# Semigeostrophic equations

From AMS Glossary

## 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 where

*Z*= [1 - (*p*/*p*_{0})^{κ}]*c*_{p}θ_{0}/*g*, the equations are*u*_{g},*v*_{g}are the geostrophic wind components;*u**_{ag},*v**_{ag}the transformed ageostrophic wind components;*w** the transformed vertical velocity; Φ = φ + (1/2)(*u*^{2}_{g}+*v*^{2}_{g}) a potential function derived from the geopotential φ;*q*_{g}the geostrophic potential vorticity; θ the potential temperature;*g*the acceleration of gravity;*f*the Coriolis parameter; ρ the density in*Z*-space; and θ_{0}a reference potential temperature.