Global warming induces ocean circulation changes that not only can redistribute ocean reservoir temperature stratification but also change the total heat content anomaly of the ocean. Here all consequences of this process are referred to collectively as “redistribution.” Previous model studies of redistributive effects could not measure the net global contribution to the amount of ocean heat uptake by redistribution. In this study, a global ocean model experiment with abrupt increase in surface temperature is conducted with a new passive tracer formulation. This separates ocean heat uptake into contributions due to redistribution temperature and surface heat flux anomalies and those due to the passive advection and mixing of surface heat flux anomalies forced in the atmosphere. For a decline in the Atlantic meridional overturning circulation of about 40%, redistribution nearly doubles the Atlantic passive anomalous surface heat input and depth penetration of temperature anomalies. However, smaller increases in the Indian and Pacific Oceans cause the net global redistributive contribution to be only 25% of the passive contribution. Despite the much larger anomalous surface heat input in the Atlantic, the Pacific gains heat content anomaly similar to that in the Atlantic because of export from the Atlantic and Indian Oceans via the global conveyor belt. Of this interbasin heat transport, most of the passive component comes from the Indian Ocean and the redistributive component comes from the Atlantic.
The absorption of heat by the ocean affects the diagnosis and prediction of global warming. Disagreement on ocean heat uptake among coupled models adds uncertainty to projections of future global warming scenarios (IPCC 2007; Watanabe et al. 2013). Warming of the subsurface ocean is a persuasive indicator of global warming (Levitus et al. 2012) and has attracted great attention as a heat sink whose variations could explain changes in the rate of surface warming, such as the apparent slower warming of the early 2000s (Meehl et al. 2011; Chen and Tung 2014; Kosaka and Xie 2013). It is not clear from these studies which basin is taking up the extra heat. Heat exchange among the basins makes it even more difficult to track the heat uptake (IPCC 2007; Lee et al. 2015). Gaps in data, especially for great depths and remote Southern Ocean locations, and heat exchange among the basins make it difficult to estimate real-world changes in subsurface ocean temperature. For all these reasons, it is of great interest to understand both the mechanisms and geographical distribution of subsurface ocean warming. Such an understanding will help interpret ocean observations and improve model performance.
In this paper, we refer to the change in heat content of a given volume as “heat uptake” and to the integral of heat flux into some area of the sea surface as “heat input.” Over the ocean as a whole, heat uptake is equal to surface heat input, but for subdomains of the ocean, such as individual basins, the two may differ because of lateral heat transport within the ocean. Ocean heat uptake is not a passive process: the evolution of ocean temperatures helps control how atmospheric radiative forcing drives surface heat input. Atmospheric radiative forcing induces ocean circulation changes that redistribute pre-existing gradients in the reservoir ocean temperature field, hence indirectly forcing what we will hereafter refer to as “redistribution temperature anomalies.” As a result of this redistribution, the spatial pattern of ocean temperature anomalies under global warming is different from the pattern due to the ocean circulation transporting surface heat flux anomalies alone; the transport here includes all ocean transport processes including advection, diffusion, and mixing. Additionally, redistribution temperature anomalies provide a feedback at the surface that influences the amount of surface heat input from the atmosphere.
Redistributive temperature anomalies have been isolated both in coupled and ocean-only warming experiments using passive tracers (Banks and Gregory 2006; Xie and Vallis 2012; Marshall et al. 2015). Redistribution temperature anomalies are the difference between temperature anomaly and tracer. Banks and Gregory (2006) show that in a coupled model subject to increasing greenhouse gas concentration both the temperature anomaly content and tracer content are different regionally, especially at the high latitudes. In several ocean-only warming experiments, with an idealized Atlantic-like basin, Xie and Vallis (2012) show that the redistributive effect is a robust feature that increases the depth of heat uptake. In both studies, North Atlantic redistribution is associated with weakening of the meridional overturning circulation (MOC). Xie and Vallis (2012) show that experiments with larger MOC weakening have cooler redistributive surface temperature anomalies at high latitudes, and as a result receive larger positive heat anomaly. Thus “redistribution” not only refers to movement of a given amount of heat within the ocean but also includes contribution to ocean heat content associated with advection of initial temperature field by circulation anomalies. Winton et al. (2013) also showed a difference in heat uptake pattern and amount in two experiments, one in which ocean circulation was free to change and the other in which ocean circulation was fixed at the equilibrium strength.
Redistribution plays an important role in determining the depth of heat uptake and hence the speed of the downward propagation of surface heat anomaly (Xie and Vallis 2012). For example, the deep and fast heat uptake in the Atlantic has often been attributed to the deep overturning circulation within it; however, the time scale of this uptake is much shorter than that associated with the overturning circulation. Hence, redistribution changes the transient response of the ocean to radiative forcing (Winton et al. 2013). Moreover, since redistribution could also occur as a result of variability in ocean circulation that is not caused by global warming, this can make it difficult to differentiate the forced response part of ocean heat uptake from heat uptake due to other causes.
Ultimately we would like to understand how ocean heat uptake and temperature change are determined by atmospheric forcing and ocean characteristics. The components of temperature evolution discussed here are controlled by different factors. The tracer advection depends on the flow field in the ocean and, for sufficiently small change in ocean circulation, can be approximated by the response to radiative forcing of the initial (preforcing) circulation (Winton et al. 2013). Redistribution depends on the change in circulation and only occurs to the extent that global warming induces circulation changes. Redistribution can even occur in cases of zero radiative forcing, because changes in wind, freshwater, or surface temperature can each separately induce circulation changes.
