1. Introduction
Large-scale ocean circulations carry and redistribute heat, freshwater, nutrients, and other important tracers throughout the coupled climate system. Being able to quantify their mean state and associated variability along with the ability to accurately simulate these systems in fully coupled climate models are key pieces to understanding present climate and making meaningful future projections. Prior to the deployment of the Rapid Climate Change (RAPID) mooring array (McCarthy et al. 2015) at 26.5°N in the subtropical North Atlantic, knowledge regarding the observed mean state and variability of large-scale ocean circulation in the North Atlantic was limited to decadal “snapshots” derived from repeat hydrographic sections obtained decades apart (Talley 2003; Bryden et al. 2005).
Since 2004, the RAPID array has provided a continuous full-basin estimate of important transports in the subtropical North Atlantic Ocean at 26.5°N at twice-daily resolution (McCarthy et al. 2015). This observing system consists of a series of dynamic height moorings, current meters, submarine cables, and bottom pressure sensors concentrated on the eastern and western boundaries of the Atlantic basin and along the Mid-Atlantic Ridge. The Atlantic meridional overturning circulation (AMOC) is calculated from these measurements as the sum of three observable transports at this latitude: the northward-flowing Florida Current confined to the Florida Strait, the net southward flow east of the Bahamas in the upper midocean, and the wind-driven surface Ekman transport. This array has both revolutionized the state of knowledge regarding the three-dimensional structure of meridional overturning in the North Atlantic and provided a crucial benchmark against which to evaluate ocean circulation in climate model simulations.
RAPID observations have clearly highlighted that the subtropical AMOC has a complex three-dimensional structure beyond the single integrated value traditionally studied, the maximum of the meridional overturning transport streamfunction in latitude–depth space. Although useful for analyzing changes in mean meridional overturning in the Atlantic, the overturning transport streamfunction diagnostic is a simplification of the complex, three-dimensional structure of the upper and lower limb of the AMOC. A two-dimensional diagnostic greatly limits the ability to directly compare climate model simulations to observational estimates. Evaluating the same components of the AMOC in coupled models that are observationally estimated by RAPID at 26.5°N, rather than a single zonally integrated value, allows for a more detailed comparison between models and observations. Such a comparison of observational data to fully coupled climate models is crucial for improving confidence in model-derived future projections by highlighting what models do and do not accurately simulate relative to the real world.
Since RAPID’s deployment, efforts have been made to compare model-simulated transports in the subtropical North Atlantic Ocean against those estimated by RAPID. However, these studies have generally used ocean-only numerical simulations rather than the fully coupled climate models used for climate projections (Baehr et al. 2009; Haines et al. 2012; Hui-Er and Yong-Qiang 2012; Xu et al. 2012; Haines et al. 2013; Mielke et al. 2013; Zhao and Johns 2014a,b; Blaker et al. 2015; Stepanov et al. 2016). Evaluation of simulated transports in the subtropical North Atlantic in fully coupled models has been limited to single-model studies (Thomas et al. 2012). No studies thus far have used RAPID observations as a benchmark to assess how well the IPCC-class models that are used for climate projections simulate the individual transport components of subtropical ocean circulation.
It has been extensively studied how the AMOC, as a single zonally integrated value, is projected to change under increased atmospheric CO2 concentrations in coupled climate models (Weaver et al. 2012; Cheng et al. 2013; Collins et al. 2013). A reduction in strength of ~40% is projected by the end of the twenty-first century under the representative concentration pathway 8.5 (RCP8.5) forcing scenario (Weaver et al. 2012). However, analyzing projected changes in the individual transports that are generally suppressed in the integration process, rather than only considering changes in a single zonally integrated value, may provide a more detailed understanding of the mechanisms governing twenty-first-century AMOC weakening in climate models.
The need for analyzing AMOC component transports and their changes in coupled climate models is evidenced by the role that atmospheric winds play in driving the interior ocean transport at the latitude of RAPID (Thomas et al. 2012; Roberts et al. 2013). Using both a forced ocean-only and a coupled ocean–atmosphere simulation, Duchez et al. (2014) provided evidence that the southward transport in the interior ocean calculated by RAPID at 26.5°N is largely wind-driven and can be approximated by Sverdrup balance at time scales longer than a year. Thomas et al. (2012) also showed a direct relationship between the interior transport at 27°N in the Atlantic and the local wind stress curl (WSC) in the eddy-permitting coupled High-Resolution Global Environmental Model (HiGEM). Furthermore, under a 100-yr climate change scenario of a 2% yr−1 increase in atmospheric CO2 concentrations, Thomas et al. (2012) found a weakening of the upper-ocean interior transport associated with the southward recirculation of the subtropical gyre at 27°N in the Atlantic attributed to a reduction in the local WSC. However, it remains to be seen whether or not this reduction in WSC over the subtropical gyre and the resulting weakened gyre recirculation is a robust feature among CMIP5 models under increased CO2 concentrations.
Observations from RAPID since the start of its deployment have shown a strengthening of the southward transport in the upper interior ocean circulation at 26.5°N, associated with the observed AMOC decline (Smeed et al. 2014; Frajka-Williams 2015; Frajka-Williams et al. 2016) and continued weakened state (Smeed et al. 2018). Wunsch and Heimbach (2013) highlight the fact that stronger upper-ocean interior flows, that is, a spinup of the wind-driven subtropical gyre, can produce a weakened AMOC. Thus, changes in the local surface momentum forcing from the overlying wind stress could play an important role in AMOC variability if the upper interior ocean circulation is driven largely through Sverdrup dynamics. Forced changes in wind stress under increased CO2 may be important in governing the evolution of the AMOC at 26.5°N if the interior transports are altered.
In this paper, we consider the complex three-dimensional structure of the subtropical North Atlantic Ocean circulation at 26.5°N as simulated in a suite of CMIP5 models, decomposing the modeled circulation into four major components similar to those RAPID observes to estimate the AMOC. For the first time, an assessment is provided of how the AMOC and each of its major transport components at 26.5°N are simulated in a suite of IPCC-class climate models at the start of the twenty-first century relative to the transports estimated by RAPID over the first decade of its deployment. We also provide estimates of how the individual transport components of the subtropical AMOC are projected to evolve throughout the twenty-first century under the RCP8.5 scenario, providing a more detailed evaluation of how the three-dimensional structure of the subtropical ocean circulation at 26.5°N is expected to change.
