Corresponding author: A. B. Sandø, Institute of Marine Research, PO Box 1870, Nordnes, NO-5817 Bergen, Norway. (firstname.lastname@example.org)
 The variable oceanic exchanges between the Nordic seas and the Atlantic proper have been investigated using an isopycnic coordinate ocean model for the period 1948–2007. Observed and simulated time series of volume transports in the Denmark Strait (DS), between Iceland and the Faroe Islands, and in the Faroe-Shetland Channel (FSC) are used to evaluate the model, and the model captures much of the variability. The inflow of Atlantic Water in the FSC and the outflow of light Polar Water in the DS and of dense Overflow Water in both FSC and DS are all found to covary with an atmospheric pattern resembling the North Atlantic Oscillation. An increase in the FSC inflow is associated with a decrease in the FSC overflow and an increase in the DS overflow. The exchanges' response to the atmospheric forcing is mainly of a barotropic nature, but they are also influenced by baroclinic processes. The modeled antiphase between FSC inflow and overflow is connected to a vertical displacement of the isopycnal separating the two water masses in the channel and along the path of the Norwegian Atlantic Slope Current, consistent with hydraulic control of the FSC exchanges.
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 The exchange of waters between the North Atlantic Ocean and the Nordic seas across the Greenland-Scotland ridge (GSR) is of major importance to the regional climate due to the ∼300 TW transport of heat into the Nordic and Arctic Seas [Østerhus et al., 2005; Rhines et al., 2008] and varies on many time scales [Olsen and Schmith, 2007; Sherwin et al., 2008]. The water masses involved are the inflow of warm and saline Atlantic Water, and the export of light Polar Water at the surface and of dense Overflow Water at depth. Furthermore, the overflow of dense water from the Nordic seas into the Atlantic Ocean across the GSR is the main source for North Atlantic deep water [Dickson and Brown, 1994].
Hansen and Østerhus gave an overview of the observations in the Faroe Bank Channel (FBC) since 1995 and possible dynamic mechanisms for the Faroe-Shetland Channel (FSC) overflow. They concluded that the stable component of the overflow to a large extent could be understood in terms of baroclinic forcing, but that in order to understand the kinematic overflow, barotropic forcing was an additional requirement. Likewise,Jungclaus et al. state that long-term overturning circulation across the GSR is determined by the production of dense water in the Nordic seas and in the Arctic, while variations in the overflows are due to wind stress forcing as well as changes in the density contrast across the GSR.
Biastoch et al.  investigated processes that influence heat and volume transport across the GSR in terms of a model with 1/6° horizontal resolution, and a general relation between changes in the wind stress and interbasin exchanges of volume and heat were established. Nilsen et al.  used a global version of Miami Isopycnic Coordinate Ocean Model (MICOM [Bleck et al., 1992]) to study the variability in the volume exchanges between the North Atlantic and Nordic seas. They found that the net volume transport through the FSC covaries with the net transport through the Denmark Strait (DS) and suggested that NAO is the main driving force for the variations. They did not split the exchanges into surface and dense outflow and did therefore not conclude on any relations between these. Serra et al. applied another model and found a low-frequency phase relation between the DS and FSC overflows associated with strong and weak phases of NAO.
Sherwin et al.  used conductivity, temperature and depth (CTD) and acoustic Doppler current profiler (ADCP) data to analyze the transport of water from the North Atlantic to the Nordic seas through the FSC. They found that seasonal variations appear to correlate with the local southwest wind stress, and that the Atlantic Water is largely pushed into the Norwegian Sea. On the other hand, Hansen et al. combined observed transport time series with sea level height from satellite altimetry and wind stress, and arrived at the conclusion that the force driving the Iceland-Faroe Ridge (IFR) inflow is mainly a pressure gradient due to a continuously maintained low sea level in the southern Nordic seas. The low sea level is caused by removal of dense water, which leads to the conclusion that Atlantic Water is pulled into the Nordic seas due to export of dense Overflow Water. It should here be noted that these two studies use data from different sections of the GSR and the forcing mechanisms associated are therefore not mutually exclusive. In a recent study,Richter et al.  showed that the Atlantic inflow to the Nordic Seas over IFR primarily responds to an oceanic regime dominated by steric height in the interior Nordic seas, and that the Norwegian Atlantic Slope Current to a large extent is driven by direct wind forcing.
