"Lecture 6: Stability [in the atmosphere]"

After much Googling, I have finally found somebody who looks at the bigger picture. From The University of California, Irvine (pdf), slide #5:

What Happens to the Temperature?

• Air molecules in the parcel (or the balloon) have to use their kinetic energy to expand the parcel/balloon
• Therefore, the molecules lose [kinetic] energy and slow down their motions
=> The temperature of the air parcel (or balloon) decreases with elevation...

All the dime store explanations stop right there and ignore the obvious follow-on questions:
- What happens to the heat aka kinetic energy of the legendary 'parcel of air' once it has risen?
- What happens to the temperature of the air that was higher up that is displaced and falls?

These lecture notes cover it very succinctly:

...=> The lost energy is used to increase the potential energy of air molecules.

• Similarly when the air parcel descends, the potential energy of air molecules is converted back to kinetic energy.
=> Air temperature rises.

That kinetic energy isn't "lost", it is just converted to a different type of energy - potential energy. That is the missing figure you need to get the whole atmosphere to balance, despite being the easiest to calculate (mass x height x gravity).

For every parcel that rises, an equal and opposite amount of air must fall elsewhere, which compresses it and causes it to warm up (for two subtly different reasons; the compression itself does not cause the warming, it is the 'falling' that causes both). Which is most of the reason that air is warmer at sea level. The dime store explanation that the sun hits the ground, warms it up and this warms up the air above it etc is only a small part of the bigger picture (it ignores... cloudy days; night time; the fact that two-thirds of the Earth's surface is ocean and stays nearly the same temperature 24/7; and the fact that the Sun shines with the same intensity on the top of mountains).
----------------------------
If this seems far fetched, let me give a real life example:

How can you use water to store electricity?

Clearly you can't, not directly. But you can do the next best thing and use spare night time electricity to pump water up into a reservoir (convert electrical energy to potential energy), then at times of peak demand, you use the water in the reservoir to generate generate hydro-electricity (convert potential energy back into electrical energy).

The air in the atmosphere does exactly the same trade-off, only the trade-off is between heat aka kinetic energy and potential energy.