Integration of the model equations, and eulerian dynamics, in the cycle 39 of ARPEGE/IFS (November 2012)

 Abstract:

This documentation can be seen as a long introduction to modelisation. 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 there 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. An example of namelist is provided.

 Contents:

 General purpose of this documentation.
 Introduction.
 Systems of horizontal coordinates.
 The different types of horizontal derivatives used.
 The 2D equations.
 The 3D equations in spherical geometry (ARPEGE/IFS).
 The 3D equations: specific features for plane geometry (ALADIN).
 Some other diagnosed quantities.
 Discretisation of the equations: general aspects.
 The hydrostatic pressure based "eta" vertical coordinate.
 The quantities "alpha" and "delta" linked to pressure depth layers.
 Treatment of the advection (2D and 3D models).
 Treatment of the physics (3D model).
 The Eulerian discretisation of the 2D shallow-water system of equations (spherical geometry).
 The Eulerian discretisation of the 3D primitive equation model.
 The Eulerian discretisation of the 3D non-hydrostatic model.
 Discretisation of some other diagnosed quantities.
 Treatment of the linear terms.
 The Asselin filter.
 Lateral coupling and spectral nudging.
 The flux form of an equation and its discretisation.
 Organigramme for the setup and control routines (direct code).
 Organigramme under STEPO for the direct Eulerian 2D model.
 Organigramme under STEPO for the direct Eulerian 3D model.
 List of GP... and GNH... routines computing intermediate dynamical quantities (direct code).
 Tangent linear code.
 Adjoint code.
 Some distributed memory features.
 Specific Eulerian model variables in modules and namelists.
 An example of namelist for ARPEGE and ALADIN.
 Bibliography.

 Appendices:

 Expressions for "grad alpha" and "grad delta" at full levels.
 Modified formulation of continuity equation in the deep layer system of equations.
 Discretisation of "grad mu_s" at full levels for spherical geometry
 Inertial Coriolis/centrifugal terms in a 3D primitive equation model, deep layer formulation, for spherical geometry.
 Transformation in the plane of the contribution "horizontal advection + horizontal curvature terms", in plane geometry (ALADIN).
 Expression of the horizontal gradient of "mu_s" in plane geometry (ALADIN).
 Expression of the vertical integration and of the vertical derivative matricial operators (vertical finite element scheme).