From Glossary of Meteorology
An atmospheric model in which the hydrostatic approximation replaces the vertical momentum equation.
This implies that vertical acceleration is negligible compared to vertical pressure gradients and vertical buoyancy forces, a good approximation for synoptic and subsynoptic scales of motion. Hydrostatic models have been successfully applied with horizontal resolutions as small as about 10 km, resolving even some mesoscale circulations. Global and regional weather prediction models have traditionally been hydrostatic models.