ICON-IAP: ICOsahedral Non-hydrostatic General Circulation Model (ICON) on a hexagonal grid

Institution: Leibniz-Institute of Atmospheric Physics at the University of Rostock (IAP), Kühlungsborn, Germany

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Test 2.00

Test 2.1

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Test 3.1

Description:

ICON-IAP (Icosahedral Nonhydrostatic model at the Institute for Atmospheric Physics) is a global non-hydrostatic dynamical core on a hexagonal C-grid which is designed to conserve mass, tracer 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. The still crude physics-package employs a process split coupling strategy.

Typical horizontal resolutions, physics and dynamics time steps, and dissipation coefficients:

Damping properties:

• horizontal diffusion with Smagorinsky-scheme: cs=0.125 (without units)
• namelist variables for upper boundary damping: (a) height where the damping starts, (b) maximum damping coefficient for 2nd order Laplacian diffusion (for instance 6e6 m²/s for R2B6)
• background shear in the Smagorinsky diffusion: 1/(270 dt)
• off-centering and extrapolation of the pressure gradient term are chosen such that total energy is conserved

The kinetic energy lost by friction is refeeded into the internal energy as dissipative heating.

Information on the computational grid:

The model uses hexagonal C-grid staggered cells (and 12 pentagonal cells), in other words a Voronoi mesh. The left picture displays the local grid entities which comprise a cell c where the divergence is defined, and a rhombus r where the vertical vorticity is defined. In fact, the full vertical vorticity information is only available at vertices v where 3 rhombi overlap. Normal/tangential vectors to describe the horizontal wind/vorticity components are locally defined on grid edges. The quadrilateral signifies the area (= distance between vertices times distance between cell centers) which is attributed to one edge e.

The model uses height-based terrain-following coordinates and is L-grid staggered in the vertical.

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References:

• Gassmann, A. (2012), A global hexagonal C-grid non-hydrostatic dynamical core (ICON-IAP) designed for energetic consistency. Q.J.R. Meteorol. Soc.. doi: 10.1002/qj.1960
• Skamarock, W. C. and Gassmann A. (2011), Conservative Transport Schemes for Spherical Geodesic Grids: High-Order Flux Operators for ODE-Based Time Integration. Mon. Wea. Rev., 139, 2962–2975. doi: 10.1175/MWR-D-10-05056.1
• Gassmann, A. (2011), Inspection of hexagonal and triangular C-grid discretizations of the shallow water equations, Journal of Computational Physics, 230, 2706-2721. doi: 10.1016/j.jcp.2011.01.014
• Gassmann, A. and Herzog, H.-J. (2008), Towards a consistent numerical compressible non-hydrostatic model using generalized Hamiltonian tools. Q.J.R. Meteorol. Soc., 134, 1597–1613. doi: 10.1002/qj.297

Members of this modeling group during DCMIP-2012 and room location:

Room: to be determined