An average height that is weighted by some other characteristic of the vertical profile. For example, the potential temperature profile in the stable boundary layer at night often has an exponential shape because the greatest cooling has occurred nearest the ground and the temperature change decreases with height. By finding the area under the potential temperature change curve and dividing by the temperature change at the surface, a height scale is obtained that is an integral measure of the depth of the stable boundary layer. For this particular example of an exponential profile, the integral depth corresponds to the e-folding depth of the profile.