  The climate system is a complex, chaotic system with many degrees of freedom
and variability on a vast range of temporal and spatial scales. Attaining a
deeper level of understanding of its dynamical processes is a scientific
challenge of great urgency, especially given the ongoing climate change and the
evolving climate crisis. In statistical physics, complex, many-particle systems
are studied successfully using the mathematical framework of Large Deviation
Theory (LDT). A great potential exists for applying LDT to problems relevant
for geophysical fluid dynamics and climate science. In particular, LDT allows
for understanding the fundamental properties of persistent deviations of
climatic fields from the long-term averages and for associating them to
low-frequency, large scale patterns of climatic variability. Additionally, LDT
can be used in conjunction with so-called rare events algorithms to explore
rarely visited regions of the phase space and thus to study special dynamical
configurations of the climate. These applications are of key importance to
improve our understanding of high-impact weather and climate events.
Furthermore, LDT provides powerful tools for evaluating the probability of
noise-induced transitions between competing metastable states of the climate
system or of its components. This in turn essential for improving our
understanding of the global stability properties of the climate system and of
its predictability of the second kind in the sense of Lorenz. The goal of this
review is manifold. First, we want to provide an introduction to the derivation
of large deviation laws in the context of stochastic processes. We then relate
such results to the existing literature showing the current status of
applications of LDT in climate science and geophysical fluid dynamics. Finally,
we propose some possible lines of future investigations.
