The dynamics of a low-order coupled wind-driven ocean-atmosphere system is investigated with emphasis on its predictability properties. The low-order coupled deterministic system is composed of a baroclinic atmosphere for which 12 dominant dynamical modes are only retained (Charney and Straus in J Atmos Sci 37:1157-1176, 1980) and a wind-driven, quasi-geostrophic and reduced-gravity shallow ocean whose field is truncated to four dominant modes able to reproduce the large scale oceanic gyres (Pierini in J Phys Oceanogr 41:1585-1604, 2011). The two models are coupled through mechanical forcings only. The analysis of its dynamics reveals first that under aperiodic atmospheric forcings only dominant single gyres (clockwise or counterclockwise) appear, while for periodic atmospheric solutions the double gyres emerge. In the present model domain setting context, this feature is related to the level of truncation of the atmospheric fields, as indicated by a preliminary analysis of the impact of higher wavenumber ("synoptic" scale) modes on the development of oceanic gyres. In the latter case, double gyres appear in the presence of a chaotic atmosphere. Second the dynamical quantities characterizing the short-term predictability (Lyapunov exponents, Lyapunov dimension, Kolmogorov-Sina < (KS) entropy) displays a complex dependence as a function of the key parameters of the system, namely the coupling strength and the external thermal forcing. In particular, the KS-entropy is increasing as a function of the coupling in most of the experiments, implying an increase of the rate of loss of information about the localization of the system on its attractor. Finally the dynamics of the error is explored and indicates, in particular, a rich variety of short term behaviors of the error in the atmosphere depending on the (relative) amplitude of the initial error affecting the ocean, from polynomial (at (2) + bt (3) + ct (4)) up to exponential-like evolutions. These features are explained and analyzed in the light of the recent findings on error growth (Nicolis et al. in J Atmos Sci 66:766-778, 2009).
