Pressure coordinate ($p$)

An atmospheric vertical coordinate using pressure instead of geometric height. Under hydrostatic balance, pressure decreases upward and geopotential obeys ${\partial }_p\Phi =-1/\rho$. With the ideal gas law, ${\partial }_{\ln p}\Phi =-RT$. Horizontal gradients taken at fixed $p$ lie on an isobaric surface. A log-pressure coordinate is a useful related coordinate with the opposite upward sign.

A surface of constant pressure. Its intersection with a fixed-height horizontal plane is an atmospheric isobar. An isobaric surface is generally not a geopotential surface: the horizontal geopotential variation on it determines the geostrophic wind.