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 delta O-18 (delta(c)) records are indispensable because they reflect changes in both deep-sea temperature and seawater delta O-18 (delta(w)); 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 delta(c), with linear scaling of residual delta(w) 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 delta O-18, and both deep-sea delta(w) and temperature and find distinct nonlinearity between sea level and delta(w) changes. Application to delta(c) 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.