The Atlantic Meridional Overturning Circulation (AMOC) depicts a simplified, zonally averaged view of rather complex, three-dimensional circulation patterns of the Atlantic Ocean, connected to the global circulation system primarily across the basin's southern boundary. Through its associated heat, salt, and tracer (e.g., carbon) transports and their effects on the ocean state, particularly on decadal-to-multi-decadal time scales, the AMOC has profound impacts on the climate of the surrounding areas and on the global climate (see reviews by Buckley and Marshall, 2016; Sutton et al., 2018; Zhang et al., 2019; Jackson et al., 2022 and references therein). These impacts mainly come about through spatial and temporal variations of sea surface temperatures (SSTs). They include impacts on Atlantic hurricane activity, shifts in the Intertropical Convergence Zone, precipitation changes over the Sahel and Amazon, changes in summertime climate over North America and Europe, and other modes of climate variability – all with significant societal and economic impacts. Furthermore, due to the presence of low-frequency (decadal and longer) AMOC variability seen in many model simulations (e.g., Msadek et al., 2010; Danabasoglu et al., 2012b), the AMOC is thought to represent a major component of dynamical memory of the climate system, thus making its proper initialization – along with associated (upper-ocean) heat content anomalies in the North Atlantic – important for decadal climate prediction simulations (see Meehl et al., 2014 and references therein). Given all these significant impacts, there is also a growing interest in how the AMOC will change in a warming climate with many recent studies focusing on weakening as well as the stability and collapse of the AMOC (e.g., Caesar et al., 2018, 2021; Weijer et al., 2020; van Westen et al., 2024).

In the absence of continuous and trans-basin observations prior to 2004, much of our knowledge of the mean state, spatial and temporal variability, latitudinal coherency, and variability mechanisms of the AMOC during the historical period comes from model simulations. Unfortunately, models remain inconsistent in their representations of the mean AMOC and its variability. For example, results from about 20 ocean model simulations forced with common, interannually varying atmospheric datasets for the 1948–2007 period as part of the second phase of the Coordinated Ocean-ice Reference Experiments (CORE-II; Large and Yeager, 2009; Griffies et al., 2009) show a rather large range of mean AMOC transports in both depth- and density-space, e.g., between ∼5 and ∼20Sv at both 26.5 and 45° N in depth space (Danabasoglu et al., 2014). There is a broad agreement among these simulations in their temporal depictions of interannual-to-decadal variability and trends – despite significant differences in the spatial structures of variability patterns – indicating that simulated variability and trends are largely dictated by the imposed forcing (Danabasoglu et al., 2016). In both Danabasoglu et al. (2014, 2016), these AMOC differences among the simulations were attributed to biases in the Labrador Sea (LS) region in upper-ocean potential temperature and salinity distributions, mixed layer depths, and sea-ice cover. Similar inter-model differences in AMOC properties are also seen in ocean reanalysis products for the historical period (Karspeck et al., 2017; Jackson et al., 2019) even though each reanalysis ingests largely the same observational datasets. In these products, differences arise due to insufficient observational data to constrain the deep and abyssal oceans as well as the continental shelf regions. As such, the fidelity of the underlying ocean model becomes as important as those used in free-running forced-ocean simulations. Large inter-model differences in AMOC properties also exist in fully coupled simulations participating in phases of the Coupled Model Intercomparison Project (CMIP; e.g., Cheng et al., 2013; Weijer et al., 2020; Bryden et al., 2024). Moreover, historical AMOC variability and trends over recent decades do not necessarily agree with those from forced-ocean simulations; the coupled simulations tend to show a somewhat stronger weakening that starts earlier compared to the forced simulations (e.g., Danabasoglu et al., 2014, 2016; Cheng et al., 2013; Xu et al., 2019; Weijer et al., 2020).

As discussed in Buckley and Marshall (2016), Zhang et al. (2019), Danabasoglu et al. (2019), and references therein, interannual AMOC variability in model simulations is primarily dictated by momentum fluxes, i.e., winds. In contrast, low-frequency AMOC variability is largely driven by buoyancy fluxes at high latitudes of the North Atlantic. Specifically, a large majority of model simulations identify deep water formation regions – usually determined by deep mixed layers – as important regions linked to downstream AMOC variability. In many simulations, the associated low-frequency variability mechanism involves surface buoyancy flux anomalies primarily over the LS region, but also with contributions over the Irminger Sea, that arise from long episodes of the positive phase of the North Atlantic Oscillation (NAO). These anomalies contribute to positive upper-ocean density anomalies and subsequent deepening of mixed layers, followed by downstream AMOC intensification, after a few years (see, e.g., Ortega et al., 2021; Sidorenko et al., 2021, and above references). Evidence for such a prominent role for the LS in low-frequency AMOC variability includes the finding that the LS remains the only active deep water formation region after low-pass filtering of mixed layer depths (Danabasoglu, 2008), and that low-frequency AMOC variability can be reproduced just by imposing NAO-related buoyancy flux anomalies over the LS region (Yeager and Danabasoglu, 2014). Furthermore, analysis of eddy-permitting/-resolving model simulations continue to show the LS as a key region on decadal time scales. For example, through sensitivity experiments with spatially refined surface forcing, Böning et al. (2023) conclude that the Irminger Sea deep water comes from the LS region and that AMOC decadal variability is governed by the LS convection, especially during exceptionally cold winters. This conclusion is consistent with Yeager et al. (2021) who find a disproportionately large role for the LS in AMOC decadal variability. Specifically, despite a weak mean surface diapycnal transformation, multidecadal AMOC variability can be traced to anomalous production of dense LS Water, with buoyancy forcing in the western subpolar gyre playing a substantial driving role. A caveat here is that models have many biases in the North Atlantic, including potential over-production of the LS Water (Li et al., 2019) and failure to adequately represent the dense water overflows from the Nordic Seas (Danabasoglu et al., 2010). We also note that low-frequency variability associated with water mass formations in the Greenland-Iceland-Norwegian Seas and the Arctic Ocean can impact downstream AMOC variability (Zhao et al., 2024).

While there have been intermittent and regionally confined measurements of the AMOC or its contributors at several latitudes as well as inferences from hydrographic sections (e.g., Larsen and Sanford, 1985; Bryden et al., 2005; Toole et al., 2011; Meinen et al., 2010; Send et al., 2011), continuous, trans-basin, and comprehensive observational efforts have gained momentum only during the last couple of decades. The RAPID Meridional Overturning Circulation and Heat-flux Array at 26.5° N is the first such observational program providing AMOC measurements since 2004 (Cunningham et al., 2007). The South Atlantic MOC Basin-wide Array (SAMBA) at 34.5° S has been operational since 2009, but it has a gap during roughly the 2011–2013 period (Meinen et al., 2018) and a large uncertainty due to the highly variable Malvinas and Agulhas systems. The Overturning in the Subpolar North Atlantic Program (OSNAP) array at approximately 57° N (Fig. 1) is the third trans-basin observational effort that has been providing data since August 2014 (Lozier et al., 2017). OSNAP fills a crucial missing observational piece focusing on the northern North Atlantic, a region identified as an important source of low-frequency, buoyancy-driven AMOC variability with deep water formation areas (again see reviews by Buckley and Marshall, 2016 and Zhang et al., 2019).

