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

ICONAM

ICON: tool for NWP and climate applicationsWishes 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: http://infoskript.de/uploads/pics/Wollmilchsau.jpg

prognostic equations

Π = Exner pressureθ

v = virtual pot. temperature

ρ = densityv = 3D velocity vectorK = spec. kinetic energyΦ = geopotentialω

a = 3D abs. vorticity vector

Rd = gas constant for dry air

cvd

= spec. heat capacity at constant volume for dry airc

pd = spec. heat capacity at

constant pressure for dry air

|·ρv (to obtain energy equ.)

Transport of virtual potential temperature is done with higher order advection.

Additional transport equations for tracers will enter the system.

+physics

Non-hydrostatic atmospheric model - model core formulation

Target system of equations:

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

Triangular and hexagonal C-grids

Further distinguishing features of the two model versions:

a) implementation of terrain-following coordinates

b) time stepping scheme

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

mw

w

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

wm

a) Acid test for terrain-following coordinates:Resting atmosphere over a high mountain

Spurious verticalvelocities remain in the range of mm/s.

No errors spoil higher levels,compared toother models.

Vertical slice model based on the hexagonal C-grid code

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)

Density current

Vertical slice model based on the hexagonal C-grid code

Essential feature:Higher order transport for potential temperature.Here: 3rd order upstream

Results for global testcases:Talk by Pilar Ripodas (DWD)

Grid refinement (triangular C-grid):Talk by Günther Zängl (DWD)

Next stepsimplementation 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 versioncoupling to ocean model (under development at MPI-M)

available for preoperational NWP runs next year