  In a low-order model of the general circulation of the atmosphere we examine
the predictability of threshold exceedance events of certain observables. The
likelihood of such binary events -- the cornerstone also for the categoric (as
opposed to probabilistic) prediction of threshold exceedences -- is established
from long time series of one or more observables of the same system. The
prediction skill is measured by a summary index of the ROC curve that relates
the hit- and false alarm rates. Our results for the examined systems suggest
that exceedances of higher thresholds are more predictable; or in other words:
rare large magnitude, i.e., extreme, events are more predictable than frequent
typical events. We find this to hold provided that the bin size for binning
time series data is optimized, but not necessarily otherwise. This can be
viewed as a confirmation of a counterintuitive (and seemingly contrafactual)
statement that was previously formulated for more simple autoregressive
stochastic processes. However, we argue that for dynamical systems in general
it may be typical only, but not universally true. We argue that when there is a
sufficient amount of data depending on the precision of observation, the skill
of a class of data-driven categoric predictions of threshold exceedences
approximates the skill of the analogous model-driven prediction, assuming
strictly no model errors. Furthermore, we show that a quantity commonly
regarded as a measure of predictability, the finite-time maximal Lyapunov
exponent, does not correspond directly to the ROC-based measure of prediction
skill when they are viewed as functions of the prediction lead time and the
threshold level. This points to the fact that even if the Lyapunov exponent as
an intrinsic property of the system, measuring the instability of trajectories,
determines predictability, it does that in a nontrivial manner.
