This is a tricky but essential subject and it’s hard to know where to begin.
Geopotential Height – The Height of a Given Atmospheric Pressure
Let’s start with something called the geopotential height. This is the height above the earth’s surface of a particular atmospheric pressure. In the example below we are looking at the 500 mbar surface. For reference, the surface of the earth is at about 1000 mbar and the top of the troposphere is at 200 mbar.
At the pole the 500 mbar height is just under 5 km, and in the topics it is almost 6 km.
Why is this?
Here is another view of the same subject, this time the annual average latitudinal value (expressed as difference from the global average):
See how the geopotential height increases in the tropics compared with the poles. And see how the difference increases with height.
The tropics are warmer than the poles – warm air expands and cool air contracts.
There is a mathematical equation which results from the ideal gas law and the hydrostatic equation:
z(p) = R/g ∫(T/p)dp
where z(p) = height of pressure p, R = gas constant, g = acceleration due to gravity, T = temperature
This is (oversimplified) like saying that the height of a “geopotential surface” is proportional to the sum of the temperatures of each layer between the surface and that pressure.
At 500 mbar, a 40ºC change in temperature leads to a height difference of just over 800 m.
Because of the pressure gradient at altitude between the tropics and the poles, there is a force (at altitude) pushing air from the tropics to the poles.
If the earth was rotating extremely slowly, the result might look something like this:
However, the climate is not so simple. Here are 3 samples of the north-south circulation for annual, winter and summer:
So instead of a circulation extending all the way to the poles we see a circulation from the tropics into the subtropics (note especially the DJF & JJA averages).
Here is an experiment shown in Goody (1972) to help understand the processes we see in the atmosphere:
Note that the first example is with slow rotation and the second example is with fast rotation.
And here is a similar experiment shown in Marshall & Plumb, but they come with videos, which help immensely. First the slow rotation experiment:
And second, the fast rotation experiment:
In both of the above links, make sure to watch the videos.
The reason the circulation breaks down from a large equator-polar cell to the actual climate with an equator-subtropical cell plus eddies is complex. We’ll explore more in the next article.
As a starter, take a look at the west-east winds:
In the next article we will look at the thermal wind and try and make sense out of our observations.
Update – now published:
Atmosphere, Ocean and Climate Dynamics – An Introductory Text, Marshall & Plumb, Academic Press (2008)
Atmospheres, Goody & Walker, Prentice Hall (1972)