Update: (26/09/2019) This paper has now been retracted. The authors says
Shortly after publication, arising from comments from Nicholas Lewis, we realized that our reported uncertainties were underestimated owing to our treatment of certain systematic errors as random errors. In addition, we became aware of several smaller issues in our analysis of uncertainty. Although correcting these issues did not substantially change the central estimate of ocean warming, it led to a roughly four-fold increase in uncertainties, significantly weakening implications for an upward revision of ocean warming and climate sensitivity. Because of these weaker implications, the Nature editors asked for a Retraction, which we accept. Despite the revised uncertainties, our method remains valid and provides an estimate of ocean warming that is independent of the ocean data underpinning other approaches. The revised paper, with corrected uncertainties, will be submitted to another journal. The Retraction will contain a link to the new publication, if and when it is published.
I wanted to just briefly mention the recent paper that [quantifies] ocean heat uptake from changes in atmospheric O2 and CO2 composition, by Resplandy et al. The interesting thing about this paper is that it uses proxies to infer the change in ocean heat content. What it finds is that the change in ocean heat content is probably at the high end of earlier estimates, which are based mostly on direct measurements of ocean temperature.
What this implies is that observationally-based estimates of equilibrium climate sensitivity (ECS) are probably also on the low side. Fortunately, BlueSkiesResearch has already repeated this calculation. Essentially, it increases the lower limit by about 0.1K, the upper limit by about 0.5K, and the median by about 0.2K. This slightly resolves the issue I had with the slightly high TCR-to-ECS ratios that come out of these type of analyses.
However, the paper suggests that this increase in the change in ocean heat content implies a reduction in the carbon budget for staying below 2oC, and I don’t think that is correct. The carbon budget depends mostly on the transient climate response (or the transient response to cumulative emissions). This doesn’t really depend on how much the ocean heat content has changed; it primarily depends on how much we we’ve warmed for a given change in external forcing.
So, I don’t think that this new ocean heat content estimate really implies anything with respect to carbon budgets; I think the main significance is that it is suggests that some observationally-based estimates of equilibrium climate sensitivity are probably too low and that the likely range for equilibrium climate sensivity is still something like 2oC to 4.5oC.
There is now a guest post on Realclimate by one of the authors in which they discuss errors in the uncertainties and in the trend estimate.