Nature Geoscience 6, 661–667 (2013); published online 28 July 2013; corrected after print 27 November 2014.

In the version of this Article originally published, in two places a typographical error led to the wrong value appearing for solar radiation absorbed; it should have read 286 W m−2 throughout. The incorrect value was not used in calculations.

There was a small error in our summation of solar fluxes at different zenith angles in the version of our numerical model used to make Fig. 4. As a result, our model yielded net solar flux values that were a few W m−2 too high. We reran our numerical simulations with the corrected calculation of solar fluxes. An updated model output archive is provided in the Supplementary Information. A version of Fig. 4 that accounts for the correction and updated model outputs is reproduced below (no other figures are affected). The only qualitative difference is that the scenario with the greenhouse gas atmosphere labelled as arbitrarily high (purple) has a marginally stable state at around 340 K in the updated version of Fig. 4f. Increasing the amount of carbon dioxide in the model reduces the outgoing thermal radiation (Fig. 4e), but has negligible effect on the net absorbed solar radiation (Fig. 4d), so more carbon dioxide would remove this small stable region.

As a result of the updated model outputs, in the 'Transition to a runaway greenhouse' section, paragraph four, the top of atmosphere solar and thermal fluxes should have read 260 and 265 W m−2. In the last paragraph of this section, the values for the hump of stability for pre-industrial, RCP 8.5 at 2100 and extreme anthropogenic scenarios should have read 27, 20 and 12 W m−2, respectively.

These errors have now been corrected in the online versions of the Article. None of the errors affect the conclusions or implications of the paper.