The new Priority Project Conservative Dynamical Core (CDC) COSMO General Meeting 07.-11.09.2009, Offenbach

Deutscher Wetterdienst

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The new Priority Project

Conservative Dynamical Core (CDC)

COSMO General Meeting07.-11.09.2009, Offenbach

Michael BaldaufDeutscher Wetterdienst, Offenbach, Germany


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Aims of the CDC priority project

• conservation properties of the dynamical core (Thuburn, 2008, JCP):• mass !!! most important• energy !!• momentum probably increasing importance for smaller scales• tracers !! important at least in convection resolving models

• should be able to handle steep orography

and of course overall:• accuracy• efficiency• stability


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Current dynamical cores (Leapfrog, RK) have no conservation properties for the dynamic variables mass, energy, momentum

Possible causes for limited use in steep terrain:• Fast waves: not vertical implicit for metric terms (would go beyond tri-

diagonal matrices) • Metric tensor identities probably not fulfilled (Task 2.1 in CDC) • Tracer advection: Bott-scheme is not multi-dimensional


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Discretization of the ‘fast waves’-solver (I): forward-steps + vertically implicit

+ equations for the divergence D, p’ and T’


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Kick off meeting: 30.06/01.07.2009 in Wierzba, Poland


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Task 1: The anelastic (EULAG) approachTesting the EULAG dynamical core as a prospective dynamical core of COSMO

Task 1.1: Idealised tests of the EULAG dynamical core•Simulate 2D and 3D idealized flows (flow over mountains, valley flows, ...)•Compare with COSMO results, laboratory flows and analytic solutions.

Test cases are defined in Task 3.1.

This task should give a first insight into the capabilities of the EULAG dynamical core and its possible advantages towards the current COSMO model.

Deliverables: results posted on the COSMO-webpage, a report with special focus on these idealized tests will be prepared for December 2009 ( talk by Marcin Kurowski)At the GM a report shall be presented with special focus on possible barriers for the usage of the EULAG model.


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Task 1.2: Tests of the EULAG dynamical core for realistic flows over the Alpine topography•case studies for different weather regimes ranging from simple (without much weather), to summer (convective) and winter (frontal) situations•real / idealised inflow•with realistic orography (Alpine area, containing deep valleys)•resolution ranging from 2.2 km, 1.1 km to 0.25 km•No physics parameterizations!

Perform EULAG-Sim. and compare with COSMO/RK and COSMO/Leapfrog Test data files are maintained in task 3.2.

•Test computational efficiency and scalability of EULAG core on parallel computers. •Adapt the implicit solver to the model resolution and orography.

Deliverables: report prepared for May 2010, recommendation on operational aspects, and estimation about model behaviour and stability in steep terrain.


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Task 1.3: Tests of the EULAG dynamical core for realistic flows over the Alpine topography with simplified physics parameterisationTo simulate realistic flows over the Alpine topography, with resolution ranging from 2.2, 1.1 km to 0.25 km, apply simplified parameterizations of basic subgrid processes:•Moist processes: only simulated on explicit grid (i.e. no shallow convection parameterization, no moist turbulence) •simple microphysics (Kessler-scheme) in both models. •Turbulent diffusion with a one-equation (TKE)-model (not necessarily the same in both models) •without interactive parameterization, but using the surface and radiation fluxes from independent COSMO 2.2 km model runs (or simplified surface fluxes)Compare results between EULAG and COSMO-sim.Carry out case studies (2 good, 2 bad cases with COSMO) for different weather regimes as for task 1.2.Deliverables: report prepared for September 2010. This report should contain a recommendation, if an implementation of the EULAG dynamical core into the COSMO model is doable and could improve the current deficiencies of the COSMO-model; estimation about resources needed to do that. Further a final estimation about the efficiency and performance.


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Task 1.4: Choice of the anelastic equation system•Several different soundproof sets of equations have been published and are available in EULAG. The possible errors implied should be investigated and a recommendation for the best approximation to use for NWP should be given.•Special focus should be given to the conservation of mass (i.e. ambiguity in the determination of the full pressure field), flows with finite-amplitude and non-linear perturbations with respect to the base state profile and the presence of large vertical gradients in the temperature field (i.e. inversions, tropopause). •The other conservation properties (i.e. which mass/energy variables are conserved by which equation sets) should also be investigated.Test the validity of conservation properties for mass, momentum and energy (possibly others like potential vorticity) in EULAG and COSMO. In COSMO a testing tool for conservation properties is available (developed in Priority project ‘Runge-Kutta’ (Baldauf, 2008) C. Nl.) and should be used for these inspections.•Implementation of the Durran equations.

Deliverables: recommendation about the anelastic approximation to use in EULAG


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Task 2.1: Metric tensor identitiesClear up the role of the ‘metric tensor identities’ (Smolarkiewicz, Prusa, 2005) and if they can empower the model to handle steep orography. Can they be applied directly to improve the current COSMO model formulation?

Task 2.3: Fully 3D, i.e. non-direction splitted, conservative advection schemeImplement a fully 3D, i.e. non-direction splitted, conservative advection scheme into COSMO. One example is MPDATA from the EULAG model (connection with tasks 1). Test this scheme with prescribed velocity fields in mountainous terrain, to show the transport properties also in terrain-following coordinates.Deliverables: MPDATA available

Task 2: the compressible approach


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Task 2.2: Complete FV-solver for the EULER equations

Starting point: Jameson (1991) Am. Inst. Aeronaut. Astron.

Finite volume discretization of the Euler-equations conservation of mass, momentum, energy(?)Implicit scheme helps in steep orography

This dynamical core is more in the state of an early-development stage model, therefore implementation into COSMO can be started relatively early after answering the most basic questions.

