Theta as a Vertical Coordinate
Isentropes slope DOWN toward warm air, UP toward cold air – this is opposite to the slope of pressure surfaces: since q = T (1000/P)k, as P increases (decreases), T increases (decreases) to keep ? constant (as on a skew-T diagram).
Isentropes slope much greater than pressure surfaces given the same thermal gradient; as much as one order of magnitude more!
On an isentropic surface an isotherm = an isobar = an isopycnic (const density); (remember: P = ?RdT)
On an isentropic surface we analyze the Montgomery streamfunction to depict geostrophic flow, where: