We use an ensemble of eddy-permitting (1/4∘ horizontal resolution) global ocean reanalyses. These are GloRanV14 (an improvement on GloSea5; MacLachlan et al., 2015), C-GLORSv7 (Storto et al., 2016), GLORYS2V4 (Lellouche et al., 2013), and ORAP6 (Zuo et al., 2021). Together, these four reanalyses form a new Copernicus Marine Environment Monitoring Service (CMEMS) reanalysis ensemble, updating product ref. 1 (see Table 1). We also use an eddy-resolving (1/12∘) global ocean reanalysis: GLORYS12V1 (product ref. 4). Each reanalysis uses the NEMO (Nucleus for European Modelling of the Ocean) model, but the sea-ice model and data assimilation techniques differ. Each reanalysis is constrained by observations and is driven by atmospheric forcing from either ERA5 (Hersbach et al., 2020) or ERA-Interim (Dee et al., 2011) over the period 1993–2020, with GloRan extended to December 2021. They all assimilate satellite SLA, sea-ice concentrations, and in situ temperature and salinity, and they either assimilate satellite sea surface temperature (SST) or implement SST nudging.

We compare the MOC and MHT from the ensemble with the SAMBA-based estimates of Kersalé et al. (2020, 2021), the altimeter-based estimate of Dong et al. (2021), and the energy-budget MHT estimates of Trenberth et al. (2019b) and Mayer et al. (2022).

The energy-budget estimates of Mayer et al. (2022) calculate the net surface heat flux using top-of-the-atmosphere radiative fluxes from CERES-EBAF (Loeb et al., 2018) with a backward extension (Liu et al., 2020) and atmospheric energy-budget quantities from ERA5 (see Mayer et al., 2021a, for methods). These are combined with ocean heat content (OHC) tendencies from ocean reanalyses to infer the MHT. Mayer et al. (2022) use OHC tendencies from ORAP6 (“Mayer_ORAP6” in figures); here we use an additional (unpublished) ORAS5-based estimate (“Mayer_ORAS5”), using OHC tendencies from ORAS5 (Zuo et al., 2019), the same as that used in the Trenberth et al. (2019b) estimate. For further details, see the Supplement. We note that energy-budget estimates may accumulate errors at southern latitudes, since they are integrated southward from high, northern latitudes (Dong et al., 2021).

Ensemble mean and spread and the time mean of the altimeter-based and Mayer energy-budget estimates are calculated over 1993–2020 and over the 2013–2017 SAMBA observational period. We calculate monthly-mean MOC across 34.5∘ S in depth coordinates, using commonly applied methods (e.g. Frajka-Williams et al., 2019), integrating monthly-mean velocity from coast to coast and from the surface down to the seafloor with a zero-net-volume transport constraint applied. Without this constraint, the ensemble mean has a net southward transport through the section over the observational period of 1.14 Sv (as do the individual reanalyses), and GLORYS12V1 has a net southward transport of 3.1 Sv, but the constraint only has a small impact on MOC estimates (Table 1). For the reanalysis, the MHT is calculated by integrating the product of monthly-mean model velocity and temperature (scaled by density and specific heat coefficient) across the whole section with a zero-net-volume transport constraint applied. Each observational product applies its own constraint to reference the flow due to differences in their geostrophic techniques. The altimeter-based dataset references the flow to the time-mean YoMaHA velocities at 1000 m (Katsumata and Yoshinari, 2010; Lebedev et al., 2007) and uses a zero-net-mass transport constraint (Dong et al., 2021). Kersalé et al. (2020) use models to reference the time-mean barotropic component at 1500 db, and bottom pressure measurements from the moorings provide the time-varying barotropic velocity component.

We calculate the overturning profiles, the monthly-to-interannual variation, and the seasonal cycles of the upper-cell MOC and the total MHT in each dataset. We separate the transports into their Ekman and geostrophic components. In the reanalyses, the Ekman component is calculated using the ERA5 or ERA-Interim wind stress, and for MHT, the zonal-mean SST across the section is used, assuming SST is representative of the Ekman layer temperature. The geostrophic component is calculated as a residual of the total and Ekman transports.

