1. Introduction
The Atlantic multidecadal oscillation (AMO) is a major mode of climate variability explaining nearly 40% of the spatially integrated annual-mean sea surface temperature (SST) variance over the North Atlantic (Delworth et al. 2007). The AMO does not only modulate the climate of the surrounding continents on decadal to multidecadal time scales (Zhang and Delworth 2006; Knight et al. 2006) but also directly impacts marine ecosystems (Edwards et al. 2013) and Arctic sea ice (Mahajan et al. 2011; Zhang 2015). Several physical mechanisms have been put forth to explain the origin of these low-frequency variations, but the diversity of those mechanisms does not allow us to provide a clear and robust picture as to which of the ocean or the atmosphere primarily drives the AMO and how it works. More specifically, modeling studies led to the emergence of (at least) two paradigms for the AMO: the first one is related to the integration of the atmospheric white noise by the ocean; the second one has dynamical origins and is related to intrinsic unstable interdecadal ocean modes. The two phenomena probably play a role in the low-frequency variability of the North Atlantic climate as suggested by a number of studies (Delworth et al. 1993; Delworth and Mann 2000; Dong and Sutton 2005; Gastineau et al. 2018), but their respective contributions in establishing the pattern and amplitude, and even in determining the very existence, of the AMO remain elusive and model dependent.
The simplest paradigm to explain low-frequency climate variability originates from the seminal work of Hasselmann (1976), who showed that the integration of atmospheric white noise by the ocean along with its large heat capacity gives rise to a reddened spectrum. This purely thermodynamic response has been invoked by Clement et al. (2015), who questioned the role of ocean circulation changes in the AMO by comparing results from fully coupled models and atmospheric general circulation models coupled to slab ocean models that do not permit circulation changes. The pattern of SST variability is remarkably similar between the two families of models, leading the authors to conclude that ocean circulation changes are not essential in determining both the pattern and existence of the AMO. Their analysis supports the null hypothesis that the ocean merely integrates the white noise atmospheric forcing of the North Atlantic Oscillation (NAO) to produce a red noise response. Similar conclusions were reached by Schneider and Fan (2007), who showed that the null hypothesis is appropriate over much of the World Ocean in the diagnosis of the SST variability in a coupled climate model. The lack of a distinct multidecadal spectral peak in models (at least in the multimodel mean) is in contrast with a number of observations including instrumental measurements (Tung and Zhou 2013), tree-ring records (Delworth and Mann 2000; Gray et al. 2004), ice-core records (Chylek et al. 2011), and multiproxy based reconstructions (Knudsen et al. 2011), that show enhanced variability in the 20–80-yr range in the Atlantic sector. Dommenget and Latif (2002) compared the statistics of large-scale SST variability in the midlatitudes of the Northern Hemisphere between different coupled models, slab ocean models and observations. In contrast to Clement et al. (2015), these authors concluded that the SST variability in the midlatitudes is significantly different from a red noise response and that processes in the ocean are responsible for these differences. Saravanan and McWilliams (1998) modified Hasselmann’s model to include steady mean oceanic advection and a spatially variable noise forcing. In contrast to Hasselmann (1976), a preferred time scale is selected by the circulation as long as advective effects dominate thermal damping effects associated with air–sea heat exchanges, leading to a phenomenon called spatial resonance.
The second paradigm relies on the large-scale baroclinic instability of the North Atlantic Current and subsequent westward propagation of unstable planetary waves leading to interdecadal (20–30 yr) oscillations of the Atlantic meridional overturning circulation (AMOC) (Colin de Verdière and Huck 1999; te Raa and Dijkstra 2002). Instability occurs at high Peclet numbers through a Hopf bifurcation. The growth rates at bifurcation
The aim of this paper is to investigate in a systematic manner the role played by intrinsic ocean modes in the variability of the Atlantic circulation of an ocean general circulation model subject to atmospheric stochastic forcing. A dynamical system approach is used whereby the characteristics and origins of the variability are systematically assessed against background oceanic conditions. Different background states are achieved by using different magnitudes of eddy-induced diffusivity, one of the most critical parameter at the relatively low resolution used here. This approach allows us to contrast different oscillatory regimes that have been previously identified in the literature, namely that driven by deterministic dynamics (self-sustained ocean mode) and that excited by atmospheric weather noise (damped ocean mode). Special emphasis will be placed upon the nature and origins of SST variability, which is the relevant field in the context of air–sea interactions. The paper seeks to address the following questions: What are the respective contributions of the NAO-like atmospheric stochastic forcing and large-scale baroclinic instability mechanism to the simulated North Atlantic SST and circulation variability? A central aspect is to determine how these contributions depend on background oceanic conditions. Does the spatial pattern of the variability, in particular in terms of horizontal propagation and vertical structure of temperature anomalies, obtained in the regime where the internal ocean mode is active, differ from that obtained in the damped regime? Are oceanic circulation changes fundamental to explain the properties (pattern, amplitude, and dominant time scale) of the low-frequency variability?
This paper is organized as follows. Section 2 describes the model and experimental design. The main characteristics of the variability along with its sensitivity to background oceanic conditions are presented in section 3. In section 4, the mechanisms responsible for the maintenance of the variability against all sources of thermal damping are identified and the associated energy sources are quantified. The role of ocean circulation changes is then investigated in section 5. Key findings are summarized and discussed in section 6.
2. Model and experiments
a. The ocean model
The model used for this study is the MITgcm (Marshall et al. 1997) in a configuration identical to that used by Arzel et al. (2018). The only difference lies in the surface heat and momentum fluxes that now include a stochastic part. The ocean model is run at 1° horizontal resolution and extends from 80°S to 80°N. There are 44 levels in the vertical with grid spacing increasing from 10 m at the surface to 250 m at the bottom. Static instability is removed by enhanced mixing (100 m2 s−1). The vertical diffusivity increases downward following Bryan and Lewis (1979) with upper and bottom values of 0.5 × 10−4 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 do not use any mixed layer turbulence parameterization. We use a spatially uniform horizontal Laplacian viscosity νh of 5 × 104 m2 s−1. The Gent–McWilliams (GM; Gent and McWilliams 1990) parameterization of mesoscale eddies is implemented along with the rotated eddy diffusion tensor for isopycnal mixing (Redi 1982). A parameter sensitivity analysis in terms of the eddy-induced turbulent diffusivity K is carried out (Table 1). The isopycnal mixing coefficient is set to 1000 m2 s−1 in all experiments. The equation of state is that proposed by Jackett and McDougall (1995), which computes the in situ density from potential temperature, practical salinity and Boussinesq hydrostatic pressure. Ocean bathymetry is taken from the historical ETOPO1 dataset (Amante and Eakins 2009) interpolated onto the model grid using a simple Gaussian filter with a width of 100 km. The model uses a climatological seasonal wind stress (Large and Yeager 2009) averaged over the years 1949–2006.
List of experiments. The low-frequency variability arising in the stochastic FTFS experiments is assessed against the value of the eddy-induced turbulent diffusivity K (m2 s−1) and in the presence or absence of stochastic wind stress forcing (noise heat flux forcing is always present). The role of circulation changes in North Atlantic SST variability is studied through the use of experiments with stochastic heat flux forcing only and prescribed oceanic circulation (details of the method given in section 5). The results obtained under stochastic forcing are also compared to those obtained by Arzel et al. (2018) under deterministic conditions (zero noise forcing).
b. Experimental design
We use flux boundary conditions at the surface for both temperature and salinity, similar to Arzel et al. (2018). The absence of feedback between sea surface salinity (SSS) and freshwater flux justifies the use of a flux formulation for salinity. The use of a flux formulation for temperature resides on the well-established result that on time scales much longer than the atmospheric response time, typically 10 days, atmospheric thermal damping of SST anomalies is relatively weak. Vallis (2009) estimates this damping time scale to be 4.4 years, 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; Arzel et al. 2018). Arzel et al. (2018) showed that the addition of a surface restoring flux with a damping time scale α−1 of one year has little influence on the characteristics of the interdecadal variability obtained under deterministic conditions (zero stochastic forcing). The main effect of thermal damping is to completely damp out the variability near bifurcation, consistent with baroclinic growth rates μ ~ α, providing a zero net growth of perturbations there. Away from bifurcation (i.e., toward higher Peclet numbers) μ ≫ α in agreement with the stronger circulation leading to a relatively minor impact of surface damping on the variability. On the basis of these results, we have chosen to use prescribed surface heat and freshwater fluxes in all numerical experiments.
