1. Introduction

The ocean and the atmosphere interact on a wide range of time scales. Understanding such interactions is important because they have a major influence on climate variability, and because it is the ocean's influence on the atmosphere that provides the primary basis for seasonal and longer time-scale climate forecasting. In many studies of ocean–atmosphere interaction attention is concentrated on sea surface temperature (SST) as the key variable. The processes that govern the generation and decay of SST anomalies, and the influence of these anomalies on the atmosphere, provide the major focus of analysis. An alternative perspective (e.g., Bjerknes 1964; Held 2001; Sutton and Mathieu 2002, manuscript submitted to Quart. J. Roy. Meteor. Soc.) can be provided by consideration of the energy transports in the two systems, and the ways in which these transports are related. In this study we seek to investigate how this latter perspective may provide insights into the interactions between the Atlantic Ocean and the atmosphere above it.

Meridional energy transport is a fundamental feature of the oceans and atmosphere. Net radiative heating in the Tropics and radiative cooling at higher latitudes imply that the climate system as a whole is transporting energy from the Tropics toward higher latitudes, with the energy transport in the ocean and the atmosphere both contributing to the total energy transport. The total energy transport in the climate system and the energy transport in the atmosphere were calculated from Earth Radiation Budget Experiment (ERBE) and reanalysis datasets by Trenberth and Caron (2001). By implication, the difference between the total and the atmospheric energy transports is the global oceanic energy transport, the values of which appear to be consistent with energy transports garnered from observations (Trenberth and Caron 2001). Of the 5 PW (1 PW = 10¹⁵W) transported by the atmosphere and oceans, roughly 1 PW is transported by the global oceans and the rest in the atmosphere.

The variability of the meridional energy transport in the oceans and in the atmosphere is governed by different processes on different time scales. For example, variability on interannual time scales in the subtropical oceans is associated with the wind-driven Ekman transport (Klinger and Marotzke 2000), while variability on decadal time scales in the Atlantic Ocean is associated with changes in the thermohaline circulation (Hakkinen 1999; Eden and Willebrand 2001). In the atmosphere, the impact on the sensible heat transport by the largest mode of atmospheric variability over the North Atlantic, the North Atlantic Oscillation (NAO), was investigated by Carleton (1988). Changes in the phase of the NAO lead to large changes in the spatial distribution of stationary sensible heat transport in the Northern Hemisphere midlatitudes, but have surprisingly little impact on the zonally averaged sensible heat transport.

In this study we are particularly interested in the relationships between the oceanic and atmospheric energy transports. There are two conceptual models that may be helpful to understanding these relationships. The first was described by Bjerknes (1964) and so has become known as Bjerknes compensation. Bjerknes argued that if the top of the atmosphere (TOA) radiative fluxes did not vary greatly, then the total meridional energy transport would not vary greatly either. It follows that if either the atmospheric or oceanic energy transport were to change significantly, for example, due to internal variability, then the other component would have to compensate. Thus a weaker atmospheric energy transport would be compensated for by stronger oceanic energy transport. This implies that oceanic and atmospheric energy transports should be anticorrelated in time.

The second conceptual model relies upon the constraint placed on the mass fluxes in the tropical atmosphere and upper oceans by Ekman processes (Held 2001). The meridional mass flux in the upper tropical ocean is primarily in the shallow, wind stress–driven Ekman layer. However, as noted by Held (2001) most of the mass transport in the returning lower branch of the atmospheric Hadley circulation can also be considered as an Ekman transport. This atmospheric Ekman transport will be equal and opposite to the Ekman transport in the upper tropical oceans. This constraint on the tropical mass transport leads to a constraint on the energy transports in the tropical atmosphere and oceans. If the strength of the Hadley circulation were to increase, for example, due to internal variability, then the meridional atmospheric energy transport would also increase, but so would the strength of the returning branch of the Hadley circulation and the strength of the easterlies in the Tropics. The increase in the easterlies would force a stronger oceanic Ekman transport and so stronger meridional energy transport in the upper tropical ocean. This implies that, in the Tropics, the oceanic and atmospheric energy transports should be correlated in time.

It is interesting that these two conceptual models should suggest contradictory behaviour for the atmospheric and oceanic energy transports. However, the reliance of Bjerknes compensation on the small variability of the TOA fluxes might suggest that it would have less relevance in the Tropics than at higher latitudes. Anomalies in the surface fluxes in the Tropics can be quickly communicated to the TOA radiative flux via atmospheric convection, while in the extratropics surface and TOA fluxes may be less closely coupled. It seems likely, therefore, that the relationship between the oceanic and atmospheric energy transports may vary with latitude. In addition, the relationship is likely to vary with time scale. There is an implicit assumption in these conceptual models that the time scale is sufficiently long that changes in heat storage are unimportant. In practice, variations in oceanic heat storage are unlikely to be negligible on interannual time scales, and may be significant on longer time scales as well. In the present study we focus our attention on interannual variability. Variability on longer time scales will be considered in a separate study.

The structure of the paper is as follows. In section 2, the coupled climate model (HadCM3) and data analysis are described. We employ a novel version of HadCM3 that enables us to focus attention on the interactions between the Atlantic Ocean and the atmosphere. In section 3, analyses of the autocorrelation and cross-correlation structure of atmospheric and Atlantic Ocean energy transports are presented. Significant correlation between the atmospheric and oceanic transports is found both in the northern midlatitudes and in the Tropics. Investigation into the origins of these correlations is the subject of section 4, which focuses on the northern midlatitudes, and section 5, which focuses on the Tropics. Finally, a summary and conclusions are given in section 6.

