Bottom pressure observations on both sides of the
Atlantic basin, combined with satellite measurements of sea level anomalies
and wind stress data, are utilized to estimate variations of the Atlantic
Meridional Overturning Circulation (AMOC) at 11

The Atlantic Meridional Overturning Circulation (AMOC) plays a major role in
the global oceanic heat budget. About 88 % of the maximum heat transport
in the subtropical North Atlantic (1.3 PW; e.g. Lavin et al., 1998) is
carried by the AMOC (Johns et al., 2011). Because of the AMOC, there is
substantial northward heat transport across the Atlantic Equator (e.g.
Talley, 2003), which is unique among global oceans. Simplifying the
circulation in the Atlantic to a two-dimensional latitude–depth plane, the
AMOC connects warm waters flowing northward in the upper ocean and cold
waters flowing southward at depth across all latitudes through water mass
transformation, for example, in the subpolar North Atlantic or near the
Southern Ocean (e.g. Buckley and Marshall, 2016). With the AMOC
representing the strongest mode of northward heat transport by the ocean, it
is essential to provide the observational evidence of the mechanisms that
control its structure and variability in order to understand the present-day
climate, validate climate simulations and improve predictions. Historically,
the strength and structure of the AMOC were estimated based on shipboard
hydrographic sections establishing the mean AMOC strength and related heat
transport (e.g. Richardson, 2008). The first trans-basin mooring array – the
Rapid Climate Change – Meridional Overturning Circulation and Heatflux Array
(RAPID/MOCHA) transport array at 26

Today, there are several ongoing international efforts monitoring the AMOC
at selected latitudes (e.g. Frajka-Williams et al., 2019), such as the
OSNAP array in the subpolar North Atlantic (since 2014; Lozier et al.,
2019), the RAPID array in the subtropical North Atlantic at 26

The western tropical South Atlantic constitutes a key region for the
exchange of water masses, heat and salt between the Southern Hemisphere and Northern
Hemisphere (Biastoch et al., 2008b; Schmidtko and Johnson, 2012;
Kolodziejczyk et al.,2014; Hummels et al., 2015; Lübbecke et al., 2015;
Herrford et al., 2017). Several observational and modelling studies (e.g.
Rühs et al., 2015; Zhang et al., 2011) suggest that 11

With the resumption of the mooring array at 11

Besides the moored observations at 11

Over the period 2013–2018, five BPRs were deployed at 11

Collection of available BP measurements at 11

For our analyses, the available BP records were de-spiked, interpolated from
an original sampling rate of 10 min to hourly values and de-tided using
harmonic fits with tidal periods shorter than 35 d. All tidal harmonics
were calculated by performing a classical harmonic analysis (Codiga, 2011). The
tidal models for

Bottom pressure (BP) anomalies measured at 11

To estimate pressure variability at the surface, we used sea level anomalies
(SLAs) from the delayed-time “all-sat-merged” data set of global sea
surface height, produced by Ssalto/Duacs and provided by the Copernicus
Marine Environment Monitoring Service (CMEMS). The multi-satellite altimeter
sea surface heights are mapped on a

Time series of SLA over the period 2013–2018 – chosen close to the
western (purple;

In order to estimate the Ekman contribution to AMOC variability at
11

To estimate the WBC transport, we computed a transport
time series of the NBUC (Sect. 5.4), which is derived from four current
meter moorings spanning the width of the NBUC at 11

To validate the observational strategy, we used the 5 d output from a
hindcast experiment with the global ocean–sea-ice ocean general circulation
model configuration “INALT0”. It is based on the NEMO (Nucleus for European
Modelling of the Ocean v3.1.1; Madec, 2008) code and developed within the
DRAKKAR framework (The DRAKKAR Group, 2014). INALT01 is a global

The structure of the AMOC is often described using the overturning transport
stream function

Variations in the basin-wide upper-ocean meridional geostrophic transport

Our method is limited by the fact that the depth levels of the instruments with respect to equi-geopotential surfaces are not known, and thus only velocity anomalies can be determined (e.g. Donohue et al., 2010). However, the differences between eastern and western boundary pressure anomalies from BPRs have successfully been used to estimate temporal fluctuations of the geostrophic contribution to AMOC variability (e.g. Kanzow et al., 2007).