In the second half of the paper, we apply the classical theory of Sverdrup balance that relates surface momentum forcing to the interior ocean flow to test the hypothesis that projected changes in the local wind stress over the subtropical gyre explain the projected changes of the interior ocean transports in the upper ocean. We provide evidence that the weakened state of subtropical ocean circulation found by Thomas et al. (2012) is a robust feature across CMIP5 models under increased CO2 forcing. This study is the first multimodel study to provide estimates of the changes projected for each of the major transports associated with the subtropical AMOC at 26.5°N over the course of the twenty-first century and the first to address the hypothesis stated above in a multimodel framework.
2. Methods
a. RAPID data
The publicly available RAPID data (http://www.rapid.ac.uk) are provided as 12-hourly, 10-day low-pass-filtered time series from April 2004 to October 2015. Details on the processing of the public data can be found in Kanzow et al. (2007) and McCarthy et al. (2015). We only use the data that span a complete year, resulting in a 10-yr time series spanning 1 January 2005–31 December 2014. The 12-hourly data are averaged into monthly data and then into an annual mean for each year, filtering out submonthly, high-frequency variations. The data are averaged in this manner to be consistent with the monthly output provided in the CMIP5 archive. All calculations are performed on the annually averaged data.
b. Model data and experiments
The CMIP5 models used in this study are chosen based on the availability of monthly meridional mass transport, zonal and meridional wind stress, and ocean meridional overturning mass streamfunction data in the CMIP5 database (https://esgf-node.llnl.gov). Only models that provide the complete set of variables needed for the analysis presented here are chosen, resulting in 13 models analyzed under the preindustrial-control (piControl) simulation and 14 analyzed under RCP8.5 (11 models have both experiments). The RCP8.5 future experiment is chosen since it is expected to produce the largest signal in response to increased radiative forcing. Table 1 lists the models and contains additional details regarding the experiments. Annual-mean values calculated from the monthly data provided in the CMIP5 archive are used in the transport calculations.
CMIP5 models and experiments used in this study. The table includes the ocean component and its version, ocean horizontal resolution (lon × lat); vertical coordinate with the number of layers/levels, country of the modeling center, and experiments used in this study. The vertical coordinates are defined as follows: z is the traditional depth coordinates; σ2 is the isopycnal vertical coordinates; and z* is the rescaled geopotential vertical coordinate for better representation of free-surface variations (Adcroft and Campin 2004). The RCP8.5 experiments are a continuation of each model’s historical simulation forced by the RCP8.5 scenario over the period 2006–2100, resulting in a radiative forcing of +8.5 W m−2 by year 2100 (Moss et al. 2010). Radiative forcing is held at constant preindustrial levels in the piControl experiments. A 100-yr period in the piControl integration is analyzed that corresponds to years 2001–2100, overlapping in time with each model’s RCP8.5 integration period. Only the first ensemble member for the piControl and RCP8.5 integrations is considered.
All transports are calculated on each model’s native grid; no regridding is performed prior to analysis. The majority of models in this study are not on a regular latitude–longitude grid. However, at low latitudes (including 26.5°N), the grids either become regular or the grid distortion is minimal; therefore, we do not expect integrations across model grid lines in the absence of regridding to greatly impact the results. These same assumptions were made by Danabasoglu et al. (2014) in calculations of zonal averages and transports in many of the same ocean models used here.
c. RAPID and model transport calculations
A brief description of the calculation of each component as measured by RAPID is described here. Readers are referred to McCarthy et al. (2015) for more details. The calculation of the respective model transport applied in this study follows each description. Readers are referred to Figs. 1 and 2a, which show where these components are found in the subtropical North Atlantic.
In situ chlorofluorocarbon-11 (CFC-11) concentrations (pmol kg−1) obtained by repeat hydrographic measurements with data made freely available from the GLODAPv2 at 24°N in the Atlantic (Key et al. 2015; Lauvset et al. 2016; Olsen et al. 2016). Transport components considered in this study as the major components of the North Atlantic subtropical AMOC are labeled where they are located in the real ocean: northward FC through the Florida Strait; southward-flowing subtropical gyre recirculation in the UMO; northward-flowing AC to the east of the Bahamas (included in the observed UMO); net southward deep transport consisting of the UNADW and LNADW; and northward surface Ekman transport assumed to be evenly distributed over the top 100 m (above the thin horizontal dashed line near the surface). Thick horizontal dashed line represents the separation between the upper and lower limb of the AMOC, which RAPID estimates as ~1100 m.
Citation: Journal of Climate 31, 23; 10.1175/JCLI-D-17-0845.1
(a) Observed structure at 24°N from CFC-11 data, as in Fig. 1, but only for the boundary region to show differences between models and observations of the location of the various transport components. (b)–(j) Volume transport (Sv) at 26.5°N in the Atlantic basin averaged over a 100-yr segment of the piControl simulation for each model as labeled in the individual panels. Red values (solid contours) indicate northward transport and blue values (dashed contours) indicate southward transport. The region calculated as the WBC’s total northward transport is the red region adjacent to the Florida coast in the upper-left corner of each panel; an example of this region is shown in (b) and (c) for two different models. The northward transport is summed from Florida to the thick zero contour line bounding the region between net northward and net southward transport and from the surface to the lower boundary of the same zero contour line. A region of inertial recirculation of the WBC can be seen as the enhanced southward flow directly adjacent to the WBC. This region is included in each model’s UMO transport. Contours are drawn at intervals of 0.15 Sv.
Citation: Journal of Climate 31, 23; 10.1175/JCLI-D-17-0845.1
1) AMOC
2) Florida Current
In the observed ocean at 26.5°N, a weaker northward western boundary current, the Antilles Current (AC), exists to the east of the Bahamas separated from the FC (Figs. 1 and 2). However, the CMIP5 models used here do not have a Florida Strait because of the coarse resolution of their ocean models, making estimation of the volume transport associated with the FC nontrivial (Fig. 2). The CMIP5 models do not resolve a separation between the FC and AC at this latitude and instead have a single western boundary current that contains the entire northward transport of the North Atlantic subtropical gyre (Fig. 2). Hereafter, we refer to the total northward flow along the coast of Florida in the models as the western boundary current (WBC; Fig. 2).
Each model’s WBC is calculated by summing the northward volume transport in each grid cell from the coast of Florida to the first grid point outside the western boundary region and from the surface to the depth of minimum northward transport (boxed region in Fig. 2). This fixed spatial area is determined individually for each model from the time average of years 2006–25 of the RCP8.5 simulation and over the full 100-yr segment of the piControl simulation. This estimate of the total WBC has been employed in a previous study using a model with an unresolved Florida Strait (Baehr et al. 2009).
