1 INTRODUCTION

The net heat flux at the top of the atmosphere is downward at low latitudes and upward at mid-high latitudes (Hatzianastassiou et al., 2004). The radiation imbalance needs to be compensated by equator-topole heat transport accomplished by both the atmosphere and the ocean. Although oceanic meridional heat transport (OMHT) is dominant near the equator, it still plays an import role at mid-high latitudes (Czaja and Marshall, 2006; Fasullo and Trenberth, 2008; Yang et al., 2015a). Thus, it plays pivotal roles in relation to the climate energy balance and to the environment inhabited by human beings. Calculations of OMHT and analyses of associated processes have been investigated theoretically (Czaja and Marshall, 2006; Ferrari and Ferreira, 2011), and based on satellite radiation measurements (Trenberth and Solomon, 1994; Fasullo and Trenberth, 2008), hydrographic observations (Ganachaud and Wunsch, 2000; Stammer et al., 2003), and model simulations (Zheng and Giese, 2009; Yang et al., 2015a).

Traditionally, OMHT is calculated indirectly based on energy budgets (Bryden and Imawaki, 2001; MacDonald and Baringer, 2013). The difference in OMHT across two latitudes is balanced by the area integral of air-sea heat fluxes between the sections, with a small modification related to the temporal changes of heat content. Thus, OMHT across a basin zonal section in the Pacific or Atlantic can be estimated based on the area integral of surface heat fluxes between the section and the Bering Strait, where the local OMHT is rather small (Trenberth and Solomon, 1994; Trenberth and Caron, 2001). In addition, the global OMHT can be calculated by subtracting the directly estimated atmospheric meridional heat transport from the total poleward heat transports required to offset the heat flux imbalance at the top of the atmosphere (Fasullo and Trenberth, 2008).

In addition to indirect methods, OMHT can also be calculated directly using an advection term based on the velocity and energy of water parcels, plus a small molecular diffusion term (Yang et al., 2015a). The advective OMHT, which includes the advection of enthalpy, kinetic energy, and geopotential (Starr, 1951), can be simplified as potential temperature fluxes with an approximation error of the order of 0.1% under modern climate (Bryan, 1962; Warren, 1999). The advection is accomplished by intrabasin circulations and interbasin throughflows (MacDonald and Baringer, 2013). The intrabasin component includes the contributions of horizontal gyres and meridional overturning cells, and it is induced by dynamic and thermodynamic forcing within the basin. The interbasin element indicates the effects of interbasin throughflows, and it is associated with forcing both inside and outside of a specific basin. For example, in the Northern Hemisphere, the pressure gradient between the North Pacific and the Arctic oceans induces the Bering Strait throughflow from the Pacific Ocean to the Arctic Ocean, which further influences the North Atlantic Ocean (Woodgate et al., 2005).

The Bering Strait is an oceanic pathway connecting the Pacific, Arctic, and Atlantic Oceans. It might act as an exhaust valve during the last glacial termination when the meltwater of continental ice sheets discharged into the North Atlantic Ocean. The freshwater inflow via the opened Bering Strait could dilutes the density and chemical properties in the North Pacific Ocean (Okumura et al., 2009; Hu et al., 2015), and help to maintain a relative steady climate of the Atlantic Ocean (Hu and Meehl, 2005; Hu et al., 2007; Hu et al., 2012b). The importance of the Bering Strait in historical climate changes has been identified based on paleo reconstructions (Bard, 2002; Sandal and Nof, 2008). However, the attention paid to the contribution of the Bering Strait throughflow to OMHT remains inadequate, mainly because the OMHT near the Bering Strait is very small. On the one hand, the volume transport of the Bering Strait throughflow (~1 Sv; 1 Sv=10⁶ m³/s) is modest (Woodgate and Aagaard, 2005; Woodgate et al., 2012), while on the other hand, the temperature near the Bering Strait is close to 0℃. Thus, even in recent papers, e.g., Yang et al. (2015b), the contributions of the varied Bering Strait throughflows remain unclear. It is true that the OMHT near the Bering Strait is hundreds of times smaller than the OMHT at mid-low latitudes. However, the Bering Strait throughflow causes net northward transport across any basin zonal section in the North Pacific Ocean, whereas net southward transport in the Atlantic Ocean, which contributes directly to OMHT at latitudes where the local temperature is much higher.

