Structural Cointegration of the Paleoclimate: Estimating Earth System Sensitivity

TL;DR

This paper tackles the challenge of estimating Earth System Sensitivity (ESS) from paleoclimate data by using a Structural Vector Error Correction Model (SVECM) to disentangle the long-run relationship between temperature and CO2 from short-run fluctuations and orbital forcing. By applying SVECM to high-resolution records from the EPICA Dome C and Vostok ice cores, it identifies a robust cointegrating link between temperature and the natural log of CO2, while conditioning on orbital forcing represented by $N60J$. The estimated ESS is approximately $12.0^\circ$C per CO2 doubling, higher than several previous model-based estimates, and FEVD indicates CO2 shocks account for about 40% of the long-term temperature variance, underscoring CO2’s role as a primary climate engine. These findings imply slow feedbacks and carbon-cycle processes play a stronger role in millennial-scale warming than some earlier assessments suggested, with important implications for long-horizon climate projections and policy planning.

Abstract

Understanding the long-term relationship between atmospheric $CO_2$ and global temperature is fundamental to assessing Earth's climate sensitivity. This study applies a Structural Vector Error Correction Model (SVECM) to paleoclimate records from the EPICA Dome C and Vostok ice cores, spanning the last 800,000 years. By leveraging the statistical property of cointegration, we identify a robust, long-term equilibrium relationship between temperature and log-transformed $CO_2$ concentrations while controlling for orbital forcing ($N60J$). Our results, based on 854 observations, reveal a strong causal link with a long-term coefficient ($β$) of 17.30, characterized by a high level of statistical significance ($z = -3.82$). This corresponds to an Earth System Sensitivity (ESS) of approximately 12.0$^\circ$C per doubling of $CO_2$. Forecast Error Variance Decomposition (FEVD) further demonstrates that $CO_2$ shocks account for approximately 40\% of the long-term temperature variance.

Figures (1)

• Figure 1: Forecast Error Variance Decomposition (FEVD) of Temperature. The blue solid line represents the estimated proportion of temperature variance explained by structural $CO_2$ shocks, which stabilizes at approximately 40% over a 10,000-year horizon (100 steps). Red horizontal lines indicate the reference boundaries at 0 and 1. This result highlights $CO_2$ as a primary driver of long-term climate variability.