A while back I introduced the ocean. a bit. Time for the atmosphere, which turns out to be much simpler than the ocean, or maybe that just is a matter of being more subtle.
In the ocean, we have names for areas bounded (usually) by land. This doesn't work for the atmosphere, since it covers the whole earth. It does turn out, however, that the circulation itself (as for the Southern Ocean) helps divide the atmosphere. For a first approximation, little air crosses the equator. (Some does, to be sure.) So we can divide the atmosphere to northern and southern hemisphere circulations. Even though the two hemispheres are greatly different in their amounts and distribution of land and ocean, it turns out that their major circulation is quite similar.
In both hemispheres, air rises from the equator, move towards higher latitude at elevation (5-15 km, 3-9 miles up) and then sinks to the surface around 30 degrees latitude (north or south). The surface circulation is from that sinking latitude back towards the equator. This is the Hadley cell. There's a similar cell between about 60 degrees latitude and the pole, called the Ferrel cell. In between the two is not so much a cell as a storm zone.
A couple of questions I haven't seen firmly answered (I do have leads on a couple of papers, but haven't read them yet) are: Why are the circulations so similar between the hemispheres? Why are there 3 zones of circulation instead of 2, 4, 5, 75, ...?
In the vertical ... how high is up? :-) There's actually a way of approaching this by way of a different question:
What is the atmosphere made of? If we sample air all around the world, and through all levels of the atmosphere, we discover a few striking things. First, only 3 gases account for almost the entire atmosphere -- Nitrogen (N2), Oxygen (O2), and Argon (Ar). They are, in order, 78%, 21%, and 1% of the atmosphere in terms of counting molecules, and 76%, 23%, and 1% by mass. Note that these figures have been rounded, but also note that they do add to 100%. A further feature is that this proportion is constant throughout the atmosphere -- until you get to about 100 km (about 60 miles) up. Above that point heavier gases separate from lighter ones.
So that's our answer to 'how high is up?' -- about 100 km.
But back to the matter of what the atmosphere is made of. We've all heard about water (H2O), Carbon dioxide (CO2), and Ozone (O3) and how important they are. They are indeed important. But, added up through the atmosphere, they account for only about 0.24% of the molecules. Considering all gases, only about 1 in 400 molecules is not one of the big 3 of Nitrogen, Oxygen, or Argon.
Yet it is these other, rare, molecules which account for almost all the interesting processes in the atmosphere! This includes rain, hurricanes, the fact that the earth is not frozen, protecting surface life from solar ultraviolet, constructing the stratosphere, ...
Ok, the stratosphere brings us back to the vertical structure of the atmosphere. Starting from the surface, we have the troposphere. Here's where almost all the weather happens, and temperatures generally decrease with height. (So it's usually cooler in the mountains than the flat land around them.) In the stratosphere, temperatures are constant or increasing with height. Above this is the mesosphere, where temperatures go back to decreasing with height. The top of the mesosphere is that 100 km (or so) boundary. Above this, things get very different, and usually are studied by people who aren't meteorologists or climatologists. (Aeronomers, chemists, physicists instead.)
The stratosphere being a warm place, compared to the air above or below it, is because of the ozone absorbing ultraviolet. Without the ozone (and the chemistry that maintains that molecule), there's nothing to be absorbing energy to warm the layer. At most, ozone is about 12 parts per million of the molecules in that layer (0.0012 % !)
Since my first cut is always to take a look at the largest scale things, the most common, and such, we're already done. 3 molecules make up almost all of the atmosphere (N2, O2, Ar), there are 3 circulation zones between equator and pole in each hemisphere, there are 3 layers in the vertical, and the atmosphere goes up about 100 km.
To understand most of what's interesting, we have to get much more subtle. Always a fun and interesting thing to find that understanding some very small part of a big system will let us understand a lot about that large system.