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    Hovmoeller plots showing decadal anomalies of (a) global ocean energy transport, (b) Atlantic Ocean energy transport, and (c) global atmospheric energy transport. The contour interval is 0.03 PW. Negative contours are dashed and negative values are shaded. (d), (e), (f) The standard deviations of the Hovmoeller in (a), (b) and (c) respectively. The units on the y axes are in PW.

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    (a) Correlation of decadal Atlantic Ocean and atmospheric energy transports for each latitude. (b) Time series of decadal anomalies in extratropical (20° to 70°N) atmospheric energy transport (bold), Atlantic Ocean energy transport (solid), and the Atlantic MOC index (dashed). The units on the y axis in (b) are in (left) PW and (right) Sverdrups

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    Hovmoeller plots showing Atlantic Ocean decadal anomalies of (a) energy transport convergence and (b) net surface flux. The contour interval in (a) and (b) is 0.008 PW m−1. Negative contours are dashed and negative values are shaded.

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    Hovmoeller plots showing Atlantic Ocean decadal anomalies of (a) the rate of change of ocean heat content and (b) the residual in the Atlantic Ocean heat budget. In (a) the contour interval is 0.0008 PW m−1 and in (b) it is 0.008 PW m−1. Negative contours are dashed and negative values are shaded.

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    (a) The time series of the Atlantic Ocean heat content anomalies averaged between 30°S and 70°N. The units on the y axis are 1023 J. (b) Depth–longitude plots showing the difference in the Atlantic Ocean temperature between the last century (years 830–930) minus first century (years 1–100). The contours are at −4, −2, −1, −0.5, 0, 0.5, and 1 K. Negative values are shaded and negative contours are dashed.

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    Hovmoeller plots showing Atlantic Ocean decadal anomalies of (a) heat content of the upper 300 m of the ocean and (b) surface temperature. In (a) the contour interval is 3 × 1020 J and in (b) the contours are at −0.2, −0.1, −0.05, 0, 0.05, 0.1, and 0.2 K. Negative contours are dashed and negative values are shaded. (c), (d) The standard deviations of (a) and (b), respectively. The units on the y axis in (a) are 1020 J and in (b) are in K.

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    The regression of (a) surface temperature and (b) net surface flux against the detrended decadal Atlantic Ocean energy transport averaged between 30°S and 70°N. The contour intervals in (a) are at −40, −20, −10, −5, −2, 0, 2, 5, 10, 20, and 40 K PW−1. In (b) the contour intervals are −400, −200, −100, −50, 0, 50, 100, 200, and 400 W m−2 PW−1. Negative contours are dashed and shading denotes regions that are 95% significant.

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    The regression of (a) TOA flux and (b) precipitation against the detrended decadal Atlantic Ocean energy transport averaged between 30°S and 70°N. The contour interval in (a) is 20 W m−2 PW−1 and contour intervals in (b) are −20, −10, −5, −2, 0, 2, 5, 10, and 20 mm day−1 PW−1. Negative contours are dashed and shading denotes regions that are 95% significant.

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    (a) Variance of decadal anomalies of zonally averaged net surface (solid) and TOA fluxes (dashed). The units on the y axis are in (W m−2)2. (b) Correlation between the decadal zonally averaged net surface and net TOA fluxes.

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    (a) Time series of decadal anomalies of energy transports averaged between 20° and 70°N for the Atlantic Ocean (solid) and the atmosphere (dashed). (b) Composite difference of atmospheric transient energy transport (solid) and stationary energy transport (dashed) for strong-minus-weak North Atlantic Ocean energy transport. The units on the y axes are in PW.

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    (a) The correlation coefficient between the total oceanic and atmospheric energy transports (20° to 70°N) for time series with differing averaging periods in years (bold). The variance of atmospheric (dashed) and Atlantic Ocean (solid) time series for different averaging periods (20° to 70°N). (b) The power spectra of the detrended atmospheric (bold) and the detrended Atlantic Ocean (dashed) energy transports as a function of frequency. The units on the y axis in (b) are in PW.

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    (a) Coherence and (b) phase as a function of frequency between the atmospheric and Atlantic Ocean energy transports averaged between 20° and 70°N. The spectral analysis was performed on the detrended data using 49 spectral estimates and a Tukey lag window. The units on the y axis in (a) are in PW and in (b) are in radians.

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Bjerknes Compensation and the Decadal Variability of the Energy Transports in a Coupled Climate Model

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  • 1 Department of Meteorology, University of Reading, Reading, United Kingdom
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Abstract

In the 1960s, Jacob Bjerknes suggested that if the top-of-the-atmosphere (TOA) fluxes and the oceanic heat storage did not vary too much, then the total energy transport by the climate system would not vary too much either. This implies that any large anomalies of oceanic and atmospheric energy transport should be equal and opposite. This simple scenario has become known as Bjerknes compensation.

A long control run of the Third Hadley Centre Coupled Ocean–Atmosphere General Circulation Model (HadCM3) has been investigated. It was found that northern extratropical decadal anomalies of atmospheric and oceanic energy transports are significantly anticorrelated and have similar magnitudes, which is consistent with the predictions of Bjerknes compensation. The degree of compensation in the northern extratropics was found to increase with increasing time scale. Bjerknes compensation did not occur in the Tropics, primarily as large changes in the surface fluxes were associated with large changes in the TOA fluxes.

