Indonesian Throughflow Slowdown under Global Warming: Remote AMOC Effect versus Regional Surface Forcing

a. The Island Rule in a warming climate

Using the classic Island Rule (Godfrey 1989), the ITF transport changes can be estimated in terms of the contour integral of wind stress anomaly (Godfrey 1989; Feng et al. 2018):

$\mathrm{\Delta }{T}_w\hspace{0.17em}=\frac{1}{f_N-f_S}{\displaystyle \oint {}_{\text{ABCDEF}}}\frac{\mathrm{\Delta }{\tau }_l}{{\rho }_0}dl,$(1)

where Δτ_l is the component of the wind stress change along the ABCDEF counterclockwise path (Fig. 1b); f_N and f_S are the Coriolis parameters at the northern and southern extents of the integral loop, respectively; ρ₀ is the mean density. The term ΔT_w is the wind-forced total volume transport changes across the section of 38°S in the South Pacific Ocean, which is also assigned as the change in the ITF transport.

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Projected anthropogenic surface forcing changes. Projected changes in (a) SST (°C; color shading), (b) SSS (psu; color shading), and (c) wind stress curl (10⁻⁷ N m⁻³; color shading), as well as wind stress (N m⁻²; vectors) from CMIP6 multimodel ensemble mean (MME). The stippled areas denote the signals significant at 95% confidence level. The solid (dashed) box in (a) indicates the region of the North Atlantic–Arctic Ocean (Indo-Pacific Ocean), in which the forcings are applied separately in the OGCM to assess the remote (regional) forcing impacts. In (b), the red line indicates the integration route for the wind stress in the traditional Island Rule calculation.

Citation: Journal of Climate 36, 5; 10.1175/JCLI-D-22-0331.1

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b. OGCM experiments

Figure 1a shows that an abrupt quadrupling of CO₂ causes robust warming over the World Ocean. The sea surface temperature change (ΔSST) is spatially uneven, locally enhanced over the cold tongue regions of the equatorial Pacific and Atlantic Oceans, and on the north flank of the Antarctic Circumpolar Current (ACC). The projected sea surface salinity change (ΔSSS) features a strong freshening in the subpolar North Atlantic and the tropical western Pacific, whereas a positive trend over the subtropical gyre in the Atlantic Ocean (Durack and Wijffels 2010) (Fig. 1b). Projected wind stress change (Δwind) is dominated by strengthened westerly wind over the ACC and weakened trade winds over the equatorial Pacific Ocean (Fig. 1c).

From an oceanographic view, the projected ITF change is forced by changes in surface buoyancy forcing (ΔSST + ΔSSS) and wind stress (Δwind) [Eq. (2)] (Fig. 1). We forced the MIT General Circulation Model (MITgcm) with the CMIP6 projected wind and buoyancy forcing changes following an abrupt four-time CO₂ increase (abrupt4xCO₂) (Fig. 1) to investigate the relative importance of each forcing in driving ITF transport change and the underlying physical mechanism (Table 1). The model is configured to a latitude–longitude–cap (LLC90) grid, with a horizontal resolution of 1° in the zonal direction and 1/3° in the meridional direction at low and high latitudes, stretching to 1° at midlatitudes. The model has 50 vertical layers, with layer thickness gradually increasing from 10 m near the surface to 456 m in the deep ocean. The diffusion and mixing parameters of the model are identical to those used in Peng et al. (2020). The present-day climatological monthly air–sea fluxes together with SST (SSTClim), SSS (SSSClim), and wind stress (WindClim) are diagnosed from a hindcast run as described in Peng et al. (2019). The initial state, including potential temperature and salinity, is obtained from a state-of-the-art ocean reanalysis, namely the Estimating the Circulation and Climate of the Ocean Version 4 Release 4 (ECCO v4r4) (Forget et al. 2015). The model is integrated for 100 years to reach a quasi-equilibrium state.

Table 1

Description of the OGCM experiments.