The passive tracer formulations that have been used in the studies of Banks and Gregory (2006) and Xie and Vallis (2012) force the tracer with the same flux as the temperature. Therefore, by definition the heat uptake must be identical for temperature anomaly and tracer value, and the redistributive contribution to heat uptake must be zero. However, for a given atmosphere and radiative forcing, we would expect that an ocean in which redistribution is absent would have a different surface heat flux than one in which redistribution occurs. The reason is that the heat flux depends on (among other factors) the temperature difference between the atmosphere and ocean. Since redistribution affects the sea surface temperature (SST), it should also affect surface heat flux. We can subdivide redistribution effects into the “internal” or “spatial” effects due to advection by the circulation anomaly and a “heat flux” effect due to feedback with SST (called the redistribution-feedback uptake). The tracers in these previous studies are forced at the surface with the total surface heat input anomaly in the warming experiments and hence can only isolate the effect of redistribution on the spatial distribution of the total heat uptake.
In this study we introduce a new passive tracer in order to isolate the effect of redistribution on surface heat flux. Like Xie and Vallis (2012), we calculate surface heat flux by restoring SST to a given target profile that represents the properties of the atmosphere (including solar radiation; see Haney 1971; Schopf 1983) and is derived from coupled experiments. The surface heat flux anomaly is based on the difference between the surface temperature anomaly, including redistribution effects, and the target temperature anomaly. In addition to a tracer that is forced by the same heat flux anomaly as SST [essentially what Xie and Vallis (2012) did], we introduce a tracer that itself is restored to the target temperature anomaly. Thus the heat flux driving this tracer does not include either spatial or heat flux effects of redistribution, and so the difference between the tracer and the temperature anomaly captures both. (The tracer is advected by the same velocity field as temperature, so it is influenced by circulation changes due to redistribution; we confirm that this effect is negligible.)
Xie and Vallis (2012) calculate the effective depth , a measure of the average depth to which heat anomalies have propagated at a given time. They find that redistribution deepens in their single-basin ocean. We show that both the surface redistributive temperature anomaly and the redistribution-feedback uptake depend on the overall change in effective depth of temperature anomaly penetration due to redistribution. We track the growth of the passive and redistributive feedback heat uptake components among the ocean basins over a century-long global warming simulation. The experiment is conducted with a global ocean model driven by surface warming based on coupled atmosphere–ocean model experiments in which atmospheric CO2 is abruptly quadrupled. The passive tracer formulations used are discussed in section 2 and the experimental design in described in section 3. Section 4 discusses the differences in the spatial distribution and downward propagation of the two passive tracers and temperature anomaly among the basins. Section 4 also discusses the relative contribution of the passive and redistributive components to the total heat uptake captured by the individual basins and the transport and time evolution of these components among the basins during the century-long run. Section 5 contains the discussion and summary.
2. Advection–diffusion and redistribution effects
The conduct and analysis of the experiments is largely based on comparing the evolution of temperature anomalies with that of passive tracers in the perturbation experiment, so we state the governing equations for different tracers here. The division of temperature anomaly [as a function of position (x, y, z) and time t] into components is based on the temperature advection-diffusion equation, which for generalized velocity υ(x, y, z, t) (including all transport processes, such as the bolus component parameterizing eddy effects and mixing) and surface heat flux Q can be written as
Note that what we refer to here as the “surface heat flux” is the surface heat flux into seawater; an additional flux is associated with melting or freezing ice. Given , the heat flux from the atmosphere, we have . For a perturbation experiment, writing variables in terms of an initial equilibrium value and an anomaly (denoted by an overline and prime, respectively; that is, ), the difference between (1) for perturbation and equilibrium experiments gives
The perturbation temperature anomaly is further partitioned between a passive component (advection of surface flux anomalies by the perturbation circulation, ), denoted as , and a redistributive component, (advection of by circulation changes, ), that is, . Both and are zero at the beginning of the perturbation experiment. The passive component is defined as a tracer that is forced by a surface flux and advected by the same velocity field as in (2):
a. Same flux-passive temperature anomaly tracer,
As in Banks and Gregory (2006) and Xie and Vallis (2012), in order to isolate temperature anomaly due only to redistribution of reservoir temperature gradients, we set . Then the only “forcing” term for (i.e., a term that can be nonzero even if = 0) is the term, which represents advection of the original equilibrium temperature gradients by the perturbation velocity. The volume integrals of (2), (3), and (4) over the whole domain give , and therefore . Hence redistribution as defined above moves heat within the ocean but does not change total ocean heat content. The conservation of reservoir heat content by circulation changes implies that redistributive warming in any volume must be compensated by redistributive cooling elsewhere. The term measures the total ocean heat uptake or ocean heat content change in the perturbation experiment; therefore, the passive uptake, as defined above, is the same as the total heat uptake.
Following the above method, we introduce a tracer denoted as in our perturbation experiment. It is initialized at zero and forced at the surface with the heat flux anomaly , which is the difference between the heat flux in the perturbation and equilibrium experiments, (the subscript AF indicates it is forced by the full or total heat flux anomaly in the perturbation experiment.). The tracer is then used to evaluate the “spatial redistribution temperature anomaly” , using . This tracer is similar to the tracer used in the Banks and Gregory (2006) coupled run, with the difference here that our is introduced in an ocean-only run. Xie and Vallis (2012) also used a similar method in an ocean-only run but used a tracer mimicking ; while the passive component is evaluated from difference between and , both methods are equivalent. As a check, the global volume integral of the and in the experiment should be the same.