In the ocean, the decadal variability of the energy transport is associated with fluctuations in the meridional overturning circulation in the Atlantic Ocean. A stronger Atlantic Ocean energy transport leads to strong warming of surface temperatures in the Greenland–Iceland–Norwegian (GIN) Seas, which results in a reduced equator-to-pole surface temperature gradient and reduced atmospheric baroclinicity. It is argued that a stronger Atlantic Ocean energy transport leads to a weakened atmospheric transient energy transport.

Corresponding author address: Dr. Len Shaffrey, Dept. of Meteorology, University of Reading, P.O. Box 243, Earley Gate, Reading, Berkshire, RG6 6BB, United Kingdom. Email: l.c.shaffrey@reading.ac.uk

Abstract

In the 1960s, Jacob Bjerknes suggested that if the top-of-the-atmosphere (TOA) fluxes and the oceanic heat storage did not vary too much, then the total energy transport by the climate system would not vary too much either. This implies that any large anomalies of oceanic and atmospheric energy transport should be equal and opposite. This simple scenario has become known as Bjerknes compensation.

A long control run of the Third Hadley Centre Coupled Ocean–Atmosphere General Circulation Model (HadCM3) has been investigated. It was found that northern extratropical decadal anomalies of atmospheric and oceanic energy transports are significantly anticorrelated and have similar magnitudes, which is consistent with the predictions of Bjerknes compensation. The degree of compensation in the northern extratropics was found to increase with increasing time scale. Bjerknes compensation did not occur in the Tropics, primarily as large changes in the surface fluxes were associated with large changes in the TOA fluxes.

In the ocean, the decadal variability of the energy transport is associated with fluctuations in the meridional overturning circulation in the Atlantic Ocean. A stronger Atlantic Ocean energy transport leads to strong warming of surface temperatures in the Greenland–Iceland–Norwegian (GIN) Seas, which results in a reduced equator-to-pole surface temperature gradient and reduced atmospheric baroclinicity. It is argued that a stronger Atlantic Ocean energy transport leads to a weakened atmospheric transient energy transport.

Corresponding author address: Dr. Len Shaffrey, Dept. of Meteorology, University of Reading, P.O. Box 243, Earley Gate, Reading, Berkshire, RG6 6BB, United Kingdom. Email: l.c.shaffrey@reading.ac.uk

1. Introduction

To attribute the recent warming of the climate system to anthropogenic causes it is essential to develop a deeper understanding of the natural variability in the climate system. The natural variability in the oceans and atmosphere occurs on all time scales, however, making attribution difficult. One way to simplify the complexity of the climate system is to envisage it as a heat engine. Energy coming in as radiation at the top of the atmosphere (TOA) in the Tropics is transported toward the poles by the atmosphere and the oceans, where the climate system cools by longwave radiation. Assuming that the total heat content of the climate system is not changing, then the divergence of the total energy transport, Hclim, is equal to the net TOA radiative flux,
i1520-0442-19-7-1167-e1
where [Ftoa] is the net TOA flux into the atmosphere and Hclim is the sum of the atmospheric and oceanic energy transports, Hclim = Hocn + Hatm. The partitioning of the energy transport into its atmospheric and oceanic components is related to the net positive surface fluxes into the atmosphere [Fsfc],
i1520-0442-19-7-1167-e2
Trenberth and Caron (2001) and others have found that the magnitude of the total energy transport is roughly 6 PW (1 PW = 1015 W). Most of the total energy is transported by the atmosphere (5 PW), while the rest is transported by the oceans (1 PW).
Viewing the climate system as a heat engine provides a way of reducing its complexity and affords potential insight into the processes by which the oceans and atmosphere couple. Bjerknes (1964) argued that if the top of the atmosphere radiative fluxes did not vary greatly and the heat storage was nearly constant then the total energy transport would not vary greatly either. Consequently, if either of 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 a stronger oceanic energy transport, that is,
i1520-0442-19-7-1167-e3
This scenario has become known as Bjerknes compensation and could potentially provide insight into the processes by which the atmosphere and the oceans couple. However the relevance of Bjerknes compensation to the climate system crucially depends upon the assumptions that the TOA fluxes and the heat storage variations in the climate system are small compared to the variations in the oceanic and atmospheric energy transport.

There has been little attempt to determine whether these assumptions hold from observations. In particular, the relatively small number of oceanic observations means that the variability of the oceanic energy transport is not as well known as it is in the atmosphere. However, a long integration of a coupled climate model has the potential to provide an excellent test bed to appraise the ideas of Bjerknes. Seager et al. (2002) studied a number of coupled-slab atmosphere models but could find no evidence that Bjerknes compensation occurred when the climatological oceanic heat convergence was removed from the slab model.

This study, however, makes use of the long control integration of the Third Hadley Centre Coupled Ocean– Atmosphere General Circulation Model (HadCM3) to investigate the potential for compensation between the oceanic and atmospheric energy transports and to determine the processes involved. In Shaffrey and Sutton (2004) it was found in HadCM3 that there was no compensation between the oceanic and atmospheric energy transports on interannual time scales, essentially as interannual fluctuation in the oceanic energy transport were balanced by changes in the oceanic heat content. The aim of this study is to focus on longer (decadal) time scales where the changes in the oceanic heat content may be less important, and so Bjerknes compensation may be a more appropriate model.

In the following section, the integration and the model are described in more detail. In section 3, the variability on decadal time scales of the oceanic and atmospheric energy transports are examined. In section 4, the emphasis is on a more detailed analysis of the decadal variability in the North Atlantic, while in section 5 the focus is on the atmospheric processes. Section 6 investigates the time-scale dependence of the compensation and section 7 summarizes the conclusions of this study and discusses possible avenues of future research.