The contribution of the Bering Strait throughflow to OMHT can be estimated by model comparisons, water transformations, and OMHT decompositions. Model simulations with an open/closed Bering Strait can be compared to investigate the influence of the Bering Strait throughflow (Hu et al., 2015). This method considers not only the Bering Strait throughflow's direct contribution to OMHT associated its temperature transport, but also its indirect contributions associated with its salt transport, which may influence oceanic stratifications and heat transport indirectly (Hu et al., 2011). However, it cannot be used for the observations. Talley (2003) diagnosed the temperature and mass transport in isopycnal layers at a subtropical latitude and estimated the contribution based on water transformations. This method is closely related to physical processes, but it requires an arbitrary choice for the maximum density of subtropical subduction and it is not useful outside of subtropical gyres. The contribution of the Bering Strait throughflow can also be separated from the total OMHT. According to Barotropic-BaroclinicHorizontal decomposition (BBH), both the potential temperature and the velocity of water parcels can be decomposed into a section-averaged barotropic component, a zonally averaged baroclinic component, and a remaining horizontal component (Bryden and Imawaki, 2001; MacDonald and Baringer, 2013). The barotropic component indicates the effects of interbasin throughflows, which induce nonzero net mass transports across basin zonal sections. The assumption of section-averaged values for interbasin throughflows is somewhat arbitrary, but the method is useful for estimating the effects of throughflows.

Based on the decomposition, we show the contribution of the Bering Strait throughflow should not be ignored when analyzing OMHT changes under different climate scenarios, such as a comparison of OMHT during the Last Glacial Maximum (LGM, ~21 ka; ka=thousand years ago) and under modern climate. The remainder of this paper is organized as follows. Section 2 includes descriptions of the model simulations under modern and LGM climate conditions, and it provides a comparison of the LGM simulation with paleo reconstructions. Section 3 describes the interbasin–intrabasin decomposition method to clarify the OMHT induced by interbasin throughflows, illustrates the Bering Strait throughflow, and compares the effects of varied Bering Strait throughflows on OMHT between the LGM and modern climate conditions. Finally, Section 4 presents a discussion and Section 5 gives our conclusions.

2 DATA DESCRIPTION 2.1 Model description

We use two simulations in this study, including one for the modern climate and another for the LGM climate. Both simulations use the National Center for Atmospheric Research (NCAR) Community Climate System Model version 3 (CCSM3). The CCSM3 is a fully coupled ocean-atmosphere-sea ice-land surface model. The ocean model is the Parallel Ocean Program (POP) version 1.4.3 (Smith and Gent, 2002). The ocean grid is the same in both simulations. It has 384×320 horizontal points with enhanced meridional resolution near the equator and high-latitude North Atlantic Ocean (~0.25°–0.6° latitude by 1.125° longitude resolution), and 40 levels in vertical z-coordinate extending to the depth of 5.5 km (~10 m resolution near the surface and 250 m resolution below 2 000 m). The poles are set to be in Antarctic and Greenland to avoid singularity problems. The ice Model is the Community Sea Ice Model version 5 (CSIM5), which has the same horizontal grid as the POP ocean model. The CSIM5 is a dynamicthermodynamic model, including a sub-grid scale ice thickness distribution and an elastic-viscous-plastic dynamics scheme (Briegleb et al., 2004). The atmosphere model is the Community Atmosphere Model version 3 (CAM3; Collins et al., 2006). Its resolution configuration is T85 (T42), which is a 256×128 (128×64) regular longitude/latitude global horizontal grid, with 26 vertical hybrid levels. The land model is the Community Land Surface Model Version 3 (CLM3). It is a soil-vegetation-atmosphere transfer model, including a river routing scheme and it shares the identical horizontal grid as the CAM3 atmosphere model (Dickinson et al., 2006). Overall, the CCSM3 can provide dynamics and climate simulations lasting several millennia with reasonable fidelity (Briegleb et al., 2004), and its performance in climate simulations is discussed detailly in a special issue of the Journal of Climate (Vol. 19, No. 11).

