**Research article**
10 Feb 2021

**Research article** | 10 Feb 2021

# Seasonal variability of the Atlantic Meridional Overturning Circulation at 11° S inferred from bottom pressure measurements

Josefine Herrford Peter Brandt Torsten Kanzow Rebecca Hummels Moacyr Araujo and Jonathan V. Durgadoo

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**Josefine Herrford et al.**Josefine Herrford Peter Brandt Torsten Kanzow Rebecca Hummels Moacyr Araujo and Jonathan V. Durgadoo

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^{1}GEOMAR Helmholtz Centre for Ocean Research Kiel, Kiel, Germany^{2}Kiel University, Kiel, Germany^{3}Alfred Wegener Institute, Bremerhaven, Germany^{4}Department of Oceanography, Federal University of Pernambuco, Recife, Brazil

^{1}GEOMAR Helmholtz Centre for Ocean Research Kiel, Kiel, Germany^{2}Kiel University, Kiel, Germany^{3}Alfred Wegener Institute, Bremerhaven, Germany^{4}Department of Oceanography, Federal University of Pernambuco, Recife, Brazil

**Correspondence**: Josefine Herrford (jherrford@geomar.de)

**Correspondence**: Josefine Herrford (jherrford@geomar.de)

Received: 28 May 2020 – Discussion started: 26 Jun 2020 – Revised: 02 Nov 2020 – Accepted: 07 Dec 2020 – Published: 10 Feb 2021

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^{∘} S. Over the
period 2013–2018, the AMOC and its components are dominated by seasonal
variability, with peak-to-peak amplitudes of 12 Sv for the upper-ocean
geostrophic transport, 7 Sv for the Ekman and 14 Sv for the AMOC transport.
The characteristics of the observed seasonal cycles of the AMOC and its
components are compared to results from an ocean general circulation model,
which is known to reproduce the variability of the Western Boundary Current
on longer timescales. The observed seasonal variability of zonally
integrated geostrophic velocity in the upper 300 m is controlled by pressure
variations at the eastern boundary, while at 500 m depth contributions from
the western and eastern boundaries are similar. The model tends to
underestimate the seasonal pressure variability at 300 and 500 m depth,
especially at the western boundary, which translates into the estimate of
the upper-ocean geostrophic transport. In the model, seasonal AMOC
variability at 11^{∘} S is governed, besides the Ekman transport, by
the geostrophic transport variability in the eastern basin. The geostrophic
contribution of the western basin to the seasonal cycle of the AMOC is
instead comparably weak, as transport variability in the western basin
interior related to local wind curl forcing is mainly compensated by the
Western Boundary Current. Our analyses indicate that while some of the
uncertainties of our estimates result from the technical aspects of the
observational strategy or processes not being properly represented in the
model, uncertainties in the wind forcing are particularly relevant for the
resulting uncertainties of AMOC estimates at 11^{∘} S.

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^{∘} N – has continuously measured the
temporal variability of the AMOC since the early 2000s (Hirschi et al.,
2003). Those observations showed that large AMOC variations can occur on a
range of timescales – from weeks to decades (e.g. Srokosz and Bryden,
2015). Kanzow et al. (2007) showed that not only the Ekman but even more so
the geostrophic contribution to the AMOC exhibit pronounced high-frequency
variability with periods up to few weeks. Kanzow et al. (2010) demonstrated
that the strong seasonal cycle in the AMOC strength at 26^{∘} N leads
to aliasing, when estimating the AMOC strength from single hydrographic
sections. They also found the upper-ocean geostrophic AMOC contribution to
dominate on seasonal timescales, while Chidichimo et al. (2010) discovered
those to be primarily driven by processes at the eastern boundary.

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^{∘} N
(since 2004; Cunningham et al., 2007; McCarthy et al., 2015), the MOVE array
in the tropical North Atlantic at 16^{∘} N (since 2001; Kanzow et
al., 2008; Send et al., 2011; Frajka-Williams et al., 2018), the SAMBA array
in the subtropical South Atlantic at 34.5^{∘} S (since 2009; Meinen
et al., 2018), as well as other programmes measuring important components of
the overturning, such as the Western Boundary Current (WBC) arrays at
53^{∘} N (since 1997; Zantopp et al., 2017), at 39^{∘} N
(line W; 2004–2014; Toole et al., 2017) and at 11^{∘} S (2000–2004 and
since 2013; Hummels et al., 2015), the array across the North Atlantic
Current at 47^{∘} N (NOAC array; Roessler et al., 2015), the deep
overflow observations through Denmark Strait (Jochumsen et al., 2017) or
Faroe Bank Channel (Hansen et al., 2016). In this study, we will present the
first estimate of basin-wide AMOC variations in the tropical South Atlantic
from the TRACOS (Tropical Atlantic Circulation and Overturning at
11^{∘} S) array.

