A finite‐volume integration method for computing pressure gradient force in general vertical coordinates

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Abstract
A finite‐volume integration method is proposed for computing the pressure gradient force in general vertical coordinates. It is based on fundamental physical principles in the discrete physical space, rather than on the common approach of transforming analytically the pressure gradient terms in differential form from the vertical physical (i.e., height or pressure) coordinate to one following the bottom topography. The finite‐volume discretization is compact, involving only the four vertices of the finite volume. The accuracy of the method is evaluated statically in a two‐dimensional environment and dynamically in three‐dimensional dynamical cores for general circulation models. The errors generated by the proposed method are demonstrated to be very low in these tests.