We thank M. Anderson, M. Auffhammer, D. Baldocchi, K. Caldeira, C. Field, A. Goldstein, D. Keith, P. Huybers, R. Kopp, D. Lobell, K. Ricke, J. Sallee and seminar participants at Berkeley, Chicago, Columbia, Cornell, Harvard, Johns Hopkins and Stanford universities, the Massachusetts Institute of Technology and the Allied Social Science Association Annual Meeting for useful comments. We thank I. Bolliger for his contributions to the project and all the members of the Global Policy Laboratory for their valuable feedback. We thank L. Thomason for generously sharing SAOD data used in Fig. 1a–c. This material is based upon work supported by the National Science Foundation Grant No. CNH-L 1715557 and the National Science Foundation Graduate Research Fellowship under Grant No. DGE 1752814.

Reviewer information

Nature thanks L. Gu and the other anonymous reviewer(s) for their contribution to the peer review of this work.