2. Model and data analysis

In this study, the decadal variability of the atmospheric and oceanic energy transports are investigated in a multicentennial control integration of the Hadley Centre coupled climate model, HadCM3. HadCM3 is particularly useful for this study since the 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). 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). 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.

In this study, we analyze 93 decades of the atmospheric and oceanic energy transports. On annual time scales and longer, the atmospheric energy transports can be calculated in a manner similar to Magnusdottir and Saravanan (1999) by integrating the divergence of the zonally averaged surface and TOA fluxes. The atmospheric energy transport, Hatm, is computed from
i1520-0442-19-7-1167-e4
where θ is latitude, a is the radius of the earth, Fsfc and Ftoa are the net surface and top-of-the-atmosphere fluxes, respectively, and [] denotes the zonal sum. The oceanic energy transports, Hocn, were calculated by Helene Banks at the Hadley Centre. The energy flux was calculated at each time step and integrated longitudinally across each oceanic section and then averaged over time,
i1520-0442-19-7-1167-e5
where υ is the meridional current, T is the temperature, c is the oceanic heat capacity, and λ is the longitude.

3. The decadal variability of energy transports in HadCM3

The focus of this section is on the relationships between the decadal variability of the oceanic and atmospheric energy transports in HadCM3, with a particular emphasis on trying to understand the variability within the context of Bjerknes compensation. The decadal variability of the global oceanic energy transport can be seen in Fig. 1a, which shows a Hovmoeller diagram of the decadal oceanic energy transport anomalies in HadCM3. The decadal variability of the global oceanic energy is typically 10% of the mean oceanic energy transport.

Figure 1b shows the decadal anomalies of the Atlantic Ocean energy transport, and it is clear from comparing Figs. 1a and 1b that the variability of oceanic energy transport in the northern extratropics is dominated by fluctuations of the energy transport in the North Atlantic Ocean. The variability in the Atlantic Ocean energy transport is typically coherent throughout the latitudinal extent of the basin, which may suggest that the variability is associated with the changes in the meridional overturning of the thermohaline circulation (e.g., Dong and Sutton 2001). In the Tropics, the decadal variability of the global oceanic energy transport is dominated by the strong fluctuations in the tropical Indo-Pacific Ocean, which isn't explicitly shown but is implied by Figs. 1a and 1b.

The question that now arises is to what extent does the covariability of the anomalies of energy transport correspond to that expected by Bjerknes compensation? The temporal variations in the global oceanic energy transport can be compared with that from the atmosphere in Fig. 1c. Positive anomalies in extratropical global oceanic energy transport (which are dominated by the variability in the North Atlantic) appear to be associated with negative anomalies of energy transport in the northern extratropical atmosphere, whilst there appears to be little relationship between the decadal variability in the tropical oceanic energy transport (which is dominated by the tropical Pacific) and the atmospheric energy transport. Although it cannot be readily determined from Fig. 1, there also appears to be little relationship between the oceanic and atmospheric energy transports in the Southern Ocean.

The relationships that are suggested by Fig. 1 can be more clearly seen in Fig. 2a, which shows the correlation at each latitude between the decadal Atlantic Ocean and atmospheric energy transports. There is a strong degree of anticorrelation between the northern extratropical Atlantic Ocean and atmospheric energy transports. This anticorrelation is strongest at around 70°N but becomes weaker (and statistically insignificant) near the equator.

Figure 2b shows the time series of the atmospheric and North Atlantic Ocean energy transports averaged from 20° to 70°N. As expected from Fig. 2a, the two time series are anticorrelated (−0.57), but it is also clear from Fig. 2b that the magnitude of the decadal variability is similar in both time series. Bjerknes compensation predicts that anomalies of the oceanic and atmospheric should be the same magnitude but of opposite sign. Figure 2b therefore suggests that in the northern extratropics the atmospheric and oceanic energy transports are, to some extent, acting to compensate each other in a manner similar to that expected by Bjerknes compensation. There are also small long-term drifts in the time series of atmospheric and oceanic energy transports, which will be discussed in more detail in the next section.

The partially compensating energy transports in Fig. 2b raise a number of questions:

  • What are the processes that lead to partially compensating decadal anomalies in the northern extratropical atmospheric and Atlantic Ocean energy transports?
  • Why is Bjerknes compensation a poor model of the Tropics in HadCM3?

A starting point for answering the first question is to recognize that the decadal variability of the Atlantic Ocean energy transport is governed by fluctuations in the strength of the meridional overturning circulation (MOC) in the North Atlantic. The magnitude of the MOC is a common measure of the strength of the thermohaline circulation (THC). The THC is responsible for transporting a large amount of heat poleward from low to high latitudes in the Atlantic (e.g., Broecker 1991; Weaver et al. 1999; Ganachaud and Wunsch 2000), and its variability is thought to accompany large changes in climate (e.g., Manabe and Stouffer 1999; Vellinga and Wood 2002). Figure 2b also shows the close correspondence between the time series of MOC and Atlantic Ocean energy transport. This close correspondence also implies that the MOC and northern extratropical atmospheric energy transport are significantly anticorrelated (−0.48).

It appears that the processes that lead to the partial compensation between energy transports involve fluctuations in the strength of the MOC. A deeper understanding of the responses of the ocean and atmosphere to changes in the MOC should unravel the processes that lead to the partial compensation of the atmospheric and the oceanic energy transports. Therefore two further question need to be addressed:

  • What changes in the Atlantic Ocean are associated with the decadal variability in the Atlantic Ocean energy transport?
  • What are the corresponding changes in the atmosphere that are associated with changes in the Atlantic Ocean?