The anomalies in (a) turbulent (sensible + latent) surface heat flux and (b) wind stress associated with a positive NAO phase. The patterns are obtained by regressing the annual-mean surface flux anomalies (1949–2006) from Large and Yeager (2009) onto the normalized station-based winter mean (DJFM) NAO index (Hurrell 1995) and multiplying the patterns by one standard deviation of the NAO index. Positive fluxes of the surface heat flux are directed out of the ocean.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
The anomalies in (a) turbulent (sensible + latent) surface heat flux and (b) wind stress associated with a positive NAO phase. The patterns are obtained by regressing the annual-mean surface flux anomalies (1949–2006) from Large and Yeager (2009) onto the normalized station-based winter mean (DJFM) NAO index (Hurrell 1995) and multiplying the patterns by one standard deviation of the NAO index. Positive fluxes of the surface heat flux are directed out of the ocean.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
The anomalies in (a) turbulent (sensible + latent) surface heat flux and (b) wind stress associated with a positive NAO phase. The patterns are obtained by regressing the annual-mean surface flux anomalies (1949–2006) from Large and Yeager (2009) onto the normalized station-based winter mean (DJFM) NAO index (Hurrell 1995) and multiplying the patterns by one standard deviation of the NAO index. Positive fluxes of the surface heat flux are directed out of the ocean.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
3. Results
a. AMOC variability
In all stochastically forced experiments, a pronounced decadal to multidecadal variability of the Atlantic Ocean circulation develops. This can be seen in the time series and power spectrum of the AMOC index in Fig. 2 for four different values of K (500, 800, 1200, and 1600 m2 s−1). The AMOC index used here is defined as the maximum value of the annual-mean meridional overturning streamfunction below 1000 m and north of 30°N in the North Atlantic. A clear distinction can be made between the AMOC variability obtained with K < 600 m2 s−1 from that obtained with K > 600 m2 s−1. As shown earlier by Arzel et al. (2018), the critical value K = Kc = 600 m2 s−1 corresponds to the existence of a threshold separating a supercritical regime (K < Kc) where the variability spontaneously emerges under deterministic conditions from a damped regime (K > Kc) where the oceanic variability does not emerge in the absence of any noise forcing. In the supercritical regime (K < Kc) the oscillations in the AMOC are large and appear quite regular, thereby producing a distinct spectral peak. In the damped regime (K > Kc), the oscillations have much weaker amplitude and appear less regular with a much broader spectrum.
(top) AMOC index (Sv; 1 Sv = 106 m3 s−1) time series for four different values of K covering both the supercritical and damped regimes. Experiments are carried out with stochastic heat flux forcing only (gray) and with the addition of a stochastic wind stress component (black). (bottom) Estimation of power spectra of the AMOC index time series with both stochastic heat and wind stress forcing applied. The calculation is based on a multitaper technique with 3 tapers. The smooth solid lines are the power of a red noise spectrum with the same AR1 coefficient as the data, and the dashed lines are the 95% confidence limits. The analysis is based on 1500 years of annual-mean model output.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
(top) AMOC index (Sv; 1 Sv = 106 m3 s−1) time series for four different values of K covering both the supercritical and damped regimes. Experiments are carried out with stochastic heat flux forcing only (gray) and with the addition of a stochastic wind stress component (black). (bottom) Estimation of power spectra of the AMOC index time series with both stochastic heat and wind stress forcing applied. The calculation is based on a multitaper technique with 3 tapers. The smooth solid lines are the power of a red noise spectrum with the same AR1 coefficient as the data, and the dashed lines are the 95% confidence limits. The analysis is based on 1500 years of annual-mean model output.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
(top) AMOC index (Sv; 1 Sv = 106 m3 s−1) time series for four different values of K covering both the supercritical and damped regimes. Experiments are carried out with stochastic heat flux forcing only (gray) and with the addition of a stochastic wind stress component (black). (bottom) Estimation of power spectra of the AMOC index time series with both stochastic heat and wind stress forcing applied. The calculation is based on a multitaper technique with 3 tapers. The smooth solid lines are the power of a red noise spectrum with the same AR1 coefficient as the data, and the dashed lines are the 95% confidence limits. The analysis is based on 1500 years of annual-mean model output.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
b. Patterns of temperature variability
Because density anomalies are dominated by temperature changes rather than salinity changes (not shown), we restrict the description that follows in terms of temperature only. Figure 3 shows the standard deviations of the annual-mean SST field as computed from 1000 years of model output from the FTFS experiments for the same four values of K as above. In all cases SST changes are maximum in the western subpolar gyre. Similarly to the AMOC variability (Fig. 2), a clear distinction can, however, be made between the patterns obtained with K < Kc from those obtained with K > Kc. For K < Kc, SST changes are large in the midlatitudes, typically between 40° and 60°N, and much weaker elsewhere. There is a significant drop in the amplitude of SST changes around K = Kc, in particular in the western subpolar region where the internal ocean mode has its largest fingerprint (Arzel et al. 2018). The amplitude of SST changes in the subtropics is in contrast nearly insensitive to K, suggesting that the variability is mostly constrained by the NAO forcing there. As a result, SST changes appear more uniform across the basin in the damped regime with similar amplitudes between the subpolar and subtropical regions.
Standard deviations of annual-mean SST anomalies in the stochastic (heat and wind stress) FTFS experiments for four different values of the eddy-induced diffusivity K. Note the different color scales between the supercritical (K < Kc) and damped (K > Kc) regimes. Long-term mean ocean currents averaged in the upper 250 m are superimposed. The calculation is based on 1000 years of model output.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Standard deviations of annual-mean SST anomalies in the stochastic (heat and wind stress) FTFS experiments for four different values of the eddy-induced diffusivity K. Note the different color scales between the supercritical (K < Kc) and damped (K > Kc) regimes. Long-term mean ocean currents averaged in the upper 250 m are superimposed. The calculation is based on 1000 years of model output.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Standard deviations of annual-mean SST anomalies in the stochastic (heat and wind stress) FTFS experiments for four different values of the eddy-induced diffusivity K. Note the different color scales between the supercritical (K < Kc) and damped (K > Kc) regimes. Long-term mean ocean currents averaged in the upper 250 m are superimposed. The calculation is based on 1000 years of model output.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
c. Propagation of SST anomalies
The time evolution of temperature anomalies in relation with the AMOC shows some striking differences between the damped and supercritical regimes. Figure 4 shows composites of SST anomalies as obtained for the same four values of K used above and for periods when the AMOC is maximum (AMOC index larger than the mean plus one standard deviation), when the AMOC anomaly is close to zero and decreasing, when the AMOC is minimum (AMOC index lower than the mean minus one standard deviation), and when the AMOC anomaly is close to zero and increasing.
Composites of SST anomalies and mean upper-ocean (250 m) currents associated with four phases of the AMOC under deterministic conditions for K = 500 m2 s−1 in the first row, and under stochastic forcing (heat and wind stress) for K = 500, 800, 1200, and 1600 m2 s−1 from the second to fifth rows. The AMOC is maximum in the first column, close to its mean value and decreasing in the second column, minimum in the third column, and close to its mean value and increasing in the fourth column. The corresponding AMOC time series have been discussed previously and shown in Fig. 2. Different color scales have been used between the supercritical and damped regimes because of the much lower amplitude of SST anomalies in the latter. The analysis is based of 1000 years of annual-mean model output.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Composites of SST anomalies and mean upper-ocean (250 m) currents associated with four phases of the AMOC under deterministic conditions for K = 500 m2 s−1 in the first row, and under stochastic forcing (heat and wind stress) for K = 500, 800, 1200, and 1600 m2 s−1 from the second to fifth rows. The AMOC is maximum in the first column, close to its mean value and decreasing in the second column, minimum in the third column, and close to its mean value and increasing in the fourth column. The corresponding AMOC time series have been discussed previously and shown in Fig. 2. Different color scales have been used between the supercritical and damped regimes because of the much lower amplitude of SST anomalies in the latter. The analysis is based of 1000 years of annual-mean model output.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Composites of SST anomalies and mean upper-ocean (250 m) currents associated with four phases of the AMOC under deterministic conditions for K = 500 m2 s−1 in the first row, and under stochastic forcing (heat and wind stress) for K = 500, 800, 1200, and 1600 m2 s−1 from the second to fifth rows. The AMOC is maximum in the first column, close to its mean value and decreasing in the second column, minimum in the third column, and close to its mean value and increasing in the fourth column. The corresponding AMOC time series have been discussed previously and shown in Fig. 2. Different color scales have been used between the supercritical and damped regimes because of the much lower amplitude of SST anomalies in the latter. The analysis is based of 1000 years of annual-mean model output.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
For K < Kc the large-scale propagation signals obtained under stochastic surface boundary conditions are almost undistinguishable from those obtained in the deterministic case. With the same ocean model and configuration, Arzel et al. (2018) shows that the interdecadal variability in the deterministic case is driven by a large-scale baroclinic instability of the North Atlantic Current (NAC). The strong resemblance between the deterministic and stochastic cases suggests that the same mechanism operate when a noise forcing is present. The effect of the noise forcing on the characteristics of the variability thus appears very limited in the supercritical regime, supporting the idea that the variability mostly originates from internal ocean processes rather than from the NAO forcing in this regime. The time evolution of SST anomalies can be described as follows. When the AMOC is at its maximum, a prominent SST dipole centered around the mean path of the NAC is present, with a warm anomaly in the east and a cold anomaly in the west, resulting in a stronger-than-usual NAC via thermal wind balance. As the AMOC decreases, the cold anomaly propagates westward until reaching the western boundary while the warm anomaly splits into two distinct parts on either side of the NAC, one propagating southeastward and the other westward. By the meantime, a cold anomaly has emerged along the NAC consistent with a reduced poleward heat transport during that period. As time proceeds, this cold anomaly grows up while the western warm anomaly barely evolves. At the AMOC minimum, the situation is exactly opposed to that obtained at the AMOC maximum with an eastern cold anomaly and a western warm anomaly. The subsequent evolution of SST anomalies is similar to that obtained during the decaying phase of the AMOC, but with opposite signs. Central to the existence of the oscillation is the reversal in the sign of the anomalous zonal pressure (temperature) gradient across the NAC. The overall sequence of events is typical of the variability found in idealized models forced by constant surface buoyancy fluxes where westward propagating unstable baroclinic planetary waves grow upon the mean circulation and stratification (Colin de Verdière and Huck 1999; te Raa and Dijkstra 2002).
