Physics–Dynamics Coupling with Element-Based High-Order Galerkin Methods: Quasi-Equal-Area Physics Grid

Abstract

Atmospheric modeling with element-based high-order Galerkin methods presents a unique challenge to the conventional physics–dynamics coupling paradigm, due to the highly irregular distribution of nodes within an element and the distinct numerical characteristics of the Galerkin method. The conventional coupling procedure is to evaluate the physical parameterizations ( physics) on the dynamical core grid. Evaluating the physics at the nodal points exacerbates numerical noise from the Galerkin method, enabling and amplifying local extrema at element boundaries. Grid imprinting may be substantially reduced through the introduction of an entirely separate, approximately isotropic finite-volume grid for evaluating the physics forcing. Integration of the spectral basis over the control volumes provides an area-average state to the physics, which is more representative of the state in the vicinity of the nodal points rather than the nodal point itself and is more consistent with the notion of a “large-scale state” required by conventional physics packages. This study documents the implementation of a quasi-equal-area physics grid into NCAR’s Community Atmosphere Model Spectral Element and is shown to be effective at mitigating grid imprinting in the solution. The physics grid is also appropriate for coupling to other components within the Community Earth System Model, since the coupler requires component fluxes to be defined on a finite-volume grid, and one can be certain that the fluxes on the physics grid are, indeed, volume averaged.