This paper is devoted to assessing the accuracy of the compact and the super-compact finite difference methods for spatial differencing of the linearized shallow water equations. The second-order centered, the fourth-order centered, the fourth-order compact, the sixth-order compact and the sixth-order super-compact schemes are used to carry out the spatial differencing of the linearized shallow water equations on Arakawa's A and C grids. For the frequency and group velocity of linear inertia gravity waves on different numerical methods, the sixth-order super-compact method shows a substantial improvement on traditional centered and compact finite difference schemes.
)