In this Article, a coding mistake occurred when calculating \(-\frac{\Delta \,\mathrm{ln}\,{\rm{COD}}}{\Delta \,\mathrm{ln}\,{R}_{{\rm{e}}}}\)and \(\frac{\Delta \,\mathrm{ln}\,{\rm{LWP}}}{\Delta \,\mathrm{ln}\,{\rm{CDNC}}}\), in which COD denotes the cloud optical depth; R e denotes the cloud droplet effective radius; LWP denotes the liquid water path; and CDNC denotes the cloud droplet number concentration. The natural logarithm of those cloud properties was mistakenly taken before, instead of after, calculating the track segment average. The mistake has been corrected in Figs. 3b, 4, 6 and Extended Data Tables 2, 4 of the original Article, and the incorrect, published figures and tables are shown as Figs. 1–5 of this Amendment, for transparency to readers. The conclusions of the paper, including the main conclusion that changes in cloud water caused by aerosols exert a weak climate-warming effect, and all other figures and tables, are not affected.

Fig. 1 This figure displays the corrected and the incorrect published Fig. 3b of the original Article. Full size image

Fig. 2 This figure displays the corrected and the incorrect published Fig. 4 of the original Article. Full size image

Fig. 3 This figure displays the corrected and the incorrect published Fig. 6 of the original Article. Full size image

Fig. 4 This figure displays the corrected and the incorrect published Extended Data Table 2 of the original Article. Full size image