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From the quasi-equilibrium state, we conduct six parallel experiments (Table 1). Each experiment is integrated forward for an additional 140 years, and the average of the last 40 years (101–140) is analyzed. In this study, we strongly restore SST and SSS toward the targeted values with a relaxation time of 10 days. Similar methods have been successfully applied to isolate ocean response to different surface forcing components (e.g., Wang et al. 2015; Chen et al. 2019; Peng et al. 2022). The control run (CTRL) restores SST and SSS toward SSTClim and SSSClim. In the Δall experiment, the model is forced by WindClim + Δwind, and SST and SSS are restored to SSTClim + ΔSST and SSSClim + ΔSSS. The difference, Δall − CTRL, implies the total effect of the surface forcings, which will be compared to CMIP6 results to assess the model performance. The Δbuoy is the same as CTRL but SSS and SST are restored to SSSClim + ΔSSS, and SSTClim + ΔSST. The solution (Δbuoy − CTRL) isolates the ocean response to buoyancy forcing changes. Similarly, Δwind isolates the ocean changes due to wind stress changes (Δwind − CTRL).

The ITF transport in a warming climate could be modulated by both regional and remote buoyancy forcing changes [Eq. (3)]. Figure 1 shows that the remote buoyancy forcing changes are characterized by SST warming (ΔSSTNA) and strong SSS freshening (ΔSSSNA) in the North Atlantic–Arctic Ocean region (the Atlantic Ocean north of 35°N and the whole Arctic Ocean; see the solid box in Fig. 1a). The Indo-Pacific regional buoyancy forcing changes are dominated by strong freshening in the tropical western Pacific (ΔSSSIP) and substantial warming throughout the Indo-Pacific basins (ΔSSTIP), with comparable amplitude to the remote buoyancy forcing changes (Figs. 1a,b). We then conducted the Δremote and Δregional experiments to assess the relative contribution of NA remote and IP regional buoyancy forcing changes; Δremote is similar to Δbuoy but SSS and SST are restored to the SSSClim + ΔSSSNA and SSTClim + ΔSSTNA, respectively. The result, Δremote − CTRL, thus indicates the remote impacts of buoyancy forcings changes over the North Atlantic–Arctic Ocean. Likewise, in Δregional, only the SSS (ΔSSSIP) and SST (ΔSSTIP) changes in the Indo-Pacific sectors (20°E–60°W, 70°S–65°N) (the dashed box in Fig. 1a) are applied in the experiment, to assess the IP regional buoyancy forcing impacts.

Similarly, we assess the wind stress (faf-wind) and buoyancy forcing (faf-buoy) as well as the remote (faf-remote) and regional (faf-regional) buoyancy forcing impacts from FAFMIP (see details in appendix A). Directly comparing the results from FAFMIP and OGCM experiments provides insight into confirming the validity of the OGCM decomposition. In addition, we also conducted a reduced gravity experiment (NADW_RG) to explore the oceanic adjustments underlying the freshening and warming effects in the North Atlantic Ocean (appendix B).

c. Climate model simulations

Anthropogenic forcings, such as anthropogenic greenhouse gases and aerosols, could have complicated impacts on ITF transport. To evaluate the response of the ITF to increasing CO₂, we analyzed the preindustrial control run (piControl, with forcings that are representative of preindustrial conditions), and the abrupt quadrupling CO₂ run (abrupt4xCO₂, with the CO₂ concentration, instantaneously quadrupled) from the latest Coupled Model Intercomparison Project (CMIP6)_. We compute the projected surface forcings from 30 models (Table S1 of Peng et al. 2022) of CMIP6. We then select 27 of the 30 models (excluding the three models due to data accessibility: E3SM-1-0, GFDL-CM4, and INM-CM4-8) to further study the ITF response to increasing CO₂. We compute the differences between abrupt4xCO₂ (year 101–140) and piControl (year 101–140) to assess the transient ocean and atmospheric response (denoted by Δ) to increased CO₂. Note that we also tested different averaging periods; the results in this study are not sensitive to the slight change in the averaging period. The first member (r1i1p1f1) of each model is analyzed.

We also analyze the outputs from the 30-member Community Earth System Model Large Ensemble (CESM-LENS) to isolate the external and internal variability of ITF and investigate the relationship between ITF and AMOC changes. Each member differs by small random perturbations to their initial air temperature field and is performed with historical greenhouse gas and aerosol forcing during 1920–2005, and with representative concentration pathway 8.5 (RCP8.5) emissions scenario thereafter (2006–2100). In contrast to the abrupt4xCO₂ with the impacts of anthropogenic greenhouse gases, the CESM-LENS contains the effects of historical greenhouse gases and aerosols, which could have distinct impacts on ITF transport. Analyzing the CESM-LENS thus also provides insight into interpreting the key reasons for the observed ITF trend.