3) Ekman transport
4) upper midocean transport
5) Deep transport
3. Results
a. Transports in models compared to observations
We evaluate whether the mean AMOC and its component transports simulated over the first 10 years (2006–15) of the RCP8.5 experiment fall within the range (maximum and minimum value of annual-mean data) of the mean transports that have been estimated by the RAPID array from 2005 to 2014. Given the limited time period of the RAPID observations, we do not attempt to assess the statistical significance of the individual model means and the interannual variability relative to that reported by RAPID. Instead, as a gross estimate, we consider the CMIP5 models to agree with RAPID estimates if the range defined by the modeled maximum and minimum annual-mean values of each transport falls within the range of the annual-mean values estimated over the 2005–14 period by RAPID (gray shading in Fig. 3). Over this time period in the RCP8.5 experiment, the radiative forcing changes are very similar among the various RCP scenarios (Moss et al. 2010), thus the results presented here are not expected to be grossly different from the 2006–15 period if the other RCP experiments were used.
Mean transports (Sv) of (a) the AMOC and (b)–(f) its components at 26.5°N for the first complete decade of the RAPID array observations (2005–14) and for 2006–2015 (solid blue) and 2091–2100 (solid red overlaid) decade of the RCP8.5 experiment for each model. The MMM for the first (blue dashed) and last (red dashed) decade of the RCP8.5 experiment is to the left of the first individual model. The error bars correspond to the maximum and minimum range of the annual-mean values of each transport reported by RAPID and simulated for each individual model in the corresponding decade. The gray shading corresponds to the range estimated by RAPID for each transport. The net southward (d) UMO and (f) deep transports are multiplied by −1 here; the mean values are negative (southward). Note the differing y axes in each panel chosen to best display each mean transport.
Citation: Journal of Climate 31, 23; 10.1175/JCLI-D-17-0845.1
For the AMOC and its component transports, a considerable spread in the mean transports is found among the models over years 2006–15. However, the majority of the models simulate transports in the range of present-day estimates from RAPID (Fig. 3). For both the AMOC and the net deep transport, only one model (CNRM-CM5 for AMOC; HadGEM2-ES for deep) simulates transports outside of the RAPID range. For all models, a clear overlap with the RAPID estimated value is found for the Ekman transport (Fig. 3b).
For the comparison of the FC and UMO transports reported by RAPID to those simulated by the CMIP5 models, we remind the reader of the caveat of the lack of a resolved Florida Strait in the models at 26.5°N (Fig. 2). Thus, the modeled WBC contains both the northward-flowing FC and AC, while the FC reported by RAPID does not include the additional northward flow from the AC. Because of this issue, it is not correct to directly compare the RAPID FC to the models’ WBC. The same is true for a direct comparison between the RAPID UMO estimate and the CMIP5 UMO transport. The UMO from RAPID contains the northward-flowing AC in addition to the southward gyre return flow (Fig. 1). However, only the southward return flow of the horizontal gyre circulation is included in the UMO transport for the models.
Given the different transport components comprising the WBC and UMO transports in the real ocean and modeled ocean, it is not surprising that most models have a WBC and UMO transport above the range of the FC and UMO components estimated by RAPID (Figs. 3c,d). For a more appropriate comparison that is not impacted by the gyre partitioning issues mentioned above, we compare the sum of the WBC + UMO CMIP5 transports to the RAPID FC + UMO (Fig. 3e). The modeled WBC + UMO (or RAPID-estimated FC + UMO) transport is equivalent to the non-Ekman, or geostrophic, AMOC at 26.5°N. Only two models (CanESM2 and CNRM-CM5) simulate a WBC + UMO transport outside of the range of present-day estimates from RAPID (Fig. 3e). This provides convincing evidence that the majority of CMIP5 models, despite having their northward and southward gyre transports partitioned differently than the observed ocean, do realistically simulate the mean transports of the horizontal gyre components relative to what has been observed.
b. Projected twenty-first-century changes under RCP8.5
To assess the significance of the changes in the AMOC and its component transports by the end of the twenty-first century under RCP8.5, we must also consider the decadal-mean transport and the associated decadal variability of the AMOC and its individual transport components in piControl integrations. These values are summarized in Table 2, with a detailed discussion of the calculation of each multimodel-mean (MMM) decadal transport and its associated 2σ spread in the online supplementary material. These values are interpreted as a measure of the decadal-mean transport and its associated variability for each component in the absence of anthropogenic forcing. Prior to discussing twenty-first-century changes, we note here that the AMOC, Ekman, WBC + UMO, and net deep transport observationally estimated by RAPID (2005–14) all lie well within the range (2σ) of decadal-mean transports simulated in piControl integrations. Under the assumption that the decadal-mean transports found in piControl integrations are a good surrogate for the long-term unforced observed variability, the present-day AMOC and its associated transports (and considering WBC + UMO together) estimated by RAPID are within the range expected from natural climate variability.
The MMM decadal-mean transports of the AMOC and its associated transport components at 26.5°N in the Atlantic (Sv). The MMM decadal-mean transports in piControl integrations and their associated 2σ decadal variability (description of calculation in the online supplemental material) are displayed in the first column. Transports observationally estimated by the RAPID array over the 2005–14 period are displayed in the second column. The MMM transports calculated over the first (2006–15) and last (2091–2100) decade of the RCP8.5 experiment are shown in the last two columns. The values in boldface are outside of the 2σ range of the decadal-mean transports simulated in the piControl integrations (first column). Because of the different definitions of the WBC and UMO transports between models and observations (see methods section), the RAPID WBC and UMO transports are both outside the modeled 2σ ranges in the piControl integrations (values in boldface under the RAPID column).
Relative to the MMM piControl decadal transport for each component (Table 2), the MMM of all transport components (with the exception of the Ekman transport) over the 2006–15 period at the start of the RCP8.5 experiment show some degree of weakening. At the start of the RCP8.5 experiment (2006–15), the WBC and UMO transports have already weakened to a decadal mean that is slightly below the range (2σ) of their respective MMM piControl decadal transport (Table 2). By the last decade of the twenty-first century (2091–2100), the MMM of all components (except the Ekman transport) show a clear forced weakening response, with decadal-mean transports well outside the range (2σ) simulated in the piControl integrations (Table 2). Conversely, the MMM Ekman transport increases slightly in magnitude, however, the mean remains within the range (2σ) of the piControl MMM.
