This document written by Pierre Bénard summarizes the principles for implementing an horizontal diffusion in a stretched model and lists the problems encountered in the development and validation of HDF scheme, and its current status. One of the goals is to have a written material in order to avoid further errors. Lack of formalization can sometimes be a source of problems with very serious consequences.

Contents :

• Introduction
• HD coefficients in non-stretched models
• "Target" diffusion operator for stretched models
• Notations for the ARPEGE stretched geometry
• Graphical examination of the spatial behaviour of diffusion operators in ARPEGE
• The HDU diffusion in ARPEGE
  • The "pure" current HDU operator
  • The "practical" current HDU operator
  • Proposal for a "new" HDU operator
• The HDF diffusion in ARPEGE
  • The "pure" current HDF operator
  • The "practical" current HDF operator
  • Alternative HDF operator
• Spatial comparison of current HDU and HDF operators
• Initial error in the specification of the hybrid character of the HDF
• Definition of the pertinent parameter for the diffusion in stretched models
  • space-independent pertinent parameter
  • space- and resolution-independent pertinent parameter
  • space-, resolution-, and stretching-independent pertinent parameter
  • Comparison of the constraints linked to the global balance vs. the non-dependence of the pertinent parameter
• Comments on the time-discretization of diffusion schemes
  • Current fully-implicit discretization
  • Proposal for a new time-discretization of spectral diffusions
  • Extension to HDF diffusion
• Choice of the diffusion parameter(s) in the current HDU
• Choice of the diffusion parameter in new HDU
• Choice of the diffusion parameter in HDF
• Choice of the diffusion parameter in proposed new-HDF
• Comparison of operational diffusion absolute intensities
  • Damping-time in operational ALADIN
  • Damping-time in operational HDU
  • Damping-time in "reference" ALADIN
  • Damping-time in the "reference" IFS
  • Damping-time in HDF
  • Spectral comparison of operational HDU vs. reference IFS
  • summary
• Conclusion
  • Recommendations
  • Comparison of new-HDU vs. HDF advantages
  • Absolute intensity of ARPEGE diffusion