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 with the semi-Lagrangian method currently implemented in ARPEGE/IFS. The following points will be described: semi-Lagrangian formulation and discretisation for different sets of equations, semi-Lagrangian trajectory research, horizontal and vertical interpolations done in the semi-Lagrangian scheme, specific geometric problems met in this type of discretisation. An organigramme is provided. An introduction to tangent linear and adjoint code is provided.

LE BUT GENERAL DE CETTE DOCUMENTATION EST DE DECRIRE LE JEU D’EQUATIONS UTILISE, ET EGALEMENT LA FACON DE DISCRETISER CES EQUATIONS AVEC UN SCHEMA D’ADVECTION SEMI-LAGRANGIEN TEL QU’IL EST UTILISE DANS ARPEGE/IFS. ON DECRIT LES POINTS SUIVANTS: FORMULATION LAGRANGIENNE DES EQUATIONS, LEUR DISCRETISATION AVEC UN SCHEMA SEMI-LAGRANGIEN, RECHERCHE DE TRAJECTOIRE, INTERPOLATIONS HORIZONTALES ET VERTICALES FAITES DANS LE SCHEMA SEMI-LAGRANGIEN, PROBLEMES DE GEOMETRIE SPECIFIQUES. ON FOURNIT UN ORGANIGRAMME. UNE INTRODUCTION AU CODE TANGENT LINEAIRE ET ADJOINT EST EGALEMENT PROPOSEE.

• 01/ Introduction.
• 02/ Definition of Eulerian and semi-Lagrangian schemes.
• 03/ The 2D equations.
• 04/ The 3D equations in spherical geometry (ARPEGE/IFS).
• 05/ Discretisation of the equations: general aspects.
• 06/ Computation of medium and origin points.
• 07/ The SL discretisation of the 2D shallow-water system of equations (spherical geometry).
• 08/ The SL discretisation of the 3D primitive equation model.
• 09/ The SL discretisation of the fully elastic non hydrostatic (NHEE) model.
• 10/ The SL discretisation of the quasi elastic non hydrostatic (NHQE) model.
• 11/ "R" operator.
• 12/ Computation of longitudes and latitudes on the computational sphere.
• 13/ Computation of "etadot" at full levels.
• 14/ Interpolations and weights computations.
• 15/ Lateral boundary conditions.
• 16/ 2D shallow water and 3D models organigrammes.
• 17/ Tangent linear and adjoint codes.
• 18/ Some distributed memory features.
• 19/ Specific SL variables in pointer modules, modules and namelists.
• 20/ Bibliography.

• Appendix 1/ Description of treatment of NHX for semi-Lagrangian advection.
• Appendix 2/ Description of dataflow for option LGWADV=T.