It takes thousands of years for the ocean to approach a new equilibrium state after the greenhouse gas (GHG) perturbation. To estimate the different ITF responses to anthropogenic forcings between the transient and equilibrium state of global warming, we analyzed the outputs from a 5900-yr CESM 1.0.4 abrupt4xCO2 experiment, which is a part of the LongRunMIP (Rugenstein et al. 2019). In this experiment, the AMOC strength used is directly obtained from the model outputs, whereas the ITF transport is diagnosed from the geostrophic currents across 113°E in the ITF outflow region based on the temperature and salinity data.

a. ITF slowdown

We first examine the ITF transport response to an abrupt quadrupling of CO₂ in 27 CMIP6 climate models. To quantify changes in the ITF transport, we calculate the zonal volume transport across a section (113°E, 23°–8°S) of the ITF outflow (Fig. 2a) between Java and Australia over the whole depth similar to Liu et al. (2015). In the CMIP6 piControl run, the climatological ITF transport is 12.85 ± 2.70 Sv (1 Sv ≡ 10⁶ m³ s⁻¹), in agreement with observations (15 Sv; Sprintall et al. 2009). Figures 2c and 2d show that all the 27 models and their ensemble mean project a decreased ITF transport, albeit with sizable intermodel differences, consistent with previous studies (Sen Gupta et al. 2016; Feng et al. 2017; Sun and Thompson 2020). The full-depth vertically integrated ITF transport decreases by 6.25 ± 2.48 Sv (∼47% ± 15%). The projected slowdown of ITF is confined to the upper 1500 m with a vertical structure that peaks between 100 and 200 m and decreases both above and beneath, in contrast to the climatological vertical profile of ITF (Fig. 2b). For this reason, we focus on the 0–1500 m vertically averaged changes in dynamic height [ΔDH; see Eq. (4)] and transport in this study. Figure 2c shows that ΔDH is markedly larger in the tropical Indian Ocean north of 10°S than that south of 15°S and in the tropical northwestern Pacific Ocean (TWPAC), corresponding to a weakened South Equatorial Current (SEC) and ITF transport. Similar to Tillinger and Gordon (2009), we compute the ΔDH difference between the ITF inflow (130°–150°E, 5°S–10°N) and outflow (90°–125°E, 15°–5°S) regions to assess the interbasin pressure gradient force (Qin et al. 2016). Figure 2c shows that there is a large interbasin pressure gradient anomaly between the tropical Indian Ocean (TIO) and TWPAC, leading to a reduction in ITF transport.

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Simulated ITF responses to anthropogenic warming. CMIP6 piControl climatological (a) 0–1500-m vertically averaged dynamic height relative to 2000 dbar [DH, color shading, dyn-m; see Eq. (4)] and currents (vectors; m s⁻¹), and (b) the vertical profile of volume transport per unit depth (10⁴ m² s⁻¹) across 113°E. Hereafter we define the westward (eastward) transport as a positive (negative) value, indicating a strengthening (weakening) of the ITF transport. (c),(d) As in (a) and (b), but for the CMIP6 projected DH, current, and vertical profile changes. (e),(f),(g),(h) As in (c) and (d), but for the outputs of Δall and faf-all, respectively. Thick curves in (b), (d), and (h) indicate regions exceeding 95% statistical significance.

Citation: Journal of Climate 36, 5; 10.1175/JCLI-D-22-0331.1

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We then compare the OGCM simulation of Δall (Δall − CTRL) with CMIP6 results to confirm the validity of the OGCM experiments. The simulated climatological ITF transport in the CTRL is 13.5 Sv, which is similar to the CMIP6 piControl run (12.85 ± 2.70 Sv). The Δall successfully captures the main characteristics of the CMIP6 projected ITF transport changes (Figs. 2c–f). For instance, the ITF transport in the Δall − CTRL decreases by ∼7.18 Sv (53%), which is similar to the CMIP6 results. The simulated ITF structure and dynamic height (DH) changes in Δall closely resemble those obtained from CMIP6 horizontally and vertically. Specifically, the OGCM successfully simulates the spatial pattern of DH changes, characterized by a large DH increase north of 10°S in the Indian Ocean, but a smaller increase in the TWPAC and along the western coast of Australia. This meridional DH gradient thus drives an anomalous eastward geostrophic flow in the South Equatorial Current region (Figs. 2c,e). The vertical structure of ITF volume transport change is also well reproduced in the Δall experiment, with the largest eastward volume transport change at ∼150 m (Fig. 2f). In addition, the faf-all (see appendix A) also successfully captures the horizontal and vertical structure of the ITF transport and DH changes but with a smaller amplitude (Figs. 2g,h), due to a smaller radiative forcing (∼2xCO₂) in FAFMIP. Overall, both OGCM (Δall) and FAFMIP (faf-all) could successfully simulate the CMIP6 projected ITF changes in a warming climate and is thus suitable for the present study.

