A global hexagonal C‐grid non‐hydrostatic dynamical core (ICON‐IAP) designed for energetic consistency

Abstract

This study describes a new global non-hydrostatic dynamical core (ICON-IAP:Icosahedral Nonhydrostatic model at the Institute for Atmospheric Physics) on a hexagonal C-grid which is designed to conserve mass and energy. Energy conservation is achieved by discretizing the antisymmetric Poisson bracket which mimics correct energy conversions between the different kinds of energy (kinetic, potential, internal). Because of the bracket structure this is even possible in a complicated numerical environment with (i) the occurrence of terrain-following coordinates with all the metric terms in it, (ii) the horizontal C-grid staggering on the Voronoi mesh and the complications induced by the need for an acceptable stationary geostrophic mode, and (iii) the necessity for avoiding Hollingsworth instability. The model is equipped with a Smagorinsky-type nonlinear horizontal diffusion. The associated dissipative heating is accounted for by the application of the discrete product rule for derivatives. The time integration scheme is explicit in the horizontal and implicit in the vertical. In order to ensure energy conservation, the Exner pressure has to be offcentred in the vertical velocity equation and extrapolated in the horizontal velocity equation.Test simulations are performed for small-scale and global-scale flows. A test simulation of linear non-hydrostatic flow over a rough mountain range shows the theoretically expected gravity wave propagation. The baroclinic wave test is extended to 40 days in order to check the Lorenz energy cycle. The model exhibits excellent energy conservation properties even in this strongly nonlinear and dissipative case. The Held-Suarez test confirms the reliability of the model over even longer timescales.

Current and Emerging Time-Integration Strategies in Global Numerical Weather and Climate Prediction

“…Inclusion of a well-represented stratosphere has implications for the chosen time-integration methods, since the stratospheric polar jet (which contributes via the advection term) reaches speeds exceeding 100 m s À1 , i.e., the advective Courant number approaches the acoustic one. As highlighted in [34], in this context the efficiency gains from the SE approach become less clear: the horizontal splitting (which defines the sub-stepping) in SE schemes is only relevant when there is a scale-separation between fast insignificant and slow significant processes. With the acoustic and advective Courant numbers being similar, the sub-step Ds and the model time-step Dt are constrained by similar stability limits and little efficiency can be gained from sub-stepping.…”

Generalization and application of the flux-conservative thermodynamic equations in the AROME model of the ALADIN system

“…This means that all hydrometeors (both suspended and precipitating) are considered as integral parts of the air, and contribute to the parcel's motion, density, and heat capacity. This barycentric view has been studied and motivated by many researchers (Wacker and Herbert, 2003;Bott, 2008;Gassmann and Herzog, 2008). …”

“…Atmospheric forecast models are usually constructed by combining a dynamical core with physical parameterizations. In general, the dynamical core describes the atmospheric behaviour up until the resolved scales, while the physical parameterizations estimate the effect of subgrid processes (Gassmann, 2013).…”

“…Common strategies include a careful selection of the prognostic variables (Ooyama, 1990(Ooyama, , 2001Klemp et al, 2007), the formulation of the equations in flux form (Satoh, 2003), or taking advantage of properties of the Hamiltonian character of the atmospheric equations (Salmon, 2004;Gassmann and Herzog, 2008;Zängl et al, 2015). In contrast with these efforts on the dynamical core, the energy conservation and consistent thermodynamics seem to be less of a priority in the development of the physical parameterizations, or in the way they are coupled to the dynamical core.…”

“…More specifically, the dynamics are usually considered adiabatic and reversible (except for numerical diffusion) (Gassmann, 2013). The physics paramePublished by Copernicus Publications on behalf of the European Geosciences Union.…”