2.2 Experiment description

The modern simulation is the case b30.030a from the 20th Century Climate in Coupled Models (20C3M) and is a part of the 4th Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR4). The 20C3M project provides historical simulations from 1870 to 1999 A.D. It is forced by historical (or estimated) record of greenhouse gases (such as CO₂, CH₄, and N₂O), volcanoes, sulfate, solar radiations, ozone, halocarbons, and aerosols. More detailed descriptions for the 20C3M project and the time-varying forcings are available from the official website http://www.cesm.ucar.edu/working_groups/Change/CCSM3_IPCC_AR4/20C3M.html. In this study, the last 30 years (1970-1999) of the outputs are averaged as the modern climatological means for the analyses below.

The LGM simulation is the case b30.104w from Paleoclimate Modeling Intercomparison Project 2 (PMIP2). The simulation uses reconstructed (or estimated) forcings and boundary conditions for the LGM climate according to the PMIP2 protocols, such as the Earth's orbital, greenhouse gas concentrations, ice sheets distributions, albedo, land-sea mask, and vegetation distributions (Otto-Bliesner et al., 2006; Otto-Bliesner and Brady, 2010). The LGM is a glacial period when continental ice sheets, which were up to 4.5 km in thickness, covered the North America and northern Eurasia (Peltier, 2004). As a result, the sea level was about 120-130 m lower during the LGM and exposed the Bering Land Bridge (Harington, 2005). The distributions of the ice sheets also had significant influences on albedo and vegetation distributions. Besides, the concentration of greenhouse gases was reduced during the LGM, such as CO₂ (185 mL/m³), CH₄ (350 μL/m³), and N₂O (200 μL/ m³). The protocols established by the PMIP2 are available from https://pmip2.lsce.ipsl.fr/. As the same treatment for the modern simulation, the last 30 years (0470-0499) of the case b30.104w outputs are averaged as the LGM climatological means for the analyses below. The experiments adapted are listed in Table. 1.

2.3 Comparisons of the LGM simulation with paleo reconstruction

The simulated annual mean Sea Surface Temperature (SST) under LGM climate conditions are compared with paleo reconstructions from the Multiproxy Approach for the Reconstruction of the Glacial Ocean Surface (MARGO) project (Fig. 1). The MARGO data represent an updated synthesis of LGM SST reconstructions after the Climate LongRange Investigation, Mapping and Prediction (CLIMAP) project, combining over 600 individual SST reconstructions (MARGO Project Members, 2009). The LGM simulation is generally consistent with the paleo reconstructions but with notable differences. The differences are small at low latitudes, especially in the warm pool region, but larger at high latitudes. The maximum difference appears in the mid-latitude North Atlantic Ocean where the reconstructed annual mean SST is up to 10℃ lower in the LGM than in the modern scenario (MARGO Project Members, 2009). Thus, the SST is considered underestimated in this region in the LGM simulation, especially in the western basin.

3 RESULT 3.1 Interbasin-intrabasin decomposition

The OMHT across a basin zonal section is accomplished by direct advection of water parcels and diffusion. Thus, it can be divided into an advection term OMHT_adv and a diffusion term OMHT_dif (Starr, 1951; Gill, 1982; IOC et al., 2010; Yang et al., 2015a):

where ρ is the in situ density, B is the Bernoulli function, v is the velocity vector, n is the unit northward vector such that a positive value indicates northward heat transport, and F^D is the sum of all molecular diffusive energy fluxes. The Bernoulli function B specifies the total energy (sometimes also called total enthalpy) per unit mass (Batchelor, 1967; Saunders, 1995; McDougall, 2003; Olbers et al., 2012):

