  The atmosphere is chaotic. This fundamental property of the climate system
makes forecasting weather incredibly challenging: it's impossible to expect
weather models to ever provide perfect predictions of the Earth system beyond
timescales of approximately 2 weeks. Instead, atmospheric scientists look for
specific states of the climate system that lead to more predictable behaviour
than others. Here, we demonstrate how neural networks can be used, not only to
leverage these states to make skillful predictions, but moreover to identify
the climatic conditions that lead to enhanced predictability. Furthermore, we
employ a neural network interpretability method called ``layer-wise relevance
propagation'' to create heatmaps of the regions in the input most relevant for
a network's output. For Earth scientists, these relevant regions for the neural
network's prediction are by far the most important product of our study: they
provide scientific insight into the physical mechanisms that lead to enhanced
weather predictability. While we demonstrate our approach for the atmospheric
science domain, this methodology is applicable to a large range of
geoscientific problems.