2. Data analysis and model

The interannual variability of the zonal mean atmospheric energy transport and the energy transport in the Atlantic Ocean are investigated in the UK Met Office coupled climate model HadCM3. This model does not require flux adjustments to maintain a realistic climate, and the zonally averaged atmospheric and oceanic energy transports agree well with observations (Gordon et al. 2000). The atmospheric model has a resolution of 19 levels in the vertical and 2.5° latitude × 3.75° longitude in the horizontal, while the ocean model has a resolution of 20 levels in the vertical and 1.25° × 1.25° in the horizontal.

For this study a novel version of HadCM3 was employed. In this version the sea surface temperatures in the tropical Indo-Pacific Ocean are relaxed back to the model's monthly mean climatology with a short time scale of 2.5 days. The relaxation of SST occurs over a region of 30°S to 30°N but between 20° and 30° the value of the relaxation time scale varies linearly between 2.5 days and infinity. This relaxation effectively removes the ENSO cycle from the model and so removes the remote atmospheric influence of ENSO on the Atlantic Ocean, for example, via the atmospheric bridge of Lau and Nath (1996) and Klein et al. (1999). The consequence is that the “signal” of interactions between the Atlantic Ocean and the atmosphere can be studied in isolation from the “noise” of ENSO. However, it should be borne in mind that by removing a potential source of noise, this version of HadCM3 will tend to overemphasize the importance of these local interactions by comparison with the fully coupled version of HadCM3.

The modified version of HadCM3 was integrated for 100 yr from initial conditions taken from the 1000-yr control run described by Gordon et al. (2000). The variability of the Atlantic Ocean energy transport in this integration of HadCM3 has been described in overview by Dong and Sutton (2001, 2002). In Dong and Sutton (2002) it was found that the mean climate of the modified version was very similar to that of the control integration of HadCM3. For instance, the Atlantic Ocean energy transport in the modified integration was 1.18 PW at 24.4°N compared with 1.08 PW in the control run (Gordon et al. 2000) and 1.22 PW at 24°N from observations (Hall and Bryden 1982).

In this study we analyze the first 50 yr of the 100-yr simulation. The annual mean oceanic energy transports are taken from Dong and Sutton (2001) and are calculated from the monthly mean meridional velocities and temperatures. The annual mean atmospheric energy transports are calculated in a manner similar to Magnusdottir and Saravanan (1999) by integrating the divergence of the zonally and annually averaged surface and TOA fluxes. The zonal mean atmospheric energy transport, [F_a], is computed from

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where θ is latitude, a is the radius of the earth, F_sfc and F_toa are the net surface and top-of-the-atmosphere fluxes respectively and [ ] denotes the zonal mean. In the Northern Hemisphere, the maximum zonally averaged atmospheric energy transport in HadCM3 is 4.5 PW at 40°N while in the observations it is 5.0 PW at 43°N (Trenberth and Caron 2001).

3. The correlation structure of the Atlantic oceanic and atmospheric energy transports in HadCM3

In this section we examine the extent to which the atmospheric and Atlantic Ocean energy transports are correlated on interannual time scales in HadCM3. We also examine the autocorrelation structure, as a function of latitude, of the transports within the atmosphere and ocean separately. Third, we investigate the processes that govern the interannual variability of the atmospheric energy transport.

Figure 1a shows the correlations of the annual mean atmospheric energy transports at each latitude with the annual mean Atlantic Ocean energy transports at each latitude. The most prominent feature in midlatitudes is the bipolar pattern of positive and negative correlation. The Atlantic Ocean energy transports at latitudes farther north than 45°N are negatively correlated with the midlatitude atmospheric energy transport, while to the south of 45°N the oceanic energy transports are positively correlated with the midlatitude atmospheric energy transport. It also appears that the atmospheric energy transport at 60°N is positively correlated with the Atlantic Ocean energy transport at 20°N.

Correlations rather than regression are shown here, but the Atlantic Ocean energy transport can be regressed against the atmospheric energy transport in a similar manner. If this is done then the result has a very similar structure to Fig. 1a, with the regression of the subtropical Atlantic Ocean energy transport against the midlatitude atmospheric energy transport having an amplitude of approximately 1. However the regression of the higher-midlatitude Atlantic Ocean energy transport against the midlatitude atmospheric energy transport has a value of −0.2. This would be consistent with the interannual variability of the Atlantic Ocean energy transport being dominated by Ekman processes. The magnitude of the Ekman heat transport diminishes for the same upper-level Ekman mass transport since the temperature difference between the upper and deep oceans diminishes at higher latitudes (Boning and Herrmann 1994).

Another issue is to what extent does the damping of ENSO in this version of HadCM3 influence the correlation seen between the midlatitude atmospheric and Atlantic Ocean energy transports? A similar plot to Fig. 1a can be obtained for the control integration of HadCM3 (not shown). The value of the correlations between the global atmospheric energy transports and the Atlantic Ocean energy transport are generally weaker in the control integration. This suggests that the larger variability in the atmospheric energy transport associated with ENSO events will effectively mask the correlation between the processes that modulate the midlatitude atmospheric and oceanic energy transports over and within the North Atlantic Ocean.

Figure 1a also shows regions in the Tropics where the atmospheric and Atlantic Ocean energy transports are correlated. For example, the Atlantic Ocean energy transport between 5°–15°N is positively correlated with the atmospheric energy transport between 5°–20°S, while the Atlantic Ocean transport from 5°–15°S is negatively correlated with the atmospheric energy transport around 20°N.

The midlatitude dipole and many of the other features in Fig. 1a become more prominent when a 5-yr running mean is removed from the time series of atmospheric and Atlantic Ocean energy transports (Fig. 1b). The dependence of the strength of the correlations and anticorrelations to the high-pass time filter suggests that the processes that give rise to the features in Fig. 1a are primarily characterized by interannual time scales. The goal of this study is to explain the relationships between the atmospheric and Atlantic Ocean energy transports that are shown in Figs. 1a,b.