In the damped regime (K > Kc), the effect of the NAO forcing becomes clearly apparent with the SST anomalies now circulating in a large portion of the North Atlantic from the western subtropical gyre to the midlatitudes. At midlatitudes, the resemblance with the time evolution of SST anomalies obtained for K < Kc is striking. Whether this implies that the SST variability draws its energy from the large-scale baroclinic instability mechanism, as obtained in the supercritical regime, remains to be determined, however, and this will be the subject of section 4. The oscillation cycle in this regime is similar to that described previously for K < Kc but now large-scale SST signals originating from the subtropics come into play. Subtropical SST anomalies are advected northeastward along the NAC from the Gulf Stream region to the eastern part of the basin at midlatitudes from where subsequent westward propagation occurs. This pattern of variability is similar to that reported by Eden and Jung (2001) and Eden and Greatbatch (2003) in ocean-only simulations either forced by realistic monthly mean surface fluxes associated with the NAO or coupled to a simple stochastic atmosphere model. The fact that similar patterns are obtained is consistent with the result that the internal oceanic variability is damped in Eden and Greatbatch (2003). It should be stressed that subtropical SST anomalies are also present for K < Kc under stochastic surface boundary conditions but their amplitude is much smaller than those present at midlatitudes so that their overall contribution to the North Atlantic SST variability is negligible.
d. Vertical structure of temperature anomalies
To provide further insight into the pattern of the variability, we examine here the vertical structure of temperature anomalies in the subpolar region. In all cases, temperature variability in the western subpolar region (30°–60°W, 40°–60°N) is surface intensified (Fig. 5a) and decreases with depth. In the damped regime (K > Kc), there is a sharp decrease of the temperature variability in the first 100 m and a weaker decrease below as revealed by the vertical derivatives of the standard deviations in the inset of Fig. 5a. This relatively strong surface attenuation of temperature changes is consistent with the theoretical vertical scale
Vertical structure of temperature anomalies in the stochastic (heat and wind stress) FTFS experiments. (top) Standard deviation of horizontally averaged temperature anomalies in the western subpolar area (30°–60°W, 40°–60°N). (bottom) First (thickness weighted) EOF of horizontally averaged temperature anomalies over the North Atlantic Current (50°–55°W, 25°–35°W). In average, the first EOF explains about 90% of the total variance in the supercritical regime and 74% in the damped regime. The light (dark) gray shading indicates the spread across the supercritical (damped) regime (centered over the mean profiles ± one standard deviation). The inset in the top panel shows the vertical derivative of standard deviations of temperature anomalies in the first 1000 m. The calculation is based on 1000 years of annual-mean model output.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Vertical structure of temperature anomalies in the stochastic (heat and wind stress) FTFS experiments. (top) Standard deviation of horizontally averaged temperature anomalies in the western subpolar area (30°–60°W, 40°–60°N). (bottom) First (thickness weighted) EOF of horizontally averaged temperature anomalies over the North Atlantic Current (50°–55°W, 25°–35°W). In average, the first EOF explains about 90% of the total variance in the supercritical regime and 74% in the damped regime. The light (dark) gray shading indicates the spread across the supercritical (damped) regime (centered over the mean profiles ± one standard deviation). The inset in the top panel shows the vertical derivative of standard deviations of temperature anomalies in the first 1000 m. The calculation is based on 1000 years of annual-mean model output.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Vertical structure of temperature anomalies in the stochastic (heat and wind stress) FTFS experiments. (top) Standard deviation of horizontally averaged temperature anomalies in the western subpolar area (30°–60°W, 40°–60°N). (bottom) First (thickness weighted) EOF of horizontally averaged temperature anomalies over the North Atlantic Current (50°–55°W, 25°–35°W). In average, the first EOF explains about 90% of the total variance in the supercritical regime and 74% in the damped regime. The light (dark) gray shading indicates the spread across the supercritical (damped) regime (centered over the mean profiles ± one standard deviation). The inset in the top panel shows the vertical derivative of standard deviations of temperature anomalies in the first 1000 m. The calculation is based on 1000 years of annual-mean model output.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
e. Oscillation period
The oscillation period is deduced from the frequency with maximum power in the multitaper spectrum of North Atlantic average kinetic energy density time series. A robust feature across all experiments is a consistent increase of the period with K (Fig. 6). The period typically increases from about 10–20 years in the supercritical regime to about 50 years for the most diffusive case. Those values are in the range of those inferred from a variety of direct observations and paleo-reconstructions (Gray et al. 2004; Chylek et al. 2011; Knudsen et al. 2011; Tung and Zhou 2013). The increase of the period with K appears consistent with the decrease of the (westward) phase speed of long baroclinic Rossby waves, given by
Dominant time scale of the variability as a function of the eddy diffusivity K in both the deterministic and stochastic cases. The period is computed from a multitaper spectral analysis of the North Atlantic average kinetic energy density time series.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Dominant time scale of the variability as a function of the eddy diffusivity K in both the deterministic and stochastic cases. The period is computed from a multitaper spectral analysis of the North Atlantic average kinetic energy density time series.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Dominant time scale of the variability as a function of the eddy diffusivity K in both the deterministic and stochastic cases. The period is computed from a multitaper spectral analysis of the North Atlantic average kinetic energy density time series.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
f. Bifurcation diagrams
Figure 7a shows that the mean AMOC strength is strongly impacted by K with a decrease of about 60% when the diffusivity increases from 200 to 1800 m2 s−1. This sensitivity was rationalized by Marshall et al. (2017) using scaling laws built upon the strong interplay between the AMOC changes, Southern Ocean upwelling and strength of the abyssal cell emanating from Antarctica. In addition to the weakening of the circulation, the North Atlantic Current tends to veer more eastward as K increases (Fig. 3). Because stronger vertical shears lead to larger growth rates of (large-scale) baroclinic instability, and because the stabilizing influence of β (the meridional gradient of planetary vorticity) is maximum in the zonal direction (Pedlosky 1987), the simulated changes in the circulation when K increases lead to a damping of the internal ocean mode. A critical threshold is indeed confirmed and clearly visible at K = Kc = 600 m2 s−1 for all quantities under deterministic conditions (Figs. 7b–d). This threshold has the nature of a supercritical Hopf bifurcation, where the amplitude of oscillations in the vicinity of the bifurcation increases with the square root of the distance from the bifurcation with the Peclet number as the control parameter (Colin de Verdière and Huck 1999; Arzel et al. 2018). For K > Kc, no variability emerges under deterministic conditions since baroclinic growth rates are too weak to overcome the large damping rates associated with eddy mixing rates: the internal ocean mode is damped in this regime. For a given value of K, the annual-mean AMOC strength in the RTRS experiments (where noise forcing is absent) is very close to that obtained in the FTFS runs. This shows that rectification of the long-term annual-mean flow strength by stochastic forcing does not occur in our model, or at least is of minor importance.
