Causal methods are analytical techniques used to determine cause-and-effect relationships, which are crucial in Earth sciences for understanding and predicting environmental changes and phenomena accurately. Causality is challenging for nonlinear feedback systems, like those in high latitudes, because these systems involve complex, interdependent interactions for which direct cause and effect can be difficult to disentangle, interpret, and predict accurately. Traditional causal methods often assume linearity and independence, causing them to inaccurately reflect the complex, interdependent interactions characteristic of nonlinear feedback systems.

The Koopman operator is a mathematical tool used in dynamical systems theory to analyze the behavior of nonlinear systems. The operator models the evolution of observables, quantities that can be measured or computed from the system's state variables, to capture global system dynamics. The Koopman operator provides a rigorous data driven methodology for causal discovery in nonlinear dynamical systems. In this talk, we present this novel data driven method, alongside some practical applications in the high latitudes.