The relationship between the global mean deep-sea and surface temperature during the Early Eocene

Our current understanding of global mean near-surface (land and sea) air temperature (GMSAT) during the Cenozoic era relies on paleo-proxy estimates of deep-sea temperature combined with assumed relationships between global mean deep-sea temperature (GMDST), global mean sea-surface temperature (GMSST), and GMSAT. The validity of these assumptions is essential in our understanding of past climate states such as the Early Eocene Climate Optimum hothouse climate (EECO, 56–48 Ma). The EECO remains relevant today, because EECO-like CO₂ levels are possible in the 22^ndcentury under continued high CO₂ emissions. We analyze the relationship between the three global temperature indicators for the EECO using 25 different millennia-long model simulations with varying CO₂ levels from the Deep-Time Model Intercomparison Project (DeepMIP). The model simulations show limited spatial variability in deep-sea temperature, indicating that local temperature estimates can be regarded representative of GMDST. Linear regression analysis indicates that compared to GMSST, both GMDST and GMSAT respond more strongly to changes in atmospheric CO₂ by factors of 1.18 and 1.17, respectively. Consequently, this model-based analysis validates the assumption that changes in GMDST can be used to estimate changes in GMSAT during the EECO. Paleo-proxies of GMDST, GMSST, and GMSAT during EECO show the best fit with model simulations having an atmospheric CO₂ level of 1,680 ppm, which matches paleo-proxies of atmospheric CO₂ during EECO. Similar analyses of other past climate states are needed to examine whether these results are robust throughout the Cenozoic, providing insight into the long-term future warming under various shared socioeconomic pathways.