## Introduction

The Atlantic meridional overturning circulation (AMOC) is a major regulator of the global climate system and its variability1. The AMOC conveys warm and saline Atlantic waters to higher latitudes, where they cool, sink, and return as dense overflow waters2,3,4. The Faroe Bank Channel Overflow (FBCO) (Fig. 1), which flows through a narrow passage across the Greenland–Scotland Ridge, is one of two key arteries (the other being the Denmark Strait, west of Iceland) of the AMOC transporting deep water from the Nordic Seas to the North Atlantic Ocean5,6. The volume transport of the FBCO has been monitored regularly since 1995 using bottom mounted ADCPs7 (see Methods section). These observations show that the FBCO represents about one-third (2 Sv) of the total overflow (5.8 Sv) across the Greenland–Scotland Ridge8. This extensive time series reveals that this deep branch feeding the AMOC is stable with no signs of any long-term slowdown6,9. Since the production of dense overflow water in the Nordic Seas is an important diagnostic for the stability of the AMOC6,9,10, any detectable change in the strength of the Nordic Seas overflows11 may be indicative of disruption of the main current systems in the North Atlantic and hence our climate.

Several studies have analyzed the wind and thermohaline processes influencing the time variability of the Nordic Seas overflow using both observations and models7,12,13,14,15,16,17,18. However, the source regions and the variable transport routes of the FBCO waters through the Nordic Seas have received limited attention4,13,14,19. In addition, most observational studies generally presume that the FBCO is fed solely by deep waters from the western Nordic Seas passing north of the Faroes and turning directly into the Faroe–Shetland Channel (FSC)3,4,19, Fig. 1. For example, the float study by Søiland et al.19 indicated that only water inside the 1750 m depth contour northwest of the Faroe plateau has the potential to be exclusively routed, under the Faroe Current20, to the Faroe Bank Channel via the FSC. However, the modeling study by Serra et al.13 suggested the existence of a two-branch system—one from the Norwegian slope and one along the Jan Mayen Ridge—that vary in strength depending on the wind forcing. This is somewhat in line with the modeling study by Köhl14 who, instead, wrote that the main source of the FBCO is the one along the Norwegian slope but with the tendency to become a two-branch system under strong cyclonic wind forcing with a smaller contribution from north of Iceland. To our knowledge, no dedicated observational study has yet demonstrated the existence of this eastern pathway from the Norwegian slope nor along which boundary in the FSC the bulk of the transport is routed before feeding the FBCO.

In this study, we investigate the existence, origin, and possible mechanisms that can activate this eastern overflow path using a combination of current measurements—moorings and vessel-mounted—and an eddy-resolving ocean model. In summary, our results reveal that overflow waters can also approach the FSC via an indirect path along the eastern margin, indicating that the western approach19 (short or direct path into the FSC) is not exclusive. Lagrangian analysis from the model further demonstrates that both pathways contribute to the FBCO, but the transport is enhanced when the eastern or indirect path is active and this depends on the prevailing atmospheric circulation via its regulation of the basin circulation in the Norwegian Sea. This study shows, for the first time, that the FBCO is, regardless of upstream pathways, primarily fed by a strong (and what seems to be a permanent) current jet at depth located, as seen in both observations the model, along the eastern rather than the western boundary of the FSC—hereafter referred to as the Faroe-Shetland Channel Jet (FSCJ).

## Results

### Inferring the eastern overflow path from observations

A strong indication that the flow feeding the FBCO does not always approach the FSC directly, as the study by Søiland et al.19 proposes, can be found in a deep current meter record moored underneath the Faroe Current at a bottom depth of 950 m20 (FCdeep; see Methods section), Fig. 1b. Although this instrument is located at the upper edge (628 m) of the overflow-feeding dense water, the variability seen by the FCdeep is representative of bottom-intensified deep flows. To support the notion that the FCdeep is representative of the entire deep water transport under the Faroe Current, slope-ward of the 1750 m isobath, we utilize an ocean general circulation model (see Methods section). This model reproduces well the monthly to interannual variability of the FCdeep (Supplementary Fig. 1). The correlation between the observed and modeled eastward deep flow is consistently positive in the deep layers within the  ~2000 m isobath north of the Faroe slope (Supplementary Fig. 1), thus indicating that the FCdeep does not only capture a localized flow.

