Convergence Rate and Stability of Ocean-Atmosphere Coupling Schemes with a Zero-Dimensional Climate Model

Abstract

A zero-dimensional climate model is considered with three thermal reservoirs, i.e., the atmosphere, the surface mixed layer and the intermediate water of the ocean. Realistic values are adopted for the rates of heat transfer between those reservoirs. If heat is added suddenly to the atmosphere, the atmospheric temperature increases a small amount in a few days. Thereafter, the atmosphere and mixed layer increase in temperature. About one-half the mixed-layer response occurs on a time scale of two years and the rest on a time scale of about 100 years. Numerical solution of atmosphere-ocean general circulation models may require asynchronous coupling strategies to link the two models. A semi-implicit approach is considered which generalizes previously suggested schemes. Its convergence and stability are examined by application to the zero-dimensional climate model. It may be unstable if it is made too explicit. On the other hand, the fully implicit approach greatly slows down the response of the mixed layer unless a very short coupling interval is used. With some fraction about equal to 0.05 of the atmosphere-ocean heat transfer made implicit, the asynchronous coupling solutions are close to the correct solution even if a large coupling interval is used.