As a first step to understanding the correlations between the atmosphere and the Atlantic Ocean energy transports seen in Figs. 1a,b it is useful to examine the spatial autocorrelations in the Atlantic Ocean and atmosphere. Figure 1c shows the spatial autocorrelations in the atmospheric energy transport. The width of the diagonal of positive correlations is indicative of the spatial coherence of the energy transports. It appears that there are two distinct regions of enhanced spatial coherence. One region is the Tropics, between 20°S and 20°N, and the other is the Northern Hemisphere extratropics where the transport at 40°N is coherent with the transport at 20° and 60°N. Figure 1c also shows there is some degree of anticorrelation between the tropical and northern midlatitude atmospheric energy transports in HadCM3, with the atmospheric energy transports in the Tropics being anticorrelated with those between 20°–35°N.

Insights into the correlation structure of the atmospheric energy transports can gained by considering the atmospheric circulations that are associated with the transports. Figure 2 shows the pattern of zonally averaged zonal, meridional, and vertical winds regressed against the time series of atmospheric energy transport averaged between 20°S and 20°N. When the tropical atmospheric energy transport is large then there is an anomalous cross-equatorial overturning circulation stretching across the Tropics, with ascent at 20°S and descent at 20°N. The low-level zonal winds are consistent with angular momentum arguments, with the sign of the winds changing sign across the equator to give an easterly anomaly in the Southern Hemisphere and a westerly anomaly in the Northern Hemisphere.

In Magnusdottir and Saravanan (1999) the total atmospheric energy transport is decomposed into overturning, stationary, and transient parts,

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where h is the moist static energy, υ is the Eulerian meridional velocity, [h] is the zonal average of h and h* is the deviation from the zonal average, while h is the time average of h and h′ the deviation from the time average. The overturning term (the first term on the rhs) is the largest in the mean tropical atmospheric energy transport (Magnusdottir and Saravanan 1999), and the overturning circulation shown in Fig. 2 would imply that there are large changes in tropical atmospheric energy transport.

The existence of a large-scale overturning circulation explains the spatial coherence of the tropical atmospheric energy transports seen in Fig. 1c. Why, though, is the tropical transport anticorrelated with the atmospheric energy transport at 20°–35°N? In the midlatitudes, meridional energy transport in the atmosphere is achieved mainly by stationary waves and by transient eddies. Hou and Molod (1995) suggested that a cross-equatorial circulation such as that in Fig. 2 would increase the midlatitude transient eddy activity by increasing the baroclinicity associated with the subtropical upper-tropospheric jet. Consequently the atmospheric energy transport associated with the midlatitude transient waves would also increase. If the variability of the atmospheric energy transport in the midlatitudes is dominated by changes in the transient energy flux it would suggest that the atmospheric energy transport in the Tropics and the northern midlatitudes should be correlated in time. The fact that such behavior is not seen in Fig. 1c suggests that the atmospheric stationary waves play a significant role in governing the atmospheric energy transport in the northern midlatitudes.

To gain insight into the role of the stationary waves, Fig. 3a shows the mean sea level pressure regressed onto the atmospheric energy transport averaged over 20°–60°N, while Fig. 3b shows the Northern Hemisphere stationary wave pattern, that is, the time-mean surface pressure with the zonal mean removed. Over the North Pacific Ocean and Asian continent the atmospheric energy transport is larger when the circulations associated with the Aleutian low and the Siberian high are stronger than usual. Over the North Atlantic the atmospheric energy transport is large when the northern flank of the Azores high is strengthened, giving anomalous westerlies around 60°N and anomalous easterlies around 40°N, which accentuate the southwest–northeast tilt of the westerlies over the North Atlantic Ocean.

A possible relationship between the tropical and midlatitude energy transports may be inferred by comparing Figs. 2 and 3. Figure 2 suggests that an increase in the tropical atmospheric energy transport is associated with westerly anomalies in the subtropics of the Northern Hemisphere that, according to Fig. 3a, would be associated with a weakened stationary wave pattern. This association may explain the anticorrelations seen in Fig. 1c. An increase in the tropical energy transport may lead to a reduction in the midlatitude energy transport by stationary waves that more than compensates for any increase in the energy transport by transient eddies. Compensation of the energy transport associated with the transient eddies and stationary waves in the midlatitudes of the Northern Hemisphere was also seen in Magnusdottir and Saravanan (1999) where an atmospheric GCM (AGCM) was forced with SST anomalies that represented the zonally averaged SST trends seen in an increased CO₂ integration of a coupled ocean–atmosphere model. It was found that the changes in the total December–January–February (DJF) midlatitude atmospheric energy transport were dominated by the stationary waves, and that the changes in the transient wave energy transport could only partially compensate for the changes in the stationary wave energy transport.

The preceding discussion offers a hypothesis, which may explain the anticorrelation between the tropical and subtropical atmospheric energy transports seen in Fig. 1c. Establishing whether this is the correct explanation will require further investigation that is beyond the scope of the present study. Here, we are primarily interested in the relationships between the atmospheric and Atlantic Ocean energy transports.

Returning to Fig. 1, panel d shows the spatial autocorrelations for the Atlantic Ocean energy transports at each latitude. The spatial coherence of the Atlantic Ocean energy transport varies dramatically with latitude, with the spatial coherence being largest in the Tropics and subtropics of the Atlantic Ocean and smallest in the extratropics. At the equator the spatial coherence is somewhat reduced but is still considerable. For example, the time series of annual mean energy transport at 10°S is significantly correlated with the energy transport at 10°N (with a value of 0.4). In the extratropics the spatial coherence is much smaller and the energy transport between 40°–55°N is anticorrelated with the energy transport between the equator and 40°N.

