The original article has been published online with 2 errors. The errors have been corrected as below: 1. The definition of pre-industrial oceanic potential oxygen(OPOpi) given in Eq. (7) reads: OPOpi=O2*+1.1 × Cpi* but should appear as: OPOpi=O2*+1.1 × Cpi*-(1/XN2)×N2 where O2* and Cpi* are the quasi-conservative ocean tracer concentrations tracking air–sea exchanges of O2 and pre-industrial CO2, N2 is the dissolved N2 ocean concentration and XN2 is the atmospheric mole fraction of N2 (XN2 = 0.7808). This definition of OPOpi and the OPOpi data shown on Fig. 1 therefore include the changes in OPO due to air–sea fluxes of O2 and pre-industrial CO2 but also due to the thermally driven air–sea fluxes of N2, which are important for understanding changes in pre-industrial atmospheric potential oxygen (APOpi). Including the N2 contribution makes OPOpi a mirror tracer of APOpi across the air–sea interface, i.e. with equivalent air–sea fluxes. The data based OPOpi to potential temperature ratio derived from Fig. 1 includes the N2 contribution and is equal to -3.9 nmol/J. Note that without the N2 contribution, this ratio would equal -4.4 nmol/J. 2. In Table 1, the isopycnal defining the base of the thermocline reads σθ = 24.7 and should read σθ = 27.4. © Springer-Verlag GmbH Germany 2017.