Statistics of key indices as a function of the eddy-induced diffusivity K under deterministic and stochastic boundary conditions and for cases with (open circles) and without stochastic surface wind stress forcing (open squares). (a) Mean strength of the AMOC (Sv) in the RTRS and stochastic FTFS experiments. The index is computed as the maximum value of the overturning streamfunction below 1000 m and north of 30°N in the North Atlantic. (b) Amplitude of North Atlantic kinetic energy density (J m−3) averaged in the upper 500 m and north of 20°N. (c) Amplitude of AMOC variations (Sv). (d) Amplitude of SST changes averaged in western subpolar area (30°–70°W, 40°–60°N). The amplitude of the variability in (b)–(d) has been estimated from a composite analysis of the last 1000 years of each experiment.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Statistics of key indices as a function of the eddy-induced diffusivity K under deterministic and stochastic boundary conditions and for cases with (open circles) and without stochastic surface wind stress forcing (open squares). (a) Mean strength of the AMOC (Sv) in the RTRS and stochastic FTFS experiments. The index is computed as the maximum value of the overturning streamfunction below 1000 m and north of 30°N in the North Atlantic. (b) Amplitude of North Atlantic kinetic energy density (J m−3) averaged in the upper 500 m and north of 20°N. (c) Amplitude of AMOC variations (Sv). (d) Amplitude of SST changes averaged in western subpolar area (30°–70°W, 40°–60°N). The amplitude of the variability in (b)–(d) has been estimated from a composite analysis of the last 1000 years of each experiment.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Statistics of key indices as a function of the eddy-induced diffusivity K under deterministic and stochastic boundary conditions and for cases with (open circles) and without stochastic surface wind stress forcing (open squares). (a) Mean strength of the AMOC (Sv) in the RTRS and stochastic FTFS experiments. The index is computed as the maximum value of the overturning streamfunction below 1000 m and north of 30°N in the North Atlantic. (b) Amplitude of North Atlantic kinetic energy density (J m−3) averaged in the upper 500 m and north of 20°N. (c) Amplitude of AMOC variations (Sv). (d) Amplitude of SST changes averaged in western subpolar area (30°–70°W, 40°–60°N). The amplitude of the variability in (b)–(d) has been estimated from a composite analysis of the last 1000 years of each experiment.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
The amplitude of the variability in the FTFS experiments is measured in terms of changes in North Atlantic kinetic energy density, AMOC strength, and western subpolar SST (the region where SST changes are maximum; Fig. 3) and is illustrated in Figs. 7b–d. In the supercritical regime, the effect of the noise forcing on the variability is relatively weak away from the bifurcation and strong near the bifurcation. In the damped regime, a low-frequency variability emerges unlike the deterministic case with peak-to-peak AMOC variations of 1–3 Sv (1 Sv ≡ 106 m3 s−1) depending on K and noise forcing characteristics. Interestingly, the amplitude of SST changes in the western subpolar gyre in this regime are relatively insensitive to eddy mixing rates unlike the amplitude of circulation changes that consistently decrease with increasing diffusivities. This behavior is at odds with the common understanding that the amplitudes of SST changes are positively correlated with the amplitude of circulation changes, as is the case in the supercritical regime, for instance. This suggests that subpolar SST changes become decoupled from the circulation anomalies in the damped regime, a hypothesis that will be further explored in section 5. Those bifurcation diagrams further show that the AMOC, SST and extratropical (north of 20°N) kinetic energy variability in the damped regime (K > 600 m2 s−1) are mainly driven by noise heat flux forcing (see also the AMOC time series in Fig. 2) in agreement with Delworth and Greatbatch (2000) with the stochastic wind component having a small amplifying effect.
4. Energy sources of the variability
To which physical process does the SST variability mostly owe its existence? Is it primarily related to atmospheric stochastic forcing or large-scale oceanic baroclinic instability or a combination of both? How do the energy sources associated with each of those two processes depend on the background state? The analysis of the SST patterns in the previous section provides a possible answer to these questions and suggests that the physical mechanism driving the SST variability is not the same across experiments: the NAO forcing is the leading process in the damped regime (K > Kc) whereas intrinsic ocean dynamics is dominant for K < Kc.
a. Method
We next take the spatial average (denoted by angle brackets below) of (1) over the western subpolar area (40°–60°N, 30°–70°W) where maximum SST changes consistently occur in all experiments. We define the quantities
b. Growth of sea surface temperature variance
Focusing first on the origin of the growth of SST variance, we see that Γ ≫ 1 in the supercritical regime whereas Γ ≪ 1 in the damped regime (Fig. 8a). This shows that the NAO forcing is the leading process for generating surface buoyancy (temperature) variance in the damped regime whereas internal ocean processes associated with large-scale baroclinic instability is the leading one in the supercritical regime. The decrease of Γ with K can only be explained by a reduction in SO (the internal generation of buoyancy variance in the ocean) since SA is nearly insensitive to the eddy diffusivity K (Figs. 8b and 9). The result that the covariance term
Buoyancy variance budget in the North Atlantic western subpolar region (40°–60°N, 30°–70°W) for cases with (denoted by “Heat+Wind” in the legend) and without (denoted by “Heat” in the legend) stochastic surface wind stress forcing, for (top) the surface and (bottom) the upper 1000 m. (a),(d) The ratios Γ = SO/SA and Λ = RO/SA (see text for the definitions) as a function of the eddy-induced diffusivity K. The stars in the supercritical regime compare the internal generation of buoyancy variance in the ocean under stochastic boundary conditions (denoted by
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Buoyancy variance budget in the North Atlantic western subpolar region (40°–60°N, 30°–70°W) for cases with (denoted by “Heat+Wind” in the legend) and without (denoted by “Heat” in the legend) stochastic surface wind stress forcing, for (top) the surface and (bottom) the upper 1000 m. (a),(d) The ratios Γ = SO/SA and Λ = RO/SA (see text for the definitions) as a function of the eddy-induced diffusivity K. The stars in the supercritical regime compare the internal generation of buoyancy variance in the ocean under stochastic boundary conditions (denoted by
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Buoyancy variance budget in the North Atlantic western subpolar region (40°–60°N, 30°–70°W) for cases with (denoted by “Heat+Wind” in the legend) and without (denoted by “Heat” in the legend) stochastic surface wind stress forcing, for (top) the surface and (bottom) the upper 1000 m. (a),(d) The ratios Γ = SO/SA and Λ = RO/SA (see text for the definitions) as a function of the eddy-induced diffusivity K. The stars in the supercritical regime compare the internal generation of buoyancy variance in the ocean under stochastic boundary conditions (denoted by
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Surface patterns of (top) atmospheric and (bottom) oceanic energy sources (×10−14 m2 s−5) for four different values of eddy diffusivity K covering both the supercritical and damped regimes, and for cases with both noise surface heat and momentum fluxes applied. The amplitude of
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Surface patterns of (top) atmospheric and (bottom) oceanic energy sources (×10−14 m2 s−5) for four different values of eddy diffusivity K covering both the supercritical and damped regimes, and for cases with both noise surface heat and momentum fluxes applied. The amplitude of
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Surface patterns of (top) atmospheric and (bottom) oceanic energy sources (×10−14 m2 s−5) for four different values of eddy diffusivity K covering both the supercritical and damped regimes, and for cases with both noise surface heat and momentum fluxes applied. The amplitude of
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
The same conclusions hold when focusing at a specific location in the western subpolar area. Figure 9 shows that the oceanic production term
We finally mention that SO is similar between the deterministic and stochastic cases in the supercritical regime (as indicated by stars in Fig. 8a) demonstrating the limited ability of the noise forcing to increase the creation of buoyancy variance by internal ocean dynamics in this regime. Advection of buoyancy variance by the mean circulation tends to extract surface buoyancy variance from the western subpolar gyre in the supercritical regime but deposits surface buoyancy variance in the damped regime (Fig. 8a). The amplitude of the terms RO and SO is similar in the damped regime (at least for some K values), but their combined effect still remains much smaller than the energy input associated with the NAO forcing.
c. Growth of UOHC variance
When the buoyancy variance budget is carried out over the upper 1000 m rather than over the forcing layer (10 m thick), the surface forcing contribution is reduced by a factor of 100. The oceanic energy source (Fig. 8e) is also reduced but much less, typically by a factor of ~4 in the supercritical regime and up to a factor of ~40 (~7) in the damped regime when stochastic wind stress forcing is present (absent). Consistently larger values of Γ are therefore obtained in this case whereas the sensitivity to K remains unchanged (Fig. 8d). The key here is that Γ becomes now larger than one over a large portion of the damped regime in contrast to what has been obtained previously for the surface buoyancy variance budget (where Γ ≪ 1). When averaged over the upper 1000 m, advection by the mean flow always extracts buoyancy variance from the western subpolar gyre (not shown) and thereby acts to reduce the growth of perturbations in this region. The analysis therefore demonstrates that fundamentally different mechanisms govern the SST and upper-ocean heat content (UOHC) variability in the damped regime: the NAO forcing is the leading process for maintaining SST variability whereas UOHC variability is mostly sustained by internal ocean dynamics.
d. Effect of a stochastic wind component
The presence of stochastic momentum fluxes does not alter the above conclusions but has nevertheless a substantial effect on the internal generation of buoyancy variance in the ocean. Its effect is strong in the damped regime and in particular near the surface and negligible in the supercritical regime. Figure 8b shows that the presence of a stochastic wind component increases the oceanic term SO at the surface by a factor ranging from O(1) at bifurcation to about 20 for the most diffusive case compared to experiments using only stochastic surface heat fluxes. The oceanic term SO results from the interaction of transient buoyancy fluxes and time-mean horizontal buoyancy gradients. These latter are very similar between the cases with and without stochastic wind forcing (not shown). As a result, the much stronger value of SO obtained when stochastic winds are present can only be caused by the much larger transient buoyancy fluxes. This feature is illustrated in Fig. 10 where the meridional contribution
(a),(b) Meridional transient buoyancy flux
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
(a),(b) Meridional transient buoyancy flux
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
(a),(b) Meridional transient buoyancy flux
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
With stochastic surface heat fluxes only, the NAO forcing explains about 90% [computed as the ratio SA/(SO + SA)] of the total production of surface buoyancy variance by the ocean and atmosphere in the damped regime (Fig. 8c). This ratio falls to about 65% in the presence of a stochastic wind component. Therefore, it is estimated that about one-third of the creation of SST variance by the ocean–atmosphere system can be directly ascribed to the noise excitation of damped ocean modes. Focusing on the creation of UOHC variance, the relative contribution of the atmosphere (Fig. 8f) is close to zero in the supercritical regime and increases with K in the damped regime. For K > 1300 m2 s−1 the dominant energy source for the UOHC variance switches from the atmosphere for noise heat flux forcing only to the ocean when both stochastic heat and wind stress forcing are applied. For smaller values of K the ocean provides the largest contribution in all cases.
