Forced versus coupled dynamics in Earth system modelling and prediction

Abstract. We compare coupled nonlinear climate models and their simplified forced counterparts with respect to predictability and phase space topology. Various types of uncertainty plague climate change simulation, which is, in turn, a crucial element of Earth System modelling. Since the currently preferred strategy for simulating the climate system, or the Earth System at large, is the coupling of sub-system modules (representing, e.g. atmosphere, oceans, global vegetation), this paper explicitly addresses the errors and indeterminacies generated by the coupling procedure. The focus is on a comparison of forced dynamics as opposed to fully, i.e. intrinsically, coupled dynamics. The former represents a particular type of simulation, where the time behaviour of one complex systems component is prescribed by data or some other external information source. Such a simplifying technique is often employed in Earth System models in order to save computing resources, in particular when massive model inter-comparisons need to be carried out. Our contribution to the debate is based on the investigation of two representative model examples, namely (i) a low-dimensional coupled atmosphere-ocean simulator, and (ii) a replica-like simulator embracing corresponding components.Whereas in general the forced version (ii) is able to mimic its fully coupled counterpart (i), we show in this paper that for a considerable fraction of parameter- and state-space, the two approaches qualitatively differ. Here we take up a phenomenon concerning the predictability of coupled versus forced models that was reported earlier in this journal: the observation that the time series of the forced version display artificial predictive skill. We present an explanation in terms of nonlinear dynamical theory. In particular we observe an intermittent version of artificial predictive skill, which we call on-off synchronization, and trace it back to the appearance of unstable periodic orbits. We also find it to be governed by a scaling law that allows us to estimate the probability of artificial predictive skill. In addition to artificial predictability we observe artificial bistability for the forced version, which has not been reported so far. The results suggest that bistability and intermittent predictability, when found in a forced model set-up, should always be cross-validated with alternative coupling designs before being taken for granted.