The results show a strong anticorrelation between the FCdeep and the FBCO transport time series on both interannual (Fig. 2a) and seasonal time scales (Fig. 2b) for the 1999–2016 period (note, however, that the relationship on interannual time scales is weaker since 2008, see discussion in ref. 18). This inverse relationship, i.e., a strong FBCO transport coinciding with a weak or even reversed FCdeep (Supplementary Fig. 2), suggests that the FBCO cannot exclusively originate from the traditionally assumed western approach19 or direct path into the FSC. Instead, it points to a second or alternate pathway by which the FBCO is fed. It is, however, important to note that the general circulation in the Norwegian Sea is clearly cyclonic21 such that in both cases the source waters produced in the western Nordic Seas must pass north of the Faroes; the eastern Nordic Seas cannot be a source for the dense overflow waters as suggested by ref. 14. It is equally important to note that the study by Søiland et al.19 was a single realization and the intermittent eastern path may have been missed as a result. In conclusion, these observational results help to infer that an alternative path, via a longer loop from north of the Faroes to the eastern boundary in the Norwegian Sea, as the above-mentioned model studies13,14 hint at, must also be feeding the FBCO and hence the lower branch of the AMOC.

### Mechanisms activating the eastern overflow path

Since the western approach cannot be the sole source for the FBCO, we must ask what could potentially drive this alternative path. We note that when the atmospheric circulation governing the Nordic Seas is, on interannual time scales, anomalously cyclonic (anticyclonic), the FBCO transport weakens (strengthens), Fig. 3a. At the same time, the FCdeep is found to strengthen (weaken) indicating that this alternative pathway is associated with an anomalously anticyclonic atmospheric circulation regime (Fig. 3b) via its regulation of the wind-driven basin-scale circulation in the Norwegian Sea as seen in sea-surface heights derived from satellite altimetry (Fig. 3c, d). Even in the seasonal cycle (Fig. 2b), weakened (strengthened) cyclonic winds during summer (winter) can also explain the high (low) FBCO transport and the low or reversed (high) velocities of the FCdeep, suggesting a fast barotropic response to wind forcing (see also ref. 18).

To investigate more closely the pathways excited by the different atmospheric forcing, we employ backward trajectory simulations (see Methods section) to identify the variable modeled pathways feeding the FBCO. To ensure that we are only tracing the densest overflow water, we only track water particles colder than 2 °C and only do so until they reach a latitudinal section corresponding to  ~ 65°N (Fig. 4). Backtracking water for several years is important, not only to demonstrate the robustness of the variable pathways, but also to show the significant role a multiyear atmospheric forcing regime plays in modulating the modeled FBCO pathways. In this regard, it is instructive to trace these deep dense waters during the early 1990s and 2000s (Supplementary Fig. 3), as these are periods with particularly strong and weak wind forcing and hence spin-up and spin-down of the top-to-bottom basin circulation in the Norwegian Sea21 (Fig. 3), respectively. Figure 4a demonstrates that when the atmospheric forcing, and hence the basin circulation in the Norwegian Sea is anomalously cyclonic (early 1990s), the FBCO is weaker than normal and the source of the deep water is predominantly via the western approach, the short or direct path around the Faroe Plateau into the FSC. In contrast, when the atmospheric circulation is in an anticyclonic regime (early 2000s), the FBCO is stronger than average and the path is predominantly along the eastern Norwegian Basin (Fig. 4b), the long or indirect path into the FSC. Thus, fluid is deflected from north of the Faroes over to the Norwegian slope before turning south into the FSC. There is, however, a subtle difference between the two periods: while the trajectories during the early 1990s seem to be more constrained to shallower depths, those pertaining to the early 2000s appear to trace deeper isobaths and hence a second path is opened up with water crossing from north of the Faroes over to the Norwegian slope.

