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

Affiliations: 1School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623 2Department of Earth and Environmental Studies, Montclair State University, Montclair, NJ 07470 3Department of Earth and Environmental Sciences, Wesleyan University, Middletown, CT, 06459 4Department of Geosciences, The Pennsylvania State University, University Park, PA, 16802 5Earth and Environmental Systems Institute, The Pennsylvania State University, University Park, PA, 16802

*Correspondence to: Tony Wong, aewsma@rit.edu; Ying Cui, cuiy@montclair.edu.

Abstract 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 ℃ (2.6-4.7 ℃; 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.

Introduction Understanding the relationship between changes in atmospheric carbon dioxide (CO2) concentration and global surface temperatures has been a scientific quest for more than a century1. The current uncertainty surrounding this relationship poses considerable challenges for the design of climate change policies2. Of particular interest is the equilibrium response of global mean surface temperature to a doubling of CO2 relative to pre-industrial conditions, termed the “equilibrium climate sensitivity”3 (ECS). The ECS is critical for mapping changes in radiative

2 forcing, including CO2 and other greenhouse gases, to changes in global temperature. ECS is based on “fast” feedback responses to changes in radiative forcing, including changes in water vapor, lapse rate, cloud cover, snow/sea-ice albedo and the Planck feedback4. Even with detailed constraints from the instrumental period, ECS estimates based on the historic record alone are still subject to large uncertainties5–8. Based on the understanding of feedback processes, historical climate and paleoclimate records, a recent summary by Sherwood et al.9 concluded that the most likely range (66% confidence) for the effective sensitivity (defined in terms of the 150-year temperature response to a quadrupling of CO2 forcing in the context of their general circulation model experiments) is 2.6 to 3.9 ºC. Similar to the ECS, the effective sensitivity does not include long-term feedbacks such as ice sheets, vegetation and carbon cycle (ref. 9 and references therein).

In contrast to the shorter-term ECS that responds to relatively fast feedback processes, consideration of longer-term responses offers a glimpse into the deep-time paleoclimate evolution of the sensitivity of the Earth-system temperature response to both fast and slow feedbacks. In particular, a deep-time perspective offers insight into the “Earth-system sensitivity” (ESS) - the long-term equilibrium surface temperature response to a given CO2 forcing, including all Earth- system feedbacks10. Sherwood et al. estimate the ESS as their effective sensitivity multiplied by an inflation factor, (1+fESS), where fESS is sampled from a normal distribution with mean value of 0.5 and standard deviation of 0.2510,11. A growing body of evidence suggests covariations in CO2 and temperature during the last 420 Myrs12. This long-term record enables improved quantification of ESS and insights into factors affecting the climate response across a wide range of climate states, including both icehouse and greenhouse conditions10,13–18. This wide range of states and variations in temperature and CO2 is also important to help distinguish the long-term climate signal from the noise.

Previous studies estimate ESS over geological timescales using varying combinations of global climate models, long-term carbon-cycle models and proxy data for temperature and atmospheric CO2. Royer et al.19 combines a geochemical model and CO2 proxies from the last 420 million years, a

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