10-13 Sept. 2012M. Baldauf (DWD)1 Michael Baldauf Deutscher Wetterdienst, Offenbach, Germany Priority Project "Conservative Dynamical Core" Final report COSMO General Meeting 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!

10-13 Sept. 2012M. Baldauf (DWD)3 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 planned far 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-scheme cent. Diff. 2nd order 3.Simple FV-scheme: fluxes calc.with cent. Diff. 2nd order time integration with RK 4. order 4.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

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

10-13 Sept. 2012M. Baldauf (DWD)8 Riemann-solver FV-scheme (equations in conservation form) FD-scheme (equations in advection form) Wrong position of the shock front

10-13 Sept. 2012M. Baldauf (DWD)9 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) 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  ?

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

10-13 Sept. 2012M. Baldauf (DWD)11 What happened until now … April 2008proposal of new PP CDC in the SMC Sept 2008proposal of new PP CDC presented at GM in Krakow= official start of the project June 2009 Kick off meeting organized by IMGW in Wirzba/Poland 2009EULAG: 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 tests with mountain flow 2010definition of the decision tree EULAG: finalize idealized tests, more semi-realistic simulations June 2010 SMC evaluation meeting in Sopot  continuation 2011start of the implementation of EULAG dyn. core into COSMO MPDATA in COSMO; comparison towards Semi-Lagr., Bott 2012testing of COSMO-EULAG with all idealized and quasi-realistic tests July 2012common CDC/POMPA meeting, status of CDC; follow-up PP

10-13 Sept. 2012M. Baldauf (DWD)12 Management issues FTE's used COSMO-yearTask 1Task 2 EULAG branch Compressible branch Total = ~0.2 FTE's/year for project leadership = 0.8 FTE in total

10-13 Sept. 2012M. Baldauf (DWD)13 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, anelastic conservation of momentum, tracer mass flux form eq. for internal energy ability to handle steep slopes Almost all items of the „EULAG branch“ (=task1) and most of the decision tree were fulfilled

10-13 Sept. 2012M. Baldauf (DWD)14 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)

10-13 Sept. 2012M. Baldauf (DWD)15 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, 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, 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, M. Baldauf: Non-hydrostatic modelling with the COSMO model, Proceedings of ‘ECMWF workshop on non-hydrostatic modelling’, ECMWF, 2010, p (compare dispersion relation of compressible eqns. with divergence damping and anelastic approximation)

10-13 Sept. 2012M. Baldauf (DWD)16 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