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.
From Marshall & Plumb (2008)
Figure 1
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):
From Marshall & Plumb (2008)
Figure 2
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.
North-South Winds
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.
From Goody (1972)
If the earth was rotating extremely slowly, the result might look something like this:
From Marshall & Plumb (2008)
Figure 3
However, the climate is not so simple. Here are 3 samples of the north-south circulation for annual, winter and summer:
From Marshall & Plumb (2008)
Figure 4
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:
Figure 5
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:
Figure 6
And second, the fast rotation experiment:
Figure 7
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:
From Marshall & Plumb (2008)
Figure 8
In the next article we will look at the thermal wind and try and make sense out of our observations.
Update – now published:
Atmospheric Circulation – Part Two – Thermal Wind
References
Atmosphere, Ocean and Climate Dynamics – An Introductory Text, Marshall & Plumb, Academic Press (2008)
Atmospheres, Goody & Walker, Prentice Hall (1972)
The Science of Doom 
SoD,
You are missing the molar mass from your formula.
Pekka,
I should have clarified terms.
p = ρRT
where p = pressure, ρ = density, R = gas constant for dry air = 287 J/kg.K, T = temperature in K
The gas constant for dry air:
R = Rg / mair
where Rg = universal gas constant = 8.31 J/K.mol, mair = 0.029 kg/mol
And then using the hydrostatic equation:
dp/dz = -gρ
Inverting and substituting the ideal gas equation:
dz/dp = -RT/gp
And we integrate to get the equation in the article.
For real-time comparison and eye-popping/boggling action, this might be useful, though it would be nice to be able to slow it down:
[…] Comments « Atmospheric Circulation – Part One […]
Hi SoD, this is a really interesting article, thanks for this.
I noticed that the empirical measurements you mentioned to help explain the difference in height of the 500mb level between equator and poles came up around 10% more than calculated for a 40C difference in T.
I was wondering if the difference might be due to gravitational elongation of the equatorial atmosphere by the Moon and Sun. What else do you think might explain the discrepancy?
Tallbloke,
On your own blog you said:
It’s great to see such high standards of ethics from you and certainly your laudable approach ensured that I stopped posting any questions on your blog.
But it does have me wondering, not for the first time, why you are posting a question here.
If you seek answers you should seek them elsewhere.
My own recommendation is try reading a few textbooks on atmospheric physics.
And you can tell your readers on your own blog that your brilliant questions had me flummoxed.
I long ago forgave you for editing my comment, after all, it was only the removal of some bold tags I’d put round a couple of key phrases. So if you’re the kind of person who is able to bury the hatchet, I’ll happily put up a post to say so and retract my unkind words.
Tallbloke,
I can easily bury the hatchet.
Just to be clear you have “forgiven me” for not re-typing HTML tags when I once copied and pasted an extract of a comment of yours?
Interested readers, if there are any, can try copying and pasting text from an article or another reader’s comment and they will find that all formatting disappears.
If that’s what happened then there has been a misunderstanding for which I apologize. My recollection is that the original comment lost its bold tags. After all this time I can’t be sure any more. Anyway, in a spirit of reconciliation, I propose we let it go, and get on with the interesting stuff.
[…] In Atmospheric Circulation – Part One we saw how the higher temperatures in the tropics vs the poles (due to higher solar insolation in the tropics) led to a greater “geopotential height”. This means simply that the height of a given atmospheric pressure (e.g. 500mbar) is greater in the tropics, and so the geopotential surfaces slope down from the tropics to the poles. […]
[…] In Atmospheric Circulation – Part One we saw the Hadley circulation: convection in the tropics and subsidence in the subtropics: […]