There are a number of caveats that are raised by the questions posed above and the analysis in the following section. The first is that by focusing on the compensation of anomalies we do not consider how those anomalies arise in the first place. Some of the processes that lead to MOC variability in HadCM3 have already been studied. In Dong and Sutton (2005) it was found that the decadal variability in the MOC was associated with changes in the high-latitude salinity advection driven by North Atlantic Oscillation (NAO)-like atmospheric forcing. This contrasts with Vellinga and Wu (2004), who investigated the multidecadal variability in the MOC and found that longer time-scale fluctuations were related to the advection of salinity anomalies that were induced by changes in the tropical surface freshwater flux.

In this study the analysis does not provide the necessary leads and lags to determine how the decadal fluctuations in the oceanic energy transport (and by implication the North Atlantic MOC) came about. The long time scales associated with the ocean result in lag times of many years between the response of the MOC and the anomalous atmospheric forcing. In this sense the cause and effect of the forcing of ocean and the atmosphere becomes blurred when the focus is on the point in time when there are compensating decadal anomalies in the energy transports.

The second caveat is that in a fully coupled system that the questions posed above cannot be regarded as independent, however the goal of posing them is to try and reduce the complexity of the coupled system by focusing on specific mechanisms. With all this in mind, the next section will focus on the changes in the Atlantic Ocean associated with the decadal variability of the Atlantic Ocean energy transport, while section 5 will focus on the associated changes in the atmosphere.

4. The decadal variability of the Atlantic Ocean and the Atlantic Ocean energy transport

The focus of this section will be on the changes in the Atlantic Ocean that are associated with the decadal changes in the oceanic energy transport. A deeper understanding can be gained by considering the heat budget of the Atlantic Ocean,
i1520-0442-19-7-1167-e6
where ohc is the Atlantic Ocean heat content, Hocn is the Atlantic Ocean northward energy transport, and [Fsfc] is the net surface flux into the atmosphere summed zonally over the Atlantic basin. The sum of these three terms equals a residual, R, which arises in these calculations from neglecting some terms that contribute to the heat budget. In particular a correction in the ocean model that is invoked under certain circumstances to prevent the ocean column from freezing has not been included in the budget and so appears in the residual term.

The first two terms of the heat budget can be seen in Fig. 3, while the third term and the residual can be seen in Fig. 4. Most of the decadal variability in the heat budget is in the northern extratropics, and the magnitude of the variability is strongest around 50°N. Figures 4 and 5 also show that the variability of the heat budget in the North Atlantic is a balance between the convergence of the oceanic energy transport and the net surface flux, that is, the first two terms, which are nearly equal and opposite to each other. The decadal variability in the rate of change of the oceanic heat content is relatively small, being roughly an order of magnitude less than those in the first two terms. The variability of the residual is also small as well in comparison to the energy transport convergence and the net surface flux.

The analysis of the Atlantic Ocean heat budget suggests that decadal changes in the heat transport do not alter the oceanic heat content but instead are balanced by the surface fluxes into the atmosphere, where they may potentially alter the atmospheric energy transport. This also suggests that one of the assumptions behind Bjerknes compensation, namely that the oceanic heat content doesn't change, is approximately true for decadal time scales in the Atlantic Ocean of HadCM3.

The focus of the analysis has been on the decadal variability in the ocean heat budget, but it should be noted that there are also smaller changes in the oceanic energy transport time series on much longer time scales (Fig. 2b). In particular, there is a trend (−2.74 × 10−4 PW yr−1) in the Atlantic Ocean energy transport that leads to a weakening of the oceanic energy transport into the Atlantic basin over time. The weakening of the energy transport is not matched by such a strong trend (−1.46 × 10−6 PW yr−1) in the net surface flux into the atmosphere averaged over the Atlantic, which implies that the Atlantic Ocean is cooling on secular time scales.

The cooling of the Atlantic Ocean is shown in the time series of the ocean heat content that is in Fig. 5a. The secular time-scale cooling dominates the time series, whilst the decadal variability is much smaller. This behavior is the opposite of the oceanic energy transport, where the decadal variability dominates over the secular trends. This suggests that the relatively small secular change in the Atlantic Ocean energy transport has a much larger impact on the oceanic heat content than the decadal variability in the oceanic energy transport. This is further evidence that on decadal time scales, the variability of the oceanic energy transport has little impact on the oceanic heat content, a prerequisite for Bjerknes compensation.

The long time-scale cooling in the Atlantic Ocean occurs at depth. Figure 5b shows the difference in the Atlantic Ocean temperature for the last century minus the first century. The strongest cooling is most prominent near the floor of the ocean, with little cooling or even a light warming occurring near the surface. The confinement of the cooling to the ocean floor suggests that long-term changes in water masses such as the Antarctic Bottom Water (AABW) may play a role in the long time-scale cooling of the Atlantic Ocean in HadCM3. These changes don't appear to be strongly communicated to the surface of the Atlantic and hence play no role in the compensating atmospheric and oceanic energy transport anomalies seen on decadal time scales.

Although the decadal variability in the energy transport has a small effect on the total heat content of the ocean, it does have a relatively larger impact on the heat content of the upper ocean. Figure 6a shows the decadal anomalies of the upper 300-m Atlantic Ocean heat content. There is little or no trend in the upper ocean heat content, and instead the largest variability appears to be on decadal time scales. The decadal variability in the upper ocean heat content is largest around 50°N, which is where the variability in the oceanic energy transport convergence is also strongest.

