Download Bjerknes Compensation and the Decadal Variability of the Energy

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SHAFFREY AND SUTTON
Bjerknes Compensation and the Decadal Variability of the Energy Transports in a
Coupled Climate Model
LEN SHAFFREY
AND
ROWAN SUTTON
Department of Meteorology, University of Reading, Reading, United Kingdom
(Manuscript received 11 October 2004, in final form 23 March 2005)
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.
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,
Corresponding author address: Dr. Len Shaffrey, Dept. of Meteorology, University of Reading, P.O. Box 243, Earley Gate,
Reading, Berkshire, RG6 6BB, United Kingdom.
E-mail: [email protected]
© 2006 American Meteorological Society
⵱ · Hclim ⫽ ⵱ · 共Hatm ⫹ Hocn兲 ⫽ 关Ftoa兴,
共1兲
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],
⵱ · Hatm ⫽ 关Ftoa ⫺ Fsfc兴.
共2兲
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.
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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,
⌬Hclim ⫽ ⌬Hatm ⫹ ⌬Hocn ⫽ 0.
共3兲
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
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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
⭸
1
共cos␪Hatm兲 ⫽ 关Fsfc ⫺ Ftoa兴,
a cos␪ ⭸␪
共4兲
where ␪ 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,
冕
Hocn ⫽ c ␷T d␭,
共5兲
where ␷ is the meridional current, T is the temperature,
c is the oceanic heat capacity, and ␭ 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
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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.
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 correla-
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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
tion 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 compen-
sating 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 atmo-
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sphere 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,
⭸共ohc兲
⭸Hocn
⫹ 关Fsfc兴 ⫹
⫽ R,
⭸y
⭸t
共6兲
where ohc is the Atlantic Ocean heat content, Hocn is
the Atlantic Ocean northward energy transport, and
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[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
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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.
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 oce-
anic 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 upperocean 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 variabil-
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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.
ity 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
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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.
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
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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.
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 com-
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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.
parable 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.
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.
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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.
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):
Hatm ⫽ ␷⑀ ⫽ ␷⬘⑀⬘ ⫹ ␷*⑀* ⫹ 关 ␷兴关 ⑀兴,
共7兲
where ␷ is meridional wind and ⑀ is the total moist static
energy, ␷⬘ is the deviation from the time average which
is denoted as ␷, and ␷* is the deviation from the zonal
average, which is denoted as [␷]. 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
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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.
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-topole 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 At-
lantic 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
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SHAFFREY AND SUTTON
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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.
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.
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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.
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 atmo-
spheric 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-topole 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 ob-
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SHAFFREY AND SUTTON
servations 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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