b. Same target-passive temperature anomaly tracer,
We can further partition the surface heat flux anomaly into heat flux anomalies originating in the atmosphere (passive heat flux anomaly) and surface flux anomalies occurring as a response to the internal or spatial redistribution of temperature gradients in the ocean (redistribution-feedback heat flux anomaly), that is, . To do this, it is necessary to isolate the redistribution temperature anomaly at the ocean surface. One way to prescribe surface heat flux is through the use of restoring boundary conditions. This forcing allows both heat flux and (to a smaller extent) temperature at the surface to change in response to ocean circulation changes:
For surface heat flux, the surface temperature is restored to a target distribution on a time scale controlled by the parameter α in (5). In the perturbation experiment, using the same notation as above, we can write the perturbation heat flux anomaly as
The variable to a large extent captures the atmospheric forcing anomaly into the ocean, due to greenhouse gas changes, similar to in Marshall et al. (2015). However, depends not only on but also on the ocean surface temperature anomaly , which includes both passive and redistributive temperature anomaly components, that is, and in the tracer notation defined earlier. In these terms we can rewrite the perturbation heat flux anomaly as
Defining this way, (7) shows that setting for is equivalent to restoring the tracer surface value to rather than to , thus including the redistributive effect in the tracer flux. Hence, we can define a new tracer surface flux obtained by restoring only the passive temperature anomaly (the tracer surface value ) rather than total temperature anomaly to the target temperature anomaly . This removes the effect of from the surface flux anomaly and isolates the perturbation heat flux anomaly originating in the atmosphere due to anthropogenic greenhouse forcing from that originating in the ocean due to ocean circulation changes. We denote the new tracer as , where the subscript AT shows the tracer surface is restored to the “same target value” as the surface temperature anomaly; this implies the atmospheric origin of the surface heat flux anomaly since will be zero if is zero. The tracer flux can thus be written as
Similar to , the evolution of is given as
Hence, we introduce a passive tracer in the perturbation experiment, which is initialized at zero and forced at the surface with a tracer flux derived using a restoring surface formulation in (8). The tracer surface value continuously restored to the target temperature anomaly and advected by the perturbation experiment’s velocity field.
We can measure the redistribution-feedback heat flux anomaly by taking the difference between (6) and (8), which quantifies how much the surface heat flux is changed by redistribution altering the surface temperature response to atmospheric forcing; (8) − (6) gives
We can thus define the redistribution-feedback temperature anomaly denoted as : this represents the total heat content and reservoir temperature distribution changes (spatial and heat flux effects) occurring as a result of ocean circulation perturbation. Subtracting (9) from (2) gives the evolution for :
Unlike , the content or redistribution-feedback heat uptake, is not zero; it is equal to the global surface integral of the redistribution-feedback heat flux anomaly . The spatial pattern of redistribution-feedback temperature anomaly will be determined by the term and the magnitude of the anomalies will be modulated by . Note that a redistribution-feedback heat uptake can occur through any atmospheric perturbation causing ocean circulation changes, not necessarily through greenhouse forcing (e.g., surface wind changes). According to (6), without greenhouse forcing and hence and will be zero; however, could still be nonzero if there is a circulation change due to other surface perturbation or circulation variability, making as well as nonzero. This heat uptake component will be useful to differentiate ocean heat content changes as a result of climate change from that due to variability of the circulation, for example.
Comparing and in (6) and (8) shows they will both approach the same value in equilibrium since they are restored to the same , but at a different rate because of the in . A net negative at the surface gives a longer time to equilibrium and more heat flux to reach equilibrium, while a net positive at the surface gives a faster approach to equilibrium and less surface heat input to get there. Hence, as shown in (10), redistribution-feedback heat flux anomaly depends on the disequilibrium difference between and at the surface. A net negative at the surface indicates an oceanic process that is making the surface temperature anomaly colder than it would be if only responding passively like . Such a process, according to (10), will yield surface redistribution-feedback heat gain, that is, more total heat uptake than the passive uptake. (Similarly a net positive at the surface implies surface redistribution-feedback heat loss, that is, less total heat uptake than passive uptake). Table 1 shows a summary of the two tracer formulations and the variables used.
3. Experimental design
The response of a global-domain ocean model to a surface warming perturbation is examined using the Parallel Ocean Program (POP) version 2.0, a z-coordinate model developed at the Los Alamos National Laboratory (LANL) (Smith and Gent 2002). The ocean model uses approximately 1° horizontal resolution and the north pole of the model coordinates moved to Greenland. Eddies are represented by the Gent–McWilliam parameterization (Gent et al. 1995), with a diffusion coefficient of 1.25 × 103 m2 s−1 used both for the bolus and Redi parts. Vertical turbulent mixing is represented with the K profile parameterization (KPP; Large et al. 1994) with a background diffusivity of 1 × 10−5 m2 s−2 and convection is represented by strong vertical diffusion.
The forcing data are derived from the coupled model simulations from the CMIP5 (phase 5 of the Climate Model Intercomparison Project; Taylor et al. 2012), done with CCSM4 (Community Climate System Model version 4; Gent et al. 2011), which uses a slightly later version of POP as its ocean component. As in Xie and Vallis (2012), using restoring boundary conditions, the target temperature is derived from the coupled model sea surface temperature values and fluxes, that is, , and target salinity is derived analogously from the coupled model virtual salt flux and sea surface salinity. The temperature restoring strength is given by α = 40 W m−2 K−1. Wind stress is also based on the coupled model output. The target values are then used to compute surface fluxes in our POP experiments using (5). The ocean-only model is thus forced to reproduce preindustrial equilibrium and 4×CO2 abrupt increase surface conditions for the equilibrium and perturbation experiments respectively.
The POP control forcing is derived from the monthly averages of the nearly-equilibrated last 100 years of the CCSM4 CMIP5 preindustrial control (piControl) run, and initialized from the start of this 100-yr period. The ocean control run is integrated to near-equilibrium, spun up for 500 years using the tracer acceleration method (Bryan 1984), then followed by another 500 years with conventional time stepping. The POP control run, shown in Fig. 1a, reproduces well the global circulation in the CCSM4–CMIP5 coupled model experiment, although with weaker Atlantic overturning circulation.
The perturbation experiment is a 100-yr-long run initialized from year 901 of the POP control run. The temperature and salinity forcings are derived from the monthly climatology (years 100–150) of the abrupt 4×CO2 CMIP5 experiment, while wind forcing is the same as the CMIP5 piControl run for simplicity and to remove additional atmospheric influence. In the CMIP5 abrupt 4×CO2 experiment, the piControl initial condition atmospheric CO2 is instantaneously quadrupled. An additional total flux-passive temperature anomaly tracer forced by the heat flux perturbation [(7)] and a same target-passive temperature anomaly tracer forced by the heat flux expression [(8)] are introduced in the perturbation experiment. The POP control heat flux climatology (years 901–1000) is supplied as input to compute , the surface flux for , while is supplied as input to compute , the surface flux for . The difference between the s for the piControl and abrupt 4×CO2 CMIP5 experiments gives .