Considering the decadal-mean transports at the start (2006–15) and end (2091–2100) of the century for each individual model, a wide spread is found among models in the degree of weakening of each transport component under RCP8.5 (Fig. 3). Despite the varied magnitude of the response, the overall weakening trend of all components (except Ekman) is robust across models. The MMM transports of the AMOC, WBC + UMO, and net transport in the deep ocean at the end of the twenty-first century (2091–2100) have weakened to transports below the range of present-day transports observed by RAPID (Figs. 3a,e,f). On the other hand, for the Ekman transport, the projected changes by the end of the century differ from model to model with respect to the sign and magnitude of the change (Fig. 3b). Seven models show a strengthened Ekman transport relative to the first decade, while the other seven show a slightly weakened transport.
To quantify the projected changes over the twenty-first century under RCP8.5, we express the changes under RCP8.5 next in terms of a subtraction of a 20-yr mean at the start of the century (2006–25) from a 20-yr mean at the end of the century (2081–2100). The time series of each component (Fig. 4) over the twenty-first century shows a wide range in the interannual to decadal variability of the AMOC and its components among models, as well as a wide spread in the magnitude of the response of the various transports under RCP8.5. The MMM (thick black line) AMOC is projected to weaken by 4.6 Sv (1 Sv ≡ 106 m3 s−1; −29%; −10% to −46% across the models). The sum of the WBC + UMO transport, or the non-Ekman AMOC, is projected to weaken by 4.7 Sv (−39%; −11% to −62%), with the northward WBC projected to weaken by 7.6 Sv (−21%; −5% to −29%) and the southward return flow in the UMO projected to decrease by 2.9 Sv (−12%; −1% to −22%). Net transport in the deep ocean is projected to weaken by 4.4 Sv (−28%; −12% to −46%). Projections of the Ekman transport range from an increase of 25% to a weakening of 11%. (Table A1 in the appendix provides the projected changes of each component for each model.) For all models, with the exception of CanESM2 and ACCESS1.0, the weakening of the deep transport is greater than the weakening of southward circulation in the upper ocean.
Time series from 2006 to 2100 at 26.5°N of the (a) AMOC, (b) Ekman transport, (c) total transport in the northward WBC, (d) net southward UMO transport, (e) WBC + UMO, and (f) net transport in the deep ocean (Sv) as simulated in the CMIP5 models analyzed under the RCP8.5 scenario (thin gray lines) and the resulting MMM transport (thick black line). The annual transports for each component estimated from RAPID are shown as the thick red lines in each panel from 2005 to 2014. The MMM changes calculated as the average of the last 20 years of the RCP8.5 integration (2081–2100) minus the average of the first 20 years (2006–25) are shown in the corner of each panel. Changes for the Ekman transport are negligible. Note the differing y axes in the panels, chosen as the range to best display the specific transport component.
Citation: Journal of Climate 31, 23; 10.1175/JCLI-D-17-0845.1
c. Projected changes in wind stress over the subtropical gyre
A robust pattern of weakened midlatitude westerly wind stress over the northern sector of the subtropical gyre is found across the models by the end of the twenty-first century (Fig. 5). All models show a weakened pattern of surface westerly wind stress, with the exception of MRI-ESM1, which shows an increase in westerly wind stress in the northeast corner of the subtropical gyre. The overall spatial pattern and magnitude of the weakening of the westerly wind stress over the northern sector of the gyre differ from model to model. The changes in the mean easterly wind stress over the southern sector of the gyre differ widely from model to model, with some models showing a clear weakening signal (CanESM2, HadGEM2-ES, ACCESS1.0, MRI-CGCM3, and CNRM-CM5), other models showing slight increases (GFDL-ESM2M, GFDL CM3, and GISS-E2-R), and the rest showing little change. Another notable feature of Fig. 5 is a northward shift of the boundary of the subtropical gyre found in some models.
Projected change in zonal wind stress (N m−2) calculated as the difference between the time average of the last 20 years (2081–2100) minus the time average of the first 20 years (2006–25) of the RCP8.5 simulation for all models considered. (a) The MMM. The zero WSC contours, representing the boundaries of the subtropical gyre, and the zero wind stress line, representing the location where the mean surface wind stress shifts from surface easterlies (south of line) to surface westerlies (north of line) for the first 20 years (dashed lines) and the last 20 years (solid lines) are displayed in each panel. In the region of surface westerly wind stress (northern portion of gyre) a negative (blue) difference indicates a reduction in zonal wind stress and a positive (red) difference indicates an increase in zonal wind stress. In the region of surface easterly wind stress (southern portion of gyre), a negative (blue) difference indicates an increase in zonal wind stress and a positive (red) difference indicates a reduction in zonal wind stress. The latitude of RAPID (26.5°N) is shown as the thick magenta dashed line.
Citation: Journal of Climate 31, 23; 10.1175/JCLI-D-17-0845.1
These changes in the surface zonal wind stress projected by the end of the century alter the local WSC. The subtropical gyre is a region of negative WSC, resulting in Ekman pumping and thus a southward circulation of waters in the upper-ocean interior following vorticity conservation (Gill 1982). A projected reduction in the WSC magnitude is found in the ocean interior over the region containing 26.5°N by the end of the twenty-first century for all models except MRI-ESM1 (Fig. 6). The projected change in the WSC magnitude over this region ranges from −33% (CanESM2) to +0.73% (MRI-ESM1). Many of the models show a reduction in WSC that is concentrated along the boundaries of the subtropical gyre in the region containing 26.5°N [GFDL-ESM2G, CCSM4, CESM1(BGC), CESM1(CAM5), GISS-E2-R, and MRI-CGCM3]. Other models show a more pronounced weakened WSC penetrating into the central region (GFDL-ESM2M, GFDL CM3, CanESM2, HadGEM2-ES, CNRM-CM5, and ACCESS1.0). The ACCESS models both show centers of pronounced weakening in the western region of the subtropical gyre.
Projected change in WSC (N m−3 × 10−7) calculated as the difference between the time average of the last 20 years (2081–2100) minus the time average of the first 20 years (2006–25) of the RCP8.5 simulation for all models considered in this study. (a) The MMM. WSC is negative over the subtropical gyre, thus a positive (red) difference indicates a reduced curl and a negative difference (blue) indicates an increased curl. The boundaries of the subtropical gyre for the first 20 years (dashed lines) and last 20 years (solid lines) are shown on each panel. The latitude of RAPID (26.5°N) is shown as the thick green dashed line. Percentages shown in each panel are the percentage change (difference divided by the average of the first 20 years) in the total integrated WSC over the central subtropical gyre, which contains the RAPID array. This region is shown as the boxed region (20°–30°N, 70°–15°W) on each panel.
