  We propose a data-driven framework to simplify the description of
spatiotemporal climate variability into few entities and their causal linkages.
Given a high-dimensional climate field, the methodology first reduces its
dimensionality into a set of regionally constrained patterns. Time-dependent
causal links are then inferred in the interventional sense through the
fluctuation-response formalism, as shown in Baldovin et al. (2020). These two
steps allow to explore how regional climate variability can influence remote
locations. To distinguish between true and spurious responses, we propose a
novel analytical null model for the fluctuation-dissipation relation, therefore
allowing for uncertainty estimation at a given confidence level. Finally, we
select a set of metrics to summarize the results, offering a useful and
simplified approach to explore climate dynamics. We showcase the methodology on
the monthly sea surface temperature field at global scale. We demonstrate the
usefulness of the proposed framework by studying few individual links as well
as "link maps", visualizing the cumulative degree of causation between a given
region and the whole system. Finally, each pattern is ranked in terms of its
"causal strength", quantifying its relative ability to influence the system's
dynamics. We argue that the methodology allows to explore and characterize
causal relationships in high-dimensional spatiotemporal fields in a rigorous
and interpretable way.
