15.09.2008günther zängl, dwd1 improvements for idealized simulations with the cosmo model günther...

15.09.2008 Günther Zängl, DWD 1

Improvements for idealized simulations with the COSMO model

Günther Zängl

Deutscher Wetterdienst, Offenbach, Germany


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


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


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


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


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


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)


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


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)


Results at t = 24 h: θ (contour interval 2 K), u (colours)

conventional relaxation condition radiation condition with weak nudging (factors 0.005 for T, 0.01 for u)


Results at t = 24 h: θ (contour interval 2 K), w (colours)



radiation condition with weak nudging radiation condition without nudging



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


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


Simulation with flat surface, u = 10m/s, and fixed relaxation b.c.‘s, t = 12 hFields: θ (contour interval 2 K), w (colours)

Old p‘ initializationError amplitude: 1 mm/s

New p‘ initializationError amplitude: 10-4 mm/s


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


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, but stability 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


Results with explicit 3rd-order vertical advection θ (contour interval 1 K), u (colours)

standard discretization with damping discretization


Results with explicit 3rd-order vertical advection θ (contour interval 1 K), w (colours)



Results with implicit 2nd-order vertical advection θ (contour interval 1 K), u (colours)



Results with implicit 2nd-order vertical advection θ (contour interval 1 K), w (colours)



Results for quasi-linear flow over a mountain, h = 300 m, u = 10 m/s θ (contour interval 1 K), u (colours)


15.09.2008günther zängl, dwd1 improvements for idealized simulations with the cosmo model günther...

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