Orvik and Skagseth  presented a relation between the Norwegian Slope Current and the wind stress curl in the North Atlantic. They found a 15 month time lag between the wind stress curl and the transport of the current which they explain as a forced baroclinic Rossby wave response to the remote wind forcing in the North Atlantic. [Sandø and Furevik, 2008] relate the generation of these relatively slowly moving baroclinic disturbances, to wind generated mixing along the western flank of the Rockall Bank. In line with observations [Macrander et al., 2007], several models studies [Nilsen et al., 2003; Kohl et al., 2007; Jungclaus et al., 2008; Serra et al., 2010] show that the variability in the DS outflows are mainly associated with barotropic adjustment processes which are suggested to be wind driven.
 In this study, observations and model results are combined in order to assess the underlying mechanisms behind the variability of the GSR exchanges. The area between Iceland and Scotland (Figure 1) is among the most frequently sampled regions of the world ocean [Hansen and Østerhus, 2000], and since the mid-1990s direct current measurements of inflows and overflows have also been done [Hansen et al., 2000; Jónsson and Valdimarsson, 2005; Macrander et al., 2007; Hansen et al., 2010]. These observations are of vital importance for surveillance, but the areas affecting the inflowing waters to the Nordic seas from the North Atlantic have usually been too large to be covered by sufficient observations in time and space. The ARGO network of autonomous profiling floats has certainly provided a strong constraint on large-scale estimates of salinity, temperature and velocities in the nonshelf regions of the North Atlantic since the mid-2000s, but this period is still too short to study variability on interannual to decadal time scales.
 To find mechanisms behind exchange variability, our approach is therefore to apply an Ocean General Circulation model (OGCM) that provides simulated ocean hydrography and currents in the region for a period of several decades. The model is driven by atmospheric forcing from daily reanalysis fields, which makes it possible to investigate the influence of different patterns of atmospheric forcing on variable inflows and overflows. Therefore, given that the model adequately represents the variable ocean circulation and hydrography, it can be used to shed light on to which extent Atlantic waters are pushed and/or pulled into the Nordic seas, and to assess the mechanisms behind the variability.
 The particular model system used for this study is presented in section 2. In section 3 a brief description of the various analysis techniques used in this study is provided, and results are shown in section 4. The implications of the various findings are discussed in section 5, and the paper is summarized and concluded in section 6.
2. Model Description
 In this study, a regional version of MICOM, covering the North Atlantic, the Nordic Seas, and the Arctic Ocean has been used to study the North Atlantic–Nordic seas exchanges. Output data from a global version of MICOM [Orre et al., 2009] has been used as time-varying boundary conditions and to initialize the model. The global model was initialized from PHC3.0 [Steele et al., 2001], and run 3 cycles from 1948 to 2005. The regional grid is constructed as a subset of the global grid of which each grid cell is subdivided into 3 by 3 grid cells. The global model has a grid spacing of about 40 km whereas the regional model has about 13 km in the Nordic seas. This implies that the model is eddy permitting, but not eddy resolving.
 The nesting method uses an open boundary condition that combines the Flather  radiation condition for the barotropic velocities and a relaxation scheme toward the outer solution for the baroclinic velocities, temperature, salinity and layer interfaces. The nesting is one way; thus, the outer solution is not affected by the inner solution. In this experiment, the radiation condition has proven effective in avoiding reflection of gravity waves at the boundary of the regional domain. Further, the bathymetries of the regional and global model are identical at the boundary, made possible by the simple subdivision of grid cells mentioned above. Thus, consistent baroclinic velocity and mass transport in the outer and inner solution are easily achieved at the boundary. Reflection of internal waves at the boundary has not been found to be an issue indicating that the relaxation scheme at the boundary provides sufficient damping of these waves. The nesting boundaries are located in the South Atlantic at ∼31°S and in the Bering Strait, relatively far from the GSR, and any inconsistencies in the nesting conditions are therefore assumed not to impose artificial constraints on the modeled exchanges of interest in this paper. Vertically, a mixed layer and 34 isopycnic layers are used with potential densities ranging from σ2 = 30.12 to σ2 = 37.80. These densities are referenced to a pressure at 2000 m depth, and are the same as in the global model.
