Abstract
Abstract A new pseudo-fourth-order finite-difference scheme for the shallow-water and primitive equations is derived. This scheme is a C-grid scheme that conserves energy and conserves enstrophy in the nondivergent limit. The accuracy of the scheme is second order, but in the nondivergent limit it has fourth-order accuracy. In the nondivergent limit, the scheme reduces to Arakawa's fourth-order Jacobian scheme for the vorticity equation for two-dimensional incompressible flow. Model runs with the shallow-water equations are discussed.
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