b. Effects of ΔBuoy and ΔWind

We force the OGCM with the projected CMIP6 ensemble mean changes in buoyancy forcing (Δbuoy) by using restoring surface conditions (see details in section 2b), and wind stress (Δwind) (Fig. 1) to assess the relative importance of each forcing on the ITF transport (Table 1). Our results show that the buoyancy forcing dominates the vertically integrated ITF change in a warmer climate, accounting for a 5.08 Sv decrease (∼71% of the total variation) (Fig. 3a). The FAFMIP (faf-buoy) experiments further confirm that buoyancy forcing is the main driver for the ITF transports, contributing ∼77% of the ITF slowdown (Fig. 3b). Dynamically, the large ITF changes in Δbuoy and faf-buoy are attributed to the ΔDH (or pressure gradient) difference between TIO and TWPAC (Figs. 3c–f): The 0–1500-m averaged DH rise induced by buoyancy forcing changes in the Indian Ocean is larger than that in the Pacific Ocean (Figs. 3e,f), generating a pressure gradient that reduces the ITF transport.

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ITF response to different surface forcing changes, showing (left) OGCM simulated and (right) FAFMIP results. (a),(b) The relative importance of individual surface forcing in regulating vertical-integrated ITF transport (Sv) under global warming. Here the positive (negative) value indicates a strengthening (weakening) of the ITF transport. (c),(d) The differences in the 0–1500 m vertically averaged DH changes [dynamic meters (dyn-m)] between tropical western Pacific Ocean (130°–150°E, 5°S–10°N) and tropical southeastern Indian Ocean (90°–125°E, 15°–5°S) in each experiment. (e),(f) 0–1500-m vertically averaged DH (color shading; dyn-m) and currents (vectors; m s⁻¹) changes in Δbuoy. Also plotted in (a) are concurrent ITF transport changes computed by the MME wind stress of piControl and abrupt4xCO₂ based on the traditional Island Rule.

Citation: Journal of Climate 36, 5; 10.1175/JCLI-D-22-0331.1

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Wind stress is important in the intraseasonal to decadal variations in ITF transport (e.g., England and Huang 2005; Lee et al. 2015; Sprintall and Révelard 2014). In a warmer climate, the projected wind stress changes are mainly characterized by a weakening of the trade winds in the tropical Pacific Ocean (Fig. 1c) (Vecchi et al. 2006; DiNezio et al. 2009), which should act to reduce the interbasin pressure gradient and ITF transport. To verify this hypothesis, we have used the traditional Island Rule [Eq. (1)] and projected wind stress change from each CMIP6 model to diagnose the wind-driven ITF change. Figure 3a shows that the diagnosed ITF transport change based on the traditional Island Rule is −1.76 ± 0.99 Sv, in good agreement with the Δwind experiment [−1.57 Sv (∼22%)]. The faf-wind further confirms that the projected wind changes contribute to the reduced ITF transport (Fig. 3b). Nevertheless, the impact of the projected wind changes is much smaller than that of the buoyancy forcing (Figs. 3a,b). Taken together, these results show that the projected ITF slowdown under global warming is primarily caused by the buoyancy forcing changes. Sen Gupta et al. (2016) and Feng et al. (2017) also show that the projected wind stress change is too small to account for the projected slowdown of ITF in a warmer climate, a result that our OGCM experiments support.

c. Remote and regional buoyancy forcings

As the wind stress effect is much smaller than buoyancy forcing (Figs. 3a,b), here we focus on the detailed ITF adjustments due to buoyancy forcing changes. We further conduct two additional experiments (Table 1) to evaluate the relative importance of NA remote (solid black box in Fig. 1a; Δremote) and IP regional (dashed box in Fig. 1a; Δregional) buoyancy forcing changes. For comparison, we also evaluate the relative importance of remote (faf-remote) and regional (faf-regional) buoyancy forcing in FAFMIP (see appendix A).

