The 14 years of observations at 26∘ N represent the most complete and longest record of the directly observed AMOC variability currently available. The RAPID array (Fig. 1) spans the middle of the North Atlantic subtropical gyre close to the latitude at which the ocean heat transport is maximum. Here, the warm northward flowing waters of the western boundary current are largely confined to the Florida Straits with a small but highly variable part flowing east of the Bahamas in the Antilles Current (Meinen et al., 2019). Across the rest of the section, there is a broad southward recirculation of the surface waters extending across to the coast of Africa where seasonally varying upwelling gives rise to cooler water along the shelf edge. The deep southward flow of the AMOC is predominantly close to the western boundary and transports two distinct water masses: one centred around 1500 m depth, formed within the subpolar gyre and often referred to as upper North Atlantic Deep Water (UNADW), and the other below 3000 m originating in the Nordic Seas and referred to as lower North Atlantic Deep Water (LNADW). Deeper still, Antarctic Bottom Water (AABW) flows northward in the western basin.

The objective of the RAPID array is to obtain a continuous and accurate record of the AMOC volume transport and the associated meridional heat and freshwater transport. Here, we focus on the volume transport; updated analyses of the heat and freshwater transport will be the subject of a separate study. There are three principal components to the measurements: (1) the flow through the Florida Straits, the Florida Current, is monitored by a subsea cable calibrated by frequent hydrographic surveys (https://www.aoml.noaa.gov/phod/floridacurrent/, last access: 16 July 2020); (2) the flow on the steep continental slope east of the Bahamas is measured by direct velocity measurements from an array of current meters referred to as the western boundary wedge (WBW); and (3) east of the WBW, geostrophic balance is used to estimate the flow from an array of dynamic height moorings. Instruments include, at present, 155 CTDs (conductivity–temperature–depth), 61 current meters, 3 ADCPs (acoustic Doppler current profilers), an additional 43 CTD-Os (CTDs with oxygen), 36 bottom pressure recorders (BPRs) and 4 PIES (pressure-inverted echo sounders). The dynamic height moorings are arranged in three sub-arrays: the western boundary array, the Mid-Atlantic Ridge (MAR) array and the eastern boundary array. The use of boundary moorings which sample at high frequency (hourly) enables high-frequency (e.g. tidal and mesoscale) variability to be resolved and not aliased (Kanzow et al., 2009). In addition, the ageostrophic meridional Ekman transport is derived from the ERA5 reanalysis for zonal surface stress. A full description of the methodology for calculating the AMOC transport is given in McCarthy et al. (2015) and updated in the dataset release notes at https://www.rapid.ac.uk/rapidmoc/rapid_data/datadl.php (last access: 16 July 2020).

In order to compare the RAPID AMOC observations to the wider Atlantic, we use an observational estimate of the AMOC at 45∘ N which uses a combination of satellite altimetry, reanalysis products and in situ ocean data (Desbruyères et al., 2019, after Mercier et al., 2015). Note, however, that the AMOC at 45∘ N is defined in density classes (AMOCρ). At 26∘ N, the transport variability is unlikely to be strongly different between the AMOC in depth space and density class as isopycnals across the broad expanse of the basin (6000 km) are nearly flat. However, in the subpolar gyre, the overturning is defined in density coordinates (Pickart and Spall, 2007; Mercier et al., 2015; Lozier et al., 2019) to better account for the dynamics of buoyancy redistribution in the ocean, which is also carried out by the horizontal gyre circulation. In the subpolar gyre, overturning is a measure of water-mass transformation between the northward “inflow” and southward “outflow”, irrespective of the depth at which it occurs. As the ad hoc reconstruction of the AMOC at 45∘ N is less constrained than the mooring-based RAPID estimates at 26∘ N, a comparison will be used to investigate their potential links.

The sea surface temperature (SST) product used here was the monthly average ERA5 reanalysis at 0.25∘ resolution (C3S, 2017) from 1979 to present. The winter (January to March) North Atlantic Oscillation (NAO) time series was calculated from the monthly mean NAO from the NOAA Climate prediction centre. The AMV is a measure of the low-frequency variability in the Atlantic on multidecadal timescales, calculated from sea surface temperatures (SSTs) as a North Atlantic average, with the background tendency (Enfield et al., 2001) or background field (Trenberth and Shea, 2006) removed. Here, we use the definition following Sutton and Dong (2012) which is the normalised difference between the 10-year smooth Atlantic SST (Equator to 65∘ N, 75 to 7.5∘ W) and global mean SST which is close to that of Trenberth and Shea (2006). This definition contrasts from earlier definitions which averaged the North Atlantic SSTs and then detrended over the record. However, detrending is subject to the time period under consideration and does not allow for nonlinear variations in the time series of global SSTs (Frajka-Williams et al., 2017; Zhang et al., 2019).

