Michael Baldauf Deutscher Wetterdienst, Offenbach, Germany

Deutscher Wetterdienst

1FE 13 – 20.04.23

Working group 2:Dynamics and Numerics

report ‘Oct. 2007 – Sept. 2008’

COSMO General Meeting, Krakau15.-19.09.2008

Michael Baldauf Deutscher Wetterdienst, Offenbach, Germany


2FE 13 – 20.04.23

2.11 Alternative discretizations (due to alternative grids)

2.11.1 [RENUMBERED] Remove grid redundancy by Serendipity GridsDWD: Steppeler 09/05 Report The serendipity grids should be investigated, which reduce the redundancy of the interpolation procedures. In this way they achieve more accuracy and more efficiency.

2.11.2 Higher order discretization on unstructured grids using Discontinuous Galerkin methodsDWD: Baldauf, Univ. Freiburg: Kroener, Dedner, Brdar 2009 start, 2011 report In the DFG priority program 'METSTRÖM' a new dynamical core for the COSMO-model will be developed. It will use Discontinuous Galerkin methods to achieve higher order, conservative discretizations. Currently the building of an adequate library is under development. The work with the COSMO-model will start probably at the end of 2009. This is therefore base research especially to clarify, if these methods can lead to efficient solvers for NWP.


3FE 13 – 20.04.23

Discontinuous Galerkin Method

•Seek weak solutions of a balance equation(correspondance to finite volume methods conservation)•Expand solution into a sum of base functions on each grid cell (correspondance to finite element methods)

•DG discretization in space arbitrary high order possible•useable on arbitrary grids suitable for complex geometries•discontinuous elements mass matrix is block-diagonal•in combination with an explicit time integration scheme (e.g. Runge-Kutta RKDG-methods) highly parallelizable code

but: how to solve vertically expanding sound waves efficiently?


4FE 13 – 20.04.23

Example of a Triangulation for 2D-flow over a mountain, produced with DUNE(D. Kröner, A. Dedner, S. Brdar, Univ. Freiburg)


5FE 13 – 20.04.23

Nonhydrostatic flow with Discontinuous Galerkin method(polynomials of order 2), preliminary results

44 km

w [m/s]


6FE 13 – 20.04.23

2.3.1 Radiative upper boundary conditionDWD: Herzog09/05 Report The Klemp Durran boundary is further developed.

2.3.2 [NEW] Radiative upper boundary condition; non-local in time NNreport in 06/2009 At the University Freiburg a Radiative upper boundary condition was developed. It is non-local in time, but nevertheless can be implemented efficiently into non-hydrostatic models. This radiation condition will be further developed during the DFG priority program METSTROEM.


7FE 13 – 20.04.23

New upper sponge layer (Klemp et al., 2008, MWR)

Purpose: Prevent unphysical reflection of vertically propagating gravity waves at upper model boundary

Unlike conventional damping layers, only the vertical wind is damped; specifically this is done in the fast-wave solver immediately after solving the tridiagonal matrix for the vertical wind speed

Analytical calculations by Klemp et al. indicate very homogeneous absorption properties over a wide range of horizontal wavelengths

work by G. Zängl


8FE 13 – 20.04.23

conventional Rayleigh damping, tdamp = 600 s w damping, tdamp = 12 s

quasi-linear flow over a mountain, u = 10m/s, h = 300 m, a = 5 km, Δx = 1 km; Fields: θ (contour interval 1 K), w (colours) t = 24h

Depth of damping layer: 10 km; top at 22 km


9FE 13 – 20.04.23

quasi-linear flow over a mountain, u = 10m/s, h = 300 m, a = 5 km, Δx = 1 km; Fields: θ (contour interval 1 K), u (colours) t = 24h

conventional Rayleigh damping, tdamp = 600 s w damping, tdamp = 12 s Depth of damping layer: 10 km; top at 22 km


10FE 13 – 20.04.23

quasi-linear flow over a mountain, u = 10m/s, h = 300 m, a = 5 km, Δx = 1 km; Fields: θ (contour interval 2 K), w (colours) t = 24h

conventional Rayleigh damping, tdamp = 600 s w damping, tdamp = 12 s Depth of damping layer: 10 km; top at 22 km


11FE 13 – 20.04.23

New upper sponge layer (Klemp et al., 2008, MWR)

Real-case simulations conducted so far indicate very little impact on forecasts results

Computing costs are slightly lower because the damping is applied to only one variable (i.e. w)


12FE 13 – 20.04.23

2.6.3 Implementation of neglected diabatic terms in p'-equation DWD: Herzog, CNMCA: L. Torrisi

2.10 Diagnostic tools

2.10.1 Application of the integration tool to energy, mass balance DWD: Baldauf, MPI-H: Petrik The integration tool to calculate balance equations by volume integrations of densities and surface integrations of fluxes developed in the Priority project 'Runge-Kutta', Task 3 will be applied to questions of energy and mass budgets.

Talk by L. Torrisi


13FE 13 – 20.04.23

Parallel session New priority project CDC

at 16:30 in Room E

Michael Baldauf Deutscher Wetterdienst, Offenbach, Germany

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