Citation: Journal of Climate 31, 23; 10.1175/JCLI-D-17-0845.1
The pattern of weakened WSC and thus the reduction in vertical Ekman pumping over the region containing 26.5°N suggests there should be a corresponding reduction in the southward geostrophic transport at this latitude if following Sverdrup balance (Sverdrup 1947). We test this hypothesis in the following section to determine the influence of these changes in WSC on the upper circulation in the interior ocean and thus the potential source of UMO weakening throughout the twenty-first century.
d. Reduced Sverdrup transport in the interior subtropical gyre
We employ Sverdrup balance to test the hypothesis that the reduction of the UMO transport found in the models at 26.5°N (MMM of −2.9 Sv; Fig. 4) is driven by changes in the momentum imparted at the ocean surface by the local wind stress. Following Sverdrup theory, we use only the atmospheric wind stress output from each model to calculate the net transport across 26.5°N, excluding the northward WBC and its associated region of southward inertial recirculation (region of enhanced southward flow directly adjacent to the WBC in Fig. 2) where Sverdrup balance is not valid (Wunsch 2011; Thomas et al. 2014).
Despite these assumptions and approximations, Sverdrup balance holds remarkably well for the entirety of the RCP8.5 experiment for the overwhelming majority of the CMIP5 models studied here, with the WSC governing the southward flow in the ocean interior (overlap of the red and black time series in Fig. 7). The largest errors between TINT and TSV are found in the GFDL models (GFDL-ESM2M, GFDL CM3, and GFDL-ESM2G). However, the SE for these models still remains below 20%. For the GFDL models, TSV is clearly capturing the variability of the net interior flow, with the exception of GFDL-ESM2G, which does not show strong agreement. Differences in magnitudes between TINT and TSV are likely from the inclusion of ageostrophic transports (other than Ekman transports) in the interior ocean not predicted by Sverdrup balance.
Net volume transport (Sv) in the interior ocean for the RCP8.5 experiment in each model and (a) the resulting MMM. The UMO transport calculated in each model from the residual method [Eq. (5)] plus the Ekman transport is shown as the blue time series. The Sverdrup transport TSV derived from the integrated WSC at 26.5°N is shown as the red time series. The net transport in the upper ocean integrated to the LNM TINT is the black time series. The 10-yr running mean is shown as the thick lines in each panel overlaid on top of the annual data. Correlation coefficients between the different transport estimates are listed in Table A2. Any large discrepancies in magnitude between the TINT time series and the TSV time series are due to the inclusion of ageostrophic flow (other than surface Ekman transport) in the ocean interior and/or errors with the assumption of the existence of a spatially and temporally constant LNM. The UMO transport includes southward flow associated with the inertial recirculation of the WBC, and thus models with significant WBC recirculation at this latitude have large discrepancies in magnitude between the UMO + Ekman transport and the other two transport time series. However, we are not concerned with an exact match in magnitude but are concerned with the correlation of the three transport time series in time. Note the differing y axis for (o) GISS-E2-R.
Citation: Journal of Climate 31, 23; 10.1175/JCLI-D-17-0845.1
The UMO transport (blue time series in Fig. 7) calculated from the residual method [Eq. (5)] contains both the southward flow associated with the wind-driven subtropical gyre at 26.5°N predicted by Sverdrup balance and the inertial recirculation of the WBC. Thus, we do not expect an exact match in magnitude between the UMO + Ekman time series and the other two estimates of the interior transport (TSV or TINT) shown in Fig. 7. Instead, we are concerned with the correlation of TSV, TINT, and UMO + Ekman transport with one another in time to determine if it is the changes in the local WSC that are governing the changes of the southward interior transport in each model.
We consider hereafter the time series of TINT, TSV, and the UMO + Ekman transport smoothed with a 10-yr running mean assuming that this time period is long enough to account for any adjustment period expected between wind forcing and the response of the interior ocean. Strong positive correlations are found between the net interior transport and the TSV time series (0.72 ≤ r ≤ 0.99; Fig. 7 and Table A2). Similarly, strong positive correlations are found when comparing the time series of the UMO + Ekman transports and TSV (0.59 ≤ r ≤ 0.98; Fig. 7 and Table A2). These strong correlations in time suggest the changes in the interior ocean transports in both the UMO and the net interior are in direct response to changes in the local WSC.
If driven by changes in the local WSC, the long-term changes in TSV should be captured in our UMO estimate with a strong correlation between the two. The projected changes for these two estimates (2081–2100 averaged minus 2006–25 averaged) plotted against each other yields a positive correlation of +0.78 (significant at the 95% level; Fig. 8a). Models with larger projected reductions in the integrated WSC across the basin at 26.5°N also exhibit larger reductions of the southward flow in the UMO. Most models project slightly larger reductions in the UMO transport than in TSV due to the additional weakening from the spindown of the WBC’s inertial recirculation (included in the UMO transport estimate) as the total flow in the WBC weakens throughout the twenty-first century. Only one model, MRI-ESM1, projects a slight increase in TSV by the end of the century. Among the other models, differing degrees of weakening of TSV are found throughout the twenty-first century, with some models showing more pronounced reductions (CanESM2, GFDL CM3, CNRM-CM5, HadGEM2-ES, ACCESS1.0, and ACCESS1.3) than the others (Fig. 7).
The (a) change in the UMO transport against the change in the Sverdrup transport TSV, (b) change in TSV against the change in total northward transport in the upper WBC, and (c) change in WBC against change in the net transport in the deep ocean. All differences calculated as the time average of the transport simulated in the last 20 years (2081–2100) minus the time average of the transport in the first 20 years (2006–25) of the RCP8.5 experiment: MMM (black square), ACCESS1.0 (red ×), ACCESS1.3 (blue ×), CanESM2 (dark green), CNRM-CM5 (purple), GFDL CM3 (red), GFDL-ESM2G (yellow), GFDL-ESM2M (blue), GISS-E2-R (black), HadGEM2-ES (gray), MRI-CGCM3 (cyan), MRI-ESM1 (lime green), CCSM4 (magenta), CESM1(BGC) (brown), and CESM1(CAM5) (orange). Correlation coefficients between the two transports are shown at the bottom of each panel. The correlation coefficients in (a) and (c) are significant at the 95% confidence interval determined using a simple t test. The positive correlation in (b) is not significant at the 95% level.
