Phase-space visualization of global warming data (Preprint)

Abstract: Global mean surface temperature anomalies are commonly analyzed using trends, warming rates, and accelerations derived from one-dimensional time series. In this article we introduce a complementary geometric perspective by representing the historical temperature record in phase space. Using four major observational temperature datasets and multiple smoothing approaches, we reconstruct smooth temperature trends T together with their first and second temporal derivatives (T', T''), yielding trajectories in the three-dimensional (T, T', T'') phase space that jointly encode temperature level, warming rate, and acceleration. Across datasets and methods, the reconstructed trajectories exhibit a coherent large-scale geometric structure: an early loop-like excursion followed by a persistent drift-like regime in which both warming rate and acceleration occupy predominantly positive regions of phase space. Within the tested ensemble of regularized reconstructions, the observed phase-space structure is stable across dataset choice, smoothing framework, and parameter variation, indicating that it reflects a robust descriptive feature of the reconstructed temperature record rather than the outcome of a single smoothing procedure. These results show that phase-space representations make the joint organization of temperature, warming rate, and acceleration explicit, providing a compact and informative diagnostic for analyzing long-term climate evolution. Open Access Data: https://doi.org/10.5281/zenodo.17447485