A general circulation model of intermediate complexity with an idealized Earth-like aquaplanet setup is used to study the impact of changes in the oceanic heat transport on the global atmospheric circulation. Focus is on the atmospheric mean meridional circulation and global thermodynamic properties.

The atmosphere counterbalances to a large extent the imposed changes in the oceanic heat transport, but, nonetheless, significant modifications to the atmospheric general circulation are found. Increasing the strength of the oceanic heat transport up to 2.5 PW leads to an increase in the global mean near-surface temperature and to a decrease in its equator-to-pole gradient. For stronger transports, the gradient is reduced further, but the global mean remains approximately constant. This is linked to a cooling and a reversal of the temperature gradient in the tropics.

Additionally, a stronger oceanic heat transport leads to a decline in the intensity and a poleward shift of the maxima of both the Hadley and Ferrel cells. Changes in zonal mean diabatic heating and friction impact the properties of the Hadley cell, while the behavior of the Ferrel cell is mostly controlled by friction.

The efficiency of the climate machine, the intensity of the Lorenz energy cycle and the material entropy production of the system decline with increased oceanic heat transport. This suggests that the climate system becomes less efficient and turns into a state of reduced entropy production as the enhanced oceanic transport performs a stronger large-scale mixing between geophysical fluids with different temperatures, thus reducing the available energy in the climate system and bringing it closer to a state of thermal equilibrium.

The climate is a forced and dissipative nonequilibrium system, which –
neglecting secular trends – can be considered to be in steady state,
i.e., its statistical properties do not depend on time. Astronomical factors
and differences in local albedo cause a difference in net incoming shortwave
radiation between low and high latitudes leading to differential heating and
a surplus of energy in the tropics. Over a global and long-term average, all
supplied energy is emitted to space, so that the incoming shortwave radiation
is balanced by the outgoing longwave radiation

The oceanic and atmospheric transports result from the conversion of
available potential energy – due to the inhomogeneous absorption of solar
radiation, with a positive correlation between heating and temperature
patterns – into kinetic energy, through instabilities arising, typically,
from the presence of temperature gradients

Recently, using tools of macroscopic nonequilibrium thermodynamics, a
connection has been drawn between a measure of the efficiency of the climate
system, the spatiotemporal variability in its heating and temperature fields,
the intensity of the Lorenz energy cycle and the material entropy production

The atmospheric compensation implies a significant impact of changes in OHT
on the atmospheric circulation as a whole. These changes in the atmospheric
circulation concern the zonally symmetric flow, the zonally asymmetric (eddy)
flow and the interplay between both. Thus, changes in OHT have been commonly
used to account for paleoclimatic changes

A way of studying the impact of changes in OHT on the atmospheric circulation
is to utilize an atmospheric general circulation model coupled to a
mixed-layer ocean. In such a model the OHT can be prescribed. Using a
present-day setup including continents,

Utilizing an idealized aquaplanet setup,

In the present study we extend and supplement the above studies. Based on the
experimental setup of

Furthermore, the integrated effect on the global atmospheric energetics is
assessed by changes in the properties of the effective warm and cold
reservoirs constructed according to the theory proposed in

The paper is organized as follows. In Sect. 2 we describe the model and the experimental design. Section 3 introduces our diagnostics. The results of the analyses are presented in Sect. 4. A summary and discussion concludes the paper (Sect. 5). Appendices A–C give comprehensive descriptions of the main diagnostics.

The Planet Simulator

Following

Oceanic heat transport (in PW) for OHT

A temporally constant flux into the ocean (

For our study we follow Rose and Ferreira but fix the location of the peak by
setting

All simulations are run for at least 100 years (360 days per year). The last
30 years are subject to the analyses. A horizontal resolution of

The dominant feature of the large-scale ocean and the atmosphere dynamics is
the transport of energy from regions featuring a net positive energy budget
at the top of the atmosphere low latitudes) to regions where such a budget is
negative (high latitudes). This reduces the temperature gradient between the
equator and the poles

In the classical view (the Eulerian mean circulation), the mean meridional circulation consists of three cells: the tropical Hadley cell, the Ferrel cell in midlatitudes and a weak polar cell. While the Hadley and the polar cell are thermally direct circulations, i.e., relatively warm air is rising and cold air is sinking, the Ferrel cell is referred to as a thermally indirect cell with warm air sinking and cold air rising. Though the mean meridional circulation can be viewed as a two dimensional circulation in the meridional-height plane, both zonally symmetric and zonally asymmetric components contribute to its existence.