Citation: Journal of Climate 31, 23; 10.1175/JCLI-D-17-0845.1
Since TSV is the theoretical net southward transport that compensates the northward WBC, a positive correlation between TSV and the total northward transport in the upper WBC is expected. Reductions in the momentum-driven TSV should reduce the total northward transport along the western boundary. Comparing the projected changes of these components by the end of the century (2081–2100) relative to the start of the century (2006–25), we find a positive correlation of +0.46 (not significant at the 95% level; Fig. 8b). A stronger relationship is found when comparing the long-term reductions in the northward WBC transport and the net transport in the deep ocean (r = +0.86, significant at the 95% level; Fig. 8c). For all models, with the exception of ACCESS1.0 and CanESM2, the projected reduction of the net transport in the deep ocean is greater than the reduction in the southward transport in the upper ocean associated with the horizontal gyre circulation. These two models appear furthest from the linear trend line in Fig. 8c and show the greatest projected reductions in the local WSC (−33%, CanESM2 and −24%, ACCESS1.0; Fig. 6) and thus the greatest reductions in interior ocean transport at 26.5°N.
4. Discussion
The assessment of state-of-the-art fully coupled climate models against observations is a crucial step toward improving confidence in climate model projections. Many studies have evaluated ocean-only numerical simulations against the RAPID observationally estimated AMOC and the components associated with its flow at 26.5°N (Baehr et al. 2009; Haines et al. 2012; Hui-Er and Yong-Qiang 2012; Xu et al. 2012; Haines et al. 2013; Mielke et al. 2013; Zhao and Johns 2014a,b; Blaker et al. 2015; Stepanov et al. 2016). However, such a comparison using the IPCC-class coupled models in a multimodel framework has been limited (Msadek et al. 2013). In the first part of this study, we address this gap in knowledge and decompose the subtropical AMOC into the major components (ageostrophic surface Ekman transport, transport in the WBC, UMO transport, and net transport in the deep ocean) used to estimate its strength at 26.5°N in a suite of CMIP5 models. An assessment is made of how well CMIP5 models simulate the AMOC and its associated transport components at 26.5°N relative to those estimated by RAPID over the first complete decade of its deployment.
The analysis reveals that the mean transport of the AMOC and its components simulated by CMIP5 models at the start of the twenty-first century under RCP8.5 (2006–15) agree well with the transports estimated by RAPID over the 2005–14 period (Fig. 3). The partitioning of the northward WBC and the southward return flow in the UMO at 26.5°N is slightly different in the observed ocean than in the models’ ocean, inhibiting a direct comparison between the CMIP5 models and the transports reported by RAPID. The existence of the Bahamas islands in the real ocean splits the total WBC into two separate northward boundary currents, the Florida Current and the Antilles Current, with the latter being included in RAPID’s UMO estimate. This separation, however, is not resolved in the ~1°-horizontal-resolution CMIP5 models used here, and the horizontal gyre components can only be separated into the total northward transport in the WBC and the net southward return flow in the UMO. Thus, we have relied here on the agreement between the sum of these two components (CMIP5 WBC + UMO compared to RAPID FC + UMO) as a measure of agreement between the horizontal gyre components observed by RAPID and that simulated in the models (Fig. 3e).
The second half of this study focuses on quantifying and understanding the projected changes in the subtropical AMOC and the components that construct its flow. Projected changes in the AMOC calculated as the maximum of the meridional overturning streamfunction have been explored extensively using CMIP5 models (Weaver et al. 2012; Cheng et al. 2013; Collins et al. 2013). However, how the components of subtropical ocean circulation that contribute to its flow are projected to evolve under increased greenhouse gas forcing has remained unexplored in CMIP5 models. This study is the first of its kind in assessing projections of the individual transport components of the AMOC at 26.5°N in a multimodel framework.
First, in order to assess the significance of the projected changes by the end of the twenty-first century, we analyzed the decadal-mean transports and the associated variability of the AMOC and its components in piControl integrations (Table 2 and online supplementary material). If we make the assumption that the decadal-mean transports found in piControl integrations are a good surrogate for the long-term unforced observed variability, our analysis reveals that the AMOC and its transport components at 26.5°N estimated from the first decade of RAPID array observations are well within range (2σ) of the decadal transports expected from natural climate variability. This result agrees with other studies (Roberts et al. 2014; Jackson et al. 2016) suggesting that the downward trend and continued weakened state of the AMOC observed by RAPID at 26.5°N over the length of its deployment (Smeed et al. 2014; Frajka-Williams 2015; Frajka-Williams et al. 2016; Smeed et al. 2018) cannot be reliably attributed to increasing concentrations of greenhouse gases at this point.
Projections of the AMOC and its component transports at 26.5°N by the end of the twenty-first century under RCP8.5 show considerable spread among models. This is expected, given the spread in the mean-state transports in the piControl simulations and at the start of the RCP8.5 experiments, a factor shown to be important in determining the sensitivity of the AMOC to future change (Gregory et al. 2005; Danabasoglu et al. 2014). Relative to the piControl decadal mean, a small forced response of the AMOC and its transport components is evident even at the start of the twenty-first century under RCP8.5, with the MMM WBC and UMO transports weakening outside of the range (2σ) of the decadal-mean piControl estimate (Table 2 and online supplementary material). By the end of the twenty-first century, the MMM AMOC and its associated components, with the exception of the Ekman transport, have reduced to magnitudes well outside of the range expected from natural variability and outside the range of annual-mean values that have been observed by RAPID thus far (Table 2 and Fig. 3). While the magnitude of the response to the RCP8.5 forcing over the twenty-first century differs between models, the weakening pattern is robust. For the Ekman transport, no consistent trend in the direction or magnitude of the projected changes is found between models, likely related to the varied response of the easterly trade winds under RCP8.5 (Fig. 5).
Our results agree with those of Thomas et al. (2012), which evaluated the changes in the AMOC component transports at 27°N under a 100-yr climate change scenario of a 2% yr−1 increase in atmospheric CO2 concentrations in the eddy-permitting (1/3° × 1/3°) coupled model HiGEM. Thomas et al. (2012) found decreased transport in the upper interior ocean, deep ocean, and the upper northward WBC. Thus, the projected weakening of the major transports composing the zonal structure of the subtropical North Atlantic Ocean circulation found in the coupled model HiGEM is not unique to this individual model but is a robust feature in the response of CMIP5 models under increased CO2 forcing.
The long-term pattern of a weakened southward transport in the UMO found in this study using 14 different CMIP5 models and in the higher-resolution model used in Thomas et al. (2012) in response to increased atmospheric CO2 concentrations is in direct contrast to what has been observed by RAPID thus far. In fact, observations from the RAPID array have shown a strengthening of the southward transport in the UMO at 26.5°N associated with the observed AMOC decline (Smeed et al. 2014; Frajka-Williams 2015; Frajka-Williams et al. 2016) and continued weakened state (Smeed et al. 2018).
