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The basic equation of the barotropic model atmosphere is solved by following the motion of a system of atmospheric parcels each of which conserves its vorticity. The wind field is computed at intervals from the vorticity field on a fixed grid and is used as a basis for calculating the motion of the parcels. Results have similar accuracy to those obtained by Eulerian methods, but being independent of the latter, serve to indicate some effects of truncation error in the usual Eulerian scheme. The semi-Lagrangian scheme is suitable for integrations with long time steps on a coarse grid.
J. S. Sawyer (Tue,) studied this question.