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^{∘} S is a
good place to monitor water mass signal propagation, changes in the WBC
transport and, with that, changes in the AMOC transport. At 11^{∘} S
the WBC regime is comprised of the northward North Brazil Undercurrent
(NBUC) with a subsurface velocity maximum at about 200 m and the southward
Deep Western Boundary Current (DWBC) below 1200 m (e.g. Schott et al.,
2005). The NBUC is known to originate from the southern branch of the South
Equatorial Current (da Silveira et al., 1994), which transports subtropical
waters towards Brazil and bifurcates between 14 and 28^{∘} S (Stramma and
England, 1999;
Boebel et al., 1999; Wienders et al., 2000). From 2000 to 2004,
a first mooring array was deployed at 11^{∘} S to observe the
variability of the WBC and its components – the NBUC and the DWBC below.
Schott et al. (2005) found the NBUC to carry 25 Sv northward on average. The
NBUC showed a strong seasonal cycle, which seems to be out of phase with the
seasonal variations in the DWBC. Intraseasonal signals could also be
observed: Dengler et al. (2004) described a spectral peak in the velocity
time series at a period of 60–70 d, which was observed in most of the
moored records but was strongest within the DWBC. They concluded that the
DWBC transport at 11^{∘} S is mainly accomplished by migrating
eddies. Further, Veleda et al. (2011) could relate variability at periods of
2–3 weeks to coastal trapped waves (CTWs) propagating from 22 to 36^{∘} S
equatorward along the Brazilian coast. In July 2013, a similar mooring
array was again deployed at 11^{∘} S (Hummels et al., 2015) and is
still in place. Comparing the two observational periods, Hummels et al. (2015)
did not find significant changes in the averaged NBUC and DWBC
transport. Furthermore, they could show that the interannual NBUC
variability observed between 2000 and 2004 is consistent with the output of a
forced ocean general circulation model (OGCM) named INALT01. Decadal
variability in INALT01 was also found to be similar to transport estimates
based on historical hydrographic observations from Zhang et al. (2011). To
date, Zhang et al. (2011) provide the only NBUC time series derived from
hydrographic observations spanning several decades. They estimated
multi-decadal variability of the NBUC to be of similar order to its seasonal
cycle and, because of the connection to the Atlantic Multidecadal
Variability, suggested the NBUC to serve as an index for AMOC variations on
these timescales. In a model study, Rühs et al. (2016) found decadal to
multi-decadal buoyancy-forced changes in the AMOC transport to manifest
themselves in NBUC transport (at 6^{∘} S); however, these changes are
also masked by interannual wind-driven variability.

With the resumption of the mooring array at 11^{∘} S in 2013, the
observational programme was also extended by installing a mooring array for
direct velocity measurements across the continental slope off Angola.
Studies based on these observations showed that the circulation there is
weak and dominated by seasonal variability associated with remotely forced
waves (Kopte et al., 2017, 2018). As shown in several model studies, most of
the intraseasonal (*T**>*120 d) to interannual variability in
that region is induced by a wave response to equatorial wind forcing that
generates equatorial Kelvin waves propagating eastward and, while reaching
the eastern boundary, transferring a part of their energy as CTWs further to
the south towards 11^{∘} S (Illig et al., 2004, 2018;
Bachèlery et al., 2016; Imbol Koungue et al., 2017).

Besides the moored observations at 11^{∘} S, PIESs (pressure-inverted
echo sounders) or single bottom pressure recorders (BPRs) were deployed on
both sides of the Atlantic. Within some of the other programmes targeting AMOC
fluctuations – such as RAPID (Kanzow et al., 2010; Meinen et al., 2013;
McCarthy et al., 2015), MOVE (Kanzow et al., 2006, 2008) and SAMBA (Meinen
et al., 2018; Kersalè et al., 2020) – bottom pressure (BP) measurements
are used to estimate the time-varying portion of a barotropic reference
velocity which is then combined with the internal geostrophic velocity
derived from differences in dynamic height derived from full-depth dynamic
height moorings or the PIES travel times. But, circulation changes in
*z* coordinates can also be estimated using only a series of bottom pressure
measurements installed at different depths on the western and eastern
continental slopes. In a model study, Bingham and Hughes (2008) showed that
this works well down to around 3000 m, even with only western boundary
measurements. In our study, we use the BP differences across the basin at
300 and 500 m depth to estimate the geostrophic contribution to AMOC
variations in the tropical South Atlantic over the period 2013–2018 and
investigate its seasonal variability.

## 2.1 Bottom pressure time series

Over the period 2013–2018, five BPRs were deployed at 11^{∘} S (Table 1).
In May 2013, together with the WBC mooring array, two bottom-mounted
PIESs were installed across the Brazilian continental slope at 300 and 500 m
depth. PIESs measure the acoustic travel time to the surface, as well as
bottom pressure. In this study, we only used the BP time series. Then, 1 year
later, another set of PIESs was deployed at the same locations. While of the
first set only the 500 m sensor could be recovered, the second set was
maintained in September 2016 and spring 2018. Note that the two PIESs at 500 m,
KPO 1109 and KPO 1135 (Table 1), were located only ∼1 km
away from each other over the period May 2014–October 2015. At the eastern
boundary off Angola, two SBE 26plus sensors (single or attached to an acoustic Doppler current profiler (ADCP)
shield) measured pressure at 300 and 500 m depth from July 2013 to November 2015.
The instruments were re-deployed but could not be recovered again. We
assume that they were lost due to extensive fishing in the region.

