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Integration of the model equations, and eulerian dynamics, in the cycle 46t1r1 of ARPEGE/IFS.

Tuesday 12 February 2019 by Karim Yessad
  Table of contents  

 Abstract:

This documentation can be seen as a long introduction to modeling. The general purpose of this documentation is to describe the set of equations used, and also the way to integrate the dynamics of the model. Two points will be examined in detail in this documentation: the Eulerian dynamics and the discretisations used. For some other aspects (semi-Lagrangian dynamics, physics, spectral transforms, horizontal diffusion, semi-implicit scheme), this documentation will not provide any detailed description, since there are other documentations describing these topics. The following points will be described: model geometry, different set of equations (non hydrostatic, primitive, shallow-water), their Eulerian formulation and their Eulerian discretisation, calculation and discretisation of some intermediate diagnosed quantities (like the geopotential height). An organigramme is provided. An introduction to tangent linear and adjoint code is provided. There is a specific chapter for the flux form of the Eulerian equation, which is the basis of the DDH diagnostics.


 RESUME:

ON PEUT VOIR CETTE DOCUMENTATION COMME UNE LONGUE INTRODUCTION A LA MODELISATION. LE BUT GENERAL DE CETTE DOCUMENTATION EST DE DECRIRE LES JEUX D’EQUATIONS UTILISES, ET AUSSI LA MANIERE D’INTEGRER CES EQUATIONS. ON EXAMINE PLUS PARTICULIEREMENT LES DEUX POINTS SUIVANTS: LA DYNAMIQUE EULERIENNE ET LES DISCRETISATIONS UTILISEES. SUR D’AUTRES ASPECTS (SEMI-LAGRANGIEN, PHYSIQUE, TRANSFORMEES SPECTRALES, DIFFUSION HORIZONTALE, SCHEMA SEMI-IMPLICITE), CETTE DOCUMENTATION NE FOURNIT AUCUNE DESCRIPTION DETAILLEE, CAR IL Y A D’AUTRES DOCUMENTATIONS DECRIVANT CES SUJETS. LES POINTS SUIVANTS SONT ABORDES: GEOMETRIE, DIFFERENTS JEUX D’EQUATIONS (NON HYDROSTATIQUE, EQUATIONS PRIMITIVES, MODELE SHALLOW-WATER), LEUR DISCRETISATION AVEC UN SCHEMA D’ADVECTION EULERIEN, LE CALCUL ET LA DISCRETISATION DE CERTAINES QUANTITES DIAGNOSTIQUEES (COMME LA HAUTEUR GEOPOTENTIELLE). ON FOURNIT UN ORGANIGRAMME. UNE INTRODUCTION AU CODE TANGENT LINEAIRE ET ADJOINT EST EGALEMENT PROPOSEE. IL Y A UN CHAPITRE SPECIFIQUE CONSACRE A LA FORME FLUX DES EQUATIONS, QUI SERT DE BASE AUX DIAGNOSTICS DDH.


 Contents:

  • 01/ Introduction.
  • 02/ Systems of horizontal coordinates.
  • 03/ The different types of horizontal derivatives used.
  • 04/ The 2D equations.
  • 05/ The 3D equations.
  • 06/ Some other diagnosed quantities.
  • 07/ Discretisation of the equations: general aspects.
  • 08/ The hydrostatic pressure based "eta" vertical coordinate.
  • 09/ Treatment of the advection (2D and 3D models).
  • 10/ Physics and physics-dynamics interface (3D model).
  • 11/ The Eulerian discretisation of the 2D shallow-water system of equations (spherical geometry).
  • 12/ The Eulerian discretisation of the 3D primitive equation model.
  • 13/ The Eulerian discretisation of the 3D fully compressible non-hydrostatic model (NHEE).
  • 14/ The Eulerian discretisation of the 3D quasi compressible non-hydrostatic model (NHQE).
  • 15/ Discretisation of some other diagnosed quantities.
  • 16/ Miscellaneous (linear terms, Asselin filter, LBC).
  • 17/ The flux form of an equation and its discretisation.
  • 18/ Organigramme.
  • 19/ Basic description of the data flow under routine STEPO.
  • 20/ Tangent linear code.
  • 21/ Adjoint code.
  • 22/ Some distributed memory features.
  • 23/ Specific Eulerian model variables in modules and namelists.
  • 24/ Bibliography.

 Appendices:

  • A1/ Vertical integrals and their discretisation.
  • A2/ Expressions for "grad alpha" and "grad delta" at full levels.
  • A3/ Expression of the vertical integration and of the vertical derivative matricial operators (vertical finite element scheme).

titre documents joints

Version cycle 46t1r1

12 February 2019
info document : PDF
752.7 kb

Version cycle 46t1

7 January 2019
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752.2 kb

Version cycle 46

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Version cycle 45

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Version cycle 44

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Version cycle 43

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Version cycle 42

7 July 2015
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