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. 2024 Sep 25;634(8034):600–608. doi: 10.1038/s41586-024-07985-x

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© The Author(s) 2024

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

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Extended Data Fig. 4 — (a) Scatter plot between residuals and fitted values in the linear regression, (b) Q-Q plot of the standardized residuals, (c) scatter plot between standardized residuals and fitted values, and (d) scatter plot between standardized residuals and leverage values. The vertical dashed line indicates the Cook’s distance in panel (d). The comparison is shown for both high- and low-frequency variability, after applying a 20-year smoothing spline. In panel (e), r represents the Pearson correlation coefficient between reconstructed and instrumental EU JSL. For the low-frequency series, the level of significance is not provided since the effective degrees of freedom were not adjusted. Panel (f) shows a complementary cross-wavelet coherency analysis between instrumental and reconstructed summer EU JSL. Instrumental data is derived from the NCEP/NCAR reanalysis product.