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 ocean and atmosphere transport the excess of energy from the tropics to high latitudes so that the horizontal divergence of the large-scale transport performed by the geophysical fluids on the average balances out the radiative imbalances at the top of the atmosphere.

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 . Such instabilities tend to reduce the same temperature gradients they feed upon by mixing oceanic and atmospheric masses. The kinetic energy is then dissipated inside the system. The production of available potential energy, its conversion to kinetic energy, and the dissipation of kinetic energy have the same average rate, which corresponds to the intensity of the energy cycle.

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 . As mentioned above, the climate can be considered as a (forced and dissipative) nonequilibrium thermodynamic system where the entropy budget is achieved in such a way that the sum of the incoming entropy flux due to the solar high-frequency photons, and the entropy generated by irreversible processes in the atmosphere and ocean, is balanced out by the radiation to space of low-frequency photons. Most of the entropy production results from optical processes, while a smaller portion – referred to as material entropy production – is related to the irreversible processes related to diffusion and dissipation taking place in geophysical fluids . So the Earth is, in contrast to a system that is isolated and therefore maintained in a state of equilibrium, a thermodynamic system that exchanges energy and entropy with space .

argued that the magnitude of the total meridional heat transport, i.e., the sum of the oceanic and the atmospheric contributions, is almost insensitive to the structure and the specific dynamical properties of the atmosphere–ocean system, so that changes in the oceanic heat transport (OHT) will be balanced out by the atmospheric flow and vice versa. In particular, he suggested that the peak of the heat transport is constrained within a narrow range of latitudes regardless of the radiative forcing. Stone concluded that features of the meridional heat transport can be related to the solar constant, the radius of the Earth, the tilt of the Earth's axis and the hemispheric mean albedo. He argued that the insensitivity to the structure and to the dynamics of the system is due to the correlation of thermal emissions to space, the albedo and the efficiency of the transport mechanisms of the atmosphere and the ocean.

discussed the limits of the hypothesis by employing a series of coupled atmosphere–ocean–sea-ice model experiments in which the oceanic circulation on an aquaplanet is constrained by different meridional barriers. The presence or absence of the barriers results in significantly different climates, in particular in climates with and without polar ice caps. Enderton and Marshall concluded that Stone's result is a good guide for ice-free climates. However, they also noted that the effect of the related meridional gradients in albedo on the absorption of solar radiation needs to be taken into account if polar ice caps are present.

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 e.g.,. Moreover, OHT is an important factor for potential anthropogenic climate change since significant modifications to it can be expected. Unfortunately, there are large uncertainties in the changes in the oceanic circulation simulated in climate change scenarios . These result from, amongst others, uncertainties in freshwater forcing due to potential melting of inland ice sheets. To assess the role of the ocean for historical and potential future climates the impact of the OHT on the atmospheric circulation and the underlying mechanisms need to be investigated systematically.

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, , , and found that increasing OHT results in a warmer climate with less sea ice. A reduction in low-level clouds and an increase in greenhouse trapping due to a moistening of the atmosphere appeared to be relevant mechanisms. In addition, a weakening of the Hadley cell with increased OHT was found by and .

Utilizing an idealized aquaplanet setup, systematically assessed the impact of the OHT on the atmospheric global mean near-surface temperature and its equator-to-pole gradient. For warm and ice-free climates, they confirm a near-perfect atmospheric compensation of the imposed changes in OHT. Like in the above studies including continents, found an increase in global mean temperature for increasing OHT, accompanied by a decrease in the equator-to-pole temperature gradient. Tropical SSTs (sea surface temperatures) were shown to be less affected than those at higher latitudes. The detailed meridional structure of the oceanic heat transport turned out to be less important. Changes in deep moist convection in the midlatitudes, together with an enhanced water vapor greenhouse effect, appear to be the major drivers. confirmed the low sensitivity of tropical SSTs to OHT changes. In their aquaplanet experiments, larger OHT leads to a weakening of the Hadley cell, which reduces cloud cover and surface winds and thus counteracts surface cooling resulting from increasing OHT.

