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 δO (δ) records are indispensable because they reflect changes in both deep-sea temperature and seawater δO (δ); 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 δ, with linear scaling of residual δ 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 δO, and both deep-sea δ and temperature and find distinct nonlinearity between sea level and δ changes. Application to δ 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.