a. Heat transport in the Hadley Centre climate model

We used data from a preindustrial control run of HadCM3 from the archive of model output of the Intergovernmental Panel on Climate Change (IPCC). The choice for this state-of-the-art model was made because it has a realistic description of the Atlantic meridional overturning component (see below), which is important for a realistic description of Bjerknes compensation. Furthermore, it allows for a straight elaboration on the work from Shaffrey and Sutton (2006) who used the same model. In HadCM3 the atmospheric component has a resolution of 15 levels in the vertical and 2.5° latitude × 3.75° longitude, whereas the ocean component has a resolution of 20 levels in the vertical and 1.25° latitude × 1.25° longitude. The preindustrial control run we use consists of a total of 341 yr. We use a different run for our analysis than Shaffrey and Sutton (2006), who used a preindustrial control run of 93 decades, which is not available via the model output of the IPCC. The model simulates a maximum of 3.8 PW for the mean atmospheric heat transport in the Northern Hemisphere compared to values of ∼4.5 PW [European Centre for Medium-Range Weather Forecasts (ECMWF)] and ∼5.2 PW [National Centers for Environmental Prediction (NCEP)] given by Trenberth and Caron (2001). The maximum mean oceanic heat transport equals 1.4 PW in our model compared to ∼1.6 PW (ECMWF) and ∼2.1 PW (NCEP) from Trenberth and Caron (2001). The sea ice model in HadCM3 uses a simple thermodynamic scheme and behaves stable and realistic. The resolution of the HadCM3 model allows one to represent the channels in the Greenland–Iceland–Scotland (GIS) ridge, which is important to diagnose the formation and transport of North Atlantic Deep Water. Wood et al. (1999) have shown that the mean flow for the GIS ridge is 8.5 Sv (1 Sv ≡ 10⁶ m³ s⁻¹) in the HadCM3 model, which is a bit higher than the observed estimate of 5.6 Sv. The strength of the meridional overturning circulation is stable and the model flow is 17.4 Sv at 24°N, which compares well with the observational estimate of 16–20 Sv (see, e.g., Talley et al. 2003; Bryden et al. 2005). There is a significant multidecadal variability, with an amplitude of 1–2 Sv, in the maximum Atlantic MOC and the model gives a reasonable quantitative simulation of the North Atlantic Deep Water. Further technical details of the HadCM3 model can be found in Gordon et al. (2000) and Wood et al. (1999).

We have calculated the global heat transport through the atmosphere H_atm following Shaffrey and Sutton (2006), by integrating the sum of the divergence of the zonally integrated surface flux from the ocean into the atmosphere F_sfc, and the energy flux coming in as radiation at the TOA F_toa. The global ocean heat transport H_ocn is obtained by integrating the divergence of the zonally integrated surface flux from the atmosphere into the ocean −F_sfc, minus the time derivative of the oceanic heat content Q̇_ocn. Mathematically, we solve H_atm and H_ocn from the two equations below:

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where a denotes the radius of the earth, θ is latitude, and ϕ is longitude. The integrand of both equations integrated over latitude from 90°S to 90°N yields a nonzero value. This arises because our method is based on calculating heat transport from fluxes rather than from the heat transport divergences, in which case model drift yields a residual. We correct for this by adding an area-dependent residual to the above set of equations such that calculating the above integrand again, we obtain exactly zero. The above procedure is carried out for each year independently. Furthermore, the calculated values for the heat transport are linearly detrended.

b. Bjerknes compensation

Our dataset consists of 341 samples of the annual mean of the atmospheric and oceanic heat transports as a function of latitude. The anomalies of these heat transports are expected to show Bjerknes compensation on decadal time scales, because at these time scales the TOA radiation flux and the heat storage of the ocean do not show large variations with respect to the variations in the heat fluxes of the atmosphere and the ocean (see, e.g., Bjerknes 1964; Shaffrey and Sutton 2006).

Throughout this paper we will apply a 15-yr running mean average to both components to emphasize decadal time scales. We take running mean averages of 15 yr, because the deviation from unity of this filter occurs at decades. To demonstrate Bjerknes compensation, we calculate the correlation coefficients between the atmospheric and oceanic heat transports as a function of latitude in the Northern Hemisphere. Figure 1a shows the result of these calculations. The atmospheric and oceanic heat transports are anticorrelated at most latitudes. The highest anticorrelation occurs close to 70°N and is −0.84. The anticorrelation between the atmospheric and oceanic heat transports shown at decadal time scales also occurs at annual time scales, but with significantly lower anticorrelation coefficients. This difference is indicating the validity of the assumptions made at the beginning of this section that Bjerknes compensation is operating at decadal time scales rather then at annual time scales. The apparent low compensation rate at annual time scales was already extensively discussed by Shaffrey and Sutton (2004).