where U is the specific internal energy, p is the pressure, Φ is the gravity potential, and h is the specific enthalpy. Equation 3 suggests OMHT includes the transports of enthalpy h (the sum of the specific internal energy U and the work done by pressure forces p/ρ), geopotential Φ, and kinetic energy v²/2. Note, the Bernoulli function B indicates total energy per unit mass. Thus, Eq.1 not only involves the transport of "heat, " but also the transports of mechanical energies. On this point, it would be more accurate if is named in the literature as the total energy transport, as suggested by Warren (1999). In fact, OMHT is the transport of potential enthalpy (McDougall, 2003; IOC et al., 2010). Despite the different physical meanings, the value between the OMHT and the meridional total energy transport is typically 0.003℃ if expressed in temperature units, and the difference is negligible. Here, we follow the traditional usage of heat transport.

The calculation of the Bernoulli function B is rather complicated and Eq.1 is traditionally calculated using potential temperature. Based on analyses of Taylor series expansions, the advective OMHT across a basin zonal section can be simplified as follows (Bryan, 1962):

where C p is the specific heat capacity at constant pressure, and θ is the potential temperature referenced to the sea surface (Bryan, 1962). Warren (1999) suggests the error of the approximation is of the order of 0.1% under modern climate conditions. Thus, Eq.4 is the formula used most often for the calculation of advective OMHT rather than Eq.1.

The calculation of advective OMHT requires zero net mass and salt transports across the basin zonal section (Bryan, 1962; Warren, 1999, 2006); otherwise, the calculated OMHT will depend on some arbitrary constants, such as the chosen temperature unit, zero geopotential height, and zero enthalpy state. For example, a change of temperature unit from degrees Celsius to Kelvin in Eq.4 will induce a robust but meaningless OMHT difference if the net mass transport is not zero. However, the requirement of zero transports can hardly be satisfied by any basin zonal section influenced by interbasin throughflows, vapor transport and river runoff, and the effects of the nonzero transports should be decomposed.

Because the contribution of nonzero net salt transport on OMHT is negligible (Bryan, 1962), we focus on the nonzero net mass transports induced by interbasin throughflows and their effects on OMHT based on the interbasin-intrabasin decomposition. Accordingly, the advective OMHT (OMHTadv) is further decomposed to an interbasin term and an intrabasin term. Following the BBH decomposition (Bryden and Imawaki, 2001; MacDonald and Baringer, 2013), we use the simplest assumption that an interbasin throughflow induces uniform meridional velocity over the entire section. The removal of interbasin throughflows forces zero net mass transports for the intrabasin circulations. Thus,

and

where v=[v]+v′ and is the section-averaged velocity. The interbasin term OMHTinterb, represents the OMHT by interbasin throughflows, associated with dynamic and thermodynamic forcing both inside and outside the basin. It varies rather than simply being a constant at different latitudes, and it is consistent with the fact that the temperature of a flow always changes along the path via interaction with the atmosphere. The remaining intrabasin term OMHTintrab, specifies the OMHT induced by circulations inside the basin, including the contributions of both horizontal gyres and meridional overturning cells, and it is mainly associated with forcing within the basin.

3.2 Comparison of Bering Strait throughflows

Under modern climate conditions, the basin zonal sections all over the globe are influenced by interbasin throughflows (Fig. 2a). In the South Pacific Ocean, the Indonesian Throughflow (ITF) induces robust northward net transport. The simulated strength is ~17 Sv, slightly larger than the value of ~15 Sv obtained from hydrostatic estimates (Ganachaud and Wunsch, 2000; Sprintall et al., 2009). The importance of the robust ITF has been realized in the analyses of OMHT variations, such as Hazeleger et al. (2004). Compared with the ITF, the interbasin transports are much weaker in the Northern Hemisphere. The net transports, which are northward in the North Pacific Ocean and southward in the Atlantic Ocean, are of the order of 1 Sv. Under LGM climate conditions (Fig. 2b), the net transport in the South Pacific Ocean (~17 Sv) is also characterized by the ITF. In contrast, in the North Pacific and Atlantic oceans, the net transports induced by interbasin throughflows are zero during the LGM.

