Significance The Atlantic Meridional Overturning Circulation (AMOC) is a key component of the climate system, and its interdecadal variability (IV) significantly modulates climate changes around the North Atlantic region and worldwide. We report a robust shortening in period and weakening in amplitude of AMOC-IV in response to future global warming, which may be contributed to by increased oceanic stratification and, in turn, speedup of Rossby wave propagation. This finding sheds light on the mechanism of AMOC-IV responses to varying background climatology and global warming and therefore should contribute significantly to our understanding and projection of future climate changes.

Abstract Interdecadal variability of the Atlantic Meridional Overturning Circulation (AMOC-IV) plays an important role in climate variation and has significant societal impacts. Past climate reconstruction indicates that AMOC-IV has likely undergone significant changes. Despite some previous studies, responses of AMOC-IV to global warming remain unclear, in particular regarding its amplitude and time scale. In this study, we analyze the responses of AMOC-IV under various scenarios of future global warming in multiple models and find that AMOC-IV becomes weaker and shorter with enhanced global warming. From the present climate condition to the strongest future warming scenario, on average, the major period of AMOC-IV is shortened from ∼50 y to ∼20 y, and the amplitude is reduced by ∼60%. These reductions in period and amplitude of AMOC-IV are suggested to be associated with increased oceanic stratification under global warming and, in turn, the speedup of oceanic baroclinic Rossby waves.

As a modulator of low-frequency climate variation in the North Atlantic region (1⇓⇓⇓–5), interdecadal variability of the Atlantic Meridional Overturning Circulation (AMOC-IV) has likely undergone significant changes in the past (6). Despite past efforts (7⇓–9), responses of AMOC-IV to global warming remain unclear, in particular regarding the amplitude and period of AMOC-IV.

Here, we investigate the responses of AMOC-IV to future global warming in the state-of-the-art Coupled Model Intercomparison Project Phase 5 (CMIP5) simulations (10). We compare AMOC-IV in the future projection simulations of four warming scenarios of different Representative Concentration Pathways (RCPs, namely, RCP26, RCP45, RCP60, and RCP85; Models and Experiments) with AMOC-IV in the preindustrial (PI) control simulations. Five models are selected based on the criterion that each has at least two sufficiently long RCP simulations of up to the year 2300 (Table S1). With two or more long RCP simulations by each model, we can assess transient AMOC-IV responses among different scenarios with reasonable statistical significance. In the PI simulations, all models give significant AMOC-IV (Fig. S1A and Definition of the AMOC Intensity), exhibiting robust periods within the range of 10–100 y (Fig. S2). Under future global warming, the mean transport of the AMOC is reduced, with the ensemble mean ranging from being reduced by 5% in RCP26 to being reduced by 48% in RCP85 in the years 2100–2300 (Fig. S1 B and D), qualitatively consistent with Intergovernmental Panel on Climate Change studies (11).

Table S1. Climate models and simulations

Fig. S1. AMOC intensity, AMOC-IV amplitude and long-term changes. AMOC intensity in the PI (A) and RCP (B) simulations. (C) SD of AMOC interdecadal variability (10−100 y) of each model in the PI simulation and their ensemble mean. (D) Ensemble mean of the amplitude ratio of AMOC intensity of each RCP simulation (averaged over the years 2100–2300) normalized by the PI case. Error bar shows the cross-model SDs in each RCP simulation. Horizontal lines in A and B show the 200-y windows for the PS analysis.

Fig. S2. Power spectrum of AMOC in the PI simulation. Shown are results for each of the five models: (A) CCSM4, (B) CESM1-CAM5, (C) MPI-ESM-LR, (D) CNRM-CM5, and (E) CanESM2. Cross-window ensemble mean power spectrum curves with different window lengths (200 y, 300 y, and 400 y) are shown as black, blue, and green solid lines, respectively, with the corresponding SDs marked as vertical bars of the same color. The power spectrum of the entire time series is shown as the dashed black curve.