We also use data from the GloSea5 global ocean and sea ice reanalysis (Blockley et al., 2014; Jackson et al., 2016), which uses the Nucleus for European Modelling of the Ocean Global Ocean (NEMO GO5) model with a nominal resolution of 0.25∘ and with 75 vertical layers (Megann et al., 2014). It assimilates in situ and satellite sea surface temperatures; subsurface ocean profiles of temperature and salinity; sea ice concentration; and sea level anomalies using the NEMOVAR v13 assimilation scheme (Waters et al., 2015). The experiment is described in more detail in Jackson et al. (2016), with a more in-depth comparison to observations and other ocean reanalyses in Jackson et al. (2019).

The Florida Current transport is produced at daily resolution after a 3-day low-pass filter is applied. Individual instrument records at 26∘ N are either half-hourly or hourly, and filtered with a 2-day low-pass filter to remove tides. Transport is then calculated on a 12 h grid, with a 10-day low-pass filter applied. Here, the data are binned to 10-day time intervals before further analysis. The seasonal cycle is calculated by least-squares fitting an annual and semi-annual harmonic, with a fixed phase and amplitude over the full (2004–2018) record. McCarthy et al. (2015) find that the accuracy of the 10-day binned data is ±1.5 Sv, a figure that was corroborated by the model analysis of Sinha et al. (2018). The accuracy of the mean annual cycle derived from 18 years of data has been estimated using Monte Carlo technique in which a normal distributed error with standard deviation of 1.5 Sv is added to the monthly data. While the annual cycle appears to vary over the record, as noted in Calafat et al. (2018), further investigation of the annual cycle of transport is beyond the scope of the current investigation. Anomalies relative to the seasonal cycle are low-pass filtered using a 540-day Tukey filter.

Spectra are calculated using Welch's overlapped segment averaging approach, with a Hamming taper and 50 % overlap on the detrended, 10-day binned time series. In order to retain variability at low frequencies, while reducing noise at high frequencies, we use three different window lengths following Kanzow et al. (2010).

For investigations into the relationship between the AMOC at 26 and 45∘ N, we consider the geostrophic portion of the AMOC transport; i.e. at 26∘ N, we subtract the Ekman component from the total AMOC. This is because the Ekman component is independently forced at different latitudes and would not be anticipated to show low-frequency coherence between latitudes. The AMOC transport at 45∘ N is computed without a contribution from surface Ekman transport. Both records are then filtered with a 5-year low-pass Tukey filter.

To analyse the variability of the AMOC transport, we use change-point analysis on the 10-day total AMOC minus Ekman (hereafter AMOC–Ekman) time series. The methodology is described in Beaulieu and Killick (2018) and is similar to that used in Smeed et al. (2018). A suite of eight models were fitted to the data, in which the short-term variability is modelled by either random white noise or a first order autocorrelation (AR(1)) process. The long-term variability is modelled as either a constant value, a linear trend, or one or more change points separating periods each linear with time. Combining all these possibilities for both the short-term and long-term variability leads to a total of eight models: (i) a constant mean with a white-noise background: “Mean”; (ii) a constant mean with first-order autocorrelation: “Mean+AR(1)”; (iii) a linear trend: “Trend”; (iv) a linear trend with first-order autocorrelation: “Trend+AR(1)”; (v) multiple change points in the mean with a background of white noise: “Mean+CP”; (vi) multiple change points in the mean with first-order autocorrelation: “Mean+AR(1)+CP”; (vii) multiple change points in the trend with white noise: “Trend+CP”; and (viii) multiple change points in the trend with first order autocorrelation: “Trend+AR(1)+CP”. For the models with change points, we find the number and locations using the pruned exact linear time algorithm (Killick et al., 2012), which performs an exact search considering all options for any possible number of change points and select the optimal number/location balancing the overall fit against the length of each segment. The most appropriate model is selected according to the Akaike information criterion (AIC). The AIC differences between each model included in the comparison and the model with the smallest AIC are also computed to assess plausibility of all models. As a rule of thumb, a difference larger than 10 indicates that there is essentially no support for a model given the data and the other models at play (Beaulieu and Killick, 2018). To verify sensitivity to the choice of information criterion, the Bayesian information criterion (BIC) for each model is also computed. The change-point analysis was conducted using the R package EnvCpt (Killick et al., 2018).