OSNAP observations, by design, provide estimates of overturning transport magnitudes for the LS and the eastern subpolar gyre side separately. Now available for the 8 year period from August 2014–July 2022 (Fu et al., 2025a), these observations show that conversion of warm and salty upper-ocean Atlantic waters into colder and fresher deep waters primarily occurs in the eastern subpolar gyre side, dominating both the mean and seasonal variability of the overturning circulation (Lozier et al., 2019; Li et al., 2021; Lozier, 2023; Fu et al., 2023). Thus, OSNAP observations reveal a minor role for the LS during this period in stark contrast with numerous modeling studies which connect deep water formation in the LS to downstream low-frequency AMOC variability. While a few earlier studies (Spall, 2004; Straneo, 2006; Pickart and Spall, 2007) also argued for a minor role for the LS in AMOC variability, OSNAP observations provide the most compelling evidence to date with direct comparisons of transport estimates at both OSNAP west and east sections. As alluded to above, a caveat here is that most modeling studies typically focus on the role of the LS on decadal-to-multi-decadal time scales, whereas OSNAP observational record is still too short to provide guidance on these longer time scales.

This finding regarding differences in the role of the LS between the OSNAP observations and the long-standing view from model simulations has sparked vast interest in the scientific community during the last few years. Published studies make use of observational datasets, both forced ocean-only and coupled model simulations (including at eddy-rich resolutions), and ocean and atmosphere reanalysis products – or their combinations. They primarily focus on the locations of deep-water formation, water mass transformation, surface buoyancy fluxes, and connectivity of these waters with the downstream AMOC, considering the recent OSNAP period. Among these, several studies identify the Irminger Sea or the broader eastern subpolar gyre as having the strongest AMOC-related variability (e.g., Petit et al., 2020; Menary et al., 2020; Sidorenko et al., 2020; Megann et al., 2021; Chafik et al., 2022; Fu et al., 2024), consistent with observations. However, the ultimate sources of these deep waters and their variability remain unsettled. For example, Petit et al. (2020) argue that local buoyancy fluxes over these basins mostly account for these dense waters of the subpolar North Atlantic. This view is also supported in a recent study by Fu et al. (2024) which shows that the overturning at the eastern part of OSNAP is significantly correlated with water mass transformation forced by surface buoyancy forcing in the Irminger and Iceland basins. Chafik et al. (2022) also indicates the Irminger Sea as the center of action for subpolar AMOC variability, arguing that the NAO is the main driving mechanism for Irminger Sea density variations on multiple time scales. However, this study finds no clear connections between the Irminger Sea density variations and atmospheric heat losses but instead finds that waters dominating the central Irminger Sea are cooled in the first place in the LS and advected into the Irminger Sea. Thus, an alternative interpretation of findings of this study could be that the Irminger Sea AMOC variability has its origins in the LS through direct local water mass transformation via surface buoyancy fluxes in the LS. In another study, Menary et al. (2020) assert that density anomalies generated by surface forcing in the Irminger Sea propagate into the LS, where they dominate the density variability. More recently, Petit et al. (2023) identify the LS as a key pathway for upper North Atlantic Deep Water with its waters sourced from the eastern subpolar gyre, but undergoing further densification within the LS. We finally note that using observational and reanalysis datasets, Zou et al. (2020) and Lozier (2023) show that due to substantial compensation of thermal and saline anomalies, the volume of newly formed dense waters exported out of the LS is relatively small over the observational period.

As indicated earlier, model fidelity remains a challenge with substantial biases in the northern North Atlantic (e.g., Danabasoglu et al., 2016). The model representations of diapycnal mixing, the Nordic Seas overflows, complex flow pathways, and local recirculations are found to be important contributing factors that impact model biases (e.g., Lozier et al., 2022; Buckley et al., 2023; Lozier, 2023). Some of these processes are represented in closer agreement with observations in high-resolution models compared to their low-resolution counterparts (Hirschi et al., 2020). Using the OSNAP observations, Li et al. (2021) show that while both the Labrador Current and West Greenland Current exhibit large density anomalies, these anomalies are strongly correlated, resulting in only modest variability for overturning in the LS. Accurately representing such correlations; temperature, salinity, and current properties, along with their pathways, with minimal departures from observations is a rather high bar for both low- and high-resolution ocean models to achieve. Indeed, Jackson and Petit (2022) find that models with a more saline LS tend to produce stronger water formation in this region, with correspondingly stronger connections with downstream AMOC. Nevertheless, they conclude that coupled models analyzed in their study are generally in good agreement with the OSNAP transport observations.

In the present study, we take a step back and provide a basic, yet much-needed evaluation of simulated transports against OSNAP observations for the 2014–2022 period using a large set of forced ocean – sea-ice (FOSI) simulations. Our effort aims to produce an assessment of model fidelity as well as a benchmark for simulated transports and related properties at the OSNAP sections in comparison to these observations. The simulations largely follow the Ocean Model Intercomparison Project (OMIP) protocol (Griffies et al., 2016; Tsujino et al., 2020) and are forced using the atmospheric datasets based on the Japanese Atmospheric Reanalysis product, suitably adjusted to run such FOSI experiments (JRA55-do; Tsujino et al., 2018). This protocol is intended to provide a controlled and coordinated framework to evaluate ocean components of coupled models that participate in CMIPs (Griffies et al., 2009; Danabasoglu et al., 2014). There are 9 participating groups/centers from around the world, contributing a total of 18 simulations with 6 different ocean models in this study. The horizontal resolutions of the simulations range from nominal non-eddying 1° to eddy-resolving resolutions of 0.1–0.05°. Thus, a goal is to assess how the representation of overturning transports at OSNAP changes with model horizontal resolution. The transports are evaluated in depth, σ0, and σ2 spaces – in the latter two, potential densities are referenced to the surface and 2000 m depth, respectively. The present manuscript is largely descriptive. We mainly provide a catalog of model solutions; detailed analyses of individual model results and specific reasons for their differences from and similarities to the observations are not fully covered here. However, an analysis of water mass formations and transformations will be presented in a separate subsequent study. Finally, we note that because the observational record is short, we cannot yet address the relative roles of the LS vs. the eastern subpolar gyre in AMOC variability on decadal and longer time scales. An analysis of such low-frequency variability and its relationship to shorter timescale variability in these simulations in comparison to available observations in the northern North Atlantic is the subject of a separate ongoing study.