Both the OGCM and FAFMIP experiments consistently show that the remote buoyancy forcing over the North Atlantic dominates the ITF slowdown (Fig. 4a). Specifically, strong freshening and warming in the North Atlantic–Arctic Ocean reduce the formation of North Atlantic Deep Water (NADW) and slows down the AMOC (Sévellec et al. 2017) (Fig. 5). The reduced NADW formation causes regional DH to rise in the North Atlantic Ocean (Fig. 6a). The positive DH signals propagate southward along the western coast of the North Atlantic Ocean, and then eastward along the equatorial waveguide. Upon arriving at the east coast, the signals split and the south branch propagates along the coast of southern Africa and then eastward along the equator to cross the Indian Ocean (Fig. 6). After arriving at the eastern boundary of the Indian Ocean, the signals split again and propagate along the eastern coast of the Indian Ocean; parts of the DH perturbations radiate westward as Rossby waves and raise DH in the interior Indian Ocean north of 10°S. The southern branch of coastal Kelvin waves further spilt into two branches: One penetrates into the narrow passage of ITF and enters the Pacific Ocean; the other continues to propagate southward around Australia and radiates westward Rossby waves south of 15°S. Due to the dispersion and damping of wave energy, the DH signals arriving at TWPAC are much weaker than that along the west coast of Java. The resulting interbasin pressure gradient (Figs. 4b and 6) weakens the ITF transport. The broad agreement in DH pattern and current changes between OGCM and FAFMIP (Figs. 4b,c) indicates a robust result that the weakened AMOC slows down the ITF in a warmer climate.

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Remote and regional forcing impacts on ITF transport. (a) Contributions of NA remote and IP regional buoyancy forcing changes computed from OGCM and FAFMIP. (b) 0–1500 m vertically averaged DH (dyn-m; color shading) and current (m s⁻¹; vectors) changes in Δremote experiment. (c),(d) As in (b), but for the results from faf-remote and reduced gravity model experiments, respectively.

Citation: Journal of Climate 36, 5; 10.1175/JCLI-D-22-0331.1

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AMOC changes in Δremote and faf-remote. AMOC changes due to buoyancy forcing changes over the North Atlantic–Arctic Ocean in (a) OGCM (Δremote), and (b) FAFMIP (faf-remote).

Citation: Journal of Climate 36, 5; 10.1175/JCLI-D-22-0331.1

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Evolution of ΔDH due to NA buoyancy forcing perturbations. Evolution of 0–1500 m vertically averaged DH changes (color shading; dyn-m) in Δremote at the model year (a) 5, (b) 20, (c) 40, and (d) 100, respectively. (e) Time series of the yearly interbasin ΔDH difference between tropical northwestern Pacific Ocean (TWPAC) and tropical Indian Ocean (TIO) (blue line; dyn-m) as well as the resultant ITF transport changes (red solid line; Sv) in Δremote.

Citation: Journal of Climate 36, 5; 10.1175/JCLI-D-22-0331.1

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We further utilize the RG model to verify this interbasin dynamical process (see appendix B). Specifically, we reduce the NADW formation rate (w_NADW) from −8.0 × 10⁻⁷ m s⁻¹ in the control run (CTRL_RG) to −2.0 × 10⁻⁷ m s⁻¹ in the sensitive experiment (NADW_RG) to simulate the freshening and warming effects in the North Atlantic Ocean. Our results show that the reduction of the NADW formation raises the upper-layer DH in the North Atlantic Ocean. As in the OGCM, the DH signals in NADW_RG propagate into the Indian and Pacific Ocean along the interbasin waveguides (not shown). Due to the bifurcation of wave energy, there is an Indo-Pacific interbasin pressure gradient force, which ultimately reduces the ITF transport (Fig. 4d). The good agreement between the RG model and OGCM indicates that the interbasin wave propagation (Cessi et al. 2004; Huang et al. 2000), rather than regional diffusion and mixing process, dominates the vertically integrated ITF transport under global warming.

The Indo-Pacific regional buoyancy forcing is also important in modulating ITF under global warming, with large impacts on the vertical structure of ITF changes. Figure 7a shows that the ITF transport change due to regional buoyancy forcing changes is of a high baroclinic-mode structure, with anomalous eastward transports between 150 and 500 m but westward transports above and beneath. The amplitude of the ITF transport induced by regional forcing is comparable to that forced by the remote forcing, but the ITF transport changes at different depths are largely compensated, resulting in little change in vertically integrated ITF transport (Fig. 4a).

