1. Conservative Dynamical Core (CDC)
Proposal for a new COSMO Priority Project
Conservative Dynamical Core (CDC)
Michael Baldauf
Deutscher Wetterdienst, Offenbach, Germany
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2. Model-resolutions for weather forecast of 1 ... 1.5 km
Aim (towards ~2015):
Model-resolutions for weather forecast of km
(cp. UK MO with 1.5 km ‚on demand‘ / for GB)
 Main requirements to the model:
again steeper orography
upper boundary condition
(stronger) resolved convection
1D-Turbulence  3D-Turb.
Radiation : slope dependency, ...
numerical aspects
physics-dynamics-coupling
physical aspects
data assimilation verification
EPS
...
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3. Conservation: general guiding principle in designing a model
The dynamical cores of COSMO-model don't have any explicit conservation properties.
Conservation: general guiding principle in designing a model
Conservation of (Thuburn, 2008):
mass !!!
energy !!
momentum
tracers !!
Strategical advantages:
general trend in atmospheric modeling (Bacon et al., 2000, Skamarock, Klemp, 2008)
collaboration with C-CLM ('climate COSMO') hint: 'regional ICON'-climate modelling could be competitive to C-CLM
collaboration with COSMO-ART (chemical/aerosol modeling)
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4. Methodology: Finite-Volume-Methods
are well established in CFD (LeVeque, 2002, ...)
become increasing meaning in atmospheric modeling
Advantages:
conserves the prognostic variable
positive definite, if desired (by flux limitation)
can handle steep gradients in the solution (e.g. by flux correction) (even shocks and other discontinuities, however they are not so important in atmosphere)
Could have advantages in steep orography (example in: Smolarkiewicz et al. (2007) JCP)
(applicable on arbitrary unstructured grids) in this project, structured grid is planned far range plans could use unstructured grid, e.g. for a more efficient implementation of a z-coordinate version
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5. Deliverables ('compressible development branch')
Until : (???)
derivation of equation set in flux form; adapted for resolutions x=500 m … 3 km
choice of prognostic variables: , v, Eint=cVT or  or Etot? (Gassmann, Herzog, 2008, …)
choice of base state
coordinate system (terrain following or tilted cells in a cartesian framework) These items have to be in close connection with the possible discretizations (spatial and temporal).
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6. Preliminary version with the focus on spatial discretization;
Until : (???)
Preliminary version with the focus on spatial discretization;
i.e. formulation of fluxes, limiters
but in a fully explicit way, no time-splitting, perhaps with RK-time integration.
fully 3D schemes, no direction splitting
In particular appropriate advection schemes should be available (examples: MPDATA, Godunov-type methods, ...)
At this stage possible advantages for use in steep orography can be investigated.
Parallel development of improved upper boundary conditions.
Until : (???)
Fully useable and optimized version available.
possible time integrations available:
fully explicit (to test spatial discret.)
horizontal explicit, vertical implicit (is absolutely necessary to get efficiency)
time splitting
Estimated resources (in FTE-years) needed: 8.0 FTEs
Minimum FTEs needed per year: (2.0 FTEs) ~< 1 FTE
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7. During the plannings, IMGW started to increase their NWP staff, in particular for numerical developments.
EULAG model (e.g. Smolarkiewicz et al., 2007): anelastic approximated, finite-volume model
Deliverables ('EULAG-development branch')
until : first insert EULAG model into the operational environment of IMGW perform efficiency tests (need some support in choosing test cases and interpretation)
until : insert EULAG dynamical core into the COSMO-model
Estimated resources (in FTE-years) needed: 6.0 FTEs
Minimum FTEs needed per year: FTEs

8. IMGW will start their work
Current planning:
IMGW will start their work
Evaluation of the abilities of EULAG for NWP after about 1 year
In parallel: develop concept for a compressible conservative dynamical core (only reduced staff)
Built up a common knowledge in the FV-methods needed
(e.g. project meetings ~3 months)
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10. Subproject: steep orography
(is the continuation of task 6 of PP RK)
What are the limitations of the terrain-following coordinate?
div-operator limited by 45° ?,
h<z ?,
...
How can these limits be shifted towards steeper orography?

11. Subproject: Advection of scalars (Moisture variables, TKE, …)
full 3D (non-splitted) scheme the problems with splitted schemes could be seen during the development of the Bott-scheme (Task 4 of PP RK)
robustness currently the (non-conserving) Semi-Lagrange-scheme is more robust than Bott
mass-consistency: should the advection scheme for scalars be the same than that for  ?
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12. Subproject: Boundary conditions
Upper boundary condition:
the currently used Rayleigh damping has some deficiencies, as can be seen rather clear in idealised simulations (e.g. task 5 of PP RK)
becomes more important with smaller grid width - must handle more resolved scales
choice between improved damping conditions and radiation conditions
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