The manuscript is organized as follows. In Sect. 2, we summarize the OSNAP observing system, model simulations and the forcing datasets, how the transport lines are determined, and how the AMOC is calculated in depth and density space. We then present results for transport timeseries in Sect. 3; time-mean transports in σ0 space in Sect. 4; time-mean transports in depth and σ2 space in Sect. 5; transport variability in Sect. 6; temperature and salinity diagrams in Sect. 7; and temperature, salinity, and density biases in Sect. 8. We provide a summary and our conclusions in Sect. 9. Brief model descriptions are given in Appendix A.

We start with the time evolution of transport profiles in depth space presented in Fig. 2 as transports per unit depth, i.e., in Svm-1. The OSNAP profiles are based on the gridded velocity datasets, and profiles only from NCAR10 and NCAR1 are shown as examples of model simulations for brevity. The OSNAP profiles at both sites exhibit a rather streaky behavior, primarily due to the methodology used to estimate basin interior geostrophic transports, which are derived from full-depth dynamic height moorings bracketing the basin interior. Temperature and salinity measurements on these moorings are typically hundreds of meters apart vertically. In general, transport magnitudes and the depth ranges of northward and southward transports are in better agreement between OSNAP and NCAR10, particularly at OE, than with NCAR1. The latter shows a very prominent, deeper-penetrating seasonal cycle at both sites which is much weaker, especially at OW, in both OSNAP and NCAR10. Nevertheless, there are differences between OSNAP and NCAR10 such as a band of northward transports between about 1700–2300 m present in OSNAP at OW but missing in NCAR10.

The corresponding timeseries in density (σ0) space are provided in Fig. 3. These are the integrated transports in Sv, and the streak-like features seen in depth-space OSNAP (Fig. 2a and d) disappear after binning. As in Fig. 2, prominent features include better agreement between OSNAP and NCAR10 than with NCAR1 and a strong seasonal cycle in NCAR1. Indeed, a seasonal cycle in OSNAP is not as pronounced as in both simulations at either site. While the magnitudes of the transports are comparable at OE among observations and model simulations, the simulated transports are larger than in OSNAP at OW, particularly so for NCAR1. The solid black lines in the panels show the density timeseries of the maximum positive transports. The details of such timeseries will be discussed below, considering all the participating simulations. Here, we note that the density at which the maximum transports occur varies considerably in time in both observations and simulations. So, even if OSNAP and simulations have similar maximum transports at a given time, the density at which this occurs can differ substantially. At OW, OSNAP has two interesting characteristics. First, the positive transport is rather weak, particularly prior to 2018, with nearly no positive transport in early 2016. Second, there are nonnegligible negative transports in density classes<27.6kgm-3 throughout the timeseries. This latter feature is somewhat present in NCAR1 but with larger magnitudes and rather strong seasonality.

To provide a broader context for the observational transport estimates and their variability, annual-mean maximum transport timeseries in σ0 space for the full forcing cycle from the simulations are presented in Fig. 4. These transports are constructed as the annual averages of the maximum monthly mean transports, where monthly mean temperature and salinity are used to compute monthly mean densities. The solid black lines represent OSNAP, while the dashed black lines indicate the respective multi-model means (MMM) for each panel. Not surprisingly, the maximum transports and their variability differ considerably among the simulations, but they show general agreement with OSNAP with their stronger transports at OE which dominate the total transports. At OW (Fig. 4a, d, and g), the simulations largely show transports of <10Sv. A few of the simulations, e.g., ANU1, ANU25, and FSU72, have near-zero transports during various time segments. There seems to be a slight weakening trend at OW roughly after the mid-1990s in simulated transports with the OSNAP observations coinciding with a period of low transports (<∼5Sv) in all (but one) of the simulations. NCAR1 is a clear outlier with a mean transport of ∼12Sv for the 1958–2022 period with a rather large amplitude. This represents an improvement compared to a mean transport of 18.7 Sv for the 1961–2007 period reported in Li et al. (2019) for a previous version of the model that was forced with the CORE-II atmospheric datasets (see Danabasoglu et al., 2014). The simulated transports at OE tend to be between 10 and 20 Sv (Fig. 4b, e, and h) with a slight weakening trend again after the mid-1990s. In contrast with OW, OSNAP at OE is at the higher end of the simulated transport magnitudes. The maximum total transport magnitudes (Fig. 4c, f, and i) primarily reflect those of OE, noting that these total transports in density space do not need to reflect the sum of the OW and OE transports as they are not obtained at a constant density. Among the simulations, E3SM27 shows the lowest transport magnitudes at both OW and OE, with very little variability.

The low-frequency variations of these transports as depicted by the MMMs show roughly three stages during the 1958–2023 period: a slight weakening until about mid-1970s; a slight strengthening until about the mid-1990s; and a more discernable weakening until the end of the simulations. While the initial weakening trend does not seem to be consistent with those of other FOSI simulations which show rather steady AMOC transports at subpolar latitudes (Danabasoglu et al., 2016), subsequent strengthening and weakening trends are consistent with what is seen in other FOSI simulations and some estimates from other products (e.g., Danabasoglu et al., 2016 and Jackson et al., 2022). For example, for the 1995–2015 period, we compute weakening trends of -0.21 (LR), -0.16 (MR), and -0.10 (HR) Svyr-1 for the total transports – dominated by those of OE – which are consistent with the range of -0.06 to -0.26Svyr-1 reported in Jackson et al. (2022) for the AMOC estimates at 45° N for a similar period.

