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:

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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

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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

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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

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Similar to , the evolution of is given as

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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

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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 :

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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.

Table 1.

Variable notation: T.Anom = Temperature anomaly; Redistr. = Redistribution.

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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.

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Basin zonal averages as function of latitude and depth, for the 81–100-yr time average. (a) Tracers and temperature anomaly (°C) for (top) , (middle) , and (bottom) . (b) Spatial redistribution temperature anomalies (°C): = − and redistribution-feedback temperature anomaly = − .

Citation: Journal of Climate 29, 20; 10.1175/JCLI-D-16-0138.1

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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.

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Surface heat flux in W m⁻² average over the century-long run. (top) Passive heat flux anomaly for tracer in the perturbation experiment. (middle) Redistribution-feedback heat flux anomaly for redistribution-feedback temperature anomaly, in the perturbation experiment. (bottom) Surface heat flux in the Control experiment. Total surface heat flux anomaly in the perturbation experiment, . Total surface heat flux in perturbation experiment, .

Citation: Journal of Climate 29, 20; 10.1175/JCLI-D-16-0138.1

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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.

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Basin horizontally averaged total temperature anomaly, redistribution-feedback and passive temperature anomalies, for years 10, 50 (offset 1.5°C to right), and 100 (offset 3°C). (a) Redistribution-feedback temperature anomaly (blue) and spatial redistribution temperature anomaly (red). (b) Temperature anomaly (black) and tracers (red) and (blue). (c) Effective depth and growth over time for (black), (red), and (blue) for each basin.

Citation: Journal of Climate 29, 20; 10.1175/JCLI-D-16-0138.1

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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

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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

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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%.

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Surface heat input anomaly through surface (light gray) and heat uptake (dark gray) within individual ocean basins based on passive tracer (right of zero line) and redistribution-feedback temperature anomaly, = − (left of zero line), in PW (note that both sides of zero line represent positive numbers, so the total width of the bar represents total tracer + redistribution values). Atlantic includes Arctic and Mediterranean values. Values are averaged over the entire 100-yr experiment.

Citation: Journal of Climate 29, 20; 10.1175/JCLI-D-16-0138.1

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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.

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Heat convergence through lateral boundaries. Surface properties (contours and shading), direction (arrows), relative amount (arrow length), and relative temperature (arrow color) of volume transport at boundaries, net basin heat convergence (numbers in ovals, PW), and pseudotransport at selected boundaries (numbers in rectangles). All quantities are 100-yr averages. (a) and Control surface temperature (c.i. = 10°C). (b) and (c.i. = 1°C). (c) and same surface field as in (a).

Citation: Journal of Climate 29, 20; 10.1175/JCLI-D-16-0138.1

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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.

Table 2.

Lateral heat transports out of each basin, averaged over the 100-yr run, for the control temperature , passive tracer , temperature anomaly , and redistributive anomaly, . First row: Heat transport through Indonesian Throughflow for Indian and Pacific basins. Second row: Sum of heat transports out of Southern Ocean boundaries of each basin. Third row: Sum of first two rows. We neglect the Bering Strait heat transport, which is very small. Negative = Export/positive = import, values in PW.

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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.

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Surface restoring temperature anomaly, (°C) and restoring salinity anomaly, (PSU) for the POP perturbation experiment.

Citation: Journal of Climate 29, 20; 10.1175/JCLI-D-16-0138.1

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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.

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(a) Circulation anomaly as measured by meridional overturning streamfunction (contour interval 1 Sv) 100-yr mean. Overturning is for zonally integrated velocity in the (top) Indo-Pacific and (lower) Atlantic basins, and (both panels) globally south of approximately 35°S. (b) Streamfunction for full-depth integrated velocity (shading, in Sv) and horizontal velocity integrated over top 1041 m.

Citation: Journal of Climate 29, 20; 10.1175/JCLI-D-16-0138.1

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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).

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Basin heat content anomaly and cumulative surface heat anomaly input growth with time. Basin volume integrated content of temperature anomaly, (black solid line) and passive tracer, (black dashed line). Cumulative time integrated surface heat flux anomaly (blue solid line) and passive tracer flux (blue dashed line).

Citation: Journal of Climate 29, 20; 10.1175/JCLI-D-16-0138.1

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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.

a. Discussion

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.

b. Conclusions

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%.