We also calculate the baroclinic and barotropic components of the ensemble's geostrophic MOC. We use thermal wind balance and the model's geopotential height anomalies to estimate the baroclinic velocities (see, e.g., Perez et al., 2011), integrating these from the deep ocean to the surface. The reference level is set ∼ 1000 m above the ocean floor, above the unphysically large zonal gradients in geopotential height anomaly that exist in the deepest layers of the model. Thus, the reference level depth varies spatially (∼ 2000 to ∼ 4000 m deep) due to the bathymetry, but it is constant in time. The reference velocity is not required to calculate the baroclinic MOC anomalies, so we set the baroclinic velocity to 0 at the reference level depth. A visual inspection confirmed that the large month-to-month spatial variations in the baroclinic velocity field are in good agreement with the associated changes in the total velocity field. We tested the method using different reference level depths that generated similar monthly-mean MOC anomalies (not shown). We calculate the baroclinic component of the MOC by integrating the baroclinic velocities from the surface down to the depth of the time-mean total MOC maximum in each reanalysis (∼ 1250 m over 2013–2017). We calculate the barotropic component as a residual of the geostrophic and baroclinic MOC anomalies. The baroclinic and barotropic MOC anomalies in the reanalyses and in SAMBA estimates are not directly comparable because the reference levels differ. However, our baroclinic MOC anomaly estimate in the reanalyses accounts for baroclinic velocity variations from around 1000 m above the ocean floor to the surface over which the velocities are greatest and have large monthly variation.

The ensemble of reanalyses captures the main structure of the observed overturning profile (Fig. 1a). The depth and strength of the maximum overturning is similar among all estimates with a range of ∼ 15–18 Sv (Fig. 1a). The profiles diverge in the deeper ocean, with a weaker than observed lower overturning cell and southward flow in the ensemble (i.e. the MOC decreases more gradually with depth). The reanalyses are less accurate at depth due to there being fewer observations to constrain the flow. The overturning profiles of the ensemble and GLORYS12V1 in density space have no negative transport (i.e. no abyssal cell), and their MOC is stronger than in depth space (Fig. 1b). The temporal variability in their upper MOC strength at 34.5∘ S, however, is fairly insensitive to the vertical coordinate system used for integration (Fig. S1 in the Supplement). We therefore focus on the MOC in depth space because the reanalyses can then be directly compared with the observational estimates.

We analyse the basic statistics of the variability in the maximum MOC strength and the MHT by looking at their time mean and standard deviation over 2013–2017 and 1993–2020. The time-mean MOC estimates have a range of 15.5–18.7 Sv, with the ensemble mean (labelled “mean” in figures) being only slightly weaker than the altimeter-based estimate and that observed across SAMBA (crosses in Fig. 2a). The time-mean MHT estimates have a range of 0.31–0.61 PW (crosses in Fig. 2c). Relative to the ensemble-mean values (MOC: 16.56 Sv; MHT: 0.36 PW), the time-mean MHT range has a 75 % increase from its minimum to its maximum value (excluding the energy-budget estimates) compared to only a 20 % increase for the time-mean MOC range. These ranges are within the documented uncertainty in SAMBA (Table 2). The ensemble-mean MHT is similar to the energy-budget estimates based on Mayer et al. (2022) (Fig. 2c). While there is inter-model spread in the ensemble time-mean transports (crosses in Fig. 2b, d), the spread is smaller than the uncertainty in SAMBA (Table 2), although it is more comparable for the MHT than for the MOC.

Monthly-mean variability (i.e. the standard deviation) of MOC and MHT in the ensemble is similar to the altimeter-based estimate over 2013–2017 and 1993–2020, whereas variability observed from SAMBA is much greater (Figs. 2a, c and 3a–d; Table 2), with significant differences (p < 0.05 in an F test for the equality of two variances). Similarly, the ensemble-mean time series is significantly (p < 0.05) correlated with the altimeter-based estimate (r = 0.63 for MOC; r = 0.77 for MHT; both over 2013–2017), but it is not well correlated with SAMBA (r < 0.1). The monthly-mean SAMBA estimates (Fig. 3a, b) and the Mayer energy-budget MHT estimates have high-frequency variations of comparable magnitude (Fig. 3b, d and Table 2), although their variability is uncorrelated. Mayer_ORAP6 is weakly correlated with the ensemble mean and altimeter-based estimate (r = 0.14 and r = 0.19 over 1993–2017 and r = 0.28 and r = 0.32 over 2013–2017, for the respective datasets). Mayer_ORAS5 has a higher correlation with the ensemble mean and altimeter-based estimate (r = 0.30 and r = 0.32 over 1993–2017 and r = 0.52 and r = 0.57 over 2013–2017, for the respective datasets). The GloRan reanalysis run with and without assimilating altimetry data (not shown) has a similar correlation with the altimeter-based estimate (r = 0.52 vs. r = 0.56 for MOC over 2013–2017). Thus, the strong correlation between ensemble mean and altimeter-based estimates is not dependent on directly assimilating altimetry data. The experimental reanalysis does, however, still assimilate in situ and satellite temperature and salinity data, which would serve to constrain thermosteric and halosteric contributions, respectively, to sea level. In the 12-month running mean estimates (Fig. 3e, f), the ensemble mean is only weakly correlated with the altimeter-based estimate (r = 0.24 for MOC; r = 0.25 for MHT), so their high monthly-mean correlation is largely due to similar seasonal variability.