The transformed Eulerian mean (TEM) formalism

Based on work by

Utilizing the Kuo–Eliassen equations allows for identifying individual
drivers of the Eulerian mean meridional circulation (Appendix

This summarizes the diagnostics tools aimed at capturing a phenomenological description of the atmospheric circulation.

A second set of diagnostic tools is based on taking a thermodynamical point
of view on the atmospheric circulation. One finds that on average a net
positive work resulting from the positive correlation between temperature and
heating fields upholds the kinetic energy of the global circulation against
the frictional dissipation

The atmospheric energy cycle

Following the work by

The diagnostics of the Lorenz formulation of the energy cycle reveal
information about the reservoirs partitioned into zonal mean and eddy
components and about the conversions due to different physical processes
(Appendix

We start with the discussion of the effect of OHT changes on the mean climate in terms of
atmospheric near-surface (2 m) temperature, sea-ice and meridional heat
transport. First, we note that, similarly to

Climatological annual averages for all simulations. Upper panel:
zonal mean near-surface temperature (solid lines) and sea-ice cover (dotted lines).
Lower panel: global mean near-surface temperatures
(

Up to about OHT

When inspecting the meridional profiles of the annual and zonal mean
near-surface temperatures, we observe that high latitudes are more sensitive
to the OHT changes than low latitudes. With increasing OHT, polar
temperatures continuously increase except that for
OHT

Sea ice gradually decreases with increasing OHT. However, even for
OHT

Climatological Northern Hemisphere summer (June–August) averages
for all simulations: zonal mean near-surface temperatures (in

Qualitatively, all findings are also true for winter and summer as can be
seen in Fig.

Despite the difference in sea-ice extent (i.e., planetary albedo), the
atmospheric heat transport compensates for the changes in OHT to a large
extent, as can be inferred from the small differences in total meridional
heat transport diagnosed from the energy budget at the top of the atmosphere
(Fig.

Now we shift our attention to the global thermodynamical properties of the system and investigate how the energetics and the entropy budget are impacted by changes in the imposed meridional oceanic heat transport.

As thoroughly discussed in Appendix

Total heat transport (in PW) diagnosed from energy budget at the top
of the atmosphere for OHT

Qualitatively,

Time average of the global mean near-surface temperature

Zonally averaged mean heating rates in the atmosphere for oceanic
heat transport ranging from 0.0 PW (top left panel) to 4.0 PW (bottom right
panel), where grey-shaded areas indicate positive and white areas negative
heating rates in K day

Upper panel: scatterplot of time-averaged global mean near-surface
temperature difference between equator and pole (blue) as well as

Time average of efficiency

The diabatic heating processes constitute the sources and sinks of internal
energy for the atmosphere and play a decisive role in the generation and
destruction of available potential energy

Simulations with 0.5 PW

We see an extension of the area of positive heating in the midlatitudes
towards the poles in the lower troposphere as well as in the equatorial mid-
and upper troposphere for larger values of OHT

We observe, on average, a decline in

As the climate warms and the temperature difference between the warm and the
cold reservoir shrinks with increased OHT

We observe a linear behavior for

We complete our analysis of the thermodynamics of the system by looking into how changes in the meridional oceanic heat transport impact the entropy budget.

As introduced in Appendix

Upper panel: steady-state global mean material entropy production

With increasing values of OHT

Entropy production from moist processes for
OHT

In Fig.

In order to further clarify the impact on the material entropy production of
increasing OHT

Atmospheric heat (moist static energy) transport (in PW) assigned to
different processes for OHT

Convective precipitation gives the largest positive contribution,
particularly in the tropics and subtropics. For increased OHT

Figure

Now we discuss the sensitivity of the atmospheric circulation and transports
to changes in OHT. Figure

In the tropics (0–30

In midlatitudes, eddies dominate the poleward heat transport and its sensitivity to OHT changes, with the contribution from latent heat transport being concentrated equatorward of the contribution from sensible heat transport. Transport of potential energy by eddies is almost absent due to their geostrophic nature (i.e., the meridional velocity is given by the zonal gradient of the geopotential, and thus the zonal average of the product of velocity and geopotential vanishes).

