Continued greenhouse gas emissions will lead to increasing global warming. Effective adaptation and mitigation policies depend on accurately estimating climate sensitivity, the Earth's surface temperature response to increasing CO2 emissions. Global Climate models (GCMs) provide the long-term simulations essential to better understand climate and quantify this temperature change. Despite advances in numerical modelling and theory, model divergence remains significant. The Intergovernmental Panel on Climate Change (IPCC) recognized the "hot model problem" in its Sixth Assessment report (2021). One source of this model uncertainty is parametrization schemes, that encode our physical understanding of subgrid-scale processes, like clouds and convection. Convective precipitation, due to its stochastic nature and dependence to fine-scale processes, is still poorly represented in GCMs.

This thesis uses dimensionality reduction and causal inference methods on multi-model ensemble outputs to address these challenges. Model complexity has become a norm in model development, and hinders their interpretability. Major progress in these areas require a rigorous search for the processes underlying the large interdependent model outputs. The d-MAPS method offers a low-level representation of datasets, while causal inference methods question the relationships between variables. The first application focuses on Sea Surface Temperature (SST) dynamics, and investigates the potential of causal network properties to narrow down the range of plausible climate sensitivity. Chapter 1 develops the methodology for a first ensemble, with the evaluation of patterns and teleconnections in a recent period. Chapter 2 expands the methodology to climate projections. We found that SST effects weaken in warmer climates, with a significant model uncertainty in the eastern Pacific Ocean. Hot models do not exhibit more realistic teleconnection effects within a fixed causal network, but their SST patterns are more realistic with a varying structure. The second application examines the dependency of convective precipitation on its environmental conditions. Chapter 3 aims to quantify interactions among variables within a specific large-scale regime. We analyzed high-resolution model outputs from Global Storm-Resolving Models (GSRM), in which deep convection is explicitly resolved, using a multivariate causal graph. This framework helped us better understand the d-MAPS method, especially its exclusion of sharp humidity gradients. We found consistent control of large-scale variable on the convective precipitation distribution across GSRMs, and a significant uncertainty of the role of vertical velocity.

Both applications aim to better understand processes and quantify the inter-model differences. Ultimately, we use causal effects to constrain climate sensitivity, and to identify the largest control of large-scale humidity on convective precipitation. This research work, based on chain of decisions - from the inference of regions to the potential constraint of a target, through the inference of links and their effects, reveals all the complexity of the climate system, but also shows promising results in the search for robust relationships.