This paper written be Pierre Bénard in December 2004 is a working document, which can serve as a starting basis for discussions between ECMWF and Météo-France about the extension of the current IFS Vertical Finite Elements (VFE) scheme to NH modelling.

The current VFE discretisation introduced in IFS by ECMWF for the HPE system is examined, in view of its extention to the NH system :
– detailed scientific description of IFS’s VFE discretisation
– some limitations and weakness in the current VFE discretisation
– possible avenues for the extension of the VFE scheme to NH modelling
– behaviour of the current VFE scheme and of the proposed avenues (accuracy, normal modes, ...).

Alternative strategies are also reviewed. When possible, the degree of chance of their success is discussed.

The present study is restricted to the behaviour of the purely linear system associated to the SI cheme.