Priority project CDC

Overview Task 1

COSMO-GM, 06.-10. Sept. 2010, Moscow

M. Baldauf (DWD)

SMC-meeting, 21./22. June 2010, Sopot (tasks 1.5, 2.4)

decision:both branches ('EULAG' and 'compressible') will be continued

In the following some basic properties of the equations sets are presented ( task 1.4)

All idealised test cases performed very well with the EULAG model (task 1.1)(reports are nearly available) The results from the (semi-)realistic test cases - with no physics parameterization (task 1.2)- or with a reduced set of paramterizations (task 1.3)did not show any recognizable drawbacks of the anelastic approach in comparison with the compressible approach ( talk Marcin Kurowski)

• Boussinesq-approximation: replace cont.eqn. by div v = 0only usable for shallow flows

• anelastic approximation by Ogura, Phillips (1962) JAS: use div 0v = 0 and isentropic base state 0=const. problem with deep convection

• anelastic approximation by Wilhelmson and Ogura (1972) JAS: 0 const. possible; but energy conservation lost

• anelastic approximation by Lipps, Hemler (1982) JAS EULAG eqn. setallows weakly variing 0=0(z); energy conserving

• pseudo-incompressible equations (Durran, 1989) JAS: replace cont.eqn. by div 00v = H/cp/0 (H=latent heating rate) is also usable in regions of strong static stability; energy conserving

A collection of sound proof equation sets

Comparison between the compressible equations and the anelastic approximation; linear analysis (normal modes)

divergencedamping

p=p0+p’T=T0+T’

Bretherton-Transformation:

switches:• compressible: all i=1• compr. + div. damp.: all i=1 • anelastic: 2,3=0, 1,4,5=1

(inverse) scale height: ~ (10 km)-1

wave ansatz: u(x,z,t) = u(kx, kz,) exp( i ( kx x + kz z - t ) ), w(x,z,t)= …

Re /a

a N cos = (kz, kx) = 0°

k * cs / a

cs sound velocity( ~ 330 m/s)

N Brunt-Vaisala-frequency( ~ 0.01 1/s)

a acoustic cut off frequency(~ 0.03 1/s)

Dispersion relation = (kx, kz) of internal waves

sound waves

gravity waves

~ 7 km ~ 3.5 km

compr. + div.damp.

Im /a

k * cs / a

~ 7 km ~ 3.5 km

Strong damping of short sound waves in the compressible equations due toartificial divergence damping.

Dispersion relation = (kx, kz) of internal waves

(timescale 1/a ~ 30 sec.)

Dispersion relation = (kx, kz) of internal waves;only gravity waves

/aN cos

= (kz, kx) = 0°

k * cs / a ~ 7 km ~ 3.5 km

quite similar dispersion relation for anelastic and compressible eqns.

N ~ 0.01 1/s

Dispersion relation = (kx, kz) of internal wavesonly gravity waves

compressible, with divergence damping

compressible

anelastic

/a

k * cs / a

= (kz, kx) = 0°

~ 70 km

smaller differences for very long gravitywaves

N ~ 0.01 1/s

compressible, with divergence damping

compressible

anelastic

Dispersion relation = (kx, kz) of internal wavesfocus on long gravity waves

~ 70 km

/a

k * cs / a

= (kz, kx) = 0°

N ~ 0.018 1/s

Work to be done:inclusion of f-planeEffects.

summary of section '7. conclusions':

• Lamb modes (external acoustic):are filtered out by all sound proof approximations

• external Rossby modes:Lipps and Hemler (1982) set: distorts the height-scalepseudo-incompressible: handles height-scale correctly

• internal Rossby modes:anelastic sets misrepresent them at wavelengths typically encountered in atmospheric models.pseudo-incompressible handles them correctly.

• internal gravity modes:all sound proof sets mishandle deep vertical modes at large horizontal scale.Good representation of smaller horizontal scales

Davies et al. (2003) QJRMS'Validity of anelastic and other equation sets as inferred from normal-mode analysis'

Nance, Durran (1994) JAS'A comparison of the accuracy of three anelastic systems and the pseudo-incompressible system'

comparison between 4 different anelastic approximationsand a compressible model (leapfrog, advection with centered differences 4th order horizontally and 2nd order vertically)

the different tests resulted in bigger errors of the numerical scheme for the compressible equations compared to the errors of the anelastic approximation. problem of 'Low-Mach number' solvers

How would this comparison look like for currently used compressible solvers?

