Correction to: Nature Geoscience https://www.nature.com/articles/s41561-024-01570-7, published online 25 October 2024.

In the version of the article originally published there was an error within the FluxEngine v4.0.7 software tools in the calculation of the fugacity of CO2 in the atmosphere (fCO2 (atm)). The error caused the fCO2 (atm) to be ~1 μatm higher (~0.2 %) across all the indirect bulk air–sea CO2 flux calculations, which are presented in Fig. 2, Fig. 3, Table 1 and Supplementary Tables 1–3. The error has now been corrected in the latest release of FluxEngine tools (v4.0.9.1), and the figures and table have been corrected in the HTML and PDF versions of the article.

In the revised Fig. 2 the indirect bulk fluxes have subtly changed and these changes are unlikely to be visible to the reader. The mean bias reported in Fig. 2d for the no vertical temperature gradients has been modified from 0.19 mmol m−2 d−1 to 0.37 mmol m−2 d−1, and the vertical temperature gradient bias modified from 0.08 mmol−2 d−1 to 0.26 mmol m−2 d−1. In the revised Fig. 3, similar changes in the reported mean bias values were observed. The original Figs. 2 and 3 and Table 1 are provided here for comparison as Figs. 1 and 2 and Table 1, below.

Fig. 1
figure 1

Original, uncorrected Fig. 2.

Full size image
Fig. 2
figure 2

Original, uncorrected Fig. 3.

Full size image
Table 1 Original, uncorrected Table 1
Full size table

The mean bias changes between the indirect bulk CO2 fluxes with no vertical temperature gradients and those with vertical temperature gradients remain the same. Therefore, the globally scaled modifications of the ocean CO2 sink due to vertical temperature gradients presented in Fig. 1 remain unchanged (as the magnitude of the difference between the ‘no gradient case’ and the ‘with gradient case’ has remained unchanged)1,2.

The conclusions of the article remain robust to this correction and these changes.