This paper shows the existence of a growing planetary-wave-like ocean mode, with a decadal period and growth rate, which appears when a stratified, diffusive ocean is coupled to a simple atmosphere via an energy balance model (EBM). Such modes are not found when simpler surface ocean conditions are applied. The mode is low order in the vertical and, because of its slow growth, is likely to be observed in Earth System Models using an EBM in place of a fuller set of atmospheric dynamics. There is no apparent physical energy source for such a mode, and therefore it should not be expected to arise in such a model. The mode is analysed through a hierarchy of simple models, which differ only through their surface boundary condition.