Abstract
A two-time-level semi-Lagrangian primitive equations model has been constructed using the efficient alternating direction implicit (ADI) procedure of Bates (1984), together with split horizontal advection and geostrophic adjustment processes. If the simplest splitting method is used, the solution suffers from large neutral-amplitude oscillations. However a more accurate splitting arrangement may be used in which the adjustment processes are staggered in time. In this case a smoothly developing solution is obtained, even without explicit diffusion.
Further improvements are obtained if the accuracy of the ADI procedure is increased by a repetition ensuring spatial symmetry. Time traces are used to show the similarity of the solutions for various timestep sizes. Only for the largest timesteps are there noticeable differences, mainly in the form of extra gravity wave activity. Comparisons using a variety of horizontal advection schemes indicate that residual truncation errors from the splitting procedure are also made with a limited-area semi-implicit model. The vertical mode initialization scheme of Bourke and McGregor (1983) was successfully applied to the semi-Lagrangian model; convergence was facilitated by the use of centered advection formulae during the initialization iterations.