The two distinct modeled pathways of deep water are further quantified by the distributions of final longitudes for the backward trajectories (Fig. 4c), which are clearly bimodal but also exhibit distinct year-to-year variability in magnitude. Strengthened cyclonicity during the early 1990s (anticyclonicity during the early 2000s) of the atmospheric circulation within the Nordic Seas and therefore that of the Norwegian Sea produces an unimodal (bimodal) probability distribution suggesting that under anomalously cyclonic (anticyclonic) wind forcing the direct (indirect) path contribution to the FBCO is dominant. These model results strongly indicate that the prevailing atmospheric circulation via its regulation of the wind-driven basin circulation is able to draw upon different upstream deep water pathways feeding the FSCJ (as discussed below) and ultimately the FBCO: one is routed directly into the FSC, and one reaching the Norwegian margin before turning south toward the FSC. Note, however, that the direct path does not disappear entirely when the indirect path develops: the FBCO sees the combined flow from both branches but there is a preference and not a simple case of either-or. It is equally important to note that the Lagrangian analysis only demonstrates two pathways (Fig. 4c), which is consistent with that water must come from depths comparable to the Faroe Bank Channel sill (~840 m). This dynamical requirement thus renders only two options: The western slope (direct path) and the eastern slope (indirect path).

### Is the eastern boundary the major route for the overflow?

A close look at the meridional velocities in the FSC (Fig. 5) suggest, however, that even when the direct path dominates, the main source feeding the FBCO is along the eastern boundary of the channel (Shetland slope), and not along the Faroe slope as has long been assumed4. Figure 5 shows that the strongest modeled deep velocities, and hence the bulk of the FBCO transport (Fig. 6 and Supplementary Fig. 4), are found at the eastern boundary for both the early 1990s (Fig. 5a) and 2000s (Fig. 5b) and therefore also for the mean state (Fig. 5c). This mean structure, with a bottom-intensified FSCJ, is reinforced by the 9-year long record of along-channel velocities obtained from ship-mounted ADCP22, Fig. 5d, suggesting that this is indeed a robust overflow pathway through the FSC. This observed mean state supports the notion that overflow waters, even when originating from the west, tend to cross over to the eastern boundary after entering the channel (It is possible that the shape of the bathymetry, cf. Fig. 1b, plays a role in guiding the flow to the eastern boundary), and indeed clear evidence of this behavior can be seen in the float trajectories reported in refs. 19,23.

To further confirm that the FSCJ carries the bulk of the FBCO, we calculate the modeled volume flux of the deep waters (see Methods section) in both the western and eastern boundary currents of the FSC (Fig. 6a). The results demonstrate that the FSCJ, in a time-mean sense, accounts for the major volume transport through this channel, while at the western boundary the transport is small. The time variability of the modeled volume transport associated with the FSCJ further suggests that the early 2000s was indeed a period of record high overflow, and that the transport during the early 1990s were comparatively weaker; a finding consistent with the observed record high FBCO and record low FCdeep during the early 2000s (Fig. 2a). Furthermore, ADCP moorings across the FSC (see Methods section) confirm, since they reach deeper than the ship-mounted ADCP (Fig. 5d), that the highest deep southward velocities are found in the eastern rather than the western boundary or any other mooring location in the FSC (Fig. 6b). We conclude, based on both model simulations and observations from multiple platforms, that the FSCJ is the main conduit of overflow waters through the Faroe Bank Channel regardless of upstream pathways.

## Discussion

A key difference between the two periods under investigation is that according to the model during the early 1990s, the flow is strongly constrained to shallower isobaths that connect directly to the FSC, while during the early 2000s an additional flow to the east opens up along deeper isobaths (Fig. 4b). This water, after passing north of the Faroes over to the Norwegian slope, turns south and continues into the FSC. It is very likely that this deeper route reflects an increased supply of water originating from along the Jan Mayen Ridge (Fig. 4a), while during the 1990s water come predominantly from north of Iceland along a shallower route or shallower isobaths connecting directly to the FSC (Fig. 4a). Thus, the different wind-forcing conditions in the Nordic Seas causes water to be drawn from preferentially different pathways (Jan Mayen Ridge vs. north of Iceland) and reach the FSC along different depths or routes (deeper vs. shallower); a result that also provides an insight into the inverse relationship between the FCdeep and the FBCO. It is also worth-stressing the fact that the large-scale patterns (Fig. 3) associated with the FBCO transport and FCdeep bear a strong similarity further supports the notion that the FCdeep is not a local feature but is more representative of the basin-scale circulation in the Norwegian Sea.

