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 22nd century 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.

Earth’s hydrological cycle is expected to intensify in response to global warming, with a ‘wet-gets-wetter, dry-gets-drier’ response anticipated. The subtropics (~15-30°N/S) are predicted to become drier, yet proxy evidence from past warm climates suggests these regions may be characterised by wetter conditions. Here we use an integrated data-modelling approach to reconstruct global- and regional-scale rainfall patterns during the early Eocene (~48-56 million years ago), with an emphasis on the subtropics. Model-derived precipitation–evaporation (P–E) estimates in the tropics (0-15° N/S) and high latitudes (>60° N/S) are positive and increase in response to higher temperatures, whereas model-derived P–E estimates in the subtropics (15-30° N/S) are negative and decrease in response to higher temperatures. This is consistent with a ‘wet-gets-wetter, dry-gets-drier’ response. However, some DeepMIP model simulations predict increasing – rather than decreasing – subtropical precipitation at higher temperatures (e.g., CESM, GFDL). Using moisture budget diagnostics we find that the models with higher subtropical precipitation are characterised by a reduction in the strength of subtropical moisture circulation due to weaker meridional temperature gradients. These model simulations (e.g., CESM, GFDL) agree more closely with various proxy-derived climate metrics and imply a reduction in the strength of subtropical moisture circulation during the early Eocene. Although this was insufficient to induce subtropical wetting, if the meridional temperature was weaker than suggested by the DeepMIP models, this may have led to wetter subtropics. This highlights the important role of the meridional temperature gradient when predicting past (and future) rainfall patterns.