How the temperature of the Earth's surface affects the air pressure above it

[GilSE]

TL;DR Summary

From one hand - hotter air is "lighter", from another - hotter air does a higher pressure

If the surface is heated, air above it will also heat, its temperature will rise. It will cause two processes: while temperature of gas rise, its pressure will also increase, but, also, as the air molecules get more energy, they will go higher from the earh surface, concentartion of the molecules near the surface will decrease, hence, the air pressure should decrease, too ($p=nkT$, $n$ is number density). So, which of these factors will prevail?

 

[Frabjous]

There are additional mechanisms. For example, differential heating of air is a cause of wind.

 

[Vanadium 50]

This is far from a system at equilibrium. Thinking about it that way is likely to be unhelpful.

 

[Lnewqban]

Please, see:
https://en.wikipedia.org/wiki/Thermal

http://www.atmo.arizona.edu/students/courselinks/spring15/atmo336/lectures/sec1/structure.html

While the temperature of certain mass of air located at sea/ground level increases, its atmospheric pressure remains the same, and its volume increases (meaning its density decreases).

As that mass of air goes higher from the Earth surface, it is cooled by the surrounding air located at higher altitudes.