It should be noted that our ocean-only model is forced with near-equilibrium monthly climatological surface conditions for both the control and perturbation experiments. This removes interannual and higher-frequency atmospheric weather noise associated with a coupled model and improves the signal-to-noise ratio, while retaining the annual cycle for both experiments. Keeping surface winds at the equilibrium strength also removes additional atmospheric influence on SST and ocean circulation changes. For the perturbation experiment, surface conditions are instantaneously forced to the near-equilibrium conditions; this not the same as the abrupt CMIP5 experiment in which surface temperature and heat flux anomalies respond more slowly to instantaneous CO2 quadrupling. This ensures that the ocean approaches an equilibrium state similar to that of the coupled model (Fig. 1b) but isolates the transient response associated only with the ocean.
4. Redistribution and ocean heat uptake
a. Temperature distribution
1) Meridional structure
We first compare how temperature anomaly and the two passive tracers evolve in the Indian, Pacific, and Atlantic basins by taking the zonal average in each basin. Each basin includes the local sector of the Southern Ocean (with boundaries between adjacent sectors shown in Fig. 6). Over the century of the perturbation experiment, the temperature anomaly and tracers and (Table 1) fill roughly the top kilometer of all the ocean basins (Fig. 2a). As in observations and coupled models, , , and reach deeper in the Atlantic than in the other basins. The passive tracer distributions are noticeably different from the field in all the basins. The distribution in latitude and depth of the two passive tracers, and , have similar features to each other because they are advected by the same velocity field. Both tracers penetrate deeply at high latitudes but more shallowly at low latitudes. This meridional gradient in depth penetration is characteristic of the shallow Ekman cells in the tropics and deep circulations in the Atlantic and the Southern Ocean. The magnitudes of the passive tracers, however, are quite different in the high latitudes, especially in the North Atlantic, where is much larger than . The temperature anomaly, on the other hand, shows less meridional gradient in depth penetration compared to the tracers; it shows deeper penetration than the tracers at low latitudes and its content is more evenly distributed across all latitudes.
The difference in tracers and temperature anomaly fields is shown by the redistribution temperature anomalies, and , (Fig. 2b). As discussed in section 2, indicates the spatial redistribution of existing ocean heat content (Table 1); warms the tropical deep layers (below 700 m) and cools the Northern Atlantic and Southern Ocean high latitudes. The tropical deep warming below 700 m, due to in all the basins, smooths out the meridional gradient in heat penetration and content for compared to the tracers, and (cf. Fig. 2a). Additionally, also explains why the difference in the content of and occurs at high-latitude regions of deep uptake, because here the spatial redistributive temperature anomaly cools the surface and as a result increases the surface heat flux anomaly into the ocean (Xie and Vallis 2012).
The redistribution-feedback temperature anomaly field differs from the field because it evolves through changes in the field and the resulting surface redistributive-feedback heat input, (Table 1). The distribution shows that regions of surface cooling are compensated by positive and regions of surface warming are compensated by negative (Fig. 3), such that only slightly cools the surface compared to the strong spatial redistributive surface cooling at high-latitude regions, especially in the Atlantic, while regions of surface warming in the tropics are only slightly warm for in the Indian and Pacific Oceans. There is also an additional redistributive warming for in the deep for the Atlantic due to the compensating redistributive-feedback heat gain. As a result, cools the surface and puts the redistribution-feedback heat gain below the surface in all the basins (Fig. 2b). Note also that the term in Fig. 3 is opposite in sign to the background surface heat flux, in most places, and hence the anomaly implies only a reduction background state.
2) Vertical structure
We can understand the vertical distribution of warming by examining quantities horizontally averaged over each basin. Despite the large values of spatial redistributive warming and cooling that occur in every basin (Fig. 2b), the horizontal averages of and are much smaller in the Pacific and Indian Oceans than in the Atlantic (Fig. 4a). Only the Atlantic shows a large net spatial redistributive cooling at the surface, which is due to the high-latitude cooling seen in Fig. 2b. In each of the other basins, the warming and cooling balance. The Atlantic gains redistribution-feedback heat as a result of this, which causes to be greater than in the Atlantic, and this difference between the Atlantic tracers continues to grow with time (cf. Fig. 4b). In contrast, the Indian and Pacific tracers remain approximately the same as each other over the century because in these basins there is no redistribution-feedback heat input.
A significant net spatial redistributive surface warming or cooling also changes the average depth penetration for compared to that of the tracers. As discussed in section 2, positive values of need to be compensated by negative values elsewhere. This is true globally and in the Atlantic; in the first half of the century, the net redistributive cooling near the surface is compensated by warming below 700 m, and as a result penetrates deeper and has a smaller vertical gradient than and . Because of lateral transport among the basins, this balance of spatial redistributive warming and cooling changes. In the Indo-Pacific, there is no net spatial redistributive surface cooling, however, there is a net spatial redistributive deep warming and hence also penetrates deeper than and . Moreover, the small surface cooling in the Indian Ocean decreases in time while the deep warming there increases. This imbalance suggests that the source of deep warming in the Indo-Pacific is being imported from the Atlantic. This export of heat reduces the spatial redistributive deep warming in the Atlantic between years 50 and 100 (Fig. 4a).