The mean seasonal cycles of maximum transports in σ0 space from each simulation are presented in Fig. 5. The solid black lines represent OSNAP with the gray shading showing ± 1 monthly standard deviation (SD). The respective MMMs for each panel are also provided by the dashed black lines. At OW (Fig. 5a, d, and g), the seasonal cycle is relatively weak, with OSNAP showing generally larger transports in spring and smaller transports in winter, but with a minimum in September. Most of the simulations do not capture this observed phasing, also displaying differing maximum and minimum transport months among each other. Except for NCAR1, LR and MR simulations largely cluster around the OSNAP spread. NCAR1 is a clear outlier with the largest transport and seasonal cycle amplitude. In contrast, ANU25, E3SM27, and FSU72 have the lowest transports, near the lower bound of the OSNAP spread. HR simulations tend to be outside the OSNAP spread with higher magnitudes. Here, ANU10 and CMCC06 are the closest to the OSNAP spread. At OE (Fig. 5b, e, and h), OSNAP has a better-defined seasonal cycle – compared to that at OW – with maximum transports in spring and minimum transports in winter. Arguably, the simulations capture the observed seasonal cycle phasing relatively well as reflected in the MMM. An exception is the last few months, particularly evident in HR simulations, where all HR models show an increasing transport after September in contrast with a decreasing trend in OSNAP. Most simulations have transports that are below or near the lower bound of the OSNAP spread, again as also depicted in the MMM. Among all the simulations, only ANU25 remains within the OSNAP spread throughout the seasonal cycle, but has a somewhat different phasing than in OSNAP with a peak in July. NCAR1 has again the highest transports among all the simulations. E3SM27 among MR and ANU10 and FSU08 among HR show the lowest transports with the largest departures from OSNAP. The total transports remain below or near the lower bound of the OSNAP spread in LR and MR, reflecting those of OE (Fig. 5c and f). In contrast, HR transports are within the OSNAP spread except for ANU10 (Fig. 5i). We note that the large-amplitude seasonal cycles at OW and OE in NCAR1 mostly cancel each other, resulting in a much smaller amplitude for the total transport. Finally, to provide a quantitative comparison of the simulated seasonal cycles and those of OSNAP, we calculate the root-mean-square differences between MMM and OSNAP as 2.7 Sv (LR), 0.8 Sv (MR), and 2.9 Sv (HR) for OW; 2.2 Sv (LR), 3.9 Sv (MR), and 2.6 Sv (HR) for OE; and 2.4 Sv (LR), 3.6 Sv (MR), and 1.5 Sv (HR) for the total transports.

NCAR1 is a clear outlier with the largest transport and seasonal cycle amplitude at OW among the simulations. The phasing of its seasonal cycle – which is out-of-phase with OSNAP – reflects that of Fig. 3c with a minimum transport in April. This results from incursions of the negative transport cells into higher density classes. Such negative transport cell incursions are also present in both OSNAP and NCAR10, but they are less well organized, and their densities and transports remain much smaller than in NCAR1. It is also interesting to note that maximum mixed or boundary layer depths in the LS region occur in March (not shown), but the OSNAP section is not co-located with these regions of maximum mixed layer depths. Instead, the OSNAP section was purposely located near the exit of the LS to capture the bulk of the waters exported from the basin. These aspects, including such seasonal cycle features, will be investigated in detail in a follow up study, considering water mass formation and transformation analysis.

Figure 6 shows the time-mean transport profiles in σ0 density space. As in the previous figures, the solid black lines represent OSNAP with the gray shading showing ± 1 monthly SDs, and the respective MMMs for each panel are also provided by the dashed black lines. The figure clearly demonstrates that the simulated transports are much larger at OE than at OW with the total transports dominated by those of OE, all in agreement with OSNAP. At OW (Fig. 6a, d, and g), the simulations largely follow the OSNAP profile. However, at high density classes (σ0>∼27.7kgm-3), there are differences from observations as well as among the simulations. While these high-density transports are relatively small, they can play an outsized role in downstream AMOC variability on decadal timescales (Yeager et al., 2021). NCAR1 has the largest maximum transport with about 9 Sv. While FSU72 shows the highest negative transport magnitude with a distinct peak around 27.65 kgm-3, a feature not present either in OSNAP or other simulations, FSU08 deviates the most from observations and the other simulations at density classes<27.5kgm-3. At OE (Fig. 6b, e, and h), a large majority of the simulations have positive transports with negative slopes for densities<∼27.3kgm-3. This contrasts with OSNAP that shows a much steeper negative density slope for ∼27.2<σ0<∼27.4kgm-3 and nearly no net flow for densities<27.2kgm-3 (see also Fig. 3d). Several factors may contribute to this discrepancy between the simulations and OSNAP, including differences in current pathways and their temperature and salinity properties, and possible under-sampling of Greenland shelf waters in OSNAP. For ∼27.3<σ0<∼27.8kgm-3, the simulations tend to agree better with OSNAP with most within the observed range, particularly for HR. Here, ANU25, FSU72, and NCAR67 show lower transport magnitudes, and NCAR1 has the largest magnitude with a transport of ∼18Sv. Observed transports at high density classes (>27.8kgm-3) appear to be shifted to somewhat lower densities in the simulations. The total transport features are mostly similar to those at OE (Fig. 6c, f, and i). FSU72 has the smallest maximum transport with ∼7Sv due to its large negative transport at OW. The maximum transport is <10Sv for E3SM27 as well. HR profiles, in general, show better agreement with OSNAP than those of LR and MR for σ0>∼27.4kgm-3. Finally, we note that all FSU08 profiles are noisy, particularly at high densities, which may be due to a mismatch between σ0 increments used in the analysis and the resolution of the model σ2 coordinates. Specifically, with relatively small σ0 increments at high density classes, transports within a σ2 model layer can be binned into different σ0 layers, thus leading to some noise.

The details of the time-mean, west-to-east cumulative volume transports for the upper and lower limbs and their total across the OSNAP sections are presented in Fig. 7. Here, the upper (lower) limb is defined as the transport between the ocean surface (bottom) and the density surface of the maximum transports. Again, the solid black lines represent OSNAP with the gray shading showing ±1 monthly SDs. In the plots, the negative and positive slopes indicate southward and northward transports, respectively.

The observations show strong boundary transports in the LS with southward and northward transports narrowly confined to the western and eastern boundaries of the basin, respectively. There are no appreciable transports within the interior of the basin, indicating little, if any, density transformation or overturning there. The upper- and lower-limb boundary current transports are about 7 and 30 Sv, respectively. Across OSNAP East, there are again strong boundary currents. The lower-limb transports clearly show the southward flowing Denmark Strait overflow waters to the east of Greenland and the Faroe Bank Channel overflow waters along the eastern flank of the Reykjanes Ridge. The total southward transports reach ∼30 and ∼15Sv, respectively, in these regions (e.g., Fig. 7g). In contrast to the Labrador Basin, there are compensating, i.e., northward, transports in the interiors of the Irminger and Iceland Basins.

Arguably, many of these observed transport features are much better reproduced in the HR simulations (Fig. 7g–i) than in LR (Fig. 7a–c) and MR (Fig. 7d–f), likely due to better representation of boundary currents in HR with its higher resolution. Nevertheless, there are a few notable differences between HR and OSNAP, including more spatial variability in the LS in the simulations in the lower limb with CMCC06 and GEOMAR05 showing somewhat smaller transports. The simulated Faroe Bank Channel overflow transports are also smaller than OSNAP. In the upper limb, CMCC06 has a slightly larger transport magnitude compared to OSNAP and the other simulations. We note that HR shows a bump around 2500 km to the east of the Iceland Basin – a feature also present in MR, indicating a strong northward transport followed by a modest southward transport. Such a feature is absent in OSNAP.

