The global-regional model interaction problem: Analysis of Carpenter's scheme and related issues

The multiscale global-regional model interaction problem for linear time-dependent waves is considered. The setup, which is sometimes called "nesting," arises in numerical weather prediction as well as in other fields concerning waves in very large domains. It involves the interaction of a crude global model and a fine limited-area (regional) model through an "open boundary. " The multiscale nature of this general problem is described. A fundamental difficulty related to spurious modes, which prevents a trivial treatment of the problem, is discussed. The Carpenter scheme, originally proposed in a Note by K. M. Carpenter (Q. J. R. Met. Soc. 108:717-719, 1982)for this type of problem, is then revisited in the context of the linear scalar wave equation. This scheme is analyzed here in the one-dimensional case. It is shown that the accuracy of the scheme hinges mainly on the numerical dispersion generated by the global model. Extension of the analysis to two dimensions is also discussed. Numerical experiments are presented for the Carpenter scheme in one dimension via some example problems, and conclusions are drawn about its performance. Ways of improving the scheme are indicated.