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Finite computer resources force compromises in the design of transient numerical experiments with coupled atmosphere-ocean general circulation models which, in the case of global warming simulations, normally preclude a full integration from the undisturbed pre-industrial state. The start of the integration at a later time from a climate state which, in contrast to the true climate, is initially in equilibrium then induces a cold start error. Using linear response theory a general expression for the cold start error is derived. The theory is applied to the Hamburg CO2 scenario simulations. An attempt to estimate the global-mean-temperature response function of the coupled model from the response of the model to a CO2 doubling was unsuccessful because of the non-linearity of the system. However, an alternative derivation, based on the transient simulation itself, yielded a cold start error which explained the initial retardation of the Hamburg global warming curve relative to the IPCC results obtained with a simple box-diffusion-upwelling model. In the case of the sea level the behaviour of the model is apparently more linear. The cold start error estimations based on a CO2 doubling experiment and on an experiment with gradually increasing CO2 (scenario A) are very similar and explain about two thirds of the coupled model retardation relative to the IPCC results.

On the cold start problem in transient simulations with coupled atmosphere-ocean models