From AMS Glossary
Geostrophic coordinates (X, Y, Z, T) are related to physical space coordinates (x, y, z, t) by
where ug and vg are the eastward and northward geostrophic winds and f is the Coriolis parameter. Through this coordinate transform the semigeostrophic equations arise. The geostrophic approximation is not used as frequently in the semigeostrophic equations as in the quasigeostrophic equations; thus the semigeostrophic equations produce a more accurate representation of certain phenomena, such as fronts and jets.