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 *T**<*35 d capture between 97.0 % and 99.6 % of the
total variance in the original BP time series. After removing these
higher-frequency tides, the remaining variance is mainly related to seasonal
variations and low-frequency instrument drifts. Instrument drifts vary
substantially between the five instruments: while KPO 1106 shows almost no
drift, all other sensors exhibit a combination of exponential and linear
behaviour but with different signs and at different rates (Fig. 1a).
Unfortunately, we were not able to directly relate individual drift
behaviour to pressure effects or material creep. Earlier studies (e.g. Watts
and Kontoyiannis, 1990; Johns et al., 2005; Kanzow et al., 2006; Cunningham, 2009)
found that subtracting a least-squares exponential–linear fit of the
form ${P}_{\mathrm{Drift}}\left(t\right)=a\left[\mathrm{1}-{e}^{-bt}\right]+ct+d$ from the
pressure time series to be the procedure that works best for the PIES. As
the SBE26plus recorders were also equipped with quartz pressure sensors, we
decided to “de-drift” all five sensors similarly by subtracting
exponential–linear fits as described above. Kanzow et al. (2006) also
discussed the problem of this empirical de-drifting being unable to
distinguish between the instrumental drift and ocean signals of the order of
or longer than the time series. This means that, for example, seasonal
signals can leak into the fit and its removal from the time series can
reduce seasonal signals in return. We attempted to solve this problem by
iteratively fitting an exponential–linear drift as well as annual and
semi-annual harmonics. The first guess of the exponential–linear drift was
removed from the original time series, and annual and semi-annual harmonics
were fitted to the de-drifted time series. This first guess was iteratively
improved by calculating new exponential–linear fits after subtracting the
iteratively improved annual and semi-annual harmonics from the original
data. After three repetitions, the fits tended to converge. Both fits from
the third repetition are shown in Fig. 1a. For further analyses, we
removed the derived instrument drift from the original BP time series and
averaged to daily values (Fig. 1b).

## 2.2 Sea level anomalies

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 $\mathrm{0.25}{}^{\circ}\times \mathrm{0.25}{}^{\circ}$ grid
(e.g. Pujol et al., 2016) and are available for the period 1993–2018 at
daily resolution. To obtain pressure variation near the boundaries, SLA grid
points were chosen closest to the Brazilian and Angolan coasts at
11^{∘} S, respectively. The sensitivity of our results to SLA changes
with distance to the coast (Fig. 2c, d) was tested: at the western
boundary, off Brazil, the phase of the annual harmonic slightly changes with
distance to the coast – about 30 d over 0.5^{∘} longitude. At the
eastern boundary, off Angola, the phases of both annual and semi-annual
harmonics are constant over the distance between the location of the 300 m
BPR and the coast.

## 2.3 Wind stress

In order to estimate the Ekman contribution to AMOC variability at
11^{∘} S, we used gridded daily wind stress fields from MetOp/Advanced Scatterometer (ASCAT)
retrievals. Those are available for the period 2007–2018 and
with a spatial resolution of $\mathrm{0.25}{}^{\circ}\times \mathrm{0.25}{}^{\circ}$ (Bentamy and
Croizé-Fillon, 2012). The near-surface Ekman transport was estimated as
the zonal integral of the zonal wind stress component between
10.5 and 11^{∘} S (see Eq. 7 in Sect. 4.1).

## 2.4 NBUC transport time series

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^{∘} S and
represents an update from previous studies (Schott et al., 2005; Hummels et
al., 2015). Record gaps were filled with empirical orthogonal functions
(EOFs) derived from the mooring data. Moored time series were finally mapped
into sections every 2.5 d using a Gaussian-weighted interpolation with
horizontal mapping scales of 20 km with a cutoff radius of 150 km and
vertical mapping scales of 60 m with a cutoff radius of 1500 m. The NBUC
transport was computed by integrating the total flow (including northward
and southward flow) within a predefined box (see Hummels et al., 2015, for
further details).

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
$\mathrm{1}/\mathrm{2}$^{∘} configuration with a $\mathrm{1}/\mathrm{10}$^{∘} refinement between
70^{∘} W–70^{∘} E and 50^{∘} S–8^{∘} N,
improving the representation of the WBC regime in the
South Atlantic and extended Agulhas region (Durgadoo et al., 2013). It uses
a tripolar horizontal grid, 46 vertical levels with increasing grid spacing
and is forced by interannually varying air–sea fluxes (1948–2007) from the
CORE2b (Coordinated Ocean-ice Reference Experiments; Large and
Yeager, 2009) data set. Sea surface elevation and wind stress are then prognostic
variables: INALT01 uses the filtered free surface formulation for the
surface pressure gradient and calculates surface wind stress from relative
winds using the CORE2b bulk formulae. This particular model configuration
has been previously used in the region. South of Africa, it was used for
validating a method of determining Agulhas leakage from satellite altimetry
(Le Bars et al., 2014). Hummels et al. (2015) found interannual variability
of the NBUC as assessed from moored observations to be consistent with the
INALT01 model output as well as decadal variability in INALT01 to be similar
to geostrophic transport estimates from Zhang et al. (2011). Further, the
simulated overturning stream function (in neutral density classes) at
11^{∘} S is in good agreement with the vertical structure and
amplitude of an estimate based on shipboard observations conducted in 1994
(Lumpkin and Speer, 2003). Our analysis employs two-dimensional
(longitude–depth) sections of temperature, salinity and velocity, as well as
surface elevation and wind stress fields along 11^{∘} S for the
simulated period (1978–2007). Surface wind stress fields are additionally
shown for the years 2008–2009.

## 4.1 Computation of AMOC transport variations from BP observations

The structure of the AMOC is often described using the overturning transport
stream function *ψ*(*y**z**t*), which is derived from integrating the
meridional velocity component, *v*, zonally (from the western (*x*_{WB}) to
the eastern boundary (*x*_{EB})) and vertically:

with *x* being longitude, *y* latitude, *z* the vertical coordinate pointing
upward and *t* time. This reduces a complex three-dimensional circulation
system to a two-dimensional one. The AMOC strength or transport is commonly
defined as the maximum of *ψ* over depth and typically expressed in
Sverdrups [1 Sv = 10^{6} m^{3} s^{−1}]. At any chosen latitude,
Ψ_{MAX} can be decomposed into Ekman and geostrophic components
(thereby generally neglecting small ageostrophic, non-Ekman components):

Variations in the basin-wide upper-ocean meridional geostrophic transport
*T*_{G} at a certain latitude can be derived from the differences between
the bottom pressure at the eastern (*P*_{EB}) and western (*P*_{WB})
basin boundaries. At 11^{∘} S, we use bottom pressure measurements on
both sides of the basin at 300 and 500 m depth. Figure 3 displays the
observational strategy.

