  Statistical physics and dynamical systems theory are key tools to study
high-impact geophysical events such as temperature extremes, cyclones,
thunderstorms, geomagnetic storms and many more. Despite the intrinsic
differences between these events, they all originate as temporary deviations
from the typical trajectories of a geophysical system, resulting in
well-organised, coherent structures at characteristic spatial and temporal
scales. While statistical extreme value analysis techniques are capable to
provide return times and probabilities of occurrence of certain geophysical
events, they are not apt to account for their underlying physics. Their focus
is to compute the probability of occurrence of events that are large or small
with respect to some specific observable (e.g. temperature, precipitation,
solar wind), rather than to relate rare or extreme phenomena to the underlying
anomalous geophysical regimes. This paper delineates this knowledge gap,
presenting some related challenges and new formalisms which arise in the study
of geophysical extreme events and may help better understand them.
