Can chaos and intransitivity lead to interannual variability?

We suggest that the atmosphere–ocean–earth system is unlikely to be intransitive, i.e. to admit two or more possible climates, any one of which, once established, will persist forever. Our reasoning is that even if the system would be intransitive if the external heating could be held fixed, say as in summer, the new heating patterns that actually accompany the advance of the seasons will break up any established summer circulation, and an alternative circulation may develop during the following summer, particularly if chaos has prevailed during the intervening winter. We introduce a very-low-order geostrophic baroclinic “general circulation” model, which may be run with or without seasonal variations of heating. Under perpetual summer conditions the model is intransitive, admitting either weakly oscillating or strongly oscillating westerly flow, while under perpetual winter conditions it is chaotic. When seasonal variations of heating are introduced, weak oscillations prevail through some summers and strong oscillations prevail through others, thus lending support to our original suggestion. We develop some additional properties of the model as a dynamical system, and we speculate as to whether its behaviour has a counterpart in the real world.