Overview New upper sponge layer for reduced wave reflection (Klemp et al., 2008)

1. Günther Zängl, DWD Improvements for idealized simulations with the COSMO modelGünther ZänglDeutscher Wetterdienst, Offenbach, Germany

2. Günther Zängl, DWD • Overview • New upper sponge layer for reduced wave reflection (Klemp et al., 2008) • Lateral radiative boundary condition that can be combined with weak nudging • More accurate initialization of perturbation pressure field • Option to turn off surface friction when using a turbulence scheme • Work in progress: modification to remove numerical noise over a steep mountain in an atmosphere at rest

3. Günther Zängl, DWD • 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

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

5. Günther Zängl, DWD 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

6. Günther Zängl, DWD 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

7. Günther Zängl, DWD • 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)

8. Günther Zängl, DWD • Lateral radiative boundary condition • Purpose: Lateral radiation of perturbations generated in the interior of the model domain (in idealized simulations) • Builds upon code previously implemented by Jochen Förstner; a namelist option has also been added (only available for RK core) • Tests with various formulations of the phase velocity of the radiated perturbations indicate very weak sensitivity • Option to combine radiation condition with weak nudging in order to prevent drifting of the model solution in long-term integrations

9. Günther Zängl, DWD • Lateral radiative boundary condition – test simulations • Nonlinear flow over a mountain; u = 10 m/s, h = 1500 m, a = 5 km, Δx = 1 km • Turbulence physics is used without surface friction • New (Klemp et al.) upper sponge layer • Experiments with • (a) conventional relaxation (nudging) condition, • (b) radiation condition without nudging • (c) radiation condition with weak nudging (for wind and • temperature, but not for pressure)

10. Günther Zängl, DWD Results at t = 24 h: θ (contour interval 2 K), u (colours) radiation condition with weak nudging (factors 0.005 for T, 0.01 for u) conventional relaxation condition

11. Günther Zängl, DWD Results at t = 24 h: θ (contour interval 2 K), w (colours) radiation condition with weak nudging (factors 0.005 for T, 0.01 for u) conventional relaxation condition

12. Günther Zängl, DWD Results at t = 24 h: θ (contour interval 2 K), u (colours) radiation condition with weak nudging (factors 0.01 for T, 0.02 for u) conventional relaxation condition

13. Günther Zängl, DWD Results at t = 24 h: θ (contour interval 2 K), w (colours) radiation condition with weak nudging (factors 0.01 for T, 0.02 for u) conventional relaxation condition

14. Günther Zängl, DWD Results at t = 24 h: θ (contour interval 2 K), u (colours) radiation condition with weak nudging radiation condition without nudging

15. Günther Zängl, DWD • Lateral radiative boundary condition - results • For longer-term simulations of nonlinear flow over a mountain, some lateral relaxation is essential to avoid unreasonable drifting of the flow field • Based on the test results, the default values of the multiplicative factor for the nudging coefficient were set to 0.01 for T and to 0.02 for u (and v); it turned out to be beneficial to apply no nudging to perturbation pressure

16. Günther Zängl, DWD • Initialization of the perturbation pressure field • The present initialization of the perturbation pressure field (executed in src_artifdata for idealized simulations; otherwise in int2LM) is not exactly consistent with the discretized buoyancy term in the vertical momentum equation • The error is too small to be noticeable in real-case applications; however, it becomes evident in idealized simulations with constant flow and a very low mountain (or no mountain at all) • To fix the problem, a new initialization procedure has been developed by solving the discretized vertical wind equation (for dw/dt = 0) for p‘; ideally, this would ensure strict absence of buoyancy at the lateral model boundaries

17. Günther Zängl, DWD Simulation with flat surface, u = 10m/s, and fixed relaxation b.c.‘s, t = 12 h Fields: θ (contour interval 2 K), w (colours) Old p‘ initialization Error amplitude: 1 mm/s New p‘ initialization Error amplitude: 10-4 mm/s

18. Günther Zängl, DWD • Spurious noise over mountains in a resting atmosphere • Tests reveal a 2Δz structure in the horizontal and vertical wind field • Depending on the difference between base state and actual temperature profile, it can take more than 12 h until the noise reaches a significant amplitude • Afterwards, it rapidly grows within a time scale of a few hours until some sort of saturation is reached • Tests indicate that a modified discretization of the dw/dz term in the pressure tendency equation may damp the noise

19. Günther Zängl, DWD • Spurious noise over mountains in a resting atmosphere • In the modified version, the term is not only evaluated between half-levels but also between full-levels (which damps 2Δz waves), followed by a weighting of both terms • A weight of 0.05 of the damping discretization turned out to suffice for eliminating the noise • Normally very small impact on flow dynamics, butstability problems over steep topography in the presence of strong winds • Setup of test experiments: mountain with h = 1500 m, a = 5 km; Δx = 1 km, no ambient winds; results are shown for t = 24 h

20. Günther Zängl, DWD Results with explicit 3rd-order vertical advection θ (contour interval 1 K), u (colours) standard discretization with damping discretization

21. Günther Zängl, DWD Results with explicit 3rd-order vertical advection θ (contour interval 1 K), w (colours) standard discretization with damping discretization

22. Günther Zängl, DWD Results with implicit 2nd-order vertical advection θ (contour interval 1 K), u (colours) standard discretization with damping discretization

23. Günther Zängl, DWD Results with implicit 2nd-order vertical advection θ (contour interval 1 K), w (colours) standard discretization with damping discretization

24. Günther Zängl, DWD Results for quasi-linear flow over a mountain, h = 300 m, u = 10 m/s θ (contour interval 1 K), u (colours) standard discretization with damping discretization