Global Pattern Formation of Net Ocean Surface Heat Flux Response to Greenhouse Warming

Shineng Hu Lamont-Doherty Earth Observatory of Columbia University, Palisades, New York, and Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California

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Shang-Ping Xie Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California

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Wei Liu Department of Earth and Planetary Sciences, University of California, Riverside, Riverside, California

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Abstract

This study examines global patterns of net ocean surface heat flux changes (ΔQnet) under greenhouse warming in an ocean–atmosphere coupled model based on a heat budget decomposition. The regional structure of ΔQnet is primarily shaped by ocean heat divergence changes (ΔOHD): excessive heat is absorbed by higher-latitude oceans (mainly over the North Atlantic and the Southern Ocean), transported equatorward, and stored in lower-latitude oceans with the rest being released to the tropical atmosphere. The overall global pattern of ΔOHD is primarily due to the circulation change and partially compensated by the passive advection effect, except for the Southern Ocean, which requires further investigations for a more definitive attribution. The mechanisms of North Atlantic surface heat uptake are further explored. In another set of global warming simulations, a perturbation of freshwater removal is imposed over the subpolar North Atlantic to largely offset the CO2-induced changes in the local ocean vertical stratification, barotropic gyre, and the Atlantic meridional overturning circulation (AMOC). Results from the freshwater perturbation experiments suggest that a significant portion of the positive ΔQnet over the North Atlantic under greenhouse warming is caused by the Atlantic circulation changes, perhaps mainly by the slowdown of AMOC, while the passive advection effect can contribute to the regional variations of ΔQnet. Our results imply that ocean circulation changes are critical for shaping global warming pattern and thus hydrological cycle changes.

Corresponding author: Shineng Hu, shineng.hu@gmail.com

Abstract

This study examines global patterns of net ocean surface heat flux changes (ΔQnet) under greenhouse warming in an ocean–atmosphere coupled model based on a heat budget decomposition. The regional structure of ΔQnet is primarily shaped by ocean heat divergence changes (ΔOHD): excessive heat is absorbed by higher-latitude oceans (mainly over the North Atlantic and the Southern Ocean), transported equatorward, and stored in lower-latitude oceans with the rest being released to the tropical atmosphere. The overall global pattern of ΔOHD is primarily due to the circulation change and partially compensated by the passive advection effect, except for the Southern Ocean, which requires further investigations for a more definitive attribution. The mechanisms of North Atlantic surface heat uptake are further explored. In another set of global warming simulations, a perturbation of freshwater removal is imposed over the subpolar North Atlantic to largely offset the CO2-induced changes in the local ocean vertical stratification, barotropic gyre, and the Atlantic meridional overturning circulation (AMOC). Results from the freshwater perturbation experiments suggest that a significant portion of the positive ΔQnet over the North Atlantic under greenhouse warming is caused by the Atlantic circulation changes, perhaps mainly by the slowdown of AMOC, while the passive advection effect can contribute to the regional variations of ΔQnet. Our results imply that ocean circulation changes are critical for shaping global warming pattern and thus hydrological cycle changes.

Corresponding author: Shineng Hu, shineng.hu@gmail.com

1. Introduction

Global warming is not spatially uniform (Xie et al. 2010). Over the instrumental era, the subpolar North Atlantic has warmed less than the ocean nearby, resulting in a so-called warming hole (Drijfhout et al. 2012; Rahmstorf et al. 2015; Sévellec et al. 2017). Similarly, the Southern Ocean has experienced suppressed surface warming since the 1950s (Armour et al. 2016). In the tropics, the Indian Ocean has warmed faster than the rest of tropical oceans by about a half (Du and Xie 2008; Hu and Fedorov 2019). Admittedly, the observed trends in the historical period resulted from various external forcing and could be influenced by internal climate variability. Some of the observed features such as the suppressed warming over the subpolar North Atlantic are also seen in general circulation model (GCM) simulations forced by increased carbon dioxide alone, although details are expected to differ across models or between models and observations.

Sea surface temperature (SST) patterns effectively modulate atmospheric circulation and hydrological cycle, a causal relationship that motivates SST-forced atmospheric GCM (AGCM) experiments, such as the Tropical Oceans–Global Atmosphere (TOGA) design (Lau and Nath 1994). Under global warming, the spatial variations of rainfall response in the tropics and subtropics are found to follow a warmer-get-wetter pattern (Xie et al. 2010), although its latitudinal distribution follows a wet-get-wetter, dry-get-drier pattern except near the equator (Held and Soden 2006). Additionally, the surface warming pattern is now recognized as a key factor to the time-varying global climate feedback that in turn constrains the transient rate of global warming (Armour et al. 2013; Andrews et al. 2015). Therefore, understanding what shapes the SST response pattern under global warming is critical for both regional and global climate changes.

Both oceanic and atmospheric processes can directly influence SST (or mixed-layer temperature) variations in time and space. Ocean circulation transports heat horizontally and vertically, and the resultant convergence or divergence of heat tends to warm or cool the local ocean temperature. Besides that, any atmospheric processes perturbing surface energy budget can also affect SST thermodynamically. Here we emphasize that the two controlling factors are inherently connected at the ocean–atmosphere interface via net ocean surface heat flux Qnet (positive being downward), including sensible and latent turbulent heat fluxes, and shortwave and longwave radiative fluxes.

There are two constraints for Qnet as summarized in the schematic diagram in Fig. 1. First, Qnet is directly influenced by SST and the atmospheric state (surface wind, air temperature, clouds, water vapor, etc.); the latter is in turn closely related to the underlying SST. This atmospheric constraint allows the possibility to infer the SST field when the Qnet field is known. Second, the heat that goes into the ocean is either stored locally or diverges away, implying a strict oceanic constraint. The current study mainly concerns the oceanic constraint, while the atmospheric constraint will be discussed in a forthcoming companion paper.

Fig. 1.
Fig. 1.

A schematic of ocean–atmosphere coupled system response to external radiative forcing. Net ocean surface heat flux Qnet serves as a key quantity that couples the ocean and the atmosphere and is fundamentally constrained by oceanic and atmospheric processes.

Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-19-0642.1

The main goal of this study is to identify the formation mechanisms for the global ΔQnet pattern in a transient warming climate; hereafter Δ represents anomalies induced by greenhouse warming. Although the radiative forcing of carbon dioxide is more or less uniform in space (Huang et al. 2017), the resultant ΔQnet after a few years of ocean–atmosphere interactions can exhibit marked spatial variations. As we will show later, the amplitude of the local ΔQnet can easily be an order of magnitude greater than its global-mean value. Such strong regional variations in ΔQnet are suggested to effectively modulate the transient climate response to greenhouse warming (Winton et al. 2010).

Specifically, we will take a closer look at the positive ΔQnet over the North Atlantic, a key region with prominent ocean heat uptake found in both observations and climate warming simulations. Some studies have attributed the positive ΔQnet to the slowdown of AMOC under global warming (Winton et al. 2013; Rugenstein et al. 2013; Marshall et al. 2015; Shi et al. 2018). The greenhouse warming–induced slowdown of AMOC implies a weaker northward ocean heat transport toward the subpolar North Atlantic, causing a suppressed local warming that allows anomalous heat uptake from the atmosphere. Winton et al. (2013) contrasted a globally fixed-currents simulation with a regular free-currents simulation under greenhouse warming and concluded that the North Atlantic heat content increase is due primarily to ocean circulation changes. Here we describe an alternative novel modeling approach that focuses on the impacts of the Atlantic Ocean circulation changes, particularly the AMOC slowdown, under global warming; our simulations support this idea.

