The reduced-order extended Kalman (ROEK) filter has been introduced by Cane et al. (J. Geophys. Res. 101(1996) 599) as a means to reduce the cost of the extended Kalman filter. It essentially consists of projecting the dynamics of the model onto a low dimensional subspace obtained via an empirical orthogonal functions (EOF) analysis. However, the choice of the dimension of the reduced-state space (or the number of EOFs to be retained) remains a delicate question. Indeed, Cane et al. found that increasing the number of EOFs does not improve, and even sometimes worsens, the performance of the ROEK filter. We speculate that this is probably due to the optimal character of the EOF analysis that is optimal in a time-mean sense only. In this respect, we develop a simple efficient adaptive scheme to tune, according to the model mode, the dimension of the reduced-state space, which would be therefore variable in time. In a first application, twin experiments are conducted in a realistic setting of the Ocean Parallèlisè (OPA) model in the tropical Pacific. The observations are assumed to be synthetic altimeter data sampled according to the Topex/Poseidon mission features. The adaptive scheme is shown to improve the performance of the ROEK filter especially during model unstable periods.