The speed of downward propagation can be seen from the vertical profiles. Even within 10 years, both passive tracers and temperature anomalies show a warming in at least the top 500 m (Fig. 4b). Throughout the experiment, there is deeper penetration in the Atlantic, with penetrating deeper than . Most of the profiles have a roughly similar shape at different times, except that Atlantic develops a slight subsurface maximum in the top 500 m. As Fig. 4b shows, the basin-averaged distribution gets continuously deeper with time over the entire run. For instance, the thickness of the “warm” tracer region increases, even for the Indian and Pacific basins where the maximum tracer values are at the surface.
For redistribution (Fig. 4a), the vertical structure is more complex. In the Atlantic, peak values of remain in the vicinity of 500 m after the first decade. Similarly, after the first few decades, the vertical profile of basin-average does not change shape much, although it grows in magnitude throughout the water column. This indicates that vertical propagation is much faster than the century-scale vertical advective time scales for . Since is caused by the velocity anomaly, we expect its vertical structure to be related to that of the meridional overturning streamfunction anomaly (section 4c). The meridional overturning also has a relatively stable meridional structure throughout most of the run, so similar behavior of is not surprising. However, this feature indicates that rather than thinking of redistribution as “speeding up” vertical propagation of (as in Xie and Vallis 2012), we should think of the evolution of as the sum of two processes with very different time scales.
Furthermore, the redistributive effect on vertical penetration of heat can be measured by comparing the effective depth among the tracers and temperature anomaly. Following Xie and Vallis (2012), we measure the average penetration depth of any property θ (representing , , or ), over a volume with surface area A, with the “effective depth” given by
We can apply this to the entire ocean or to individual basins. We can relate the redistributive influence on to surface properties by remembering that or and that for the case of the global volume integral of and are equal. Comparing the values for and , we get
The total effect of redistribution is measured by the difference between and . Separately, the two effects of redistribution on the depth of heat anomaly penetration can be measured by the difference between and and by the difference between and . As shown in Fig. 4c, the growth in due to the “spatial” redistributive effect is greater than the growth due to the “heat flux” effect of redistribution. This is because and are advected by the same velocity field, although with different surface distributions and magnitudes; hence they both have similar depth of penetration (cf. also Fig. 2a), while is largely affected by the term in (13). Note that when the surface average of , indicating surface cooling by redistribution; the opposite is also true when . This change in the effective depth of due to a nonzero at the surface is also an implication of the conservation of explained earlier; that is, near-surface cooling (warming) is balanced by deep warming (cooling) and hence deepening (shallowing) of . Since the sign of the redistributive feedback uptake depends also on the sign of the , the difference between the effective depth for the tracer and is a good indication for the sign of redistributive feedback uptake; that is, implies redistributive heat gain, while implies redistributive feedback heat loss.
For all three tracers, the effective depth grows over time and is larger for the Atlantic than for the Pacific or Indian (Fig. 4c). Redistribution greatly deepens only in the Atlantic, with being about 45% larger than (although with similar uptake) and 65% larger than for . Note, however, that while the total uptake for is very similar in the Pacific and Atlantic (see section 4b), their depths of penetration are very different; the passive uptakes in the Pacific and Indian are also very different, yet their effective depths are very similar. Hence, differences in effective depths of tracers and temperature anomaly among the basins do not necessarily imply differences in their uptake. This occurs due to transport among the basins and the different sizes and dynamics of the basins.
b. Heat uptake and lateral heat transport among basins
In the discussion below we consider the uptake of the passive and redistribution-feedback components. “Heat” refers to (where θ is any of the tracers) and “surface heat input” into an ocean basin is the integral of over the top surface of the heat flux; “heat uptake” is the change in heat content of a given volume. Here we do not consider because the surface heat input for and are equal and their lateral fluxes between basins are almost equal as well. We refer to the integrals and as the passive surface heat input and heat uptake components respectively and the integrals and as the redistribution-feedback surface heat input and uptake components respectively. The integral of and gives the total surface heat input and heat uptake. Averaging over the surface area of the ocean, the total surface heat input into the ocean of about 1 PW is equivalent to an average heat flux of 3 W m−2.
The 100-yr average passive surface heat input is similar for all three basins (Fig. 5, light gray bars on the right), despite the different sizes and dynamics of the different basins. In the Atlantic, the faster downward propagation of heat compensates for the basin’s small area. In contrast to the passive surface heat input, the additional heat input associated with redistribution (Fig. 5, light gray bars on the left) is very different in each basin. In the Atlantic, it is more than 50% of the passive contribution; here the division for the Atlantic basin includes the Arctic Ocean and Mediterranean Sea, to balance the global input. Excluding these basins, redistribution-feedback surface input into the Atlantic is about 80% of the passive contribution. In the Indian Ocean, it is about 15% of the passive, and in the Pacific it is negligible. Including both passive and redistribution-feedback parts, about 50% of total surface heat input into the three basins enters the Atlantic alone. For the globe as a whole, redistribution-feedback increases heat uptake by about 25%.
The individual basin total heat uptake (Fig. 5, deep gray bars) tell a somewhat different story than their surface heat input. The Pacific has a little more total heat uptake than the Atlantic, while the Indian Ocean has the smallest total heat uptake. In the Pacific, the total heat uptake is 80% greater than its total surface heat input, its passive heat uptake is 50% greater its surface input, and its redistribution-feedback heat uptake grows to 40% of the total surface heat input, although the redistribution-feedback surface heat input is negligible. As a result, the Atlantic and the Pacific have about the same heat uptake, each accounting for 40% of the global heat content, while the Indian Ocean accounts for the remaining 20%. In summary, the Atlantic has the greatest gain in total surface heat input due to redistribution, while the Pacific has the greatest gain in total heat uptake from lateral heat transport.
Differences between surface heat input and change in internal heat content indicate transport of heat between basins. For a given region, lateral heat transport L consists of the area integral along the side boundaries of the flux terms in (2), (9), and (11): for transport ; for total heat, transport ; for passive heat, transport ; and for redistributive heat, transport , where refers to the component of velocity normal to the boundary. POP outputs horizontal heat flux at each grid point and we estimate the individual terms from annual-average, temperature, and tracer fields and the term is the estimated from the and terms.
