Conservative Space and Time Regularizations for the ICON Model

Abstract

In this article, we consider two modified (regularized) versions of the shallow water equations which are of potential interest for the construction of global oceanic and atmospheric models. The first modified system is the Lagrangian averaged shallow water system, which involves the use of a regularized advection velocity and which has been recently proposed as a turbulence parametrization for ocean models in order to avoid an excessive damping of the computed solution. The second modified system is the pressure regularized shallow water system, which provides an alternative to traditional semi-implicit time integration schemes and which results in larger freedom in the design of the time integrator and in a better treatment of nearly geostrophic flows. The two modified systems are both nondissipative, in that they do not result in an increase of the overall dissipation of the flow. We first show how the numerical discretization of the two regularized equation sets can be constructed in a natural way within the finite difference formulation adopted for the ICON general circulation model currently under developed at the Max Planck Institute for Meteorology and at the German Weather Service. The resulting scheme is then validated on a set of idealized tests in both planar and spherical geometry, and the effects of the considered regularizations on the computed solution are analyzed concerning: stability properties and maximum allowable time steps, similarities and differences in the behavior of the solutions, discrete conservation of flow invariants such as total energy and enstrophy. Our analysis should be considered as a first step toward the use of the regularization ideas in the simulation of more complex and more realistic flows.