 A dynamic and thermodynamic sea ice model has been coupled to MICOM [Bentsen, 2002]. The models share the horizontal grid, the exchange of fluxes are handled internally, and the sea ice model can therefore be considered as an integrated part of MICOM. The thermodynamic part of the sea ice model is based on Drange and Simonsen . The dynamical part of the sea ice model uses viscous-plastic rheology [Hibler, 1979] and is based on the implementation of Harder . The continental runoff is also provided by the NCEP/NCAR reanalysis and the Total Runoff Integrating Pathways data set [Oki and Sud, 1998] has been used to assign land grid cells of the reanalysis to appropriate coastal discharge grid cells of the ocean model.
 To maintain a stable Atlantic Meridional Overturning Circulation and avoid model drift in coupled ocean sea ice models, many models require restoring of SSS toward climatological values [Griffies et al., 2009]. For these reasons, restoring of SSS was also necessary in this model experiment, and a piston velocity corresponding to the mixed layer depth over 30 days was used. In the computation of the relaxation fluxes the mixed layer depth is limited to 50 m and the absolute value of salinity difference between model and climatology is limited to 0.5 psu. When comparing with values for the piston velocity in Griffies et al.  this should be considered a rather strong SSS restoring. The available computational resources did not allow us to explore weaker restoring strengths. The monthly PHC3.0 climatology [Steele et al., 2001] was used in the SSS restoring.
 The atmospheric forcing is taken from daily NCEP/NCAR reanalysis fields [Kalnay et al., 1996]. A forcing scheme reproduces the NCEP/NCAR turbulent and longwave fluxes if the model has the same surface state as the reanalysis. If not, the turbulent fluxes are modified consistently with the bulk formulation of Fairall et al.  and the longwave fluxes with Berliand and Berliand .
 In the model, the inflowing Atlantic Water through the FSC between the Faroes and Scotland is distinguished from the dense Overflow Water below by the isopycnal that on average has northward transport above it and a southward transport below it.The mean boundary between these waters is found to be the isopycnal between model layer 16 and 17, with density anomalies σ2 = 36.85 and σ2 = 36.95, respectively. This interface is used throughout the study to separate the inflowing and outflowing water masses both in the GSR gaps and in the adjacent oceans. It is hereafter referred to as the “reference isopycnal.” Polar Water is defined as southward transport above this reference isopycnal in the DS.
 The volume transports through the different GSR gaps vary as a function of the velocity and the thickness of the layers involved. To test the sensitivity of the inflow and overflow to the choice of the reference isopycnal, the analysis has been repeated by shifting the interface up and down a model layer. The corresponding anomalies are both small in mean, and shifting does not change the correlation between the depth of the reference isopycnal, and inflow and overflow significantly.
3.2. Correlation and Regression
 To investigate the relation between inflow and overflow, time series of these are correlated with each other. For practical purposes the terms “inflow” and “overflow” are used throughout for volume transports (in Sv; 1 Sv = 106 m3 s−1). The reference directions for the flows are, according to their names, positive in the direction of mean flow (Figure 1). Known plausible mechanisms will guide the further analysis of causal relations and the nature of exchange. Time series of inflow and overflow are also correlated and regressed with two-dimensional atmospheric and oceanic fields in the overall search to find the governing mechanisms for their variability.
 All correlations and regressions are done on monthly time series which are detrended and deseasoned by detrending of each calendar month separately. The effective degrees of freedom are found according to Chelton , i.e., taking into consideration the autocovariance of all time series (at each point in space, as well as each variable). Significance levels are calculated by the standard Student's t test, using α = 0.05 (5% significance level).
3.3. Model Evaluation
 In order to use the model as a laboratory to find the mechanisms behind the North Atlantic–Nordic seas exchanges, it is necessary to evaluate the model's ability to reproduce the observed variability of the particular GSR exchanges in question. Inflow of Atlantic Water has been observed in the IFR section (Faroe Current) since 1997 [Hansen et al., 2010], and in the DS (Hornbanki section) since 1994 [Jónsson and Valdimarsson, 2005]. For the FSC transport of Atlantic inflow there are no documented long-term time series, based on measurements, available. Observations of overflows are more limited, but measurements in the deep FBC have been taken since 1995 [Hansen and Østerhus, 2007], while intermittent measurements in the DS have been taken since 2000 [Macrander et al., 2007].