We consider the energy budget for individual basins. The lateral heat transport between the basins is dominated by advection. The basins are connected in the Southern Ocean with large eastward flows into and out of each basin. The Southern Ocean Pacific-to-Atlantic flow of about 102 Sv (1 Sv ≡ 106 m3 s−1) through the Drake Passage is balanced by an equal Atlantic-to-Indian flow south of Africa, so that the Southern Ocean net volume transport is approximately zero for both the Atlantic and the Indo-Pacific, with small flow through the Bering Strait (Fig. 6a). The Indian and Pacific Oceans, however, exchange an almost equal opposite net volume transport of about 12 Sv in the Southern Ocean, with the Indian exporting volume to the Pacific. This occurs due a stronger Indian-to-Pacific flow of about 114 Sv south of Australia and 102 Sv exiting the Pacific through the Drake Passage. This Southern Ocean Indian-to-Pacific net volume export returns to the Indian Ocean in the 12-Sv Pacific-to-Indian flow via the Indonesian Throughflow, which in turn returns to the Pacific south of Australia as part of the zonal Southern Ocean flow, so that the net basin volume transport into each basin is zero. This exchange plays an important role in the “conveyor belt,” which also links shallow inflow and deep outflow in the Atlantic to the other basins.
In the control climate, the equilibrium basin temperatures are maintained by lateral heat transports balanced by surface heat input. However, with close to zero Southern Ocean net volume transport for the Atlantic and the Indo-Pacific, the relative temperatures at the boundaries results in lateral heat transport of 0.23 PW flowing out of the Indo-Pacific, through the Southern Ocean, and into the Atlantic (Table 2, column 1; see also Fig. 6a), where it is augmented by tropical heating and exported to the Arctic (including the Labrador and Nordic Seas). In the Indo-Pacific, a much warmer Pacific-to-Indian volume transport through the Indonesian Throughflow is exchanged for an equal but relatively colder Indian-to-Pacific net volume transport through their respective Southern Ocean boundaries. This volume exchange within the Indo-Pacific means heat export for the Pacific and import for the Indian Ocean because the Pacific (Indian) Ocean loses (gains) warmer volume through the Indonesian Throughflow, but gains (loses) colder volume through the Southern Ocean. Hence, in steady state the Pacific exports heat to the Indian and Atlantic Oceans via the Southern Ocean and Indonesian Throughflow. This exchange transfers the surface heat input into the Pacific to the Indian and Atlantic Oceans in steady state.
In the warming climate, the direction of heat anomaly transport is opposite that of the control heat transport, with the Pacific importing heat anomaly from both the Indian Ocean and the Atlantic. The direction of heat transport reverses for two reasons: the distribution of heat anomaly (affecting the and terms) and the weakening circulation (affecting the term) described in section 4c. The total heat transport will be described in terms of the passive and redistributive transports respectively.
The velocity in the term is in the same direction in the perturbation experiment as in the control equilibrium. However, the term integrated over all the boundaries of each basin has the opposite sign of integrated . A swath of relatively high water circling Antarctica in the Southern Ocean weakens near the Drake Passage where water flows into the Atlantic sector. This pattern comes from the forcing and ultimately from the coupled experiments (Fig. 7a), so it is seen in the distribution too. It is a robust feature and can also be seen in CMIP3 models forced by A1B radiative forcing (Kuhlbrodt and Gregory 2012, see their Fig. 4). Thus for the Atlantic and Indo-Pacific, the exchange reverses: high water leaves the Atlantic and low water enters, so that the Atlantic exports heat (Fig. 6b). For the Pacific, the same feature in the Southern Ocean of higher- water entering from the Indian sector and lower- exiting to the Atlantic implies Pacific heat import and Indian heat export. In contrast to the control, does not have the strong equator-to-pole contrast that does, so the Indonesian Throughflow does not imply a large lateral heat loss from the Pacific or gain for the Indian Ocean. Instead, the lateral heat transport in the Southern Ocean dominates, for both the Indian Ocean and the Pacific. The advections of the tracer and temperature anomaly are the same sign and similar in magnitude, hence the transport direction is similar.
The redistributive heat transport and hence is dominated by advection of control temperature by circulation anomaly with volume transport anomalies opposite that of the control. The Indonesian Throughflow anomaly flow is from the Indian Ocean to the Pacific. The Southern Ocean flow anomaly strengthens the Drake Passage flow and Atlantic-to-Indian flow relative to the Indian-to-Pacific flow so that there is an equal but opposite net volume transport anomaly out of the Pacific to the Indian Ocean balancing the Indian-to-Pacific Indonesian Throughflow volume transport anomaly. Therefore, relatively warm water enters the Pacific at the equator and relatively cold water leaves in the Southern Ocean; the reverse is true for the Indian, so that the Pacific is importing redistributive heat and the Indian is exporting. The net effect of all these transports is for the term to export heat from the Atlantic to the Pacific, with little heat export also to the Indian Ocean (Table 2, column 4). The Pacific thus gains redistributive content, although with negligible redistributive surface input. The Pacific gains all of its redistributive import from the Atlantic via the Indonesian Throughflow. The combined passive and redistributive transport increases the import of the temperature anomaly into the Pacific from the other two basins.
c. Circulation perturbation
The circulation changes caused by the perturbation in forcing include changes to the meridional overturning and interocean flow. The control equilibrium overturning has the familiar pattern of Atlantic inflow in the top kilometer and outflow in the abyss; Indo-Pacific deep inflow, widespread upwelling, and middepth outflow; and Southern Ocean upwelling associated with surface Ekman divergence. The perturbation weakens the overturning, which is equivalent to adding a reverse Atlantic MOC (AMOC) of 10 Sv (100-yr average) (Fig. 8a, top) and a decrease of Indo-Pacific upwelling of 4 Sv (100-yr average) (Fig. 8a, bottom). The weakened circulation is caused by warming and freshening of the North Atlantic deep water formation regions relative to other parts of the ocean.