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 ${V}_{\mathrm{G}}^{\prime}\left(zt\right)$ were calculated as

${P}_{\mathrm{EB}}^{\prime}$ and ${P}_{\mathrm{WB}}^{\prime}$ are the pressure anomalies at the eastern and
western boundaries with respect to the time mean, respectively, *f* the
Coriolis parameter and *ρ*_{0} a mean sea water density. At the
surface, ${V}_{\mathrm{G}}^{\prime}(z=\mathrm{0},t)$ can be calculated accordingly from sea level
anomalies, *η*^{′}:

with *g* being the acceleration of gravity. Additionally, a level of no motion
is prescribed at 1130 m, such that ${V}_{\mathrm{G}}^{\prime}(z=-\mathrm{1130}\phantom{\rule{0.125em}{0ex}}\mathrm{mt})=\phantom{\rule{0.125em}{0ex}}\mathrm{0}$ at all
times. This “level of no motion” is based on the velocity field from the
INALT01 model configuration and defined as the local zero-crossing depth of
*v*, averaged across the basin and over time. The maximum of the corresponding
stream function averaged over time is located at *z* = −1072 m. Earlier
studies in this region used a level of no motion at the depths of *σ*_{1}=32.15 kg m^{−3} (at about 1150 m; e.g. Stramma et al., 1995;
Schott et al., 2005). The sensitivity to the choice of the level of no
motion was tested between 800 and 1300 m, and the obtained AMOC transport changed
by less than 10 %.

We use two different methods to approximate the vertical structure of ${V}_{\mathrm{G}}^{\prime}$: piecewise linear interpolation of ${V}_{\mathrm{G}}^{\prime}$ between the four data points at 0, 300, 500 and 1130 m depth – denoted as ${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{Points}}^{\prime}$ or ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{Points}}^{\prime}$ throughout the study.

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, ${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}P\left(z\right)}^{\prime}$ (see Sect. 4b), onto the three data points at 0, 300 and 500 m depth, thereby relaxed the no-flow condition at 1130 m depth. The first (second) dominant vertical structure function explains 90.3 % (9.6 %) of the variance contained in ${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}P\left(z\right)}^{\prime}$. The resulting transport variations are denoted as ${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{EOFs}}^{\prime}$ or ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{EOFs}}^{\prime}$.

Upper-ocean geostrophic transport variations, ${T}_{\mathrm{G}}^{\prime}$, were then calculated by vertically integrating the approximated ${V}_{\mathrm{G}}^{\prime}$ profile from ${z}_{\mathrm{3}}=-\mathrm{1130}$ m up to the surface.

Using the first method, *z*_{3} is defined as the “level of no motion”
(${V}_{\mathrm{G}}^{\prime}\left({z}_{\mathrm{3}}\right)=\mathrm{0}$), whereas for the second method
${V}_{\mathrm{G}}^{\prime}\left({z}_{\mathrm{3}}\right)$ might vary with time.

Finally, AMOC transport variations (${T}_{\mathrm{AMOC}}^{\prime}$) can be derived by adding local Ekman transport anomalies ${T}_{\mathrm{EK}}^{\prime}$.

The latter can efficiently be estimated from the zonal component of the wind
stress, *τ*_{x}, at 11^{∘} S according to

and subtracting the temporal average.

In the following, all mean transport is presented together with the
standard error (SE $=\mathit{\sigma}/\sqrt{N/{n}_{\mathrm{d}}}$), where
*σ* is the standard deviation and *n*_{d} the decorrelation timescale
of the respective time series of length *N*.

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.

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^{∘} S. Therefore, we
decided to “replace” the missing sensors with the combined annual and
semi-annual harmonics derived from the available BP time series. This means,
for example, that the geostrophic transport after November 2015 is derived from
the differences between measured BP variations at the western boundary and
repeated annual and semi-annual harmonics – as derived from earlier years
– at the eastern boundary. We derive confidence in our method from the
comparison of the observed BP variations with variations in the simulated BP
time series and in the SLA time series off Angola, both covering longer
periods.

## 4.2 Using the INALT01 OGCM as a “testing area”

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, ${T}_{\mathrm{AMOC}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}}^{\prime}$, from the
velocity field using Eqs. (1) and (2), i.e. by directly integrating the
simulated meridional velocity component at 11^{∘} S horizontally
across the basin and vertically from 1130 m to the surface. The zonally
integrated Ekman transport *T*_{EK SIM} at 11^{∘} S is derived with
Eq. (7) from INALT01 wind stress. According to Eq. (6), the simulated
upper-ocean geostrophic transport anomaly ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}}^{\prime}$ is then
${T}_{\mathrm{AMOC}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}}^{\prime}-{T}_{\mathrm{EK}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}}^{\prime}$.