Both MR and LR show large discrepancies with OSNAP in both lower- and upper-limb transports with no apparent advantage for MR. These differences are particularly obvious in the LS with simulated boundary current transports ranging between about -5 to about -40Sv in the lower limb. Here, NCAR1 and NOC25 show transports comparable to those of OSNAP, with NCAR1 tending to be larger than in OSNAP. The simulation spreads are also large in the Irminger and Iceland Basins. We note that FSU72 and UKMO25 have mostly weaker and stronger lower-limb transports, respectively, across the sections compared to OSNAP and the other models.

The time-mean overturning transports in both depth and σ2 density space from OSNAP and all the simulations at OW and OE are provided in Figs. 8, 9 and 10, 11, respectively. In these figures (as well as in those in Sect. 7), an alphabetical ordering of simulations is adopted to expedite comparisons within a set of simulations from the same group, except for swapping GFDL and GEOMAR simulations to keep the GEOMAR pair in the same figures. In each set of plots, the main panels (color shading) show southward (blue) and northward (red) transports as a function of density and depth. These are transports in Sv, calculated using the common σ2 bins, listed in Sect. 2.5, and each model's vertical grid. We prefer to use Sv for this purpose, rather than transport per unit depth, i.e., Svm-1, because this way the transports can be summed easily in either depth or density space. As such, the profile panels on the right then show the summed transports in depth space. Specifically, the thin blue, red, and black lines display the summed transports in depth space for the southward, northward, and total, i.e., the sum of the southward and northward, transports, respectively. When the total transports are aggregated (or integrated) in the vertical, starting from the bottom, the familiar overturning transport profiles in depth space are obtained (thick black lines). Similarly, when the transports of the main panels are summed across constant density bins, the top plots are obtained, showing the transport profiles in density space. The thick black lines show the overturning transports in density space, aggregated starting from the densest bin class. These are essentially the same profiles shown in Fig. 6, but they are now calculated in σ2 space instead of σ0. Therefore, calculated maximum transports differ as noted below. We note that this analysis can be easily extended to depth – temperature or depth – salinity space to obtain respective transports (not shown). As Figs. 8–11 contain a lot of information, we only discuss a few notable features for brevity.

In OSNAP, the OE transports are more distinctly organized in comparison to those of OW, with continuous southward and northward transport bands occurring at higher and lower density classes, respectively, throughout all depths. At OW, the structure is a bit more complex. A continuous southward transport band between about 1000–3500 m depth splits two northward bands occurring at mid-depth and abyssal ocean. With rather similar high-density waters, OE exhibits broader density ranges at all depths due to the presence of lighter density waters compared to OW. At both sections, the transports can exceed 0.5 Sv in both directions. The summed transports (right panels) reveal substantial cancellations of southward and northward flows in depth space, producing relatively small total transports, at both sections. These profiles have some noise in the upper 500 m. The integrated overturning profile in depth space has a rather odd shape at OW without a well-defined maximum or flow structure, essentially reflecting the noisy velocity bands of Fig. 2a. Nevertheless, its maximum transport is slightly less than 2 Sv. In contrast, the depth-space overturning profile at OE is well-defined, with a maximum transport of about 8.2 Sv. There are cancellations of southward and northward transports in density space as well (top panels). The maximum transports are 5.3 and 14.0 Sv for OW and OE, respectively. We note that these transports in σ2 space are larger than the corresponding transports of 3.8 and 12.9 Sv in σ0 space presented in Fig. 6. These indicate that while the ratio of the transports at OE and OW is 3.4 in σ0, it drops to 2.6 in σ2 space, representing a 25 % reduction. We will come back to this point later in the manuscript.

It is interesting to note that some degree of cancellation of northward and southward flows in OSNAP occurs at all depths. In density space, these cancellations are less uniform, especially at OW where they are pronounced for σ2>36.9kgm-3. At OE, any cancellation is confined to intermediate density classes with not much cancellation of northward flow of σ2<36.4kgm-3 in the upper 1000 m and the southward flow of σ2>37.1kgm-3 below ∼2000m.

Arguably, the simulations capture observed transport features better at OE (Figs. 10 and 11) than at OW (Figs. 8 and 9). In all simulations, a well-defined southward transport band at high density classes that extends through almost the entire depth and an upper-ocean northward transport region extending from the surface to about 1500 m depth and diagonally in density from roughly 35.5–36.75 kgm-3 are captured at OE. However, the northward transport band at deeper levels and at higher densities seen in OSNAP is largely missing in all simulations except for FSU08 and UKMO25. Consequently, summed northward transports do not cancel much of southward transports below about 1500 m depth and in high density classes. In depth space, the maximum aggregated transports at OE are between 4.5 Sv (GFDL25) and 8.9 Sv (ANU25 and ANU1) occurring between 750–1250 m, but mostly around 1000 m depth, noting that the OSNAP estimate is ∼8.2Sv. In σ2 space, the maximum aggregated transports range from about 10 Sv in E3SM27 to about 15 Sv in ANU1, ANU25, CMCC06, NCAR10, and NCAR1, bracketing the OSNAP transport of 14 Sv. While most simulations show a density range of 35.75–37.25 kgm-3 for the positive transport segment in σ2 profiles in agreement with OSNAP, this range is much narrower in ANU25 and FSU72, remaining between about 36.25 and 36.75 kgm-3 (top panels for all simulation sets). The secondary peak near 36.9 kgm-3 seen in OSNAP is present in FSU08, NCAR1, and NOC1, likely due to larger northward flows near this density in these simulations compared to the other simulations. Among the simulations, FSU08 and FSU72 exhibit somewhat noisier transports in depth – density binned transports, likely due to the choice of their hybrid vertical levels.

At OW, the simulations appear to struggle to capture observed binned transport features in depth – σ2 panels with notable differences among the simulations as well. Although these binned transports show similar transport magnitudes to those at OE, their summed and aggregated transport magnitudes are smaller than at OE, consistent with observations. There are cancelling southward and northward transports in both depth and σ2 space and most simulations reproduce the observed structure of the aggregated transports reasonably well. In depth space, the maximum aggregated transports are mostly around 2 Sv within 1000–2000 m depth range, with a few exceptions. Specifically, ANU1, E3SM27, and GFDL25 have rather weak transports of about <0.5Sv. In E3SM27, there is essentially no significant transport at OW. In ANU1 and GFDL25, there are significant cancellations between southward and northward transports. While some simulations exhibit noise in their summed southward and northward transport profiles which are cancelled in the aggregated transports, such noise is particularly large and remains in aggregated transport profiles in FSU08 and FSU72. In density space, E3SM27 does not show any notable transports for σ2>∼36kgm-3. At the opposite end, NCAR1 has the highest transport with 13.1 Sv (off scale in Fig. 9).

