1. Priority project CDC – Overview COSMO General Meeting
05-09 Sept. 2011, Rome
M. Baldauf (DWD)

2. Task 1: the anelastic (EULAG) approach
Marcin Kurowski, Bogdan Rosa, Damian Wojcik, Michal Ziemianski
talk by Bogdan Rosa
Task 2: the compressible approach
Pier Luigi Vitagliano, Guy deMorsier
Task 3: Validation, Verification
28 Feb PP CDC Meeting, Langen
05 Sept PP CDC Meeting, Rome

3. Task 1.1: Idealized tests
publications now accepted for Acta Geophysica 59 (6) , 2011
(collection of papers for the EULAG workshop, Sopot, Sept. 2010)
B. Rosa, M. J. Kurowski, and M. Z. Ziemiański:Testing the anelastic nonhydrostatic model EULAG as a prospective dynamical core of a numerical weather prediction model. Part I: Dry Benchmarks  
M. J. Kurowski, B. Rosa and M. Z. Ziemiański:Testing the anelastic nonhydrostatic model EULAG as a prospective dynamical core of numerical weather prediction model. Part II: Simulations of a supercell  
one issue about EULAG workshop
June visit of Damian Wojcik at NCAR (P. Smolarkiewicz)
March 2011 visit of Marcin Kurowski at NCAR (P. Smolarkiewicz)
2011 permanent stay of Zbigniew Piotrowski at NCAR (P. Smolarkiewicz)

4. Task 1.2: Semi-idealized tests with EULAG without parameterizations
Task 1.3: Semi-idealized tests with EULAG with a simplified set of parameterizations
publications now accepted for Acta Geophysica 59 (6) , 2011
(collection of papers for the EULAG workshop, Sopot, Sept. 2010)
M. Z. Ziemiański, M. J. Kurowski, Z. P. Piotrowski, B. Rosa and O. Fuhrer: Toward very high resolution NWP over Alps: Influence of the increasing model resolution on the flow pattern

5. Task 1.4: Choice of anelastic equation system
publication:
M. Baldauf: Non-hydrostatic modelling with the COSMO model, proceedings of ‘ECMWF workshop on non-hydrostatic modelling’,
ECMWF, p
Normal mode analysis of the gravity wave expansion.
Extensions towards the results presented last year:
inspection of the Lipps, Hemler (1982) JAS, anelastic equation system (additionally to Ogura, Phillips (1962) JAS, Wilhelmson, Ogura (1972) JAS
inclusion of Coriolis forces

6. Dispersion relation for horizontally propagating gravity waves
isothermal stratification
 ~ 63 km

7. Dispersion relation for horizontally propagating gravity waves
isothermal stratification
 ~ 2.5 km

8. Dispersion relation for horizontally propagating gravity waves
N=0.01 1/s
 ~ 63 km

9. Dispersion relation for horizontally propagating gravity waves
N=0.01 1/s
 ~ 2.5 km

10. 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 results with 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 with large scale mountain flows (upstream blocking, ...)
are there changes in the assessment when moist processes are studied?

11. Task 1.6: Coupling of EULAG dyn. core with COSMO via an interface
intermediate 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

12. Task 1.6
18-29 Oct visit of Damian Wojcik at DWD introduction to the COSMO code by U. Schättler, U. Blahak, M. Baldauf
18-22 July visit of D. Wojcik at DWD (M. Baldauf, A. Seifert)
coupling with physics
until February 2011: conversion of EULAG code from Fortran 77 to F90
free format syntax
remove GOTO as far as possible
remove COMMON blocks, EQUIVALENCE statements
remove DATA and BLOCKDATA statements
introduce dynamic memory allocation
Names and comments in English
...
March 2011:
adapting COSMO's MPI communication
Configuration via namelists

13. Physics-Dynamics-coupling in COSMO
fields n=(u, v, w, pp, T, ...)n
Physics (I)
Radiation
Convection
Coriolis force ('old' scheme)
Turbulence
‚Physics (I)‘-tendencies n(phys I)
Dynamics
Runge-Kutta [(phys) + (adv) --> fast_waves ]
fields *=(u, v, w, pp, T, ...)*
Physics (II)
Cloud Physics
‚Physics (II)‘-tendencies n(phys II)
fields n+1=(u, v, w, pp, T, ...)n+1
FE 13 –

