1. Introduction
Analyses of observations over the instrumental era show a pronounced multidecadal variability in the North Atlantic, with alternating basinwide warming and cooling phases with a dominant time scale of 60–90 yr (Schlesinger and Ramankutty 1994; Enfield et al. 2001). This mode of variability, referred to as the Atlantic multidecadal oscillation (AMO) or Atlantic multidecadal variability (AMV), explains nearly 40% of the total integrated annual mean sea surface temperature (SST) variance over the basin (Delworth et al. 2007). These low-frequency variations are associated with changes in African Sahel rainfall, Atlantic hurricanes, and North American and European summer climate (Knight et al. 2006). Multiproxy-based reconstructions show that this natural mode of variability has existed before the instrumental era, with periodicities spanning the 50–70-yr range over the past millennia (Knudsen et al. 2011). Shorter time scales in the range of 20–30 yr have also been reported in a variety of observations, based on either multiproxy analyses (Chylek et al. 2011) or direct measurements of tide gauge records around the North Atlantic (Frankcombe and Dijkstra 2009).
The fluctuations of North Atlantic SST associated with the AMO form the classical horseshoe-shaped pattern that consists in an SST anomaly of one sign extending from the subpolar gyre to the tropics, and an anomaly of opposite sign in the western subtropical gyre (Kushnir 1994; Deser et al. 2010). SST changes are maximum in the western part of the subpolar gyre and weaker in the tropics and in the subtropical area. What determines the spatiotemporal structure of this natural mode of variability and whether the ocean or the atmosphere primarily drives the variability remains controversial. The instrumental record is unfortunately too sparse in terms of spatial coverage and too short compared to the time scales of the variability to address these questions. In addition, the observational record cannot provide the North Atlantic SST response to anthropogenic and aerosols forcings needed to disentangle the forced response from the intrinsic variability (Knight 2009). Consequently, progress in both the determination and understanding of the North Atlantic interdecadal variability comes mostly from studies based on numerical models, either idealized or fully coupled and realistic. As a whole, these studies are inconclusive about the respective role of the ocean and the atmosphere for the AMO because of the large diversity of the proposed mechanisms and the comparisons of the patterns and time scales of the variability with observations. Two strong paradigms emerged: 1) the first one is related to the integration of the atmospheric white noise by the ocean along with its large heat capacity giving rise to a reddened spectrum (Hasselmann 1976); and 2) the second one has dynamical origins and is related to intrinsic unstable interdecadal ocean modes that spontaneously develop under steady surface buoyancy fluxes, a hypothesis that has only been tested in models ranging in complexity from idealized to intermediate (Greatbatch and Zhang 1995; Colin de Verdière and Huck 1999; te Raa and Dijkstra 2002; Arzel et al. 2007; Jamet et al. 2016).
The debate has recently been reinvigorated following the study of Clement et al. (2015), who compared outputs of a suite of coupled models as part of phase 3 of the Coupled Model Intercomparison Project (CMIP3) and atmospheric models coupled to slab-ocean mixed layer components without ocean dynamics. The observed AMO pattern is well reproduced and remarkably similar in both fully coupled and slab-ocean models, leading the authors to conclude that the AMO does not rely on ocean circulation changes but is rather a consequence of the integration by the ocean of short-term atmospheric fluctuations embodied in the NAO, thereby supporting the first paradigm. Theoretical spectra based on stochastically forced conceptual models (Barsugli and Battisti 1998) show a flattening of the spectra at low frequencies as a result of the large heat capacity of the ocean compared to that of the atmosphere. Observational spectra of midlatitude temperature anomalies fail to flatten into a white spectrum at long time scales, but instead continue to redden (Dommenget and Latif 2002), suggesting a possible role of ocean dynamics at these latitudes. This view is supported by observations and results from realistic coupled models (Gulev et al. 2013; Zhang et al. 2016; O’Reilly et al. 2016), which show that midlatitude SST changes and (turbulent) surface heat flux anomalies (positive downward) are negatively correlated on decadal time scales, indicating that dynamical ocean processes are essential in producing variance on these time scales. Cane et al. (2017) used a simple red noise model to interpret this negative correlation as the result of negligible ocean forcing, with the atmospheric stochastic forcing being the main driver of the AMV. Zhang (2017) resolved the controversy and showed that adding oceanic damping in the red noise model of Cane et al. (2017) brings back the oceanic forcing as the main driver of low-frequency subpolar North Atlantic SST anomalies associated with the AMV.
In addition to the atmospheric white noise that certainly plays a role, a number of studies based on stand-alone ocean models have demonstrated the unstable character of the ocean circulation on interdecadal time scales. This is the second paradigm: the variability originates from an instability internal to the ocean circulation itself, without the need for time-varying surface fluxes or coupling with the atmosphere. When these intrinsic ocean modes are damped rather than self-sustained, for example when the lateral eddy diffusion is beyond a critical threshold, the addition of a small amount of atmospheric noise can be sufficient for the variability to emerge with resonant frequencies characteristic of the damped ocean mode. Examples of such a noise-induced oceanic interdecadal variability can be found in Herbaut et al. (2002), Dong and Sutton (2005), or Frankcombe et al. (2009).
