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 PDriftt=a1-e-bt+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).

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 0.25∘×0.25∘ 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.

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 0.25∘×0.25∘ (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).

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).

The structure of the AMOC is often described using the overturning transport stream function ψ(yzt), which is derived from integrating the meridional velocity component, v, zonally (from the western (xWB) to the eastern boundary (xEB)) and vertically: 1ψy,z,t=∫z0∫xWBxEBvx,y,z′,tdxdz′, 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 = 106 m3 s-1]. At any chosen latitude, ΨMAX can be decomposed into Ekman and geostrophic components (thereby generally neglecting small ageostrophic, non-Ekman components): 2ψMAXy,t=TAMOCy,t≈TGy,t+TEKy,t.

Variations in the basin-wide upper-ocean meridional geostrophic transport TG at a certain latitude can be derived from the differences between the bottom pressure at the eastern (PEB) and western (PWB) 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 VG′(zt) were calculated as 3VG′z,t=1ρ0⋅f⋅PEB′z,t-PWB′z,t. PEB′ and PWB′ are the pressure anomalies at the eastern and western boundaries with respect to the time mean, respectively, f the Coriolis parameter and ρ0 a mean sea water density. At the surface, VG′(z=0,t) can be calculated accordingly from sea level anomalies, η′: 4VG′z=0,t=gf⋅ηEB′(t)-ηWB′(t), with g being the acceleration of gravity. Additionally, a level of no motion is prescribed at 1130 m, such that VG′(z=-1130mt)=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 σ1=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 VG′: piecewise linear interpolation of VG′ between the four data points at 0, 300, 500 and 1130 m depth – denoted as VGPoints′ or TGPoints′ 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, VGSIMP(z)′ (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 VGSIMP(z)′. The resulting transport variations are denoted as VGEOFs′ or TGEOFs′.

Upper-ocean geostrophic transport variations, TG′, were then calculated by vertically integrating the approximated VG′ profile from z3=-1130 m up to the surface. 5TG′t=∫z30VG′z,tdz Using the first method, z3 is defined as the “level of no motion” (VG′z3=0), whereas for the second method VG′(z3) might vary with time.

Finally, AMOC transport variations (TAMOC′) can be derived by adding local Ekman transport anomalies TEK′. 6TAMOC′(t)=TG′t+TEK′(t) The latter can efficiently be estimated from the zonal component of the wind stress, τx, at 11∘ S according to 7TEK(t)=-∫xWBXEBτx(x,t)ρ0⋅fdx, and subtracting the temporal average.

In the following, all mean transport is presented together with the standard error (SE =σ/N/nd), where σ is the standard deviation and nd 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.

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, TAMOCSIM′, 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 TEKSIM at 11∘ S is derived with Eq. (7) from INALT01 wind stress. According to Eq. (6), the simulated upper-ocean geostrophic transport anomaly TGSIM′ is then TAMOCSIM′-TEKSIM′.

Alternatively, we can derive TGSIMP(z)′ according to our observational strategy based on BP fields from the modelled hydrographic fields and sea level. The model pressure field is given by 8px,z,t=g⋅∫z0ρx,z′,tdz′+g⋅ρ0⋅ηx,t, 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, VGSIMP(z)′ and TGSIMP(z)′, 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, TGSIM′ and TGSIMP(z)′ should agree and particularly should show the same seasonal cycles. Additionally, we test the two methods used to approximate the vertical structure of VG′ from the observations (see Sect. 4.1): (1) piecewise linear interpolation between values of VGSIMP(z)′ at 0, 300, 500 m depth and a level of no motion at 1130 m depth – denoted as VGSIMPoints′ or TGSIMPoints′ in the following and (2) regression of the first and second EOFs of VGSIMP(z)′ onto the values VGSIMP(z)′ at 0, 300, 500 m depth – deriving VGSIMEOFs′ or TGSIMEOFs′. 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.

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.

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).

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 TG′, TEK′ and the sum of both components TAMOC′ at 11∘ S. The different versions of TG′ 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 TGEOFs2BPRs′ (July 2013 to May 2014), TGEOFs4BPRs′ (May 2014 to November 2015) and TGEOFs2BPRs′ (November 2015 to March 2018; compare Fig. 8a).

While from the BP observations we could only derive anomalies of TG, 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 TAMOCSIM=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 TG′ and TEK′ time series, and hence also TAMOC′, show variability on different timescales but are clearly dominated by seasonal variability. Mean seasonal cycles of TG′, TEK′ and TAMOC′ from observations and INALT01 are shown in Fig. 9.

TEK′ 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 TEK′ 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 (TG′) 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, TGPoints′ and TGEOFs′, 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 TGEOFs′, which we consider to be the more realistic solution in the following, is about 2 Sv smaller than the corresponding amplitude of TGPoints′. 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, TGPoints′ and TGEOFs′, are substantially more pronounced than that of TGSIM′ derived directly from the velocity fields of the 30-year model run (Fig. 9b). The peak-to-peak amplitude of the seasonal cycle of TGSIM′ 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 TGEOFs′ 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 TG′ agree quite well (cf. Fig. 9a, b). The larger peak-to-peak amplitudes of the seasonal cycle of TG′ from observations (cf. Fig. 9a, b) as well as the ASCAT Ekman transport (cf. Fig. 9c, d) result in a larger seasonal cycle of TAMOC′ with a peak-to-peak amplitude of 13.9 Sv compared to TAMOCSIM′ (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 (TGSIM′) to the one being derived from simulated BP time series. Using the full vertical resolution of the model when deriving TGSIMP(z)′, we obtained good agreement with TGSIM′ 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 (VGSIMPoints′; TGSIMPoints′; Fig. 10c, d), we found this method to miss certain parts of the vertical structure of VGSIMP(z)′ and, with that, to substantially overestimate the peak-to-peak amplitude of the seasonal cycle of TGSIMP(z)′ 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 VGSIMP(z)′ onto the values at the three depth levels of pressure observations at 0, 300 and 500 m depth (TGSIMEOFs′; VGSIMEOFs′; Fig. 10e, f), thereby relaxing the no-flow condition at 1130 m depth. As the first two EOFs of VGSIMP(z)′ explain 99 % of the variance contained in VGSIMP(z)′, TGSIMEOFs′ agrees well with TGSIMP(z)′ 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 VG′ in reality.

Figure 11 compares the mean seasonal cycles of VG′ from observations for the two different methods. Using the vertical structure from the EOFs of VGSIMP(Z)′ 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 VGPoints′ being constrained by a level of no motion at 1130 m, while VGEOFs′ is not. However, independent of the applied method, the peak-to-peak amplitude of the seasonal cycle of TG′ 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 TGSIM′ from INALT01, 2–8 Sv for TEK′ from INALT01 or 6–11 Sv for TEK′ 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 TGPoints′ or TGEOFs′ (Fig. 9a) and the range of possible mean seasonal cycles of TGSIM′ calculated for subsets of the model run (Fig. 9b), the observed values are significantly larger than simulated ones.

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