A Scale-Invariant Formulation of the Anticipated Potential Vorticity Method

Abstract

he long-term success of climate models that operate on multiresolution grids depends on access to subgrid parameterizations that act appropriately across a wide range of spatial and temporal scales. As the first step in a series of efforts to obtain such scale-aware subgrid parameterizations, the authors focus on the anticipated potential vorticity method (APVM) on a sequence of quasi-uniform grids with varying resolutions. Through a scale analysis technique and phenomenological theories for two-dimensional turbulent flows, they derive a new formulation of the APVM that depends on a single parameter that is formally independent of the time-step size, the grid resolution, and the flow itself. Results of numerical experiments with this new formulation demonstrate that the optimal parameter of the new APVM formulation is invariant with respect to the time-step size, is insensitive to the flows, and is only weakly dependent on the grid resolution.