  The deterministic equations describing the dynamics of the atmosphere (and of
the climate system) are known to display the property of sensitivity to initial
conditions. In the ergodic theory of chaos this property is usually quantified
by computing the Lyapunov exponents. In this review, these quantifiers computed
in a hierarchy of atmospheric models (coupled or not to an ocean) are analyzed,
together with their local counterparts known as the local or finite-time
Lyapunov exponents. It is shown in particular that the variability of the local
Lyapunov exponents (corresponding to the dominant Lyapunov exponent) decreases
when the model resolution increases. The dynamics of (finite-amplitude) initial
condition errors in these models is also reviewed, and in general found to
display a complicated growth far from the asymptotic estimates provided by the
Lyapunov exponents. The implications of these results for operational (high
resolution) atmospheric and climate modelling are also discussed.