 Comparison of observed and modeled inflows and overflows in these sections constitute our evaluation, and the time series of observed and modeled transport anomalies are shown in Figure 2. All calculations in this model evaluation are done on data in the time range shown, 1994–2007, except for mean values of FSC overflow and IFR and DS inflow, which are calculated only using months with both observations and model data available. Error estimates on the mean transports are 2 standard deviations of the series used. Anomalies are made by subtracting the empirical cycle of mean monthly values. For observations, gaps of 5 months or less are filled by linear interpolation in the anomalous series, prior to making the 12 month running mean filtered time series. This is done in order to avoid large loss of data around each minor gap by the end clipping that is necessary during filtering. Filling holes less than half the filter length is judged to introduce negligible bias to the filtered series. Observations of DS overflow, provided as daily data, were bin meaned into monthly values prior to any other treatment.
Figure 2a shows the deseasoned modeled FSC inflow which has a mean value of 4.7 ± 2.4 Sv. This is somewhat higher than the observed estimate of 3.8 Sv made by Østerhus et al. , but agrees well when taking the modeled uncertainties into account. Figure 2b shows the deseasoned observed FSC overflow from ADCP data plotted together with deseasoned modeled overflow, and the covariability of the two time series is evident. The correlation on monthly time scales is significant (r = 0.55), but the modeled mean overflow (1.0 ± 0.4 Sv) is only about half the observed (2.1 ± 0.6 Sv). It should be noted that the FSC overflow for simplicity is calculated in the same section as the FSC inflow as indicated by the line in Figure 1 since comparisons of simulated overflow in FSC and FBC reveal the same variability (not shown). Taking the modeled IFR overflow of 0.6 ± 0.3 Sv into account (Figure 2d), the overflow between Iceland and Scotland adds up to 1.6 Sv. Similar results with respect to variability were achieved in the model study by Olsen and Schmith .
 The observed and modeled inflow in IFR (Figure 2c), showed no significant correlations. However, mean values of the observed and modeled inflow compare well at 3.6 ± 1.6 Sv and 4.7 ± 1.2 Sv, respectively. No observed data were available for the IFR overflow, but Hansen and Østerhus estimate the Iceland-Scotland overflow to be ∼3 Sv. Combining this value with the observed FBC overflow of ∼2.1 Sv, leaves an estimate of ∼0.9 Sv to the IFR overflow which is within the modeled value of ∼0.6 ± 0.3 Sv.
 Finally, the corresponding time series for DS inflow and overflow are shown in Figures 2e and 2f, respectively. The model seems to capture much of the observed variability in DS, and the filtered time series of inflow correlates significantly at r = 0.47. The modeled mean inflow of 1.3 ± 0.6 Sv compares well with the observed mean of 0.8 ± 0.7 Sv. Observations of overflow in the DS are sparse, but in overlapping periods the modeled time series is close to the observed, and mean values are 3.6 ± 1.5 Sv and 3.2 ± 1.2 Sv, respectively.
 This regional model system has also been evaluated against hydrography and tracers in the FSC region, in the Nordic seas and in the North Atlantic in other studies: Hátún et al. [2005a]found that the simulated long-term temperature variations in the poleward flowing Atlantic Water closely resembles observations south of the ridge (Rockall Trough), north of the ridge (Svinøy), and between (FSC). In addition, the model was found to reproduce the observed seasonal variations and the seasonal modulations during the hindcast simulation. In the study byHátún et al. [2005b], the model was used to show that the salinity of the Atlantic Inflow is tightly linked to the dynamics of the North Atlantic subpolar gyre circulation. The model has also been evaluated through observed spreading of tracer sulphur hexafluoride in the Nordic seas [Eldevik et al., 2005] and to observed northward volume transports in the FSC (1999–2002) in Sandø and Furevik . Further details of the evaluations are given in Hátún et al. [2005a, 2005b], Eldevik et al. , and Sandø and Furevik  and show that the model gives a realistic representation of the hydrography and circulation in the GSR region.
4.1. Inflow and Overflow Over the Greenland-Scotland Ridge
 Based on the general consistency of modeled and observed GSR inflows and overflows as demonstrated in section 3.3, the analysis of variability is carried further by use of model results only.
Figure 3 shows modeled inflow plotted together with overflow in the FSC for the period 1948–2007, with variations on time scales from interannual to decadal. The two time series show a clear antiphase variability (r = −0.67), even though the amplitude of the inflow is larger than that of the overflow. The correlation between inflow and overflow in the DS is smaller (r = −0.34), while the one for the IFR section is not significant.
