Sea level and deep-sea temperature reconstructions suggest quasi-stable states and critical transitions over the past 40 million years.

Sea level and deep-sea temperature variations are key indicators of global climate changes. For continuous records over millions of years, deep-sea carbonate microfossil-based δ18O (δc) records are indispensable because they reflect changes in both deep-sea temperature and seawater δ18O (δw); the latter are related to ice volume and, thus, to sea level changes. Deep-sea temperature is usually resolved using elemental ratios in the same benthic microfossil shells used for δc, with linear scaling of residual δw to sea level changes. Uncertainties are large and the linear-scaling assumption remains untested. Here, we present a new process-based approach to assess relationships between changes in sea level, mean ice sheet δ18O, and both deep-sea δw and temperature and find distinct nonlinearity between sea level and δw changes. Application to δc records over the past 40 million years suggests that Earth's climate system has complex dynamical behavior, with threshold-like adjustments (critical transitions) that separate quasi-stable deep-sea temperature and ice-volume states.