Although these correlations give a qualitative indication for Bjerknes compensation, they do not yield a quantitative measurement. Therefore, we use the following recipe to define a compensation rate CR expressed in percentages, which will be applied to the 15-yr running mean samples of the atmospheric and oceanic heat transports. We define

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The notation above is such that dH denotes the anomaly of the considered heat transport with respect to the mean value of all 341 samples for each latitude. Figure 1b shows the resulting compensation rate averaged over all 341 heat transport estimates with a running mean of 15 yr and weighted with the amplitude of the anomalies. One can see that a maximum compensation rate of 55% is obtained at a latitude of 70°N for the samples with a running mean of 15 yr. The other line in this panel shows the compensation rate for the annual heat transport estimates. Comparing these two curves, one can clearly see that a significant increase in Bjerknes compensation occurs between 50° and 80°N by going from annual to decadal time scales.

We elucidate the above results by performing a linear regression of the divergence of the atmospheric heat transport [term on the left-hand side of Eq. (1)] onto the flux at the atmosphere–ocean interface and onto the flux at the top of the atmosphere [both terms are on the right-hand side of Eq. (1)]. The resulting regression coefficients are shown in Fig. 2a. Similarly we perform a linear regression of the divergence of the oceanic heat transport onto the flux at the atmosphere–ocean interface and onto the time derivative of the ocean heat storage. The resulting regression coefficients are shown in Fig. 2b. The two panels in Fig. 2 show that we observe a strong compensation mechanism between 60° and 80°N. It should be noted that the variations at the top of the atmosphere have an overall negligible influence on the heat budget. However, the ocean heat storage still has a significant influence on the heat budget outside of the region between 60° and 80°N.

Figure 3 is an extension of Fig. 1a by showing correlation coefficients between the atmospheric and oceanic heat transport anomalies on decadal time scales at different lags in time. The time axis is such that positive (negative) times indicate that the ocean (atmosphere) leads. The anticorrelation rate in Fig. 3 is highest at 70°N when the ocean leads the atmosphere by 1 yr. In the rest of this paper we take this lead time of 1 yr as a reference value. We note, however, that the distribution of correlation rates shown in Fig. 3 are rather smooth around 70°N and that with the decadal averaging we applied, differences in lead times of the order of a few years are sometimes hard to distinguish. Furthermore, one can see clearly that for latitudes lower than 60°N, the highest anticorrelation coefficients are obtained when the atmosphere leads the ocean.

The fact that the atmosphere is leading the ocean at midlatitudes is probably related to the mechanism described by Dong and Sutton (2005, see their Fig. 12). They describe the interdecadal variability of the Atlantic MOC and suggest that the latter is stimulated by direct forcing of the atmosphere, via the NAO. Furthermore they show that although the forcing of the MOC variations is through an NAO-related wind stress curl and heat flux anomalies, the time scale of these variations is set by the oceanic circulation. These authors find a typical time scale of ∼9 yr between forcing from the atmosphere and the subsequent response of the ocean, which is of the same order of magnitude as the lead time for which maximum correlation between atmosphere and ocean heat transports occurs from 40° to 60°N (Fig. 3). Note that their work was based on data analysis from a preindustrial control run of 1000 yr, with the same coupled atmosphere–ocean model as we consider here, that is, HadCM3.

We analyzed the connection between the atmospheric and oceanic heat transports and the NAO by calculating correlation coefficients. Figure 4a is consistent with Eden and Willebrand (2001), who show that there is a positive correlation between the NAO index and the ocean heat transport at 48°N (see their Fig. 3). Figure 4a shows a time scale of 10 yr at midlatitudes for the delay between the actual forcing from the atmosphere via the NAO and the subsequent response of the ocean—a similar time scale as the delayed baroclinic response mentioned by Eden and Willebrand (2001).

The negative lag correlation in Fig. 3 implies that a positive NAO phase is associated with decreased heat transport by the atmosphere at high latitudes. This apparently contradicts Carleton (1988), who finds that a positive NAO phase is associated with an increased heat transport by the atmosphere. In our model this specifically occurs in the tropics and subtropics (Fig. 4b) and obviously not in the mid- and high northern latitudes, since in that case there would be no Bjerknes compensation. Notice that Carleton (1988) shows strong longitudinally varying patterns at high latitudes (see, e.g., Figs. 5 and 6 of his paper), which do show negative correlation coefficients at higher latitudes of the North Atlantic Ocean (in his Figs. 5 and 6).

a. SST and heat flux from the ocean into the atmosphere

In the previous section, we have shown the occurrence of Bjerknes compensation at decadal time scales between 50° and 80°N, with a maximum compensation rate of 55% at 70°N. In this section we investigate why Bjerknes compensation is occurring at these latitudes and in particular why the compensation rate is showing a local maximum at 70°N. From the lead/lag correlations we infer that decadal oceanic heat transport variability leads the atmospheric heat transport variability at these latitudes, with maximum anticorrelation occurring at an ocean lead time of 1 yr. In this section we elucidate the mechanism that is responsible for this air–sea interaction.

