 This schematic shows the relationship between height surfaces and pressure surfaces. Typically, pressure surfaces slope downward in height from the equator where it is warmer to the pole where it is colder. You were able to show this in activity 2.2 and you saw it again in lesson 2.4 on thickness. Note that on a constant height surface from the equator to the pole, the pressure surface is decreased with latitude. Note also on a constant pressure surface from the equator to the pole that height surfaces decrease on a constant pressure surface. Thus changes in pressure are proportional to changes in height. After a little math we can show that 1 over rho, that is 1 over the density times the change in pressure with respect to x or y on a height surface is equal to g times the change in z with respect to x or y on a constant pressure surface. Finally we note that g dz is just a differential of the geopotential, phi, which has units of meter squared per second squared which are the same units as energy divided by mass. So changes in height on a constant pressure surface are the same as changes in geopotential on a constant pressure surface.