The AMOC volume transport is given in units of Sverdrups, where 1 Sv = 106 m3 s-1. To investigate the variability in the AMOC total and component transport, we calculate frequency spectra (Fig. 2). We only consider fluctuations with periods longer than 20 days as the method of calculating the AMOC transport assumes zero net meridional mass transport; this assumption is only valid on timescales longer than about 10 days (Kanzow et al., 2007). For periods shorter than about 60 days, Ekman transport dominates the variability of the AMOC; at other sub-annual periods, the variability is similar among all three components. Broad peaks in the spectra are found at both annual and semi-annual frequencies, particularly for the upper mid-ocean (UMO) transport; however, on timescales shorter than 1 year, fluctuations in the UMO and Florida Current transport are anti-correlated (Frajka-Williams et al., 2016). This anti-correlation results in reduced power at the semi-annual frequency in the total AMOC as compared to the UMO. At periods longer than a year, the AMOC variability is dominated by the UMO transport.

In view of the large and broad spectral peaks, we have decomposed the time series into three parts: the seasonal cycle, an interannual signal and the residual high-frequency signal (Fig. 3). There is a substantial seasonal cycle with an amplitude of 2.0±0.1 and 0.7±0.1 Sv (mean and standard error from Monte Carlo estimation) for the annual and semi-annual harmonic, explaining 11 % and 2 % of the variance, respectively. The residual time series, likewise, retains substantial variability with a range of 21.6 Sv and a standard deviation of 3.4 Sv. About 20 % of the residual variance is associated with the estimated error of ±1.5 Sv for the 10-day binned data. The large-amplitude, sub-annual variability is a compelling reason why continuous, time-resolved in situ observations are required to firmly establish the mean value of the AMOC transport.

For the remainder of the paper, we focus on the low-frequency (interannual) variability of the AMOC and component transport (Fig. 4). Both from the spectra and the time series in Fig. 4, it is clear that the low-frequency variability in the total overturning transport is governed primarily by the mid-ocean transport, i.e. the upper mid-ocean component and the LNADW layer. This is consistent with previous investigations into the AMOC variability, which showed smaller interannual variability in the Ekman and Florida Current transport than the mid-basin (Bahamas to Canary Islands). It is interesting to note, however, that a reduction in the Ekman transport closely follows the two minima in the UMO transport (2009 and 2012).

The low-frequency changes in the AMOC are acyclic and, based on data through 2012, were described using a linear trend by Smeed et al. (2014). However, the tendency of the time series through 2016 was not monotonic (Smeed et al., 2018), rendering a linear trend less useful at describing the observed variability. Instead, a change-point analysis was used to fit a model to the total AMOC transport, concluding that for the record through 2016, the total AMOC transport variations were best described by two periods with constant mean values, separated by a single change point in 2008–2009 (Smeed et al., 2018). Here, we apply an updated version of the change-point analysis to the AMOC–Ekman time series through 2018 (Fig. 5). This analysis also finds a change point in 2008 (Fig. 5b) in accordance with the previous result.

Overall, these results are consistent with the previous analyses of the low-frequency variability of the AMOC transport and its component parts. However, we note from the table of annual means (Table 1) that the mean in 2017/18 (calculated over the period 1 April 2017–31 March 2018) was 17.8±1.4 Sv (mean ± standard error, computed on the 10-day binned time series). The standard errors are large due to substantial sub-annual fluctuations in the AMOC strength. The AMOC transport in the 2017/18 period (17.8±1.4 Sv) is larger than the recent minimum in 2009/10 (13.5±1.3 Sv), but this does not represent a return to the high AMOC transport values near the beginning of the observational record (2005/06, 20.9±1.2 Sv). While the interannual time series appears to show a steadily, if weakly, increasing AMOC transport (Fig. 4a), this is not identified as the leading behaviour in the change-point analysis and so is not yet a statistically significant increasing tendency.

