  In this paper we analyze the stability of different coupling strategies for
multidomain PDEs that arise in general circulation models used in climate
simulations. We focus on fully coupled ocean-atmosphere models that are needed
to represent and understand the complicated interactions of these two systems,
becoming increasingly important in climate change assessment in recent years.
Numerical stability issues typically arise because of different time-stepping
strategies applied to the coupled PDE system. In particular, the contributing
factors include using large time steps, lack of accurate interface flux, and
singe-iteration coupling. We investigate the stability of the coupled
ocean-atmosphere models for various interface conditions such as the
Dirichlet-Neumann condition and the bulk interface condition, which is unique
to climate modeling. By analyzing a simplified model, we demonstrate how the
parameterization of the bulk condition and other numerical and physical
parameters affect the coupling stability.