4.2. Relation Between Faroe-Shetland Channel Inflow, Overflow, and Depths of Isopycnals in the Nordic Seas
 The model used here shows a tight link between inflow and overflow in the FSC, where more inflow is accompanied by less overflow. Based on analytical theories, observations, and model results, several studies [e.g., Whitehead, 1998; Girton et al., 2006; Hansen and Østerhus, 2007; Jungclaus et al., 2008] have suggested that the FSC overflow is hydraulically controlled (i.e., that the overflow is controlled by density gradients and width of the sill). The model therefore gives the opportunity to study this process in more detail, and it is here focused on the interface between these water masses, both in the FSC and in the neighboring seas, to see if there is any vertical displacement of this isopycnal when inflow and/or overflow change.
 One method is to correlate the exchanges with the depth of the reference isopycnal throughout the North Atlantic and the Nordic seas. Correlations between the depth of this interface and FSC inflow and overflow for the period 1948–2007 are shown in Figure 4. An area with strong positive correlation between FSC inflow and the reference isopycnal shows up in the FSC and northward along the continental slope into the Nordic seas (Figure 4, top). This reflects the deepening of the isopycnic layers containing Atlantic Water when the inflow is strong. Likewise, negative correlation between the FSC overflow and this isopycnal appears in the same area (Figure 4, bottom), which means that the interface rises here as the overflow increases. These areas of high positive and negative correlation for inflow and overflow, respectively, are therefore related to the path and depth of the North Atlantic Current and its continuation into the Nordic seas: the Norwegian Atlantic Slope Current. Correlations between FSC inflow and overflow, and the depth of the reference isopycnal in the FSC (see Figure 4 for location) are listed in Table 1. The perturbations correspond to coherent upward and downward shifts in the FSC of around ±70 m around a mean depth of 610 m.
Table 1. Peak Correlations Between Monthly Time Seriesa
Nonsignificant correlations are indicated by dashes. The NAO is the index from the NOAA Climate Prediction Center.
DS Polar Water
FSC isopycnal depth sill
4.3. Compensating Flows
 The time series of inflow and overflow through the FSC in Figure 2 implicate that on average, the net inflow must be compensated by net outflow in the other straits surrounding the Nordic Seas. To study the effect of FSC Atlantic Water inflow variability on the transports in the IFR and DS, the FSC inflow is also correlated to IFR inflow and overflow, and DS overflow and outflow of Polar Water. The correlations are listed in Table 1. The analysis shows significant correlations between FSC inflow and all the flows, but largest correlations are found with the overflows in FSC and DS. The correlation between FSC and DS overflows is negative (r = −0.21), while the correlation between FSC and IFR overflows is positive (r = 0.43).
4.4. Large-Scale Atmospheric Forcing
 As the inflow is strongly influenced by wind [Biastoch et al., 2003; Nilsen et al., 2003; Sherwin et al., 2008; Jungclaus et al., 2008; Richter et al., 2009; Serra et al., 2010; Richter et al., 2012], the volume transport of FSC inflow is regressed onto sea level pressure (SLP) to find the pattern of SLP variability that potentially has the strongest influence on the inflow variability (and given the correlation found, thereby also on the overflow). Figure 5(top) shows the resulting pattern for the period 1948–2007. It is composed of a low-pressure center in the Nordic seas northeast of Iceland and a high pressure in the eastern North Atlantic and western Mediterranean. The same pattern is also found for volume transports of light Polar Water and dense Overflow Water in the DS (not shown). This system of high and low centers of pressure variability resembles the pattern of the NAO [Hurrell, 1995], which have strong influence on both the marine and terrestrial climate variability in Europe and adjacent seas. A similar, but opposite pattern is found for the overflow in FSC (Figure 5, top). Both Figures 5 (top) and 5 (bottom) show correlations at no time lag, and have maximum correlations of −0.68 and −0.59. Lagged correlations at ±1 month show no clear correlation patterns (not shown). Peaks of correlations between the NAO index from the NOAA Climate Prediction Center, and the FSC inflow and overflow are 0.45 and −0.32, respectively (Table 1). Based on these numbers it can be concluded that the NAO and atmospheric forcing has a near immediate covariability with the FSC inflow and overflow.
 The negative correlation between the FSC inflow and overflow in section 4.1 shows no lag and clearly indicates an instant, barotropic response where high inflow corresponds to low overflow. In the same way as increased southwesterly winds cause higher sea level at the continental shelf and thereby a barotropic response in the FSC volume transports, the same winds may increase the depth of the reference isopycnal by Atlantic Water getting piled up along the shelf (Figure 4), and thereby a baroclinic response in the FSC volume transports. Such a baroclinic response would tend to increase both the FSC inflow and overflow, while the barotropic response would tend to increase the inflow and reduce the overflow.