A reduced return flow in the UMO in CMIP5 models under increased greenhouse gas emissions provides an additional local contribution to the reduction of the transport in the WBC. This reduction in the UMO is in response to changes in surface momentum forcing by local wind stress over the subtropical gyre. Our analysis of the zonal wind stress across the subtropical gyre reveals a robust feature across models of weakened surface westerly wind stress across the northern sector of the gyre (Fig. 5). Across the southern sector, the changes in the surface easterly wind stress are more varied among models. A poleward shift of the northern boundary of the subtropical gyre, consistent with the expansion of the subtropical zone in a warming climate (Saenko et al. 2005; Lu et al. 2007; Collins et al. 2013) is found in some models.
A single mechanism to explain the reduced surface westerly wind stress found across models in the northern sector of the subtropical gyre and the varied response of the easterly wind stress is unlikely; these patterns depend strongly on the projected changes in the vertical and equator-to-pole temperature gradients in the upper and lower troposphere, which differ from model to model (Collins et al. 2013). As summarized in the latest IPCC report and highlighted in more recent studies, the dynamical mechanisms behind the projected changes in the tropospheric jet in the Northern Hemisphere are still not completely understood (Collins et al. 2013; Barnes and Polvani 2015; Kidston et al. 2015; Shaw et al. 2016; Screen et al. 2018). Understanding the mechanisms behind the changes in the zonal wind stress projected by the end of the century is beyond the scope of this study. The focus here is on how the resulting altered WSC pattern impacts the subtropical ocean circulation.
The change in the gradient of zonal wind stress across the subtropical gyre, specifically at the central region where RAPID is located, produces a pattern of weakened WSC by the end of the century (Fig. 6). While the magnitude differs considerably among models (−33% to −7.8%), all but one of the models show patterns of reduced WSC magnitude at the central region of the gyre by the end of the twenty-first century. A reduced WSC at subtropical latitudes was also found by Thomas et al. (2012) under increased atmospheric CO2 forcing in HiGEM.
The reduced WSC across models drives a reduction in the interior ocean transport in accordance with the mechanism of Sverdrup balance (Sverdrup 1947). Gradients in the surface wind stress, and hence gradients in Ekman transport, lead to the convergence and divergence of mass in the Ekman layer, generating vertical velocities in the boundary layer that disturb the isopycnals in the upper ocean and in turn generate ocean currents (Gill 1982). Recent studies using ocean state estimates and high-resolution coupled climate models show that Sverdrup balance can be used to estimate the transport in the interior of the North Atlantic’s subtropical gyre at time scales of a few years or more (Wunsch 2011; Thomas et al. 2012; Duchez et al. 2014; Thomas et al. 2014). Strong evidence of the validity of Sverdrup balance over large areas of the tropics and subtropics has also been shown using geostrophic velocities derived from salinity and temperature profiles from the global Argo array (Gray and Riser 2014).
Motivated by the existence of Sverdrup balance in the interior subtropical North Atlantic and by two recent studies that applied this mechanism to estimate interior geostrophic transport associated with the upper limb of the AMOC (Thomas et al. 2012; Duchez et al. 2014), we test the hypothesis that the projected reduction in the transport in the interior ocean is in response to the projected changes in the overlying wind stress forcing. Our results show that net interior transports simulated in CMIP5 models can be estimated by only invoking the local WSC, with the Sverdrup transport TSV estimating net transports down to an assumed LNM with errors in magnitude ranging from 0.05% to 18% at the annual time scale. A strong positive correlation is found between TSV and the net transport integrated down to the LNM (TINT). This strong positive correlation is also found between TSV and the UMO + Ekman (we add the northward Ekman at the surface to recover the net interior flow) transport calculated from the residual method [Eq. (5)]. The correlation between these time series and the small errors between the interior transport and the TSV provides strong evidence that the interior transport in the upper ocean at 26.5°N is explained largely through Sverdrup balance for the entirety of the RCP8.5 experiment. In all models, the interior transports in the upper ocean are responding directly to local wind stress forcing, with their long-term behavior governed by long-term changes in the local WSC.
5. Summary and conclusions
Using a suite of CMIP5 models, we have shown that despite their coarse resolution and limited parameterizations, the current state-of-the-art coupled climate models simulate the mean subtropical AMOC and its individual transport components well relative to what has been observed by the RAPID array at 26.5°N. Our analysis has also revealed that present-day estimates of the AMOC and its component transports observed by RAPID are currently within the range of what is expected from natural climate variability, as estimated by transports simulated in preindustrial control experiments. We have presented a first-of-its-kind multimodel analysis of the future evolution of the AMOC in terms of the projected changes in each of the individual transport components that construct its flow at 26.5°N: the northward western boundary current (WBC), wind-driven Ekman transport, net transport in the deep ocean, and the southward transport in the upper midocean (UMO) associated with the wind-driven circulation of the subtropical gyre. A projected weakening is found in all transport components, with the exception of the Ekman transport, at 26.5°N under increased greenhouse gas emissions.
We show here that the changes in surface momentum imparted by the local wind stress forcing over the North Atlantic subtropical gyre under increased greenhouse gas concentrations cause a reduction in the local WSC, driving a decrease in the net southward transport in the interior ocean following Sverdrup balance. This reduction in the southward interior flow of 2.9 Sv, averaged across the models at 26.5°N, reduces the gyre contribution to the northward-flowing WBC. On average, the reduced UMO transport accounts for 38% of the decrease in the WBC transport at 26.5°N. The other 62% (−4.7 Sv) of the weakening in the total northward transport can be accounted for by changes in the southward deep transport, likely associated with changes in buoyancy forcing at high latitudes in the North Atlantic (Gregory et al. 2005), which are not addressed in this study.
Similar results of a weakened northward flow in the WBC, reduced deep transport, and a weakened interior transport due to a reduced WSC under increased atmospheric CO2 forcing have been shown previously in an eddy-permitting model, HiGEM (Thomas et al. 2012). However, it remained to be understood, until now, if these weakened subtropical ocean circulation patterns were a robust feature across coupled model simulations under increasing CO2 concentrations. Here, we show that a projected weakening of all non-Ekman ocean transports at 26.5°N is a robust feature under the RCP8.5 scenario in CMIP5 models. Furthermore, we have shown that Sverdrup balance holds throughout the entirety of the RCP8.5 experiment for all models, another feature that was found by Thomas et al. (2012).
Observations from the RAPID array at 26.5°N suggest that the decreasing strength of the AMOC observed from 2007 to 2011 and the reduced state it has remained in is mainly associated with a persistent strengthening of the southward flow of the subtropical gyre recirculation (Smeed et al. 2014; Frajka-Williams 2015; Frajka-Williams et al. 2016; Smeed et al. 2018). The results presented here are in contrast to what has been observed thus far, with a weakening of the subtropical gyre projected by the end of the twenty-first century in response to changes in the momentum forcing from the overlying wind stress. Such changes in the North Atlantic subtropical ocean circulation have the potential to impact heat and tracer transport and thus feed back onto the climate system.