The 2013/14 and 2014/15 winters saw the return of deep convection in the Labrador Sea in two great impulse events (Yashayaev and Loder, 2016). These localised deep convection events are part of wider and longer-term intensification in subpolar water-mass transformation following the minimum in 2005 (Desbruyères et al., 2019). While deep convection is not equivalent to water-mass transformation (a distinction emphasised by the OSNAP results; Lozier et al., 2019), it is a potential consequence of the continued buoyancy loss in the subpolar gyre. The overall intensification of the light-to-dense water-mass transformation rates starting from 2005 has led to an intensification of the AMOC at the southern exit of the subpolar gyre since 2010, after a delay of 5–6 years, as found in a recent observational analysis (Desbruyères et al., 2019). Building on previous studies, the arrival of such a signal at subtropical latitudes can be anticipated after 3–9 years based on models (Johnson and Marshall, 2002; Zhang, 2007) and observations (Molinari et al., 1998; van Sebille et al., 2011). Lagrangian studies have been used to identify when newly formed dense waters from the subpolar gyre reach the subtropics, with anomalies moving with the currents via advection (e.g. Bower et al., 2009; Zou et al., 2016; Jackson et al., 2016). However, transport time series can also adjust more rapidly through a fast boundary-wave mediated response of lower-latitude AMOC variability to high latitudes forcing. Such a response can potentially be identified by lag correlation or coherence analysis of AMOC transport time series rather than hydrographic anomalies. Based on the increase in subpolar water-mass transformation peaking in 2013–2015 and various time lags between the subpolar-to-subtropical AMOC strength determined from numerical simulations, we would anticipate a sign of the increasing subtropical AMOC by 2018–2022. Determining the particular timing of the adjustment would provide critical ground truth to meridional coherence investigations.

To investigate meridional coherence, we use the AMOC variations at 26 and 45∘ N (Fig. 6a). We have removed the ageostrophic Ekman component to isolate AMOC–Ekman as the geostrophic part of the overturning. Ekman transport is forced independently at each latitude, while the geostrophic part of the overturning is the part of the signal that we would expect to show meridional coherence. The records are short, particularly the in situ observations at 26∘ N, for the filtering applied (5 years), but both latitudes show a decrease in AMOC–Ekman over the 2004–2011 period of more than 3 Sv (45∘ N) and 2 Sv (26∘ N). This is followed by an increase at 45∘ N commencing around 2010–2011. Due to the length of the filter (5 years) and the relatively short duration of the in situ 26∘ N observations, we additionally use GloSea5 estimates at 26∘ N for a longer overlap period (Fig. 6a).

Comparing the AMOC–Ekman strength between altimetry/hydrography observations 45∘ N and GloSea5 estimates at 26∘ N, we find that they show similar timing of relative peaks (1996–1997, 2004–2005) and troughs (2000–2001, 2011, 2011–2013). The near coincidental occurrence of peaks and troughs is consistent with an expectation of some meridional coherence between latitudes. Since 2010, the AMOC at 45∘ N has been increasing. However, at 26∘ N, the AMOC transport does not yet show a significant increase (see Sect. 3.2).

With the relatively short duration records and the absence of a clear impulse anomaly to track between latitudes, it is not yet possible to identify the timescale of adjustment between the subpolar and subtropical AMOC strength. It appears, however, from comparing the 45∘ N observational estimate of the AMOC and 26∘ N from Glosea5, that the adjustment timescale may be short (0–2 years). In contrast, within the GloSea5 reanalysis itself, there was a mean lag of 7 years between a peak in Labrador Sea density and the AMOC at 26∘ N (Jackson et al., 2016). This discrepancy is difficult to reconcile. While GloSea5 has been validated against the 26∘ N observations, there does not exist an equivalent long AMOC record in the subpolar gyre to verify GloSea5: the OSNAP estimate of the AMOC is too short (21 months) to verify interannual variability of reanalyses (Lozier et al., 2019) and the method used at 45∘ N with altimetry and gridded hydrography may be subject to errors particular in resolving higher-frequency anomalies at the boundary.

