How fast is Earth warming?

 From Open Mind (Tamino)

[By 0.3 to 0.4 degrees C per decade]

Another paper has appeared showing an increase in the rate of global warming since about 2011, and using their new rate estimates to forecast when we will pass the 1.5°C and 2°C thresholds of global temperature warned about in the Paris agreement. Since there’s little doubt left that warming accelerated recently, the question becomes “By how much?” Different methods of analysis give different answers, and estimates from this latest research are very high indeed.

After scanning global temperature data sets, they settled on the year 2011 as a “changepoint” when the warming rate increased and estimated its value before and after that. They did so by fitting data from 1970 through 2010, and from 2011 through 2025, separately, using the Theil-Sen slope estimate. It is a robust, non-parametric method which, since it is applied separately to separate time spans, produces a fit which is discontinuous, i.e. at the changepoint time temperature shows a jump as well as a slope change.

Since the pertinent question is “What’s the warming rate since 2011?”, I’ll answer that with three methods. One is a least-squares regression to the data since 2011. Another is the Theil-Sen slope estimate over that same interval (as done in the new paper). Last, I’ll use a PLF (Piecewise Linear Fit) which allows for a slope change but does not allow a jump discontinuity, and it too can be fit by least squares regression. Thus I can use models with and without jump discontinuity at the changepoint time (which I call “L.Sq.” and “PLF”), and here’s what they look like when fit to the global temperature data from HadCRU (yearly averages as black dots, L.Sq. fit as blue line, PLF as red line):

Here’s a close-up on the time since 2011, showing yearly averages (from HadCRU) with both the L.Sq and PLF fits, as well as a dashed line showing the best-fit line estimated by the Theil-Sen method:

From this it’s clear that of the three methods, the PLF gives the lowest slope while the Theil-Sen estimate gives the highest. It’s also worthwhile looking at the uncertainty ranges for all three methods when applied to various data sets; here are the rates for each (blue x’s for L.Sq, black dots for Theil-Sen, red triangles for PLF) and their 95% confidence ranges:

It’s clear that for all four data sets, the highest warming rate estimate comes from the Theil-Sen analysis, the lowest from PLF. It’s also clear that the error bars for PLF cover a smaller range (i.e. the PLF rate estimates are more precise), because the PLF model requires the underlying trend to be continuous across a changepoint. None of which addresses any of the further uncertainties in the problem.

I would emphasize that whatever method is chosen, the uncertainties are sizeable. The global warming rate, even after the recent acceleration, might be merely 0.025°C/yr (0.25°C per decade) or as high as 0.06°C/yr (0.6°C per decade). The high end of that range is more than twice the low end, and if the planet heats up that much then by the year 2050 we’ll not only pass 1.5°C and 2°C, we’ll be well past 2.5°C. Even at the lower end of the range we’ll still cross 2°C by the year 2050.

This does not look good.

We're looking at a rise in global temperatures of somewhere between 0.3 and 0.4 degrees C per decade.  We might be lucky, and it's at the lower end at just 0.25 degrees per decade.  Or unlucky, and it's 0.6 degrees.  If we use the PLF estimate, which is the lowest, we're looking at 0.3 to 0.35 per decade.  We shouldn't assume we're going to get lucky.  Prudence suggests that we assume it'll be at the higher end, and accelerate the roll-out of renewables, EVs, and heat pumps.  And, as I've said before, you can at least cut your own emissions by giving up meat.  And if it isn't at the higher end, good.  Every 0.1 degrees C that global temperatures rise is worth being avoided.