Climatological annual mean mass stream function (in
10

In summary, the atmospheric compensation for changes in OHT takes place according to the relative importance of the respective component for the transport in the reference state where no OHT is present. Even if changes in OHT are very large, it appears that the role of the different mechanisms in controlling the total heat transport remains unchanged: in the inner tropics eddy transport is not important and the poleward energy transport is due to the transport of potential energy by the zonal mean flow. Here, the transport of sensible and latent heat by the zonal mean flow is directed towards the equator, reducing the net transport. Poleward of the outer tropics the eddy transport becomes dominant. The importance of eddy latent transport increases for increasing temperatures as the moisture content is broadly controlled by the Clausius–Clapeyron law, so that the latent heat transport is more important for lower latitudes. Eddy transport of potential energy is negligible, while the transport of potential energy by the zonal mean flow in the midlatitudes is equatorward and counteracts the eddy transport.

The meridional atmospheric energy transport is closely linked to the mean
meridional circulation, which we will study in the following. We start with
the classical Eulerian mean circulation described by a mass stream
function

Climatological annual mean mass stream function (Northern
Hemisphere): strength (in 10

With increasing OHT, the strength of both cells decreases
(Fig.

The Kuo–Eliassen equation allows for identifying individual drivers of the
Eulerian mean meridional circulation (Appendix

Climatological annual mean mass stream function (in
10

Sources (in 10

As an example, Fig.

For the Hadley cell both the contributions coming from heating and friction
decrease linearly with increasing OHT (Fig.

The residual mean stream function

Climatological annual mean residual stream function (in
10

As given in Appendix

Figure

Figure

Concerning the total heat transport, including latent heat,

Figure

Eddy (E–P flux) source of the residual circulation and Stokes
stream function (in 10

Upper panels: climatological annual mean mass stream function (in
10

For increasing OHT, both the dry and the moist isentropic circulation slow
down, and the maxima shift poleward. In accordance with

Finally, we give a synopsis of the above results in terms of the global
energetics provided by the classical Lorenz energy cycle

Figure

As pointed out in Appendix

From energy conservation we know that the decrease in

We conclude that assigning the overall strength of the Lorenz energy cycle to
either the zonal mean or the eddy flow would lead to different results
depending on whether we choose the generation of available potential energy

Consistent with the sensitivity of the transports and the meridional
circulation, the overall decline in the reservoirs and sources with
increasing OHT is also present for conversion terms related to the baroclinic
conversion, i.e.,

We have studied the impact of the oceanic heat transport (OHT) on the atmospheric circulation focusing on two important aspects: changes in the atmospheric meridional heat transport and circulation and changes in global thermodynamic properties of the atmosphere including efficiency, irreversibility and the Lorenz energy cycle.

Using a general circulation model of intermediate complexity (PlaSim)
including an oceanic mixed layer, we have adopted an experimental design from

Climatological mean Lorenz energy cycle: reservoirs (upper panel, in
10

We found a compensation of the changes in oceanic heat transport by the
atmosphere consistent with Stone's (1978) conclusions. The presence of sea
ice may explain the deviations from a perfect compensation as discussed in

In agreement with Rose and Ferreira, we have found an increase in the global
mean near-surface temperature and a decrease in the equator-to-pole
temperature gradient, with increasing OHT for OHT

A tropical cooling for imposed oceanic heat transports somewhat larger than
present-day values has also been found by

Time average of the intensity of the Lorenz energy cycle

Confirming the results of previous studies

Sea ice gradually decreases with increasing OHT. Though in annual averages
sea ice is present for all simulations, for OHT

Separating individual sources by applying the Kuo–Eliassen equation showed
that the characteristics of the Hadley cell can be explained by the mean
meridional circulations related to the diabatic heating and, to a smaller
extent, to the friction. In our simulations, the meridional circulation
induced by friction also controls the behavior of the Ferrel cell. Eddy
transports of heat and momentum appear to be less important for the Eulerian
mean circulation. This is different from results by

The importance of the eddies for the circulation becomes clear when considering the combined effect of the eddies by applying the TEM formalism. Here, the eddies set up an eddy-related (Stokes) circulation dominating the midlatitudes with strong sensitivity to changes in OHT.