It is further worth noting that the AMOC at 45∘ N is in density space, following the choice in Desbruyères et al. (2019); the AMOCz at 45∘ N is in phase with the AMOCρ but with lower amplitude (Desbruyères et al., 2019, Fig. S4). In addition, the ratio of meridional heat transport to AMOC, a measure of how “efficient” the overturning circulation is at fluxing heat, is greater at 26∘ N than 45∘ N (Johns et al., 2011; Desbruyeres et al., 2019). This means that smaller-amplitude fluctuations of the AMOC 26∘ N than 45∘ N may be associated with equivalent heat transport variability. More thorough investigations into the depth distribution and zonal distribution of changes at 26∘ N that accompany the subtle intensification of the overturning strength are pending. These may enable a more conclusive determination of the arrival of the buoyancy-forced signals in the subtropical North Atlantic.

To place the low-frequency variability of the AMOC noted above in the wider Atlantic context, we consider large-scale variations in SST and atmospheric variability. On the one hand, the AMOC is anticipated to respond to wind and buoyancy forcing, and on the other, it drives heat transport and through it, heat content and SST changes. On multidecadal timescales, Gulev et al. (2013) provided observational evidence that in the midlatitude North Atlantic and on timescales longer than 10 years, surface turbulent heat fluxes are indeed driven by the ocean and may force the atmosphere, whereas on shorter timescales the converse is true. Numerical simulations identified a driving role in the subtropical meridional heat transport for temperature tendencies in the subpolar North Atlantic (Moat et al., 2019). While the current record of in situ observations is too short to fully investigate multidecadal relationships, we can look more closely at the period of the observations and the longer records of SST to evaluate whether the observed variations in the Atlantic, as indexed by the AMV, follow the patterns predicted by the numerical simulations.

The AMV is a record of the multidecadal variations in the North Atlantic, based on SST (Fig. 6b). During the period prior to 2007/2008, the AMOC is generally in a positive state (Fig. 6a), which leads to greater than average northwards heat transport as the AMOC volume transport and meridional heat transport are proportional (Johns et al., 2011). This northward heat transport then leads to a warming North Atlantic, consistent with a positive AMV state (Fig. 6b – from increased SST). After 2007/2008, the AMOC moves into a negative state with less than average northwards heat transport, which is followed by decreasing SSTs and reducing AMV. Using a coupled climate model Moat et al. (2019) showed that on decadal timescales changes the AMOC leads the AMV by about 5 years. There is evidence here to suggest that the AMV does not respond instantaneously with the AMOC and the AMOC may lead the AMV. However, the length of the AMOC at 26∘ N is currently too short for the lagged correlations to be statistically significant.

The long-timescale fluctuations in the AMV contrast with atmospheric variability, as measured by the NAO index which tends to vary on shorter 3- to 5-year timescales. The low-passed NAO was in a positive state with a maximum around 1990 and declining to near zero in 2005. During this period, AMOC was in a positive state moving more than average heat northwards (GloSea5; Fig. 6a). As the NAO declines into a negative state there is a reduction in the surface heat loss in the subpolar region of the North Atlantic, which is followed by a reducing AMOC strength. Since 2010, the NAO has been recovering from a minimum and moving towards a NAO+ state, resulting in enhanced heat loss in the subpolar North Atlantic and strengthening the AMOC. Given the lag between the AMOC and AMV described above, we would anticipate an increase in the AMV with increasing AMOC, which is consistent with the hypothesis illustrated in Sutton et al. (2018).

From this large-scale view of the Atlantic, we can conclude that the observed and simulated AMOC variability (using 14 years of RAPID observations and GloSea5 reanalysis), SST variability (indexed by the AMV) and atmospheric forcing (captured by the NAO) are consistent with other studies (Moat et al., 2019; Sutton et al., 2018). A positive NAO period is associated with stronger heat loss from the subpolar North Atlantic, providing buoyancy forcing to strengthen the AMOC. In addition, a strong AMOC will transport more heat northward leading to a warmer North Atlantic (more positive AMV). While the recent decade offers a change in state of the Atlantic (AMV) as well as anomalous buoyancy forcing in subpolar North Atlantic (2013–2015), the time series of directly measured AMOC variability at 26∘ N is not yet long enough to conclusively test the mechanisms linking buoyancy forcing to circulation change and leading to changes in ocean heat content. A more complete diagnosis of the short-term heat budget (2014–2020) and the relative contributions of ocean transport and surface fluxes is beyond the scope of this paper but currently under way.