Filtering inertia-gravity waves from the initial conditions of the linear shallow water equations

A method for filtering inertia-gravity waves from elevation and depth-averaged velocity is described. This filtering scheme is derived from the linear shallow water equations for constant depth and constant Coriolis frequency. The filtered solution is obtained by retaining only the eigenvectors corresponding to the geostrophic equilibrium and by discarding explicitly the eigenvectors corresponding to the fast moving inertia-gravity waves. An alternative formulation is derived using a variational approach. Both filtering methods are tested numerically for a periodic domain with constant depth and the variational approach is implemented for a closed domain with large topographic variations. The filtering methods significantly reduce the amplitudes of the inertia-gravity waves while preserving the mean flow. The variational method is compared to the Incremental Analysis Update technique and the benefits of the variational filter are presented.