The Kinematics of Global Warming: Semiparametric Analysis of Warming Level, Rate, and Acceleration

Abstract

Three features of the global warming process are of central scientific interest: its level, its warming rate, and changes in that warming rate. We develop a semiparametric kinematic state-space framework for estimating the latent kinematic path of global warming from noisy monthly temperature observations. The framework estimates the warming level, warming rate, and warming acceleration jointly, while incorporating covariates, serial dependence, and time-varying error variance directly in the model. Applying the framework to five major global temperature records, and comparing it with nonparametric kernel and parametric benchmark estimators, we show that the inferred recent warming dynamics depend strongly on the object being estimated. The current underlying warming level is estimated precisely and is robust across datasets and methods, with estimates close to 1.4 °C above pre-industrial levels. Estimates of the current warming rate are consistently positive and elevated, but differ materially across estimator classes: flexible local estimators imply substantially higher current rates than long-window parametric specifications, which instead summarize average post-break or restricted-curvature behaviour. Our preferred state-space specification estimates the current warming rate at approximately 0.47 °C per decade. Evidence on acceleration is necessarily more uncertain, because acceleration is a local second derivative. Nevertheless, the estimated kinematic paths show positive acceleration in the recent period, and the endpoint acceleration estimates are positive across datasets and methods.

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Recommended citation

Text

Bennedsen, M., and J. Eduardo Vera-Valdés. 2026. “The Kinematics of Global Warming: Semiparametric Analysis of Warming Level, Rate, and Acceleration.” arXiv (2608.18298).

BibTex

@article{Bennedsen2026,
      title={The kinematics of global warming: Semiparametric analysis of warming level, rate, and acceleration}, 
      author={Mikkel Bennedsen and J. Eduardo Vera-Valdés},
      year={2026},
      eprint={2608.18298},
      doi={10.48550/arXiv.2608.18298},
      url={https://arxiv.org/abs/2608.18298}, 
}