Text S2.
Autocorrelation of WCTH
Much of the autocorrelation in WCTH is dominated by the ENSO cycle, which has been found to have decorrelation times between 6 and 10 months (Berner et al., 2020; Burgers & van Oldenborgh, 2003). Autocorrelation functions of WCTH are shown in Figure S3 where it can be seen that in each of the five latitude bands the autocorrelation is well below the e-fold point (indicated by the red line) within 12 months lag.
Sensitivity tests were performed to determine what block length is acceptable. In the tropics the moving block resampling scheme was applied to the WCTH averaged over the tropics (the region with the latest decorrelation) using 6-, 12-, 24-, and 48-month block lengths. There is no significant difference using a block length of 24 or 48 months, however results based on lengths below 24 months differ substantially, and so a block length of 2 years was used for all results shown in the main text.
Berner, J., Christensen, H. M., & Sardeshmukh, P. D. (2020). Does ENSO regularity increase in a warming climate? Journal of Climate ,33 (4), 1247–1259. https://doi.org/10.1175/JCLI-D-19-0545.1
Burgers, G., & van Oldenborgh, G. J. (2003). On the impact of local feedbacks in the central Pacific on the ENSO cycle. Journal of Climate , 16 (14), 2396–2407. https://doi.org/10.1175/2766.1