The decadal variability of the surface temperature over the high-latitude Atlantic Ocean appears to be a bit different from the decadal variability of the upper-ocean heat content (Fig. 6b). North of 50°N, the variability in the surface temperature appears to be roughly twice that of the variability in the subtropics, while for the upper-ocean heat content the high-latitude variability is only slightly larger than the subtropical variability. The differences between the high-latitude variability in the surface temperature and the upper-ocean heat content arise for a number of reasons. The average surface temperature is weighted toward regions where the Atlantic basin is narrower, whilst the oceanic heat content is an integral measure across the basin. Air–sea flux variability and sea ice interactions also play a role in enhancing the high-latitude variability of the surface temperature. When the Atlantic Ocean energy transport is stronger than usual, than over the Greenland–Iceland–Norwegian (GIN) Seas there is a reduction in sea ice (not shown). It is also possible that oceanic transports will play a role in enhancing SST variability at higher latitudes.

This section has described the changes in the Atlantic Ocean associated with the decadal variability in the Atlantic Ocean energy transport in HadCM3. On secular time scales there is a cooling of the Atlantic Ocean that is associated with a weakening of energy transport into the basin and changes in the AABW. On decadal time scales, the variability in the convergence of the oceanic energy transport is balanced by changes in the net surface flux. The decadal changes in the total oceanic heat content are relatively unimportant in the vertically integrated heat budget, although there are small changes in the upper-ocean heat content and the high-latitude surface temperature. The impact of the variability of the energy transport on the surface flux and the surface temperature leads us to the question that is posed in the next section, namely, what are changes in the atmosphere that accompany a change in the Atlantic Ocean energy transport?

5. The decadal variability of the atmosphere and the Atlantic Ocean energy transport

In this section, the focus is on the changes in the atmosphere that are associated with the decadal variability of the energy transport in the Atlantic Ocean. In particular the emphasis will be on the processes that lead to changes in the atmospheric energy transport in the northern extratropics, where the negative correlation between atmospheric and Atlantic Ocean energy transports is largest (Fig. 2a).

To determine the processes that lead to changes in the atmospheric energy transport, a regression analysis will be used. Figure 7a shows the decadal surface temperature regressed against a decadal index of the Atlantic Ocean energy transport, averaged between 30°S and 70°N. It is worth noting that the results in this section are insensitive to the choice of the index of the Atlantic Ocean energy transport used in the regressions. The reason for this can be seen in the Hovmoeller Fig. 2b, where the sign of the decadal anomalies in the Atlantic Ocean energy transport is mostly the same across the Atlantic basin.

During decades when the Atlantic Ocean energy transport is large, there is an interhemispheric pattern of surface temperature change, with surface temperatures generally cooling in the Southern Hemisphere and warming in the Northern Hemisphere. An interhemispheric pattern of surface temperature changes might be expected since these regressions are based upon a measure of the pole-to-pole oceanic transport of heat. The pattern of warming in the Atlantic is strongest at higher latitudes and becomes weaker at lower latitudes. The strongest local warming is in the GIN Seas, where the typical surface temperature anomaly for a large deviation in the Atlantic Ocean energy transport is of the order of 1.5 K. The pattern of surface temperatures associated with decadal variability of the Atlantic Ocean energy transport is very similar to the pattern of SST that is associated with the variability of the MOC (Vellinga and Wu 2004).

The changes in the net surface fluxes that are associated with changes in the Atlantic Ocean energy transport are shown in Fig. 7b. Over the North Atlantic, the pattern of changes in the surface fluxes closely mirrors the changes in the surface temperature, in that there is an increased flux into the atmosphere from the warmer North Atlantic. The increases in surface flux, however, only appear to be statistically significant over the GIN Seas where the warming in surface temperature is strongest.

What happens to the extra energy that is input into the atmosphere from the surface? In particular, is the energy that is input into the atmosphere from the surface simply radiated out into space by longwave radiation? Figure 8a shows the net TOA fluxes regressed against the Atlantic Ocean energy transport. There are statistically significant changes in the TOA fluxes over the GIN Seas, where the surface temperature changes are strongest, but they are much smaller than the changes in the net surface flux. The increase in the surface flux for a typically large increase in the energy transport (0.1 PW) would be of the order of 20 W m−2 over the Greenland Sea. The corresponding increase in the TOA flux would be 2 W m−2. This implies that the changes in the net surface flux must be related to compensating changes in the atmospheric energy transport rather than changes in the TOA fluxes, an essential assumption of Bjerknes compensation.

The behavior of the surface and TOA fluxes in the North Atlantic is very different from that in the tropical Atlantic, where the changes in surface fluxes are associated with large changes in the TOA fluxes. It appears that a change in the tropical surface flux can be communicated to the top of the atmosphere quickly and efficiently, for example, via changes in tropical deep convection and precipitation (Fig. 8b). Therefore, it is unlikely that the changes in tropical surface fluxes will be associated with compensating changes in the atmospheric energy transport (as shown in Fig. 2a).

The difference between the Tropics and extratropics can be seen more clearly in Figs. 9a and 9b. Figure 9a shows the variance of the decadal anomalies of the net TOA and net surface fluxes as a function of latitude, while Fig. 9b shows the correlation between the decadal TOA and net surface fluxes. In the northern extratropics, the variance of the surface fluxes is much larger than the variability in the TOA fluxes, and there is no statistically significant relationship between the net surface and the TOA fluxes. This suggests that Bjerknes compensation might hold in the northern extratropics since large changes in the surface fluxes are not related to large changes in the net TOA flux.