In the present study we extend and supplement the above studies. Based on the experimental setup of , we focus on the impact of OHT changes on the atmospheric dynamics and thermodynamics. Our overall goal is to understand how the atmospheric energy transport and transformations are affected by modulations in the oceanic transport. We analyze the changes in the atmospheric heat transport and the mean meridional circulation by employing, amongst others, the Kuo–Eliassen equation in order to understand the various drivers of the mean meridional circulation.

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 and . This allows for defining a measure of the efficiency of the climate system viewed as an (equivalent Carnot) engine. Attention is directed to measuring the irreversibility of the atmosphere and the material entropy production. This point of view is useful for providing a general physical framework to relevant climatic processes, trying to advance the understanding of the climate as a nonequilibrium, forced and dissipative macroscopic system. Links between the climate engine view and the classical Lorenz energy cycle provide a consistent picture of the observed changes and document the relevance of the climate engine approach.

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 PlaSim; is an open-source general circulation model (GCM) of intermediate complexity developed at the University of Hamburg. For the atmosphere, the dynamical core is the Portable University Model of the Atmosphere (PUMA) based on the primitive-equation multilevel spectral model of and . Radiation is parameterized by differentiating between shortwave and longwave radiation and between a clear and a cloudy atmosphere. The respective schemes follow the works of for the shortwave part and for the longwave part. The radiative properties of clouds are based on and . Cloud fraction is computed according to . The representation of boundary-layer fluxes and of vertical and horizontal diffusion follows , , , and . The cumulus convection scheme is based on . The ocean is represented by a thermodynamic mixed-layer (slab ocean) model including a one-layer thermodynamic sea-ice component.

Following we used an Earth-like aquaplanet setup with zonally symmetric forcing utilizing reference present-day conditions for the solar constant (1365 W m-2) and the CO2 concentration (360 ppm). The solar insolation comprises an annual cycle (with obliquity = 23.4∘), but eccentricity is set to 0. Thus, on annual average the forcing is hemispherically symmetric as well. The mixed-layer depth is set to 60 m.

A temporally constant flux into the ocean (q-flux) is used to prescribe the oceanic heat transport (OHT) according to the analytic expression given by : OHT=OHT0⋅sin⁡(ϕ)cos⁡(ϕ)2N, where ϕ denotes the latitude. N is a positive integer which determines the latitude of the maximum of the transport and the shape of its meridional profile, and OHT0 is a constant defining its magnitude. Rose and Ferreira made sensitivity experiments by varying N (ranging from 1 to 8) and by varying the peak transport (ranging from 0 to 4 PW), which is controlled by OHT0.

For our study we follow Rose and Ferreira but fix the location of the peak by setting N = 2 (which corresponds to maximum transport at 27∘). We perform nine sensitivity simulations with respect to the magnitude of the transport by changing OHT0 to obtain peak transports OHTmax from 0 to 4 PW (with 0.5 PW increment). OHTmax = 0 PW (i.e., no OHT) serves as the control simulation. The OHT for OHTmax = 0, 1, 2, 3 and 4 PW is displayed in Fig. .

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 T31 (96 × 48 grid points) with five σ levels in the vertical is used. The time step is Δt = 23 min.

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 e.g.,. In present conditions, the partitioning of heat transport between atmosphere and ocean reflects two limits: the dominance of the atmospheric mass transport in mid- to high latitudes and the dominance of the oceanic energy transport in the tropics. The atmospheric transport can be further subdivided in the sensible-heat, latent-heat and potential-energy components. We will investigate the response of changes in the imposed OHT for each of these components and will further focus the analysis by considering both the zonally symmetric contributions, due to the mean meridional circulation (MMC) and the zonally asymmetric contributions, due to the atmospheric eddies.

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 accounts for the role of the eddies in the mean meridional transport. In particular, it provides a closer link to the total atmospheric meridional heat transport. The TEM residual circulation approximates the (dry) isentropic mean circulation resulting in a single cell from the equator to the pole.

Based on work by , showed that the atmospheric heat transport can be represented by the product of a moist TEM residual circulation and the vertical contrast in moist static energy (or equivalent potential temperature θe). The moist residual circulation is given by replacing all terms containing dry static energy (or potential temperature) by their moist analogs.

