A Stability Analysis of Divergence Damping on a Latitude–Longitude Grid

Abstract

The dynamical core of an atmospheric general circulation model is engineered to satisfy a delicate balance between numerical stability, computational cost, and an accurate representation of the equations of motion. It generally contains either explicitly added or inherent numerical diffusion mechanisms to control the buildup of energy or enstrophy at the smallest scales. The diffusion fosters computational stability and is sometimes also viewed as a substitute for unresolved subgrid-scale processes. A particular form of explicitly added diffusion is horizontal divergence damping.In this paper a von Neumann stability analysis of horizontal divergence damping on a latitude-longitude grid is performed. Stability restrictions are derived for the damping coefficients of both second-and fourthorder divergence damping. The accuracy of the theoretical analysis is verified through the use of idealized dynamical core test cases that include the simulation of gravity waves and a baroclinic wave. The tests are applied to the finite-volume dynamical core of NCAR's Community Atmosphere Model version 5 (CAM5). Investigation of the amplification factor for the divergence damping mechanisms explains how small-scale meridional waves found in a baroclinic wave test case are not eliminated by the damping.

MCore: A non-hydrostatic atmospheric dynamical core utilizing high-order finite-volume methods

“…The results along the equator at t = 96 h are also shown in Fig. 10 for the spectral-transform-based CAM Eulerian (CAM-EUL) dynamical core both without and with explicitly added fourth-order hyperdiffusion using the diffusion coefficient K 4 = 5 Â 10 14 m 4 s À1 , the CAM finite-volume (CAM-FV) [22] dynamical core without its divergence damping mechanism [54], and the spectral-element-based CAM-SE model with fourth-order hyperdiffusion and K 4 = 9.6 Â 10 14 m 4 s À1 [27]. The CAM-FV and CAM-SE models are run with a corresponding 1°Â 1°L20 grid spacing, which translates to a triangular truncation of T106 for the L20 CAM-EUL model.…”

DART/CAM: An Ensemble Data Assimilation System for CESM Atmospheric Models

“…A more scale-selective damping operator was therefore implemented, that is, a fourthorder divergence damping scheme. This higher-order damping operator provides, in general, a more scaleselective damping of divergent modes near the grid scale, although its implementation on the regular latitudelongitude grid may provide less damping in the polar regions (Whitehead et al 2011). The fourth-order divergence damping more effectively reduced grid-scale noise in the divergence field while not damping the divergence of ''well resolved '' scales (Figs.…”

“…3 in Lauritzen et al 2012) both in free-running CAM and DART/CAM. For more details on the stability properties of the divergence damping as implemented on the regular latitude-longitude grid, see Whitehead et al (2011) and, more generally, for the damping/dispersion properties of the CAM-FV scheme, see Lauritzen (2007) and Skamarock (2008).…”

Assessing Tracer Transport Algorithms and the Impact of Vertical Resolution in a Finite-Volume Dynamical Core

“…Although the experiment is idealized, these velocities might be considered more realistic than those prescribed by the tracer advection test cases specified in previous sections. The CAM-FV dynamical core is utilized in an adiabatic mode (i.e., without physical parameterizations) and uses the fourth-order divergence damping as explained in Whitehead et al (2011). We use the PPM tracer advection scheme with the default limiter in all gravity wave tests.…”