Improving Paleosol‐Based Atmospheric CO ₂ Reconstruction via Joint Proxy Inversion

Abstract The carbon isotopic composition of pedogenic carbonate (δ 13 C c ) is a widely used proxy for paleoatmospheric CO 2 levels. However, the estimated CO 2 is often highly uncertain due to the lack of constraints on other variables that influence this system. To improve paleosol‐based CO 2 reconstructions, here we propose the Joint Proxy Inversion (JPI) of a paleosol‐based proxy system model, which integrates various proxies (e.g., pedogenic carbonate δ 13 C and δ 18 O) that share sensitivities to common environmental parameters (e.g., CO 2 , precipitation) via a forward proxy model in a Bayesian hierarchical framework. JPI generates self‐consistent posterior distributions of environmental parameters conditioned on multi‐proxy data sets while accounting for proxy and model uncertainties. The JPI was applied to data from Quaternary loess deposits from the Chinese Loess Plateau to test its performance. Sensitivity tests and posterior CO 2 estimates suggest insensitivity of proxy values to CO 2 when the analysis integrates δ 13 C, δ 18 O c , and clumped isotope values of pedogenic carbonates only. Improved results were achieved after incorporating a precipitation‐sensitive proxy, a model component representing environmental variation as a function of time, and a parameterized relationship between global temperature and CO 2 . The improved model performance is indicated by agreement between posteriors of environmental parameters (i.e., CO 2 , temperature, precipitation) and other independent records. Compared to the traditional proxy interpretation approach, the paleosol‐JPI offers a more holistic and rigorous way to interpret multi‐proxy records with shared environmental sensitivities, provides additional information on climate and environmental systems, and is capable of reconstructing paleo‐CO 2 levels with higher precision and fidelity.