# Quasi-hydrostatic approximation

From AMS Glossary

## quasi-hydrostatic approximation

(Or quasi-hydrostatic assumption;

*also called*hydrostatic approximation.) The use of the hydrostatic equation as the vertical equation of motion, thus implying that the vertical accelerations are small without constraining them to be zero.This compromise takes advantage of the smallness of organized vertical accelerations in cyclonic- scale motions while allowing theoretically for a realistic distribution of vertical velocities, which may be computed from the other equations of a closed system. Dynamically, the effect of the quasi-hydrostatic approximation is to eliminate or filter out the higher frequencies, corresponding to sound waves and certain (but not all) gravity waves, from the fundamental equations, while retaining the frequencies corresponding to cyclonic-scale motions. Combined often with the quasigeostrophic approximation, this assumption is much used in theoretical work associated with numerical forecasting. An example of phenomena to which it is inapplicable is the lee wave. For the discussion of this and other types of gravity waves, it is common to assume hydrostatic equilibrium in the basic flow but not in the perturbation.

*See*filtering approximations.