The existence of intrinsic interdecadal modes of the overturning circulation was first shown in idealized ocean models forced by prescribed and steady surface fluxes (Greatbatch and Zhang 1995; Huck et al. 1999; te Raa and Dijkstra 2002; Arzel et al. 2006). Although very idealized, these models capture several aspects of the observed North Atlantic low-frequency variability. These aspects include in particular a westward propagation of midlatitude temperature signals (Feng and Dijkstra 2014) and a one-quarter phase lag between surface and subsurface temperature anomalies (Frankcombe et al. 2008). The emerging periodicities remain within the interdecadal band (20–30 yr) and depend on the choice of forcing characteristics and mixing parameters. The internal mode has proven to be robust to the presence of mesoscale turbulence (Huck et al. 2015) and coupling with a hierarchy of atmospheric components (Chen and Ghil 1996; Huck et al. 2001; Arzel et al. 2007; Jamet et al. 2016). In addition, the sensitivity of the properties of interdecadal oscillations of the meridional overturning circulation to horizontal turbulent eddy diffusivities has also been studied extensively (Huck et al. 1999; Colin de Verdière and Huck 1999). Because these sensitivity studies are based on numerical models with either simplified physics [e.g., planetary geostrophic dynamics, linear equation of state, or use of horizontal eddy diffusivity instead of along-isopycnal mixing that produces the so-called Veronis effect (Veronis 1975) where an unphysically large downwelling occurs in the ocean interior] or idealized geometries (e.g., mostly flat bottoms and single-hemispheric sectors of the sphere), the relevance of this internal ocean mode for the observed low-frequency variability remains untested. We extend these sensitivity studies to a higher level in the hierarchy of complexity following Held (2005) by using a realistic geometry (continental boundaries and ocean bathymetry), which may significantly alter the domain of existence of the variability identified with lower levels of complexity. The effect of bottom topography for instance is not robust across models: while intrinsic interdecadal modes are completely damped out in the study of Winton (1997), they survive in the study of te Raa et al. (2004), suggesting that the details of the model configuration and choice of forcing and/or parameters are critical in determining the response of the system. Ferjani et al. (2013) showed that the direct effect of bottom topography on mode characteristics is quite limited and suggested instead that changes in the mean flow structure resulting from bottom topography may have more influence. Given the importance of the mean flow structure for the development of intrinsic oceanic interdecadal modes (Huck and Vallis 2001), it is necessary to pursue the sensitivity studies in more realistic contexts than those previously used. By contrast to previous works that used horizontal eddy diffusivity as the control parameter, the sensitivity analysis we propose here is based on the more physically relevant eddy-induced and isopycnal mixing parameters. Within this framework we aim to determine the range of turbulent eddy diffusivity values for which spontaneous interdecadal oscillations of the Atlantic circulation emerge. The variability is shown to exist for eddy-induced diffusivity values lower than those traditionally used in realistic coupled models, implying that some noise excitation would be required for these intrinsic oceanic modes to emerge in such models.
The objective of this paper is to test the hypothesis that internal generation of interdecadal variability of the ocean circulation may be relevant to explain North Atlantic climate variability. To this end we use a realistic ocean general circulation model (OGCM) forced by prescribed surface fluxes of heat, freshwater, and momentum, and assess the ability of the Atlantic circulation to exhibit self-sustained oscillations on interdecadal time scales. This modeling study uses a realistic geometry, a model configuration that sharply contrasts with previous studies on the same kind based on idealized geometries. The surface boundary condition remains idealized in the sense that it does not include any coupling with the atmosphere, but as will be shown, adding atmospheric thermal damping with realistic e-folding times has a limited impact on the variability. The paper explores the signature and the physics of intrinsic oceanic modes that have been suggested to play a significant role in realistic model studies (Muir and Fedorov 2017). We assess the robustness of the interdecadal modes found previously in these idealized models, explore the nature of the transition from the steady to the oscillatory regime, the mechanism of the variability, its pattern, and its origin. This study therefore puts the conclusions obtained with these idealized models in a more realistic context, which is a necessary step up in the model hierarchy. The difficulty to extract the cause of the events in realistic coupled models is the reason why a model hierarchy-based approach is necessary.
The paper is structured as follows. Section 2 describes the model and the experimental design. The sensitivity of the internally generated interdecadal variability to eddy-induced and isopycnal mixing coefficients is presented in section 3. Section 4 provides a description of the structure of the mode including both its horizontal and vertical structure. In section 5, a local linear stability calculation including dissipative effects supports the baroclinically unstable character of the North Atlantic Current with growth rates of O(1) yr−1 and scales of O(1000) km. The paper finally concludes with a summary and a discussion in section 6.
2. Model description, methodology, and model climatology
a. The model
We use the MITgcm (Marshall et al. 1997) run at 1° horizontal resolution. The World Ocean model domain extends from 80°S to 80°N, with vertical walls at those latitudinal boundaries. There are 44 levels on the vertical with grid spacing increasing from 10 m at the surface to 250 m at the bottom. Static instability is removed by strong mixing of the water column with a vertical diffusivity coefficient of 100 m2 s−1. The vertical diffusivity kυ increases downward following a Bryan and Lewis (1979) vertical profile with upper and bottom values of 0.5 and 1.3 × 10−4 m2 s−1, respectively. These values are in line with those inferred from large-scale inversion experiments (Lumpkin and Speer 2007), direct measurements (Waterhouse et al. 2014) and more recent robust diagnostic calculations (Arzel and Colin de Verdière 2016). We use a spatially uniform horizontal Laplacian viscosity νh of 5 × 104 m2 s−1, which is sufficient to resolve the frictional boundary layer, whose width is given by 
Summary of experiments designed to assess the sensitivity of the model solution to K and KGM. Experiments using spatially varying KGM coefficients, based on the Visbeck et al. (1997)’s parameterization, require the maximum value reached by KGM to be specified (indicated by asterisks). The sensitivity to isopycnal mixing is performed for two values of KGM. The reference experiment uses K = 1000 m2 s−1 and KGM = 550 m2 s−1.
b. Experimental design
We use flux boundary conditions at the surface for both temperature and salinity in our ocean-only experiments. A flux formulation is justified for salinity because of the absence of feedback between sea surface salinity (SSS) and freshwater flux. The justification for temperature is more difficult because a fraction of the surface buoyancy flux (turbulent heat fluxes, evaporation, longwave radiation) depends on SST. On time scales much longer than the atmospheric spindown time scale ρaCpaHa/λ = O(10) days (with ρa the atmospheric density, Cpa the specific heat of dry air, Ha the atmospheric scale height, and λ the surface heat flux feedback), the heat capacity resides in the ocean and the atmosphere becomes slaved to changes in ocean circulation. In this limiting case the surface boundary condition on temperature reduces to a weak damping on SST anomalies. Vallis (2009) estimates this damping rate to be O(1/1600) days−1 (~4.4 yr−1), which is on the same order as a typical e-folding time of perturbations found in models forced by prescribed surface fluxes (Huck et al. 2001). However, characteristics of the variability in coupled models are very similar to those obtained under climatological forcing diagnosed from the coupled simulation (Arzel et al. 2007; Zhu and Jungclaus 2008; Jamet et al. 2016). This indicates, at least in those specific cases, that the flux formulation captures the essential behavior of low-frequency air–sea interactions. The standard experiments discussed in this paper therefore use prescribed surface buoyancy fluxes. As will be shown, adding a realistic thermal damping with a time scale of 1 yr to the prescribed surface heat flux has a limited impact on the variability.
Surface buoyancy fluxes are diagnosed from a model integration under restoring boundary conditions rather than prescribed from observations, in a similar manner as Arzel et al. (2007) and Frankcombe et al. (2009). This procedure allows the perturbations in the flux boundary condition experiments to grow from an equilibrium state obtained under restoring boundary conditions, leading to a straightforward relationship between the characteristics of the variability and the structure of this equilibrium state. Thermal damping, when included, is computed by restoring the SST under flux boundary conditions toward the observed annual mean SST field (Locarnini et al. 2010) with a time scale of 1 yr.
The sensitivity to the GM coefficient KGM is explored here through a set of 14 experiments (keeping isopycnal mixing K = 1000 m2 s−1 in all runs) spanning the 200–600 m2 s−1 range (Table 1). Twelve of these experiments use a spatially uniform coefficient and two of them use the Visbeck et al. (1997) formulation that allows KGM to vary with the Eady growth rate. The sensitivity to isopycnal turbulent diffusivity K is explored through a set of 12 experiments, spanning the 500–2000 m2 s−1 range, for two fixed values of KGM, namely, 500 and 550 m2 s−1. The sensitivity analysis is thus made around the pivot or reference experiment using K = 1000 m2 s−1 and KGM = 550 m2 s−1.
For each set of mixing parameters K and KGM, the model is first brought to equilibrium through relaxation of SST and SSS fields toward the World Ocean Atlas climatology (Locarnini et al. 2010; Antonov et al. 2010). The restoring procedure occurs on a monthly time scale in order to mimick seasonal variations of the surface buoyancy flux. The temperature- and salinity-restoring time scales (both uniform in space and time) have been adjusted to produce a model solution (under restoring boundary conditions) as close as possible to observations in terms of both circulation (Lumpkin and Speer 2007) and surface buoyancy fluxes (Large and Yeager 2009). The best compromise that emerged from a number of trials was to choose a restoring time scale of 10 days for SST, which corresponds to an air–sea turbulent heat transfer coefficient of about 40 W m−2 K−1 for an upper-layer thickness of 10 m. This value is in the range of observed surface heat flux sensitivities, which were estimated to be in the range 10–50 W m−2 K−1 depending on seasons and geographical location (Frankignoul et al. 2004). A longer time scale of 6 months is used for SSS, consistent with the absence of feedback between SSS and the freshwater flux. These experiments, termed restoring temperature and restoring salinity (RTRS), start from the same initial condition corresponding to the end state of a previous 6000-yr model integration. Each RTRS run is 1200-yr long, which is sufficient to reach a new equilibrium. Monthly mean surface heat and freshwater fluxes are diagnosed over the last year of each RTRS run to form a synthetic seasonal cycle. Averaging over the last year of the experiments is justified since internal variability is totally absent in these runs (mesoscale turbulence does not appear at this coarse horizontal resolution). This synthetic seasonal forcing is then applied repetitively to the ocean surface for a further model run, named prescribed flux for temperature and salinity (FTFS), whose length (typically >1000 yr) is adjusted to yield reasonable stationary statistics. The goal of the paper is to discuss the physics of interdecadal modes that develop in these experiments.
c. Model climatology
Figure 1 shows the mean ocean circulation state diagnosed over years 1201–1400 of the reference experiment (FTFS experiment with KGM = 550 m2 s−1 and K = 1000 m2 s−1). Both the spatial structure and strength of the Atlantic meridional overturning circulation (AMOC) are consistent with hydrographic data (Lumpkin and Speer 2007) with a 16 Sv (1 Sv ≡ 106 m3 s−1) North Atlantic Deep Water (NADW) cell in the upper 2500 m and a weaker (5 Sv) Antarctic Bottom Water cell below (Fig. 1a). NADW formation occurs in the northern part of the Labrador Sea and in the Greenland–Iceland–Norwegian Seas (Fig. 1b), consistent with observations, although convective mixing seems excessively deep (de Boyer Montégut et al. 2004). The barotropic transports (Fig. 1c) are underestimated compared to observations (Colin de Verdière and Ollitrault 2016), a bias that is related to the low resolution of the model that does not permit mesoscale turbulence. The Gulf Stream remains attached to the coast (Fig. 1d), presumably because of the absence of the Northern Recirculation Gyre (Fig. 1c) usually observed between Cape Hatteras and the Grand Banks (Zhang and Vallis 2007). After passing the Grand Banks, the Gulf Stream continues too far north of the North Atlantic Current instead of veering more to the east, a common problem in low-resolution circulation studies (Denng et al. 1996).
North Atlantic Ocean state diagnosed over years 1201–1400 of the reference FTFS experiment (K = 1000 m2 s−1 and KGM = 550 m2 s−1). (a) AMOC (Sv) with the zero contour line (black), (b) March mixed layer depth (m), (c) barotropic streamfunction (Sv) with the zero contour line (black), and (d) ocean currents in the upper 250 m and SSH (m).
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0884.1
3. Parameter sensitivity analysis
The results of this sensitivity analysis are summarized in Figs. 2 and 3. The readers interested in the description of the variability may skip this section.
Sensitivity of the model solutions to (a),(c),(e) KGM and (b),(d),(f) K: (left) mean strength of the AMOC computed as the maximum strength of the meridional overturning streamfunction below 1000 m and north of 30°N, (center) AMV index computed as the peak-to-peak amplitude of the area-weighted North Atlantic SST anomalies using a high-pass filter with a cutoff frequency of 1/100 yr−1, and (right) dominant period estimated from a multitaper spectral analysis of the basin mean kinetic energy density time series of the North Atlantic. The sensitivity to K in (b),(d),(f) has been evaluated for KGM = 500 (circles) and 550 m2 s−1 (squares). The two circles in each of (a),(c),(e) indicate the statistics obtained for the experiments using the Visbeck et al. (1997) formulation. For those specific cases the GM diffusivities used to build the individual plots have been averaged in region of maximum SST variance. Note the different vertical scales for the oscillation period in (e) and (f).
