The addition of carbon dioxide (CO₂) in the atmosphere due to human activities is the main driver of global warming. How much the Earth will warm in the future is often represented by the Earth's equilibrium climate sensitivity (ECS), the long-term temperature response considering the effect of climate feedbacks after an abrupt and sustained doubling of atmospheric CO₂ from pre-industrial concentration. Assessing ECS is critical as it is one of the most relevant metric to evaluate global temperature change by 2100 in a fast warming climate. However, there have been considerable difficulties in constraining ECS for more than a century. In recent years, there has been a focus on alternative lines of evidence to elicit ECS, such as the study of past climates.

The work of this thesis investigates the evidence on ECS and climate feedbacks obtained from paleoclimates. In our studies, we use past climate reconstructions and climate modelling to estimate ECS out of the cold Last Glacial Maximum (LGM) and the warm Pliocene. Our work focuses on the statistical relationship existing between simulated past temperatures and ECS following the emergent constraint theory, and how the physics of modelled paleoclimates can affect such relationship. We explore further how climate feedbacks behave and depart from a linear behaviour in extreme cold conditions by performing simulations of snowball Earth states.

This thesis demonstrates that both LGM and Pliocene are relevant candidates to elicit ECS and highlights the contribution of paleoclimates in understanding modern and future climate change. In particular, we show that the Pliocene is a robust constraint on ECS under the emergent constraint theory despite large observational uncertainties. Our estimate of ECS using the most recent generation of climate models is 4.8 K, which lies in the high end of previous assessment from Pliocene evidence. On the contrary, the LGM constraint is weak due to substantial differences in ice sheet forcing as well as differences in the behaviour of climate feedbacks in cold temperatures in climate models. Our results suggest that LGM simulated temperatures are challenging to use in emergent constraint framework on ECS. An alternative difficulty in using the LGM arises from the lack of high ECS models in the ensemble. Our results indicate that the minimum global temperature for the LGM state is around 0°C, where the strengthening of the sea-ice albedo feedback with cooling temperatures and a substantial contribution of cloud feedbacks will then move the climate towards a snowball state. Highly sensitivity models are most likely to fail at simulating the LGM when approaching these low temperatures.

The thesis highlights the importance of using a variety of models with different sensitivity to simulate paleoclimates and use them in estimating ECS and feedbacks. Warm paleoclimates such as the Pliocene are likely the best candidates to infer ECS. These estimates of ECS are dependent on geological reconstructions which are continuously improving. Assessments on the role of past climates in constraining ECS and feedbacks are therefore key elements in understanding both paleoclimates and future climate change and should be considered with great interest.