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A computationally efficient mass-conservative transport scheme over the sphere is proposed and tested. The scheme combines a conservative finite-volume method with an efficient semi-Lagrangian scheme based on the dimension splitting ''cascade'' method. In the regions near the poles where the conservative cascade procedure breaks down, a globally conservative, but locally approximate scheme is used. This procedure is currently restricted to polar meridional Courant numbers less than one. The resulting conservative cascade scheme is evaluated using a solid-body rotation test and deformational flow test, and found to be both accurate and efficient. Compared to the traditional semi-Lagrangian scheme employing a bicubic-Lagrange interpolator, the proposed scheme is considerably more accurate and almost twice as fast while conserving mass exactly.

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We describe a finite volume semi-Lagrangian method for the numerical approximation of conservation laws arising in fluid-dynamic applications. A discrete conservation relation is satisfied by using conservative interpolation for the material (or property) being conserved. The method was developed with a view to application in climate prediction. 0 1995 John Wiley & Sons, Inc.

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