At the BPR depths, anomalies of the geostrophic transport per unit depth

We use two different methods to approximate the vertical structure of

Regression of the first and second EOFs, i.e. the two dominant vertical
structure functions of the geostrophic transport per unit depth derived from
density and sea level anomalies in INALT01,

Upper-ocean geostrophic transport variations,

Finally, AMOC transport variations (

In the following, all mean transport is presented together with the
standard error (SE

Annual and semi-annual harmonics for all pressure time series (Sect. 5.1) are presented together with uncertainties for their amplitudes, which were derived by low-pass filtering the pressure time series with a cutoff of 170 d and subsequently calculating the 95th percentile of the deviations from the derived annual and semi-annual harmonics for every day of the year.

Experimental setup and strategy to estimate

Following the observational strategy (Fig. 3), BPRs at least at four
different locations (two depth levels) are required to derive basin-wide
geostrophic transport variations in the upper 1130 m of the water column.
While five recorders were in place over the period May 2014–October 2015, no BP
measurements at 300 m depth off Brazil are available before May 2014 and none
at all off Angola since November 2015. In this study, we found combined annual and
semi-annual cycles explaining 44 %–61 % of the variance in the daily BP
time series at the eastern boundary and 18 %–24 % of the variance at the
western boundary (see Sect. 5.1). Despite the smaller numbers at the
western boundary, the annual and semi-annual cycles are still the dominant
signals in all pressure time series at 11

To validate our strategy for the computation of AMOC variations from the BP
observations and to better understand the observed seasonal variability, we
simultaneously analysed the output of the INALT01 OGCM (see Sect. 3). In
INALT01, we can diagnose AMOC variations,

Alternatively, we can derive

All of the ocean pressure time series in this study, i.e. at the surface from SLA (Fig. 2a, b), at 300 and 500 m depth from the BPRs (Fig. 1b), at the western or eastern boundary, are dominated by seasonal variability. The corresponding periodograms all exhibit pronounced peaks at periods of the annual and semi-annual cycles (coloured curves in Fig. 4).

Periodograms of

The main focus here is on seasonal variability; however, there are some other
interesting peaks in the periodograms indicating energy on intraseasonal and
interannual timescales. Off Brazil, variability at a period of 70 d
(Fig. 4c, d) is very likely related to the DWBC eddies described by
Dengler et al. (2004), which are thought to dominate the DWBC flow at
11

We found the relative importance of seasonal variability to be most
pronounced near the surface off Angola in both the observations and the
model (Fig. 4). The combined annual and semi-annual harmonics of the
observed pressure time series explain most of the variance there – 61 %
at the surface, 58 % at 300 m depth, 44 % at 500 m depth – and their
amplitudes decrease with depth. To make this statement, we converted SLA
variance into pressure variance using the hydrostatic equation. The combined
annual and semi-annual harmonics at the eastern boundary (Fig. 5b, d, f)
show a similar structure at different depths with maxima in austral autumn
and spring, and a minimum in winter. Nevertheless, the phases of the annual
and semi-annual cycles change with depth at different rates (Fig. 6). With a
phase shift of about 5 months, the annual harmonics at the surface and 500 m
depth are almost out of phase. The semi-annual harmonic is rather in phase,
peaking about 1.5 months earlier at depth. This difference in the phase
changes with depth can be associated with CTWs of certain baroclinic modes.
Kopte et al. (2018) associated the annual and semi-annual cycles of the
alongshore velocity from the mooring at 11

Combined annual and semi-annual harmonics calculated for

At the western boundary (Fig. 5a, c, e), the seasonal variability of the
observed pressure time series is less pronounced. The combined annual and
semi-annual harmonics explain only 12 % of the total variance at the
surface and are barely different from zero, considering the uncertainty
estimate of the amplitude. Seasonal variability of the surface pressure is
decoupled from the pressure variability at depth, which supports the
undercurrent character of the NBUC. The BP measurements at 300 and 500 m
depth, which are both located in the depth range of the NBUC, have annual
and semi-annual harmonics of similar amplitude and phase (Fig. 5d, f).
The phase of the annual harmonic changes by 2 months between the surface and
300 m depth and the semi-annual harmonic by

Annual and semi-annual harmonics of the individual pressure time series simulated in the INALT01 model (grey shading in Fig. 5) agree quite well with the observations regarding the timing of the maxima and minima. On the other hand, there are large differences in the amplitudes: the model tends to overestimate the annual harmonic at the surface and generally underestimate seasonal variability at depth – especially at the western boundary the seasonal cycle of the simulated BP at 300 and 500 m depth is almost non-existent.

