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Inelastic and Compressible Approaches in Weather Prediction Modeling

This overview provides information on the anelastic and compressible approaches used in weather prediction modeling. It includes details on the testing, validation, and parameterization of these approaches. The coupling of EULAG dyn. core with COSMO via an interface is also discussed.

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Inelastic and Compressible Approaches in Weather Prediction Modeling

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  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. 2011 PP CDC Meeting, Langen 05 Sept. 2011 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 anelasticnonhydrostatic model EULAG as aprospective dynamical core of a numericalweather prediction model. Part I: Dry Benchmarks M. J. Kurowski, B. Rosa and M. Z. Ziemiański:Testing the anelasticnonhydrostatic model EULAG as a prospective dynamical core of numerical weather prediction model. Part II: Simulations of a supercell June 2011 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. 161-169 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 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?

  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. 2010 visit of Damian Wojcik at DWD introduction to the COSMO code by U. Schättler, U. Blahak, M. Baldauf 18-22 July 2011 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 – 07.01.2020

  14. Task 1.6 • Couplingwithphysics:shouldbepossibleasin COSMO • usethetendenciesofthemostoftheparameterizations • exception: microphysicsupdatethermodynamicfieldsbymicrophysics; u, v, w (on A-grid) are not affected! • usediffusionoperatorfromEULAGinsteadofthe COSMO one? • Work to do: • transferthemetricsoftheterrain-followingcoordinatefrom • COSMO toEULAG. • No fundamental problem, becauseEULAGallows a greaterclassof • coordinatetransformationsandtopologies (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 60-70 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 1.8 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 Initial distribution for the solid body rotation tests • Cone tracer with 5 grid points radius • NO background • NO orography • Δx = 2.2km • Δt = 20s • Courant nb. ~ 0.3

  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 • 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 • 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 = 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 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 Bretherton-Transformation: (inverse) scale height: ~ (10 km)-1

  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) NBrunt-Vaisala-frequency ( ~ 0.01 1/s) aacoustic cut off frequency (~ 0.03 1/s) Re /a sound waves compr. + div.damp. gravity waves a N cos   =  (kz, kx) = 0° k * cs / a  ~ 7 km  ~ 3.5 km

  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.) k * cs / a  ~ 7 km  ~ 3.5 km

  34. Dispersion relation  = (kx, kz) of internal waves; only gravity waves /a N cos  N ~ 0.01 1/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 ~ 0.01 1/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 ~ 0.018 1/s anelastic compressible, with divergence damping compressible Work to be done:inclusion of f-plane Effects. k * cs / a  ~ 70 km

  37. 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-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

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