4.5. Gradients in SSH and Reference Isopycnal Across FSC
 To see the interaction between the FSC exchanges, sea surface height (SSH) and vertical displacements of the reference isopycnal, correlations between time series of FSC inflow and overflow, and gradients in SSH and the depth of the reference isopycnal across the FSC are shown in Table 2. The gradients are based on differences between two points at each side of the FSC (61.3°N, −4.7°E and 60.7°N, −4.1°E) close to the red ring in Figure 4. The resulting correlations show that increased FSC inflow covary with deeper reference isopycnal, as well as stronger gradients in the SSH and isopycnal across the FSC.
Table 2. Correlations Between FSC Inflow and Overflow and the Depth of the Reference Isopycnal (H), ∇SSH and ∇Ha
The gradients are calculated across the FSC close to the FBC sill (61.3°N, −4.7°E and 60.7°N, −4.1°E), and the point correlation with the isopycnal depth is done for (59.8°N, −6.0°E) (indicated by the red ring in Figure 4).
4.6. Barotropic and Baroclinic Transports
 To what degree is the exchanges in the different GSR sections dominated by barotropic and baroclinic processes? In the model output, the velocity consists of a barotropic and a baroclinic component (e.g., as vertical mean velocity and deviations from the mean) [Bleck and Smith, 1990],
and time series for the respective FSC transport components are shown in Figure 6. Both the total and the barotropic inflows and overflows are anticorrelated, while the baroclinic are positively correlated. The amplitude of the barotropic variability is greater than that of the baroclinic. On the other hand, the mean baroclinic FSC overflow is about three times greater than the mean barotropic, and is therefore the main constituent in the total overflow. Nearly the same applies to the IFR overflow, where the mean baroclinic contribution is about twice the mean barotropic (not shown). This is the opposite of the DS, where the mean barotropic overflow is almost five times larger than the mean baroclinic (not shown).
 To find which component that explains most of the variability of the total inflow and overflow, the barotropic and baroclinic inflows and overflows are correlated to their respective total volume transports in each of the GSR sections. The results are listed in Table 3. The most important conclusions to be drawn from Table 3 is that all barotropic correlations exceed the baroclinic, and that there are relatively large contributions from the baroclinic components in the FSC volume transports.
Table 3. Correlations Between Barotropic and Baroclinic Volume Transports Versus Their Total Volume Transportsa
Nonsignificant correlations are indicated by dashes.
 Based on the literature presented in section 1, there seems to be a general agreement that the stable overflow across GSR to a large degree is determined by baroclinic forcing and production of dense water in the Nordic seas, while variations in the overflow are caused by a combination of barotropic forcing and changes in density gradients across the ridge.
 The interplay between variable atmospheric forcing, perturbation of isopycnals in the ocean, and exchanges of water masses between the North Atlantic and the Nordic seas have here been investigated. Modeled time series of Atlantic Water inflow, Polar Water outflow and dense Overflow Water have been compared with each other, with SLP and SSH, and with the depth of the isopycnal separating inflow and overflow, in order to improve the understanding of the mechanism behind the variability of the exchanges.
 Most upper layer flows are forced by wind stress, and the importance of wind forcing for the inflow of Atlantic Water through the FSC is demonstrated in various studies [Biastoch et al., 2003; Nilsen et al., 2003; Orvik and Skagseth, 2003; Skagseth et al., 2004; Sherwin et al., 2008; Jungclaus et al., 2008; Sandø and Furevik, 2008; Richter et al., 2009, 2012]. From the monthly time series used here, it is difficult to reveal any time lags between the atmospheric forcing and its response on the ocean, since the effect of high- and low-pressure systems on the Atlantic inflow to the Nordic seas is found on order of daily rather than monthly time scales [Richter et al., 2009]. It is therefore difficult to state in which order things happen based on time lags in correlations. This study is therefore based on a systematic analysis of how different parts of the ocean respond to atmospheric forcing, and how the different inflows and overflows relate to each other.
