Quantitative uncertainty analyses of ancient atmospheric CO2 estimates from fossil leaves

The relationship between atmospheric CO~2~ and ancient climate is of fundamental importance for gauging the climate sensitivity of the Earth system to a changing CO~2~ regime. One of the most widely adopted paleobiological CO~2~ proxies for reconstructing Earth9s atmospheric CO~2~ history exploits the inverse relationship between leaf stomatal index, the fraction of leaf epidermal cells that are stomatal structures, and atmospheric CO~2~. However, fossil leaf-based CO~2~ reconstructions make *a priori* assumptions about the form of the empirical relationship between SI and CO~2~ 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 CO~2~ estimate. The utility of our statistical tools is demonstrated by showing how they revise earlier atmospheric CO~2~ 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 CO~2~ reconstructions therefore help to resolve the paradox of warm Paleogene and Neogene "greenhouse" climates co-existing with near present-day levels of CO~2~ 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 paleoCO~2~ estimates from fossil leaves.