Atmosphere-Ocean Coupling Schemes in a One-Dimensional Climate Model

In this paper, the coupling schemes of atmosphere-ocean climate models are discussed with one-dimensional advection equations. The convergence and stability for synchronous and asynchronous schemes are demonstrated and compared.Conclusions inferred from the analysis are given below. The synchronous scheme as well as the asynchronous-implicit scheme in this model are stable for arbitrary integrating time intervals. The asynchronous ex-plicit scheme is unstable under certain conditions, which depend upon advection velocities and heat exchange parameters in the atmosphere and oceans. With both synchronous and asynchronous stable schemes the discrete solu-tions converge, to their unique exact ones. Advections in the atmosphere and ocean accelerate the rate of convergence of the asynchronous-implicit scheme. It is suggested that the asynchronous-implicit coupling scheme is a stable and efficient method for most climatic simulations.