Utilizing the Kuo–Eliassen equations allows for identifying individual drivers of the Eulerian mean meridional circulation (Appendix ). A similar partitioning is done for TEM residual stream function which provides a direct link to the atmospheric heat transport. However, and pointed out that there is no simple way to represent a well-defined moist isentropic circulation in the latitude–pressure plane. Therefore, in order to assess the effect of moisture, we additionally investigate the mean circulation on dry and moist isentropes.

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 is one of the most important concepts used to understand the global atmospheric circulation as it provides a comprehensive look at the integrated effects of physical mechanisms involved, the generation of available potential energy by external forcing, the dissipation of kinetic energy and the energy conversions by baroclinic and barotropic processes. If the climate system is in a statistical steady state, the rate of generation of available potential energy G˙, the rate of conversion of potential into kinetic energy W˙, and the dissipation rate of kinetic energy D˙ are equal when averaged over a long period of time (e.g., several years). Thus, G˙‾ = W˙‾ = D˙‾ > 0, where the bar indicates the operation of time averaging. This allows for characterizing the strength of the energy cycle in several ways.

Following the work by and , we consider the global energy cycle as resulting from the work of an equivalent Carnot engine operating between the two (dynamically determined) reservoirs at temperature Θ+ and Θ-. According to this concept, an efficiency of the climate system (η) can be defined by η=Θ+-Θ-Θ+. Furthermore, following the same theoretical point of view, we analyze the entropy production which leads to a measure of the irreversibility of the climatic processes. An outline of the theory and the according diagnostics is given in Appendix .

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 gain evidence about the relative importance of the individual components contributing to the energy cycle and the related thermodynamic properties. Furthermore, the classical Lorenz energy cycle helps to provide a link between the phenomenological view (given by the circulation and transports) and the thermodynamic view (the equivalent Carnot engine), thus demonstrating the relevance of the latter.

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 . Here, an imposed oceanic heat transport of simple analytic form and with varying strengths allows for systematic analyses.

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 . While all components of the atmospheric heat transport are affected by the compensation, their relative importance for the total transport remains almost unchanged. While the atmosphere counterbalances the changes in the OHT very effectively, so that the total meridional heat transport is weakly altered, the climate as a whole strongly depends on the OHT value chosen. The basic reason for this is that the atmosphere and the ocean transport heat at different heights and across different temperature gradients.

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 OHTmax < 3 PW. For larger OHT, the temperature gradient still decreases but the global average remains constant. For the tropics, there is a significant decrease in both temperature and its gradient for OHTmax > 2 PW, with a reversal of the gradient for OHTmax > 3 PW. For smaller OHT, we observed a slight warming and a reduction in the gradient with increasing OHT. The latter is consistent with results from . However, on their aquaplanet the tropical temperature showed little sensitivity, with small increases for all imposed (positive) OHTs (up to 3 PW).

A tropical cooling for imposed oceanic heat transports somewhat larger than present-day values has also been found by in a more complex coupled atmosphere–slab ocean model with a present-day land–sea distribution. They argue that this suggests that present-day climate is close to a state where the warming effect of OHT is maximized. related the tropical cooling to a strong cloud–SST feedback and showed that the results are sensitive to the particular parameterizations. Though our simulations are highly idealized and do not represent all the complexities of the real climate system, it is interesting to note that we find almost no further increase in the global near-surface temperature for OHTmax > 2.5 PW and maxima in Θ+ and Θ- at about the same value of OHT.

Confirming the results of previous studies , we have found a decrease in the Hadley cell for increasing OHT. In addition, the Hadley cell broadens and the maxima of the Hadley and the Ferrel cell shift poleward when OHT obtains large values (OHTmax > 2.5 PW).

Sea ice gradually decreases with increasing OHT. Though in annual averages sea ice is present for all simulations, for OHTmax > 2 PW areas of open water are present for all latitudes during summer. This may suggest that sea ice plays an important role in controlling the global mean temperature and/or the position of the Ferrel cell. However, we did not find sufficient evidence to support this hypothesis.

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 , where the mean meridional circulation related to eddy fluxes accounts for about 50 % of the Ferrel cell's strength. The coarse vertical resolution may be responsible for a reduced eddy activity.