Materials and Methods Models and Experiments. We analyzed 19 experiments from five models in the CMIP5 archive (10), and each experiment has one preindustrial (PI) control simulation and four future warming scenarios (Table S1). The PI simulation uses the fixed forcing at the year 1850. Four simulations of future global warming scenarios are used, which are forced according to RCP26, RCP45, RCP60, and RCP85 (additional radiative forcing of 2.6 W⋅m−2, 4.5 W⋅m−2, 6.0 W⋅m−2, and 8.5 W⋅m−2, respectively, near year 2100, relative to the PI forcing). All potential density and pressure at sea level were regridded to a 1° × 1° grid before analysis. Different periods of the RCP simulations are used for the EMD method (period of 2100–2300) and the running mean method (period of 2050–2250). The entire period of the PI simulation in each model is used. Annual mean data are used in all of the analyses. Definition of the AMOC Intensity. The intensity of the AMOC is defined as the maximum overturning streamfunction below 500 m in the Atlantic. Identification of Interdecadal Variability. Interdecadal variability is identified using the Fast Fourier Transform (41) in power spectrum (42) after filtering out the variability longer than 100 y. In the simulations of different warming scenarios, the long-term trends are removed with the EMD method (12) (or with a high-pass 100-y running mean). Power Spectral Analysis and Major Period/Amplitude of AMOC-IV. The long PI simulation is separated into a batch of 200-y windows with a 150-y overlay in adjacent windows (Fig. S1A). The power spectrum of each 200-y window and its mean are calculated for comparison with the results of the RCP experiments (years 2100–2300). The cross-window ensemble mean power spectrum (for the 200-y window) can capture the major period of AMOC-IV (about 70 y or shorter), which is derived from longer windows, including the entire time series (Fig. S2). This implies that most of the 200-y windows are sufficient for the detection of the dominant features of AMOC-IV. In some cases, the lower variance for the major period of AMOC-IV is caused by the coarse period/frequency resolution at the interdecadal scale. The ensemble mean power spectrum for each scenario is performed after being normalized by the spectral peak of the PI simulation of each model, so that the variance ratio between each warming scenario and the PI case is comparable among different models. For each model, the major period and amplitude of AMOC-IV for an RCP simulation are defined by the spectral peak of the 200-y window of 2100–2300, whereas those for the PI simulation are calculated as the arithmetic mean of the spectra of all of the 200-y windows, instead of the spectrum of the entire PI simulation (although the two are similar). The cross-model ensemble mean spectrum is the mean of the spectra across different models.