5. The role of circulation changes
This section examines the role that ocean circulation changes have in determining the amplitude, pattern, and time scale of North Atlantic SST variability in the FTFS experiments.
In the supercritical regime (K < Kc), transient buoyancy fluxes associated with (westward) planetary wave propagation are at the heart of the existence of the variability: these fluxes are the process by which unstable waves extract energy from the mean flow to grow against all dissipative processes (Colin de Verdière and Huck 1999). It is therefore not surprising to see that in this regime circulation changes are central to the variability as we shall confirm below. In the damped regime (K > Kc), the buoyancy variance budget analysis shows that the NAO forcing is essential in maintaining the SST variability against all sources of dissipation. It is thus tempting in this case to expect circulation changes to be of minor importance, at least for determining both the amplitude and pattern of the SST variability.
To determine the role of ocean circulation changes in North Atlantic SST variability, we compare the reference experiments where the circulation is free to evolve to experiments with prescribed oceanic velocities from the climatological seasonal cycle diagnosed from the RTRS runs. In these experiments, the circulation is decoupled from the buoyancy field, which is thus passively advected by the seasonally varying prescribed circulation but can still respond to atmospheric stochastic forcing. The noise forcing includes only a heat component (Table 1). Adding a stochastic wind stress component in those experiments has no effect on the ocean circulation (which is prescribed by definition) and thereby on the oceanic tracer field. Figure 11 compares the amplitude of SST variations in the subpolar box (40°–60°N, 30°–70°W) between cases with and without circulation changes against the eddy diffusivity K. When the circulation is prescribed, the subpolar SST variance increases with eddy mixing rates: the larger the eddy diffusivity K, the slower the circulation and the larger the SST response consistent with the Hasselmann’s theory modified by the addition of steady mean oceanic advection (Saravanan and McWilliams 1998). In the supercritical regime, circulation changes substantially increase the subpolar SST variance compared to the case with prescribed oceanic currents. In the damped regime, a significant fraction (typically between 70% and 85%) of the subpolar SST variance obtained when both stochastic heat and wind stress forcing are present is captured by the pure thermodynamic response without circulation changes. As expected, the SST patterns strongly project onto the NAO forcing when the circulation is prescribed (Fig. 12), with the leading EOF explaining about 70% of the spatially integrated annual-mean SST variance. The comparison of the SST patterns between the prescribed and free circulation cases further indicates the minor (strong) impact of changes in ocean circulation on the leading pattern (Fig. 12) and amplitude of SST variability (Fig. 3 and right panels in Fig. 12) in the damped (supercritical) regime. We finally note that the pure thermodynamic response obtained with a prescribed circulation shows maximum SST variance in the western subpolar gyre. These SST changes add up to the internally generated SST changes that also reach their maximum in this area.
Impact of ocean circulation changes on the amplitude of SST changes in the western subpolar region (30°–70°W, 40°–60°N). The amplitude of the changes is estimated from a composite analysis of the last 1000 years of each experiment. The crossed thick line corresponds to the deterministic case. Black dots (open circles) correspond to the prescribed (free) circulation case with stochastic surface heat flux only. Open squares correspond to the free circulation case with stochastic surface heat and wind stress forcing.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Impact of ocean circulation changes on the amplitude of SST changes in the western subpolar region (30°–70°W, 40°–60°N). The amplitude of the changes is estimated from a composite analysis of the last 1000 years of each experiment. The crossed thick line corresponds to the deterministic case. Black dots (open circles) correspond to the prescribed (free) circulation case with stochastic surface heat flux only. Open squares correspond to the free circulation case with stochastic surface heat and wind stress forcing.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Impact of ocean circulation changes on the amplitude of SST changes in the western subpolar region (30°–70°W, 40°–60°N). The amplitude of the changes is estimated from a composite analysis of the last 1000 years of each experiment. The crossed thick line corresponds to the deterministic case. Black dots (open circles) correspond to the prescribed (free) circulation case with stochastic surface heat flux only. Open squares correspond to the free circulation case with stochastic surface heat and wind stress forcing.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Impact of circulation changes on SST patterns for two values of the eddy-induced diffusivity, namely (top) K = 500 m2 s−1 in the supercritical regime and (bottom) K = 1000 m2 s−1 in the damped regime. Shown is the leading (area-weighted) EOF of annual-mean SST anomalies obtained when the circulation is (left) free to evolve and (center) prescribed to a repeating seasonal cycle diagnosed from the RTRS runs. (right) The standard deviations of the SST field for the prescribed circulation case. The analysis is based on 1000 years of model output. The streamlines indicate the long-term mean upper-ocean (250 m) currents.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Impact of circulation changes on SST patterns for two values of the eddy-induced diffusivity, namely (top) K = 500 m2 s−1 in the supercritical regime and (bottom) K = 1000 m2 s−1 in the damped regime. Shown is the leading (area-weighted) EOF of annual-mean SST anomalies obtained when the circulation is (left) free to evolve and (center) prescribed to a repeating seasonal cycle diagnosed from the RTRS runs. (right) The standard deviations of the SST field for the prescribed circulation case. The analysis is based on 1000 years of model output. The streamlines indicate the long-term mean upper-ocean (250 m) currents.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Impact of circulation changes on SST patterns for two values of the eddy-induced diffusivity, namely (top) K = 500 m2 s−1 in the supercritical regime and (bottom) K = 1000 m2 s−1 in the damped regime. Shown is the leading (area-weighted) EOF of annual-mean SST anomalies obtained when the circulation is (left) free to evolve and (center) prescribed to a repeating seasonal cycle diagnosed from the RTRS runs. (right) The standard deviations of the SST field for the prescribed circulation case. The analysis is based on 1000 years of model output. The streamlines indicate the long-term mean upper-ocean (250 m) currents.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
We now investigate whether oceanic circulation changes are essential in setting the oscillation period. Figure 13 shows power spectra of western subpolar SST for three different values of K covering both the supercritical and damped regimes. In all cases changes in ocean circulation are essential to produce a preferred time scale in the system. The purely thermodynamic response obtained with a prescribed circulation is consistent with a red noise response, which demonstrates that the spatial resonance mechanism put forth by Saravanan and McWilliams (1998) does not operate in our simulations. The case with K = 1600 m2 s−1 and prescribed circulation (Fig. 13c) does indicate enhanced power in the 40–50-yr range, as in the free circulation case, but is not statistically significant. As discussed in section 3e, Fig. 13 clearly shows that the peak period increases with K in agreement with Fig. 6.
Power spectra of the western subpolar SST index, defined as the average of SST in the region (30°–70°W, 40°–60°N). Shown are the results obtained under stochastic heat and momentum fluxes for three different values of eddy-induced diffusivities K covering both the supercritical and damped regimes. The blue (red) lines correspond to cases where the circulation is free to evolve (prescribed). Estimation of power spectra is based on a multitaper technique with 3 tapers. The smooth solid lines are the power of a red noise spectrum with the same AR1 coefficient as the data, and the dashed lines are the 99% confidence limits. The analysis is based on 1000 years of model output without any temporal filtering.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Power spectra of the western subpolar SST index, defined as the average of SST in the region (30°–70°W, 40°–60°N). Shown are the results obtained under stochastic heat and momentum fluxes for three different values of eddy-induced diffusivities K covering both the supercritical and damped regimes. The blue (red) lines correspond to cases where the circulation is free to evolve (prescribed). Estimation of power spectra is based on a multitaper technique with 3 tapers. The smooth solid lines are the power of a red noise spectrum with the same AR1 coefficient as the data, and the dashed lines are the 99% confidence limits. The analysis is based on 1000 years of model output without any temporal filtering.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
Power spectra of the western subpolar SST index, defined as the average of SST in the region (30°–70°W, 40°–60°N). Shown are the results obtained under stochastic heat and momentum fluxes for three different values of eddy-induced diffusivities K covering both the supercritical and damped regimes. The blue (red) lines correspond to cases where the circulation is free to evolve (prescribed). Estimation of power spectra is based on a multitaper technique with 3 tapers. The smooth solid lines are the power of a red noise spectrum with the same AR1 coefficient as the data, and the dashed lines are the 99% confidence limits. The analysis is based on 1000 years of model output without any temporal filtering.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0522.1
6. Summary and discussion
Understanding the ocean’s response to atmospheric stochastic forcing requires us to separate explicitly the thermodynamic contribution from the dynamical one, the latter being associated with either self-sustained ocean modes or a noise excitation of damped ocean modes. This issue becomes fundamental when applied to the North Atlantic interdecadal climate variability problem, and more specifically to the Atlantic multidecadal oscillation (AMO) for which the precise roles of the ocean and atmosphere continue to be fiercely debated (Clement et al. 2015; Zhang et al. 2016; Cane et al. 2017; Zhang 2017). In this paper a method has been proposed to objectively determine the contribution of atmospheric stochastic forcing and internal ocean dynamics to the North Atlantic SST and circulation variability, in the limit of no feedback to the atmosphere. Numerical simulations of an ocean general circulation model have been carried out at a 1° horizontal resolution under prescribed surface fluxes including a climatological seasonal forcing and NAO-related stochastic surface fluxes. The analysis was carried out across a range of eddy-induced diffusivities that was chosen to be sufficiently large to explore the physics of two contrasting regimes: a supercritical regime where intrinsic oceanic variability spontaneously develops in the absence of any noise forcing and a damped regime where the oceanic variability requires some atmospheric noise to show up.