Figures 1c and 1d give some indication of the origin of the midlatitude dipole in the correlation between the atmospheric and Atlantic Ocean energy transports seen in Figs. 1a and 1b. The atmospheric energy transport is spatially coherent right across the midlatitudes (Fig. 1c), while the Atlantic Ocean energy transports south of 40°N are anticorrelated with those north of 40°N (Fig. 1d). Given these features, then a midlatitude dipole in correlation would arise naturally if there is any relationship between the atmospheric and Atlantic Ocean energy transports in the midlatitudes. In the next section the origin of the midlatitude dipole and the physical processes that govern the variability of the Atlantic Ocean and atmospheric energy transports will be considered in more detail.

4. The atmospheric and Atlantic oceanic energy transports in the midlatitudes of the Northern Hemisphere

In this section the processes that govern the interannual variability of the atmospheric and Atlantic Ocean energy transports in the midlatitudes of the Northern Hemisphere are investigated. As we shall see, the forcing by the atmosphere of Ekman transports in the Atlantic Ocean plays a key role in understanding the relationship between the atmospheric and oceanic energy transports.

Evidence that points to the importance of the Ekman transports in the North Atlantic Ocean can be seen in Fig. 4a, which shows the regression of the annual mean surface pressure against the time series of the Atlantic Ocean energy transport averaged between 45°–60°N. The regression produces a spatial pattern that projects onto the North Atlantic Oscillation in the negative phase with weakened surface westerlies over the North Atlantic Ocean around 50°N and weakened easterly trade winds around 30°N. The changes in the surface wind stress implied by the pattern of surface pressure in Fig. 4a would be expected to drive a poleward Ekman transport around 50°N and an equatorward Ekman transport around 30°N. These opposing Ekman transports might explain the midlatitude dipole in the Atlantic Ocean autocorrelations seen in Fig. 1d.

The hypothesis that the Ekman transports are determining the interannual variability of the midlatitude Atlantic Ocean energy transport can be investigated by examining the fluctuations of the meridional currents in the Atlantic Ocean. Figure 4b shows the regression of the meridional ocean velocity integrated across the Atlantic basin regressed against the Atlantic Ocean energy transport averaged over 45°–60°N. A clear signal in the Ekman layer can be seen in the upper 50 m of the midlatitude Atlantic Ocean. North of 40°N poleward Ekman currents are positively correlated with the Atlantic Ocean energy transport averaged over 45°–60°N, while south of 40°N the opposite sign in the Ekman currents are seen. The latter are associated with the weakened easterly trade winds over the subtropical Northern Atlantic Ocean implied by Fig. 4a.

Figure 4b shows, in addition to the signal in the Ekman layer, a significant signal at greater depths in the North Atlantic. The meridional currents from 100 to 500 m are positively correlated with the energy transport. This pattern suggests a deep meridional overturning circulation is also partly responsible for variations in Atlantic Ocean energy transport. Figure 5a shows the results of the same analysis applied to high-pass-filtered data from which a 5-yr running mean has been removed. In this case the significant signal is restricted to the Ekman layer. This result indicates that variations in the deep meridional circulation are mainly associated with longer time scales and the interannual variability of the Atlantic Ocean energy transport is indeed dominated by variations in the Ekman component.

The dominance of the Ekman transport can also be seen in Fig. 5b, which shows the time series of the total, overturning, and gyre Atlantic Ocean energy transports averaged between 45° and 60°N. The time series have had a 5-yr running mean subtracted from them, to remove the lower frequency fluctuations associated with variations in the thermohaline circulation. The dominance of Ekman processes in the higher midlatitudes in HadCM3 differs from the conclusions of other studies. Eden and Willebrand (2001) found that an oceanic barotropic Sverdrup response to the NAO dominated the Atlantic Ocean energy transport at higher latitudes. Consequently the gyre component was more important for the interannual variability of the total Atlantic Ocean energy transport than the overturning. The fact that two models have very different mechanisms governing the interannual variability in the high-latitude Atlantic Ocean energy transport in these two models is an area that warrants further study.

The question that now arises is what is the relationship between the midlatitude atmospheric energy transport and the changes in wind stress that are driving the Ekman transports? We can see that the relationship is not entirely straightforward since the pattern of surface pressure corresponding to an increase in the midlatitude atmospheric energy transport (Fig. 3a) does not project strongly onto the NAO-like pattern of surface pressure that is most important for the energy transport in the North Atlantic Ocean (Fig. 4a). Figure 3a does, however, resemble other leading patterns of surface pressure variability. In Fig. 6 are shown the first, second, and third (EOFs; empirical orthogonal functions) of the annual mean surface pressure over the North Atlantic. Figure 3a is very different from the first EOF, which describes the spatial pattern of the NAO, but shows more similarity to the patterns of the second and third EOFs. This similarity raises the possibility that the second and third EOFs might be more important for the midlatitude atmospheric energy transport than the NAO, a hypothesis that is confirmed by Fig. 6d. It shows the regression of the atmospheric energy transport at each latitude against the principal components of the first three EOFs scaled by their respective eigenvalues. It is clear that in the midlatitudes of the Northern Hemisphere the second and third EOFs are much more important for the atmospheric energy transport than the first EOF.

