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. We have used a normal-mode analysis to investigate the impactsof the horizontal and vertical discretizations on the numerical solutions ofthe nonhydrostatic anelastic inertia–gravity modes on a midlatitude f plane. The dispersion equations are derived from the linearized anelasticequations that are discretized on the Z, C, D, CD, (DC), A, E and Bhorizontal grids, and on the L and CP vertical grids. The effects of bothhorizontal grid spacing and vertical wavenumber are analyzed, and the roleof nonhydrostatic effects is discussed. We also compare the results of thenormal-mode analyses with numerical solutions obtained by running linearizednumerical models based on the various horizontal grids. The sources andbehaviors of the computational modes in the numerical simulations are alsoexamined. Our normal-mode analyses with the Z, C, D, A, E and B grids generally confirmthe conclusions of previous shallow-water studies for the cyclone-resolvingscales (with low horizontal wavenumbers). We conclude that, aided bynonhydrostatic effects, the Z and C grids become overall more accurate forcloud-resolving resolutions (with high horizontal wavenumbers) than for thecyclone-resolving scales. A companion paper, Part 2, discusses the impacts of the discretization on theRossby modes on a midlatitude β plane.

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 1: Nonhydrostatic inertia–gravity modes