Quantitative uncertainty analyses of ancient atmospheric CO2 estimates for fossil leaves

The relationship between atmospheric CO2 and ancient climate is of fundamental importance for gauging the climate sensitivity of the Earth system to a changing CO2 regime. One of the most widely adopted paleobiological CO2 proxies for reconstructing Earth's atmospheric CO2 history exploits the inverse relationship between leaf stomatal index, the fraction of leaf epidermal cells that are stomatal structures, and atmospheric CO2. However, fossil leaf-based CO2 reconstructions make a priori assumptions about the form of the empirical relationship between SI and CO2 required for transfer functions and have failed to correctly propagate error terms. These effects can translate into erroneous interpretations that undermine the value of the proxy. Here we report the development and application of a rigorous generalized statistical framework overcoming these limitations that generates probability density functions for each atmospheric CO2 estimate. The utility of our statistical tools is demonstrated by showing how they revise earlier atmospheric CO2 estimates from fossil cuticles of Ginkgo and Metasequoia trees during the early Eocene and middle Miocene warm periods upwards by +150 to 250 ppm to 450 to 700 ppm. The revised CO2 reconstructions therefore help to resolve the paradox of warm Paleogene and Neogene "greenhouse" climates co-existing with near present-day levels of CO2 and support the emerging view from independent paleoclimate studies for a high climate sensitivity of the Earth system. The statistical tools presented are sufficiently versatile to permit their use in other investigations of paleoCO2 estimates from fossil leaves