5.1. Faroe-Shetland Channel and Iceland-Faroe Ridge
 The relation between NAO and the GSR exchanges is well known and has been reported in earlier studies [e.g., Biastoch et al., 2003; Nilsen et al., 2003; Mauritzen et al., 2006; Olsen and Schmith, 2007; Serra et al., 2010]. Nilsen et al.  suggest that NAO is the main driving force for the variations, involving Ekman transports and barotropic adjustment. In this study, a correlation of −0.68 between FSC inflow and SLP is found, and means that SLP explains 46% of the FSC inflow variance. The westerlies associated with the characteristic NAO pattern that emerged from the correlation analysis (Figure 5) is therefore very important for the variability. The corresponding values for the overflow are 0.59 and 34%, which is also a considerable part of the variance. Increased FSC inflow in combination with increased FSC interface depth, increased gradients of SSH and reference isopycnal depth across the FSC (Table 2) support effects of wind forcing and Ekman transport in the FSC. These findings are supported by Skagseth et al.  and Richter et al. , who investigated the relation between wind and the Norwegian Atlantic Slope Current. Richter et al. found, by means of leading modes of altimeter-derived SSH, that the current is largely driven by wind forcing, and that wind anomalies cause Ekman transports onto or away from the shelf area where the signal is captured by tide gauges.Hansen et al.  suggest that the driving force behind the IFR inflow is a pressure gradient caused by a continuously low sea level in the southern Nordic seas. Figure 7 shows time series of modeled FSC, IFR inflow, and the SSH difference between the North Atlantic (60.9°N, −15.7°E) and the Nordic seas (66.4°N, −3.3°E), and reveals similarities between the SSH difference and the FSC inflow, not between SSH and IFR inflow. From Figure 2 it is also clear that modeled FSC inflow has similar variability as the observed IFR inflow. The modeled inflow therefore seem to respond to the SSH difference, but for unknown reasons, only through the FSC.
 The strong relation between the FSC inflow, overflow, and the reference isopycnal is seen in the dynamically important FSC region (Figure 4). This is similar to the results achieved by Jungclaus et al. [2008, Figure 22.7], with strong correlations between overflow and reference isopycnal depth (r > 0.8) west and northeast of the FBC sill. A notable difference is that medium high correlations (r < 0.8) in our study extend further north along the Norwegian continental shelf. This difference might be due to the different type of vertical discretizations (z coordinates versus σ coordinates) used in the two models, and thereby less mixing across the isopycnals in the isopycnic model used here.
 Much of the variability in the FSC exchanges therefore seems to be governed by increased wind driven inflow which alters the interface depth in the dynamically important FSC region, and thereby reduces the FSC overflow via hydraulic control. The hydraulic control of the FSC overflow has earlier been discussed in different studies [e.g., Whitehead, 1998; Girton et al., 2006; Hansen and Østerhus, 2007; Jungclaus et al., 2008; Serra et al., 2010], where the main focus has been on the relation between the overflow and the interface depth upstream the FBC sill, or close to the entrance region [Helfrich and Pratt, 2003]. This study places the maximum correlation between the interface depth and FSC inflow (r = 0.81) and overflow (r = −0.94) southwest of the FBC sill at about (60°N, −9°E). As shown by Figure 4, strong correlations are found both west and northeast of the FBC sill, but maxima southwest of the sill supports the impression that much of the variability in the FSC exchanges is caused by southwesterly winds and piling up of Atlantic Water against the coast. On the other hand, the correlation between the interface depth and the FSC overflow is larger than that for the FSC inflow, suggesting additional influence from the FSC overflow on the interface depth.
 The low-frequency antiphase between the DS and FSC overflows found bySerra et al.  was attributed to local wind stress forcing of the barotropic component of the transports. In their model, the largest changes in the isopycnal between the dense and light waters occurred in the central Arctic and in the Norwegian and Lofoten Basins. They found that the reduction of the cyclonic flow in the Norwegian Sea promoted spreading of dense water to the cyclonic flow surroundings which again promoted strengthening of the dense slope flow that feeds the FSC. This seems like a plausible mechanism, but can only partly be confirmed by the results in this study and the time scales considered here.
 The tilting of SSH as function of wind stress and Atlantic Water getting piled up along the coast gives the process a strong barotropic character (Table 3), but this is not the whole story. As the interface depth gets deeper (Figure 4), it also gets steeper and becomes tilted downward toward the Scottish continental shelf (Table 2) which tends to increase the baroclinic inflow and overflow as shown by Figure 6 and Table 3.
 A schematic description of the ocean's response to atmospheric forcing and the interaction between inflow and overflow in terms of barotropic and baroclinic processes are as follows.