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0884.1
Amplitude of the circulation variability as a function of the Peclet number (with U = 1 cm s−1 and L = 75 km the grid size at midlatitudes) based on (a) KGM and (b) K. The index is computed as the peak-to-peak variations of the North Atlantic kinetic energy density time series. The inset in (a) emphasizes the presence of a supercritical Hopf bifurcation where the amplitude of the limit cycle in the vicinity of the critical Peclet number Pec = 1.31 increases as (Pe − Pec)1/2, as indicated by the thick black line. In (a) the two circles correspond to the case with spatially varying GM coefficients. The associated Peclet numbers have been computed as the average in the region of maximum SST variance. The crosses correspond to the standard experiments under flux boundary conditions, while the black dots correspond to the case where a thermal damping has been added to the prescribed heat flux with a restoring time scale of 1 yr.
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0884.1
a. Sensitivity to thickness diffusivity KGM
Figure 2a shows that the AMOC strength decreases by 25%, from 20 to 15 Sv, as KGM is varied between 200 and 600 m2 s−1. Marshall et al. (2017) interpreted those changes in terms of scaling laws and invoked the central role of the Southern Ocean in interhemispheric dynamics. Interdecadal variability disappears for thickness diffusivities KGM larger than about 600 m2 s−1, that is, for an overturning strength (15 Sv) that is comparable to that observed today. This critical diffusivity value is associated with a nondimensional Peclet number (Pe = UΔx/KGM) of 1.31, where U = 1 cm s−1 is a scale for horizontal velocity and Δx = 75 km approximately corresponds to the model horizontal grid size at midlatitudes. The amplitude of oscillations (as measured by the peak-to-peak amplitude of basin mean kinetic energy density in the North Atlantic) in the vicinity of this critical threshold approximately follows a square root law, suggesting the existence of a supercritical Hopf bifurcation (Fig. 3a). This behavior was first recognized in an idealized ocean model coupled to an energy balance model of the atmosphere by Chen and Ghil (1996) but with the inverse of the heat exchange coefficient as the control parameter. Colin de Verdière and Huck (1999) later confirmed the nature of the bifurcation in an idealized ocean model forced by prescribed surface buoyancy fluxes with the horizontal Peclet number as the control parameter.
A second (abrupt) transition in the oscillation amplitude occurs around Pe = 1.5 corresponding to KGM = 525 m2 s−1 (Fig. 3a). Trials have been made to rationalize this behavior, such as to compare the mean circulation states obtained from the RTRS runs for GM coefficients apart from this critical value, but no significant changes in the mean flow structure or stratification could be found. This is consistent with the initial evolution of the circulation under flux boundary conditions, which exhibits a relatively small amplitude limit cycle for all experiments (typically during the first few centuries; Fig. 4). The difficulty here is that it is the circulation under flux boundary conditions that undergoes an abrupt shift (i.e., at year 650 for KGM = 525 m2 s−1 and at year 400 for KGM = 500 m2 s−1; Fig. 4). We suggest that as the GM coefficient is reduced, typically to values smaller than 525 m2 s−1, the mean path of the North Atlantic Current under flux boundary conditions becomes less stable and eventually undergoes at some point an abrupt shift, which may ultimately favor much larger amplitude oscillations.
Time series of the AMOC index obtained under flux boundary conditions for KGM varying from 500 to 575 m2 s−1, keeping K = 1000 m2 s−1 in all experiments. Note the different vertical scales between panels.
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0884.1
All experiments based on steady and spatially uniform thickness diffusivities need to be contrasted with those using a variable KGM (Visbeck et al. 1997). Increasing the maximum possible value of KGM from 500 to 1000 m2 s−1 with this formulation tends to slightly weaken the AMOC and decrease the oscillation amplitude. The effect on the oscillation period is, however, significant with a drastic decrease of about 50% between the two experiments.
b. Sensitivity to isopycnal mixing K
Keeping now KGM fixed and varying K in the 500–2000 m2 s−1 range has a negligible effect on the strength of mean circulation but not on the oscillation properties (Figs. 2 and 3). The boundary between the weak and strong variability regimes occurs around K = 1000–1200 m2 s−1. The transition between the two regimes is quite abrupt, in particular for KGM = 550 m2 s−1 (Fig. 3b), and may eventually be traced back to the different structure of the mean circulation rather than its strength, which appears to be weakly dependent of K (Fig. 2b). By contrast to the sensitivity to KGM where a Hopf bifurcation occurs, the amplitude of the limit cycle does not reduce to zero as K increases. The period of oscillations in the strong variability regime [K < O(1000) m2 s−1] is relatively constant, with periods of O(20) yr. We finally note a drastic increase of the period to about 50 yr in the weak variability regime [K > O(1200) m2 s−1 and AMOC standard deviation O(0.1) Sv] for KGM = 550 m2 s−1.
c. The variability in terms of SST-based indices
The amplitude of the variability in terms of SST is usually estimated by computing the AMO index, which is defined as the detrended low-pass-filtered SST area-weighted average over the North Atlantic (0°–70°N) (Enfield et al. 2001). In the present case, coherent multicentennial variations are found in most of the simulations [see Sévellec et al. (2006) for a mechanistic understanding of intrinsic centennial modes in zonally averaged ocean models]. This long-term variability appears to be driven by North Atlantic SSS changes (not shown), similar to Delworth and Zeng (2012) realistic coupled model simulations. Its amplitude in terms of area-average SST sometimes exceeds its counterpart at the decadal time scale, in particular when approaching the Hopf bifurcation. By contrast to AMOC index spectra, AMO spectra tend to have a much stronger peak at centennial than at decadal time scales. A measure of the amplitude of the decadal variability in terms of SST is thus best obtained by applying a high-pass filter to the AMO index time series, with a cutoff frequency of 1/100 yr−1, leading to what we define as the AMV index. The correlation between the AMOC and the new AMV index typically increases by a factor of 2–3 compared to that obtained with the standard AMO index, with correlation r reaching 0.7–0.9 depending on the experiments, significant at the 95% confidence level. The peak-to-peak amplitude of the AMV index is 0.2°C (Figs. 2b,c) for KGM < 525 m2 s−1 and K < 1250 m2 s−1, which is smaller than the observed AMO index [0.3°–0.4°C, depending on the method used to remove the anthropogenic signal (Enfield et al. 2001; Knight 2009)]. This difference is presumably due to SST changes in the tropics that are absent in the model and are thought to be caused by thermal coupling between the ocean and the atmosphere (Xie 1999).