Alternatively, we can derive ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}P\left(z\right)}^{\prime}$ according to our observational strategy based on BP fields from the modelled hydrographic fields and sea level. The model pressure field is given by

with *g* being the acceleration of gravity, *ρ* the seawater density as
function of *z* and *η* the sea level. Taking the BP along the continental
slopes (at each depth level) of Brazil and Angola from Eq. (8), the
simulated upper-ocean geostrophic transport anomalies, ${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}P\left(z\right)}^{\prime}$ and ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}P\left(z\right)}^{\prime}$, can be derived from the pressure
differences across the basin using Eqs. (3) and (5), respectively. Under
the assumption that ageostrophic non-Ekman velocities are negligible,
${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}}^{\prime}$ and ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}P\left(z\right)}^{\prime}$ should agree and
particularly should show the same seasonal cycles. Additionally, we test the
two methods used to approximate the vertical structure of ${V}_{\mathrm{G}}^{\prime}$ from
the observations (see Sect. 4.1): (1) piecewise linear interpolation
between values of ${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}P\left(z\right)}^{\prime}$ at 0, 300, 500 m depth and a
level of no motion at 1130 m depth – denoted as ${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}\mathrm{Points}}^{\prime}$ or
${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}\mathrm{Points}}^{\prime}$ in the following and (2) regression of the
first and second EOFs of ${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}P\left(z\right)}^{\prime}$ onto the values
${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}P\left(z\right)}^{\prime}$ at 0, 300, 500 m depth – deriving ${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}\mathrm{EOFs}}^{\prime}$ or ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}\mathrm{EOFs}}^{\prime}$. These different transport
estimates from INALT01 were used to validate the methods applied to the
observations (see Sect. 5.3). In Sect. 5.4, we use INALT01 to identify
relevant mechanisms of the seasonal AMOC variability at 11^{∘} S,
including specifically a comparison of the seasonal variability of the NBUC
transport derived from observations and INALT01. For the sake of simplicity,
in INALT01, unlike for the calculations from observations, the NBUC
transport was calculated above a fixed depth of 1130 m and west of
34.55^{∘} W.

## 5.1 Ocean pressure variability at 11^{∘} S

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).

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^{∘} S and influence the upper water column as well (e.g. Schott et
al., 2005). The periodograms of SLA at the eastern boundary (Fig. 4b)
exhibit peaks at 90 d, 120 d and 2 years. Variability at periods of 90
and 120 d was also observed by Kopte et al. (2018) in velocity time
series from moored observations off Angola and is likely associated with
the passage of CTWs. Based on numerical experiments, Bachèlery et al. (2016)
showed that SLA variability along the African coast is on
intraseasonal timescales (*T**<*105 d) primarily driven by local
atmospheric forcing, while at periods *>*120 d it can mostly be
explained by equatorial forcing. Further, Polo et al. (2008) suggested that
part of the intraseasonal variability is related to year-to-year variations
of the seasonal cycle. Interestingly, the INALT01 OGCM does reproduce the
spectral peaks at 2 years, 120 and 90 d in the SLA off Angola but
not the 70 d period observed in any of the BP time series.

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^{∘} S with basin-mode
resonance in the equatorial Atlantic of the fourth and second baroclinic
modes, respectively (Brandt et al., 2016). Corresponding CTWs propagate
along the African coast towards 11^{∘} S, thereby impacting the local
velocity and pressure fields.

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 ∼ 1 month, and both peak later at depth (Fig. 5b, d). At depth, seasonal pressure variations also become more important; at 500 m depth, for example, the annual and semi-annual harmonics explain up to 29 %. We found similar results for 2-year subsets of the western boundary BP time series.

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^{∘} S, we observed that
near the surface eastern boundary pressure variations prevail, whereas at
500 m depth the western and eastern boundary pressure variations are of
similar importance. In the INALT01 model, the eastern boundary pressure
variations dominate even more over western boundary ones.

## 5.2 Wind stress variability

Prevailing winds along 11^{∘} S are from southeast, which results in
a mean meridional Ekman transport toward south. Using wind stress derived
from ASCAT for the period 2013–2018, the mean and standard error of the
meridional Ekman transport amount to −11.7 ± 0.9 Sv and for the full
available period (2007–2018) to −11.8 ± 0.6 Sv. The mean and standard
error of the meridional Ekman transport derived from INALT01 wind stress
amount to −10.7 ± 0.3 Sv. Zonal wind stress in the tropical South
Atlantic varies on different timescales but is clearly dominated by
seasonal variability. Periodograms of the Ekman transport based on ASCAT and
INALT01 wind stress (Fig. 7a, b) both show the strongest peaks at the
frequency of the annual cycle. Note that the two products cover very
different periods and that their periodograms both also hint towards
longer-term variability whenever considering the full records.

The zonal wind stress anomalies at 11^{∘} S for the two analysed wind
products for the overlapping years (2008–2009) (Fig. 7c, d) agree in the
following characteristics: seasonal wind stress variability is more
pronounced in the western part of the basin than in the eastern part. Across
the whole width of the basin, the zonal wind stress anomalies along
11^{∘} S are typically eastward (positive) in January to March –
resulting in a weaker basin-wide southward Ekman transport. In austral
winter, zonal wind stress anomalies are rather westward (negative) and the
southward Ekman transport is strongest – changing again towards the end of
the year. For both wind products, the Ekman transport across 11^{∘} S
is mainly governed by the seasonal cycle of the southeasterly trade winds
(e.g. Philander and Pacanowski, 1986). However, there are also recognizable
differences between both products: for 2008–2009, the mean and the monthly
standard deviation of the Ekman transport at 11^{∘} S (not shown) are
about 0.5 Sv larger for ASCAT than for INALT01, respectively. Wind stress
anomalies along 11^{∘} S reveal differences in its spatial structure,
as well as in the course and amplitudes of its seasonal cycle (Fig. 7c,
d).

