The coupled ocean-atmosphere system has instabilities that span time scales from a few minutes (e.g., cumulus convection) to years (e.g., El Niño phenomenon). It is not clear whether a data assimilation focused on long-term variability should include the smaller time scales, since the fast time scales have stronger growth rates and within linear approximations used in data assimilation they do not saturate, and may thus distort the slower longer time-scale solution.

To study this problem, we consider a very simple triple coupled Lorenz (1963) model that includes a slow “ocean” component strongly coupled with a fast “tropical atmosphere component” in turn weakly coupled with a fast “extratropical atmosphere”. The questions that we will explore include whether one can use one-way or two-way coupled systems, whether Optimal Interpolation (OI), Ensemble Kalman Filter (EnKF) and 4-dimensional variational (4D-Var) data assimilation methods can be used with similar results, and whether a 4D-Var system with initial and surface fluxes as control variables can be used for a long ocean reanalysis.