The atmosphere has coupled
instabilities that span many
scales, from ENSO to brownian motion:
ENSO has a doubling
time of about one month
Baroclinic weather
waves 2 days doubling time
Mesoscale phenomena
a few hours
Cumulus convection
10 minutes
Linear approaches, like Lyapunov and Singular Vectors can only handle the fastest growing instability
present in the model, nonlinear integrations allow fast
instabilities to
saturate
This has major implications for ensemble forecasting and data assimilation