This is in contrast to the subtropics, where the variability of the surface and TOA fluxes is roughly comparable and the net surface and TOA fluxes are negatively correlated. The negative correlation in the subtropics implies that an increase in the surface flux into the atmosphere is balanced by a similar increase in the flux out of the TOA, most likely an increase in the clear-sky outgoing longwave radiation. Near the equator, the variance of the surface fluxes is larger than that of the TOA fluxes, but there is also strong positive correlation between the surface and the TOA fluxes. The positive correlation may arise since an increase in the net surface flux will lead to an increase in deep convection and hence result in a decrease in the outgoing longwave radiation. The strong relationship between the TOA and surface fluxes throughout the Tropics implies that Bjerknes compensation is not an appropriate model for the Tropics.

The question that now arises is what are the atmospheric processes involved in the compensation between the northern extratropical atmospheric and Atlantic Ocean energy transports? One argument is that Eq. (2) implies that the increased surface fluxes in the GIN Seas will result in a reduction in the meridional gradient of the net surface flux. To balance the energy budget, this will lead to a reduced total atmospheric energy transport. This simplistic argument does not, however, provide an explanation as to what aspects of the atmospheric circulation are actually altering to compensate the stronger Atlantic Ocean energy transport.

One way in which the atmosphere may be altering is suggested by Fig. 7a. As noted before, the warming of the North Atlantic Ocean associated with an increase in the oceanic energy transport varies with latitude. The largest warming is in the GIN Seas, while the weaker warming is in the subtropical North Atlantic. The pattern of warming in the North Atlantic is therefore reducing the equator-to-pole surface temperature gradient and hence reducing the baroclinicity of the atmosphere. A reduction in the baroclinicity will result in a weaker transport of heat and moisture by the midlatitude storm tracks, that is, a weaker transient energy transport.

To test this hypothesis the atmospheric energy transport could be partitioned into its requisite components. Contributions to the net northward transport of heat and moisture come from the moving air masses in the storm tracks, the quasi-stationary planetary waves and the overturning of the Hadley circulation. The total atmospheric energy transport can be partitioned into contributions from the transient, stationary, and mean motions of the atmosphere (e.g., Magnusdottir and Saravanan 1999):
i1520-0442-19-7-1167-e7
where υ is meridional wind and ϵ is the total moist static energy, υ′ is the deviation from the time average which is denoted as υ, and υ* is the deviation from the zonal average, which is denoted as [υ]. Unfortunately, the 1000-yr control run did not include the diagnostics to calculate this partitioning. However to gain some understanding of the atmospheric processes involved in the partial compensation of the atmospheric and oceanic energy transport, a rerun of 100 yr of the control integration, which includes the necessary data, has been performed.

Figure 10a shows the decadal time series of the atmospheric and Atlantic Ocean energy transports for this 100-yr rerun. During the first 50 yr of the run, the Atlantic Ocean energy transport is larger than average and then weakens for the last 50 yr of the run. The anomalies of the atmospheric energy transport are in the opposite sense but do not completely compensate for the oceanic energy transports. It would be difficult to use a regression analysis on such a short time series to determine the impact of the oceanic energy transport on the components of the atmospheric transport. However, an analysis can be performed by constructing two composites, one that has stronger-than-average oceanic energy transport (decades 2, 4, and 5) and one with a weaker oceanic energy transport (decades 6, 7, and 8).

The composite difference between the atmospheric transient and stationary energy transports for the strong minus weak oceanic energy transports is shown in Fig. 10b. As suggested above the weaker equator-to-pole surface temperature gradient is associated with a weaker transient energy transport in the atmosphere, that is, the weaker baroclinicity in the atmosphere results in weaker transports of heat and moisture in the extratropical storm tracks. The largest changes in the transient energy transport occur at high latitudes where the anticorrelation between the atmospheric and Atlantic Ocean energy transports is strongest (Fig. 2a). It should also be noted that the largest changes in surface temperature gradient also occur at high latitudes. This suggests that it is the strong changes in surface temperature gradient that are most important for the changes in the transient energy transport.

There are also some smaller changes in the stationary energy transport in the midlatitudes. In particular there is a reduction in the stationary energy transport around 30°N when the Atlantic Ocean energy transport is strong. The changes in the stationary energy transport are associated with changes in the atmospheric circulation in the midlatitudes (not shown).

This section has focused on the processes in the atmosphere that are responsible for the partial compensation between the atmospheric and Atlantic Ocean energy transport on decadal time scales. A stronger Atlantic Ocean energy transport leads to a warming of the North Atlantic, this warming being largest in the GIN Seas and weaker in the subtropics. The warming in the GIN Seas leads to significantly increased surface flux into the atmosphere. However, the increase in the TOA fluxes at high latitudes is much weaker than the increase in the surface fluxes. This is not true in the Tropics, where the warming of surface temperature results in changes in the TOA fluxes that are of a similar magnitude. The relative changes in the net surface and TOA fluxes imply that Bjerknes compensation may hold in the midlatitudes, but not in the Tropics.

The warming of surface temperatures in the GIN Seas leads to a reduction in the equator-to-pole surface temperature gradient and hence to a reduction in the baroclinicity of the atmosphere. The reduced baroclinicity leads to a weaker transient energy transport in the midlatitude atmosphere when the Atlantic Ocean energy transport is stronger. The compensation can arise as the weaker transient (and to a lesser extent the weaker stationary atmospheric) energy transports act to partially compensate for the stronger Atlantic Ocean energy transport.

