A scale-invariant formulation of the anticipated potential vorticity method

TL;DR

This paper introduces a scale-invariant formulation of the anticipated potential vorticity method (APVM) for climate modeling, enabling consistent subgrid parameterizations across different resolutions and time steps.

Contribution

It derives a new APVM formulation that depends on a single parameter invariant to grid resolution, time step, and flow, advancing scale-aware subgrid modeling.

Findings

Parameter is invariant to time step size

Insensitive to flow variations

Weakly dependent on grid resolution

Abstract

The long-term success of climate models that operate on multi-resolution grids will depend 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 parametrizations, in this article we focus on the anticipated potential vorticity method (APVM) on quasi-uniform grids with varying resolutions. By a scale analysis technique and the phenomenological theories for two-dimensional turbulent flows, we derive a new formulation of the APVM, which depends on a single parameter that is, in principle, invariant with respect to 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 APVM is invariant with respect to the time step size, insensitive to the flows, and is only weakly dependent on the grid resolution.