We introduce the climate model used and the experimental setup in section 2. The methodology we use to diagnose the model outputs, including the decomposition of ΔQnet, is also described in section 2. Section 3 discusses the transient climate response to an abrupt doubling of CO2. Section 4 presents the general results from the ΔQnet decomposition. Section 5 investigates the positive ΔQnet over the North Atlantic in more detail and discusses the role of AMOC slowdown in a warming climate based on our freshwater perturbation simulations. We summarize in section 6.

2. Model, experiments, and diagnosis

a. Model

We use the Community Earth System Model (CESM) version 1.0.6 developed by the National Center for Atmospheric Research (NCAR). Due to the limitation of computational resources, we choose a relatively coarse resolution, T31_g37. The ocean component, Parallel Ocean Program version 2 (POP2; Smith et al. 2010), uses a displaced pole grid and has a spatial resolution of approximately 1.6° latitudinally and 3.6° longitudinally that varies in space; for example, the latitudinal resolution is about 0.6° in the tropics and 2° in the Southern Ocean. Ocean mesoscale eddies (~100 km) are parameterized using the Gent–McWilliams scheme (Gent and McWilliams 1990) as bolus velocities, and the restratifying effects of ocean submesoscale eddies (~1 km) are accounted for by the parameterization scheme proposed by Fox-Kemper et al. (2008). Isoneutral diffusion of tracers is parameterized by the Redi scheme (Redi 1982) and vertical mixing uses the K-profile parameterization (KPP; Large et al. 1994). The atmosphere component, Community Atmosphere Model version 4 (CAM4; Neale et al. 2010), uses spectral grids and has a spatial resolution of about 3.7° both latitudinally and longitudinally. Other active model components include the Community Land Model (CLM), the Community Ice CodE (CICE), and the Community Ice Sheet Model (Glimmer-CISM). More details about the model can be found in Gent et al. (2011).

b. Experimental setup

We first conducted two sets of experiments, one preindustrial control (named PI) and the other with abrupt doubling of CO2 (named Cx2). Each set contains 10 ensemble members that start from slightly different atmospheric initial conditions on the order of 10−14 K, following the methodology used in the CESM Large Ensemble Project (Kay et al. 2015). Each experiment is integrated for 50 years to study the transient climate response to greenhouse forcing. The PI control run is in a quasi-equilibrium state with a relatively small climate drift (~0.01°C century−1 for global mean surface temperature as is estimated from the 10-member 50-yr simulations).

We also conducted another set of 10-member, freshwater perturbation experiments to explore the global impacts of AMOC slowdown under greenhouse warming. In addition to the CO2 doubling, we imposed a spatially uniform negative freshwater flux (i.e., freshwater removal) over the subpolar North Atlantic (50°–70°N, 45°W–25°E) and imposed a weaker, spatially uniform positive freshwater flux in the rest of global oceans (except for marginal seas) so that the globally averaged freshwater perturbation is zero. The freshwater perturbation we impose stays constant with time throughout the 50-yr integration and its impact acts to offset the AMOC weakening effect of greenhouse warming. After tuning the magnitude of the imposed freshwater flux, we found that, for this particular model, a freshwater flux of 0.1 Sv (1 Sv ≡ 106 m3 s−1) out of the North Atlantic could more or less cancel the effect of greenhouse warming on the AMOC intensity. This new set of ensemble simulations is named Cx2&FW.

By comparing the freshwater perturbation experiments (Cx2&FW) and the free-running CO2-doubling experiments (Cx2), we can explicitly isolate the impacts of freshwater perturbation in the background of global warming. A similar modeling technique has recently been applied to study the atmospheric impacts of AMOC slowdown under the RCP8.5 warming scenario (Liu et al. 2020). This type of experiments is motivated by the commonly adopted water hosing technique in the context of paleoclimate (Manabe and Stouffer 1995; Zhang and Delworth 2005; Stouffer et al. 2006; Bitz et al. 2007; Cheng et al. 2007; Hu et al. 2008; Kageyama et al. 2013; Liu et al. 2014). Similar experiments with perturbed CO2 concentration and freshwater flux together have been reported in previous studies but with different focuses (Smith et al. 2014; Wen et al. 2018).

Note that the current study concerns transient climate change, not the equilibrium climate after CO2 doubling. Therefore, we do not aim to run the simulations until equilibrium. In Cx2&FW, although the AMOC strength seems almost constant in time, the climate system is far from the equilibrium state after 50 years of integration. For all three sets of simulations, we choose the last 10 years of integration as an example transient stage following CO2 doubling for further analysis.

c. Decomposing Qnet

The ocean heat decomposition presented below is greatly informed by previous studies (e.g., Yang et al. 2015; Morrison et al. 2016; Liu et al. 2018). At the ocean surface Qnet consists of the sensible (SHF) and latent (LHF) turbulent heat flux, and shortwave (SW) and longwave (LW) radiative flux, with positive going into ocean:

Qnet=SHF+LHF+SW+LW.

Note that LHF includes both the latent heat of vaporization associated with water vapor and the latent heat of fusion associated with ice and snow.

When additional heat is absorbed by the ocean, it is either stored in the local water column or diverges away. The heat balance can thus be written as

Qnet=OHS+OHD,

since no heat source or sink is specified at the bottom of the ocean model. OHS is the local ocean heat storage that measures the change rate of ocean heat content column integrated from the ocean bottom (z = zB) to the surface (z = 0) during the period of interest, here estimated from the linear trend analysis:

OHS=(z=zBz=0ρ0cpT dz)/t,

where T is ocean potential temperature, and ρ0 and cp are the density and heat capacity of seawater, respectively. OHD is the local column-integrated ocean heat divergence that includes an advective term (ADV) and a diffusion term (DIF):

OHD=z=zBz=0ρ0cp[(vT)+R] dz.

Here, R is the divergence of the isoneutral diffusive flux that is parameterized by the Redi scheme; v is the three-dimensional ocean velocity that includes three components: model-resolved ocean currents veu (called Eulerian velocity in POP2), diagnosed velocities associated with the parameterized mesoscale eddies vbl (called bolus velocity in POP2), and submesoscale eddies, that is,

v=veu+vbl+vsm.

Note that the vertical mixing term is not included in Eq. (4) since it naturally vanishes as the column integration is conducted from the ocean bottom to the top.

Since ocean is nearly incompressible, the mass conservation requires ∇ ⋅ v = 0, which also applies to each individual component in Eq. (5), and as a result, the expression of OHD can be rewritten as

OHD=z=zBz=0ρ0cp(vT+R) dz.

Note that the column integration of wT/∂z is not necessarily zero, although it could be small when compared to its column-integrated horizontal counterparts. Similarly, the zonal integration of the zonal advection component uT/∂x does not necessarily vanish to zero and so it is important to keep both horizontal components even when calculating the zonally integrated OHD.

Meridional ocean heat transport (OHT) at a given latitude ϕ can be obtained by meridionally integrating the zonally integrated OHD from that latitude to the North Pole, as follows:

OHT(ϕ)=ϕNPr2 cosϕOHD dλ dϕ,

where a negative sign is added in the front to keep the convention that a positive OHT indicates a northward transport. In the following discussion, OHT refers to zonally integrated meridional OHT as calculated in Eq. (7).