6. The dependence of the compensation on time scale

One issue that remains to be raised is the time-scale dependence of the partial compensation. This dependence is indicated in Fig. 11a, which depicts the correlation between the time series of Atlantic Ocean and atmospheric energy transports for different averaging periods. At interannual time scales, the anticorrelation between the atmospheric and Atlantic Ocean energy transports is weak (−0.3) but becomes stronger (−0.9) for multidecadal time scales. Figure 11a also shows that the ratio of the variability of the atmospheric and ocean energy transport does not vary a large amount for time scales longer than multiannual. Since the ratio of variabilities is the same and the anticorrelation increases with time scale, it implies that the degree of compensation between the atmospheric and oceanic energy transports becomes more important at longer time scales.

The increasing degree of compensation with increasing time scale can be seen more clearly in Figs. 11b and 12. Figure 11b shows the power spectra of the detrended time series of atmospheric and Atlantic Ocean energy transports as a function of frequency, while the coherence and phase between these two time series is shown in Figs. 12a and 12b. Figure 12a suggests that there is little compensation on time scales less than decadal and that most of the compensation occurs on longer time scales. Figure 12b suggests that the relationship between the energy transports alters at time scales longer than decadal, with the variability in the atmospheric and Atlantic Ocean energy transports becoming out of phase.

The question that is raised by Figs. 11 and 12 is why does the degree of compensation increase with time scale. There are two possible explanations. The first is that the variability of the oceanic heat content may be large on shorter time scales. In Shaffrey and Sutton (2004) it was found that compensation did not occur on interannual time scales, as changes in the oceanic heat content become an important part of the heat budget. In particular, there are large changes in the oceanic heat content around the Gulf Stream region of the North Atlantic in response to interannual changes in Ekman transport.

The second possible explanation is that the increasing degree of compensation at longer time scales is related to the increasing dominance of long time-scale fluctuations in the energy transport time series (Fig. 11b). For instance, one interpretation of the results in the previous sections would be that the compensation arises primarily as a response of the atmosphere to the variability of the MOC in the Atlantic Ocean. If this were true then the dominant time scales of variability in the MOC will determine the dominant time scales in the compensation. Figures 11b and 12a are consistent with this interpretation.

It unclear from the analysis in this study whether the interpretation presented above is correct, that is, the atmosphere is responding to changes in the ocean. This is particularly true since the analysis does not contain any lead or lags to determine how the compensating anomalies arise. However, it is easier to contemplate a scenario in which an increased MOC gives rise to a warming of SST in the GIN Seas (Fig. 7a) to which the atmosphere responds than to imagine the opposing scenario. It remains a focus of future research to fully untangle the causality of the partially compensating energy transports.

7. Conclusions

This study has investigated the decadal variability of the atmospheric and oceanic energy transports in a coupled climate model, HadCM3, with a particular focus on the potential for compensation between decadal anomalies of atmospheric and oceanic energy transports that was suggested by Bjerknes (1964).

A summary of the conclusions of this study is as follows:

  • In the northern extratropics, the decadal variability of the Atlantic Ocean dominates the total oceanic energy transport. The decadal variability of the Atlantic Ocean energy transport is associated with fluctuations in the meridional overturning circulation in the North Atlantic, a common measure of the strength of the thermohaline circulation.
  • Decadal anomalies of atmospheric and Atlantic Ocean energy transport are significantly anticorrelated (−0.57). In addition, the decadal variability of the atmospheric energy transport has magnitude similar to the decadal variability in the Atlantic Ocean energy transport. This suggests that the atmospheric and Atlantic Ocean energy transport partially compensate on decadal time scales in a manner that is consistent with Bjerknes (1964) compensation.
  • The compensation between the atmospheric and Atlantic Ocean energy transports is more prominent at high latitudes in the northern extratropics than it is in the subtropics or Tropics. In the Tropics, changes in the surface fluxes are associated with large changes in the TOA fluxes. This suggests that Bjerknes compensation is an inappropriate model for the Tropics.
  • The partially compensating anomalies in the atmospheric and Atlantic arise since an increase in the Atlantic Ocean energy transport results in a strong warming of surface temperature in the GIN Seas and a weaker warming of surface temperature in the subtropical North Atlantic. The changes in the surface temperature result in a reduction in the equator-to-pole surface temperature gradient in the Northern Hemisphere, which reduces the baroclinicity of the atmosphere. As a result, the midlatitude transient energy transport weakens.
  • The degree of compensation between the atmospheric and Atlantic Ocean energy transports is dependent upon time scale, reaching a maximum on multidecadal time scales. This appears to be due to the decreasing importance of oceanic heat storage and the increasing importance of the variability in the oceanic energy transport.

The issues that now arise are to what extent can Bjerknes compensation be seen in other coupled climate models, and whether Bjerknes compensation can be seen in observations of the climate system. In HadCM3, the processes that lead to the partially compensating energy transport are processes that are fundamental to governing the climate. Other coupled models exhibit strong multidecadal variability in the North Atlantic (e.g., Delworth et al. 1993; Eden and Willebrand 2001), but whether this suggests that Bjerknes compensation is a mechanism that is present in other coupled climate models remains to be determined.

Determining whether the atmospheric and Atlantic Ocean energy transport compensate in the climate system is a much more difficult proposition. Although observations show that there is strong multidecadal variability in the North Atlantic (e.g., Delworth and Mann 2000; Curry and McCartney 2001), the variability of the global oceanic energy transports is not well known at present. Another important area for future research is the extent to which Bjerknes compensation is relevant for understanding climatic fluctuations on paleoclimate time scales.

