This is a Preprint and has not been peer reviewed. The published version of this Preprint is available: https://doi.org/10.31223/X53V2Q. This is version 3 of this Preprint.
Stable estimates of when global temperature thresholds will be crossed: least-squares fits as the end date of the fitted span is reduced
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Authors
David Joseph Hendy 
Abstract
Estimates of when global mean temperature will reach 2°C above the 1850–1900 mean are generally derived from emissions scenarios and climate models rather than from the observed temperature record itself. This study does the latter by progressively truncating observed temperature records at their most recent end and fitting different curve types to fixed-width spans. It examines both the coefficient of determination across the complete record from 1850 to 2026 and the standard deviation of the projected year in which the fitted curves cross 2°C. Exponential, quadratic and linear curves were fitted to monthly temperature anomalies from the HadCRUT5, NASA GISS v4 and NOAA v6.1 datasets. When looking at the crossing year, fitting spans ranged from 20 to 150 years for HadCRUT5 and NOAA, and from 20 to 120 years for NASA. In total, 1,089 combinations of dataset, curve type and fitting span were evaluated for truncation end years from 2020 to 2000. Of the three curves the exponential consistently gave the best fit and the HadCRUT5 dataset using an exponential gave the most stable 2°C crossing date. The projected crossing dates presented in this study depend on three conditions: first, that the observed temperatures accurately reflect actual temperatures; second, that the fitted trajectory adequately represents the observed trajectory; and third, that the temperature trajectory in the next 10 years continues to follow the temperature trajectory observed in the last 100 or so years. Provided these conditions are met, the most stable 2°C crossing estimates identified in this analysis are 2041 using a 148-year fitting span and 2035 using a 96-year fitting span.
DOI
https://doi.org/10.31223/X53V2Q
Subjects
Climate, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics
Keywords
HadCRUT5, global warming, temperature anomaly, exponential fit, 1.5°C, 2°C, Paris Agreement, climate projections, least squares, temperature threshold
Dates
Published: 2026-07-07 20:51
Last Updated: 2026-09-25 16:03
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License
CC BY Attribution 4.0 International
Additional Metadata
Conflict of interest statement:
None
Data Availability:
Temperature crossings were estimated using Python code downloadable from https://doi.org/10.5281/zenodo.21201587. This code reads three datasets of observed temperature anomalies compiled by the Met Office, NASA and NOAA from https://doi.org/10.5281/zenodo.20588286, https://doi.org/10.5281/zenodo.20679028 and https://doi.org/10.5281/zenodo.20682032 respectively. This code also created x-y plots and added these plots to PDF documents. These documents are downloadable from https://doi.org/10.5281/zenodo.20699641 as ZIP files.
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