Now consider the change in a warming climate, and each advective term in Eq. (6) can be decomposed into three parts, two linear and one nonlinear. Such decomposition is carried out in three-dimensional space on a depth coordinate using monthly climatological variables. Here we use the total advective term v ⋅ ∇T as an example (see below), and the same decomposition can be applied to each individual component (i.e., Eulerian, bolus, and submesoscale) for this model:

Δ(vT)=vPI(ΔT)+(Δv)TPI+(Δv)(ΔT).

The subscript PI represents the pre-industrial state, and Δ represents the change in a warming climate. Among the terms on the right, vPI ⋅ ∇(ΔT) represents the passive advection effect (control-state advection of anomalous temperature) and (Δv) ⋅ ∇TPI represents the circulation change effect (anomalous advection of control-state temperature). Here the nonlinear term (Δv) ⋅ ∇(ΔT) is relatively small when compared to the two linear terms, as is also reported by Gregory et al. (2016). But note that when the perturbation is larger (e.g., abrupt quadrupling of CO2), the nonlinear term could be regionally important (Oldenburg et al. 2018).

3. Transient response to global warming

In response to the abrupt doubling of CO2, global-mean SST experiences a fast warming during the first decade, followed by a slow warming (Fig. 2a; Held et al. 2010). In half a century, ocean surface warms by about 1°C on global average and the warming varies with latitude ranging from 0° to 2°C (Fig. 2c). The strongest warming is observed over the midlatitude oceans peaking around 40°S and 40°N (Wang et al. 2015), while tropical oceans warm less. The Southern Ocean warming is argued to be muted due partly to the mean upwelling of pristine water from the deep ocean (Bryan et al. 1988; Armour et al. 2016). Another center of muted warming is found over the subpolar North Atlantic, located within 40°–60°N, 40°W–0° for this particular model (Fig. 3a), which is presumably related to the AMOC slowdown and the reduced heat convergence (Drijfhout et al. 2012; Rahmstorf et al. 2015; Sévellec et al. 2017).

Fig. 2.
Fig. 2.

(a),(b) Time series of anomalies in annual-mean global-mean (a) SST (°C) and (b) Qnet (W m−2) for Cx2 with respect to PI. The thin and thick lines are for the 10 ensemble members and the ensemble means, respectively. (c),(d) Hovmöller diagrams of anomalies in annual-mean zonal-mean (c) SST (°C) and (d) Qnet (W m−2).

Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-19-0642.1

Fig. 3.
Fig. 3.

(a) Anomalies in SST (shadings; °C). (b) Anomalies in Qnet (shading; W m−2) and SST (contours; 0.3°C interval) for Cx2 with respect to PI. SST values above (below) 1.2°C are shown as solid (dashed) gray contours; the black solid line is for 0°C annual-mean climatological SST (indicator for climatological sea ice coverage). Anomalies are averaged in years 41–50.

Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-19-0642.1

As climate warms, global-mean ΔQnet drops from 3.5 to 2 W m−2 in the first few years and then decreases slowly afterward (Fig. 2b). Strong latitudinal variations emerge in less than five years (Fig. 2d). After half a century, global-mean ΔQnet is reduced to 1.3 W m−2, but its latitudinal variations are an order of magnitude greater, ranging from −3 to 20 W m−2. Overall, ΔQnet is more variable than SST anomalies in both time and space, suggesting the necessity of employing ensemble experiments to study the ΔQnet pattern (Hu and Deser 2013; Frölicher et al. 2015; Hogan and Sriver 2017, 2019; Shi et al. 2018).

Positive ΔQnet is found over the extratropics in both hemispheres, partially compensated by the negative ΔQnet in the tropics (Figs. 2d and 3b), consistent with the multimodel mean results from the archive of phase 5 of the Coupled Model Intercomparison Project (CMIP5) (Kostov et al. 2014). Three positive ΔQnet bands are identified in the Northern Hemisphere: the strongest one around 65°N is mostly in the Atlantic basin, and the other two around 45° and 30°N are contributed by both the Pacific and the Atlantic. In the Southern Hemisphere, a prominent, positive ΔQnet band is found over the Southern Ocean, around 55°S. In the tropics, negative ΔQnet is found over all three ocean basins. Robust negative ΔQnet is also found poleward of the positive high-latitude ΔQnet in both hemispheres, collocated with the area of sea ice reduction. As sea ice cover shrinks, relatively warm ocean surface is exposed to the cold air and thus releases more heat to the atmosphere. The negative ΔQnet also seems to be associated with the increased northward ΔOHT out of the subpolar gyre, as suggested by previous studies (Nummelin et al. 2017; Oldenburg et al. 2018; also see our Fig. 4d).

Fig. 4.
Fig. 4.

(a)–(c) Decomposition of anomalies in zonal-integrated Qnet (107 W m−1) into (a) ocean basins, (b) surface flux components, and (c) ocean heat divergence and storage for Cx2 with respect to PI. (d) Decomposition of anomalies in zonal-integrated OHT (PW) into different oceanic processes for Cx2 with respect to PI. All the quantities shown are anomalies averaged in years 41–50.

Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-19-0642.1

In Fig. 3b, the overlying gray contours show SST anomalies with values above (below) 1.2°C shown as solid (dashed) lines for better comparison with ΔQnet. The spatial variations in ΔQnet have some resemblance with that in SST warming; more specifically, positive ΔQnet typically occurs where ocean surface warms less (Xie et al. 2010). This negative correlation makes sense from the view of surface heat flux because a stronger ocean surface warming tends to release more heat to the air and is thus more likely to be associated with negative ΔQnet (e.g., Armour et al. 2016; Liu and Fedorov 2019). As illustrated by slab mixed layer ocean–atmosphere coupled simulations (Kiehl et al. 2006), on the other hand, regional variations in SST change can also result from surface flux adjustments without any changes in OHT, for example through the wind–evaporation–SST (WES) feedback (Xie and Philander 1994). Our forthcoming companion paper will address how the information of global ΔQnet pattern can be used to reconstruct the SST warming pattern. The present study focuses on the role of the ocean heat transport in the global ΔQnet pattern.

4. Decomposing ΔQnet

In this section, we aim to better understand the formation of global ΔQnet pattern through a comprehensive decomposition as described in section 2, using the same set of abrupt doubling of CO2 experiments as discussed in section 3. We believe that this diagnostic framework serves as a key step to understanding the ocean’s role in transient climate change. From now on, all the latitudinal profiles shown will be for zonal-integrated quantities accounting for the area of ocean surface at each latitudinal band, which is physically more meaningful.

Even though zonal-mean ΔQnet (over the ocean only) peaks around 65°N (Fig. 2d), the peak of zonal-integrated ΔQnet is found in the Southern Ocean due to the broad coverage of ocean surface area (Fig. 4a), as was noted by previous studies (e.g., Kuhlbrodt and Gregory 2012; Frölicher et al. 2015). In the Northern Hemisphere, the subpolar peak at 65°N entirely comes from the Atlantic and the heat uptake within 15°–55°N has comparable contributions from the Atlantic and the Pacific. Collectively, the North Atlantic takes up 33% of the global ΔQnet and the North Pacific contributes 13%.