The equilibrium depth-integrated streamfunction includes an Indo-Pacific circulation with 10 Sv flowing from Pacific to Indian in the Indonesian Throughflow and returning to the Pacific from south of Australia. This circulation also weakens by about 4 Sv (Fig. 8b). The reduction is curious because the depth-average circulation is usually associated with wind stress, which is not perturbed in the experiment. Much of the circulation perturbation in the vicinity of the Indonesian Throughflow occurs in the top kilometer (Fig. 8b), with an Indian-to-Pacific flow. This looks to be a consequence of the weakening of the conveyer belt circulation associated with the decreases in overturning.
The horizontal flow also shows signs of the decrease in the meridional overturning, with perturbation velocity flowing southward in the Atlantic and then flowing eastward out of the Atlantic and then northward from the Southern Ocean into the Indian and Pacific Oceans (the reverse of the equilibrium upper-limb flow out of the Indo-Pacific and into the Atlantic). The change in the Indian–Pacific exchange may be a consequence of this change in the overturning.
d. Time evolution of heat uptake components
By design, the strong restoring and constant (Fig. 7a) of the perturbation experiment ensures that most of the surface temperature increase occurs in the first few years (Fig. 9b), but the system is far from steady state even at the end of the experiment. This can be seen in the time-integrated surface heat input anomaly into the ocean and global heat content anomaly (Fig. 9a). We expect such a long time scale based on AOGCM experiments that show millennial-scale adjustment after radiative forcing is changed (e.g., Li et al. 2013).
Time evolution within different basins reflects the features discussed in section 4b. In the Pacific, heat input anomaly (slope of curves in Fig. 9a) is small after about 50 years, but heat content continues to vigorously grow. During the last 50 years of the experiment, the basin acquires about a third of its heat content increase but only about 10% of its surface heat input. The disparity is because of the heat import from other basins, which becomes the dominant source of warming in the Pacific after the first 50 years. In the last 50 years, the Atlantic, in contrast, receives about half of its surface heat input but only experiences about a third of its heat content growth. The changing composition of heat sources for the two basins reflects increasing lateral heat transport into the Pacific and out of the Atlantic in the last 50 years. The Indian Ocean exports heat at a more constant rate for the entire century.
5. Discussion and conclusions
Here we compare the results in this study to previous studies. Similar to the previous tracer studies of Banks and Gregory (2006), Xie and Vallis (2012), and Marshall et al. (2015), the difference between our tracer and isolates the effect of redistribution on spatial pattern of heat uptake. These earlier studies show that the spatial rearrangement of the existing ocean heat content occurs by cooling the high latitudes and warming the deep tropics. Our interbasin comparison shows that this spatial rearrangement, which yields a net cooler redistributive surface temperature anomalies and as a result deeper effective depth for temperature anomalies, is only significant in the Atlantic, but not in the Indian and Pacific Oceans, in agreement with the idealized study of Xie and Vallis (2012). This result is not surprising because these basins do not have the deep overturning circulation of the Atlantic. However, our results show that the Atlantic heat exchange with the other basins is also very important, allowing the Pacific to gain as much heat content anomaly as the Atlantic. The lack of this exchange likely explains why the effect of redistribution in deepening heat uptake in the Atlantic is much bigger in the study of Xie and Vallis (2012), since the idealized single Atlantic basin used in their study does not allow for exchange with the other basins.
Recent studies have suggested that passive Southern Ocean meridional heat anomaly transport is main the reason for the delayed Southern Ocean warming poleward of the Atlantic Circumpolar Current (ACC) and heat convergence north of it (Armour et al. 2016; Morrison et al. 2016). In agreement with these earlier results, this study shows that the heat anomaly transport in the Southern Ocean is dominated by the passive component; however, the redistributive heat anomaly transport also enhances the total heat anomaly transport in the Southern Ocean. In addition, the results here show that this Southern Ocean meridional transport converges in the Pacific, putting the Pacific as well as the Atlantic in a central role for global heat uptake. The Indonesian Throughflow closes the path for the Southern Ocean heat exchange among the basins. The central role of the Indonesian Throughflow plays in the interbasin heat exchange is not surprising, as its importance in regulating global climate has been demonstrated in several studies. However, the connection of the Indo-Pacific and Indonesian Throughflow volume transport weakening to the AMOC weakening in this study is noteworthy, because the Indonesian Throughflow transport changes have only been linked to wind forcing, which is not perturbed in this experiment.
The global conveyor belt connecting the Indo-Pacific to the Atlantic via Southern Ocean and the Indonesian Throughflow plays a central role in this interbasin heat exchange. The possible connection between AMOC weakening and Indonesian Throughflow weakening has been implied in some previous studies. Gnanadesikan (1999), Klinger and Cruz (2009), and Schewe and Levermann (2010) studied the roles of surface winds and buoyancy distribution in the basins in determining the deep circulation strength within the basins and the strength of the global conveyor belt connecting the circulation in the basins. Some of the Southern Ocean wind-driven upwelling volume transport demand is drawn from the basins depending on their buoyancy distribution. The Atlantic meets the Southern Ocean upwelling demand due to its larger buoyancy gradient. According to Schewe and Levermann (2010), an imbalance between the Southern Ocean upwelling demand (due to an increase in Southern Ocean wind strength in their experiments) and the supply from the Atlantic is met from the Indo-Pacific. In our experiment, the imbalance is caused by the weakening of the AMOC rather than Southern Ocean wind changes. The anomalous upwelling demand drawn from the Indo-Pacific via the Southern Ocean weakens the steady state Southern Ocean Indian-to-Pacific inflow, as well the Indonesian Throughflow Pacific-to-Indian outflow balancing it. This mechanism of interbasin heat content anomaly exchange suggests an accurate simulation of the AMOC and global conveyor belt strength and weakening may help to improve global warming projections and heat distribution among the basins.
