Conservative Dynamical Core (CDC) Proposal for a new COSMO Priority Project Conservative Dynamical Core (CDC) Michael Baldauf Deutscher Wetterdienst, Offenbach, Germany FE 13 – 25.05.2019

Model-resolutions for weather forecast of 1 ... 1.5 km Aim (towards ~2015): Model-resolutions for weather forecast of 1 ... 1.5 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 ... FE 13 – 25.05.2019

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) FE 13 – 25.05.2019

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 FE 13 – 25.05.2019

Deliverables ('compressible development branch') Until 01.06.2009: (???) 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). FE 13 – 25.05.2019

Preliminary version with the focus on spatial discretization; Until 01.03.2010: (???) 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 01.09.2011: (???) 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 FE 13 – 25.05.2019

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 01.07.2009: first insert EULAG model into the operational environment of IMGW perform efficiency tests (need some support in choosing test cases and interpretation) until 31.12.2010: insert EULAG dynamical core into the COSMO-model Estimated resources (in FTE-years) needed: 6.0 FTEs Minimum FTEs needed per year: 2.0 FTEs

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) FE 13 – 25.05.2019

FE 13 – 25.05.2019

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?

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  ? FE 13 – 25.05.2019

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 FE 13 – 25.05.2019