We next decompose ΔQnet into four surface heat flux components (Fig. 4b). The positive ΔQnet over the Southern Ocean within 40°–65°S is realized mainly through the reduced upward sensible heat flux that is caused by the suppressed ocean surface warming as compared to the atmospheric warming. In addition, the reduction of low clouds leads to enhanced shortwave flux over the broad area of the Southern Ocean (Zelinka et al. 2012). Latent heat flux change has a positive contribution to ΔQnet locally within 50°–60°S, but its net contribution over the Southern Ocean is negative. Over 40°–65°S where the positive ΔQnet occurs, sensible heat flux and shortwave radiative flux changes each contribute to about 60% of the total ΔQnet, with some compensation by the latent heat flux change. Similar mechanisms are also operating in the extratropical Northern Hemisphere: sensible heat flux and shortwave flux are the two main components that contribute to the positive ΔQnet within 35°–70°N, while latent heat flux change is positive only over a narrow band within 58°–67°N but negative elsewhere.

In the lower latitudes, the most significant changes are found among latent heat flux and longwave and shortwave radiative flux changes but they largely cancel out (Fig. 4b). Although the equatorial warming tends to enhance the emitted longwave radiation, it is overwhelmed by the greenhouse effect of the increased CO2 and water vapor, and the net longwave radiation change is positive (i.e., into the ocean). The increased water vapor enhances the absorption of shortwave radiation and thus reduces the net incoming shortwave radiation at the surface, and the increase of cloud amounts further reduces the shortwave radiation reaching the surface. Outside the equatorial region, the increase of upward latent heat flux is substantial, offsetting the net radiative flux changes.

The partitioning among the four surface heat flux components is clearly important, but in terms of the oceanic energetic constraint, the addition of the four (i.e., ΔQnet) is more relevant. In principle, the ΔQnet at any grid point should be balanced by the addition of the column-integrated ΔOHD (ocean heat divergence change) and the local ΔOHS (ocean heat storage change); see Eq. (2). As we described in section 2, we calculate those three terms individually (Fig. 4c), and the relatively small mismatch between the black solid and dashed lines can come from, for example, computational errors associated with gridding or rough estimates of ΔOHS based on 10-yr trends.

The anomalous heat is mainly absorbed by the high-latitude oceans but is however stored in lower latitudes, which thus requires ocean heat divergence in higher latitudes and heat convergence in lower latitudes (Fig. 4c). This point has also been shown in previous studies (Banks and Gregory 2006; Kuhlbrodt and Gregory 2012; Frölicher et al. 2015; Marshall et al. 2015; Armour et al. 2016). Note that, since meridional OHT itself only acts to redistribute heat in space, globally integrated ΔOHD must vanish to zero. In other words, globally integrated ΔQnet should exactly match ΔOHS. However, in terms of meridional structure, ΔQnet variations mainly follow the variations of ΔOHD, which at a given latitudinal band can readily be an order of magnitude greater than ΔOHS.

The dominance of anomalous ocean heat divergence over storage appears more evident in horizontal space (Fig. 5). The global pattern of ΔQnet (Fig. 3b) largely resembles that of ΔOHD with local ΔOHS being much smaller. The strongest ΔOHS is found over the tropical Atlantic and this local amplification is partly related to the slowdown of the AMOC (see section 5).

Fig. 5.
Fig. 5.

Global pattern of anomalies in (a) OHD (W m−2) and (b) OHS (W m−2) for Cx2 with respect to PI. Anomalies are averaged in years 41–50.

Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-19-0642.1

The ΔOHD (divergence) and ΔOHT (transport) are two closely related quantities. Mathematically, meridional ΔOHT is simply an integral of meridional ΔOHD in latitude [see Eq. (7)] and thus one can always convert one to the other; ΔOHT itself is a physically meaningful quantity that can provide additional insights, but only if the associated net mass flux is zero. Also, the meridional profile of ΔOHT is often less noisy, sometimes simplifying the interpretation. The dominant pattern of ΔOHT changes is the equatorward heat transport in both hemispheres that carries the absorbed heat in the higher latitudes toward the lower latitudes (Fig. 4d). As a result, tropical oceans experience strong ΔOHS, despite the local heat loss to the atmosphere (Fig. 5). The equatorward ΔOHT is mainly realized through the Eulerian component, and the effects of mesoscale eddies are only significant in the Southern Ocean where strong eddy compensation occurs (Fig. 4d). The contributions from submesoscale eddies and horizontal diffusions are relatively small.

The ΔOHT is nearly symmetric between the hemispheres and small at the equator (Fig. 4d), although one might expect it to be negative (southward) due to the slowdown of the AMOC. We find that the cross-equatorial ΔOHT within the Atlantic basin is indeed negative, −0.05 PW (1 PW = 1015 W), but it is compensated by the northward ΔOHT in the Pacific basin (not shown). Consistent with the energy theory of Kang et al. (2008), zonal-mean changes in the Hadley circulation and tropical precipitation are to first order symmetric about the equator in response to greenhouse warming [not shown; see Wang et al. (2016) for an example].

The changes in ΔOHD or ΔOHT can result from either the passive advection effect (i.e., control-state advection of anomalous temperature) or the circulation change effect (i.e., anomalous advection of control-state temperature). We conduct further decomposition to explore the relative importance of those two effects (section 2) and the results are presented in Fig. 6. Such decomposition is only applied to the three advective terms, but not for the isoneutral diffusion term both due to that the data necessary for decomposition are not available and that the isoneutral diffusion is relatively small (see Fig. 4d).

Fig. 6.
Fig. 6.

Anomalies in advection-induced zonal-integrated (a) OHD (107 W m−1) and (b) OHT (PW) and their decomposition into the mean circulation effect and the circulation change effect, for Cx2 with respect to PI. The dashed lines are for the addition of the mean circulation and circulation change effects, which closely match the total term, implying that the nonlinear term is relatively small. All the quantities shown are anomalies averaged in years 41–50.

Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-19-0642.1

We find that the overall global pattern of ΔOHD is primarily induced by the circulation change effect (cf. the black and the red lines in Fig. 6). In other words, it is the ocean circulation changes acting on the control-state temperature field that give rise to the global ΔOHD or ΔQnet pattern. The combination of passive advection and circulation change effects on ΔOHD associated with the Eulerian currents largely resembles the ΔQnet pattern (cf. Figs. 3b and 7a). The global spatial correlation with the ΔQnet pattern based on a 2° × 2° grid size is 0.30 for the circulation change effect (Figs. 3b and 7b) and is only −0.06 for the passive advection effect (Figs. 3b and 7c), confirming the dominance of circulation changes in shaping the ΔQnet pattern. The close match between the black solid and dashed lines in Fig. 6 suggests that the nonlinear term is relatively small, as was also found in Gregory et al. (2016).

Fig. 7.
Fig. 7.

Anomalies in (a) Eulerian advection-induced OHD (W m−2), and its decomposition into (b) the circulation change effect and (c) the mean circulation effect, for Cx2 with respect to PI. Anomalies are averaged in years 41–50.

Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-19-0642.1

Compensation between passive advection effect and circulation change effect on Qnet

We note a remarkable negative global spatial correlation in ΔOHD between the passive advection effect and the circulation change effect mainly from the Eulerian component (Figs. 7b,c; r = −0.82). Such compensation also exists for the latitudinal variations of zonally integrated ocean heat divergence or transport, even though it is less evident for the Southern Ocean (Fig. 6). A similar feature in the latitudinal structure has also been noted or seen in previous studies. Marshall et al. (2015) and He et al. (2019) both identified a significant anticorrelation between the passive advection–induced and the circulation change–induced OHT anomalies in their latitudinal variations excluding the Southern Ocean. Chen et al. (2019) found a strong compensation between the passive advection– and circulation change–induced ocean heat content changes within the Southern Ocean. Nevertheless, the mechanisms of the compensation are not fully understood.

Here, we provide one tentative explanation based on the basic physics of geostrophy and thermal wind balance. For global oceans in general, thermal wind balance in z coordinates is written as

fuz=gρy,fυz=gρx,

where f is the Coriolis parameter, g is gravitational acceleration, and ρ is ocean density. Note that ρ can be approximated as a linear function of temperature and salinity with respect to some reference density ρ0:

ρ=ρ0(1αT+βS).

Let us neglect the contribution from salinity for now, and rewrite the thermal wind balance as

uz=ATy,υz=ATx,

where A = 0α/f is a constant that only varies with latitude. Integrating Eq. (11) from a level of no motion in the deep ocean, z = z0, we get

u=Az0zTy dz,υ=Az0zTx dz.

Taking a step further, let us assume that the vertically integrated horizontal gradient of temperature below any given level z can be parameterized by the local temperature gradient, that is,

z0zTy dzByTy, z0zTy dzBxTx.

The relation expressed in Eq. (13) is not so obvious, but for a thermal structure with a vertically uniform horizontal temperature gradient, Bx (or By) equals zz0. Therefore, Eq. (12) becomes

uAByTy,υABxTx.

If Eq. (14) holds for both the preindustrial state,

uPIABy,PITPIy,υPIABx,PITPIx,

and the changes under global warming,

ΔuABy,ΔΔTy,ΔυABx,ΔΔTx,

then, combining Eqs. (15) and (16), we have

uPIΔTx(By,PIBx,Δ)Δυ TPIy,υPIΔTy(Bx,PIBy,Δ)ΔuTPIx.

Adding the two equations in Eq. (17) together, we get that the two horizontal components of the passive advection effect, vPI ⋅ ∇(ΔT) are approximately balanced by that of the anomalous circulation effect, (Δv) ⋅ ∇TPI, with the compensation rate determined by the ratios By,PI/Bx and Bx,PI/By. Note that the parameter B is not guaranteed to be the same for zonal and meridional directions, either for the preindustrial state or for future change. In the current study, we have not resolved the exact magnitude of the compensation rate, which will be investigated in our follow-up studies.

To further verify the compensation shown in Eq. (17), we calculated the column-integrated zonal and meridional components for the ΔOHD field associated with the passive advection effect and the circulation change effect, and for those calculations we only included the dominant Eulerian part. We find that the anomalous ΔOHD fields in Figs. 7b and 7c are dominated by their horizontal components with the corresponding vertical components being relatively small (not shown) and therefore, we only show the horizontal components in Fig. 8. Indeed, Δυ(∂TPI/∂y) and −uPI(∂ΔT/∂x) largely resemble each other (r = 0.73; Figs. 8a,b); this is also true for Δu(∂TPI/∂x) and −υPI(∂ΔT/y) (r = 0.53; Figs. 8c,d). We notice that the spatial covariation holds particularly well in higher latitudes where the Coriolis effect is sufficiently strong. Such compensation can potentially explain the negative spatial correlation seen in Figs. 7b and 7c.

Fig. 8.
Fig. 8.

Anomalies in OHD (W m−2) induced by the Eulerian (a) anomalous meridional advection of mean temperature Δυ(∂TPI/∂y), (b) mean zonal advection of anomalous temperature −uPI(∂ΔT/∂x), (c) anomalous zonal advection of mean temperature Δu(∂TPI/∂x), and (d) mean meridional advection of anomalous temperature −υPI(∂ΔT/∂y).

Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-19-0642.1

5. Impacts of AMOC slowdown: Freshwater perturbation experiments

The North Atlantic takes up a substantial amount of heat under greenhouse warming (Fig. 3b), due primarily to the AMOC slowdown (Delworth and Dixon 2006; Xie and Vallis 2012; Winton et al. 2013; Rugenstein et al. 2013; Marshall et al. 2015; Shi et al. 2018). Delworth and Dixon (2006) identified that greenhouse gas–forced AMOC weakening is associated with net surface heat uptake in the extratropical North Atlantic, while aerosol-induced AMOC strengthening is associated with net heat loss to the atmosphere. Rugenstein et al. (2013) compared multiple climate models in their response to increased CO2 and found that models with a greater AMOC decline are associated with a stronger North Atlantic ΔQnet.

The AMOC is expected to slow down under global warming (e.g., Gregory et al. 2005; Schmittner et al. 2005; Yin et al. 2009; Cheng et al. 2013; Bakker et al. 2016; Liu et al. 2017). In our simulations, the AMOC weakens by about 5 Sv in half a century in response to the abrupt doubling of CO2 (Fig. 9a). According to our decomposition analysis, ocean circulation changes lead to a southward ΔOHT of 0.23 PW at 20°N, while the passive advection leads to a northward ΔOHT of 0.12 PW, partially compensating the circulation change effect (Fig. 6b). In other words, ocean circulation changes, presumably the slowdown of the AMOC, lead to substantial ocean heat divergence north of 20°N. It is noteworthy that the circulation change–induced ΔOHT converges toward the equator and vanishes to near zero (slightly negative) at the equator (Fig. 6b), consistent with previous studies (Marshall et al. 2015; He et al. 2019). This results from the cancellation between the southward cross-equatorial ΔOHT in the Atlantic and the northward ΔOHT in the Pacific that are induced by circulation changes (not shown); also see Fig. 3 in He et al. (2019).

While our heat decomposition analysis seems to imply the importance of AMOC slowdown, such diagnostic analysis based on ordinary CO2-increase experiments cannot address the question how the climate would be different if without ocean circulation or, more specifically, AMOC changes. Winton et al. (2013) tried to address the problem by fixing ocean circulation under global warming and were able to separate the impact of ocean circulation changes by comparing it to the standard, freely evolving circulation experiment. Their insightful modeling approach clearly pointed out the importance of ocean circulation changes, which however is concerned with global oceans rather than the Atlantic Ocean alone.

Here we have proposed an alternative, novel modeling approach to more explicitly identify the impact of Atlantic Ocean circulation changes, mainly the AMOC slowdown, under global warming. The details of experimental setup are described in section 2. Briefly, we imposed a time-invariant uniformly distributed freshwater flux of −0.1 Sv (negative being out of ocean) over the subpolar North Atlantic and a compensating flux in the rest of global oceans, in the CO2-doubling experiment (Cx2&FW). The freshwater removal makes the subpolar North Atlantic less stratified and therefore acts to strengthen the AMOC, nearly compensating the AMOC weakening in response to the CO2 increase (Fig. 9). The net changes in the subpolar North Atlantic vertical stratification and in the AMOC strength, due together to the CO2 increase and the freshwater perturbation, are small; for example, the net change in the AMOC is within 0.3 Sv, smaller than its internal variability on interannual-to-longer time scales (~0.9 Sv). Gregory et al. (2016) suggested that, under greenhouse warming, the surface heat flux change is the primary cause for the slowdown of the AMOC, but here we decide to perturb freshwater (salinity) flux alone so that the heat budget is not manually modified. Our freshwater perturbation experiments serve as an intermediate step from the fixed-circulation experiment in Winton et al. (2013) to the free-running CO2 experiment.