d. The period of the variability
The time scale of the variability (estimated from a multitaper spectral analysis of the basin mean kinetic energy density time series) near this bifurcation point appears to be nearly constant with a period of about 22 yr. This time scale is consistent with that found in the analyses of tide gauge records from around the North Atlantic (Frankcombe and Dijkstra 2009) and from the central England temperature record (Plaut et al. 1995). Similarly, a number of studies based on idealized models (Huck et al. 2001; Arzel et al. 2006, 2007), realistic ocean models (Arzel et al. 2012; Sévellec and Fedorov 2013; Ortega et al. 2015), and coupled models (Timmermann et al. 1998; Cheng et al. 2004; Dai et al. 2005; Dong and Sutton 2005; Danabasoglu 2008; Zhu and Jungclaus 2008) show an intrinsic variability in the 20–30-yr range. The period of the variability decreases down to about 10 yr for the smallest eddy-induced diffusivities used here, typically for KGM < 300 m2 s−1. Larger-amplitude oscillations are also associated with shorter periods and stronger circulation.
e. Impact of thermal damping
Adding thermal damping to the prescribed heat flux (with a time scale of 1 yr) displaces the domain of existence of oscillations toward slightly higher Peclet numbers, without significantly changing the bifurcation structure (Fig. 3a). The disappearance of the variability for 600 < KGM < 550 m2 s−1 suggests that e-folding times of perturbations near the bifurcation under flux boundary conditions is O(1) yr or less, an intuition that will be confirmed in section 5.
4. Description of variability
We describe here the spontaneous oscillations that arise under flux boundary conditions after the model has been spun up for thousands of years under restoring boundary conditions. Hot spots of intrinsic variability as measured by the standard deviation of annual mean SST occur at different locations, namely, in a large area centered at about 40°S in the southeastern Pacific with enhanced variance between southeastern Australia and New Zealand, in the core of the Leeuwin Current and its western extension off western Australia, in the western part of the North Atlantic Subpolar Gyre, and to a lesser extent in the tropical Pacific (Fig. 5). Intrinsic ocean modes in the southeastern Indian Ocean Basin and in the southeastern Pacific have been studied by Wolfe et al. (2017) and O’Kane et al. (2013), respectively, and we concentrate here on the North Atlantic.
Standard deviation (°C) of annual mean SST computed over years 1201–1400 for the reference experiment (flux boundary conditions with KGM = 550 m2 s−1 and K = 1000 m2 s−1). Contours of 0.5°, 1°, and 1.5°C are also shown for clarity. No time filtering was applied prior to the analysis. Applying a high-pass filter to remove the multicentennial variability leads to a very similar pattern.
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0884.1
a. Growth of perturbations and bidecadal oscillations
Figure 4 shows the time series of the AMOC index (computed as the maximum strength of the meridional overturning streamfunction below 1000 m and north of 30°N) for KGM varying from 500 to 575 m2 s−1. In all cases, the oscillations slowly grow around a circulation state that roughly corresponds to that obtained under restoring boundary conditions. This behavior suggests that the variability originates from a linear instability of the mean circulation obtained under restoring boundary conditions, similar to results deduced from idealized model studies (Fig. 1 in Arzel et al. 2006). For KGM = 500 and 525 m2 s−1 the small-amplitude oscillations initially experienced by the circulation for several hundred years are followed by an abrupt transition to a new limit cycle with much larger amplitude, as discussed previously. By contrast, the most diffusive model solutions (KGM ≥ 537.5 m2 s−1) presented here exhibit relatively small-amplitude oscillations with AMOC variations of O(1) Sv over the entire model integration duration (1400 yr). For KGM = 537.5 and 550 m2 s−1, multicentennial oscillations are clearly visible in the AMOC time series. These long time scales are present in all simulations and best seen in the averaged North Atlantic SST and SSS.
The time series in Fig. 4 also indicate that the closer the model state to the bifurcation (near KGM = 600 m2 s−1), the smaller the growth rate of oscillations and the longer the time needed for the circulation to settle into a statistically steady limit cycle. This behavior can be appreciated by computing the linear growth rate of oscillations over the growing phase of oscillations (Huck et al. 2001). This growing phase is defined as the time period during which the amplitude of oscillations in North Atlantic–averaged kinetic energy density increases with time. This period typically lasts between 200 and 1000 yr at the beginning of each experiment. The exponential growth of oscillations is deduced from the logarithm of the successive maxima of the North Atlantic–averaged kinetic energy density over this specific time period. This gives exponential growing times in the range of 80–200 yr for KGM varying from 537.5 to 575 m2 s−1, which have to be compared to critical damping terms: using a turbulent diffusivity of 1000 m2 s−1 and a horizontal scale for perturbations of 1000 km, one obtains a damping time scale of about 30 yr. The similarity of the growing and diffusive time scales indicates that the model solutions that are being analyzed (537.5 < KGM < 575 m2 s−1) are close to the bifurcation and that the existence of intrinsic oceanic variability under prescribed surface fluxes critically depends on lateral diffusion of tracer variance, in agreement with earlier idealized model studies. It should be noted that these exponential growing times are proportional to the oscillation period, and are therefore intrinsically very different from the e-folding times of perturbations that are on the order of 1 yr (section 5).
The amplitude of the decadal variations of the AMOC near the bifurcation (KGM > 525 m2 s−1) is relatively small, with peak-to-peak amplitude of O(1) Sv, which is sufficient to generate decadal SST anomalies on the order of 1°C in the western part of the North Atlantic Subpolar Gyre (Fig. 5). Associated sea surface height (SSH) anomalies are on the order of 10 cm (not shown), consistent with the magnitude of observed SSH changes during the past 20 years in the subpolar gyre (Häkkinen et al. 2013). This region of maximum variability holds for circulation states far from the bifurcation. However, for KGM < 525 m2 s−1, peak-to-peak AMOC fluctuations can reach 4–9 Sv.
