  We use a simple yet Earth-like atmospheric model to propose a new framework
for understanding the mathematics of blocking events. Analysing error growth
rates along a very long model trajectory, we show that blockings are associated
with conditions of anomalously high instability of the atmosphere.
Additionally, the lifetime of a blocking is positively correlated with the
intensity of such an anomaly, against intuition. In the case of Atlantic
blockings, predictability is especially reduced at the onset and decay of the
blocking, while a relative increase of predictability is found in the mature
phase, while the opposite holds for Pacific blockings, for which predictability
is lowest in the mature phase. We associate blockings to a specific class of
unstable periodic orbits (UPOs), natural modes of variability that cover the
attractor of the system. The UPOs differ substantially in terms of instability,
which explains the diversity of the atmosphere in terms predictability. The
UPOs associated to blockings are indeed anomalously unstable, which leads to
them being rarely visited. The onset of a blocking takes place when the
trajectory of the system hops into the neighbourhood of one of these special
UPOs. The decay takes place when the trajectory hops back to the neighbourhood
of usual, less unstable UPOs associated with zonal flow. This justifies the
classical Markov chains-based analysis of transitions between weather regimes.
The existence of UPOs differing in the dimensionality of their unstable
manifold indicates a very strong violation of hyperbolicity in the model, which
leads to a lack of structural stability. We propose that this is could be a
generic feature of atmospheric models and might be a fundamental cause behind
difficulties in representing blockings for the current climate and
uncertainties in predicting how their statistics will change as a result of
climate change.