## 5.3 Seasonal variability of the AMOC components at 11^{∘} S

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 ${T}_{\mathrm{G}}^{\prime}$,
${T}_{\mathrm{EK}}^{\prime}$ and the sum of both components ${T}_{\mathrm{AMOC}}^{\prime}$ at 11^{∘} S.
The different versions of ${T}_{\mathrm{G}}^{\prime}$ derived from four BPRs or from two to three BPRs
complemented with the combined annual and semi-annual harmonics (Fig. 8a; see Sect. 4.1)
show a general good agreement within the overlapping
period. In the following sections, we analysed the combined time series of
${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{EOFs}\phantom{\rule{0.125em}{0ex}}\mathrm{2}\phantom{\rule{0.125em}{0ex}}\mathrm{BPRs}}^{\prime}$ (July 2013 to May 2014), ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{EOFs}\phantom{\rule{0.125em}{0ex}}\mathrm{4}\phantom{\rule{0.125em}{0ex}}\mathrm{BPRs}}^{\prime}$ (May 2014 to November 2015) and ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{EOFs}\phantom{\rule{0.125em}{0ex}}\mathrm{2}\phantom{\rule{0.125em}{0ex}}\mathrm{BPRs}}^{\prime}$
(November 2015 to March 2018; compare Fig. 8a).

While from the BP observations we could only derive anomalies of *T*_{G}, in
INALT01, we could also calculate mean values: the AMOC transport at
11^{∘} S based on the INALT01 velocity field averaged over the whole
model run (1978–2007) is *T*_{AMOC SIM}=14.1 ± 0.5 Sv (mean
and standard error). This is within the uncertainty range of 3 Sv for the
AMOC estimate of 16.2 Sv derived from a hydrographic ship section along
11^{∘} S in 1994 (Lumpkin and Speer, 2007).

Both the ${T}_{\mathrm{G}}^{\prime}$ and ${T}_{\mathrm{EK}}^{\prime}$ time series, and hence also ${T}_{\mathrm{AMOC}}^{\prime}$, show variability on different timescales but are clearly dominated by seasonal variability. Mean seasonal cycles of ${T}_{\mathrm{G}}^{\prime}$, ${T}_{\mathrm{EK}}^{\prime}$ and ${T}_{\mathrm{AMOC}}^{\prime}$ from observations and INALT01 are shown in Fig. 9.

${T}_{\mathrm{EK}}^{\prime}$ is characterized by a maximum southward transport in June–August and minimum southward transport in January–March, with the individual extrema slightly varying between ASCAT and INALT01 (Fig. 9c, d). Note again that both products are averaged over different periods. The peak-to-peak amplitude of seasonal Ekman transport variations is 7.1 Sv for ASCAT wind stress (2007–2018; Fig. 9c) and 4.9 Sv for INALT01 wind stress (1978–2009; Fig. 9d). The seasonal cycles may vary from year to year as well as on longer timescales. Here, such variations are, for example, estimated with the range of mean seasonal cycles calculated for running 5-year subsets of the available wind stress data: while the timing of the seasonal cycle of ${T}_{\mathrm{EK}}^{\prime}$ is rather stable between different periods, the peak-to-peak amplitudes have a range of 6–11 Sv for ASCAT and 2–8 Sv for INALT01.

The observed upper-ocean geostrophic transport anomaly (${T}_{\mathrm{G}}^{\prime})$ shows a maximum northward transport in June, while minima occur in October and January with a weak secondary maximum in December (Fig. 9a, b). The two estimates, ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{Points}}^{\prime}$ and ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{EOFs}}^{\prime}$, referring to the two different methods, agree well in the timing of minima and maxima (Fig. 9a). However, the amplitude of the seasonal cycle of ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{EOFs}}^{\prime}$, which we consider to be the more realistic solution in the following, is about 2 Sv smaller than the corresponding amplitude of ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{Points}}^{\prime}$. A possible explanation for the difference between the two estimates based on observations is given below.

Nevertheless, the seasonal cycles of both estimates based on observations, ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{Points}}^{\prime}$ and ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{EOFs}}^{\prime}$, are substantially more pronounced than that of ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}}^{\prime}$ derived directly from the velocity fields of the 30-year model run (Fig. 9b). The peak-to-peak amplitude of the seasonal cycle of ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}}^{\prime}$ calculated over 30 years is 5.5 Sv, while amplitudes can range between 2 and 10 Sv when calculated for 5-year subsets. The peak-to-peak amplitude of ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{EOFs}}^{\prime}$ calculated over the observed 4.5 years is 12.2 Sv and thus larger than the model range. Even when comparing the total range of possible seasonal cycles obtained by considering only single years, the observed values are just out of the range of the simulated values. Regarding the timing of minima and maxima, the observed and simulated seasonal cycles of ${T}_{\mathrm{G}}^{\prime}$ agree quite well (cf. Fig. 9a, b). The larger peak-to-peak amplitudes of the seasonal cycle of ${T}_{\mathrm{G}}^{\prime}$ from observations (cf. Fig. 9a, b) as well as the ASCAT Ekman transport (cf. Fig. 9c, d) result in a larger seasonal cycle of ${T}_{\mathrm{AMOC}}^{\prime}$ with a peak-to-peak amplitude of 13.9 Sv compared to ${T}_{\mathrm{AMOC}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}}^{\prime}$ (cf. Fig. 9e, f), which is 6.3 Sv calculated over 30 years and can be as large as 10.5 Sv when calculated for 5-year subsets.