b. The relative role of temperature and salinity
(a) Horizontally averaged temperature 
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0884.1
c. The spatial pattern of the variability
The dominant patterns of variability are determined here by performing an empirical orthogonal function (EOF) analysis of detrended annual mean SST over the North Atlantic region (from the equator to 80°N) and over years 1201–1400 of the reference experiment (Table 1). The dominant pattern of SST variability, explaining 67.3% of the spatially integrated variance, is characterized by a strong anomaly in the western subpolar gyre region and weaker anomaly of opposite sign in the east (Fig. 7a). The AMOC anomaly associated with this temperature pattern is characterized by a thermally direct circulation (Fig. 7c). The second EOF, which evolves in quadrature with the first one, explains 26.3% of the spatially integrated variance, so that most of the variability (93.6%) is captured by the first two EOFs. The amplitude of SST anomalies corresponding to the second EOF is weaker than those associated with the first one (Fig. 7b). The pattern is characterized by a large-scale anomaly extending throughout most of the subpolar gyre, and a smaller-scale anomaly of opposite sign in the Newfoundland Basin. The AMOC anomaly associated with this second EOF features a thermally indirect circulation in the upper 2500 m (south of 55°N) and a circulation of opposite sign below. At about 60°N, a positive streamfunction anomaly extends from the surface to the bottom, which might be related to stronger deep water formation resulting from colder than usual conditions at the surface in the Labrador Sea (Fig. 7b). The EOF time series shown in Fig. 7c indicate that the second EOF leads the first one by 5 yr, which corresponds to a fourth of an oscillation cycle. From this analysis we anticipate that the relatively weak SST anomaly present around 40°W, just south of the southern tip of Greenland in Fig. 7b, is amplified when propagating westward and reaches a maximum in the western part of the subpolar gyre five years later (Fig. 7a).
Dominant patterns of variability deduced from an EOF analysis of annual mean SST over years 1201–1400 of the reference experiment (KGM = 550 m2 s−1 and K = 1000 m2 s−1). Linear regressions of annual mean (a),(b) SST and (c),(d) overturning streamfunction onto the time series of the (a),(c) first and (b),(d) second EOF of annual mean SST multiplied by one standard deviation of these time series. The patterns thereby indicate SST (°C) and AMOC (Sv) anomalies associated with one standard deviation of the corresponding EOF. (e) The first two principal components of annual mean SST. The first (second) EOF explains 63.7% (25.5%) of the spatially integrated variance.
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0884.1
This analysis has been repeated for all experiments. No significant differences from what is presented in Fig. 7 was noticed for most experiments except that the fraction of the first two EOFs explaining the total integrated variance decreases with decreasing values of KGM (until 43.4% for KGM = 200 m2 s−1).
d. Propagation of surface-intensified temperature signals
Westward propagation of temperature anomalies in the first 1000 m or so are ubiquitous in idealized models (Chen and Ghil 1996; te Raa and Dijkstra 2002; Colin de Verdière and Huck 1999). This propagation has been attributed to long unstable baroclinic planetary waves. The zonal phase speed is generally difficult to rationalize because of the strong wave–mean flow interaction. In realistic coupled models, however, westward propagation is not the rule and a number of models exhibit eastward propagation instead (Muir and Fedorov 2017). These differences do not however necessarily imply that different mechanisms are at play: the source of the variability may well be the same and it may be simply the expression of the variability that differs. The latter point is intimately related to the mean flow structure that influences the propagation direction. In the present case, the characteristic phase diagram of SST anomalies in the longitude–time (x–t) plane (Fig. 8) shows a partition between the region west of the North Atlantic Current (centered at about 40°W at 50°N) where the temperature anomalies are large and propagate westward, and the region east of that position where the temperature anomalies are weak and propagate eastward. This pattern of propagation can also be inferred from the evolution of SST anomalies during an oscillation cycle in Fig. 9.
Longitude–time phase diagram of (detrendred) SST anomalies averaged between 45° and 55°N over years 1201–1300 of the reference experiment (KGM = 550 m2 s−1 and K = 1000 m2 s−1). West of 40°W, the average position of the NAC at 50°N, westward propagation of relatively large SST anomalies stands out. East of that area, weaker SST anomalies propagate eastward.
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0884.1
Evolution of SST anomalies (°C) during an oscillation cycle for the reference experiment (KGM = 550 m2 s−1 and K = 1000 m2 s−1).
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0884.1
The western anomalies take about 10 years (half an oscillation period) to travel from the western flank of the North Atlantic Current (NAC) to the western boundary, a time scale broadly consistent with the transit time of the first baroclinic Rossby mode, given by 
e. Energy source
Positive meridional eddy fluxes of buoyancy 
Terms responsible for the growth of buoyancy variance and eddy kinetic energy. (a) Vertically averaged creation of buoyancy variance 
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0884.1
f. Vertical structure of perturbations
In what follows we focus on the situation at 52°N, which corresponds to the latitude where westward propagation is the most apparent and instability of the mean flow is thought to occur. On the western flank of the NAC, the temperature and the meridional flow correlate positively (Fig. 11a). The meridional flow is to a high degree geostrophic at the (coarse) horizontal resolution used here so that the pressure field must reach an extrema east of the temperature extrema coinciding with 
(a) Eddy temperature fluxes 
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0884.1
g. Potential vorticity structure
To gain further insight into the mechanism responsible for the variability, we examine here the mean potential vorticity structure in the North Atlantic. The mean state is diagnosed from the RTRS reference experiment with KGM = 550 m2 s−1 and K = 1000 m2 s−1. Note that this state is nearly identical to that computed from the FTFS run since perturbations basically grow and evolve around the equilibrated state obtained at the end of the spinup phase (Fig. 4). We compute the large-scale potential vorticity (PV) Q = fN2, where f is the Coriolis parameter, and N2 is the buoyancy frequency. A necessary condition for baroclinic instability is that the meridional gradient Qy changes sign in the domain (Pedlosky 1987). We examine the possibility that this occurs in the subpolar gyre between 40° and 35°W, that is, within the longitude band where temperature anomalies are one-quarter phase-lagged on the vertical. The zonal section of Qy at our working latitude of 52°N confirms this expectation (Fig. 12a). The northward decrease of Q between the northern part of the subsurface subtropical ocean and the subpolar gyre is clearly apparent between 40° and 35°W at 52°N and 200-m depth (Fig. 12b). No reverse in the sign of Qy occurs at other locations at this specific latitude. Such a vertical structure (Qy > 0 in the upper ocean and Qy < 0 below) is associated with westerly sheared flows, as discussed by Tulloch et al. (2011). The depth of the sign reversal in Qy is also consistent with the vertical structure of perturbations that are strongly tilted at about 200-m depth (Fig. 11b). Although the condition that Qy changes sign in the domain is only a necessary condition for instability, this brief analysis gives further support to the idea that the interdecadal variability in the model is driven by a baroclinic instability of the North Atlantic Current at subpolar latitudes.
