Fig. 1: Uncertainties of the restoring rate λ for sea-surface-temperature-based fingerprints.

Significance of trend in the restoring rate λ of subpolar gyre Atlantic Meridional Overturning Circulation (AMOC) index in HadSST4 (a, d, g, j), HadCRUT5 (b, e, h, k) and ERSSTv5 (c, f, i, l). a, b, c Median (mean) AMOC index (black) and min-max range (turqouise) of 20000 samples (200 and 1000 ensemble members) for HadSST4 (HadCRUT5 and ERSST). We use the mean instead of the median for HadCRUT5 as that is the default product a user would download when not investigating uncertainties, and for ERSSTv5 we use the operational data product (see main text). d, e, f Same as (a, b, c) but for the λ of the AMOC indices, computed using a window size of 60 years. g Distribution (orange) of linear trends of λ computed from 100 Fourier surrogates for each AMOC index sample from HadSST; distribution (turquoise) of linear trends of λ of samples from HadSST4 with a fitted gausian distribution (solid black). The linear trend of the median HadSST4 index is shown in dashed black. f, i Same as e but for HadCRUT5 and ERSSTv5, using 1000 fourier surrogates (FS) of the ensemble member AMOC indices, and the linear trend of the mean and operational data. j p-value of linear trend of λ of each sample of the HadSST4 AMOC index with respect to its own 100 Fourier surrogates. The p-values of the median with respect to 10000 Fourier surrogates is shown as a dashed black line, and the 0.05 significance value is shown as a solid grey line. k, l Same as g but for the AMOC index of the HadCRUT5 (ERSST) ensemble members, with the p-value of the mean (operational) AMOC index as a dashed black line.