Comment on 'On the relationship between Atlantic meridional overturning circulation slowdown and global surface warming'

The recent Environmental Research Letters article by Caesar, Rahmstorf and Feulner (hereafter CRF) is essentially a Comment on our Nature paper (Chen and Tung 2018 Nature 559 387-91), but without an accompanying rebuttal from us. In this unusual format for the exchange outside Nature, our rebuttal then becomes a Comment here at Environmental Research Letters. Our original proposal that the rate of global warming is enhanced by a weak Atlantic Meridional Overturning Circulation (AMOC) remains valid and is strengthened with this exchange. CRF used "established evidence" to argue against our finding, but such evidence is either misapplied (i.e. applying model results from preindustrial control runs with constant greenhouse gasses to the industrial era with increasing greenhouse gasses), or misinterpreted (i.e. climate model results for the industrial era specifically for the trends interpreted as for the AMOC cycles). While we used the observed energy budget to show that a strong (weak) AMOC transports more (less) heat to below 200 m, CRF replaces the actual budget with a simple energy-balance equation. They used an inappropriate equilibrium approximation to their simple equation to argue that global mean surface temperature (GMST) and AMOC should be in phase. We show here that the exact solution to that same equation actually supports our claim on the relationship between the rate of change of GMST and the AMOC state, which they misunderstood as we claiming a negative correlation between GMST and AMOC themselves. They claimed, incorrectly, that a positive correlation coefficient, no matter how small and even though none of them is statistically significant, is strong evidence that the two time series are in phase. The correlation coefficients that they found using observational data (0.01, 0.28 and 0.45), though positive, correspond to 89 degrees, 74 degrees, 63 degrees out of phase, far from being in-phase. Visually they were made to look somewhat in-phase with decadal smoothing and short-period detrending. Both model and observational evidence supports the conclusion of our original paper that the period of AMOC minimum is a period of rapid rate of surface warming.