Meridional gradient of large-scale PV Qy (m−1 s−3) along a zonal cross section at (a) 52°N and (b) zonally averaged between 40° and 35°W in the North Atlantic. The dashed lines in (a) delineate the 40°–35°W area where the temperature anomalies are strongly tilted on the vertical (see Fig. 11b). Potential density contours (black solid, contour interval of 0.2 kg m−3) are superimposed.
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0884.1
5. Local linear stability analysis
The nonlinear model integrations described previously show that the subpolar circulation is spontaneously unstable on decadal time scales with horizontal scales much larger than the first deformation radius. Other regions in the North Atlantic remain remarkably quiescent (see also Sévellec and Fedorov 2013). In this section, we show that the region of maximum variance east of Newfoundland in our simulations can be predicted by a local linear stability analysis of the mean flow, similar to that of Smith (2007) at the eddy scale and Hochet et al. (2015) at the longwave limit. The local approximation represents of course a strong simplification to the full problem as emphasized by Tulloch et al. (2011). The approximation assumes in particular that at each location ocean properties are horizontally uniform. This is obviously not the case near continental margins such as western boundary currents for instance. Therefore, unstable modes emerging near continental boundaries will not be considered wherever their horizontal scale is larger than the distance separating them from the coast.
In the present case, we focus our attention on the unstable modes developing around the background state obtained in the reference RTRS experiment with KGM = 550 m2 s−1 and K = 1000 m2 s−1. Within this framework, perturbed velocities are at least an order of magnitude smaller than the mean flow (not shown), consistent with the result that this state lies at proximity of the (Hopf) bifurcation. The linear approximation used in the local stability analysis is therefore expected to be well suited to this specific experiment.
We use the quasigeostrophic (QG) scaling and restrict our attention to unstable modes with horizontal scales larger than 500 km to filter out instability at the mesoscale that is absent in our simulations. The QG scaling assumes that background velocities are horizontally nondivergent. This is not the case of surface Ekman flow. In addition, Ekman velocities near the surface generate very strong vertical shears leading to instabilities at scales much smaller than the first deformation radius, which are irrelevant for both the QG scaling and the present scales of interest. The Ekman flow will thus be discarded and the surface velocities are computed from geostrophy using annual mean SSH. The results from the local linear stability analysis are identical when the ageostrophic part is computed from the annual mean surface wind stress and is removed from the total surface flow (not shown).
Results of the linear stability analysis performed around the mean oceanic state obtained in the reference RTRS experiment with KGM = 550 m2 s−1 and K = 1000 m2 s−1. Only unstable vertical modes with horizontal scales larger than 500 km are considered. [Eddy viscosity and turbulent diffusivity are progressively added in the standard analysis when moving from (a) to (f).] Shown are the spatial distributions of growth rates ωi (yr−1) under various conditions: (a) adiabatic, (b) viscous with νh = 5 × 104 m2 s−1, (c) as in (b), but νυ = 10−4 m2 s−1 is added (same value as in the model), (d) as in (c), but with kh = 500 m2 s−1, (e) as in (d), but with a kυ following a Bryan–Lewis vertical profile (as in the model), and (f) as in (e), but with convective mixing acting in the March mixed layer diagnosed from the reference RTRS run. Note the different color scales in (e) and (f).
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0884.1
An estimation of the growth of baroclinic waves in the presence of viscosity can be obtained by assuming a balance between the lhs of (3a) and the viscous term on the rhs, leading to 
Adding vertical viscosity (Fig. 13c) has a negligible impact, consistent with 
Growth rate as a function of horizontal wavenumber at the specific location 47°N, 40°W in the western part of the subpolar gyre. The different curves correspond to different sets of mixing parameters: νh = 5 × 104 m2 s−1 (black line with dots), same but with kυ following a Bryan–Lewis vertical profile (black line), same but with convective mixing (black line with crosses), and same but with kh = 200 (blue), 500 (red), and 1000 m2 s−1 (green).
Citation: Journal of Climate 31, 16; 10.1175/JCLI-D-17-0884.1
The largest growths are found along the western boundary current with a typical horizontal scale of O(1000) km (not shown), which is much larger than the distance separating these modes from the coast. It is thus expected that side boundary effects will have a large influence. Since these effects have not been included in our calculations, these western boundary unstable modes become irrelevant. We are thus left with the only unstable region identified by the method, which lies in the western part of the subpolar gyre, just to the east of Newfoundland. This site roughly coincides with that where the variability peaks in the model. The growth of baroclinic waves is O(1) yr−1 with a horizontal scale of O(1000) km (Fig. 14).
6. Summary and discussion
The objective of this paper was to test the hypothesis that internal generation of interdecadal variability of the ocean circulation may be relevant to explain North Atlantic climate variability. This work is an extension of previous studies that identified a robust internal ocean mode in a hierarchy of idealized configurations and models. Here the robustness of this mode has been assessed in a realistic ocean model at 1° horizontal resolution under prescribed surface fluxes. Both the numerical experiments and the diagnostic tools were designed to unravel both the phenomenology and the origin of the variability. The dependence of the ocean mode upon turbulent eddy diffusivities (isopycnal mixing K and eddy-induced diffusivity KGM) was also explored.
The main result of this study is the robustness of the mechanism identified earlier in idealized box-ocean models forced by prescribed surface buoyancy fluxes (Colin de Verdière and Huck 1999; te Raa and Dijkstra 2002). The bifurcation structure of the variability, its spatial pattern, the temporal evolution of SST anomalies, and the energy sources and instability mechanism driving the variability are recovered here in a more realistic setting, showing the value of the idealized box-ocean models for inferring generic physical processes in the context of internal variability of the North Atlantic circulation.
The strength and existence of the internal variability in the model is sensitive to eddy-induced turbulent diffusivity KGM and isopycnal mixing K. The transition from steady solutions to oscillatory ones is shown to be consistent with a supercritical Hopf bifurcation with the eddy-induced Peclet number UL/KGM as the critical parameter. Such a behavior was recognized quite early in idealized ocean models forced by prescribed surface fluxes or coupled to energy-balanced models with the horizontal turbulent diffusivity and the inverse of the heat exchange coefficients as control parameters, respectively (Chen and Ghil 1996; Colin de Verdière and Huck 1999). In the present case, the variability disappears for KGM > 600 m2 s−1 (keeping K = 1000 m2 s−1). This critical value is much smaller than typical eddy-induced diffusivities used in realistic coupled models, suggesting that atmospheric stochastic forcing will be needed for these internal ocean modes to emerge.