Our key aim in this discussion is to explain the midlatitude dipole in the correlation between the atmospheric and Atlantic Ocean energy transports (seen in Fig. 1b). To this end we now investigate how the different modes of atmospheric variability contribute to this correlation pattern. We employ a simple statistical model in which the atmospheric energy transport is represented in terms of the three leading EOFs shown in Fig. 6, and the Atlantic Ocean energy transport is estimated from the Ekman transports driven by the winds associated with each EOF. The total atmospheric energy transport, H_a, is modeled as

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where b_i(y) is the regression coefficient for the principal component of the ith EOF against the atmospheric energy transport at latitude y, T_i(t) is a white noise time series with unit variance, and ϵ is the white noise with a variance equal to that of the residuals calculated from the regression, that is, the variance calculated from the difference between Σ³_i=1 b_i(y)PC_i(t) [where PC_i(t) is the principal component of the ith EOF] and the atmospheric energy transport in HadCM3. It should also be noted the regressions shown in Fig. 6 assume that the relationship between the mean sea level pressure and the atmospheric energy transport can be modeled by a linear processes. This assumption clearly does not hold in the real atmosphere, nevertheless it is still possible to use linear methods to gain insight into the mechanisms of atmospheric energy transport, for example, the atmospheric transient eddy fluxes can be reasonably modeled by a linear damped-stochastic forced model (Whitaker and Sardeshmuhk 1998).

To estimate the Atlantic Ocean Ekman transport for each year, the surface pressure and geostrophic surface winds over the North Atlantic are (partially) reconstructed from the first three EOFs. The surface winds are then rotated by 20° to the left, which is a typical value of the difference between the geostrophic and observed surface winds over the Northern Hemisphere oceans. An estimate of the zonal surface wind stress, τ_x is made by using the bulk aerodynamic formula, τ_x = c_d|u′|u′, where c_d = 10⁻³ kg m⁻² s is the drag coefficient and u′ are the rotated zonal geostrophic winds. The meridional Ekman mass transport is then M_e = −τ_x/f, where f is the Coriolis parameter. The energy transport associated with this Ekman mass transport is estimated by assuming that the transport takes place in the upper 50 m of the Atlantic Ocean and a return flow occurs in the deep ocean. The energy transport, H_o, across the whole of the Atlantic Ocean is then,

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where y is latitude and c_w is the specific heat of seawater; T₅₀ is the mean temperature of the upper 50 m of the Atlantic Ocean and T_deep is the mean temperature of the remainder. Both mean temperatures are calculated from the time-averaged oceanic temperatures.

Figure 7a shows the mean correlation of the atmospheric and the Atlantic Ocean energy time series calculated from a 1000-yr integration of the simple EOF model. The values from 30°S to 0° are zero since the EOF analysis only extends to the equator but are retained here in order to produce a figure that can be directly compared to Fig. 1b. The simple model is capable of predicting most of the features of the midlatitude correlations in Fig. 1b, mainly that the midlatitude atmospheric energy transports should be positively correlated with the Atlantic Ocean energy transports to the south of 45°N and negatively correlated to the north. The results from the same model but only based on the second and third EOFs are shown in Fig. 7b. When the NAO is excluded the correlations are similar to those from the simple EOF model except in the subtropics (around 25°N) where the NAO has a substantial impact on the atmospheric energy transport (Fig. 6b). This result restresses the relationship shown in Fig. 6d, that is, that the second and third EOFs play a more dominant role in the midlatitude atmospheric energy transport. Figure 7b also shows that although the second and third EOFs only explain 27% of the variance of the annual mean sea level pressure over the North Atlantic, they can still force enough variability in the oceanic Ekman transport to recover most of the structure in Fig. 1b.

The simple EOF model is also able to capture some of the more subtle features present in Fig. 1b. For example, the regions of positive and negative correlation in midlatitudes appear to be slanted rather than having a vertical orientation. It can be inferred from Fig. 6 that the farther north the latitude of the maximum of the atmospheric energy transport associated with each EOF then the further north are the Ekman transports driven by that particular EOF. The result is that the regions of correlation in Fig. 7a have the same slant as is seen in HadCM3.

The fact that the simple EOF model can reproduce to a high degree of accuracy the correlations seen in HadCM3 is evidence that it is the Ekman response to atmospheric variability that is primarily response for the midlatitude correlations seen in Fig. 1b. There are, however, some discrepancies between the correlations found in HadCM3 and those found in the simple EOF model. In HadCM3 the Atlantic oceanic energy transports around 20°N and the atmospheric energy transport around 60°N are significantly positively correlated, while in the simple model this correlation is not significant. Similarly, the simple model predicts that the midlatitude atmospheric energy transport and the Atlantic Ocean energy transport between 0° and 20°N should be negatively correlated, where HadCM3 suggests that there should be no significant correlation. Both these discrepancies point to the likelihood that the Atlantic Ocean energy transport in the Tropics is not adequately predicted by the simple model. Such a failure will occur if processes other than Ekman transports may play a significant role. In the next section we investigate the extent to which other processes are important.

5. The atmospheric and Atlantic oceanic energy transports in the Tropics

In this section we investigate the relationship between the energy transport in the tropical Atlantic Ocean and the energy transport in the tropical atmosphere. As a first stage of this investigation we examine the processes that govern the variability of energy transport in the tropical Atlantic ocean.

Figure 1a shows only small regions in the Tropics where the Atlantic Ocean energy transport and the atmospheric energy transport are significantly correlated. For example, the Atlantic Ocean energy transport between 5°–15°N is correlated with the atmosphere between 5°–20°S, while the oceanic transport from 5°–15°S is anticorrelated with the atmospheric energy transport around 20°N. It might have been expected that these regions of correlation in the Tropics would be more extensive, given the high spatial coherence in the Tropics of both the atmospheric and Atlantic Ocean energy transports (Figs. 1c,d). The high spatial coherence of the tropical Atlantic Ocean energy transport was also noted by Dong and Sutton (2001) who showed a Hovmoeller diagram (their Fig. 1) in which many of the anomalies in the energy transport are coherent right across the Tropics, that is, from 20°N to 20°S. The first question that must be addressed is what are the processes that explain the high spatial coherence in the tropical Atlantic Ocean?