Fig. 9.
Fig. 9.

(a) Time series of AMOC intensity (Sv), which is estimated as the maximum streamfunction within 500–5500 m, 28°–90°N. (b) Anomalies of Atlantic MOC streamfunction (Sv) for Cx2 with respect to PI. (c) Anomalies of Atlantic MOC streamfunction (Sv) for Cx2&FW with respect to PI. Anomalies are averaged in years 41–50. In (b) and (c), the black contours highlight the Atlantic MOC streamfunction in the PI control run; the contour interval is 2 Sv and the thick contours represent zero values of the streamfunction.

Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-19-0642.1

Even though our aim is to perturb the meridional overturning, other changes of the ocean state are hard to avoid. For example, the weakening of subpolar barotropic gyre induced by the greenhouse warming is also largely compensated for by the freshwater perturbation (Fig. 10), consistent with the recent finding that the North Atlantic subpolar gyre is tightly coupled with the AMOC (Yeager 2015). Fedorov et al. (2004) suggest that a freshwater perturbation in high latitudes might also affect low-latitude wind-driven circulations by modulating the depth of ventilated thermocline, but this effect is presumably small in the Atlantic where the thermohaline circulation dominates. Indeed, the low-latitude barotropic gyre response to the freshwater perturbation is rather weak (Figs. 10b,c). Here we argue that the global climate impacts induced by the freshwater perturbation is mainly via the AMOC slowdown and we will further illustrate this point in the next subsection when discussing OHT changes.

Fig. 10.
Fig. 10.

(a) Time series of subpolar barotropic gyre intensity (Sv) in the Atlantic, which is estimated as the peak barotropic streamfunction within 40°–70°N, 80°W–0°. (b) Anomalies of barotropic streamfunction (Sv) for Cx2 with respect to PI. (c) Anomalies of barotropic streamfunction (Sv) for Cx2&FW with respect to PI. Anomalies are averaged in years 41–50. In (b) and (c), the black contours highlight the barotropic streamfunction in the PI control run; the contour interval is 4 Sv, and the thick contours represent zero values of the streamfunction.

Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-19-0642.1

Figure 11a shows the SST response to global warming when the AMOC intensity keeps unchanged due to the imposed freshwater perturbation. The Northern Hemisphere SST becomes significantly warmer than the free-running CO2 doubling scenario, leading to a stronger interhemispheric asymmetry (cf. Fig. 3a). The interhemispheric asymmetry is particularly evident for high-latitude oceans and is also present for tropical oceans, albeit weaker, associated with a northward shift of the intertropical convergence zone (not shown).

Fig. 11.
Fig. 11.

(a) Anomalies in SST (shading; °C). (b) Anomalies in Qnet (shading; W m−2) and SST (contours; 0.3°C interval) for Cx2&FW with respect to PI. In (b), SST values above (below) 1.2°C are shown as solid (dashed) gray contours; the black solid line is for 0°C annual-mean climatological SST (indicator for climatological sea ice coverage). (c) Anomalies in SST (shading; °C) and precipitation (contours; 0.15 mm day−1 interval). (d) Anomalies in Qnet (shading; W m−2) and SST (contours; 0.3°C interval) for Cx2 with respect to Cx2&FW. In (c), the green and brown contours represent positive and negative precipitation anomalies, respectively, and start from the values of 0.075 and −0.075 mm day−1, respectively. In (d), SST values above (below) −0.6°C are shown as solid (dashed) gray contours. Note that (c) and (d) are plotted to isolate the impacts of perturbation in the background of global warming. Anomalies are averaged in years 41–50.

Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-19-0642.1

We next subtract Cx2&FW from Cx2 to isolate the impact of freshwater perturbation in a warming climate. Overall, the global climate response to the freshwater perturbation under global warming is similar to that found in the classic water hosing experiments in the context of paleoclimate (e.g., Manabe and Stouffer 1995; Zhang and Delworth 2005; Stouffer et al. 2006; Cheng et al. 2007; Hu et al. 2008; Kageyama et al. 2013; Liu et al. 2014). Due to the AMOC slowdown, the Northern Hemisphere is significantly cooler particularly over the North Atlantic basin, and the Southern Hemisphere is slightly warmer, giving rise to a so-called bipolar seesaw response (Fig. 11c). The ITCZ shifts southward away from the cooler hemisphere in all three ocean basins.

a. Impacts on ΔQnet and ocean heat budget

We next study the potential role of AMOC slowdown in the global (particularly North Atlantic) ΔQnet and the associated ocean heat budget. In Cx2&FW, the positive Qnet change over the high-latitude North Atlantic becomes significantly weaker than that in Cx2 (Figs. 3b and 11b), implying a significant impact of the imposed freshwater perturbation (Fig. 11d). In the extratropical Northern Hemisphere, anomalous OHD alternates between positive and negative values at different latitudinal bands in Cx2&FW (Fig. 12a), in contrast with the mostly positive values in Cx2 (Fig. 4c). As an integrated measure, the strong southward ΔOHT in the Northern Hemisphere in Cx2 (Fig. 6b) now drops to near zero poleward of 20°N in response to the additional freshwater perturbation (Fig. 12c).

Fig. 12.
Fig. 12.

(left) Decomposition of anomalies in zonal-integrated (a) Qnet (107 W m−1) and (c) advection-induced OHT (PW), for Cx2 with respect to PI. (right) Decomposition of anomalies in zonal-integrated (b) Qnet (107 W m−1) and (d) advection-induced OHT (PW), for Cx2&FW with respect to Cx2; (b) and (d) are plotted to isolate the impacts of freshwater perturbation in the background of global warming. All the quantities shown are anomalies averaged in years 41–50.

Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-19-0642.1

Interestingly, the positive ΔQnet over the high-latitude North Atlantic does not completely vanish in Cx2&FW (Fig. 11b), suggesting that only a portion of that is caused by the AMOC slowdown. This is consistent with the previously suggested mechanism on the AMOC–heat flux feedback (Gregory et al. 2016): an increase of CO2 induces an anomalous heat flux into the high-latitude North Atlantic and results in the slowdown of AMOC, which in turn further amplifies the surface heat uptake. Concerning the meridional structure, the three latitudinal peaks of positive ΔQnet still exist in Cx2&FW, even without the AMOC slowdown, and they largely follow the pattern of ΔOHD (Fig. 12a). This implies that, under global warming, the passive advection effect can significantly contribute to the detailed pattern of ΔQnet within the North Atlantic.

Figure 12b highlights the net impact of the freshwater perturbation on OHT in the background of global warming (i.e., the difference between Cx2 and Cx2&FW). A basinwide anomalous southward OHT extends from 65°N to 30°S, peaking around 30°N, and a further decomposition suggests that it is mainly through the circulation change effect (Fig. 12d). This is accompanied by a northward cross-equatorial atmospheric heat transport associated with the southward ITCZ shift [Fig. 11c; see Kang et al. (2008) and Hwang et al. (2017) for examples]. We argue that the primary cause of the southward OHT anomaly is the AMOC slowdown, rather than the horizontal gyre changes. Previous studies suggest that horizontal gyres contribute less than the meridional overturning circulation to the climatological Atlantic OHT at most latitudes except for north of 50°N (Dong and Sutton 2002; Ferrari and Ferreira 2011; Johns et al. 2011; Tiedje et al. 2012); furthermore, in our simulations, the relative change of subpolar barotropic gyre is only half of that in meridional overturning (14% vs 29%; see Figs. 10a and 9a, respectively). More importantly, the spatially coherent OHT anomaly within 30°S–65°N is consistent with the AMOC coverage. The latitude of peak OHT anomaly (~30°N) coincides well with that of the strongest meridional streamfunction change (Figs. 9b,c), while the gyre change there is rather small (Figs. 10b,c). All the evidence above leads us to conclude that the OHT change in response to the freshwater perturbation is mainly driven by the AMOC slowdown.