Spatial scheme:Central schemes with added artificial viscosity and upwind schemes can be adopted for spatial discretisation. Higher order schemes are more accurate, but lower order schemes at higher resolution could turn out to be more efficient, particularly when implemented on vector hardware architectures.

talk by Pier Luigi Vitagliano


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Prognostic variables: different representations of energy or maybe entropy could help to reduce the discretisation error. The choice should go toward functions that do not present large variations through the flow field.

Boundary conditions, hydrostatic equilibrium, ...

Task 2.2.1: Carry out a reduced set of the test cases from task 3.1

Deliverables: for June 2010, Report on test cases Deliverables: for Sept. 2010 evaluation report; this report should contain a recommendation, if the implementation of this dynamical core into the COSMO-model is doable and could improve the current deficiencies of the COSMO-model; with an estimation of resources needed.


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Task 3.1: Maintenance of idealized test casesPP 'Runge-Kutta': Several idealised test cases are already availableaim: carry out these tests ‘at the push of a button’ and compare automatically

with reference solutions. (output format: netCDF for CLM group).

0. advection test + nonlinear dyn. (Schär et al. (2002))1. Atmosphere at rest (G. Zängl (2004) MetZ) additional decision needed, which reference + initial

profile has to be taken?2. Cold bubble (Straka et al. (1993)) (unstationary density flow)3. Mountain flow tests (stationary, orographic flows)

3.1 Schaer et al. (2002), sect. 5b (for EULAG cite Wedi ,Smolarkiewicz (2004))3.2 Bonaventura (2000) JCP, (e.g. linear solution developed during Task 5, priority project RK

(Baldauf, 2008a))3.3 3D-case (dry), ? Klemp, Wilhelmson (?), Schmidli (?)

4. Linear Gravity waves (Skamarock, Kemp (1994), Giraldo (2008))5. Warm bubble (Robert (1993), Giraldo (2008))6. Moist, warm bubble (Weisman, Klemp (1982) MWR)

issue of steep terrain: test cases 0, 1, and 3issue of anelastic approximation: ?

Task 3: Assessment of dynamical cores


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Test of the dynamical core: density current (Straka et al., 1993)

RK2 + upwind 3. order

RK3 + upwind 5. order

‘ after 900 s. (Reference)by Straka et al. (1993)

P. Prohl, DWD


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Mountain flow (Schär et al. (2002) MWR)

Comparison with analytic solution (black lines) from Baldauf (2008) COSMO-Newsl.

z / 300m

a = 5 km / l=4 kmh= 25 mu=10 m/sT(z=0)=288 KN=0.01 1/sdx=500 mdz=300 m

12 km ~


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Bonaventura (2000) JCP: (1) linear, hydrostatic case

a = 16 kmh = 1 mdx = 3000 mdz = 250 mu = 32 m/sT = 273 K

P. Prohl, DWD

‘Reference’:

COSMO-model:


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Bonaventura (2000) JCP: (2) linear, nonhydrostatic case

a = 500 mh = 100 mdx = 100 mdz = 250 mu = 14 m/sT = 273 K

P. Prohl, DWD

‘Reference’:

COSMO-model:


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Bonaventura (2000) JCP: (3) nonlinear, hydrostatic case

a = 16 kmh = 800 mdx = 2800 mdz = 200 mu = 32 m/sN = 0.02 1/s

P. Prohl, DWD

correct mountain width or labeling?

‘Reference’:

COSMO-model:


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a = 16 kmh = 800 mdx = 2800 mdz = 200 mu = 32 m/sN = 0.02 1/s

Bonaventura (2000) JCP: (3) nonlinear, hydrostatic case

P. Prohl, DWD

‘Reference’:

COSMO-model:

correct mountain width or labeling?


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a = 1000 mh = 900 mdx = 200 mdz = 100 mu = 13.28 m/sN =

Bonaventura (2000) JCP: (4) nonlinear, nonhydrostatic case

correct labeling?

COSMO-model remains not stable in this steep mountain test! P. Prohl, DWD

‘Reference’:

COSMO-model:


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Task 3.2 Collection and maintenance of semi-idealized test casesA test bed with some semi-idealized (quasi-realistic) tests (steep mountains, valley flows, deep convection, …) should be maintained also with a documentation about the specific weather situation and what should be expected by the simulation. Input format: GRIBs from COSMO-model (e.g. 7km)Alpine region

A competition between the current and newly developed dynamical cores by these tests will be essential to decide the further direction of developments. For a broad acceptance it is advisable to include several groups in these tests.

Deliverables: collection of semi-idealised test cases


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Task 3.3: Decision tree for Steering CommitteeIn former projects concerning the development of a new dynamical core it has been proven to be rather difficult to decide about the continuation or the abort of the project, due to a lack of clear decision criteria. Here such a decision tree (a cascade of benchmarks) shall be set up.Deliverables: Dec. 2009: list of requirements for a dynamical core based on tasks 1.1-3.2, which have to be fulfilled. This should serve as a decision tree for the Steering Committee

Task 3.4: Verification of the whole modelA verification of the model by real observation data (Synop, upper air, radar data). Probably such a verification is only useful for a model with the full set of parameterizations.Deliverables: verification reportDepends on: task 1, 2


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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, ...

physics-dynamics-coupling

numerical aspects

physical aspects

data assimilation verificationEPS...


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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)

The dynamical cores of COSMO-model don't have any explicit conservation properties.Conservation: general guiding principle in designing a model


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Methodology: Finite-Volume-Methods• are well established in CFD (LeVeque, 2002, ...) • 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, 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 plannedfar range plans could use unstructured grid, e.g. for a more efficient implementation of a z-coordinate version

Documents

The new Priority Project Conservative Dynamical Core (CDC) COSMO General Meeting 07.-11.09.2009, Offenbach