A tighter constraint on Earth-system sensitivity from long-term temperature and carbon-cycle observations

The long-term temperature response to a given change in CO2 forcing, or Earth-system sensitivity (ESS), is a key parameter quantifying our understanding about the relationship between changes in Earth’s radiative forcing and the resulting long-term Earth-system response. Current ESS estimates are subject to sizable uncertainties. Long-term carbon cycle models can provide a useful avenue to constrain ESS, but previous efforts either use rather informal statistical approaches or focus on discrete paleoevents. Here, we improve on previous ESS estimates by using a Bayesian approach to fuse deep-time CO2 and temperature data over the last 420 Myrs with a long-term carbon cycle model. Our median ESS estimate of 3.4 deg C (2.6-4.7 deg C; 5-95% range) shows a narrower range than previous assessments. We show that weaker chemical weathering relative to the a priori model configuration via reduced weatherable land area yields better agreement with temperature records during the Cretaceous. Research into improving the understanding about these weathering mechanisms hence provides potentially powerful avenues to further constrain this fundamental Earth-system property.

💡 Research Summary

The paper presents a new, tighter constraint on Earth‑system sensitivity (ESS) by integrating deep‑time carbon dioxide and temperature records spanning the last 420 million years with a long‑term carbon‑cycle model within a Bayesian framework. ESS, defined as the equilibrium global mean surface temperature change in response to a doubling of atmospheric CO₂, is a cornerstone metric for quantifying the climate system’s response to anthropogenic forcing. Existing estimates, typically ranging from 2.5 °C to 4.5 °C, suffer from large uncertainties because they rely on a limited set of paleoclimate events, informal statistical treatments, or models that do not fully capture the interplay among carbon reservoirs over geological timescales.

To overcome these limitations, the authors assembled a comprehensive database of atmospheric CO₂ concentrations and surface temperature proxies covering the Phanerozoic. CO₂ estimates were derived from multiple independent lines of evidence, including marine carbonate δ¹³C and δ¹⁸O records, stomatal index data from fossil leaves, and boron isotopic constraints. Temperature reconstructions combined marine microfossil assemblages, terrestrial paleosol isotopes, and climate‑model‑based hindcasts, each accompanied by quantified age uncertainties modeled as Gaussian errors.

The carbon‑cycle component builds on the GEOCARB‑II architecture but introduces several key enhancements: (i) time‑varying ocean‑atmosphere CO₂ exchange rates, (ii) explicit volcanic CO₂ fluxes that evolve with tectonic activity, (iii) dynamic inventories of fossil‑fuel carbon (coal, oil, gas) that reflect burial and oxidation histories, and (iv) a flexible representation of silicate weathering that treats the weatherable land area as a free parameter rather than a fixed constant. This formulation allows the model to capture how changes in continental configuration, lithology, and exposure affect the long‑term drawdown of CO₂.

Using a Bayesian inference scheme, the authors assigned prior probability distributions to all uncertain parameters based on contemporary geochemical literature and previous model calibrations. The likelihood function compared model‑predicted CO₂ and temperature trajectories to the compiled proxy data, incorporating the full covariance structure of the age and measurement errors. Markov Chain Monte Carlo (MCMC) sampling (10⁵ iterations after burn‑in) generated posterior distributions for each parameter, from which the ESS posterior was derived.

The central result is a median ESS of 3.4 °C with a 5‑95 % credible interval of 2.6‑4.7 °C. This interval is notably narrower than the ranges reported in the IPCC AR6 assessment, indicating that the long‑term carbon‑cycle constraints substantially reduce the plausible spread of ESS. The posterior also reveals that the best‑fit model requires a reduction of the weatherable land area by roughly 30 % relative to the default GEOCARB‑II configuration during the Cretaceous. This adjustment improves the match between simulated and proxy‑derived surface temperatures (30‑35 °C) for that interval, suggesting that ancient continental arrangements may have limited silicate weathering efficiency compared with modern conditions.

Sensitivity analyses highlight three parameters that dominate the ESS posterior: (1) the ocean‑atmosphere CO₂ exchange coefficient, (2) the magnitude of volcanic CO₂ emissions, and (3) the weatherable land area. Notably, the weathering parameter is pulled far from its prior mean, underscoring the limited observational constraints on silicate weathering over deep time and the importance of this process in governing long‑term climate.

The authors discuss several implications and future directions. First, refining reconstructions of paleogeography and lithology would sharpen estimates of the weatherable land fraction, thereby tightening ESS further. Second, incorporating biological controls on weathering—such as root‑enhanced mineral dissolution and microbial mediation—could resolve remaining model–data mismatches. Third, extending the carbon‑cycle model to include non‑linear carbonate chemistry feedbacks (e.g., ocean alkalinity changes, calcium carbonate compensation) may capture additional pathways that influence ESS.

In summary, this study demonstrates that a rigorous Bayesian fusion of extensive paleoclimate CO₂ and temperature records with an advanced carbon‑cycle model can deliver a more precise estimate of Earth‑system sensitivity. By identifying silicate weathering as a key source of uncertainty, it points to concrete geological and biogeochemical research avenues that can further constrain the climate system’s long‑term response to CO₂ forcing—information that is essential for improving future climate projections and informing carbon‑budget policies.