In agreement with

We utilized an alternative approach to assess the sensitivity of the climate
system by studying the response of global thermodynamical properties of the
climate system following a theoretical framework introduced by

Increasing OHT leads to a reduction in the difference between the warm pool
temperature

The effect of thermalization leading to the reduction in the efficiency of
the system with increasing intensity of the ocean heat transport can be
related to the decrease in the reservoir of the potential energy available
for conversion in the Lorenz energy cycle. The strength of the Lorenz energy
cycle linearly decreases with increasing OHT. A change to smaller sensitivity
is observed at OHT

Consistent with the changes in heat transport and meridional circulation, the
magnitude of all reservoirs and conversions of the Lorenz energy cycle
decreases with increasing OHT. However, the sensitivities differ.

When considering stronger oceanic transport, the climate system is
characterized by a declining total material entropy production, while the
degree of irreversibility

Recently,

Overall, our study demonstrates the large impact of the oceanic heat transport on the atmospheric circulation affecting the zonally symmetric flow, the zonally asymmetric flow and the interaction between both. By reducing the meridional temperature gradient, an increased oceanic heat transport slows down the atmospheric mean meridional circulation and shifts the Hadley and the Ferrel cell. In addition, changes in OHT substantially modify global thermodynamic properties such as the strength of the Lorenz energy cycle, the efficiency, the entropy production and the irreversibility.

The reduction in the meridional gradient of the near-surface temperature is
one of the major features of global warming.

Apart from the meridional overturning circulation in the Atlantic,
significant modifications to the oceanic circulation in a warmer climate can
also be found in the equatorial Pacific, and they are strongly linked to El
Niño–Southern Oscillation (ENSO) variability

Complementing the investigation by

Another possible future line of investigation may deal with studying planets
with different astrophysical parameters, such as rotation rate, eccentricity,
and obliquity, with the goal of contributing to the rapidly growing field of
the investigation of the atmospheres of exoplanets along the lines of some
recent investigations

To analyze the mean meridional circulation we make use of the so-called
Kuo–Eliassen equation

Applying the quasi-geostrophic approximation and defining a stream
function

We solve the Kuo–Eliassen equation for

While the Kuo–Eliassen equation gives us the classical three-cell picture of
the mean meridional circulation, the TEM formalism

Defining the residual stream function

Here, the total effect of the eddies on the meridional circulation (viewed
from a Lagrangian perspective) is given by the divergence of the
Eliassen–Palm flux (

Though representing a different view of the circulation, and, in particular
of the role of the eddies, the Kuo–Eliassen equation and the TEM equation
represent the same physics. This can be seen by rearranging the terms of the
Kuo–Eliassen or the TEM equation (and neglecting differences between
globally and zonally averaged stability) to give

Let

Hence, the motion of the general circulation of the system can be sustained against friction because zones being already relatively warm absorb heat, whereas the relatively low-temperature zones are cooled.

The Lorenz energy cycle can thus be seen as resulting from the work of an
equivalent Carnot engine operating between the two (dynamically determined)
reservoirs at temperatures

Let us now delve into such irreversible processes. In the climate system two
rather different sets of processes contribute to the total entropy production

The entropy budget of geophysical fluids at steady state, following

In a steady-state climate the material entropy production

One needs to underline that a more refined treatment of the entropy
production related to the hydrological cycle has been proposed by, e.g.,

Note that one can compute the entropy production as

We can now separate in Eq. (

If we take the ratio of the two terms on the right-hand side in
Eq. (

The atmospheric energy cycle proposed by

Referring to the reservoirs of zonal available potential energy, eddy
available potential energy, zonal kinetic energy and eddy kinetic energy as

To compute the individual contributions, we follow the work of

The external sources and/or sinks are diagnosed from the respective residuals. We note that in Ulbrich and Speth (1991) these energetics were formulated for a mixed space–time domain. In our case, however, the contributions by stationary eddies are 0 because of the zonally symmetric forcing.

We also note that by using above equations the computed annual averaged
values include contributions from the annual cycle. It turns out, however,
that only the reservoirs

The authors wish to acknowledge support by the Cluster of Excellence CliSAP. V. Lucarini wishes to acknowledge the financial support provided by the FP7 ERC-Starting Investigator Grant NAMASTE – Thermodynamics of the Climate System (Grant no. 257106). We thank the anonymous reviewers for constructive criticism and, in particular, F. Laliberté for his thorough evaluation and his valuable suggestions. The preparation of this work greatly benefitted from interactions with D. Battisti, J. Marshall, O. Pauluis, T. Schneider, and P. Stone. Edited by: D. Kirk-Davidoff