 As a consequence if higher inflow through the FSC, the amount of Atlantic Water along the path of the North Atlantic Slope Current increases (Figure 4). This influences both an upward tilting of the sea surface and a downward tilting of the reference isopycnal toward the Scottish shelf (Table 2). In addition to the barotropic increase in northward flow from the SSH gradient, the downward tilting of the isopycnals (pink time series in Figure 7) increases the baroclinic transport in both directions. There is also a deepening of the interface associated with increased inflow (green time series in Figure 7). Thus changes in the inflow may alter the interface height and reduce the overflow in terms of hydraulic control.
 Dividing the volume transports into barotropic and baroclinic components reveals that the amplitude of the barotropic inflow is much greater than the baroclinic (Figure 6). Correlation of the different components with the total transports also gives best fit for the barotropic components (Table 3), but the results also illustrate the importance of baroclinic adjustments in FSC in terms of tilted isopycnals.
5.2. Denmark Strait
 FSC inflow and FSC overflow correlate with southward transport of DS overflow and Polar Water (Table 1), which is likely due to the same barotropic adjustment process described by Nilsen et al.  and Jungclaus et al. . This suggests an antiphase relationship between FSC and DS overflows. Such a relation was found in the model study by Serra et al. , and for the time series in our study there is also a small, but significant anticorrelation between the FSC and DS overflows (Table 1). Different from the results of Serra et al. , the correlation remains about the same after the mid-1990s when the intensity of the subpolar gyre (SPG) was decoupled from the NAO [Lohmann et al., 2009]. The antiphase in this study therefore seems to be independent of the hydrographic changes that took place in the North Atlantic and Nordic seas after the mid-1990s [Hátún et al., 2005b].
 The baroclinic transports in the FSC, shown to dominate the mean transports, constitute an important component in the average deep water circulation in that section. This is not the case in the DS, where the barotropic transport is almost five times larger than the baroclinic, which is in line with the results of Kohl et al. . They state that shorter-term changes of the DS overflow are mainly found to be concurrent with the variability of the barotropic transport, which they suggest to be wind driven. Also the modeled variability in our study shows that the DS overflow is dominated by the barotropic component (Table 3).
6. Summary and Conclusions
 The evaluation of the model used in this study reveals a close covariance between the observed and modeled inflows and overflows in the FSC and DS (Figure 2).
 The inflow of Atlantic Water in the FSC, the outflow of light Polar Water in the DS, and the overflows of dense Overflow Water in both FSC and DS are all found to be forced by winds and an atmospheric pattern resembling the NAO. An increase in the FSC inflow is associated with a decrease in the FSC overflow and an increase in the DS overflow. The antiphase between the FSC inflow and overflow is associated with surface tilting and vertical displacement of the isopycnal separating the two water masses along the path of the Norwegian Atlantic Slope Current. The adjustments are shown to be barotropic mainly, but they are also influenced by baroclinic processes in the FSC due to tilting of isopycnals across the channel.
 Based on these findings, possible mechanisms for the above relations between inflow, Polar Water outflow and overflow are as follows: (1) FSC inflow increases due to stronger southwesterly winds and increased SSH toward the Scottish coast. (2) As a result, the depth of the reference isopycnal increases along the path of the Norwegian Atlantic Slope Current. (3) Deeper reference isopycnal in FSC hamper the transport of Overflow Water in terms of hydraulic control. (4) The simultaneous increase in FSC inflow and reduction in FSC overflow gives rise to a barotropic adjustment process in DS with increased southward transport of both Overflow and Polar Water. (5) The tilting of the reference isopycnal across the FSC sets up baroclinic currents in both directions.
 This said, an influence of the overflow on the inflow variability cannot be excluded as long as no time lag between the flows is revealed, especially not on longer times scales. However, the strong correlation between SLP and the FSC inflow and overflow suggest a direct impact on the exchanges from the atmosphere. The analysis strongly indicates that the variability of FSC and DS overflows, as well as the outflow of Polar Water in DS, are mainly barotropically regulated and covary with the FSC inflow and the vertical movement of the isopycnal between the FSC inflow and overflow. The main conclusion is therefore that the overflow variability, and exchange in general, to a large extent reflects an inflow which is forced by an NAO-like wind pattern.
 We thank all members of the EU project THOR who have contributed with data on observed inflow and overflow in the GSR sections. This work was supported by the Norwegian Research Council projects NorClim, POCAHONTAS, BIAC, the EU project THOR, and the Norwegian Supercomputer Committee through a grant of computing time. This is publication 405 from the Bjerknes Centre for Climate Research.