Joint Proxy Inversion for Robust Paleoenvironmental Reconstruction

Traditional interpretations of paleoclimate proxies are based on the errant inversion of conditional probabilities. As a consequence, the resulting climate reconstructions fail to formally consider proxy response to alternative forcing factors, giving biased estimates of uncertainty in these reconstructions. We argue that proxy reconstruction is more appropriately posed as a Bayesian inversion of the response functions that are the typical product of proxy calibration studies. This requires developing proxy models, composed of the response functions for variables known to influence the proxy plus the covariance structure of model parameters. These models can then be inverted numerically to estimate the multivariate environmental space that is consistent with a particular proxy observation. In addition to providing a more correct and comprehensive approach to interpretation of individual proxies, this framework offers a simple and formal solution for multi-proxy integration through ‘joint proxy inversion’. We illustrate JPI by presenting a simple proxy model for the foraminiferal oxygen isotope and Mg/Ca proxy systems and applying this to revisit reconstructions of past seawater salinity and temperature.