If the variability of the energy transport in the tropical Atlantic Ocean is determined by Ekman transports, then coherence across the equator could only arise in response to zonal wind fluctuations with opposite signs to the north and south of the equator. The changes in zonal wind stress that are associated with an increase in the tropical atmospheric energy transport (Fig. 2) do have this property, with anomalous easterlies just north of the equator and anomalous westerlies to the south. (Note that although Fig. 2 describes the zonally averaged winds it is also reflects the changes in the zonal winds over the tropical Atlantic Ocean alone.) The changes in zonal wind stress can be expected to drive northward Ekman transports in both hemispheres, and these currents can be seen in Fig. 8a, which shows the meridional currents averaged across the Atlantic Ocean basin regressed against the atmospheric energy transport averaged between 20°S and 20°N.

The situation implied by Figs. 8a and 2, in which the atmosphere and ocean are closely coupled via their Ekman layers, is reminiscent of the arguments invoked by Held (2001) to explain the partitioning of the time-mean zonally averaged energy transports in the atmosphere and global oceans. If, however, this mechanism provided a complete account of the variability in the energy transports, then we should expect strong positive correlations in the tropical regions of Figs. 1a,b. In fact, as we have seen, the significant correlations in this region are restricted to a small fraction of the total area. This result suggests that the variability of the Ekman transport is not the dominant process determining the variability of the tropical Atlantic Ocean energy transport. More direct evidence is presented in Fig. 8b, which shows the mean currents in the upper 375 m of the ocean regressed against the Atlantic Ocean energy transport averaged between 20°S and 20°N. An increase in the northward energy transport in the tropical Atlantic Ocean is associated with an increase in the strength of the western boundary current from 9°S to 20°N, a strengthening that is seen throughout the upper ocean down to 500 m (not shown). Quantitative analysis demonstrates that it is the variations in the western boundary current rather than variations in the Ekman transports that dominate the variability of the total Atlantic ocean energy transport in HadCM3. It is also worth noting that the regressions shown here are insensitive to the use of a high-pass filter, since the variability of the tropical Atlantic Ocean energy transport is dominated by interannual time scale rather than by longer time scales, which can be seen in the Hovmoeller plot of Dong and Sutton (2001).

How do the variations in the western boundary current arise, and what is the explanation for their coherence across the equator? One way for a fast adjustment of the tropical Atlantic Ocean to occur is outlined in Kawase (1987) and Johnson and Marshall (2002). In these studies shallow water models of the Atlantic have been driven with idealized mass flux forcing in the high-latitude Northern Hemisphere. The effects of the forcing are communicated southward by a coastally trapped Kelvin wave traveling along the western boundary. As the Kelvin wave is in geostrophic balance, it travels only as far as the equator where it excites an equatorially trapped Kelvin wave, which then traverses across the ocean basin. At the eastern boundary, the equatorial Kelvin wave excites two coastally trapped Kelvin waves, one moving northward and one moving southward. Rossby waves excited by the coastally trapped Kelvin waves are then radiated into the interior of the ocean in both hemispheres. The time scale for adjustment of the energy transport is dependent on the time taken for baroclinic Rossby waves to cross the basin, which itself is dependent on latitude. The time scale is months near the equator and years or decades in the midlatitudes.

The wave adjustment process offers a possible mechanism via which the Southern Hemisphere can respond to forcing in the Northern Hemisphere. If this mechanism operates in HadCM3 then it could provide an explanation for the coherence of the tropical Atlantic ocean energy transport. Evidence that the mechanism does operate in HadCM3 is shown in Fig. 9. Figure 9a is a Hovmoeller diagram of monthly anomalies from the seasonal cycle of the mean temperature of the upper 1250 m of the Atlantic Ocean along the path shown in Fig. 9b. The temperature is averaged along the path into sections which are 20 grid points in length, which effectively filters out slow-moving signals, and has an 11-month running mean removed from the temperatures to remove signals associated with lower-frequency changes in the meridional overturning of the Atlantic. Coherent temperature signals can be seen in Fig. 9a that are typically excited around point 6, which corresponds to the Venezuelan coastline, and take up to 6 months to propagate around the path shown in Fig. 9b to point 12. These signals correspond to Kelvin waves propagating southward along the South American coastline, across the equator and northward along the African coastline, and then to a Rossby wave signal propagating westward at 10°N. The variations in amplitude of the temperature signals are probably due to variations in the temperature difference across the thermocline as the upwelling signals propagate.

The impact of the Kelvin and Rossby waves on the tropical Atlantic Ocean can be seen in Fig. 10a, which shows the mean oceanic temperature of the upper 375 m of the ocean regressed against the Atlantic Ocean energy transports averaged between 20°S and 20°N. The largest signal is a cold anomaly that extends along the north coast of South America. A cold anomaly can also be seen extending along the equator and stretching into both hemispheres along the eastern boundary of the tropical Atlantic. The signal is coherent across the equatorial Atlantic Ocean, in that the regression is of the same sign, but the signal is not significant in the western equatorial Atlantic Ocean, which suggests that other processes must play a role in determining the heat content of the upper ocean in that region.