So far little has been said on the consequences such a two-branch overflow system would have on water mass properties, although the Lagrangian particles that reach the FSC via the indirect path from the Norwegian slope are seen to be much colder than those entering the channel via the direct path (cf. Fig. 4a, b). This is evidently the case for the early 2000s, a period when the eastern pathway is activated and the FSCJ transport is anomalously strong. Correlation analysis between the modeled density variations across the FSC and the FSCJ transport variations further supports this view, Fig. 7. The latter shows that the modeled FSCJ transport is strongly positively correlated with deep water density, which reinforces that the indirect path not only coincides with stronger FSCJ transport but also leads to denser waters feeding the overflow through the Faroe Bank Channel. This unanticipated bimodality of deep water pathways through the southern Norwegian Sea thus has implications for the Iceland–Scotland overflow water and hence the state of the subpolar overturning circulation10.

Although suggestive evidence for deep southwestward flow along the Shetland slope can be found in several previous studies16,24, the existence of the FSCJ has not been demonstrated before ref. 16 found, using an ocean general circulation model, an antiphase relationship between the FBCO transport and the slope current in the Norwegian Sea, but without noting the presence of a southward flow connecting the two; perhaps it went unrecognized because the FSCJ flows at depth along the outer edge of the slope current (Fig. 5). Our discovery that the FSCJ—a deep-reaching current that flows along the eastern boundary in the FSC—carries the bulk of the FBCO transport completely alters our view of the flow dynamics in the FSC. It does so in a similar way that the North Icelandic Jet25,26 (cf. Fig. 1a), which we recognize bears strong resemblance in its structure and location to the FSCJ, has done for the Denmark Strait overflow. Although we have established that, regardless of upstream pathways, the bulk of the FBCO will be carried by the FSCJ, further work beyond the scope of this study is required to understand the involved dynamics and sensitivity to changing forcing in future climate.

In summary, we have in this study showed evidence of an eastern path feeding the overflow through the Faroe Bank Channel from both observations and an eddy-resolving ocean model. The deep current north of the Faroes, i.e., FCdeep, underneath the main core of the Faroe Current is found to be closely connected to the FBCO and key in inferring the eastern overflow path from observations. The FCdeep showed a weakening in the early 2000s (even a reversal during 2002–2003), while the FBCO was concurrently experiencing the highest transports on record. This observed antiphase relationship, which holds on seasonal as well as on interannual timescales, could not be reconciled, pointing to an alternative pathway feeding the FBCO along the eastern slope of the southern Norwegian Sea. This perspective was validated though a Lagrangian approach using an eddy-resolving ocean model forced by realistic winds. The Lagrangian analysis further suggested that the prevailing atmospheric regime via its regulation of the basin-scale circulation is key, not only in forcing anomalous FBCO years as previously discussed13,18, but also in dynamically activating a previously unrecognized overflow path along the eastern Norwegian Sea. Finally, based on the modeled transport, ship-mounted and moored ADCPs, we have established that the water feeding the FBCO is routed through the FSC along its eastern rather than western boundary, regardless of upstream pathways in the Nordic Seas. The FSCJ is thus the main conduit of overflow water through the Faroe Bank Channel and hence connects to the lower branch of the AMOC.

## Methods

### Observations of Faroe Bank Channel overflow

Since November 1995, the FBCO has been monitored continuously (except for annual 2–3 week servicing breaks) by an upward-looking 75 kHz RDI BroadBand ADCP moored close to the bottom centrally in the Faroe Bank Channel. This has been complemented by additional shorter term mooring deployments at each side of the sill, and regular conductivity-temperature-depth cruises, conducted 3–4 times each year. The time series used in this study, i.e., the kinematic overflow, is based on the data from the long-term central ADCP, which by analysis of the complete data set has been shown to be representative of the volume transport of the deep flow and approximately proportional to the volume transport of FBCO defined in other ways7,9 (e.g., σθ > 27.8 kg m−3).

### Measurement of the deep flow north of the Faroes

As part of a long-term monitoring effort of the inflow of warm Atlantic water to the Nordic Seas, an upward-looking 75 kHz RDI BroadBand ADCP has been moored at a location (62.92°N, 6.08°W) north of the Faroes with bottom depth around 950 m20. From the ADCP measurements, a time series of daily averaged horizontal velocity was generated by interpolation. The time series represents velocities at a depth of 628 m, which is located beneath the Atlantic water layer associated with the Faroe Current. The time series commenced in July 1998 and is continuous except for the annual 2–3 week servicing breaks.

