High-latitude filtering in global grid-point models

Latitude-longitude grid-point models with explicit time schemes require filtering of unstable short waves at high latitudes to avoid the use of prohibitively short time steps. By using a shallow water model and a Rossby-Haurwitz wave as an initial condition, an examination of the effect of several filtering procedures on the numerical solution is performed. It is found that ad hoc filtering techniques can cause spurious energy and momentum transfers to occur which ultimately affect the solution at all latitudes. These spurious transfers are related to a nonconservation of vorticity under the pressure gradient force as well as to a nonconservation of the irrotationality of the gradients of the streamfunction and velocity potential in finite-difference form. Conserving the curl of the gradients of the scalar quantities defined by the heights, the streamfunction and the velocity potential are crucial in order to prevent vorticity and divergence source terms from being generated near the poles. In this paper, an examination of various filtering techniques is presented, in addition to a filtering procedure that conserves the irrotational properties of the system in finite-difference form.