The atmospheric forcing that is exciting these signals can be seen in Fig. 10b, which shows the surface winds regressed against the Atlantic Ocean energy transports averaged between 20°S and 20°N. Figure 10b shows an increase in the strength of easterly trade winds across the Atlantic basin with the largest signal being an increase in the winds parallel to the Venezuelan coastline. The Ekman transports driven by the surface winds parallel to the coast will induce coastal upwelling along the Venezuelan coast and result in the strong cold anomaly, which then propagates southward toward the equator as an upwelling Kelvin wave. In the real ocean, north of Venezuela is a region where the upwelling varies strongly. Inoue et al. (2002) studied the annual cycle of upwelling in this region, and found that the temperature of the upper ocean typically changes by 0.75 K for a 1 m s⁻¹ westerly wind. This corresponds to typical temperature change in HadCM3 of 1 K for a westerly wind of 1 m s⁻¹, which suggests that the modeled temperatures of the upwelling induced in the south Caribbean are larger than those observed.

The approximate extent of the adjustment in the Southern Hemisphere has been indicated on Fig. 10a by the bold black line. This indicates the distance from the eastern boundary that an oceanic baroclinic Rossby would propagate in one year. The propagation speeds of the Rossby waves have been estimated by calculating the speed of propagating anomalies at each latitude in the upper 375-m temperature. The Rossby wave speeds estimated by this method closely match those of observed Rossby waves. The estimated extent of the upwelling corresponds with the region of upwelling associated with the tropical Atlantic Ocean energy transport. This region is delineated by the zero line in Fig. 10a that extends from 25°S on the eastern boundary of the Atlantic to 8°S on the western boundary. The latitude at which a Rossby wave can propagate across the basin within a year (approximately 8°S) corresponds to the latitude at which significant coherent signals in the western boundary current are seen (9°S in Fig. 8b). This suggests that the adjustment of the western boundary current is due to the propagation of oceanic waves induced by the upwelling along the Venezuelan coastline. The adjustment of the western boundary current to the upwelling leads to the spatially coherent interannual variability in the tropical Atlantic Ocean energy transport.

In Johnson and Marshall (2002), the Kelvin wave signals were excited at much higher latitudes than the south Caribbean. Similarly, in a study by Yang (1999) Kelvin waves were excited at much higher latitudes in an ocean general circulation model, which then propagated along the western boundary to the Tropics. Kelvin waves excited at higher latitudes do not appear to play such a strong role in the interannual variability of the Atlantic Ocean energy transport in HadCM3. It is clear from Fig. 9a that no coherent signals propagate around the Caribbean from higher latitudes, but it is possible that deep Kelvin wave signals could propagate from the coastline of Florida along the ridge on which Cuba and the islands of the Lesser Antilles are situated on (i.e., from section 2 to section 7 in Fig. 9b). However, using the monthly temperatures from Fig. 9a, a nonsignificant maximum correlation of 0.15 is found at a lag of 3 months between sections 2 and 7. This is in comparison to the significant maximum correlation of 0.32 at a lag of 3 months between sections 6 and 10. This suggests that it is the Kelvin waves excited off the north coast of South America are more important for the interannual variability of the tropical Atlantic Ocean energy transport, although Kelvin waves excited at higher latitudes may play a larger role at longer time scales.

There also remains the possibility that the preceding analysis might be oversimplifying the aspects of the atmospheric forcing that induce the upwelling across the tropical Atlantic Ocean. In Fig. 10b there are weak southerly surface winds parallel to the African coastline that could, in addition to the winds along the Venezuelan coast, induce coastal upwelling and potentially contribute to the upwelling across the whole of the tropical Atlantic Ocean. Figure 11 suggests, however, that these winds in fact play little role. Figures 11a,b show the upper ocean currents and surface winds regressed against the Atlantic Ocean energy transports averaged between 0° and 20°N. It is clear that regressing against this Northern Hemisphere index yields essentially the same signal in the western boundary current as was seen in Fig. 8b. However, in this case the pattern of surface winds shows no significant signal along the African coast. This result suggests that atmospheric forcing of the tropical Atlantic Ocean energy transport primarily comes from the variability of the Northern Hemisphere trade winds and the coastal upwelling induced along the Venezuelan coast.

One aspect of this study is how the removal of ENSO might affect the modes of variability found in this particular version of HadCM3. In the control integration of Gordon et al. (2000) the variability of the tropical Atlantic Ocean has very similar characteristics to those found here, that is, that the variability is dominated by interannual time scales and is spatially coherent across the equator. The largest differences between the two versions of HadCM3 is that the tropical wind variability in the control integration will be strongly influenced by ENSO. In particular, ENSO has an impact on the strength of the easterly trade winds over the subtropical Atlantic, for example, Klein et al. (1999). This raises the possibility that ENSO may have an influence on the Atlantic Ocean energy transport.

We can now return to the correlations seen in the Tropics of Figs. 1a,b between the atmospheric and Atlantic ocean energy transport. Recall in particular the significant positive correlation between the atmospheric transport at ∼20°S and the oceanic transport between 5°–15°N. The changes in the energy transports associated with the wind stress along the Venezuelan coast can be seen in Fig. 12a, which shows the atmospheric and Atlantic Ocean energy transports regressed against the annual mean surface wind stress along the northern coast of South America. Consistent with the preceding analysis, an increase in the westerly wind stress is associated with significant decreases in the northward Atlantic Ocean energy transport between 15°S and 35°N. For the atmospheric energy transport the only significant values are around 20°S, where an increase in westerly wind stress is associated with an increase in the southward atmospheric energy transport.

Insight into the origin of the peak in atmospheric energy transport at 20°S is provided by Fig. 12b. This figure shows the zonally averaged winds regressed against the index of wind stress along the Venezuelan coast. An increase in westerly wind stress along the Venezuelan coast is associated with strong westerly winds around 20°N and anomalous meridional overturning. In the Tropics, there is a large-scale overturning circulation with prominent descent on the southern flank of the southern cell of the Hadley circulation around 20°S. Figure 2 showed that a similar anomalous overturning circulation is the primary process responsible for modulating the atmospheric energy transport in the Tropics. Figure 12b suggests, therefore, that it is a strengthening of the southern flank of the Hadley circulation that is the reason for the peak in energy transport at 20°S in Fig. 12a.