The North Atlantic subtropical gyre is of climatic importance because of the large amount of heat and salt that this circulation transports meridionally from the tropics toward the subpolar latitudes and zonally across the Atlantic, impacting both the local air–sea heat fluxes and the deep- and intermediate-water formation in higher latitudes of the North Atlantic. While most of the poleward heat transport in the subtropical Atlantic is due to the transformation of surface waters to intermediate- and deep-water masses at high latitudes (Talley 2003; Johns et al. 2011; Msadek et al. 2013), the gyre circulation and its associated shallow subduction processes that occur regardless of the presence or strength of deeper overturn is not an insignificant component of the total ocean heat transport (Manabe and Stouffer 1988; Talley 2003). Thus, a reduction in the strength of the subtropical gyre, such as that found here under increased atmospheric CO2, could lead to enhanced heat and salt content in the gyre rather than these properties being transported to the subpolar region.
Furthermore, alterations in the strength of the Gulf Stream are dynamically linked to regional sea level change along the East Coast of the United States; a weakened northward transport is associated with anomalous sea level rise (Ezer et al. 2013; Goddard et al. 2015). Here, we show that the weakened subtropical gyre serves as an additional source to the weakening of the northward western boundary current, which could induce further anomalous sea level rise under continued warming. While we speculate here on the potential climatic importance of a decline in the subtropical gyre transport through its impacts on heat and tracer transport and regional sea level changes, this subject deserves a detailed follow-up study to parse out and quantify the impacts of such changes at the regional and global scale. The projected twenty-first-century changes in the mean AMOC are quantified and discussed at length in the latest IPCC report (Collins et al. 2013); however, the weakened subtropical gyre transport occurring alongside the reduced overturning found in this study and by Thomas et al. (2012) has neither been documented nor extensively explored to understand its implications for projected climate.
Here, the subtropical AMOC has been decomposed into the transport components that are generally suppressed in the integration process when the AMOC is assessed simply as the maximum of the two-dimensional meridional streamfunction in modeling studies. The analysis provides for the first time 1) an assessment of the simulation of the AMOC in terms of the individual transport components that construct its flow in the subtropical ocean in IPCC-class fully coupled climate models relative to a decade of RAPID observations and 2) a more detailed understanding of how each component of the large-scale circulation is projected to change by the end of the twenty-first century under RCP8.5. Nevertheless, this analysis should be repeated using higher-resolution coupled climate models and the more advanced models contributing to CMIP6, as all models considered here are not eddy permitting at mid- and high latitudes. Furthermore, this assessment should be repeated as more RAPID data become available, given that the present data length remains too short to assess long-term trends or to provide a good baseline for comparison of mean transports at the seasonal scale or at time scales longer than 10 years.
Acknowledgments
We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling responsible for CMIP. We thank the modeling groups listed in Table 1 for producing and making available their output. For CMIP, the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. Data from the RAPID-WATCH MOC monitoring project are funded by the Natural Environment Research Council and are freely available (www.rapid.ac.uk/rapidmoc). We acknowledge the use of the Ferret program from NOAA’s Pacific Marine Environmental Laboratory for analysis and graphics (http://ferret.pmel.noaa.gov/Ferret). Figure 1 was created using the Ocean Data View software (Schlitzer 2016), with the CFC-11 data obtained by repeat hydrographic measurements and made freely available from the Global Ocean Data Analysis Project, version 2 (GLODAPv2; Key et al. 2015; Lauvset et al. 2016; Olsen et al. 2016). We extend a huge thank you to Dr. Lynne Talley and Dr. Isabella Rosso from Scripps Institution of Oceanography, Dr. Alison Gray from the University of Washington, and to the editor and reviewers for their valuable insights, comments, and suggestions. This research was funded by the U.S. EPA Assistance Agreement FP-91780701-0. This publication has not been reviewed by the EPA and the views expressed herein are solely those of the authors. This work was sponsored by NSF’s Southern Ocean Carbon and Climate Observations and Modeling (SOCCOM) Project under the NSF Award PLR-1425989, with additional support from NOAA and NASA. Logistical support for SOCCOM in the Antarctic was provided by the U.S. NSF through the U.S. Antarctic Program.
APPENDIX
Additional Details for Individual Models and Level of No Motion Determination
To supplement the time series and multimodel-mean values presented in the main manuscript, additional details are provided here (Table A1) regarding the projected changes under RCP8.5 of the transports considered in this study for the individual models. The results of the analysis performed to estimate the LNM, used as the vertical integration boundary for the interior ocean transports TINT, are shown in Fig. A1. The resulting correlations discussed in the manuscript between the Sverdrup transport TSV and TINT and between TSV and the UMO + Ekman transports are summarized in Table A2.
Projected changes in the AMOC and its component transports at 26.5°N under the RCP8.5 scenario. The changes are calculated as the time average of the transport over the last 20 years of the century (2081–2100) minus the time average of the transport over the first 20 years (2006–25). Percentages are calculated as the difference divided by the time average over the first 20 years.
SE (%) vs vertical integration depth at 100-m intervals at 26.5°N in the Atlantic. SE corresponds to the difference between the Sverdrup transport TSV calculated from each model’s local WSC [Eq. (7)] and the net interior transport integrated zonally across 26.5°N TINT [Eq. (8)]. The upper northward WBC and the adjacent WBC recirculation region that are not predicted by Sverdrup balance are not included in TINT. The horizontal boundaries for integration of TINT are chosen individually for each model to ensure exclusion of these regions, as each model has a different width of the WBC and any WBC recirculation present at this latitude (Fig. 2). SE is time averaged over the course of the entire RCP8.5 simulation to get the average SE at each depth, and the depth of integration is constant across the basin. The LNM is determined for each model as the depth between 500 and 3000 m at which the SE is minimized, and therefore, the best agreement between TSV and TINT is obtained. The symbols along each model’s line denotes this depth. This assumed LNM is used as the vertical boundary for calculating TINT shown as the black line in Fig. 7.
Citation: Journal of Climate 31, 23; 10.1175/JCLI-D-17-0845.1
Correlation coefficients between the time series of net interior transport TINT and Sverdrup transport TSV and the time series of TSV and UMO + Ekman at the annual time scale and with a 10-yr running mean applied. The corresponding time series are shown in Fig. 7. Values in boldface are not significant at the 95% confidence interval determined using a simple t test.
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