The net transports in the North Pacific and Atlantic oceans are associated with the Bering Strait throughflow (Fig. 3). Under the modern climate, the Pacific-Arctic pressure-head induces northward transport across the Bering Strait, against the local winds (Woodgate et al., 2005, 2012). The throughflow further influences the Atlantic Ocean through the Canadian Arctic Archipelago and Fram Strait (Serreze et al., 2006). The simulated annual mean Bering Strait throughflow is 0.98 Sv, consistent with in situ observations (Woodgate et al., 2012). During the LGM, the continental ice sheets in North America and northern Eurasia were up to 4.5-km thick (Peltier, 2004). Consequently, the sea level was about 120– 130 m lower at that time, and the exposed Bering Land Bridge blocked oceanic flows between the North Pacific and Atlantic oceans (Harington, 2005).

3.3 Decomposed interbasin OMHT induced by Bering Strait throughflow

The Bering Strait throughflow induces net northward water advection in the North Pacific Ocean, whereas net southward advection in the Atlantic Ocean, which contributes directly to OMHT. The basic patterns of OMHT in the Northern Hemisphere are illustrated in Fig. 4. The diffusive OMHT is calculated according to Eq.2 based on parameterized model outputs and it is included in the solid lines. However, it is not shown individually because it is negligible away from strong oceanic fronts (Yang et al., 2015a) and because OMHT is accomplished mostly by direct advection of water parcels. Thus, we focus on the total OMHT and the effects of the Bering Strait throughflow in this paper.

The patterns of OMHT are similar under modern and LGM climate conditions. In the North Pacific Ocean, OMHT is weak near the equator; it peaks at low latitudes around 15°N, and then decreases rapidly in subpolar regions. The OMHT in the North Pacific Ocean is dominated by shallow wind-driven thermohaline subtropical cells confined to the tropics and subtropics (Fig.S1). Warm water is transported poleward by surface winds and western boundary currents, and it returns with decreased temperature within the ocean interior (McCreary and Lu, 1994; Gu and Philander, 1997). In the Atlantic Ocean, northward OMHT is robust near the equator and at high latitudes, and it is associated with the deep thermohaline circulation (Fig.S1). The temperature contrasts between the northward flows in the upper ocean and the southward flows of the North Atlantic Deep Water (NADW) dominate OMHT in the Atlantic Ocean (Bryden and Imawaki, 2001; Ferrari and Ferreira, 2011; MacDonald and Baringer, 2013). The magnitude of the calculated OMHT under the modern climate agrees reasonably well with previous estimations by MacDonald and Baringer (2013) based on hydrographic observations and model simulations. According to previous estimations (the modern simulation), OMHT is about 1.20 (1.11) PW (1 PW=10¹⁵ W) at 25°N and 0.43 (0.43) PW at 60°N in the Atlantic Ocean, and it is about 0.64 (0.60) PW at 23°N in the Pacific Ocean. Comparison of the OMHTs in the LGM simulations with paleo records is rather difficult because of limited data.

The contribution of interbasin throughflows was decomposed further. Based on the interbasinintrabasin decomposition, the interbasin OMHT induced by interbasin throughflows is determined by the production of the strength of the throughflows and the section-averaged potential temperature (Eq.5). Under the modern scenario, OMHT induced by the Bering Strait throughflow is about 0.02 PW in the North Pacific and North Atlantic oceans, and it is about two orders of magnitude smaller than at low latitudes. Under the LGM scenario, the interbasin OMHT is zero because of the absence of the Bering Strait throughflow.