Figure 12a also explains the positive correlation between the atmospheric energy transport between 10° and 20°S and the Atlantic Ocean energy transports between 5° and 15°N (Fig. 1a). As we have just seen, an increase in westerly wind stress along the Venezuelan coast is associated with southward energy transport in the tropical atmosphere that peaks at 20°S. At the same time, these winds force anomalous coastal downwelling and a decrease in the northward energy transport in the tropical Atlantic Ocean. Hence the correlation between the atmosphere and ocean energy transports is positive. The anticorrelation between the atmospheric energy transport around 20°N and the Atlantic Ocean energy transports between 5° and 15°S is more difficult to explain as the regression between the wind stress index and the atmospheric energy transport is not significant around 20°N. Figure 12a does indicate, however, that the atmospheric energy transport changes sign at ∼15°N. As the ocean energy transport does not change sign anywhere in the Tropics, this feature points to a change in the sign of the atmosphere–ocean correlation as is seen in Fig. 1a.

In summary, the variability in the tropical atmospheric energy transport is associated with anomalous meridional overturning of the tropical atmosphere. Meanwhile, the variability in the Atlantic Ocean energy transport is primarily associated with coastal upwelling induced by zonal wind stress along the Venezuelan coast that is then communicated to the rest of the tropical Atlantic by Kelvin and Rossby waves. However, changes in the wind stress along the Venezuelan coast are not strongly correlated with changes in the tropical atmospheric energy transport (except at 20°S). This is the reason why correlations between the atmospheric and Atlantic Ocean energy transports in the Tropics of HadCM3 are generally weak.

6. Conclusions

We have investigated the interannual variability of the meridional atmospheric and Atlantic Ocean energy transports in a version of the HadCM3 climate model, modified to remove the effects of ENSO. Our approach was based on analyses of the correlation structure of the energy transports in the atmosphere and Atlantic Ocean as a function of latitude, and of the cross correlation between the two systems. We identified significant cross correlations in the northern midlatitudes and in the Tropics, and used regression analyses to elucidate the processes responsible. Our principal findings are as follows:

• On interannual time scales the variability of the meridional energy transport in the northern midlatitude Atlantic Ocean is dominated by Ekman processes. Anticorrelated zonal winds in the subtropics and at midlatitudes, particularly those associated with the NAO, drive anticorrelated meridional Ekman transports in the Atlantic Ocean.

• The variability of the meridional energy transport in the northern midlatitude atmosphere appears to be governed primarily by changes in the stationary waves. Over the North Atlantic, the NAO is not as important for the variability of the atmospheric energy transport as patterns of variability that accentuate the southwest–northeast tilt of the surface westerlies.

• The response of the Atlantic Ocean Ekman transports to atmospheric variability results in a dipole pattern of correlation in the northern midlatitudes between the atmosphere and Atlantic Ocean energy transports. The Atlantic Ocean energy transports to the south of 40°N are positively correlated with the midlatitude atmospheric energy transport, while the Atlantic Ocean energy transports to the north of 40°N are negatively correlated with the midlatitude atmospheric energy transport.

• In the Tropics, the interannual variability of the atmospheric meridional energy transport is associated with a cross-equatorial meridional overturning circulation.

• The variability of the meridional energy transport in the tropical Atlantic Ocean is associated with spatially coherent changes in the western boundary current. The changes in the western boundary current are governed by the adjustment of the tropical Atlantic to coastal upwelling induced by a strengthening of the easterly trade winds along the Venezuelan coast.

• The strengthening of the easterly trade winds along the Venezuelan coast is not significantly correlated with the tropical atmospheric energy transport except at 20°S. Consequently, there is only very limited correlation between the atmosphere and Atlantic Ocean energy transports in the Tropics.

In the introduction we described two conceptual models that might be relevant to understanding the relationship between atmosphere and Atlantic Ocean energy transports, these being the Bjerknes compensation hypothesis and Held's ideas concerning coupled Ekman transports. We have found that neither of these models provides an appropriate account of the interannual variability of energy transports in HadCM3. In midlatitudes, the atmospheric forcing of oceanic Ekman transports does not connect the atmosphere and oceanic energy transports in the direct way envisaged by Bjerknes (1964). In the Tropics, we have seen that interannual variability of the oceanic energy transport is dominated by the western boundary current rather than by Ekman processes.

The lack of Bjerknes compensation on interannual time scales should not surprise us. The compensation ideas rely on the surface heat fluxes to provide a direct connection between the atmosphere and ocean energy transports. On interannual time scales, however, variability in heat storage plays a key role in the heat budget of the upper ocean, and the connection between oceanic energy transport and surface heat fluxes is consequently less direct. On longer time scales, however, variations in heat storage are likely to be less important. In our next study we plan to investigate the relevance of the compensation hypothesis to understanding longer time-scale decadal-to-centennial variability. The coupling between the Atlantic thermohaline circulation and the atmosphere will be a key focus.

As with any modeling study an important question is whether our results may be sensitive to the particular model, and to the model version employed here without an ENSO cycle. One of the more surprising results in our study is the fact that interannual variability in the tropical Atlantic Ocean energy transport is so strongly determined by wind-driven upwelling along the Venezuelan coast. It would be very valuable to investigate whether the same is true in the other models and in the real world, particularly as a comparison with Inoue et al. (2002) suggests the upwelling may be rather strong in HadCM3. The implications of this behavior for understanding other aspects of variability in the tropical Atlantic Ocean merit considerable further study.