Detecting acceleration in global mean temperature using supralinear trends
Abstract
Whether global mean surface temperature has accelerated has received opposite answers in quick succession, reported as undetectable on data to 2023 and as significant on data to 2024. This raises two questions: since when is acceleration detectable, and how far does the answer depend on the test used? We show that structural-break tests, often used for this purpose, cannot reliably date the onset of a continuously accelerating warming rate. We therefore test for curvature directly, under specifications whose null is exactly a constant warming rate and whose alternative is curvature rather than a break. One is a linearithmic trend, a lower bound for the supralinear polynomial class; the other estimates the curvature freely from the data. We report alongside them the quadratic trend used in the recent literature. Over 1970–2025, the linearithmic and quadratic coefficients are positive and statistically significant in all five major temperature datasets once El Niño and solar variability are controlled for. The onset of acceleration is dated by re-estimating over expanding windows and correcting for multiple testing. Under the linearithmic specification, acceleration first becomes detectable in windows ending in mid-2023 for NOAA, late 2023 for GISTEMP and mid-2024 for ERA5, and not yet in HadCRUT or Berkeley. The free-curvature specification agrees on direction and on which datasets show the acceleration most strongly, but rejects in fewer of them, since estimating the shape costs precision. Among the three specifications the linearithmic implies the least curvature, so the acceleration it reports, and the warming that follows from extending it to 2050, are the lowest of the three, a conservative basis for policy.
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A previous version of the paper was circulated under the title “Global warming has been accelerating since at least 1990” and is available on ArXiv here.
Recommended citation
Vera-Valdés, J. Eduardo. 2026. “Global Warming Has Been Accelerating Since at Least 1990.” arXiv (2606.04114).
@article{VeraValdes2026acceleration,
title = {Global Warming Has Been Accelerating Since At Least 1990},
author = {Vera-Vald{\'e}s, J. Eduardo},
journal = {arXiv (2606.04114)},
year = {2026},
doi = {10.48550/arXiv.2606.04114},
url = {https://arxiv.org/abs/2606.04114}
}