First, we study the relationship between AMOC strength and the forcing corrected global surface warming with a correlation analysis over the whole length of the time series for which all data is available (1948–2012). The forcing correction is done in two different ways: on the one side by just removing the long-term warming signal (either by removing the linear trend or by removing a nonlinear trend as done by Chen and Tung (2018)) and on the other side by using a simple equation for the global mean energy balance. This will answer the question whether the opposing course of the two variables between 1975–1998, as identified by Chen and Tung (2018) (their figure 3(b)), is also valid during other time periods. While this correlation analysis will not suffice to determine the contribution of different processes to global temperature changes, it is sufficient to identify whether periods of a weaker AMOC over the last decades had a distinct cooling, warming or close to no effect on the global surface temperature.

Second, we investigate the trend reversal in the ocean heat content in the North Atlantic Ocean from positive, during a time period of increasing AMOC strength (2000–2004), to negative, during a time period of a decreasing AMOC (2005–2016), considering the role of the AMOC in transporting heat horizontally from the Southern Ocean into the Atlantic.

Global mean surface temperature changes—i.e. the lower atmosphere and upper ocean, which are well-mixed and thermally tightly coupled—are forced by radiative forcing from the top and heat exchange with the deep ocean below (Trenberth et al 2010, Brown et al 2014):

Here, T is the global mean surface temperature, c m is the effective heat capacity of the system (dominated by the ocean mixed layer), Q rad the radiative forcing and Q ocean the vertical heat transport across the bottom of the ocean mixed layer e.g. through diffusion (fluxes are positive downward) (Brown et al 2014). Δ indicates differences to a previous equilibrium state (e.g. preindustrial). The term λ ΔT represents the equilibrium response ΔT of the surface temperature to the forcing anomaly, which depends on the climate feedback parameter λ. The equation holds for the global mean temperature, therefore horizontal transport processes play no role. Solved for ΔQ ocean this equilibrium is:

Since we are looking at temperature changes at multidecadal timescales we can assume that the mixed layer is close to equilibrium and thus neglect the transient term on the left hand side in equation (1). This term would lead to some delay of the surface temperature response to forcing changes, yet empirical correlation shows that the lag of the global surface temperature response to a change in the radiative forcing, e.g. the 11 year solar cycle, is of the order of a month (Foster and Rahmstorf 2011), so for our purposes this lag is not significant.

With given time series for ΔT and ΔQ rad (both with respect to the preindustrial equilibrium state of 1850) and the different estimates for the feedback parameter λ we can now use equation (2) to test how AMOC variations (represented by the AMOC indices) correlate with the part of surface temperature changes that are not directly radiatively forced (i.e. the right hand side of the equation (2)).

The correlation values (figure 1) are positive (with r = 0.49, 0.57 or 0.22 depending on the AMOC proxy) with particularly warm GMST anomalies coinciding with a strong AMOC. This is in direct contradiction to the idea that a strong AMOC acts to cool the surface and in full agreement with the established understanding of the AMOC's role in vertical heat transport (Drijfhout 2015). We use the smoothed time series to determine the influence of the AMOC since the short-term fluctuations in the ocean heat uptake in the North Atlantic are dominated by atmospheric variability (Gulev et al 2013).

Figure 1. Time evolution of the multidecadal variability of the AMOC compared to the global mean surface temperature adjusted by the historical forcing for the time period 1948–2012. In grey the time period from 1975 to 1998 is marked during which the AMOC was in a relatively weak state. Proxies for the AMOC are the salinity based proxies A ISHIIS+Scripps , A EN4 and the temperature based proxy A HadISST (shades of blue), which are compared to the linear trend of the 2005–2015 measurements form the RAPID array (thick black line). The global mean temperature deviation is based on HadCRUT4.6 data and is corrected for the linear, long-term warming trend (ΔT, orange), the nonlinear trend as done by Chen and Tung (2018) (ΔT, magenta) or adjusted by the historical forcing used for CMIP5 (ΔT'=ΔT−1/λ ΔQ rad , red line). The default value for the feedback parameter is λ = 2.3 ± 0.7 W K−1 m−2 and the numbers in brackets give the range of correlation coefficients resulting from other values for λ that are additionally shown in table 1. Thin lines are annual values; thick lines are 10 year LOWESS smoothed values. The LOWESS (Locally Weighted Scatterplot Smoothing) filter fits a regression curve to a scatterplot using weighted local linear regressions depending on the smoothing span, in this case 10 years (Cleveland 1979). The correlation coefficients r were calculated with the smoothed time series. (To remove any correlations due to common trends the time series were first linearly detrended.) Download figure: Standard image High-resolution image Export PowerPoint slide

