Abstract:
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.
RESUME:
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.
Contents:
– 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.