Is the Carbon Budget for 1.5 Degrees Much Larger than We Thought?

An article in Nature Geoscience by Millar et al. on carbon budgets has attracted a lot of attention and debate.* A blogpost by the lead author explains that current human-induced warming has increased in the 2010's by 0.93C over the the 1861-1880 period, while the mean CMIP5 climate model run projected that given cumulative carbon emissions to date the temperature should be 0.3C warmer than that. They argue that that means that the remaining carbon emissions budget allowed for staying within a 1.5C increase in temperature is larger than previously thought as we have 0.6C to go at this point rather than 0.3C. I think there a number of issues with this claim.

First, the value for human-induced warming is based on averaging the orange line in this graph:

The orange line is derived by fitting estimated radiative forcing to observed temperature given by the HADCRUT4 dataset by regression. HADCRUT4 shows less increase in surface temperature than either the GISS or Berkeley Earth datasets because of how it covers the polar regions, in particular.
Using the Berkeley Earth dataset, the temperature increase from the 1861-80 mean to the 2010's mean – shown by black lines in this graph:

is 1.1C. As you can see, even that increase is assuming that conditions during the "hiatus" are more usual than those during the post-2014 increase in temperature. 0.93C is a very conservative estimate of warming to date. Though the recent period was affected by El Nino conditions, it's possible that it represents catching up to the long term trend rather than an excursion above the trend. Throughout the hiatus period ocean heat content was increasing. I do think it is likely that the jump in temperature in the last two years is a recoupling of surface temperature to this more fundamental trend. We have a paper under review that supports this view.**

Also, I think that averaging the orange trend line in the previous graph definitely is too conservative given the strongly non-stationary behavior of the trend. The most recent estimate of the trend would be a better guess.

Second, I think there are a few reasons*** why we might update the carbon budget (as measured from the beginning of the Industrial Revolution):

1. Our estimate of the transient climate sensitivity changes – we think that the short-run temperature for a given concentration of carbon dioxide in the atmosphere is higher or lower than we previously thought.

2. Our estimate of the airborne fraction changes – our estimate of the amount by which the carbon dioxide in the atmosphere increases in reaction to a given amount of emissions changes. CO2 in the atmosphere has increased by about half cumulative emissions.

3. Our estimate of non-CO2 forcing changes. There are important other sources of radiative forcing such as methane and sources of negative forcing such as sulfate aerosols.

Observations of warming to date, isn't one of these. So the paper is implicitly saying that these observations lead them to reduce their estimate of the climate sensitivity.

Third, though the paper says that Earth System Models overestimated warming to date, it seems that the authors use the same models to estimate the remaining carbon budget.

* I have extensively revised this post following a comment from Myles Allen, one of the paper's authors. Also, I realized that the second part of the post didn't really make much sense, so I deleted it.

** The paper has been in review since February, but we haven't posted a working paper, as one of my coauthors didn't want to do so before receiving referee comments.

*** The emissions path also affects the carbon budget as we can see from the mean values for the various RCP paths in the graph below from Millar et al. and the difference between the red plume of RCP paths and the grey plume which are paths where emissions grow at a constant 1% per annum rate. The slower we release carbon, the bigger the budget.