The Euler Equations of Motion with Hydrostatic Pressure as an Independent Variable

A novel form of the Euler equations is developed through the use of a different vertical coordinate system. It is shown that the use of hydrostatic pressure as an independent variable has the advantage that the Euler equations then take a form that parallels very closely the form of the hydrostatic equations cast in isobaric coordinates. This similarity holds even when topography is incorporated through a further transformation into terrain-following coordinates. This leads us to suggest that hydrostatic-pressure coordinates could be used advantageously in nonhydrostatic atmospheric models based on the fully compressible equations.