1. ICONAM ICOsahedral Non-hydrostatic Atmospheric Model -
ICONAM
ICOsahedral Non-hydrostatic Atmospheric Model -
model core formulation
on triangular and hexagonal C-grids
Almut Gassmann (Max Planck Institute for Meteorology, Hamburg, Germany) Günther Zängl (Deutscher Wetterdienst, Offenbach (Main), Germany)
and the ICON group at MPI-M and DWD

2. ICON: tool for NWP and climate applications
ICON: tool for NWP and climate applications
Wishes for the project some years ago:
non-hydrostatic atmospheric model
dynamics in grid point space
triangular icosahedron grid
local zooming with static or dynamic grid refinement
transport scheme: conservative, positive definit, efficient
dynamics conserves mass, energy, potential vorticity, and potential enstrophy
coupling to ocean model, atmospheric chemistry, hydrology, and land model
modulartity
portability
scalability and efficiency on multicore architectures
from:

3. Non-hydrostatic atmospheric model - model core formulation
Non-hydrostatic atmospheric model -
model core formulation
Target system of equations:
prognostic equations
|·ρv (to obtain energy equ.)
Π = Exner pressure
θv = virtual pot. temperature
ρ = density
v = 3D velocity vector
K = spec. kinetic energy
Φ = geopotential
ωa = 3D abs. vorticity vector
Rd = gas constant for dry air
cvd = spec. heat capacity at constant volume for dry air
cpd = spec. heat capacity at constant pressure for dry air
+physics
Transport of virtual potential temperature is done with higher order advection.
Additional transport equations for tracers will enter the system.

4. Triangular and hexagonal C-grids
Triangular and hexagonal C-grids

5. Triangular and hexagonal C-grids
Triangular and hexagonal C-grids
Triangular C-grid
divergence averaging
C-grid dispersion properties lost
4-point tangential wind reconstruction
horizontally (2D) vector invariant form
conserves mass
needs diffusion for stability
Miura advection for ρ and ρθ
static grid refinement implemented
nearer to operational availability
Hexagonal C-grid
no divergence averaging
C-grid dispersion properties retained
14-point tangential wind reconstruction
3D vector invariant form
conserves mass and energy
needs diffusion for nonlinear processes
3rd order upstream advection for θ
static grid refinement not yet implemented
still farther away from operational availability

6. Triangular and hexagonal C-grids
Triangular and hexagonal C-grids
Further distinguishing features of the two model versions:
a) implementation of terrain-following coordinates
b) time stepping scheme

7. a) L-grid staggering + terrain-following coordinates
a) L-grid staggering + terrain-following coordinates
Triangular C-grid
main levels height-centered between interface levels
horizontal pressure gradient:
search for neighboring point in the same height
reconstruct Exner function using a second order Taylor expansion w m w

8. a) L-grid staggering + terrain-following coordinates
a) L-grid staggering + terrain-following coordinates
Hexagonal C-grid
interface levels height-centered between main levels
horizontal pressure gradient:
covariant velocity equations
remove background reference profile in each of them separately
solve inverse problem for the lower boundary w m w

9. a) Acid test for terrain-following coordinates:
a) Acid test for terrain-following coordinates:
Resting atmosphere over a high mountain
Vertical slice model based on the hexagonal C-grid code
Spurious vertical
velocities remain in
the range of mm/s.
No errors spoil
higher levels,
compared to
other models.

10. b) Time stepping scheme
b) Time stepping scheme
Common features
horizontally explicit (forward-backward) for waves
vertically implicit scheme for waves
no time splitting
Triangular C-grid
Adams-Bashford-Moulton time stepping for momentum advection
Hexagonal C-grid
approximately conserves energy (integration by parts rule in time)
resembles in parts the Matsuno scheme (needs v(n+1) for the kinetic energy term)

11.
Density current
Vertical slice model based on the hexagonal C-grid code
Essential feature:
Higher order transport
for potential temperature.
Here: 3rd order upstream

12. Results for global testcases: Talk by Pilar Ripodas (DWD)
Results for global testcases:
Talk by Pilar Ripodas (DWD)
Grid refinement (triangular C-grid):
Talk by Günther Zängl (DWD)
Next steps
implementation of physics parameterizations which are available from the COSMO model (DWD)
hydrostatic version: implementation of ECHAM physics (MPI-M)
grid refinement also for hexagonal C-grid version
coupling to ocean model (under development at MPI-M)
available for preoperational NWP runs next year