While the exact values of the correlation coefficients depend on the choice of the feedback parameter and the AMOC index, they are positive in all cases (i.e. between 0.01 and 0.65, see table 1) and therefore do not support the hypothesis that a weak AMOC enhances surface warming by decreasing the ocean heat uptake (in that case the correlation coefficients would be negative). The fact that most of the correlation values are not significant at the 5% level (this was tested using amplitude-adjusted Fourier transform (AAFT) surrogates (Donges et al 2015)) is also irrelevant for deducing that an AMOC weakening does not enhance surface warming, as it is sufficient to show that the coefficients are not negative. As can be seen in figure 1 there is no apparent lag between the adjusted surface warming and the AMOC strength, consistent with our assumption that the ocean's mixed layer and the atmosphere are responding to the changes in forcing within a year. This was verified with a lag-correlation analysis that showed no significant time lag between the two.

Table 1. Results of the sensitivity analysis of the correlation values considering the uncertainties of the feedback parameter λ. The correlation values were calculated for the whole time period (1947–2012). Values that are significant at the 5%-level are shown in boldface. λ in W K−1 m−2 1.3 1.5 1.9 2.3 3 Linear warming trend removed Nonlinear warming trend removed AMOC proxy ISHII + Scripps 0.28 0.34 0.40 0.49 0.62 0.62 0.57 EN4 0.45 0.49 0.53 0.57 0.63 0.42 0.39 HadISST 0.01 0.07 0.12 0.22 0.37 0.65 0.61

Our analysis takes the role of radiative forcing in affecting GMST as a given and looks at any additional effect of the AMOC. Alternatively, the internal climate variability can be estimated by removing the warming trend from the original time series. This is the approach taken by Chen and Tung (2018) who removed a nonlinear secular trend (their figure 3) that is very similar to the 100 year linear trend. In the case that we remove either a linear warming trend or a nonlinear trend (using the exact same data as Chen and Tung (2018)) we get even larger positive correlation values with r = 0.62, 0.42, 0.65 for the linear warming trend removed and r = 0.57, 0.39, 0.61 when removing the nonlinear trend (for A ISHIIS+Scripps, A EN4 and A HadISST , see right columns of tables 1 and 2).

Table 2. Results of the sensitivity analysis of the correlation values considering the uncertainties of the feedback parameter λ. The correlation values were calculated for the time period 1975–2012, values in brackets for the time period 1975–1998. λ in W K−1 m−2 1.3 1.5 1.9 2.3 3 Linear warming trend removed Nonlinear warming trend removed AMOC proxy ISHII + Scripps −0.14 0.00 0.14 0.29 0.48 0.84 0.82 (−0.30) (−0.24) (−0.18) (−0.09) (0.03) (0.50) (0.75) EN4 −0.15 −0.01 0.12 0.27 0.47 0.84 0.84 (0.06) (0.11) (0.05) (0.06) (0.11) (0.33) (0.73) HadISST −0.15 −0.02 0.09 0.24 0.43 0.83 0.83 (−0.03) (0.01) (−.08) (−0.07) (−.02) (0.30) (0.68)

Even if we consider only the period after 1975, on which Chen and Tung rested their argument, we find mostly positive correlation values (see table 2). While certain combinations of λ and AMOC proxy yield a negative correlation (especially for smaller values for the feedback parameter), the correlation between AMOC strength and GMST variability is still positive when the radiative forcing is taken into account by removing the linear or nonlinear trend from the data (right columns of table 2).

These results are consistent with several model studies which likewise found a positive correlation with no lag between the AMOC strength and global as well as northern hemisphere temperature (e.g. Knight et al 2005, Maroon et al 2018). It is also in alignment with the fact that the decline of the AMOC over the last decade (Smeed et al 2014), for which direct AMOC measurements exist, coincided with an increase in the rate of ocean heat uptake (figure 2), not a decrease.