The peak southward OHT anomaly at 30°N indicates a heat divergence north of 30°N and convergence within 30°S–30°N (Fig. 12b). The high-latitude ocean heat divergence drives a strongly positive Qnet anomaly associated with a substantial surface cooling over the extratropical North Atlantic; their residual is balanced by a negative OHS anomaly. Its counterpart low-latitude heat convergence is mainly balanced by a positive OHS anomaly with only small changes in Qnet and SST. In the northern subtropics, substantial heat storage is associated with anomalously cold SST (Fig. 11c), suggesting that the cold SST within 0°–30°N is very likely driven by atmosphere–surface ocean processes rather than changes in OHT (Chiang et al. 2008).

b. Impacts on global mean surface temperature and top-of-atmosphere radiation

In this subsection, we explore the potential role of AMOC slowdown in modulating global mean temperature and top-of-atmosphere (TOA) energy budget under global warming. The zero-order feature of climate evolution after the abrupt doubling of CO2 can be described by the equation of energy balance below:

N(t)=R+λeqT(t),

where R is the CO2-induced radiative forcing at TOA. The term λeq is equilibrium climate feedback that is, in the simplest form, assumed to be time-invariant. The terms T(t) and N(t) are global mean surface temperature and net radiative flux at TOA (positive being downward), respectively, and are linearly related given a constant λeq. In actuality, the system evolution does not really follow a straight line in the NT diagram, and instead exhibits some curvature. Various modifications to Eq. (18) have been proposed to account for this feature and one of the most popular paradigms is to invoke a time-varying “effective climate feedback” λeff (Murphy 1995; Senior and Mitchell 2000). In that framework, Eq. (18) is revised as

N(t)=R+λeff(t)T(t).

Effective climate feedback can then be estimated by regressing N(t) onto T(t) for the period of interest.

How does the slowdown of AMOC affect the transient evolution of T(t) and N(t)? To ease the discussion, we use ΔA to denote the difference between Cx2 and Cx2&FW. First of all, a stronger global warming is found in Cx2&FW as the AMOC does not weaken (Fig. 13a), consistent with previous studies suggesting that AMOC decline will lead to a hemispheric-scale cooling centered on the North Atlantic (e.g., Stouffer et al. 2006; Cheng et al. 2007; Maroon et al. 2018) and therefore reduce global warming (Winton et al. 2013; Trossman et al. 2016). The negative ΔAT gradually grows with time and during years 41–50 it reaches −0.13°C, about 8% of the global warming signal (Fig. 13a). Previous modeling studies using the technique of fixed ocean currents seem to suggest a higher global mean temperature sensitivity due to ocean circulation changes (Winton et al. 2013; Trossman et al. 2016). But it is noteworthy that their approach is different from ours and neither could cleanly isolate the impact of AMOC slowdown: the fixed-ocean-currents technique would include all the aspects of circulation changes in the global oceans, and the freshwater-perturbation approach, albeit designed to concentrate on the Atlantic, could also lead to, for example, horizontal gyre changes.

Fig. 13.
Fig. 13.

Evolution of ensemble-mean annual-mean global-mean (a) surface temperature and (b) net TOA radiative flux (downward being positive). (c) Scatterplots for ensemble-mean annual-mean global-mean net TOA radiative flux vs surface temperature.

Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-19-0642.1

The reduced global warming in Cx2 as compared to Cx2&FW is accompanied by a stronger downward net radiative flux at TOA, and ΔAN is about +0.09 W m−2 during years 41–50 (Fig. 12b). In contrast, those global warming simulations with freely evolving ocean currents tend to produce a weaker downward TOA radiative flux than the cases with fixed ocean currents (Winton et al. 2013; Trossman et al. 2016). The inconsistency might partly result from, again, the different ocean circulation changes involved in the two distinct modeling techniques (freshwater removal vs fixed ocean currents).

What do the impacts of AMOC slowdown on T and N imply for the changes in effective climate feedback λeff? By linearly regressing annual-mean N onto T over the whole 50 years, we estimated λeff to be −1.58 W m−2 K−1 for Cx2 and −1.48 W m−2 K−1 for Cx2&FW. The AMOC slowdown only leads to a relatively small change in λeff by −0.1 W m−2 K−1, which is about 7% of the total climate feedback.

Andrews et al. (2015) analyzed the CO2-quadrupling experiments in the CMIP5 archive and found that the negative effective climate feedback was significantly weaker during years 21–150 as compared to the initial 20 years. Lin et al. (2019) analyzed further argued that the intermodel spread in the climate feedback change between the two periods was positively correlated with their AMOC change index (defined as the change of AMOC decline rate per unit of global warming between the two periods).

Here we also estimated λeff separately for years 1–20 and years 21–50 to investigate how the effective climate effective feedback and the impact of AMOC slowdown evolve with time; note that the latter period here is shorter than that in Andrews et al. (2015) and Lin et al. (2019). In Cx2, λeff decreases in magnitude from −1.93 W m−2 K−1 for years 1–20 to −1.36 W m−2 K−1 for years 21–50, consistent with the finding of Andrews et al. (2015). Without the AMOC slowdown under global warming (i.e., in Cx2&FW), an even greater temporal reduction in the magnitude of λeff is observed, from −1.87 W m−2 K−1 for years 1–20 to −1.10 W m−2 K−1 for years 21–50. In other words, the AMOC slowdown has a particularly strong influence on λeff during the latter period (24% for years 21–50), in contrast with the small impact at the initial stage (3% for years 1–20). To better compare with Lin et al. (2019), we also computed the AMOC change index (see the previous paragraph for definition) from our simulations. The temporal change of λeff between the two periods decreases from 0.77 W m−2 K−1 in Cx2&FW to 0.57 W m−2 K−1 in Cx2, and this is accompanied by an decrease of the AMOC change index from −2.5 to −6.5 Sv K−1; this is generally consistent with Lin et al. (2019) wherein a positive intermodel correlation is found between the two quantities.

6. Summary

We have examined the global pattern of ΔQnet in a warming climate using ensemble simulations by NCAR’s ocean–atmosphere coupled model, CESM. In response to the abrupt doubling of CO2, global ΔQnet pattern emerges in less than a decade, associated with regional variations in SST anomalies. A comprehensive ocean process-based heat decomposition is conducted to understand the formation mechanism of ΔQnet. First, ΔQnet is separated into column-integrated ΔOHS (local storage of ocean heat) and ΔOHD (divergence of ocean heat by ocean circulation, eddies, diffusion, etc.), with the overall residual found to be relatively small. Then, the ΔOHD is further decomposed into the effect of control-state circulation acting on temperature anomalies and the effect of circulation change acting on the control-state temperatures; the nonlinear term due to changes in both circulation and temperature is small.

Substantially positive ΔQnet takes place in high latitudes, particularly in the North Atlantic and the Southern Ocean where the surface warming is suppressed, and it is mainly realized by the reduction of turbulent sensible heat flux and the enhanced net shortwave radiative flux due to reduced sea ice and cloud cover. Ocean circulation acts to transport the heat equatorward in both hemispheres and store the heat in lower latitudes; a part of the heat converged to the tropical oceans goes back to the atmosphere (i.e., negative ΔQnet in the tropics). The overall global pattern of the changes in ocean heat transport or its divergence is primarily due to the circulation change effect as opposed to the passive advective effect, except for the Southern Ocean that requires further investigations for a more definitive attribution.

The circulation change–induced ΔOHD tightly covaries in space with and opposes that induced by the passive advection effect with a weaker magnitude for the latter. Such spatial compensation could potentially be explained by the fundamental constraint of thermal wind balance but the details of compensation, for example what determines the magnitude of compensation, require further investigations. Our findings suggest it is important to treat ocean temperature as an active tracer because the circulation change induced by ocean temperature change could redistribute the reservoir ocean heat in such a way to cancel out the effect of control-state circulation advecting temperature anomalies.

The heat decomposition shows that the North Atlantic ΔQnet mainly results from ocean circulation changes, specifically the slowdown of the AMOC as is hypothesized in previous studies (Delworth and Dixon 2006; Winton et al. 2013; Rugenstein et al. 2013; Marshall et al. 2015; Shi et al. 2018). To further demonstrate that, we have developed a novel modeling approach wherein freshwater flux over the subpolar North Atlantic is perturbed, by 0.1 Sv out from the ocean, in conjunction with the abrupt CO2 doubling. The resultant AMOC stays at a similar strength with the control state as climate warms. These freshwater perturbation experiments confirm that the AMOC slowdown is the primary, but not the only, factor for the positive ΔQnet over the North Atlantic, while the passive advection effect could significantly contribute to the regional variations of ΔQnet. The surface heat uptake over the North Atlantic is mainly stored in the tropical ocean, with relatively small surface heat loss back to the tropical atmosphere.

It is important to note that in the real climate system two-way coupling exists between Qnet and AMOC. The existence of positive North Atlantic ΔQnet in the absence of AMOC slowdown (i.e., in Cx2&FW) is consistent with the argument that the AMOC slowdown actually results from, not only drives, surface heat flux changes under greenhouse warming (Gregory et al. 2016). How Qnet and AMOC, or ocean circulation in general, are coupled at process level remains an open question.

Another open question to be resolved is the cause of the positive ΔQnet over the Southern Ocean under global warming. Some modeling studies suggest that the climatological Southern Ocean meridional overturning circulation can transport warm anomalies equatorward, while the associated mean upwelling acts to suppress the local SST increase, giving rise to the positive Qnet (e.g., Bryan et al. 1988; Marshall et al. 2015; Armour et al. 2016; Garuba and Klinger 2016; Garuba et al. 2018; Swart et al. 2018; He et al. 2019). Others argue that ocean circulation changes might have played a comparable or dominant role over the Southern Ocean in various aspects, including deep ocean warming magnitude (Newsom et al. 2016) and the horizontal and the vertical structures of ocean heat content change (Winton et al. 2013; Chen et al. 2019). Based on our heat decomposition analysis, we find that circulation change effect dominates for the positive ΔQnet and northward OHT anomaly over the Southern Ocean, which is more consistent with the latter view. He et al. (2019) used the same model but with a higher resolution and a different warming scenario (RCP8.5), and their results supported the former view. Our preliminary analysis suggests that both stationary meanders and meridional overturning circulation, and their changes, are important in shaping the OHT changes over the Southern Ocean (not shown). This could partly explain the discrepancies with the results of He et al. (2019), in which only the meridional overturning was decomposed into the passive advection and circulation change components. Our results concerning OHT decomposition, while not conclusive, are useful perhaps in raising the issue of the role of stationary eddies in OHT changes under global warming.

At this point we are not able to draw solid conclusions for the mechanisms of the Southern Ocean heat uptake, and a more definitive attribution will require further investigations. For example, decomposing OHT changes on different vertical coordinates (isopycnal versus depth) could potentially lead to different conclusions on the relative importance of circulation change versus passive advection effects, or the relative importance of meridional overturning versus horizontal meanders. More in-depth analysis is now underway and will be reported elsewhere. In addition, high-resolution ocean models will be particularly helpful as they can resolve mesoscale eddies and better represent stationary meanders (due partly to more realistic bathymetry) that are known to play important roles in meridional heat transport (e.g., Marshall 1995; Hughes and Killworth 1995; Marshall and Radko 2003; Abernathey et al. 2011; Dufour et al. 2012; Bryan et al. 2014; Thompson and Naveira Garabato 2014; Rintoul 2018).

We advocate that different modeling groups use a common diagnostic approach to analyze the global warming simulations with the same setup, for a more direct intermodel comparison. We note that the choice of decomposition and grouping procedure, including the one used here, is somewhat arbitrary and subjective, which should later be guided by the ocean adjustment dynamics. Different decomposition and grouping procedures used can provide different perspectives on ΔQnet pattern formation. For example, our study mainly focuses on the decomposition of passive advection effect and the circulation change effect, as was inspired by the recent debate on their relative importance in shaping the global ΔQnet pattern. One can also focus on the decomposition into meridional overturning versus horizontal meanders as we mentioned above. Novel modeling approaches like passive tracer experiments or partial coupling experiments are extremely useful in isolating physical processes (e.g., Banks and Gregory 2006; Xie and Vallis 2012; Winton et al. 2013; Marshall et al. 2015; Armour et al. 2016; Garuba and Klinger 2016; Huber and Zanna 2017; Liu et al. 2018), and common diagnostic methods can be applied to those experiments for a complete understanding and for a better comparison with the standard global warming experiments.

Net ocean surface heat flux Qnet is a key quantity that bridges the ocean and the atmosphere, but its future changes are not well constrained and suffer large intermodel spread. This is partly due to the fact that both atmospheric and oceanic processes can influence, and at the same time are influenced by, ΔQnet at their interface. A complete understanding of ΔQnet requires a coupled approach (Fig. 1): first to understand the connection between ΔQnet and ocean processes and then to understand the connection between ΔQnet and atmospheric processes (e.g., Kang et al. 2008; Hwang et al. 2017). The current study represents the first step, which we hope provides a useful diagnostic framework to decipher the formation of global ΔQnet pattern. Many aspects of the problem, such as dynamical mechanisms of ocean circulation response, remain unsolved. The companion paper on the second step to bridge SST and hydrological cycle changes to the global ΔQnet pattern under global warming is currently underway.

Acknowledgments

We thank three anonymous reviewers for their instructive and thoughtful comments that have greatly improved the manuscript. We thank Qing Li for sharing the code to compute ocean heat transport in CESM. S. Hu was supported by the Scripps Institutional Postdoctoral Fellowship and the Lamond-Doherty Postdoctoral Fellowship, S.-P. Xie by the National Science Foundation (AGS-1637450), and W. Liu by the Regents’ Faculty Fellowship and the Alfred P. Sloan Foundation as a Research Fellow.

Data availability statement

The data used to plot the figures in this study are available at https://doi.org/10.5281/zenodo.3888453.

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