We have studied the impact of time scales in a coupled data assimilation (CDA) system based on an ensemble Kalman filter (EnKF). As a neat example, we consider the MAOOAM model, which is a reduced quasi-geostrophic model with an atmosphere (hence fast) and ocean (hence slow) compartment. We deduce that (i) cross components effects are strong from the slow to the fast scale, but, (ii) intra-component effects are much stronger in the fast scale. While observing the slow scale is desirable and benefits the fast, the latter must be observed with high frequency otherwise the error will grow up to affect the slow scale. The numerical experiments on MAOOAM confirm the importance of observing the fast scale, but show also that, despite its slow temporal scale, frequent observations in the ocean are beneficial. We also discuss the properties of the dynamics (in particular the covariant Lyapunov vectors) and their connection for to performance of the CDA.

The paper has been published in the Journal of Statistical Physics and is open access. Check it out!.