Fig. 4 from Nance, Durran (1994) JAS

W‘ u‘

eqn- error

numer. error

Smith, Bannon (2008) MWR'A comparison of Compressible and Anelastic Models of Deep Dry Convection'

• Simulation of an initial warm bubble• 2-dim., dry case, very high resolution (dx=dz=200 m)• interesting aspect: different initialization of compressible and anelastic

models needed for idealised setups

Results:

• bigger differences in compressible and anelastic model for times t << 2/N ~ 10 min.

• only small differences for times t 2/Nmain difference: Lamb wave expansion

• better efficiency of the anelastic model

First conclusions about anelastic approximations

• for smaller scale models and dry Euler equations the anelastic approximation seems to work quite good

• keep in mind that short sound waves are also strongly damped in our compressible solver (divergence damping)

• all of the idealised tests studied in task 1.1 delivered satisfying resultswith the anelastic approx.

• objectives against the anelastic approach from Davies et al. (2003) mainly stem from larger scale applications

• what is the meteorological meaning of long sound waves and the Lamb mode?

• relevance of deviation for very long gravity waves? tests withlarge scale mountain flows (upstream blocking, ...)

• are there changes in the assessment when moist processes are studied?

extension of task Task 1.1: Idealised tests of the EULAG dynamical core

Meanwhile it was found that tests for very large scales should also be performed, because climate applications require larger regions. A large mountain test case (new item 3.4 in task 3.1) could be suitable as a training study for the new colleague at IMGW. If this test should show serious obstacles for the anelastic equation set, one should consider the use of alternative equation sets like the pseudo-incompressible set (Durran, 1989).Deliverables: results will be posted on the COSMO-webpage, a report with special focus on these idealized tests will be prepared for December 2009At the General Meeting in Offenbach a report shall be presented with special focus on possible barriers for the usage of the EULAG model.

Task 1.6: Coupling of EULAG dyn. core with COSMO via an interfaceintermediate step and to keep the amount of work in a reasonable range: coupling via an interface. This means that the EULAG dyn. core keeps his own variables, data structure, … It is not the aim to have a very efficient code version at this stage but to have a useable model version.- advance the EULAG code to a minimum set of technical requirements for the coupling:

- convert the code from F77 to F90 style without changing too much of the structure (mainly introduce free formatting, replace goto, continue-statements by end if, end do, …)- replace all fields with fixed dimensions into allocatable fields- where necessary, replace COMMON-blocks by MODULES

- define an interface for the coupling of COSMO and EULAG dyn. core. A call like ‘org_runge_kutta’ in organize_dynamics.f90 should be aimed at.

This interface must treat - the transformation of the variable set (u,v,w, p’, T’ in COSMO, rho, rho*u, rho*v, rho*w, Theta in EULAG)- probably the grid position (staggered in COSMO, unstaggered in EULAG)- the metric coefficients of the terrain following coordinate. In COSMO a more transparent treatment of such terms should be considered also.- the coupling of physics tendencies with the dynamical core- the use of MPDATA as a tracer advection scheme- the domain decomposition in COSMO and EULAG should be the same, i.e. the same grid points should lie on the same processor domains

Deliverables: COSMO version which uses EULAG dynamical core instead of Runge-Kutta or Leapfrog

Task 1.7: Technical testing with COSMO by idealised casesThe correct coupling of the EULAG dyn. core into COSMO can be at first tested with the implemented idealised test cases (see task 3.1). This testing can be performed ‘by a press of a button’ in COSMO. The staff is now well trained with the idealised tests (see task 1.1), therefore it is not necessary to perform an extended analysis of such idealised tests, but simply to check if any technical coupling problems occur.Deliverables: (very) short report about the success of the idealised tests in COSMO

Task 1.8: Real case simulations with the preliminary coupled versionAfter finishing task 1.7 real case simulations with full physics parameterisations with COSMO are possible. Stand-alone runs for several weather regimes can be performed for both dynamical cores (EULAG, RK) at different resolutions. One has to obey that physical parameterizations have to be adapted to the new dynamical core. This probably requires support from the physical parameterization working group.Deliverables: report about the behaviour of real case test simulations with COSMO