The GLORYS12V1 reanalysis has a larger time-mean MOC and MHT than the ensemble mean (and GLORYS2V4). It has similar monthly-mean variability to the lower-resolution reanalyses: slightly larger than the ensemble mean but smaller than GLORYS2V4 (Table 2). It is also significantly correlated with the ensemble mean (r = 0.80 for MOC and r = 0.84 for MHT over 1993–2019). Thus, fully resolving (as opposed to only permitting) eddies in the ocean reanalyses considered here is important to infer the time-mean transports across 34.5∘ S, but it has minimal impact on the variation in the monthly-mean transports.

The 12-month running mean MOC and MHT in the ensemble over 1993–2020 are relatively stable (Fig. 3e, f), with similar ensemble-mean values to those during 2013–2017 (Table 2) and no significant trend over 1993–2020. However, the individual reanalyses have significant (p < 0.05) trends in the MOC over 1993–2020 with differing sign and magnitude (Table 2). In contrast, only GloRan has a significant (increasing) trend in MHT (∼ 0.042 PW per decade). GLORYS12V1 has no significant trend in MOC or MHT. Hence, there is uncertainty in the long-term trends amongst the reanalyses.

The altimeter-based estimate has significant (p < 0.05) increases in MOC (∼ 0.66 Sv per decade) and MHT (∼ 0.036 PW per decade) over 1993–2020. The aforementioned MHT trends are similar over 1993–2016 (GloRanV14: ∼ 0.047 PW per decade; altimeter: ∼ 0.032 PW per decade). There is a significant increase in MHT over 1993–2016 in both the ORAS5-based (∼ 0.086 PW per decade) and the ORAP6-based (∼ 0.094 PW per decade) Mayer estimates. The Trenberth estimate has a significant but weak decline (∼ -0.010 PW per decade) over 2000–2016; the Mayer estimates also decline over this period, but the trend is insignificant.

The 12-month running mean from SAMBA is entirely different to other estimates (Fig. 3e, f), with a rapid increase in the MOC (∼ 14 Sv) and MHT (∼ 0.7 PW) from March 2014 to June 2016, followed by a rapid decline. Although an extended time series is needed to determine longer timescale variations, the interannual variability captured by SAMBA over 2013–2017 exceeds that of other estimates. Only the Mayer MHT estimates have interannual variations of comparable magnitude, but those variations occur before 2013 (Fig. 3f).

There is a predominantly annual cycle in the ensemble mean and altimeter-based transports, unlike the SAMBA seasonal cycle that has a stronger semi-annual variability (Fig. 3c, d). While we show the ensemble mean and altimeter-based seasonal cycles over 2013–2017 (Fig. 4), the seasonal cycles derived over the full record lengths are similar (not shown). The ensemble and altimeter-based overturning are weakest in austral summer, but the ensemble is strongest in May/June, peaking 2 months after the altimeter-based estimate (Fig. 4a, b). In contrast, the MOC in SAMBA is dominated by a semi-annual signal, with minima in April and September and maxima in August and December. There are year-to-year variations in the annual cycles of all estimates (not shown), with variations in phase, shape, and magnitude. In SAMBA, 4 years of observations are not long enough to examine the sensitivity of the seasonal cycle to changing the time period, but given the strong high-frequency variations, the seasonal cycle based on 4 years of data is unlikely to be robust.

