The heart of the scientific enterprise is a rational effort to understand the causes behind the phenomena we observe. In disciplines dealing with complex dynamical systems, such as the Earth system, replicated real experiments are rarely feasible. However, a rapidly increasing amount of observational and simulated time series data opens up the use of observational causal inference methods beyond the commonly adopted correlation techniques. Observational causal inference is a rapidly growing field with enormous potential to help answer long-standing scientific questions. Unfortunately, many methods are still little known and therefore rarely adopted in Earth system sciences. In this overarching project we address key major challenges for causal discovery in Earth system sciences.