To expand upon our earlier discussion, we assess the impacts of using different potential densities on overturning transports considering the scatter plots presented in Fig. 12. Panels a–c show the time-mean maximum transport magnitudes as a function of σ0 and σ2 densities for the OW, OE, and total transports, respectively. For OW and the total, the σ2 transports are consistently higher than those in σ0 in all simulations, on average, by 2.52 and 1.73 Sv, respectively. At OE, all but one simulations are larger in σ2 than in σ0 with an average increase of 1.18 Sv which is smaller than those for OW and the total. To quantify these transport changes, we first compute the ratios of OW and OE transports for σ0 and σ2 separately which can be denoted as Rσ0 and Rσ2, respectively. We then produce a scatter plot of Rσ2/Rσ0 presented in Fig. 12d. This measure considers the relative changes in the maximum transports with density at both OW and OE. The figure shows that this ratio exceeds unity for all simulations, with most of them clustering roughly between 1.2–1.5, indicating larger OW contributions in σ2 space compared to those of σ0. ANU25 and FSU72 have the largest ratios with ∼1.9 and 2, respectively. We note that the spread of the LR and MR simulations is much larger than that of the HR simulations, which cluster around a ratio of 1.3. These model-based findings are consistent with the OSNAP observations which are included as black dots in all the panels, showing roughly a middle-of-the-pack value of ∼1.4 in Fig. 12d.

We examine the variability of maximum transports, considering the scatter plots of time-mean maximum transports and their monthly SDs given in Fig. 13 for OW, OE, and their total. Obtained in σ2 space, these plots show statistically significant correlations between the strengths of the maximum transports and the amplitudes of variability at both OW and OE, with larger transports associated with larger variability. While all the simulations are subject to the same external variability, their SDs differ considerably due to differing internal variabilities, primarily in response to buoyancy forcings: especially at high latitudes, convective/deep-water formation events can differ across simulations. The simulated ensemble mean SDs are slightly higher at OE than at OW, but the spread of the simulated SDs is larger at OW than at OE. While OSNAP SD (=1.64Sv) at OW is lower than those of most simulations, OSNAP SD (=3.18Sv) at OE is larger than in all simulations. Relatedly, there are 9 and 16 simulations within 1 SD of the observational maximum transports at OW and OE, respectively. At OW, CMCC25, NCAR67, NOC1, and NOC25 are the closest to OSNAP SD. Here, FSU08 and NCAR1 have the largest SDs (>3.5Sv), and E3SM27 shows the smallest SD with ∼0.5Sv. At OE, SDs of ANU1, NCAR10, and NCAR1 are in better agreement with that of OSNAP, and E3SM27 SD of <2Sv is the lowest among the simulations. For the total transports, OSNAP SD is again larger than those of nearly all simulations, with FSU08 and GFDL25 closest to it. E3SM27 and CMCC25 have the lowest SDs with slightly lower than 2.0 Sv.

We next consider (potential) temperature–salinity (T–S) diagrams for depths>500m as depicted in Figs. 14–17. These are based on monthly mean data and densities are in σ2 space. We note that some of the differences in the spread of T and S values among the panels, especially at mid-depths, are due to the use of each model's native vertical grid. We further note that because we are primarily interested in deep and abyssal ocean properties, we choose to use a 500 m cutoff depth here to exclude even larger spreads in the upper ocean which result from the models' fine vertical resolutions near the surface.

For OW (Figs. 14 and 15), T–S diagrams span 1–7 °C in temperature and 34.5–35.2 psu in salinity to cover the spread of the simulations. As with the previous figures, we only highlight several key features for brevity. In OSNAP, S is rather uniform around 34.9 psu for depths>∼1500m. As such, waters with σ2>37.0kgm-3 show densification with depth associated with cooling from roughly 3 °C to about 1.5 °C. We note that these T–S diagrams do not necessarily identify mechanisms driving these T and S properties which can result from various processes both locally and remotely, including mixing and advection. All the simulations also show dense waters with σ2>37kgm-3 at depth, consistent with OSNAP, but there are differences in their T and S properties. Except for FSU08 and UKMO25, the simulations have a rather thin, line-like, diagonal structure at high density classes. Most simulations show densification through high-to-low T and S, i.e., via cooling. However, in ANU25, CMCC25, FSU08, GEOMAR25, NOC25, and UKMO25 densification occurs again through cooling, but at relatively constant S. In contrast with all the other simulations, and indeed OSNAP, NCAR67 has densification due to both lower T and higher S values. The discontinuous nature of T and S properties in FSU08 and FSU72 reflect the HYCOM's discrete isopycnic coordinates. We also note that FSU27 does not appear to show much density distribution at depth. Among the simulations, UKMO25 attains densities greater than 37.0 kgm-3 with the highest S and warmest T values likely due to too high S associated with the overflow waters (see below).

At OE (Figs. 16 and 17), we employ wider ranges than at OW for both T and S, i.e., 1–12 °C and 34.5–36.0 psu, respectively. The observations show a diagonal band extending from high T (∼10°C) and S (∼35.4psu) to lower T (∼1.2°C) and S (∼34.9psu) values with a maximum density of ∼37.2kgm-3 around 3000 m depth. Like OW, the deep ocean has a rather uniform S, and densification is due to colder T. This diagonal structure is reproduced by all the simulations. However, all but three have maximum densities of about 37.0 kgm-3. In FSU08, NCAR1, and UKMO25, the maximum densities are closer to the observed values, but with slightly saltier and warmer waters. FSU08, FSU72, and NCAR67 show a discontinuous (banded) T and S structure, reflecting their density layers. Again, FSU72 does not seem to capture high-density classes.

High density classes at OE are thought to be associated with the properties of the Denmark Strait (DS) and Faroe Bank Channel (FBC) overflows. Observational estimates of the product water T and S are 2.1 °C and 34.84 psu for DS (Legg et al., 2009; Girton and Sanford, 2003) and 3.3 °C and 35.1 psu for FBC (Legg et al., 2009; Mauritzen et al., 2005). OSNAP shows much colder water masses than the above estimates for DS and FBC overflows. This discrepancy may be due to different observational periods that these estimates are based on. As stated above, among all the simulations, only FSU08, NCAR1, and UKMO25 reach maximum densities closest to the observed values at OE. Among these, NCAR1 uses an overflow parameterization to represent the DS and FBC overflows. In NCAR1, the parameterization (Danabasoglu et al., 2010) appears to maintain distinct properties of the two overflow waters. In UKMO25, the overflow waters are warmer and saltier than observed. This is probably due to a synergy between their hybrid vertical coordinate system and the large-scale T and S biases affecting their North Atlantic subtropical and subpolar gyres. While their hybrid vertical grid is able to significantly reduce numerical diapycnal mixing when simulating the Nordic overflows, this inevitably results in transporting the density-compensated T and S biases of the upper water column down to greater depths (see Bruciaferri et al. (2024) for the details). FSU08 is the only simulation that has minimum temperatures colder than 2 °C, closer to those observed at OE.

