The subject of available potential energy (APE) in atmospheric science is a bit abstract, but it’s very interesting once you get past some of the subtle complexities. Any dynamics textbook should have a better explanation than I can give, but in short APE is the amount of total potential energy that can be converted into kinetic energy.
A more technical definition of APE would be something like this:
APE is defined as the difference between the total static energy of the atmosphere and that of a reference state that minimizes the total static energy after a sequence of reversible adiabatic transformations.
A more intuitive way to think about potential energy is to think of the center of mass of the atmosphere. If the center of mass is higher, then there is more potential energy. It is impossible to convert all of the potential energy to kinetic energy, because we would be left with an infinitely thin layer of finite mass at the surface. Barring any weird physics or end-of-the-universe scenarios, this is obviously ludicrous.
In any case, defining the APE and studying the sources and sinks can tell us a lot about the dynamics of the atmosphere. Generally, the sun generates APE by heating the tropics more than the poles, and the atmosphere acts to reduce APE by mixing air across the equator-to-pole temperature gradient.
In the case of tropical transient disturbances (i.e. synoptic waves), we can also define a “perturbation available potential energy” (PAPE) that is useful for variability in a localized region.
I recently wrote up some notes on the derivation of the PAPE budget, whic can be found here:
This also relates to some notes I wrote on the perturbation kinetic energy budget, which you can find here: