Robust warming rates, marginal evidence of acceleration and unstable extrapolation: a reproducible reanalysis of statistical trend models for the Berkeley Earth global temperature record
Abstract
Simple trend fits to the global temperature record are widely used to summarise warming, but their uncertainty, their evidence for acceleration and their predictive value are often overstated. We re-analysed an earlier linear and quadratic analysis of the Berkeley Earth Land/Ocean record (1850–2024) that reported in-sample R² values of 0.74 and 0.90 and a post-1970 warming rate of 0.194 °C per decade. The original results reproduced exactly, but the parser averaged the two sea-ice versions contained in the data file, lowering recent anomalies by about 0.06 °C. With the recommended version, the 1970–2024 rate is 0.206 ± 0.022 °C per decade (95%, AR(1)-adjusted), consistent across HAC, GLS and monthly ARMA(1,1) estimates and with NASA GISTEMP (0.199) and HadCRUT5 (0.202). Berkeley Earth's observational uncertainty and individual warm years change this rate by less than 0.015 °C per decade; the choice of start and end years matters more. A continuous hinge fitted to 1970–2024 places a rate increase of 0.176 °C per decade in 2013, but a sup-F test with a simulated AR(1) null gives p = 0.064; p was at least 0.23 for every end year from 2000 to 2023, and fixing the break at 2010 after inspecting the data gives a misleading nominal p = 0.006. With current noise levels, increases below about 0.20 °C per decade beginning in 2010 are not reliably detectable by 2024. In rolling-origin retrospective forecasts, every method under-predicted later warming and nominal 90% intervals from the quadratic and 30-year linear trends covered only 0.38–0.53 of 30-year outcomes. The quadratic's extrapolated 2100 anomaly ranged from 1.58 to 3.69 °C depending on the last year fitted, and from 1.16 to 16.43 °C across polynomial degrees 1–5. Trend fits describe the observed record well but provide no defensible long-range forecast.
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BibTeX
@misc{mestry2026robust,
title = {{Robust warming rates, marginal evidence of acceleration and unstable extrapolation: a reproducible reanalysis of statistical trend models for the Berkeley Earth global temperature record}},
author = {Arav Siddharth Mestry},
howpublished = {EarthArXiv},
year = {2026},
month = oct,
doi = {10.31223/x5c529},
url = {https://eartharxiv.org/repository/view/15639/},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Robust warming rates, marginal evidence of acceleration and unstable extrapolation: a reproducible reanalysis of statistical trend models for the Berkeley Earth global temperature record
AU - Arav Siddharth Mestry
PY - 2026
DA - 2026/10/21
PB - EarthArXiv
DO - 10.31223/x5c529
UR - https://eartharxiv.org/repository/view/15639/
AB - Simple trend fits to the global temperature record are widely used to summarise warming, but their uncertainty, their evidence for acceleration and their predictive value are often overstated. We re-analysed an earlier linear and quadratic analysis of the Berkeley Earth Land/Ocean record (1850–2024) that reported in-sample R² values of 0.74 and 0.90 and a post-1970 warming rate of 0.194 °C per decade. The original results reproduced exactly, but the parser averaged the two sea-ice versions contained in the data file, lowering recent anomalies by about 0.06 °C. With the recommended version, the 1970–2024 rate is 0.206 ± 0.022 °C per decade (95%, AR(1)-adjusted), consistent across HAC, GLS and monthly ARMA(1,1) estimates and with NASA GISTEMP (0.199) and HadCRUT5 (0.202). Berkeley Earth's observational uncertainty and individual warm years change this rate by less than 0.015 °C per decade; the choice of start and end years matters more. A continuous hinge fitted to 1970–2024 places a rate increase of 0.176 °C per decade in 2013, but a sup-F test with a simulated AR(1) null gives p = 0.064; p was at least 0.23 for every end year from 2000 to 2023, and fixing the break at 2010 after inspecting the data gives a misleading nominal p = 0.006. With current noise levels, increases below about 0.20 °C per decade beginning in 2010 are not reliably detectable by 2024. In rolling-origin retrospective forecasts, every method under-predicted later warming and nominal 90% intervals from the quadratic and 30-year linear trends covered only 0.38–0.53 of 30-year outcomes. The quadratic's extrapolated 2100 anomaly ranged from 1.58 to 3.69 °C depending on the last year fitted, and from 1.16 to 16.43 °C across polynomial degrees 1–5. Trend fits describe the observed record well but provide no defensible long-range forecast.
ER -