Causal deep learning models for studying the Earth system: soil moisture-precipitation coupling in ERA5 data across Europe

The Earth system is a complex non-linear dynamical system. Despite decades of research, many processes and relations between Earth system variables are still poorly understood. Current approaches for studying relations in the Earth system may be broadly divided into approaches based on numerical simulations and statistical approaches. However, there are several inherent limitations to current approaches that are, for example, high computational costs, reliance on the correct representation of relations in numerical models, strong assumptions related to linearity or locality, and the fallacy of correlation and causality. Here, we propose a novel methodology combining deep learning (DL) and principles of causality research in an attempt to overcome these limitations. The methodology combines the recent idea of training and analyzing DL models to gain new scientific insights in the relations between input and target variables with a theorem from causality research. This theorem states that a statistical model may learn the causal impact of an input variable on a target variable if suitable additional input variables are included. As an illustrative example, we apply the methodology to study soil moisture-precipitation coupling in ERA5 climate reanalysis data across Europe. We demonstrate that, harnessing the great power and flexibility of DL models, the proposed methodology may yield new scientific insights into complex, nonlinear and non-local coupling mechanisms in the Earth system.