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Before we finish, here's a quick application of this newfound skill. On a sunny afternoon, particularly in the summer, you often see cumulus clouds forming. These clouds are at the top of the boundary layer, and are produced by air which has been warmed (and sometimes moistened) at the ground and has risen until its water vapor has begun to condense.
You can determine the height of these cloud bases if you know the pressure, temperature, and dew point of the air at the ground. Let's take a concrete example: typical summertime conditions in College Station feature a temperature of 31 C and a dew point of 25 C. A typical sea level pressure is 1016 mb; correct for the elevation of College Station (115 m) and you get 1005 mb, which is close enough to 1000 mb that I'm not going to worry about the difference.
The points are pretty far to the right on the sounding diagram. (You knew it gets hot in College Station, didn't you?) To find the cloud base height, you want to determine the height to which the surface air would have to ascend before it becomes saturated. So find the dry adiabat and the saturation mixing ratio. Where do they intersect?
Somewhere near 900 mb, at a temperature of 23 C. So that's cloud base, 900 mb.
What's the cloud base height in meters? You need to use the approximate conversion: if the elevation changes by 10 m, the pressure changes by 1 mb. So if cloud base is 100 mb above the ground, its height must be 100 x 10, or 1000 m (1 km). There's your answer.
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