The contribution of the Bering Strait throughflow to OMHT is rather small, consistent with previous articles. However, it should not be ignored in analyses of the changes of OMHT under different climate conditions, such as the comparison of the OMHT under modern and LGM climate conditions. Note, it is not proper to compare OMHT across a basin zonal section under different conditions if the net transport is different. For example, under LGM climate conditions, a change of the temperature unit from degrees Celsius to Kelvin would not change the value of the calculated OMHT based on Eq.4 because the constant is eliminated. However, under modern climate conditions, the calculated OMHT depends on many indeterminate constants. A change of the temperature unit would induce a very robust northward heat transport increase in the North Pacific Ocean. Therefore, it is improper to compare them directly when one is dependent on some indeterminate constants and the other is not; thus, the nonzero transports should be decomposed before the comparison.

According to the interbasin-intrabasin decomposition, the OMHT induced by the Bering Strait throughflow is about 0.02 PW (Fig. 5), i.e., much smaller than the total OMHT that is of the order of 1 PW. However, in the comparison of the OMHT under LGM and modern climate conditions, the mean absolute changes of the intrabasin OMHT are 0.05 and 0.20 PW in the North Atlantic Ocean and North Pacific Ocean, respectively. This suggests the interbasin OMHT induced by the Bering Strait throughflow could be of the same order as the OMHT variations; thus, the effects of the Bering Strait throughflow cannot be ignored.

In the North Atlantic Ocean, the simulated OMHT under the LGM climate is slightly stronger at low latitudes and weaker at high latitudes, even though the Atlantic Meridional Overturning Circulation was much shallower (Fig.S1). This might seem controversial but it is consistent with paleo records. Paleo reconstructions suggest the NADW was replaced by Glacial North Atlantic Intermediate water (GNAIW, ~2 000 m) during the LGM (Lynch-Stieglitz et al., 2007), and that the transport of intermediate water was at least as strong as the transport of the NADW today (Lippold et al., 2012). Thus, the change of intrabasin OMHT in the North Atlantic Ocean is small (generally < 0.1 PW), and it is of the same order of magnitude as the OMHT induced by the Bering Strait throughflow.

In the North Pacific Ocean, the simulated OMHT under the LGM climate is weaker at low latitudes and slightly stronger at high latitudes. The changes of OMHT in the North Atlantic and North Pacific oceans are approximately opposite, which might represent an example of the Atlantic-Pacific seesaw (Saenko et al., 2004; Hu et al., 2012a; Freeman et al., 2015). At high latitudes, the changes of interbasin OMHT and intrabasin OMHT are of the same order of magnitude. At low latitudes where the main thermocline exists, however, the portion of the interbasin term is much smaller. The change of intrabasin OMHT there is roughly 0.2 PW, i.e., about an order of magnitude larger than the effects of the Bering Strait throughflow. The contribution of the Bering Strait throughflow may be underestimated at mid-low latitudes, and this is discussed further in Section 4.

4 DISCUSSION

Previous articles have suggested it is inappropriate to discuss OMHT unless the net mass transport is zero (Bryan, 1962; Warren, 1999, 2006; MacDonald and Baringer, 2013); otherwise, the calculated OMHT would depend on some indeterminate constants such as the chosen temperature unit, zero geopotential height, and zero enthalpy state. However, McDougall (2003) and the IOC et al. (2010) have argued it is legitimate to discuss OMHT irrespective of net mass transport. This is because the energy conservation equation is independent of the selected constants, and because the difference of OMHT across two latitudes is equal to the area integral of surface heat fluxes between them, after consideration of the effects of heat content changes. This is true, however, only if the net transports across the two latitudes are equal when there are no mass sources/sinks between them. For example, it does not hold for a region bounded by one section in the South Pacific Ocean when the other is in the North Pacific Ocean because of the ITF. Furthermore, the constants cannot be eliminated when comparing historical OMHT across a latitude when it is influenced by a time-varying interbasin throughflow. Thus, the nonzero transport should be separated. The separation of the interbasin term not only forces a zero net mass transport for the intrabasin term but it also provides a useful method with which to diagnose the effects of interbasin throughflows. The interbasin throughflows induce advection of water parcels and contribute directly to OMHT. In contrast to the intrabasin term, which is associated with the circulations and forcing within a basin, interbasin throughflows are associated with forcing both inside and outside the basin.

