Abstract
A semi-Lagrangian semi-implicit finite-difference nonhydrostatic global atmospheric model on a flat terrain has been developed. Starting from the initialized ECMWF analysis of 0000 UTC 15 January 1979, a series of 5-day test runs have been performed. The global nonhydrostatic model is stable and preserves the characteristics of the solution at large finer steps of up to one hour using typical resolution of GCMs. Although use of large time steps does not necessarily guarantee improved efficiency, it is apparent that the new scheme is potentially more efficient than a corresponding Eulerian explicit model that would require time steps two or three orders of magnitude smaller. The present simulations therefore demonstrate the potential computational advantages of the semi-Lagrangian semi-implicit method over the more traditional numerical methods in integrating the fully compressible nonhydrostatic equations of the atmosphere over the entire globe. One of the options adopted in the model to control computational noise is the combination of the traditional first-order-accurate uncentering and the filter proposed by McDonald and Haugen. However, use of second-order-accurate uncentering recently proposed by Rivest et al. is more effective in removing the noise and eliminates the need for the additional filter on the nonlinear terms. This noise, which depends mainly on the magnitude of the nonlinear terms, is found to be quite sensitive to the choice of the constant reference state temperature T̄ when first-order-accurate centering is employed. Systematic inspection of the relationship between the distribution of the nonlinear term contribution in the vertical momentum equation and the temperature of the isothermal reference state indicates that T̄ must be confined to a narrow range to obtain stable numerical solutions. The sensitivity of stability on the choice of T̄ is virtually eliminated introducing second-order-accurate uncentering. There is some indication that it may be desirable to specify T̄ as a function of both height and latitude. The model conserves mass and energy well, changing less than 0.05% in 5 days. As expected, at the typical resolution of GCMs, the results for the nonhydrostatic and hydrostatic versions of the model yield practically identical results.
