Stable estimates of when global temperature thresholds will be crossed: least-squares fits as the end date of the fitted span is reduced

David Joseph Hendy

Reliable estimates of when global mean temperature will exceed the Paris Agreement's 2°C threshold¹ are generally derived from emissions scenarios and climate models rather than from the observed temperature record itself. This study investigates whether the observed warming trajectory alone can provide a stable empirical estimate of the crossing date. Least-squares exponential, quadratic and linear curves were fitted to monthly global temperature anomalies from the HadCRUT5, NASA GISS v4 and NOAA v6.1 datasets over fitting spans ranging from 20 to 150 years for the HadCRUT5 and NOAA datasets and from 20 to 120 years for the NASA dataset. In total, 1,089 combinations of dataset, curve type and fitting span were evaluated. For each combination, predicted 1.5°C and 2°C crossing dates were recalculated as the fitted record was progressively truncated by one month at a time from 2026. Standard deviations of the 2°C crossing dates were then calculated after truncation had reached each final year between 2020 and 2000. Exponential fits using the HadCRUT5 dataset using fitting spans of approximately 148 and 96 years accounted for most of the lowest-standard-deviation solutions. Assuming (a) these fitted trajectories adequately represent the underlying warming trend, (b) the temperature datasets accurately reflect global mean temperature, and (c) recent warming behaviour continues, the analysis projects a 2°C crossing around 2041 for the longer span and 2035 for the shorter span.