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 the total atmospheric meridional heat transport is related to the strength and vertical extent of the circulation on isentropes both for the dry and the moist case. As obtained by scale analysis by Czaja and Marshall, the residual mean stream function in the midlatitudes is dominated by the so-called eddy stress which is given by the meridional transport of static energy.

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 . Here, the climate system is viewed as an (equivalent Carnot) engine with a certain efficiency. Linking the climate engine view and the classical Lorenz energy cycle provided a consistent picture of the observed changes and, thus, demonstrated the relevance of the climate engine approach.

Increasing OHT leads to a reduction in the difference between the warm pool temperature Θ+ and the cold pool temperature Θ-. The latter implies that the atmospheric system becomes more isothermal in the horizontal. The temperature difference between the warm (Θ+) and the cold (Θ-) heat reservoir decreases for increasing oceanic heat transport. This is basically caused by enhanced warming in the extratropics and by tropical cooling for increasing OHT. One of the main drivers for this is the poleward relocation of latent heat release patterns (not shown). This may lead to further warming due to the water vapor feedback .

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 OHTmax = 2.5 PW.

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. PM and the conversion from PM to PE exhibit the largest changes. Eddy kinetic energy, the barotropic conversion from eddy kinetic energy to zonal mean kinetic energy, and the conversion from zonal mean kinetic energy to PM are least affected.

When considering stronger oceanic transport, the climate system is characterized by a declining total material entropy production, while the degree of irreversibility α increases, since the decrease in entropy production by frictional dissipation is more intense than the decrease in entropy generation due to sensible and, in particular, latent heat flux. The increase in the index of irreversibility is a direct consequence of the decrease in the efficiency η, due to the reduction in temperature gradients inside the system, in agreement with what is found in and . The flux of latent heat contributes most to the material entropy production in the climate system. When increasing the heat transport in the ocean from 0.0 to 1.5 PW, material entropy production due to latent heat flux increases, which can be explained by an outspread of convection from the deep tropics into the midlatitudes, while the maximum latent release is still located in the central tropics. When increasing the heat transport further, convective processes collapse in the deep tropics and, thus, affecting evaporation intensities at tropical sea surface by reducing it. As a result, a decrease in material entropy production by latent heat fluxes can be noted from the increase in the oceanic heat transport larger than 2.0 PW.

Recently, proposed a different thermodynamic point of view from the one taken here, indeed confirming the relevance of looking at the climate system as a heat engine. They studied using models and reanalyzed the work output of the climate engine. In doing so, they showed that it is constrained by the power necessary to maintain the hydrological cycle, which accounts for the moisture inefficiency related to the addition of water vapor to unsaturated air. For a warmer climate they found a reduction in the work output consistent with our results for increasing OHT. attributed most of the response to an increase in the moistening inefficiency. There is a strong indication that this is also true in our case due to a large increase in near-surface specific humidity and evaporation with only moderate changes in near-surface relative humidity. However, further diagnostics are necessary to quantify the impact of moistening inefficiency.

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. showed a consistent weakening and poleward expansion of the Hadley cell in IPCC AR4 simulations. Hence, changes in the oceanic heat transport may significantly modify the response of the atmospheric circulation to greenhouse warming. A weakening of the oceanic meridional overturning circulation, as predicted by the majority of coupled ocean–atmosphere general circulation models (though with large uncertainties; ), would therefore act as a negative feedback mechanism. This negative feedback might become even more important when strong melting of inland ice sheets, due to global warming, is taken into account. The associated input of large amounts of freshwater has a huge potential to slow down the oceanic circulation.

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 e.g.,. This gives rise to an additional potential feedback mechanism related to oceanic dynamics which is not captured by slab ocean models e.g.,.

Complementing the investigation by and helping to understand the properties of warm equable climates, a subsequent study may focus on the role of latitudinal location of the peak OHT. In the present set of experiments, the peak oceanic transport was fixed at the latitude of 27∘. Due to the local atmospheric compensation, this preferentially affects the atmospheric eddy transport of latent heat, which is dominant in this region. The overall response may be different if the OHT peak is located in regions where other components of the atmospheric heat transport are more important.

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 .