A buoyancy variance budget in the western subpolar region is used to objectively determine which of the ocean or atmosphere primarily sustains interdecadal oscillations against dissipation. Our results demonstrate that the fraction of the variability explained by the ocean and atmosphere is a strong function of background oceanic conditions. In the supercritical regime, intrinsic ocean dynamics is the determining factor for all aspects of the low-frequency variability with stochastic forcing having a relatively weak impact except near bifurcation, in agreement with Frankcombe and Dijkstra (2009). In the damped regime, the analysis provides evidence of a stochastic excitation of the intrinsic ocean mode. Despite this clear stochastic excitation, however, the maintenance of the SST variability in this regime is shown to be mostly caused by the NAO forcing. In contrast, upper-ocean heat content (0–1000 m) variability in the damped regime is mostly sustained by internal ocean dynamics. Caution must therefore be granted when interpreting low-frequency variability in terms of SST alone or upper-ocean heat content alone.
Stochastic wind stress forcing is shown to substantially increase the internal generation of buoyancy variance in the ocean. The effect is strong in the damped regime and near the surface and is shown to be caused by the much stronger transient buoyancy fluxes in relation with anomalous Ekman velocities in the western subpolar area. Without stochastic wind stress forcing the growth of surface buoyancy variance caused by atmospheric stochastic fluxes is between one and two orders of magnitude larger than its oceanic counterpart. With stochastic wind stress forcing, the atmospheric energy source is only about twice larger than the oceanic energy source. To put this another way, our results indicate that in the damped regime about 90% (65%) of the entire production of surface buoyancy variance is accomplished by the atmosphere when stochastic wind forcing is absent (present).
The transition from the self-sustained to the damped regime produces changes in the spatial structure of the variability that are consistent with baroclinic instability. In the supercritical regime, the SST signal is strong and intensified at midlatitudes and features a zonal dipolar structure centered around the mean path of the North Atlantic Current. In the damped regime, the SST pattern has a much broader latitudinal extent and features a basin-scale dipole extending from the western subtropical gyre to the subpolar area, in good agreement with the large-scale spatial pattern of the NAO forcing. Temperature anomalies in the supercritical regime are baroclinic with a clear westward phase shift with depth and are relatively deep. Temperature anomalies in the damped regime do not exhibit such a vertical structure and are concentrated in the thermocline. We further note that the SST variability be primarily stochastically forced (damped regime) or internally generated (supercritical regime) does not modify the region of peak SST variance, which is always found in the western part of the subpolar gyre.
Ocean circulation changes are shown to be unimportant for establishing the leading pattern of SST variability in the damped regime but are fundamental to select a preferred time scale in the system. Hence the spatial resonance mechanism (Saravanan and McWilliams 1998) does not occur in our simulations. The amplitude of the variability in the damped regime is to a large extent (from 70% to 85% depending on K and with stochastic wind stress forcing) imposed by the pure thermodynamic oceanic response to atmospheric stochastic forcing. In the supercritical regime by contrast, ocean circulation changes are central to all aspects of the variability, as expected. Clement et al. (2015) showed that ocean circulation changes are unimportant for establishing the pattern and amplitude of the North Atlantic low-frequency SST variability in fully coupled climate models. Clement et al. (2016) and Colfescu and Schneider (2017) further argue that changes in oceanic heat transport convergence plays a minor role on interdecadal time scales in coupled climate models. The present results suggest that this behavior is consistent with damped interdecadal internal ocean modes in fully coupled models with the NAO forcing providing the main energy source for the growth of SST variance.
The above model results reveal that a clear dichotomy exists in the characteristics and leading patterns of the variability between the supercritical and damped regimes, which is remarkably captured by a single dimensionless number Γ measuring the ratio between the oceanic and atmospheric energy sources, as inferred from the buoyancy variance budget of the western subpolar region. The abrupt change in Γ around the stochastic Hopf bifurcation (≫1 in the supercritical regime and ≫1 in the damped regime) strongly suggests that it is a very useful quantity to objectively separate the two regimes, at least in the limit of no feedback to the atmosphere. In any case, applying this diagnostic to coupled climate model configurations would be certainly very informative about the profound nature of the variability (either sustained by atmospheric noise or driven by deterministic dynamics), as for instance recently done by Gastineau et al. (2018). Addressing this issue using observations remains unfortunately very difficult if not impossible because of the too-short instrumental record compared to the time scales of the AMO and the too-low spatial coverage, in particular at depth.
Nevertheless the comparison of our model results with the statistics of the observed ocean temperature record can give some hints on the relative importance of the two mechanisms, stochastic forcing and internal ocean mode, and eventually tell if the real ocean belongs to either the supercritical or damped regime. First, the stochastic forcing is based on the actual amplitude of the atmospheric NAO forcing, so we can expect the amplitude of the oceanic response to be fairly well constrained. In contrast, the amplitude of the internal ocean mode critically depends on model parameters, here the strength of eddy diffusivity, that is not sufficiently constrained (and varying spatially) to infer the mode amplitude. The standard deviation of annual-mean SST in observations (detrended to get rid of the warming signal) is globally stronger than in the model for the damped regime. The peak amplitude, around 1°C, has a similar intensity and location, east of Newfoundland, around 50°N, 45°W, but the pattern is more widely spread over the whole subpolar gyre (the comparison in the subtropical region is probably not relevant because of the importance of air–sea coupling). The vertical structure of the temperature variability in the western subpolar gyre, based on annual anomalies of the World Ocean Atlas (Levitus et al. 2012) is also suggesting that the variability in the damped regime is too weak by a factor of 4. The characteristic sign change of temperature anomalies on the vertical in the supercritical regime is not seen in observations. However, observations extend only to 700 m, a depth close to that where the sign change is found in the model. On the other hand, EOFs of SST anomalies (taken from the HadISST dataset; Rayner et al. 2003) show a dipole pattern in the meridional direction more similar to the damped regime, whereas the internal ocean mode shows a dipole pattern in the zonal direction maximum around 50°N as was shown in Fig. 12. As a whole the comparison with observations is not fully conclusive and does not allow us to rule out any of the two candidate mechanisms. Very likely, the actual ocean regime is close to the bifurcation such that the internal ocean mode strengthens the response to stochastic forcing at the surface, and increases the variability in the thermocline. If the ocean mode is supercritical, its amplitude is probably similar to the oceanic response to stochastic forcing at the surface, as found in coupled model simulations by Gastineau et al. (2018).
Our experimental setup has several simplifying assumptions, the most critical one being the absence of air–sea coupling. First the effective damping rate of SST anomalies by air–sea fluxes is on the order of that associated with the large-scale baroclinic instability mechanism near bifurcation. It is thus expected that the bifurcation structure of interdecadal variability be preserved under coupling with the atmosphere with the transition between the two regimes occurring at slightly higher horizontal Peclet numbers (Arzel et al. 2018). Barsugli and Battisti (1998) showed that the effect of (local) ocean–atmosphere coupling is to reduce internal damping of temperature anomalies causing greater thermal variance in both the ocean and atmosphere compared to an uncoupled situation. Whether the same amplifying effect applies to the covariance terms of the buoyancy variance equation remains to be determined, since thermal coupling between the ocean and atmosphere does not only affect the variance of each quantity (in particular the oceanic temperature and oceanic currents), but also the correlation between these quantities.
The eddy-induced diffusivity K has been used here to place the ocean state into either the damped or supercritical regimes. The coefficient K was deliberately chosen to be spatially uniform. Observationally based studies show, however, that eddy mixing rates are highly variable in space (Liu et al. 2012; Abernathey and Marshall 2013) with values ranging from
Finally, our model configuration uses a relatively low spatial resolution and does not represent mesoscale eddies. These latter do not only impact the mean current positions but also strongly interact with the larger scales. Oceanic mesoscale turbulence can force strong interannual to decadal fluctuations of the AMOC (Le Roux et al. 2018) and induce an inverse cascade of kinetic energy toward the larger spatial scales and lower frequencies (Sérazin et al. 2018). Huck et al. (2015) investigated the nature of the multidecadal variability in the presence of eddy turbulence using an idealized ocean model configuration. Mesoscale eddies were shown to strongly rectify the mean circulation, but the generic mechanism driving the variability was found to be identical to that obtained at coarse resolution. In view of the buoyancy variance budget investigated in the present study, it remains to determine the impact that the oceanic mesoscale has on the internal generation of temperature variance at large scales and multidecadal periods.
Acknowledgments
We thank Edwin Schneider and two anonymous reviewers for valuable comments that helped to improve the manuscript. We also thank A. Colin de Verdière for comments on an early draft of this manuscript. This research was supported by the MesoVarClim project funded through the French CNRS/INSU/LEFE program. The authors acknowledge the Pôle de Calcul et de Données Marines (PCDM at Ifremer, Brest) for providing DATARMOR computational resources for the MITgcm simulations. We thank the MITgcm group for making the model publicly available.
