10-13 Sept. 2012M. Baldauf (DWD) 1

Michael BaldaufDeutscher Wetterdienst, Offenbach, Germany

Priority Project "Conservative Dynamical Core"

Final report

COSMO General Meeting10-13 Sept. 2012, Lugano

10-13 Sept. 2012M. Baldauf (DWD) 2

Conservation of • mass (total and tracer)• energy• momentum

project : 'Conservative dynamical core'

Strategical advantages:• general trend in atmospheric modeling• collaboration with CLM ('climate COSMO')

hint: 'regional ICON'-climate modelling could be competivie to CLM• collaboration with COSMO-ART (chemical/aerosol modeling)

from project proposal: April 2008

Motivation:The current COSMO dynamical core does not possess any conservation properties!

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Methodology: Finite-Volume-Methods (applied to equations in conservation form)

• well established in CFD• become increasing meaning in atmospheric modeling

Advantages:• conserves the prognostic variable• big flexibility• positive definite, if desired (by flux limitation)• can handle steep gradients in the solution (e.g. by flux correction)

(even shocks and other discontinuities, though they are not so important in atmosphere)• advantages in steep orography (?) implicit solver important• (applicable on arbitrary unstructured grids)

in this project, structured grid is plannedfar range plans could use unstructured grid, e.g. for a more efficient implementation of a z-coordinate version

from project proposal: April 2008

Why conservation can be important … the less obvious aspect

Example: 1-dim. Shallow water equations, Dam break problem expansion of a shock (to the right) and a rarefaction wave (to the left)

Initial state for H and u:Solution methods:1.Exact Riemann-solver(Godunov method)2.Simple FD-schemecent. Diff. 2nd order3.Simple FV-scheme: fluxes calc.with cent. Diff. 2nd ordertime integration with RK 4. order4.as 3.: but with artificial diffusion

H

u

Riemann-solver

FV; cent. Diff.;+ diffusion

FV; cent. Diff.;

FD; cent. Diff.+diffusion

H

u

H

H u

H

H

H u H u

Riemann-solver

FV; cent. Diff.;+ diffusion

FV; cent. Diff.;

FD; cent. Diff.+diffusion

‚Exact‘ Riemann-solver

FV; cent. Diff.;+ diffusion

FV; cent. Diff.;

FD; cent. Diff.+diffusion

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Riemann-solver

FV-scheme(equations in conservation form)

FD-scheme(equations in advection form)

Wrong position of the shock front

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Issue: steep orography

• Motivation: COSMO with 1 km resosution (MeteoCH, PP CORSO, …)• What are the limitations of the terrain-following coordinate?• How can these limits be shifted towards steeper orography?

from project proposal: April 2008

Issue: Advection of scalars (Moisture variables, TKE, …)

• full 3D (non-splitted) schemethe problems with splitted schemes could be seen during the development of the Bott-scheme (Task 4 of PP RK)

• robustnesscurrently 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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Solutions came up soon ...

• Implicit Finite-Volume solver CONSOL'borrowed' from aeronautics(proposal by Pier Luigi Vitagliano, CIRA)transfer to meteorological applications is quite innovative compressible branch

• EULAG model(proposal by Michal Ziemianski, IMGW) there exist a quite large community that uses the EULAG model EULAG (anelastic) branch

(further ideas (finite volume form of current RK, ...) were stopped by STC)

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What happened until now …

April 2008 proposal of new PP CDC in the SMCSept 2008 proposal of new PP CDC presented

at GM in Krakow = official start of the projectJune 2009 Kick off meeting organized by IMGW in Wirzba/Poland2009 EULAG: Idealized (cold density current, rising thermals, inertia-gravity waves,

mountain flows) and first semi-realistic tests (COSMO 2.2 km over the Alps)CONSOL: implementation of buoyancy processes and idealized testswith mountain flow

2010 definition of the decision treeEULAG: finalize idealized tests, more semi-realistic simulations

June 2010 SMC evaluation meeting in Sopot continuation2011 start of the implementation of EULAG dyn. core into COSMO

MPDATA in COSMO; comparison towards Semi-Lagr., Bott2012 testing of COSMO-EULAG with all idealized and quasi-realistic testsJuly 2012 common CDC/POMPA meeting, status of CDC; follow-up PP

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Management issues

FTE's used

COSMO-year Task 1 Task 2

EULAG branch

Compressible branch

2008-2009 1.5 0.25

2009-2010 3.1 0.72

2010-2011 2.9 0.15

2011-2012 2.6 0.4

Total = 10.1 1.5

+ ~0.2 FTE's/year for project leadership = 0.8 FTE in total

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What did we get (I)

EULAG-branch:

•we learned quite a lot about the anelastic approximations

•we got a sound feeling about principal properties of the EULAG dynamical core

•a new dynamical core is available in COSMO as a prototype

• split-explicit, HE-VI (Runge-Kutta, leapfrog): finite difference, compressible

• semi-implicit: finite difference, compressible

• COSMO-EULAG: finite volume, anelasticconservation of momentum, tracer massflux form eq. for internal energy ability to handle steep slopes

•Almost all items of the „EULAG branch“ (=task1) and most of the decision treewere fulfilled

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compressible branch

•we learned a lot about implicit Finite-Volume solver

•Toy model CONSOL for meteorological tests available

•dual time stepping as an alternative time-integration (?)

•MPDATA as a possible alternative tracer advection algorithm is available(not yet in the official version)

What did we get (II)

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What did we get (III) : Publications

M. Z. Ziemiański, M. J. Kurowski, Z. P. Piotrowski, B. Rosa and O. Fuhrer: Toward very high resolution NWP over Alps: Influence of the increasing model resolution on the flow pattern, Acta Geophysica 59 (6), 2011, 1205-1235

B. Rosa, M. J. Kurowski, and M. Z. Ziemiański: Testing the anelastic nonhydrostatic model EULAG as a prospective dynamical core of a numerical weather prediction model. Part I: Dry Benchmarks, Acta Geophysica 59 (6), 2011, 1235-1266 M. J. Kurowski, B. Rosa and M. Z. Ziemiański: Testing the anelastic nonhydrostatic model EULAG as a prospective dynamical core of numerical weather prediction model. Part II: Simulations of a supercell, Acta Geophysica 59 (6), 2011, 1267-1293 M. Baldauf: Non-hydrostatic modelling with the COSMO model,Proceedings of ‘ECMWF workshop on non-hydrostatic modelling’,ECMWF, 2010, p. 161-169(compare dispersion relation of compressible eqns. with divergence damping and anelastic approximation)

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What next?

The 'compressible branch' CONSOL will (hopefully) be continued in WG2

The 'EULAG-branch' will (probably) be continued in a follow-up project"COSMO-EULAG operationalization (CELO)"project leader: Zbigniew Piotrowski (IMGW)

Many thanks to the CDC development team (in alphabetical order):

Oliver Fuhrer, Marcin Kurowski, Guy de Morsier, Marie Müllner, Zbigniew Piotrovski, Bogdan Rosa, Pier Luigi Vitagliano, Damian Wojcik, Michal Ziemianski