Because upper-ocean hydrographic properties can significantly affect mixed layer depths and deep convection, impacting overturning transports, we present the scatter plots of the upper-ocean (0–700 m) and section-average T, S, and σ2 biases against the respective maximum transports in σ2 space at OW and OE in Fig. 18. Thus, the figure is intended to provide a quantitative assessment of these biases and their relationships with the overturning transports. The biases are computed with respect to the gridded T and S data from the OSNAP observations (Sect. 2.1). At OW, the number of simulations with negative and positive T biases is roughly evenly split with all, but two, within a range of -0.5 and +0.5°C (Fig. 18a). The exceptions are FSU72 and NCAR1 with respective biases of about -1.15 and 0.70°C. There is no statistically significant relationship between these T biases and the transports. In contrast, the relationship between the S biases and the transports is significant, showing generally larger (smaller) transports with positive (negative) S biases (Fig. 18b). Many of the simulations have biases within a range of -0.1 and +0.1psu, but most (12) have a salty bias. While the largest fresh biases occur in ANU25 and FSU72 with -0.21psu, the largest salty bias is in NCAR1 with +0.22psu. In density, except for ANU25 and E3SM27, the biases are within a range of about -0.03 and +0.10kgm-3, with no significant relationship with the transports (Fig. 18c). ANU25 and E3SM27 show negative density biases of about -0.21 and -0.15kgm-3, respectively. In more than half of the simulations, T and S biases compensate each other in their contributions to density. At OE, both T and S biases are strongly correlated with the transports, indicating generally larger transports with warmer and saltier biases (Figs. 18d and e). However, a large majority of the simulations has cold biases of up to about -0.9°C, with negative and positive S biases evenly split. NCAR1 has the largest warm (∼+1.1°C) and salty (0.22 psu) biases among all the simulations. ANU1 is a close second with warm and salty biases of >+0.5°C and about +0.2psu, respectively. All these biases substantially compensate each other in density, producing no significant relationship between the density biases and the transports (Fig. 18f). Most of the simulations show a positive density bias of <+0.1kgm-3. We note that the sign and magnitude of these T, S, and σ2 biases do not reveal any systematic dependencies on model resolution.

Finally, we show the scatter plots of the spatial-averaged T, S, and σ2 density biases against the maximum total transport in σ2 space in Fig. 19, where the biases are with respect to the EN4 dataset (Good et al., 2013). A goal is to briefly explore if the above relationships between the overturning transports and the upper-ocean hydrographic properties change when broader regions are considered – as done in previous studies (e.g., Danabasoglu et al., 2014). So, the biases are calculated in the upper 700 m separately for the Labrador Sea (60–45° W and 50–65° N) and Irminger Sea (45–25° W and 50–65° N) regions (see Fig. 1 for these regions), chosen as two representative areas. In the LS, there are generally larger (smaller) overturning transports with positive (negative) T and S biases, with most simulations showing warm and salty biases (Fig. 19a and b). While FSU72 has the largest cold bias with -0.75°C, GEOMAR05, NCAR1, and UKMO25 are the warmest models with biases of slightly larger than +0.5°C. In salinity, ANU25 and E3SM27 are the freshest models – both with biases of around -0.2psu, while UKMO25 has the largest salty bias with 0.4 psu. These T and S biases partially compensate each other in their contributions to density in 13 simulations, but the resulting density biases in the LS are all positive except for ANU25 and E3SM27 (Fig. 19c). These positive biases primarily reflect those of S as density changes are largely determined by S at low temperatures. No statistically significant relationship exists between the LS density biases and the transports for the LS. In the Irminger Sea, the simulations show generally cold biases, with an even split of fresh and salty biases among the simulations (Fig. 19d and e). There is a tendency towards larger (smaller) overturning transports with positive (negative) T and S biases, but this relationship is statistically significant only for S. ANU10 and FSU72 have the largest cold and warm biases with about -0.85 and +0.65°C, respectively. E3SM27 and UKMO25 bracket the S biases on opposite sides with bias magnitudes of ∼0.2psu. As in the LS, T and S biases partially compensate each other in their contributions to density in 12 simulations in the Irminger Sea (Fig. 19f). The resulting density biases are largely positive, due either to negative T or positive S biases. Again, there is no statistically significant relationship between the Irminger Sea density biases and the transports. As in Fig. 18, the sign and magnitude of these broader region T, S, and σ2 biases do not show any systematic dependencies on model resolution.

The result that generally larger transports are associated with positive S biases appears to be a robust feature of model simulations as also documented in, e.g., Danabasoglu et al. (2014) and Lin et al. (2023) for a large set of FOSI and coupled simulations, respectively. Furthermore, Jackson and Petit (2022) also report stronger mean overturning and larger variability in saline models in the LS, compared to those with a fresher LS. Partial compensation of T and S biases in their contributions to density has been reported also in previous studies, e.g., Danabasoglu et al. (2014). Recently, Zou et al. (2020) and Lozier (2023) provided observation-based evidence for similar compensations for the LS (or OW) region. Thus, while such compensations seem to be a robust finding, the degree of compensation varies considerably among simulations as discussed above. Biases in simulations arise from various model deficiencies due to, e.g., flow pathways, lateral and vertical mixing, missing processes, and surface fluxes. It is likely that the resulting T and S biases significantly impact the degree of density compensation among the simulations.

We have presented a comparison of simulated and observed transports and related properties, including hydrographic characteristics, across the OSNAP sections for the ∼2014-2022 observational period. Our effort aims to provide a benchmark for the modeling community for evaluations of their simulations at OSNAP, considering both depth and density space transports. There are 9 participating groups from around the world providing 18 simulations with 6 different ocean models. These FOSI simulations use a common set of atmospheric datasets, largely following the OMIP protocol. The horizontal resolutions of the simulations range from coarse nominal 1° to eddy-resolving resolutions of 0.1–0.05°. In the vertical, many of the simulations use depth/level coordinates, but a few simulations employ hybrid coordinates. The number of vertical levels/layers varies from 36–98, with most models using between 46 and 75.

