Dynamical implications of prescribing part of a coupled system: Results from a low-order model

Abstract. It is a common procedure in climate modelling to specify dynamical system components from an external source; a prominent example is the forcing of an atmospheric model with observed sea surface temperatures. In this paper, we examine the dynamics of such forced models using a simple prototype climate system. A particular fully coupled run of the model is designated the "true" solution, and an ensemble of perturbed initial states is generated by adding small errors to the "true" initial state. The perturbed ensemble is then integrated for the same period as the true solution, using both the fully-coupled model and a model in which the ocean is prescribed exactly from the true solution at every time step. Although the prescribed forcing is error-free, the forced-atmosphere ensemble is shown to converge to spurious solutions. Statistical tests show that neither the time-mean state nor the variability of the forced ensemble is consistent with the fully-coupled system. A stability analysis reveals the source of the inconsistency, and suggests that such behaviour may be a more general feature of models with prescribed subsystems. Possible implications for model validation and predictability are discussed.