REFERENCES
Abernathey, R. P., and J. Marshall, 2013: Global surface eddy diffusivities derived from satellite altimetry. J. Geophys. Res. Oceans, 118, 901–916, https://doi.org/10.1002/jgrc.20066.
Amante, C., and B. W. Eakins, 2009: ETOPO1 1 arc-minute global relief model: Procedures, data sources and analysis. NOAA Tech. Memo. NESDIS NGDC-24, 25 pp., https://www.ngdc.noaa.gov/mgg/global/relief/ETOPO1/docs/ETOPO1.pdf.
Antonov, J. I., and Coauthors, 2010: Salinity. Vol. 2, World Ocean Atlas 2009, NOAA Atlas NESDIS 69, 184 pp.
Arzel, O., and A. Colin de Verdière, 2016: Can we infer diapycnal mixing rates from the world ocean temperature–salinity distribution? J. Phys. Oceanogr., 46, 3751–3775, https://doi.org/10.1175/JPO-D-16-0152.1.
Arzel, O., T. Huck, and A. Colin de Verdière, 2006: The different nature of interdecadal variability of the thermohaline circulation under mixed and flux boundary conditions. J. Phys. Oceanogr., 36, 1703–1718, https://doi.org/10.1175/JPO2938.1.
Arzel, O., A. Colin de Verdière, and T. Huck, 2007: On the origin of interdecadal oscillations in a coupled ocean–atmosphere model. Tellus, 59A, 367–383, https://doi.org/10.1111/j.1600-0870.2007.00227.x.
Arzel, O., M. H. England, A. Colin de Verdière, and T. Huck, 2012: Abrupt millennial variability and interdecadal–interstadial oscillations in a global coupled model: Sensitivity to the background climate state. Climate Dyn., 39, 259–275, https://doi.org/10.1007/s00382-011-1117-y.
Arzel, O., T. Huck, and A. Colin de Verdière, 2018: The internal generation of the Atlantic Ocean interdecadal variability. J. Climate, 31, 6411–6432, https://doi.org/10.1175/JCLI-D-17-0884.1.
Barsugli, J. J., and D. S. Battisti, 1998: The basic effects of atmosphere–ocean thermal coupling on midlatitude variability. J. Atmos. Sci., 55, 477–493, https://doi.org/10.1175/1520-0469(1998)055<0477:TBEOAO>2.0.CO;2.
Bryan, F., 1987: Parameter sensitivity of primitive equation ocean general circulation models. J. Phys. Oceanogr., 17, 970–985, https://doi.org/10.1175/1520-0485(1987)017<0970:PSOPEO>2.0.CO;2.
Bryan, K., and L. Lewis, 1979: A water mass model of the world ocean. J. Geophys. Res., 84, 2503–2517, https://doi.org/10.1029/JC084iC05p02503.
Buckley, M. W., D. Ferreira, J.-M. Campin, J. Marshall, and R. Tulloch, 2012: On the relationship between decadal buoyancy anomalies and variability of the Atlantic meridional overturning circulation. J. Climate, 25, 8009–8030, https://doi.org/10.1175/JCLI-D-11-00505.1.
Cane, M. A., A. C. Clement, L. N. Murphy, and K. Bellomo, 2017: Low-pass filtering, heat flux, and Atlantic multidecadal variability. J. Climate, 30, 7529–7553, https://doi.org/10.1175/JCLI-D-16-0810.1.
Chen, H., E. K. Schneider, and Z. Wu, 2016: Mechanisms of internally generated decadal-to-multidecadal variability of SST in the Atlantic Ocean in a coupled GCM. Climate Dyn., 46, 1517–1546, https://doi.org/10.1007/s00382-015-2660-8.
Chylek, P., C. K. Folland, H. A. Dijkstra, G. Lesins, and M. K. Dubey, 2011: Ice-core data evidence for a prominent near 20 year time-scale of the Atlantic multidecadal oscillation. Geophys. Res. Lett., 38, L13704, https://doi.org/10.1029/2011GL047501.
Clement, A., K. Bellomo, L. N. Murphy, M. A. Cane, T. Mauritsen, G. Radel, and B. Stevens, 2015: The Atlantic multidecadal oscillation without a role for ocean circulation. Science, 350, 320–324, https://doi.org/10.1126/science.aab3980.
Clement, A., M. A. Cane, L. N. Murphy, K. Bellomo, T. Mauritsen, and B. Stevens, 2016: Response to comment on “The Atlantic multidecadal oscillation without a role for ocean circulation.” Science, 352, 1527, https://doi.org/10.1126/science.aaf2575.
Colfescu, I., and E. K. Schneider, 2017: Internal atmospheric noise characteristics in twentieth century coupled atmosphere–ocean model simulations. Climate Dyn., 49, 2205–2217, https://doi.org/10.1007/s00382-016-3440-9.
Colin de Verdière, A., and T. Huck, 1999: Baroclinic instability: An oceanic wavemaker for interdecadal variability. J. Phys. Oceanogr., 29, 893–910, https://doi.org/10.1175/1520-0485(1999)029<0893:BIAOWF>2.0.CO;2.
Delworth, T. L., and R. J. Greatbatch, 2000: Multidecadal thermohaline circulation variability excited by atmospheric surface flux forcing. J. Climate, 13, 1481–1495, https://doi.org/10.1175/1520-0442(2000)013<1481:MTCVDB>2.0.CO;2.
Delworth, T. L., and M. E. Mann, 2000: Observed and simulated multidecadal variability in the Northern Hemisphere. Climate Dyn., 16, 661–676, https://doi.org/10.1007/s003820000075.
Delworth, T. L., S. Manabe, and R. J. Stouffer, 1993: Interdecadal variations of the thermohaline circulation in a coupled ocean–atmosphere model. J. Climate, 6, 1993–2011, https://doi.org/10.1175/1520-0442(1993)006<1993:IVOTTC>2.0.CO;2.
Delworth, T. L., R. Zhang, and M. E. Mann, 2007: Decadal to centennial variability of the Atlantic from observations and models. Ocean Circulation: Mechanisms and Impacts—Past and Future Changes of Meridional Overturning. Geophys. Monogr., Vol. 173, Amer. Geophys. Union, 131–148.
Deser, C., M. A. Alexander, S.-P. Xie, and A. S. Phillips, 2010: Sea surface temperature variability: Patterns and mechanisms. Annu. Rev. Mar. Sci., 2, 115–143, https://doi.org/10.1146/annurev-marine-120408-151453.
Dommenget, D., and M. Latif, 2002: Analysis of observed and simulated SST spectra in the midlatitudes. Climate Dyn., 19, 277–288, https://doi.org/10.1007/s00382-002-0229-9.
Dong, B., and R. T. Sutton, 2005: Mechanism of interdecadal thermohaline circulation variability in a coupled ocean–atmosphere GCM. J. Climate, 18, 1117–1135, https://doi.org/10.1175/JCLI3328.1.
Eden, C., and T. Jung, 2001: North Atlantic interdecadal variability: Oceanic response to the North Atlantic Oscillation (1865–1997). J. Climate, 14, 676–691, https://doi.org/10.1175/1520-0442(2001)014<0676:NAIVOR>2.0.CO;2.
Eden, C., and R. J. Greatbatch, 2003: A damped decadal oscillation in the North Atlantic climate system. J. Climate, 16, 4043–4060, https://doi.org/10.1175/1520-0442(2003)016<4043:ADDOIT>2.0.CO;2.
Edwards, M., G. Beaugrand, P. Helaouët, J. Alheit, and S. Coombs, 2013: Marine ecosystem response to the Atlantic Multidecadal Oscillation. PLOS ONE, 8, e57212, https://doi.org/10.1371/journal.pone.0057212.
Feldstein, S. B., 2000: The timescale, power spectra, and climate noise properties of teleconnection patterns. J. Climate, 13, 4430–4440, https://doi.org/10.1175/1520-0442(2000)013<4430:TTPSAC>2.0.CO;2.
Frankcombe, L. M., and H. A. Dijkstra, 2009: Coherent multidecadal variability in North Atlantic sea level. Geophys. Res. Lett., 36, L15604, https://doi.org/10.1029/2009GL039455.
Frankcombe, L. M., H. A. Dijkstra, and A. V. D. Heydt, 2009: Noise-induced multidecadal variability in the North Atlantic: Excitation of normal modes. J. Phys. Oceanogr., 39, 220–233, https://doi.org/10.1175/2008JPO3951.1.
Gastineau, G., J. Mignot, O. Arzel, and T. Huck, 2018: North Atlantic Ocean internal decadal variability: Role of the mean state and ocean–atmosphere coupling. J. Geophys. Res., 123, 5949–5970, https://doi.org/10.1029/2018JC014074.
Gent, P. R., and J. C. McWilliams, 1990: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20, 150–155, https://doi.org/10.1175/1520-0485(1990)0200150:IMIOCM 2.0.CO;2.
Gray, S., L. Graumlich, J. Betancourt, and G. Pederson, 2004: A tree-ring based reconstruction of the Atlantic Multidecadal Oscillation since 1567 AD. Geophys. Res. Lett., 31, L12205, https://doi.org/10.1029/2004GL019932.