The view that has been put forward in this paper is that the complex behavior of the various components of the coupled climate system might be more easily understood in terms of their energy transports. The partially compensating decadal anomalies of the atmospheric and Atlantic Ocean energy transport have vindicated this perspective and the ideas of Bjerknes (1964). It remains to be seen just how general the results presented here are, but it is clear that further investigation in observational datasets and in other coupled climate models is warranted.

Acknowledgments

This work was supported by the NERC-funded COAPEC thematic program. The authors thank Helene Banks for the use of the oceanic energy transport data, Alan Iwi for use of the 100 yr of atmospheric data, Jonathan Gregory for the MOC data, and Chris Old for advice on calculating the North Atlantic heat budget.

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Fig. 1.
Fig. 1.

Hovmoeller plots showing decadal anomalies of (a) global ocean energy transport, (b) Atlantic Ocean energy transport, and (c) global atmospheric energy transport. The contour interval is 0.03 PW. Negative contours are dashed and negative values are shaded. (d), (e), (f) The standard deviations of the Hovmoeller in (a), (b) and (c) respectively. The units on the y axes are in PW.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3652.1

Fig. 2.
Fig. 2.

(a) Correlation of decadal Atlantic Ocean and atmospheric energy transports for each latitude. (b) Time series of decadal anomalies in extratropical (20° to 70°N) atmospheric energy transport (bold), Atlantic Ocean energy transport (solid), and the Atlantic MOC index (dashed). The units on the y axis in (b) are in (left) PW and (right) Sverdrups

Citation: Journal of Climate 19, 7; 10.1175/JCLI3652.1

Fig. 3.
Fig. 3.

Hovmoeller plots showing Atlantic Ocean decadal anomalies of (a) energy transport convergence and (b) net surface flux. The contour interval in (a) and (b) is 0.008 PW m−1. Negative contours are dashed and negative values are shaded.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3652.1

Fig. 4.
Fig. 4.

Hovmoeller plots showing Atlantic Ocean decadal anomalies of (a) the rate of change of ocean heat content and (b) the residual in the Atlantic Ocean heat budget. In (a) the contour interval is 0.0008 PW m−1 and in (b) it is 0.008 PW m−1. Negative contours are dashed and negative values are shaded.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3652.1

Fig. 5.
Fig. 5.

(a) The time series of the Atlantic Ocean heat content anomalies averaged between 30°S and 70°N. The units on the y axis are 1023 J. (b) Depth–longitude plots showing the difference in the Atlantic Ocean temperature between the last century (years 830–930) minus first century (years 1–100). The contours are at −4, −2, −1, −0.5, 0, 0.5, and 1 K. Negative values are shaded and negative contours are dashed.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3652.1

Fig. 6.
Fig. 6.

Hovmoeller plots showing Atlantic Ocean decadal anomalies of (a) heat content of the upper 300 m of the ocean and (b) surface temperature. In (a) the contour interval is 3 × 1020 J and in (b) the contours are at −0.2, −0.1, −0.05, 0, 0.05, 0.1, and 0.2 K. Negative contours are dashed and negative values are shaded. (c), (d) The standard deviations of (a) and (b), respectively. The units on the y axis in (a) are 1020 J and in (b) are in K.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3652.1

Fig. 7.
Fig. 7.

The regression of (a) surface temperature and (b) net surface flux against the detrended decadal Atlantic Ocean energy transport averaged between 30°S and 70°N. The contour intervals in (a) are at −40, −20, −10, −5, −2, 0, 2, 5, 10, 20, and 40 K PW−1. In (b) the contour intervals are −400, −200, −100, −50, 0, 50, 100, 200, and 400 W m−2 PW−1. Negative contours are dashed and shading denotes regions that are 95% significant.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3652.1

Fig. 8.
Fig. 8.

The regression of (a) TOA flux and (b) precipitation against the detrended decadal Atlantic Ocean energy transport averaged between 30°S and 70°N. The contour interval in (a) is 20 W m−2 PW−1 and contour intervals in (b) are −20, −10, −5, −2, 0, 2, 5, 10, and 20 mm day−1 PW−1. Negative contours are dashed and shading denotes regions that are 95% significant.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3652.1

Fig. 9.
Fig. 9.

(a) Variance of decadal anomalies of zonally averaged net surface (solid) and TOA fluxes (dashed). The units on the y axis are in (W m−2)2. (b) Correlation between the decadal zonally averaged net surface and net TOA fluxes.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3652.1

Fig. 10.
Fig. 10.

(a) Time series of decadal anomalies of energy transports averaged between 20° and 70°N for the Atlantic Ocean (solid) and the atmosphere (dashed). (b) Composite difference of atmospheric transient energy transport (solid) and stationary energy transport (dashed) for strong-minus-weak North Atlantic Ocean energy transport. The units on the y axes are in PW.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3652.1

Fig. 11.
Fig. 11.

(a) The correlation coefficient between the total oceanic and atmospheric energy transports (20° to 70°N) for time series with differing averaging periods in years (bold). The variance of atmospheric (dashed) and Atlantic Ocean (solid) time series for different averaging periods (20° to 70°N). (b) The power spectra of the detrended atmospheric (bold) and the detrended Atlantic Ocean (dashed) energy transports as a function of frequency. The units on the y axis in (b) are in PW.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3652.1

Fig. 12.
Fig. 12.

(a) Coherence and (b) phase as a function of frequency between the atmospheric and Atlantic Ocean energy transports averaged between 20° and 70°N. The spectral analysis was performed on the detrended data using 49 spectral estimates and a Tukey lag window. The units on the y axis in (a) are in PW and in (b) are in radians.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3652.1

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