Abstract
Abstract : A horizontal difference scheme that conserves both potential enstrophy and energy for general flow and, in addition, yields fourth-order accuracy for the advection of potential vorticity in case of non-divergent flow, is derived for the shallow water equations on the staggered grid as a simple extension of the second-order potential enstrophy and energy conserving scheme presented by Arakawa and Lamb (1981). This fourth-order scheme is derived both for a Cartesian grid and for a spherical grid. Comparison by means of numerical experiments between the newly derived scheme and the second-order scheme showed the distinct advantage of the new scheme in giving better development and faster moving speed of the law.
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