Hasselmann, K., 1976: Stochastic climate models. Part I: Theory. Tellus, 28, 473–484, https://doi.org/10.3402/tellusa.v28i6.11316.
Herbaut, C., J. Sirven, and S. Fevrier, 2002: Response of a simplified oceanic general circulation model to idealized NAO-like stochastic forcing. J. Phys. Oceanogr., 32, 3182–3192, https://doi.org/10.1175/1520-0485(2002)032<3182:ROASOG>2.0.CO;2.
Huck, T., and G. K. Vallis, 2001: Linear stability analysis of the three dimensional thermally-driven ocean circulation: Application to interdecadal oscillations. Tellus, 53A, 526–545, https://doi.org/10.3402/tellusa.v53i4.12225.
Huck, T., G. K. Vallis, and A. Colin de Verdière, 2001: On the robustness of the interdecadal modes of the thermohaline circulation. J. Climate, 14, 940–963, https://doi.org/10.1175/1520-0442(2001)014<0940:OTROTI>2.0.CO;2.
Huck, T., O. Arzel, and F. Sévellec, 2015: Multidecadal variability of the overturning circulation in presence of eddy turbulence. J. Phys. Oceanogr., 45, 157–173, https://doi.org/10.1175/JPO-D-14-0114.1.
Hurrell, J. W., 1995: Decadal trends in the North Atlantic Oscillation—Regional temperatures and precipitation. Science, 269, 676–679, https://doi.org/10.1126/science.269.5224.676.
Jackett, D. R., and T. J. McDougall, 1995: Minimal adjustment of hydrographic profiles to achieve static stability. J. Atmos. Oceanic Technol., 12, 381–389, https://doi.org/10.1175/1520-0426(1995)012<0381:MAOHPT>2.0.CO;2.
Jamet, Q., T. Huck, A. Colin de Verdière, O. Arzel, and J.-M. Campin, 2016: Oceanic control of multidecadal variability in an idealized coupled GCM. Climate Dyn., 46, 3079–3095, https://doi.org/10.1007/s00382-015-2754-3.
Knight, J. R., C. K. Folland, and A. A. Scaife, 2006: Climate impacts of the Atlantic multidecadal oscillation. Geophys. Res. Lett., 33, L17706, https://doi.org/10.1029/2006GL026242.
Knudsen, M. F., M. S. Seidenkrantz, B. H. Jacobsen, and A. Kuijpers, 2011: Tracking the Atlantic multidecadal oscillation through the last 8,000 years. Nat. Commun., 2, 178, https://doi.org/10.1038/NCOMMS1186.
Kuhlbrodt, T., R. S. Smith, Z. Wang, and J. M. Gregory, 2012: The influence of eddy parameterizations on the transport of the Antarctic Circumpolar Current in coupled climate models. Ocean Modell., 52–53, 1–8, https://doi.org/10.1016/j.ocemod.2012.04.006.
Large, W. G., and S. G. Yeager, 2009: The global climatology of an interannually varying air–sea flux data set. Climate Dyn., 33, 341–364, https://doi.org/10.1007/s00382-008-0441-3.
Le Roux, S., T. Penduff, L. Bessière, J.-M. Molines, J.-M. Brankart, G. Sérazin, B. Barnier, and L. Terray, 2018: Intrinsic and atmospherically forced variability of the AMOC: Insights from a large-ensemble ocean hindcast. J. Climate, 31, 1183–1203, https://doi.org/10.1175/JCLI-D-17-0168.1.
Levitus, S., and Coauthors, 2012: World ocean heat content and thermosteric sea level change (0–2000 m), 1955–2010. Geophys. Res. Lett., 39, L10603, https://doi.org/10.1029/2012GL051106.
Liu, C., A. Köhl, and D. Stammer, 2012: Adjoint-based estimation of eddy-induced tracer mixing parameters in the global ocean. J. Phys. Oceanogr., 42, 1186–1206, https://doi.org/10.1175/JPO-D-11-0162.1.
Locarnini, R. A., A. V. Mishonov, J. I. Antonov, T. P. Boyer, H. E. Garcia, O. K. Baranova, M. M. Zweng, and D. R. Johnson, 2010: Temperature. Vol. 1, World Ocean Atlas 2009, NOAA Atlas NESDIS 68, 184 pp.
Lumpkin, R., and K. Speer, 2007: Global ocean meridional overturning. J. Phys. Oceanogr., 37, 2550–2562, https://doi.org/10.1175/JPO3130.1.
Mahajan, S., R. Zhang, and T. L. Delworth, 2011: Impact of the Atlantic meridional overturning circulation (AMOC) on Arctic surface air temperature and sea ice variability. J. Climate, 24, 6573–6581, https://doi.org/10.1175/2011JCLI4002.1.
Marshall, J., C. Hill, L. Perelman, and A. Adcroft, 1997: A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. J. Geophys. Res., 102, 5753–5766, https://doi.org/10.1029/96JC02775.
Marshall, J., J. R. Scott, A. Romanou, M. Kelley, and A. Leboissetier, 2017: The dependence of the ocean’s MOC on mesoscale eddy diffusivities: A model study. Ocean Modell., 111, 1–8, https://doi.org/10.1016/j.ocemod.2017.01.001.
Pedlosky, J., 1987: Geophysical Fluid Dynamics. 2nd ed. Springer-Verlag, 710 pp.
Rayner, N. A., D. E. Parker, E. B. Horton, C. K. Folland, L. V. Alexander, D. P. Rowell, E. C. Kent, and A. Kaplan, 2003: Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century. J. Geophys. Res., 108, 4407, https://doi.org/10.1029/2002JD002670.
Redi, M. H., 1982: Oceanic isopycnal mixing by coordinate rotation. J. Phys. Oceanogr., 12, 1154–1158, https://doi.org/10.1175/1520-0485(1982)012<1154:OIMBCR>2.0.CO;2.
Saravanan, R., and J. C. McWilliams, 1998: Advective ocean–atmosphere interaction: An analytical stochastic model with implications for decadal variability. J. Climate, 11, 165–188, https://doi.org/10.1175/1520-0442(1998)011<0165:AOAIAA>2.0.CO;2.
Schneider, E. K., and M. Fan, 2007: Weather noise forcing of surface climate variability. J. Atmos. Sci., 64, 3265–3280, https://doi.org/10.1175/JAS4026.1.
Sérazin, G., T. Penduff, B. Barnier, J.-M. Molines, B. Arbic, M. Muller, and L. Terray, 2018: Inverse cascades of kinetic energy as a source of intrinsic variability: A global OGCM study. J. Phys. Oceanogr., 48, 1385–1408, https://doi.org/10.1175/JPO-D-17-0136.1.
te Raa, L. A., and H. A. Dijkstra, 2002: Instability of the thermohaline circulation on interdecadal timescales. J. Phys. Oceanogr., 32, 138–160, https://doi.org/10.1175/1520-0485(2002)032<0138:IOTTOC>2.0.CO;2.
Tung, K.-K., and J. Zhou, 2013: Using data to attribute episodes of warming and cooling in instrumental records. Proc. Natl. Acad. Sci. USA, 110, 2058–2063, https://doi.org/10.1073/pnas.1212471110.
Vallis, G. K., 2009: Mechanisms of climate variability from years to decades. Stochastic Physics and Climate Modelling, T. Palmer and P. Williams, Eds., Cambridge University Press, 1–33.
Visbeck, M., J. Marshall, and T. Haine, 1997: Specification of eddy transfer coefficients in coarse-resolution ocean circulation models. J. Phys. Oceanogr., 27, 381–402, https://doi.org/10.1175/1520-0485(1997)027<0381:SOETCI>2.0.CO;2.
Waterhouse, A. F., and Coauthors, 2014: Global patterns of diapycnal mixing from measurements of the turbulent dissipation rate. J. Phys. Oceanogr., 44, 1854–1872, https://doi.org/10.1175/JPO-D-13-0104.1.
Zhang, R., 2015: Mechanisms for low-frequency variability of summer Arctic sea ice extent. Proc. Natl. Acad. Sci. USA, 112, 4570–4575, https://doi.org/10.1073/pnas.1422296112.
Zhang, R., 2017: On the persistence and coherence of subpolar sea surface temperature and salinity anomalies associated with the Atlantic multidecadal oscillation. Geophys. Res. Lett., 44, 342, https://doi.org/10.1002/2017GL074342.
Zhang, R., and T. Delworth, 2006: Impact of Atlantic Multidecadal Oscillation on India/Sahel rainfall and Atlantic hurricanes. Geophys. Res. Lett., 33, L17712, https://doi.org/10.1029/2006GL026267.
Zhang, R., R. Sutton, G. Danabasoglu, T. L. Delworth, W. M. Kim, J. Robson, and S. G. Yeager, 2016: Comment on “The Atlantic multidecadal oscillation without a role for ocean circulation.” Science, 352, 1527, https://doi.org/10.1126/science.aaf1660.
Zhu, X., and J. Jungclaus, 2008: Interdecadal variability of the meridional overturning circulation as an ocean internal mode. Climate Dyn., 31, 731–741, https://doi.org/10.1007/s00382-008-0383-9.