In this and the next section we will consider a positive ocean heat transport anomaly and its consequences. The line of reasoning for the case of negative ocean heat transport anomalies is the same except for the sign of the correlation/regression coefficients. Previous work has already indicated that an increasing ocean heat transport is leading to an increase of the SST at northern midlatitudes (see, e.g., Shaffrey and Sutton 2006). We perform a linear regression of the ocean heat transport at 70°N with the SST to investigate the response of the latter to variations of the ocean heat transport at 70°N. We find that maximum values of the regression coefficient occur in the Greenland and Norwegian Seas, when the ocean heat transport at 70°N leads the SST in that region by 1 yr. Figure 5a shows the regression coefficient of SST on the ocean heat transport at 70°N for this specific time lag. Comparing the regression coefficients shown in Fig. 5a with the root-mean-square (RMS) variance of the SST in Fig. 5b, one can see that a large part, typically 50%, of the variance of the SST is coupled to the variations in the ocean heat transport at 70°N. The regression coefficients shown are normalized to a 0.01-PW variation in the ocean heat transport, obtained from the standard deviation of heat transport anomalies (not shown). One can see a maximum value of the regression coefficient of ∼0.45 degree on a 0.01-PW heat transport variance. Inspection of Fig. 5a reveals that the SST response to heat transport variations across 70°N is mainly confined to the northeast Atlantic—in particular, the Norwegian and Greenland Seas in a latitude band between 70° and 80°N. Both the mean heat transport and its variability are low north of 80°N. Any variation in ocean heat transport across 70°N is associated with anomalous convergence of heat transport in the 70°–80°N latitude band. Such heat transport variations are likely associated with variations in the MOC (Dong and Sutton 2005). For this reason, variations in global ocean heat transport at 70°N display an SST imprint that is almost exclusively confined to the northeastern Atlantic. On a minor note, we observe a positive SST anomaly off Newfoundland in Fig. 5a, which we associate with a deviation of the strength and direction of the North Atlantic Current. This change in the North Atlantic Current also explains the negative anomaly in the Irminger and Labrador Seas.

Ocean heat transport variations assert their impact on the atmosphere through a heat exchange between the interface dividing the atmosphere and ocean. A large fraction of the variance of the heat flux is coupled to the variations in the ocean heat transport at 70°N, with a maximum regression coefficient of 12 W m⁻² per 0.01-PW heat transport variance (not shown) in the 70°–80°N latitude band. We investigated the relation between this heat exchange with ocean heat transport variations at 70°N by performing a lead/lag correlation between the ocean heat transport at this latitude and the heat flux from the ocean into the atmosphere zonally integrated between 70°W and 40°E and meridionally integrated between 60° and 80°N. The choice for this particular area was motivated by the results shown in Fig. 5a, that is, the region where the regression coefficients of the SST display maximum values. The result of this calculation is shown in Fig. 6a. It displays a maximum response of the heat flux when the ocean heat transport at 70°N is leading by 2–3 yr. We therefore conclude that the low-frequency atmospheric variability is forced by the ocean at 70°N. Notice that, although the ocean is forcing the atmosphere, the lead time of the ocean is slightly larger than the lead time found in section 2b.

The increase of the heat exchange at latitudes north of 70°N, when the oceanic heat transport increases, also leads to a decrease of the atmospheric heat transport at 70°N, according to the Bjerknes compensation displayed in Fig. 1. To gain more insight into the mechanisms that causes Bjerknes compensation at this latitude, we decompose the atmospheric heat transport into its mean meridional circulation component and eddy component. The total atmospheric heat transport is calculated by integrating the surface heat flux from the ocean and the TOA into the atmosphere, which yields the time-averaged total meridional transport of energy, that is, [(gz + c_pT + L_υq)υ]. The bar denotes time average, the square brackets denote the zonal average, and the three terms multiplied by the total meridional velocity υ are respectively potential, internal, and latent energy. Next we calculate g[υz] + c_p[υT] + L_υ[υq], which subtracting from the time-averaged total meridional transport yields the transient synoptic eddies. We find that the transient synoptic eddy component dominates the variations in total atmospheric heat transport at this latitude (not shown). We do find the strongest correlation between the eddy component of the atmospheric heat transport and the ocean heat transport at 70°N when the latter leads by approximately 4 yr (see Fig. 6b). It is therefore concluded that Bjerknes compensation at 70°N is regulated by the transient eddy component in the atmospheric heat transport responding to variations in ocean heat transport. It is expected that a decrease of the transient eddy heat transport is coupled to a decrease of the baroclinicity of the atmosphere. This aspect is investigated in section 3b. The maximum anticorrelation rates found from Figs. 3 and 6 all indicate that the ocean is forcing the atmosphere at 70°N. However, they also show that it is not possible to allocate an exact response time of the atmosphere from the forcing by the ocean. They rather indicate that this time scale is of the order of a few years.