Our analysis clearly demonstrates that the simulated transports are, in general, in broad agreement with those of observational estimates. Specifically, the transports are larger at OE than at OW with the total transports dominated by those of OE. There are, of course, many differences between the simulations and observations as well as among the individual simulations in details of the transport properties. These include differences (or biases) in the maximum transport densities, transport directions and magnitudes in a given density class or depth, phase of the seasonal cycle of the transports, and T and S properties. A notable difference from OSNAP occurs at OE where a large majority of the simulations have positive transports with negative slopes for densities<∼27.3kgm-3 (in σ0 space), contrasting with observations which show a much steeper negative density slope and nearly no net flow for densities<27.2kgm-3 (Fig. 6). There are also seemingly small differences in high density classes at OW. While these high-density transports are themselves relatively small, they can play an outsized role in downstream low-frequency AMOC variability (Yeager et al., 2021). NCAR1 seems to be an outlier in its representation of transports at OW with its rather large maximum transport magnitude.

Analyzing overturning circulations in both depth and density space together provides a more complete picture of overturning properties and features. Our preferred approach uses binned southward and northward transports in Sv as a function of depth and density as a starting point, similar to that used in Zhang and Thomas (2021). These depictions provide a clear view of how these transports are distributed across both depth and density space. They can then be summed or aggregated either in depth or density space to produce the familiar overturning transport profiles. In both the simulations and observations, northward and southward flows substantially cancel each other at a given depth or density, producing much smaller net transports. Such cancellations tend to be much more prominent (larger) in depth space than in density space. As discussed in Zhang and Thomas (2021), these cancellation differences in depth- and density-space depend on density differences of horizontally circulating water masses, i.e., isopycnal slopes. In general, the simulations seem to capture the observed transport features better at OE than OW. Not surprisingly, the total velocity and transport profiles tend to agree better between the simulations and observations due to summations involved. However, actual binned transports show large differences in their depth and density ranges among the simulations and with the observations, i.e., similar-looking northward or southward transports may occur at differing depths and/or densities.

The simulations show T and S biases of both signs in the upper ocean at both OW and OE. Statistically significant relationships exist between overturning transports and S biases at OW, and transports and both T and S biases at OE. Specifically, larger (smaller) transports are associated with positive (negative) T and S biases. In about half of the simulations, T and S biases compensate each other in their contributions to density, and there is no evident relationship between density biases and the corresponding section transports. When broader regions are considered for such bias calculations, i.e., the LS and the Irminger Sea rather than just the OSNAP sections, we again find larger (smaller) overturning transports with positive (negative) T and S biases, but no such clear relationship with density biases. The LS typically shows warm and salty biases. In contrast, the simulations show mostly cold biases in the Irminger Sea region, with roughly an even split of fresh and salty biases among the simulations. While the LS density biases are largely determined by those of salinity, both temperature and salinity biases contribute to the density biases in the Irminger Sea. For both the OSNAP sections and the broader regions considered here, the sign and magnitude of T, S, and σ2 biases do not show any systematic dependencies on model resolution.

We note that generally larger transports associated with positive salinity biases seem to be a robust result, supported by previous modeling studies. Similarly, presence of density compensating T and S biases (or anomalies) is also supported by several earlier modeling and observation-based studies. However, the degree of such compensations obviously depends on the magnitudes of the respective T and S biases which arise from various model deficiencies. If the amount of the newly formed dense water exported out of the LS is crucially determined by a very delicate compensation of T and S contributions to density as argued by Zou et al. (2020) and Lozier (2023), it will be rather challenging for models to get that balance right in the presence of many deficiencies.

The transport profiles from high-resolution simulations show better agreement with OSNAP than those of the low- and medium-resolution simulations, particularly in the high-density classes. There are also significant improvements in the representation of the seasonal cycle of the transports as well as the transports at OW with the high-resolution version of the NCAR model compared to its low-resolution counterpart. However, for some of the other metrics considered in our analysis, the high-resolution simulations face similar challenges as the low- and medium-resolution ones, with no obvious improvements. These issues may be related to different levels of bias compensations or to differences in the representation of certain processes, such as overflows and (sub)meso-scale eddies, across resolutions.

An important finding is that when transports are calculated in σ2 space, rather than the σ0 space used in observations, transports at both OW and OE increase. Specifically, in observations, the OE transport increases by 1.1 Sv from 12.9 to 14.0 Sv, while the OW transport increases by 1.5 Sv from 3.8 to 5.3 Sv, representing a reduction of the OE/OW transport ratio from 3.4 to 2.6. On average, model simulations show increases of 2.53 and 1.18 Sv for OW and OE, respectively. A comparative measure of these changes, also taking the changes in the OE transports into consideration, indicates that the relative contribution of OW transports increase by about 35 % in both observations and simulations. As discussed in Sect. 2.5, we think that using potential densities referenced to a depth of 2000 m provides a more accurate depiction of deep transports relevant for our analysis, better representing effects of pressure on density. Therefore, we recommend employing σ2 densities going forward.

When transports are reported in density space, it is important to provide details of exactly how they are obtained for apples-to-apples comparisons. Specifically, the density space overturning timeseries usually use maximum transports obtained from monthly mean transport profiles. Then, these monthly maximum transports are averaged to produce, say, annual-mean values. Due to the inherent nonlinearity of this process, when annual-mean transports are calculated as averages of the monthly mean transport profiles, maximum transports based on these annual-mean transports differ modestly from those obtained with the former approach. This difference results from substantial changes of the density at which the maximum transport occurs each month. In contrast, such a problem with the nonlinearity of the overturning strengths is much more muted in depth space calculations as the depth of the maximum transport does not change substantially from month to month (see Fig. S1 of Lozier et al., 2019). Transports computed from averaged profiles will be always smaller than those derived from averaging the monthly maximum transports. Indeed, these differences can be ∼2Sv for the OE and total transports in observations (∼15Sv vs. ∼13Sv) as reported in Lozier et al. (2019).

The OSNAP observations have been incredibly valuable in providing separate overturning transport estimates for the eastern subpolar gyre and the LS sides. These datasets have been used in evaluation of model simulations as described in this manuscript. Now available for the 8 year period from August 2014–July 2022, the OSNAP observations provide a comprehensive view of the respective roles of the eastern and western sections on inter-annual (or sub-decadal) time scales. While the model simulations are in general agreement with the OSNAP observations regarding the respective transport magnitudes during this observational period, studies that attribute a prominent role for the LS primarily focus on decadal-to-multi-decadal time scales, which cannot be evaluated against observations yet. Therefore, it is important to continue the OSNAP observational program so that they can provide future guidance on longer time scales.