14. Task 1.6
Coupling with physics: should be possible as in COSMO
use the tendencies of the most of the parameterizations
exception: microphysics update thermodynamic fields by microphysics; u, v, w (on A-grid) are not affected!
use diffusion operator from EULAG instead of the COSMO one?
Work to do:
transfer the metrics of the terrain-following coordinate from
COSMO to EULAG.
No fundamental problem, because EULAG allows a greater class of
coordinate transformations and topologies (sphere, torus, ...) than COSMO
(exception: hybrid coordinate not trivial)
Nov. 2011: two week visit of Damian Wojcik at DWD is planned

15. Task 1.7: Technical testing with COSMO by idealised cases
The 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

16. Task 1.8: Real case simulations with the preliminary coupled version
After 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

17. Task 1.9: Idealized and Real case simulations with a vertically extended domain
Motivation:
possible future use of satellite data  much higher model top is needed.
use of COSMO for scientific studies e.g. of gravity waves in the middle atmosphere.
Is COSMO well suited for that ? (first steps: ‘new reference atmosphere’,...)
Of course a new dynamical core also should be investigated (or improved) in this respect.
try the COSMO simulations,
start with idealized flows over mountains and
the atmosphere at rest test case.
For real case simulations: for model tops until km boundary data from IFS can be used.Test accuracy of int2lm
Comparison of the EULAG implementation with COSMO runs (test this by atmosphere at rest idealized test case)

18. Task 1.10: Development of open boundary conditions at the outflow boundary
(see item 3.4 of the 'decision tree for CDC', 26. Jan. 2010)
The nesting of an anelastic approximated model to a compressible one (COSMO or e.g. ICON in the future) poses problems at the boundary. The solution of an elliptic equation for the pressure with prescribed values at all the boundaries affects the inner solution of the EULAG very strongly. At least at the outflow boundaries a better solution using open (non-reflecting) boundaries should be found.

19. If tasks 1. 6, 1. 7 are finished and task 1
If tasks 1.6, 1.7 are finished and task 1.8 is in a reasonable state, then:
Task 3.4: Verification of the whole model
... by real observation data (Synop, upper air, radar data);
model runs over several weeks in a quasi operational environment (like NUMEX at DWD). This should not be too difficult because the whole I/O of COSMO is not affected.
One should distinguish two stages:
1.) pure forecast runs starting from an initial state generated by COSMO runs can be performed (data assimilation based on nudging is not possible!)
(can a simplified version of DFI be used to filter out initial disturbances?)
2.) To install a complete data assimilation cycle with COSMO/EULAG, probably the success of KENDA is a prerequisite.
Every contribution to such a verification is welcome!

20. Task 2: The compressible approach
Task 2.2 Complete FV-solver for the EULER equations
and subsequent tasks 2.5, 2.6, 2.7
no further work done in 2010/11
estimation about useability of dual time stepping during the next COSMO year
possible future of this part of the project:
treat it as a priority task in WG2 (?)

21. Task 2.3: Fully 3D conservative advection scheme
G. deMorsier (MeteoCH), M. Müllner
Aim of the diploma thesis (6 months) was to implement, evaluate and test a fully three-dimensional advection scheme in the COSMO model
New advection scheme: MPDATA (Multidimensional Positive Definite Advection Transport Algorithm)
Main differences:
MPDATA is multidimensional and conservative
Bott is approximately conservative , but direction splitted
semi-Lagrangian is 3D, but not conservative

22. Solid Body Rotation Tests
Cone tracer with 5 grid points radius
NO background
NO orography
Δx = 2.2km
Δt = 20s
Courant nb. ~ 0.3
Initial distribution for the solid body rotation tests

23. Solid Body Rotation Test I
MPDATA (iord=2, nonos=1) Bott_2 advection scheme
(a)
(a)
Max. 1
(b)
(b)
(d)
(d)
(c)
(c)
Min. 0
Tracer at the beginning (a), after 1h (b), after 2h (c) and after 3h (d)

24. Error measures
Phase shift: distance of exact maximum to computed maximum
Diffusion: difference between computed and exact maximum value

25. Error measures for Test I
Advection Scheme
Maximum value after one rotation
Phase error
Diffusion error
Bott_2
0.501
1.414
0.499
Semi Lagrange
0.510
0.490
MPDATA:
iord=2, nonos=0
0.219 2
0.781
iord=3, nonos=0
0.348
2.236
0.652
iord=2, nonos=1
0.217
0.783
iord=3, nonos=1
0.344
0.656
Conclusions: • MPDATA is very diffusive
large phase errors for MPDATA
smallest diffusion error for SL