In order to test our observational strategy, we compared the upper-ocean geostrophic transport anomaly derived directly from the simulated meridional velocity component (${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}}^{\prime}$) to the one being derived from simulated BP time series. Using the full vertical resolution of the model when deriving ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}P\left(z\right)}^{\prime}$, we obtained good agreement with ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}}^{\prime}$ as expected (Fig. 10a and b). Reducing the vertical resolution to the depths of the pressure observations at 0, 300 and 500 m depth and using piecewise linear interpolation between those and a “level of no motion” at 1130 m (${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}\mathrm{Points}}^{\prime}$; ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}\mathrm{Points}}^{\prime}$; Fig. 10c, d), we found this method to miss certain parts of the vertical structure of ${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}P\left(z\right)}^{\prime}$ and, with that, to substantially overestimate the peak-to-peak amplitude of the seasonal cycle of ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}P\left(z\right)}^{\prime}$ by 6 Sv (Fig. 10d). While in the model a strong seasonal cycle is confined to the near-surface ocean, linear interpolation between the surface and 300 m artificially increases the seasonal signal in the layer from 50 to 250 m depth. To improve the approximation, another method was applied that is based on a regression of the first and second dominant vertical structure functions of ${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}P\left(z\right)}^{\prime}$ onto the values at the three depth levels of pressure observations at 0, 300 and 500 m depth (${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}\mathrm{EOFs}}^{\prime}$; ${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}\mathrm{EOFs}}^{\prime}$; Fig. 10e, f), thereby relaxing the no-flow condition at 1130 m depth. As the first two EOFs of ${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}P\left(z\right)}^{\prime}$ explain 99 % of the variance contained in ${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}P\left(z\right)}^{\prime}$, ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}\mathrm{EOFs}}^{\prime}$ agrees well with ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}P\left(z\right)}^{\prime}$ in INALT01 (Fig. 10f). However, the comparison of the observed BP time series with the BP simulated in INALT01 (Fig. 4) shows that the model tends to underestimate the seasonal pressure variability at depth (see Sect. 5.1), leaving some uncertainty regarding the vertical structure of ${V}_{\mathrm{G}}^{\prime}$ in reality.

Figure 11 compares the mean seasonal cycles of ${V}_{\mathrm{G}}^{\prime}$ from observations for the two different methods. Using the vertical structure from the EOFs of ${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}\phantom{\rule{0.125em}{0ex}}P\left(Z\right)}^{\prime}$ from INALT01 especially reduces the amplitude of the subsurface variability (50–200 m). In this depth range, the transition from negative to positive transport anomalies also shifts from April to March. At larger depths, differences between both methods are the result of ${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{Points}}^{\prime}$ being constrained by a level of no motion at 1130 m, while ${V}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{EOFs}}^{\prime}$ is not. However, independent of the applied method, the peak-to-peak amplitude of the seasonal cycle of ${T}_{\mathrm{G}}^{\prime}$ from observations (Fig. 9a) remains to be substantially larger than that from INALT01.

For the period 2013–2018, the geostrophic contribution to the seasonal cycle
of the AMOC at 11^{∘} S, as we observed it, exceeds the Ekman
contribution almost by a factor of 2 (cf. Fig. 9a, c). In INALT01, on the
other hand, averaged over the 30-year model run, the geostrophic and Ekman
contributions are of similar magnitude (Fig. 9b, d). The seasonal cycles
of both contributions vary substantially between years (calculated for
5-year subsets of the model run), e.g. 2–10 Sv for ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}}^{\prime}$ from
INALT01, 2–8 Sv for ${T}_{\mathrm{EK}}^{\prime}$ from INALT01 or 6–11 Sv for ${T}_{\mathrm{EK}}^{\prime}$
from ASCAT; hence, there is a modulation of the ratios of both contributions
on interannual timescales. However, even when considering the uncertainties
of the seasonal cycle of ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{Points}}^{\prime}$ or ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{EOFs}}^{\prime}$ (Fig. 9a)
and the range of possible mean seasonal cycles of ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}}^{\prime}$
calculated for subsets of the model run (Fig. 9b), the observed values
are significantly larger than simulated ones.

## 5.4 Dynamics of the seasonal cycle at 11^{∘} S

In order to better understand the mechanisms that set the seasonal cycle of
${T}_{\mathrm{AMOC}}^{\prime}$ at 11^{∘} S, we investigated the longitudinal
structure of the geostrophic velocity field and transport along that section
in INALT01. We were able to distinguish three different regimes – the NBUC,
the western basin interior and the eastern basin – all showing seasonal
variability of similar magnitude (Fig. 12).

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^{∘} W) and a westward phase propagation
(not shown).

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^{∘} S is mainly set in
the eastern basin (Fig. 12f). Both the vertically integrated upper-ocean
geostrophic velocity and the wind stress curl (Fig. 14) exhibit strong
seasonal variability throughout most of the eastern basin. However, the
largest amplitudes of the annual and semi-annual harmonics of the vertically
integrated upper-ocean geostrophic velocity are found near the eastern
boundary, east of 12^{∘} E, where seasonal variability in the wind
stress curl is weak.

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^{∘} S over the period 2013–2018.

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^{∘} S to be sufficiently
long to investigate the seasonal variability in the region, but, clearly,
longer time series will allow us to refine these estimates in the future.

At 11^{∘} S, seasonal variability is strong in most of the time
series presented in this study. After removing tides with periods shorter
than 35 d, the combined annual and semi-annual harmonics explain a large
part of the variability at the eastern boundary – from 60 % at the
surface to 44 % at 500 m depth. We found hints towards a baroclinic
structure in the annual and semi-annual harmonics of the pressure time
series at the eastern boundary (Fig. 6), which could be related to CTWs of
specific baroclinic modes that can travel from the Equator towards
11^{∘} S along the African coast, thereby impacting the local pressure
and velocity fields.