In summary, for the seasonal variability at 11

Prevailing winds along 11

Periodograms of the Ekman transport at 11

The zonal wind stress anomalies at 11

As described in the methods, we were able to estimate AMOC transport
variations in the tropical South Atlantic from BP measurements over the
period 2013–2018. Figure 8 displays the derived time series of

Anomaly time series at 11

While from the BP observations we could only derive anomalies of

Both the

Mean seasonal cycles of

The observed upper-ocean geostrophic transport anomaly (

Nevertheless, the seasonal cycles of both estimates based on observations,

In order to test our observational strategy, we compared the upper-ocean
geostrophic transport anomaly derived directly from the simulated meridional
velocity component (

Mean seasonal cycles of the geostrophic transport per unit depth,

Figure 11 compares the mean seasonal cycles of

Mean seasonal cycle of the geostrophic transport per unit depth,

For the period 2013–2018, the geostrophic contribution to the seasonal cycle
of the AMOC at 11

In order to better understand the mechanisms that set the seasonal cycle of

Mean seasonal cycle of the geostrophic transport per unit depth,

The mean seasonal cycle of the NBUC, as calculated for the 30-year INALT01 model run, has its maximum in April, minimum in November and a peak-to-peak amplitude of 10 Sv (Fig. 12b). Peak-to-peak amplitudes of up to 15 Sv can be found in 5-year subsets of the model time series. Having a mooring array installed off the coast off Brazil measuring the Western Boundary Current system there (e.g. Hummels et al., 2015; see Sect. 2.4) allowed us to directly compare the seasonal variability of the NBUC in INALT01 with observations. The seasonal cycle of the NBUC in INALT01 agrees quite well with the seasonal cycle observed in recent years – regarding the peak-to-peak amplitude (7.6 Sv in 2000–2004 and 7 Sv in 2013–2018) and the timing of maximum and minimum transport (Fig. 13b). During the earlier deployment period (2000–2004), there was a stronger semi-annual cycle, creating a secondary minimum in March, which was neither found in the observations during 2013–2018 nor in INALT01.

In INALT01, the contribution of the NBUC to the AMOC on seasonal timescales
is largely compensated by the flow in the western basin interior. The
seasonal cycle of the geostrophic transport per unit depth in the western
basin interior is of similar strength and vertical structure but of opposing
sign to the one of the NBUC (cf. Fig. 12a, c). In the western basin
interior, the vertically integrated upper-ocean geostrophic velocity is
mainly associated with an annual harmonic and likely related to a strong
seasonal cycle in the local wind stress curl (Fig. 14). The annual harmonic
of the wind stress curl exhibits relatively large amplitudes over the region
(10 to 34.55

As the contributions of the NBUC and western basin interior seasonal cycles
to the AMOC tend to cancel each other out, in INALT01, seasonal variability
of the upper-ocean geostrophic transport at 11

From this analysis, we conclude that a compensation between the NBUC and western basin interior results in a major contribution of the upper-ocean geostrophic transport of the eastern basin to the AMOC transport on seasonal timescales. As described in Sect. 5.1, however, the model tends to underestimate the seasonal pressure variability at 300 and 500 m depth – especially at the western boundary. This leaves some uncertainty in the relative importance of western and eastern basin contributions to the seasonal AMOC variability in reality.

In this study, we used bottom pressure observations on both sides of the
basin at 300 and 500 m depth, combined with satellite measurements of sea
level anomalies, different wind stress products and model results, to
estimate the upper-ocean geostrophic and Ekman transport contributions to
AMOC variability at 11

The use of bottom pressure measurements to compute basin-wide integrated
northward transport is not straightforward: firstly, the sensors experience
instrumental drifts, which limits the BPRs capabilities to recover
variability on longer timescales. Secondly, the deployment depth is not
precisely known, which only allows the calculation of transport anomalies.
We found the available BP time series at 11