26. Tracer Test in a deformation flow
Cone tracer with 5 grid points radius
NO background
NO orography
Δx = 2.2km
Δt = 20s
max. Courant nb. ~ 0.04

27. Error measures for deformation flow
Advection Scheme
Maximum value after 5h
Maximum value after 10h
Bott_2
0.297
0.148
Semi Lagrange
0.334
0.164
MPDATA:
iord=2, nonos=0
0.278
0.126
iord=3, nonos=0
0.299
0.149
iord=2, nonos=1
0.267
0.128
iord=3, nonos=1
0.287
0.146
Conclusions: • best performance for SL
small impact of MPDATA parameter choice
small advantage of MPDATA over Bott

28. Summary and Conclusions
MPDATA can be much more diffusive than Bott and SL schemes
High phase errors with MPDATA in rotation tests
MPDATA is better than the Bott scheme for divergent/convergent flows
More computer time needed for MPDATA
MPDATA scheme was not tested in a 3D configuration
For the moment MPDATA runs only on one processor
What would be the results of Bott with a full strang splitting at each time step (zyxyz)?

29. Thank you for your attention

30. A collection of sound proof equation sets
Boussinesq-approximation: replace cont.eqn. by div v = 0 only 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. set allows weakly variing 0=0(z); energy conserving
pseudo-incompressible equations (Durran, 1989) JAS: replace cont.eqn. by div 00v = H/cp/0 (H=latent heating rate) is also usable in regions of strong static stability; energy conserving

31. Comparison between the compressible equations and the anelastic
approximation; linear analysis (normal modes)
p=p0+p’
T=T0+T’
divergence
damping
switches:
compressible: all i=1
compr. + div. damp.: all i=1
anelastic: 2,3=0, 1,4,5=1
Galilei-Invarianz nur, falls delta2 = delta3 und delta4=1
Bretherton-Transformation:
(inverse) scale height:
~ (10 km)-1 32

32. Dispersion relation  = (kx, kz) of internal waves
wave ansatz: u(x,z,t) = u(kx, kz,) exp( i ( kx x + kz z -  t ) ), w(x,z,t)= …
cs sound velocity
( ~ 330 m/s)
N Brunt-Vaisala-frequency
( ~ /s)
a acoustic cut off frequency
(~ /s)
Re /a
sound waves
compr. + div.damp.
anelast. approx: keine Schallwellen
volle kompress. Gln und anelast. Gln: omega ist rein reell
kompress. Gln + Div. dämpfung: omega ist komplex
gravity waves a
N cos 
 =  (kz, kx) = 0°
k * cs / a
 ~ 7 km
 ~ 3.5 km 33

33. Dispersion relation  = (kx, kz) of internal waves
Strong damping of short sound waves in the compressible equations due to
artificial divergence damping.
Im /a
(timescale 1/a ~ 30 sec.)
Im omega < 0  Dämpfung ~ exp ( - i omega t ) ~ exp( (Im omega/omega_a) * ( t/T_a) ) wenn man Zeiten in Vielfachen von T_a = 1/omega_a ~ 30 sec misst.
k * cs / a
 ~ 7 km
 ~ 3.5 km 34

34. Dispersion relation  = (kx, kz) of internal waves;
only gravity waves
/a
N cos 
N ~ /s
 =  (kz, kx) = 0°
quite similar dispersion
relation for anelastic and
compressible eqns.
k * cs / a
 ~ 7 km
 ~ 3.5 km

35. Dispersion relation  = (kx, kz) of internal waves only gravity waves
 =  (kz, kx) = 0°
/a
N ~ /s
anelastic
smaller differences
for very long gravity
waves
compressible, with divergence damping
compressible
k * cs / a
 ~ 70 km

36. Dispersion relation  = (kx, kz) of internal waves
focus on long gravity waves
 =  (kz, kx) = 0°
/a
N ~ /s
anelastic
compressible, with divergence damping
compressible
Work to be done: inclusion of f-plane
Effects.
k * cs / a
 ~ 70 km

37. summary of section '7. conclusions':
Davies et al. (2003) QJRMS
'Validity of anelastic and other equation sets as inferred from normal-mode analysis'
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-scale pseudo-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