIP where it is stronger. This may indicate that the Florida Current could act as a general precursor of the AMOC trend, but is unable to exactly quantify it. This is confirmed by the observations itself, where the Florida Current decline represents just 15% of the AMOC decline. It is obvious that the Florida Current is not just a simple 670 closure of Sverdrup dynamics but rather shielded by the shallow bathymetry west of the Bahamas and fed through the Gulf of Mexico, with upstream anomalies determining its transport (Hirschi et al., 2019). This may also explain the disagreement between modelled and observed trends of the Florida Current, even though both show comparable mean transports (Table 6. At 11 • S, the WBC system is more exposed to the open ocean. Although the experiments show a robust AMOC decline of about 15%, their NBUC changes are much less consistent and do not necessarily reflect the AMOC: for VIKING20X-JRA-675 long the NBUC trend does equal the one of the AMOC, while for VIKING20X-JRA-OMIP the NBUC trend is almost twice as large as the AMOC trend. For the DWBC instead, trends in VIKING20X-JRA-short and VIKING20X-JRA-OMIP fit to that of the AMOC, whereby VIKING20X-JRA-long simulates a 50% weaker trend than for the AMOC. While the signs of also be attributed to the overlying wind-driven subtropical cell (viz. counter-clockwise circulation in the upper few 100 meters in Fig. 3 and in Fig. 21b), at this latitude requiring the addition of the wind-induced gyre circulation for the interpretation of AMOC changes (Rühs et al., 2015). We also have to acknowledge that the large variability of transports associated with (3) Can regional observations help to verify modelled AMOC trends?
Together with the AMOC measurements at 26.5 • N, the WBC array at 53 • N provides the longest observational time series.
As shown above, the latter has (according to the model) a good potential to provide trends of the basin-scale AMOC. The

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observational AMOC estimate at 26.5 • N indicates a decline that is in the range of all three experiments (Table 9), again with a stronger trend in VIKING20X-JRA-short. We note that the observational AMOC trend has to be taken with caution since the evolution of the AMOC measured at RAPID does not show a continuous decline but rather a strong minimum around 2010 and a stabilisation thereafter (Fig. 5a). A strong argument for a realistic AMOC trend in the past two decades emerges from the comparison at 53 • N. Both VIKING20X-JRA-long and VIKING20X-JRA-OMIP are within 0.1 Sv of the observed reduction of 695 the DWBC transport of 2.5 Sv per decade (Table 9), hence seem to realistically simulate the decline of the subpolar AMOC. For the subtropical North Atlantic at 26.5 • N this reduces 1.3 Sv, again with VIKING20X-JRA-long and VIKING20X-JRA-OMIP realistically representing the AMOC as derived from RAPID.
Apart from the observation-model comparison, additional insight comes from the Ocean Model Intercomparison Project 2 (OMIP-2), performed under JRA55-do forcing. According to Tsujino et al. (2020), the ensemble average of 11 models, 700 performed with different numerical code bases and mainly configured at eddy-parameterising (few at eddy-present) resolutions, show a linear trend of -1.19 Sv per decade over the time frame 2000-2018 at 26.5 • N, which is weaker than RAPID. We cannot conclude if the stronger decline simulated by VIKING20X-JRA-OMIP and VIKING20X-JRA-long is caused by the better representation of mesoscale eddies, as indicated by the resolution dependence throughout this study, or by the details of the freshwater flux application. An important factor could be the 5th cycling of the simulations through the forcing period done for 705 OMIP-2. While 5 cycles are not achievable at such high resolution, the comparison of the 1st and the 2nd cycle of ORCA025-JRA-OMIP already suggests that this may play a role. The trend in ORCA025-JRA-OMIP reduces from -0.88 Sv per decade in the 1st cycle to -0.67 in the 2nd cycle. On the other hand, it is quite foreseeable that the overall strength of the AMOC and the related water masses may also drift away from the observations causing a general reduction of the AMOC strength and its key components (Fig. 8).

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Even though we find good agreement with estimates at 26.5 • N and 53 • N, we can not conclusively assess how much of the trends simulated by the different experiments are still related to the model settings. We can also not be entirely sure whether the trends provided by the JRA55-do forcing are realistic. If we consider VIKING20X-JRA-OMIP as the most promising simulation given good agreement of mean transports, it is clear that the AMOC is subject to multi-decadal variability with a stable evolution in the 1960s and 1970s, an increase towards the mid-1990s and a decline thereafter. For the past two decades 715 our experiments suggest that the AMOC (in density coordinates) in the subpolar North Atlantic was subject to a decline of up to 3 Sv. For the subtropical North Atlantic and further south this reduces to about 1.5 Sv and less. This is generally in line with a compilation of proxy observations presented by Caesar et al. (2021). On a longer timescale, it also fits the 4-Sv decline from the 1950s/1960s towards the recent decade indicated by an SST-based proxy (Caesar et al., 2018).
What is needed to better quantify trends in future experiments and limit the influence of model drift? Apart from further 720 improvements of ocean model configurations, it is clear that multi-decadal hindcasts would directly benefit from a better closure of the heat and freshwater budget. This can only be achieved up to a certain degree since the fluxes are by construction less variable due to the prescribed atmospheric state. Further relaxation of the Bulk formulae or a move towards coupled atmosphere-ocean models may help. While the latter are now routinely available, even at basin-scale mesoscale resolution (Matthes et al., 2020), additional 'constraints' such as the 'partial coupling' approach described by Thoma et al. (2015), could 725 be a potential solution to re-introduce the interannual to multi-decadal hindcast 'timing' into coupled experiments.
In this study we had to concentrate to a limited set of long-term observations. In addition, a number of historic ocean observations exist, from individual measurements dating back to the 19th century, repeated ship sections during the WOCE era in the 1990s, to a drastic increase through satellite measurements and autonomous instruments such as ARGO in the 2000s.
Ocean modellers usually make use of those for model initialisation or verification. More systematic approaches to combine 730 model and data through assimilation are powerful, but also fail in terms of their ability to exactly quantify the required trends (Karspeck et al., 2015;Jackson et al., 2019). A novel route in this respect that has only been started to be explored, are data science approaches. These have demonstrated to push the limits of the interpretation of big data and provide insight not only to pattern and distributions but also the interpretation (and ultimately the understanding) of dynamics (Sonnewald et al., 2019;Aksamit et al., 2020;Reichstein et al., 2019). Nevertheless, our results demonstrate the value and importance of thoroughly 735 and carefully adjusting forcing, grid resolution and settings of 'classic' ocean models to the tasks of simulating the AMOC and filling observational gaps for the benefit of an improved understanding of the ocean.