The variability is caused by a linear instability of the mean circulation and stratification as evidenced by the evolution of the perturbations upon the switch from surface restoring to flux boundary conditions. The mechanism relies on a (large scale) baroclinic instability of the North Atlantic Current at subpolar latitudes, which radiates long baroclinic planetary waves that grow on the mean potential vorticity gradient. This view is supported by a local linear stability calculation including both viscous and diffusive effects that demonstrates the baroclinically unstable character of the NAC on horizontal scales of O(1000) km with growth rates of O(1) yr−1. Despite its inherent limitations, the results from the linear stability analysis appear in strikingly good agreement with the location of interdecadal perturbations when all the dissipative processes of the nonlinear model are taken into account.
Specific features include a westward propagation of relatively strong SST anomalies west of the NAC and a one-quarter phase lag between upper and subsurface (800 m) temperature anomalies in the unstable region. The same features have been inferred from observations (Feng and Dijkstra 2014; Frankcombe et al. 2008). Eastward propagation of weaker SST signals is obtained east of the NAC. Additional experiments including relatively strong surface restoring east of the NAC but not detailed in this study demonstrate that these eastward-propagating waves are not essential to the existence of the variability and can therefore be interpreted as a consequence rather than a cause of the variability. The horizontal structure of the mode is characterized by a dipole of SST anomalies in the subpolar area, with the first two EOFs explaining between 40% and 90% of the total integrated variance depending on turbulent eddy diffusivities. SST variability in the other parts of the North Atlantic is totally absent, including in the tropical area. This suggests that intrinsic ocean circulation variability does not participate to the observed AMO signature in this area. Instead, thermal coupling with the atmosphere must be invoked (Xie 1999). The period of the variability is O(20) yr at bifurcation and decreases down to O(10) yr for the smallest KGM used here. A number of observations based on different methods around the North Atlantic also underline the existence of such a bidecadal time scale (Plaut et al. 1995; Frankcombe and Dijkstra 2009; Chylek et al. 2011).
There are obvious drawbacks associated with the model configuration used in this study. The absence of mesoscale turbulence and the lack of a proper representation of ocean–atmosphere coupling are all factors that certainly participate to reduce the realism of the simulated North Atlantic circulation and variability. Perhaps the main shortcoming of the mean circulation concerns the mean path of the North Atlantic Current that is too far to the west compared to observations, a well-known problem in low-resolution OGCMs (Denng et al. 1996; Zhang and Vallis 2007). The pathway of the Gulf Stream and the NAC could eventually be made more realistic in such coarse-resolution ocean models when KGM becomes vertically dependent (Eden et al. 2009), as opposed to the Visbeck et al. (1997) formulation that assumes a vertically constant coefficient. The impact that this choice of the GM scheme might have on the variability remains to be studied. Corrections of the NAC in a coupled model increases the realism of the spatial pattern of the AMO (Drews and Greatbatch 2016). The region of maximum SST variability in their flux-corrected coupled simulations appears to be in the northwestern corner of the Atlantic basin, just to the east of Newfoundland, as in observations (Deser et al. 2010). Despite this bias, our model simulations also reveal maximum SST variance in this region, a central region where unstable long baroclinic planetary waves draw their energy from the mean flow.
At the coarse resolution used here, mesoscale eddies are parameterized rather than resolved. Huck et al. (2015) demonstrated than the basic mechanism driving the interdecadal variability under flux boundary conditions in idealized geometry ocean models is robust in the presence of mesoscale turbulence. In particular the coherence of the large-scale SST and SSH anomalies during their westward propagation and the O(20–30)-yr period are maintained from coarse to eddy-resolving simulations. The flux boundary conditions used here tend to maximize the growth rate of perturbations. This probably makes the amplitude of the variability larger than it would be if more realistic boundary conditions, including at least the damping effect of air–sea turbulent heat fluxes, were considered. We show that adding thermal damping with a time scale of 1 yr, typical of that deduced from energy-balance models (Vallis 2009), displaces the domain of existence of oscillations toward slightly higher Peclet numbers (lower KGM values), without significantly changing the bifurcation structure.
The intrinsic oceanic mode described here has also the same characteristics as the one obtained by Sévellec and Fedorov (2013). These authors used a linear tangent and adjoint technique to identify the least damped oceanic eigenmode in a realistic configuration of the OPA model at a lower 2° horizontal resolution. The major difference between the two studies is the self-sustained character of the oscillations found here as opposed to the damped character (over a 40-yr time scale) of interdecadal oscillations in Sévellec and Fedorov (2013). This mode may eventually be sustained in coupled simulations (Ortega et al. 2015; Muir and Fedorov 2017) but the precise role of the NAO, air–sea coupling, and the Nordic seas overflows is still uncertain (Delworth and Greatbatch 2000; Dai et al. 2005; Dong and Sutton 2005; Danabasoglu 2008; Danabasoglu et al. 2012; Tulloch and Marshall 2012; Kwon and Frankignoul 2012).
The internal oceanic mode presented here is robust across a hierarchy of ocean models and shares many similarities with observations, in particular the westward propagation and vertical phase lag of perturbations at subpolar latitudes (Frankcombe et al. 2008; Feng and Dijkstra 2014; Chylek et al. 2011). These similarities indicate that a leading role of the ocean for the AMO cannot be ruled out. This stresses the need for continued effort to improve understanding of intrinsic low-frequency ocean variability. Not considered in this study is the atmospheric stochastic forcing that has been recognized as a strong paradigm for low-frequency climate variability. This weather noise affects the behavior of the coupled system through both thermodynamical (Hasselmann 1976) and dynamical (Frankcombe and Dijkstra 2009) processes. This paper has shown that ocean dynamics alone is sufficient to reproduce the observed maximum of SST variance in the subpolar area. A natural question is, therefore, to ask how the ocean response to atmospheric stochastic forcing is affected by the presence of this internal oceanic mode, and in particular how it differs from the pure thermodynamical response of slab oceans put forward by Clement et al. (2015).
Acknowledgments
This study was supported by the CNRS French national program LEFE/INSU. We thank two anonymous reviewers for their comments and suggestions, which helped to improve the manuscript. Numerical computations were conducted using the Pôle de Calcul Intensif pour la Mer at Ifremer, Brest, France. We thank the MITgcm development group for making their model freely available.
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