### Current velocities from the ADCP mounted on MS Norröna

Velocity transects across the FSC (cf. ref. 27, their Fig. 2b) are obtained by means of a 75 kHz RDI Ocean Surveyor ADCP mounted in the hull of the high seas ferry MS Norröna. The ADCP operates in the narrow-band mode to reach as deep as possible,  ~600 m, although the data returns drop rather sharply beyond  ~500 m depth. For our analysis the single ping profiles are averaged every 3 min to provide along track sampling of currents every 3 km (at a vessel speed of 20 Kt) with a vertical resolution of 16 m and an uncertainty of  ±0.02 ms−1. A Thales ADU-5 with 10 m antenna separation (8 m fore-aft and 14 m port-starboard) provides vessel heading once per second with an accuracy 0.03T, which at 20 Kt translates into a cross-track error of  ~0.005 ms−1. All velocity data between 2008 and 2016 have been detided prior to analysis. Additional information can be found in refs. 22,28.

### Current velocities from moored ADCPs in the FSC

The FSC Transport Mooring Array, a collaboration between Scottish, Faroese, Norwegian, and German scientists, collects moored current velocities at several locations across the FSC. Here, data from the S-line of moorings29 (Fig. 1b) has been used to investigate the circulation deeper than 600 m. The mooring SG/SC/SY/SB is located at a bottom depth of 1044/1069/909/786 m and the depth of its deepest bin is at 810/617/668/642 m. More information on data collection can be found in ref. 29.

### Atmospheric reanalysis

We use both the daily and monthly mean sea level pressure data from ERA-interim30 provided by the European Center for Medium-range Weather Forecasts. The fields have a horizontal grid resolution of 1° × 1° and span the 1993–2016 period.

### Ocean model and trajectory code

We use the three-dimensional velocity, temperature and salinity fields from a simulation of the global ocean using the NEMO ocean model31, version 3.6. The simulation, ORCA0083-N001, uses a global grid of nominally 1/12° horizontal resolution and 75 vertical z-star levels. We choose to use a relatively high-resolution model since it is able to explicitly resolve much of the mesoscale eddy–eddy and ocean–atmosphere interactions, unlike lower resolution models, where such processes are not well represented32. The ocean model is forced by the DRAKKAR forcing set v5.2, which is based on the ERA-40 and ERA-interim reanalysis for the 1958–1978 and 1979–2010 period, respectively. The simulation is free-running except for a restoring of sea-surface salinity toward climatology. The model was started from rest in 1958 and run until 2010, but the model output before 1979 is discarded as a model spin-up.

We use the TRACMASS Lagrangian trajectory code v6.033 to trace water masses backwards in time from the FSC. Numerical particles are seeded every five days in all grid cells of the section channel, where the overflow is transported, and are then traced backward in time until they either cross the northern boundary of our domain  ~65°N or until they leave the domain (Fig. 4a, b) or until five years have passed. For our statistics (Fig. 4c), we exclude trajectories that remain south of the northern boundary ~65°N after one year (note, however, that the results are not sensitive to the arrival times of the particles, Supplementary Fig. 5) and also trajectories that reach a temperature above +2 °C. These criteria allow us to clearly isolate the trajectories representing deep water in our analysis.

### Satellite altimetry

We utilize daily multimission satellite altimetry34 (DUACS DT2014) to study the sea-surface height spatial patterns associated with the FBCO transport and the FCdeep (Fig. 3). The grid resolution is 0.25° × 0.25° and the period under investigation is between January 1993 and April 2016.

### Volume flux

The model volume transport calculation across the FSC is defined as follows:

$$\varPsi (t)=\int_{0}^{L}\int_{-h(x)}^{482}v(x,z,t){\mathrm{d}}z{\mathrm{d}}x,$$
(1)

where v is the along-channel velocity component, L is width of section, x and z are the along-section distance and the depth, respectively, h(x) refers to bottom depth, and t is time. This flux calculation is done for both the western and eastern parts of the channel, which here are separated by the deepest part of the channel. The flux calculation has also been done for distinct layers below 482 m to demonstrate, where the largest transport is found (Supplementary Fig. 4). The model transport calculations were done with the CDFTOOLS package (https://github.com/meom-group/CDFTOOLS).