We study the effect of regime switches on finite size Lyapunov exponents
(FSLEs) in determining the error growth rates and predictability of multiscale
systems. We consider a dynamical system involving slow and fast regimes and
switches between them. The surprising result is that due to the presence of
regimes the error growth rate can be a non-monotonic function of initial error
amplitude. In particular, troughs in the large scales of FSLE spectra is shown
to be a signature of slow regimes, whereas fast regimes are shown to cause
large peaks in the spectra where error growth rates far exceed those estimated
from the maximal Lyapunov exponent. We present analytical results explaining
these signatures and corroborate them with numerical simulations. We show
further that these peaks disappear in stochastic parametrizations of the fast
chaotic processes, and the associated FSLE spectra reveal that large scale
predictability properties of the full deterministic model are well approximated
whereas small scale features are not properly resolved.Comment: Accepted for publication in Chao