We introduce an approach to isolate and quantify of the passive and redistributive feedback components of the ocean heat uptake. Although the redistributive feedback uptake has not been quantified in previous studies, we can compare the results here to the redistributive feedback uptake implied in these studies (Xie and Vallis 2012; Winton et al. 2013; Marshall et al. 2015). The redistributive feedback uptake implied in the study of Xie and Vallis (2012) is positive (increases effective depth for temperature anomalies compared to that of tracers and hence increases total ocean heat uptake); however, the redistributive feedback uptake implied in the studies of Winton et al. (2013) and Marshall et al. (2015) appears to be negative. The passive tracer in the warming experiment of Marshall et al. (2015) showed deeper depth of penetration than that of the actual temperature anomalies. The total heat uptake in the Winton et al. (2013) experiment for which the circulation is fixed at the equilibrium strength is greater than the total heat uptake in the experiment for which the circulation is free to change under CO2 increase. This implies negative redistributive feedback uptake since their free-circulation experiment includes passive and redistributive uptake while the fixed-circulation experiment will have only a passive uptake. These earlier results do not necessarily contradict the results here; as shown in section 2, redistributive feedback uptake could be negative (heat loss to the atmosphere) if the net spatial redistributive surface temperature anomaly is positive, which would also result in a shallower effective depth for total temperature anomaly compared to that of the passive tracer. Redistributive feedback uptake will thus depend on the pattern of ocean circulation weakening in an experiment, which could either cool or warm reservoir surface temperatures. Our further investigation of the redistributive feedback and passive heat uptake components among warming experiments with different surface perturbation shows this possibility.
One implication of these results is that redistributive uptake can significantly change ocean heat uptake and, as a result, change ocean heat uptake efficiency and its transient response to radiative forcing by increasing (decreasing) heat uptake while cooling (warming) SSTs. As suggested by Watanabe et al. (2013), ocean heat uptake efficiency is a source of spread among GCMs in estimating the transient response to radiative forcing, since the AMOC strength and weakening vary greatly among the models. Hence, isolating ocean heat uptake components among models can be useful in diagnosing the differences in model response to radiative forcing. The variability in ocean circulation can also cause redistributive uptake, which may mask or amplify the trend in the passive uptake at different time periods. This method will be useful for isolating ocean heat content changes and temperature anomalies pattern due to CO2 increase from that due to ocean circulation variability.
Some caveats in these results worth mentioning include the following. The target temperature anomaly used is derived from the coupled model run and hence includes some redistributive surface temperature pattern, which changes the redistributive heat uptake estimate. The separation of the passive and redistributive heat content in this study is also made possible through the use of restoring boundary formulation for this study. This method may not be reproducible in a coupled ocean–atmosphere simulation, like the one used in Banks and Gregory (2006). However, this method will be useful for idealized studies or in diagnosing or differentiating redistributive temperature change pattern from that due to ocean dynamical processes. The aim of this study is only to isolate mechanisms ocean heat uptake and its distribution among basins; it does not represent realistic transient radiative forcing and the influence of atmospheric changes (even excluding change in surface wind) due to global warming.
The novelty of this study is quantifying the redistribution-feedback contribution to the total amount of ocean heat uptake by separating the passive and redistribution-feedback components of ocean heat uptake, and tracking the growth and distribution of these of heat uptake components among the basins. As shown from previous studies redistribution has two effects on ocean heat content: 1) the spatial distribution of temperature anomalies through the rearrangement of existing ocean heat content and 2) the amount of heat uptake. The latter effect (heat uptake) is a consequence of the first (spatial rearrangement). The consequence of deeper (shallower) temperature anomalies is to cool (warm) redistributive sea surface temperature anomalies and as a result increase (decrease) heat flux anomaly into the ocean. Our tracer separates the redistributive effect on surface heat flux, thus allowing us to quantify the passive and redistribution-feedback components of ocean heat uptake. The distribution of these components show that the Atlantic uptakes redistribution-feedback heat at the surface, which is about 70% of its passive uptake, while surface redistribution-feedback uptake is negligible in the other basins; hence the Atlantic contributes about half of the global surface heat anomaly input. Globally, the passive component contributes about 75% of the total ocean heat uptake, while redistribution contributes the remaining 25%. Also this additional redistribution-feedback uptake occurs without an increase in surface temperature and slows down the ocean’s approach to equilibrium.
Another major result of this study is that the global conveyor belt plays a big role in distributing ocean heat uptake components across the basins, thus allowing Pacific heat content anomaly to be as large as that of the Atlantic. The global conveyor belt connects the AMOC Southern Ocean inflow to the Indo-Pacific outflow, while the Indian Ocean and Pacific are connected through the Indonesian Throughflow. The relative temperatures of the Indonesian Throughflow and the Southern Ocean exchanges allow the Pacific either to lose (control experiment) or to gain (forced experiment) heat to the other basins. In the warming experiment, the Pacific Ocean gains passive heat content anomaly largely from the Indian Ocean and also from the Atlantic due to the reversed temperature anomaly gradient between the Indonesian Throughflow and the Southern Ocean. Southern Ocean Indo-Pacific and Indonesian Throughflow volume transport weaken via the global conveyor connection to the AMOC weakening, although without wind-driven forcing weakening in this experiment. This allows redistributive heat content anomaly to accumulate in the Pacific by reducing its mean state heat export to the Indian and Atlantic. This exchange allows the Pacific and Atlantic to contribute almost equally, each about 40%, to the global heat uptake while the Indian Ocean contributes the remaining 20%.
We would like to thank Bohua Huang, Jim Kinter, and Jian Lu for helpful conversations. We also thank Helene Hewitt and two anonymous reviewers for their constructive reviews. Work on this project was supported by NSF Grants 1249156 and 1338427 and high performance computing resource from Yellowstone (ark:/85065/d7wd3xhc) provided by NCAR CISL sponsored by NSF.