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^{∘} S includes an energetic undercurrent, the NBUC, with
weak or reversed flow above. From moored observations, Schott et al. (2005)
showed strong gradients in the amplitude of the annual harmonic in the upper
few hundred metres of the water column (their Fig. 11a), suggesting a
decoupling of the variability at the surface from the subsurface.

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^{∘} N (2004–2017; Frajka-Williams et al., 2019)
to 13 Sv at 34.5^{∘} S (2014–2017; Kersalè et al., 2020).

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^{∘} S, as
derived from ASCAT winds. However, this comparison also reveals
model–observation discrepancies regarding seasonal variability in the bottom
pressure fields and the resulting geostrophic transport variations.

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 ${T}_{\mathrm{G}}^{\prime}$ over 2013–2018 (Fig. 9a) and the total range of possible seasonal cycles of ${T}_{\mathrm{G}\phantom{\rule{0.125em}{0ex}}\mathrm{SIM}}^{\prime}$ calculated for subsets of the model run period (1978–2007) (Fig. 9b), the observed values are significantly larger than the simulated values.

The ratios of the NBUC and AMOC seasonal amplitudes are different between
the observations (*<*1) and the model (*>*1).

In the model, seasonal upper-ocean geostrophic transport variability at
11^{∘} S is governed by the variability in the eastern basin. The
seasonal cycle of the simulated upper-ocean geostrophic transport in the
western basin becomes comparable small due to a compensation of the western
basin interior and the NBUC transport. This could be explained by an almost
equilibrium response of the circulation in the western basin at low
baroclinic modes to the wind stress curl (e.g. Döös, 1999). Locally
wind-forced annual Rossby waves would travel westward and after arriving at
the western boundary directly force WBC variability. The seasonal
variability in the eastern basin is instead forced by the local wind stress
curl and, additionally, by Rossby waves radiated from the eastern boundary
via poleward propagation of seasonal CTWs (e.g. Brandt et al., 2016; Kopte
et al., 2018). Similar Rossby-wave radiation from the eastern boundary has
been reported for the tropical North Atlantic (e.g. Chu et al., 2007) and
proposed to be one of the main mechanisms for seasonal variations in the
geostrophic transport there (e.g. Hirschi et al., 2006; Zhao and Johns,
2014).

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^{∘} S but may also depend on the wind curl forcing
further south and associated equatorward signal propagation along the
western boundary.

We conclude that the seasonal variability of the geostrophic contribution to
the AMOC at 11^{∘} S is mainly wind forced, as it is modulated by
oceanic adjustment to local and remote wind forcing. While some of the
uncertainties of our analysis result from the technical aspects of the
observational strategy or processes being not properly represented in the
model, our results indicate that uncertainties in the wind forcing are
particularly relevant for AMOC estimates in the tropical South Atlantic.
Differences between wind products are an important source of uncertainty for
estimates of the AMOC and its variability. Especially when comparing
estimates of AMOC strength and variability between different projects,
latitudes or from observations and models, the choice of wind product is
crucial.

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^{∘} S, if continued into the future, has potential for monitoring
long-term AMOC changes. As the western tropical Atlantic is a crossroad for
the different branches of the AMOC and a region with high signal-to-noise
ratios, 11^{∘} S is a good place to monitor AMOC variations. Having a
sustainable AMOC observing system there, linking northern and southern AMOC
variability, would contribute to the general understanding of related
mechanisms. There is potential to use the BPRs for investigating longer-term
AMOC variability. While progress is made in solving the problems of bottom
pressure sensors on longer timescales (e.g. Kajikawa and Kobata, 2014;
Worthington et al., 2019), the advantage of our method is that the BPRs are
less expensive and easier to deploy than full-height mooring arrays.
Learning from the use of long-term PIES arrays at 47^{∘} N (Roessler
et al., 2015) or 34.5^{∘} S (e.g. Meinen et al. 2018), we think that
the travel times derived from the PIES installed off Brazil could add
information to or reduce the uncertainty of our results. Additionally, we
can fall back on more than 20 years of shipboard hydrographic measurements
in the tropical South Atlantic – at the western (e.g. Hummels et al., 2015;
Herrford et al., 2017) and eastern boundaries (e.g. Tchipalanga et al., 2018).
Ongoing work includes combining all of these hydrographic measurements to
extend the time series of the WBC system and AMOC at 11^{∘} S back
into the 1990s.

The bottom pressure data described in Sect. 2.1 are available through https://doi.org/10.1594/PANGAEA.907589 (Herrford et al., 2019, last access: 11 December 2020). SLA data were distributed by the EU Copernicus Marine Service information. INALT01 was developed at GEOMAR, with details of its configuration and access to data available at https://www.geomar.de/forschen/fb1/fb1-od/ocean-models/inalt01 (Durgadoo et al., 2013, latest access: 12 December 2020).

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 *Meteor* and R/V *Sonne*, as well as our
technicians, for the assistance during the shipboard and moored station work.
We would like to thank
Gerd Krahmann and Marcus Dengler for helpful discussions, and we are very grateful
for the constructive comments by two anonymous reviewers. Jonathan V. Durgadoo
acknowledges funding from the Helmholtz Association and
the GEOMAR Helmholtz Centre for Ocean Research Kiel.

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 *Meteor*
cruises.

The article processing charges for this open-access

publication were covered by a Research

Centre of the Helmholtz Association.

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

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