Introduction of a local mapping factor in the spectral part of the Météo‐France global variable mesh numerical forecast model

For variable horizontal resolution simulations, a new formulation of spectral computations has been implemented in the ARPEGE/IFS spectral global numerical weather forecast model. The formulation makes use of a property of the conformal transformation which defines the stretched geometry: the local mapping factor is a combination of zero and first‐order Legendre polynomials only. Consequently, the mapping factor dependency in the spectral part of the computations can be introduced by simple extra multi‐diagonal operator multiplication. This idea is applied to both the semi‐implicit and the horizontal diffusion schemes to eliminate problems occurring when variable resolution is used together with either long time‐steps or steep orographies. The positive impact of these modifications is presented for semi‐Lagrangian and high‐resolution integrations. The relatively small extra computation and memory cost of the modified schemes is well suited to operational applications.