Semi-Lagrangian computations in the cycle 39 of ARPEGE/IFS (November 2012)

 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. An example of namelist is provided.

 Contents:

 Introduction.
 Definition of Eulerian and semi-Lagrangian schemes.
 The 2D equations.
 The 3D equations in spherical geometry (ARPEGE/IFS).
 Discretisation of the equations: general aspects.
 Computation of medium and origin points.
 The SL discretisation of the 2D shallow-water system of equations (spherical geometry).
 The SL discretisation of the 3D primitive equation model.
 The SL discretisation of the 3D non hydrostatic model.
 "R" operator.
 Computation of longitudes and latitudes on the computational sphere.
 Interpolations and weights computations.
 Computation of "etapt" at full levels.
 Lateral boundary conditions.
 2D shallow water and 3D models organigrammes.
 Tangent linear and adjoint codes.
 Some distributed memory features.
 Specific SL variables in pointer modules, modules and namelists.
 An example of operational SL2TL namelist for ARPEGE.
 Bibliography.