We present results from a conservative formulation of the spectral element method applied to global atmospheric circulation modeling. Exact local conservation of both mass and energy is obtained via a new compatible formulation of the spectral element method. Compatibility insures that the key integral property of the divergence and gradient operators required to show conservation also hold in discrete form. The spectral element method is used on a cubed-sphere grid to discretize the horizontal directions on the sphere. It can be coupled to any conservative vertical/radial discretization. The accuracy and conservation properties of the method are illustrated using a baroclinic instability test case.

The new compatible formulation of the spectral element method ensures exact local conservation of mass and energy in global atmospheric circulation modeling, with potential applications in baroclinic instability simulations.

A mass and energy conserving spectral element atmospheric dynamical core on the cubed-sphere grid

Key Takeaway: The new compatible formulation of the spectral element method ensures exact local conservation of mass and energy in global atmospheric circulation modeling, with potential applications in baroclinic instability simulations.