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, which grows faster than linear but more slowly than any polynomial of degree greater than one; the other estimates the curvature freely from the data. We report alongside them the quadratic trend used in the recent literature. Over 1970-2025, in a single full-sample test, 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 but rejects in fewer datasets, since estimating the shape costs precision. The linearithmic specification implies the least curvature of the three, with an acceleration that declines over time, and so the lowest warming of the three when extended to 2050.
Versions
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BibTeX
@misc{veravaldes2026detecting,
title = {{Detecting acceleration in global mean temperature using supralinear trends}},
author = {J. Eduardo Vera-Valdés},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.04114},
eprint = {2606.04114},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.04114},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Detecting acceleration in global mean temperature using supralinear trends
AU - J. Eduardo Vera-Valdés
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2606.04114
UR - https://arxiv.org/abs/2606.04114
AB - 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, which grows faster than linear but more slowly than any polynomial of degree greater than one; the other estimates the curvature freely from the data. We report alongside them the quadratic trend used in the recent literature. Over 1970-2025, in a single full-sample test, 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 but rejects in fewer datasets, since estimating the shape costs precision. The linearithmic specification implies the least curvature of the three, with an acceleration that declines over time, and so the lowest warming of the three when extended to 2050.
ER -