Correction to: Nature https://doi.org/10.1038/s41586-019-1423-9Published online 31 July 2019

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; Re 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. 15 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.

The correction has minor effects on the results of the paper, which remain qualitatively the same. The radiative forcing exerted by LWP adjustments is now estimated at +0.15 W m−2, instead of +0.12 W m−2. Consequently, the observed decrease in cloud water now offsets 29%, up from 23%, of the global climate-cooling effect caused by aerosol-induced increases in the concentration of cloud droplets. In addition, the y-axis label in Fig. 4 should be ΔlnLWP/ΔlnCDNC without a minus sign. The original Article has been corrected online.