At 11

At the western boundary, seasonal pressure variability is weaker with its
relative importance compared to other variability increasing with depth;
the annual and semi-annual harmonics explain about 10 % of the variability
at the surface and 30 % at 500 m depth. The seasonal variability of the
zonally integrated geostrophic velocity anomaly in the upper 300 m is
therefore mainly controlled by pressure variations at the eastern boundary,
while at 500 m depth contributions from the western and eastern boundaries
are similar. Annual and semi-annual harmonics at the western boundary also
exhibit a vertical structure as seasonal variability at the surface is
decoupled from the pressure variability at 300 and 500 m depth. Based on
geostrophic velocity fields from hydrographic measurements, studies like
da Silveira et al. (1994) or Stramma et al. (1995) already stated that the WBC
system at 11

Amplitudes of the annual (solid curves) and semi-annual (dashed
curves) harmonics of the vertically integrated upper-ocean geostrophic
velocity in INALT01 (blue curves; left axis) and the INALT01 wind stress
curl (green curves; right axis) along 11

Over the period 2013–2018, the upper-ocean geostrophic transport variations
derived from pressure differences across the basin are dominated by
seasonal variability – with a peak-to-peak amplitude of 12–14 Sv, depending
on the method used to approximate its vertical structure. The peak-to-peak
amplitude of the mean seasonal cycle of the Ekman transport is 7 Sv and of
the resulting AMOC transport 14–16 Sv. For the subtropics, recent estimates
of the peak-to-peak amplitude of the mean seasonal cycle of the AMOC range
from 4.3 Sv at 26.5

The output of the INALT01 OGCM was compared to the observed characteristics
of the seasonal cycles of the AMOC, its components as well as the NBUC. It
reproduces the seasonal cycles of the NBUC as observed in recent years with
current meter moorings and of the Ekman transport across 11

The INALT01 model tends to underestimate the seasonal bottom pressure variability at 300 and 500 m, especially at the western boundary. This translates into the vertical structure of the simulated geostrophic transport variations, which is also used for the calculation of the observational estimate (method 2) adding to its uncertainty.

In the observations, the geostrophic contribution to seasonal AMOC
variability exceeds the Ekman contribution by almost a factor of 2, while in
INALT01, averaged over the 30-year model run, or in earlier studies based on
models (e.g. Zhao and Johns, 2014), the contributions are similar. Even
when considering the multi-year variations of the seasonal cycle of

The ratios of the NBUC and AMOC seasonal amplitudes are different between
the observations (

In the model, seasonal upper-ocean geostrophic transport variability at
11

The compensation between the western basin interior and the NBUC on seasonal
timescales found in INALT01 results in a minor contribution of the western
basin compared to the eastern basin and limits the importance of the NBUC
for AMOC variability on seasonal timescales. However, in this study, we
found that INALT01 tends to underestimate seasonal variability at 300 and
500 m off Brazil. In two different model studies, Rodrigues et al. (2007) and
Silva et al. (2009) related seasonal variability in the NBUC to seasonal
variations in the bifurcation region of the South Equatorial Current. Thus,
the phases of the annual and semi-annual harmonics of the NBUC may not
simply be set by the response to the local wind curl forcing in the western
basin at 11

We conclude that the seasonal variability of the geostrophic contribution to
the AMOC at 11

This study adds to the overall understanding of local and shorter-term AMOC
variations, which is important for estimating the significance of long-term
AMOC changes and thus for the detectability of its meridional coherence.
To predict the long-term behaviour of the AMOC and its impacts, continuous
observations from purposefully designed arrays are required in different key
locations. We would like to argue that the observational programme at
11

The bottom pressure data described in Sect. 2.1 are available through

The methodology was first proposed TK, then further developed and conceptualized by JH and PB. PB and RH raised the project funding and, together with MA, administered the project. The investigation was made by JH, supervised and validated by PB and TK. JH processed the observational data, performed all analyses, drafted the manuscript and designed the figures. JVD developed INALT01 and performed the simulations. PB supervised work at sea. RH calculated and provided the NBUC transport time series. All authors contributed to the discussion of the results or the review and editing of the manuscript.

The authors declare that they have no conflict of interest.

We thank the
captains and crews of the R/V

This study was funded by the Deutsche Bundesministerium für Bildung und Forschung (BMBF) as part of the projects RACE (grant nos. 03F0651B, 03F0729C, 03F0824C), SACUS
(grant no. 03G0837A) and BANINO (grant no. 03F0795A), by EU H2020 under grant agreement no. 817578 TRIATLAS project and by the Deutsche Forschungsgemeinschaft (DFG) through funding of R/V

This paper was edited by Erik van Sebille and reviewed by two anonymous referees.