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Vertical structure of Indian Ocean response to NA remote and IP regional buoyancy forcings. OGCM simulated vertical profile of anomalous eastward volume transports per unit depth (10⁴ m² s⁻¹) across 113°E due to regional and remote buoyancy forcing as well as wind stress changes. (b) The ITF vertical partitioning index for Δremote, Δregional, and Δwind, respectively. Indian Ocean zonal mean (c),(d) ocean temperature (°C), (e),(f) density (color shading; kg m⁻³) and salinity (black line contours at interval of 0.5 psu; zero contour thickened; positive contours in black and negative contours in gray), and (g),(h) DH (dyn-m) changes due to (left) remote and (right) regional buoyancy forcing changes. Also plotted in (c) and (d) are zonal mean climatological ocean temperature (black line contours at intervals of 5°C, and the 10°C contour thickened). All zonally averaged in 100°–120°E.

Citation: Journal of Climate 36, 5; 10.1175/JCLI-D-22-0331.1

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d. Distinct vertical structures of ITF

Figure 7 compares the vertical structure of ITF response to the NA remote and IP regional buoyancy forcing changes. In the North Atlantic–Arctic Ocean, the mean vertical stratification is weak, and the surface buoyancy changes in a warming climate induce positive DH/pressure perturbations over a deep layer there. These positive DH signals propagate away along the coastal and equatorial waveguide. Upon reaching the tropical Indo-Pacific Ocean, these wave signals of deep vertical structure raise the temperature (and reduce the density) from below the surface mixed layer to 2000 m in the lower thermocline (as represented by the 10°C isotherm, Wang et al. 2015) (Figs. 7c,e), reducing the ITF transport over a deep layer: the ITF transport per unit depth monotonically changes from −7 × 10³ m² s⁻¹ at the surface to zero at ∼1300 m (Fig. 7a). To analyze the vertical structure of the ITF changes, we performed a baroclinic modal decomposition of the current profile (Brandt et al. 2016). Figure 8 (left panels) shows that the remote buoyancy forcing-induced ITF velocity profile is dominated by the first baroclinic mode, explaining why an idealized 1.5-layer reduced gravity model in Sun and Thompson (2020) could capture the ITF response to a weakened AMOC. The remote buoyancy forcings excite both high and low baroclinic mode signals but the high-baroclinic modes are largely damped along the waveguide due to the slow phase propagation. Consequently, the ITF velocity profile is dominated by the low (first) baroclinic mode signals in Δremote (Fig. 8, left panels).

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Vertical structure decomposition of ΔU across 113°E from OGCM experiments, (left) Δremote, (center) Δregional, and (right) Δwind, showing (a)–(c) contributions from barotropic and each vertical baroclinic mode on the zonal current changes (ΔU) and (d)–(f) the coefficient (10⁻⁴) for each baroclinic mode. The coefficient here could be used as an indication of the relative contribution of each baroclinic mode.

Citation: Journal of Climate 36, 5; 10.1175/JCLI-D-22-0331.1

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The impact of the IP regional surface buoyancy forcing, by contrast, is confined above the 10°C isotherm owing to the strong vertical stratification in the mean state (Figs. 7d,f,h). Unlike the remote buoyancy forcing with strong damping on the high-baroclinic mode signals, the temperature and salinity changes confined in the upper ocean affect the ITF velocity profile mainly through the third and fourth baroclinic modes (Fig. 8e), leading to a high-baroclinic mode profile in the ITF outflow region (Fig. 8b). Such high-order baroclinic ITF response to IP regional buoyancy forcing changes cannot be represented in a simple 1.5-layer model and has not been previously documented.

Large-scale wind stress anomalies are important for the upper-layer ITF transports at interannual-decadal time scales, particularly in the upper thermocline (50–200 m) (Tillinger and Gordon 2009). Indeed, the results of Δwind show that wind stress changes have strong impacts on the ITF at the depth of ∼150 m in the upper thermocline through both low (first) and high (fourth) baroclinic modes (Fig. 8, right panels). These wind-driven ITF changes are largely governed by the traditional Island Rule and wave dynamics.