SI Materials and Methods Time Scale of Rossby Wave. The Rossby wave speed is calculated from the eigenvalue problem in the linearized quasi-geostrophic potential vorticity equation (43), with the buoyancy frequency (N2) vertical profiles derived for each model’s mean ocean state in the high-latitude North Atlantic (40°N−60°N), ∂ t [ ∂ z ( f 0 2 N 2 ∂ z φ ) ] + β ∂ x φ = 0 where N 2 = − g ρ 0 d ρ d z , and φ denotes the streamfunction. Set φ = ϕ ( z ) e i ( k x − ω t ) , d d z ( f 0 2 N 2 d ϕ d z ) − λ ϕ = 0 , λ = − β k ω . [S1]The vertical boundary condition of no motion at the top and bottom reduces to d ϕ d z | z = 0 , D = 0 . [S2]The buoyancy frequency N2 in each experiment is interpolated to a uniform 5-m layer in the depth range of 4,000 m. A centered three-point finite difference scheme is used to solve the eigenvalue problem of Eqs. S1 and S2. The finite difference form of the eigenvalue problem is therefore of the form A ϕ m = λ m ϕ m where λ m is the mth eigenvalue and ϕ m is the mth eigenfunction. For specific values of f 0 and N 2 , we can obtain the values of λ m and ϕ m . The phase speed of the first baroclinic Rossby wave is c 1 = ω k = β λ 1 . The time scale of the first baroclinic Rossby wave propagating from the east to the west in the latitude band of 40°N−60°N of the North Atlantic is T = L c 1 where L denotes the mean width of the North Atlantic between 40°N and 60°N and is set to 3,700 km. The application of the eigenvalue problem to different models shows that the wave speed increases rapidly with global warming (Fig. S9A) whereas the eigenfunction of the wave (Fig. S9 B−F) exhibits a typical first baroclinic mode structure. It is worth noting that the domain of 40°N–60°N in the North Atlantic is selected here as a crude representation of the subpolar region where AMOC-IV is dominant (Fig. S7). The exact latitude of the Rossby wave that is relevant to the time scale of the AMOC-IV, if it exists, still remains to be explored. Here, however, the robust feature is the relative change of the wave speed with global warming, with a rapid speedup of ∼200% (Fig. 2A). This feature is determined mainly by the change of stratification. In contrast to the stratification, the major latitude factor, f2 in Eq. S1, although it affects the absolute magnitude of the wave speed, remains the same across different warming scenarios and therefore does not contribute directly to the relative change of the wave speed with global warming. Because the magnitude of the speedup due to stratification is roughly comparable to the shortening of the AMOC-IV (∼280%, Fig. 2A), we speculate that the Rossby wave mechanism can be an important mechanism. Meanwhile, we note that it is likely that other mechanisms can also contribute to the shortening of the AMOC-IV, such as the latitudinal density change and the associated thermal Rossby wave, as discussed in the second paragraph of Mechanism of the AMOC-IV Changes (Fig. S6). Amplitude of Rossby Wave. The weakening of the AMOC-IV may be interpreted in terms of forced Rossby wave. The equation for the Rossby wave forced by atmospheric forcing Q can be written as (43) ∂ t φ + c 1 ∂ x φ = Q [S3]where ∂ x φ = v denotes the northward geostrophic velocity. For the low-frequency forcing case in which temporal variability is not dominant, we may have a quasi-stationary response c 1 v ∼ Q . If the atmospheric forcing Q remains largely unchanged in response to global warming while the wave speed c 1 is accelerated, the amplitude of the forced response will be inversely proportional to the wave speed, or proportional to the cross-basin time scale, namely, v ∼ Q c 1 ∼ Q T . Therefore, a faster wave also leads to a smaller amplitude of response, as long as the wave is not too fast to lead to a failure of the quasi-equilibrium response. AMOC-IV Amplitude in Delayed Oscillator Perspective. The weakening of the AMOC-IV may also be interpreted from a nonlinear delayed oscillator (34) perspective. With global warming and the speedup of Rossby wave, the delay time is reduced such that the amplitude of the AMOC-IV is reduced monotonically as shown in Fig. S11. Indeed, this reduction of wave amplitude with wave delay can be calculated as a robust feature in a more general delayed oscillator model, such as that of Suarez and Schopf (44). Mechanistically, when the wave delay diminishes, the negative feedback associated with the delay becomes an instantaneous negative feedback that cancels the instantaneous growth rate, leading to a reduced amplitude of the oscillation.

Acknowledgments We thank Drs. H.-J. Yang, K. Fraedrich, H. Dijkstra, and X.-Y. Shen for valuable discussions, and Drs. Y. G. Liu and W. Zhang at Geophysical Fluid Dynamics Laboratory for their useful comments on an early version of the manuscript. We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for Coupled Model Intercomparison Project, and we thank the climate modeling groups for producing and making available their model outputs. This work is supported by the National Basic Research Program of China (Grants 2012CB955200 and 2015CB953902) and the National Natural Science Foundation of China (Grants 41206024 and 41130105).

Footnotes Author contributions: J.C., Z.L., and S.Z. designed research; J.C. and W.L. performed research; L.D., P.L., and H.L. analyzed data; J.C. and Z.L. wrote the paper; and Z.L., S.Z., and W.L. interpreted the results.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

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