  Extreme geophysical events are of crucial relevance to our daily life: they
threaten human lives and cause property damage. To assess the risk and reduce
losses, we need to model and probabilistically predict these events.
Parametrizations are computational tools used in Earth system models, which are
aimed at reproducing the impact of unresolved scales on resolved scales. The
performance of parametrizations has usually been examined on typical events
rather than on extreme events. In this paper we consider a modified version of
the two-level Lorenz'96 model and investigate how two parametrizations of the
fast degrees of freedom perform in terms of the representation of extreme
events. One parametrization is constructed following Wilks (2005) and is
constructed through an empirical fitting procedure; the other parametrization
is constructed through the statistical mechanical approach proposed by Wouters
and Lucarini (2012, 2013). The two strategies show different advantages and
disadvantages. We discover that the agreement between parametrized models and
true model is in general worse when looking at extremes rather than at the bulk
of the statistics. The results suggest that stochastic parametrizations should
be accurately and specifically tested against their performance on extreme
events, as usual optimization procedures might neglect them.
