Semigeostrophic equations

From Glossary of Meteorology

semigeostrophic equations

The system of momentum and thermodynamic equations in geostrophic coordinates X, Y, Z, T, derived through the geostrophic momentum approximation, that fulfills the requirements of semigeostrophic theory.

At the momentum level, and using the pseudoheight coordinate Z = [1 - (p/p0)κ]cpθ0/g, the equations are
where ug, vg are the geostrophic wind components; u*ag, v*ag the transformed ageostrophic wind components; w* the transformed vertical velocity; Φ = φ + (1/2)(u2g + v2g) a potential function derived from the geopotential φ; qg the geostrophic potential vorticity; θ the potential temperature; g the acceleration of gravity; f the Coriolis parameter; ρ the density in Z-space; and θ0 a reference potential temperature.