In light of the distinct vertical structure of ITF responses to different surface forcings, here we define an ITF vertical partitioning index (VPI) as the ratio of vertically integrated volume transport (V) in the deep layer (350–1500 m) to transport in the upper layer (0–350 m): $\text{VPI}=(V_{350\text{–}1500}/V_{0\text{–}350})$. For the NA remote forcing (Δremote), the ITF response is of a deep profile (Fig. 7a) with VPI ∼1 (Fig. 7b). For the IP regional buoyancy forcing (Δregional), the ITF vertical profile is highly baroclinic in the upper and deep layers with negative VPI (Fig. 7b). Nevertheless, for the wind stress case, the ITF transport in the deep layer is negligible and the VPI should equal ∼0 (Fig. 7b). These results imply that the VPI can be used to assess the remote thermohaline forcing effect on ITF: a large positive index indicates a larger contribution of the remote buoyancy forcing over the North Atlantic. Sustained observations that reach 1500 m or deeper across the transect of ITF outflow can help monitor the ITF change and the Atlantic forcing contribution in a warming climate.

e. Island Rule generalized for AMOC change

We analyze the CESM1 Large Ensemble (CESM-LENS) results to investigate the relationship between AMOC and ITF changes. Figure 9 shows that the AMOC-induced ITF changes are proportional to the AMOC perturbations. The ΔT_remote could also be expressed as

$\mathrm{\Delta }{T}_{\text{remote}}=0.37\hspace{0.17em}\mathrm{\Delta }\text{AMOC},$(7)

where ΔAMOC is the AMOC strength changes due to global warming at 26.5°N. The generalized Island Rule including the effect of a changing AMOC is

$\mathrm{\Delta }T=\frac{1}{f_N-f_S}{\displaystyle \oint {}_{\text{ABCDEF}}}\frac{\mathrm{\Delta }{\tau }_l}{{\rho }_0}dl\hspace{0.17em}+0.37\mathrm{\Delta }\text{AMOC}.$(8)

In a steady state, the impacts of AMOC are negligible (ΔAMOC = 0), and the ITF change is then largely determined by Godfreys’s Island Rule. When the AMOC exhibits significant changes (Fig. 9), the second term on the right-hand side of Eq. (8) is important and should be considered in estimating the total ITF changes. Note that the AMOC-induced ITF changes are only nonnegligible during the transient stage of global warming, which is verified by a 5900-yr abrupt4xCO₂ experiment from the CESM 1.0.4 (Table 2). Figure 10 shows that the AMOC and resultant ITF transports decrease rapidly in response to the increasing CO₂ in the first 100 years due to the hosing effects (Kleinen et al. 2009), characterized by an AMOC collapse at year ∼80. Importantly, when the warming simulations continue for a substantial time (>2000 yr), the AMOC and ITF gradually recover to its original preindustrial values due to the warming of subsurface waters at low and middle latitudes (Stouffer and Manabe 1999) and the increased northward salinity advection (Krasting et al. 2018; Wen et al. 2018). These results imply that the ITF transport in the equilibrium stage of global warming (after the model year 2000) is close to the steady-state value without CO₂ perturbations, which could again be approximated by Godfrey’s traditional Island Rule [the first term on the right-hand side of Eq. (8)]. However, during the transient stage of global warming (from the model year 1 to 2000), the total ITF transport changes are dominated by AMOC changes (Fig. 10), which are not included in the traditional Island Rule.

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Yearly AMOC and ITF changes (Sv) from CESM-LENS. The AMOC and ITF strengths are calculated from the velocities of CESM-LENS. Each member is integrated forward under historical (1920 to 2006) and future (RCP8.5 for 2006–80) emissions scenarios with different initial conditions for air temperature. The CESM-LENS ensemble mean is shown as the thick black curve (dots) and a randomly selected individual run is shown as the thin red curve. The AMOC and ITF changes are obtained by subtracting the 1920–2000 mean values. Here we define the westward (eastward) transport as a positive (negative) value, indicating a strengthening (weakening) of the ITF transport.

Citation: Journal of Climate 36, 5; 10.1175/JCLI-D-22-0331.1

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AMOC and ITF changes (Sv) from a 5900-yr CESM 1.0.4 abrupt4xCO₂ experiment. The ITF transport in this run is computed from the diagnostic geostrophic currents across 113°E in the ITF outflow region. The AMOC and ITF transport are averaged every 10 years, and the first 10-yr value are subtracted to compute the changes.

Citation: Journal of Climate 36, 5; 10.1175/JCLI-D-22-0331.1

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Table 2

List of climate models and numerical experiments used in this study.

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