The shape of the seasonal cycle in MHT is similar to that of the MOC for each estimate as expected given the high correlation between the monthly-mean MHT and MOC (r = 0.90, r = 0.91, and r = 0.96 for the ensemble mean, altimeter-based estimate, and SAMBA, respectively, over 2013–2017). The Mayer energy-budget estimates have seasonal cycles dominated by an annual signal, with a larger magnitude range than other estimates. They are similar to the Trenberth estimate but with greater month-to-month variability. However, when averaged over the 2000–2016 period used in the Trenberth estimate rather than 2013–2017, they become smoother and closer to the ensemble (“Mayer_ORAS5_2000–16” in Fig. 4).

Year-to-year variations in the annual cycles of each estimate over 2013–2017 (not shown) and differences in the climatological seasonal cycle between each estimate (Fig. 4) stem from their geostrophic differences (Fig. 4e, f) because the Ekman annual cycles are similar year to year (not shown) and for all estimates (Fig. 4c, d). Differences between estimates are clearer in the geostrophic component, peaking before the ensemble mean in the altimeter-based estimate and after the ensemble mean in SAMBA. Thus, the Ekman and geostrophic components tend to counteract each other in the altimeter-based estimate and augment each other in SAMBA. This causes a greater increase in the magnitude of the total MOC and MHT seasonal cycles (relative to their geostrophic components) in SAMBA than it does in the altimeter-based estimate but a greater change in the seasonal cycle phase and shape in the altimeter-based estimate (cf. Fig. 4a, b and e, f). The relative contribution of the Ekman component to the total MOC and MHT in the ensemble is nonetheless significantly greater than in SAMBA. In the ensemble mean (and in GLORYS12V1 and SAMBA), the geostrophic component of the MOC (Fig. 4e) has a second peak in November or December (i.e. austral spring or summer) and thus has a semi-annual signal. Although the increase in the MOC to this end-of-year peak relative to the magnitude of decrease from the preceding peak is smaller in the ensemble mean than in SAMBA, it is noteworthy, increasing by 52 % of the preceding decrease (and by 77 % in the seasonal cycle over 1993–2020) compared to 84 % in SAMBA. The altimeter-based estimate has no significant increase in the geostrophic component in austral spring, and there is also no increase in the ensemble-mean MHT, unlike in SAMBA (Fig. 4f).

We investigate possible causes of the difference in variability between SAMBA and the ensemble by separating the geostrophic MOC anomalies into their baroclinic and barotropic components. The baroclinic and barotropic components of the MOC are not directly comparable between the ensemble and SAMBA due to differences in the reference level depth, but this probably has little impact on the differences between these estimates (see Sect. 2.2). The seasonal cycles of these components largely counteract each other in the ensemble, with their sum equal to the geostrophic component (Fig. 5). By contrast, these components tend to augment each other in SAMBA (Fig. 5), so their geostrophic seasonal cycle has variations of a greater magnitude. The baroclinic component tends to dominate in both datasets, primarily controlling the phase of the geostrophic MOC seasonal cycle (Fig. 5). Although the barotropic component tends to counteract the baroclinic component in the ensemble, it has a notable effect on the phase of the geostrophic MOC seasonal cycle over 2013–2017 unlike over 1993–2020. Thus, while differences in the seasonality of the baroclinic MOC component account for most of the difference in the seasonality of the geostrophic MOC, differences in the barotropic component between the ensemble and SAMBA also play a role.

We also analyse the monthly-mean and interannual variations in the baroclinic and barotropic components of the MOC anomalies (Fig. 6). Both the baroclinic and the barotropic components of the MOC have similar monthly-mean variability in the ensemble and in SAMBA over 2013–2017 (Fig. 6d, e), although the baroclinic variability is slightly higher in SAMBA (7.5 Sv vs. 5.3 Sv). Similarly, the interannual variability in the baroclinic and barotropic components has similar peak-to-trough magnitudes over 2013–2017 in the ensemble and SAMBA (Fig. 6f). However, since the barotropic component counteracts the baroclinic component in the ensemble, the geostrophic and total MOC anomalies in the ensemble have much smaller monthly-mean and interannual variability than in SAMBA (Fig. 6a, b, f and Table 2). The monthly-mean and 12-month running mean baroclinic and barotropic components in the ensemble have even larger variability over 1993–2020, but these components counteract each other over the whole period (Fig. 6f).