My paper with Stefan Rahmstorf showing that global warming has accelerated was published in Geophysical Research Letters today. The main result is that global warming is NOT proceeding at the same old rate it has been since 1975. It’s going faster.

The Guardian has a good article about it. It points out that our estimate is faster than that of other experts, and quotes some of them who express caveats. Honestly, I agree with most of their caveats — I think that the rate over the last 10 years is quite high but isn’t likely to sustain for very long. The truly important point is what we and (almost) all seem to agree on: that the warming rate really has increased. The latest year’s data — which didn’t make it into our study — only strengthens that conclusion.

We have another year’s data since the analysis was done, so I retrieved updated data and repeated the analysis to include the year 2025. We studied data from five sources: NASA (the Goddard Institute for Space Studies), NOAA (National Oceanic and Atmopsheric Administration), HadCRU (the Hadley Centre/Climate Research Unit in the U.K.), Berkeley (Berkeley Earth Surface Temperature project), and ERA5 (reanalysis data from C3S, the Copernicus Climate Change Service in Europe). I’ve transformed their numbers to “warming since pre-industrial times,” which is what we seek to keep below 2°C, and here is a graph of yearly average temperature since 1880 for data from Berkelely Earth:

In this data set, 2025 turned out to be the 3^rd-warmest year on record (as in the other data sets except NASA, where it came in 2^nd). When I adjust the data to remove the estimated impact of el Niño, volcanic eruptions, and solar variation, I get this:

The trend is unaffected, but the noise level is much reduced, which emables us to estimate warming rates with less uncertainty. I’ve added a red line to this graph which is a modified lowess smooth of the adjusted data.

To test for acceleration we isolated the data since 1975, and the simplest way to test for it is to fit a parabola to the data; if the quadratic term is statistically significant, we can reject the null hypothesis, that the signal is just a straight line. Of course we must correct for autocorrelation of the noise, but still the quadratic term turns out to be strongly significant. We can safelly reject the null hypothesis, there has been acceleration.

According to this model, the warming rate right now is the slope at the endpoint of the parabola, which is 0.28 ± 0.05 °C per decade (i.e. between 0.23 and 0.33 °C per decade, 95% CI). I will emphasize that this is the “best estimate” and those are the correct uncertainty levels IF (and this is a BIG IF) the data actually follow a parabola plus stationary noise. If not (which is the overwhelmingly likely case), we can consider the estimate good but not best, and the uncertainty levels are a lower bound on the actual uncertainty.

Another test for acceleration is to find the best fit of a continuous piecewise-linear function which is allowed to change slope at a time chosen by changepoint analylsis. This is a challenge to evaluate statistically because we have to allow for autocorrelation and account for the extra degree of freedom to choose the changepoint time. But it can be done, and the best-fit model again turns out to be strongly statistically significant.

This time the estimated warming rate during the last leg of the journey is a whopping 0.38 ± 0.07 °C per decade. Again, this is the “correct” estimate and uncertainty only if the data actually are a continuous piecewise-linear function plus stationary noise, with a slope change at that one particular time.

Both those models serve excellently to demonstrate the presence of acceleration. But I doubt they are best to estimate what the warming rate is right now, and what it will be in the near future. For that, I offer yet another model, which I will apply to the data since 1880, a continuous piece-wise linear fit (PLF) which is allowed to change its slope every 15 years from 1905 through 2010. I call this model “PLF15”

The PLF15 model not only estimates the signal value, it conveniently gives us an estimate of the average warming rate over each segment between the knots. I can plot the warming rate itself (which for this model is constant during each segment) along with light blue shading to show the uncertainty range.

All these graphs plot the warming rate in °C per year, but when quoting numbers I have followed the custom these days to talk about the rate in °C per decade. According to this analysis, the current estimated rate is 0.31 ± 0.07 °C/decade.

Which estimate is best? I don’t know, but I do know that even 0.24 °C per decade will take us past 2 °C right around the year 2050. The whole point of the Paris agreement is: DON’T GO THERE. My advice: fasten your seat belt, things are going to get ugly.

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