# The hydrostatic and nonhydrostatic global model IFS/ARPEGE: deep-layer model formulation and testing

## Yessad, Karim ; Wedi, Nils P.

A nonhydrostatic dynamical core, formerly coded in the limited area model ALADIN, has been extended to the global model IFS/ARPEGE, for both the uniform and the rotated/stretched meshes, respectively. Options have been developed to run the global model under the spherical geopotential approximation using either the hydrostatic primitive equations, the quasi-hydrostatic equations, the nonhydrostatic shallow-atmosphere equations or the nonhydrostatic deep-atmosphere equations. The latter includes the additional accelerations in the zonal and vertical components of the momentum equation due to the Coriolis force and (optionally) the vertical variations of the gravitational acceleration. The nonhydrostatic deep model is equally stable compared with the hydrostatic shallow-atmosphere model when the aspect ratio of the vertical extent of the atmosphere compared to the radius of the sphere is << 1. The four different formulations are compared in idealised simulations as well as against results from the (optionally) shallow or deep nonhydrostatic EULAG model. Both the deep- and shallow-atmosphere IFS model versions give practically equivalent results in four-member ensembles of 13 months simulations, and practically equivalent statistics in medium-range weather forecasts, suggesting a negligible effect when the resolved flow regime is hydrostatic.

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