geostrophic coordinates

The coordinate system used in the semigeostrophic equations. Geostrophic coordinates (X, Y, Z, T) are related to physical space coordinates (x, y, z, t) by

where u_g and v_g 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.