b. The atmospheric response

In Fig. 7a the correlation coefficients of the ocean heat transport at 70°N with dU/dp is shown. In Fig. 7b the regression coefficient of sea level pressure and the surface velocities onto the normalized heat transport at 70° are shown. Figures 7a and 7b both show maximum values for correlation and regression coefficients when the ocean heat transport variations at 70°N leads with 1 yr. In Fig. 7a one can see that when the ocean heat transport increases, dU/dp increases. This implies, using thermal wind balance, that dT/dy decreases and hence the baroclinicity of the atmosphere decreases. Obviously this is in agreement with the finding that the response of the atmospheric heat transport on ocean heat transport variations occurs via its eddy component. Furthermore, we notice that Fig. 7a also indicates that the response of the atmosphere occurs in the lower troposphere. Figure 7b shows the influence of the increase of the baroclinicity of the atmosphere on the circulation, which shows a cyclonic anomaly in the region centered in the GIN Seas. The circulation anomaly is centered right above the SST anomaly shown in Fig. 5a and can be explained as the atmospheric response to the SST anomaly—that is, for positive SST anomalies, a thermal low.

The conclusion of section 3b is that in case of an increase of the ocean heat transport at 70°N, the baroclinicity of the atmosphere will decrease, because of an increase of the heat flux from the ocean into the atmosphere. It is obvious that the decrease of the baroclinicity of the atmosphere leads to a decrease of the heat transport through the atmosphere, since the eddy transport variations dominate the atmospheric heat transport variations at 70°N. This implies a dampening of variations of radiation at the top of the atmosphere.

c. The particularity of 70°N: The role of sea ice

Figure 8 shows the regression coefficient between the ocean heat transport at 70°N and sea ice coverage when the ocean leads by 1 yr. Comparing the value of these regression coefficients with the RMS value of the sea ice coverage (not shown), we infer that the variability of the sea ice coverage in the region is mainly due (∼75%) to variations in the ocean heat transport at 70°N. This result helps us to understand why the compensation rate at 70°N has its maximum value (Fig. 1b): the heat exchange between the ocean and the atmosphere scales with the temperature gradient at the interface dividing the ocean and the atmosphere. Because of the sea ice coverage, the surface air temperature and the SST are not coupled; hence the difference between both temperatures can be large. At the same time, the presence of sea ice prevents large heat fluxes between the atmosphere and the ocean. However, at those regions where occasionally transitions take place from coverage by sea ice to open water and vice versa, the large temperature gradient will lead to large heat fluxes between the ocean and atmosphere during these transition times. The region where most of the transitions from sea ice coverage to open water (and vice versa) takes place is the latitude band of 70°N, the latitude where Bjerknes compensation reaches its maximum compensation rate. Obviously the 70°N latitude band is not the only place where ocean heat transport and MOC variations are associated with SST anomalies. However, in general the associated heat flux anomaly is too small to assert a significant impact on the atmosphere, because of the strong coupling between extratropical SST and surface air temperature anomalies on decadal time scales (Drijfhout et al. 2001). It is only in regions where SST anomalies invoke changes from sea ice coverage to open water that the ocean–atmosphere heat flux can become large enough to yield a significant atmospheric response. The importance of the ocean heat transport on sea ice coverage and therefore on climate was already emphasized by Winton (2003). Furthermore, Poulsen et al. (2001) raises similar issues in another context, that is, the Neoproterozoic “snowball Earth.” Also, our work is in line with the direct response of SST anomalies onto the atmosphere as reported by Deser et al. (2004). They also find an adaption of the baroclinic structure in the atmosphere associated with an equivalent barotropic thermal low caused by a positive SST anomaly.

From the above analysis we conclude that at latitudes ∼70°N, the increase of the ocean heat transport leads to an increase of the SST. Subsequently, the increase of the SST yields a lower sea ice coverage, which in turn yields an increase of the heat flux from the ocean into the atmosphere. This heat flux is large enough to yield a significant atmospheric response due to the sea ice coverage, which prevents a direct coupling between SST and surface air temperature.