The decomposed interbasin OMHT according to Eq.5 is compared with previous observations (or estimations based on observations) in Table 2. The BBH decomposition and interbasin-intrabasin decomposition provides a mathematical method, with coarse assumptions, to estimate the contribution of the Bering Strait to OMHT. On the contrast, Shallow Subducting Overturn Decomposition (SOV) is a physical approach to estimate the contribution based on water mass transformation (Talley, 2003). Along Bering Strait, the observed OMHT is 3–6 10²⁰ J/yr (0.01–0.02 PW) obtained from oceanographic moorings (Woodgate et al., 2010, 2012), and our estimation (0.013 PW) is consistent well with the observations. At 24°N in the Atlantic Ocean, the throughput from the Bering Strait throughflow is below the main thermocline, and it contributes to a southward OMHT of 0.02 PW based on the SOV decomposition (Talley, 2003). Our estimation there (0.022 PW) is consistent with the result from the SOV decomposition, but smaller than the result from the BBH decomposition (0.04 PW). The main difference among the estimations appears at 24°N in the Pacific Ocean. Our estimation (0.015 PW) is of the same order of the result from the BBH decomposition (0.03 PW), but one order of magnitude smaller than the result from the SOV decomposition (0.14 PW). This is because the water feeding the Bering Strait throughflow is primarily from the upper and intermediate Pacific Ocean (Talley, 2003). Consequently, the assumption of section-averaged temperature may underestimate the associated temperature and OMHT at low latitudes where the main thermocline exists.

5 CONCLUSION

A key finding of this work is that the effects of the Bering Strait throughflow on OMHT variations should not be ignored. According to the interbasinintrabasin decomposition, the interbasin OMHT induced by the Bering Strait throughflow is found to be ~0.02 PW under modern climate conditions and zero during the LGM because of the closed Bering Strait. Because the interbasin OMHT is two orders of magnitude smaller than at low latitudes, it is always ignored. However, in the comparison of the OMHT under modern and LGM climate conditions, intrabasin circulations, which include horizontal gyres and meridional overturning cells, induce a typical OMHT difference of 0.05 PW in the North Atlantic Ocean and 0.20 PW in the North Pacific Ocean. Thus, the effects of the Bering Strait throughflow (~0.02 PW) on OMHT variations cannot be ignored. This also suggests that diagnostics of the OMHT variations in the North Pacific and North Atlantic oceans should not focus only on forcing within a basin, but also consider external forcing that might influence the Bering Strait throughflow. In addition, it has been proposed that the Bering Strait throughflow could have been reversed during the last deglacial period, based on paleo proxies (Pelto, 2014) and model simulations (Hu and Meehl, 2005; Okumura et al., 2009; Hu et al., 2012b). Thus, the contribution of the Bering Strait throughflow to OMHT variations might have been even greater historically.

6 DATA AVAILABILITY STATEMENT

The modern experiment was based on case b30.030a from the 20th Century Climate in Coupled Models (20C3M run1), and the LGM experiment was based on case b30.104w from the Paleoclimate Modeling Intercomparison Project 2. Both databases are available from the website of the Earth System Grid https://www.earthsystemgrid.org after registration.

The reconstructed SST data shown in Fig. 1 were obtained from the MARGO project, available from https://www1.ncdc.noaa.gov/pub/data/paleo/paleocean/margo/.

7 ACKNOWLEDGEMENT

We thank the Earth System Grid Federation and the MARGO group for sharing their data with the public. We thank YANG Haijun, LI Qing, and WANG Kun from Beijing University for their help with the calculations of heat transport. We also thank two anonymous reviewers, LI Ziguang, GUO Yongqing, and ZHANG Cong for their valuable advice. We also thank Liwen Bianji, Edanz Group China (www.liwenbianji.cn), for editing the English text of a draft of this manuscript.