Funding for this research was provided by the Science Foundation Arizona Bisgrove Scholar award (BP 0544-13), the National Science Foundation (AGS-1602105 and EAR-1347221), and the State of Arizona Technology and Research Initiative Fund administered by the Arizona Board of Regents. We acknowledge support by the USGS Climate and Land Use Program (any use of trade, product or firm names is for descriptive purposes only and does not imply endorsement by the US government). H.G. is Research Director at the Fonds de la Recherche Scientifique–FNRS (Belgium). We thank D. Coumou and USGS reviewers M. Robinson and T. Cronin for comments on the manuscript. This work benefited from the new compilation of proxy temperature records for the past 2,000 years that was led by the Past Global Changes (PAGES) project, and from discussions with colleagues at PAGES-sponsored workshops. We thank all original data contributors who made their data available. We also thank the leaders of, and the many contributors to, the data compilations that were integrated in this study.

Reviewer information

Nature thanks Matthew Kirby, Fredrik Charpentier Ljungqvist and the other anonymous reviewer(s) for their contribution to the peer review of this work.