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The main equation used to diagnose vertical motion is called the omega equation (after the Greek symbol for vertical motion in pressure coordinates). Technically, the Laplacian of vertical motion is expected in areas where the vorticity advection increases upward and where the Laplacian of temperature advection is large. (Someday, you'll understand what I just said.)
If a computer's doing your work, it could compute all that for you and diagnose the vertical motion. But with the typical flow patterns in the atmosphere, you can get a rough estimate of the vertical motion caused by the large-scale flow features by assuming that upward motion should occur where there is positive 500 mb vorticity advection and 850 mb warm advection. (This sounds crude, but it's really quite important. Among other things, you can predict the distribution of precipitation and the motion of storm systems by making use of this assumption.) Did you say vorticity? Oh, yeah, great, another word to learn. Well, you'll hear this one a lot. It's illegal* for TV meteorologists to use it, but other meteorologists talk about it all the time. It's essentially the rate of horizontal spin of the air.
Imagine a hot-air balloon with a gigantic propeller suspended from it. If the wind would cause the propeller to spin counterclockwise, the vorticity is cyclonic (or positive), and if the wind would cause the propeller to spin clockwise, the vorticity is anticyclonic (or negative). Frequently, meteorologists add in the Earth's spin, which makes the vorticity positive nearly everywhere. But our maps just show the vorticity due to the wind alone.
And what about advection? Way back when, we considered temperature advection, the tendency for the wind to carry warmer (or colder) air to a particular location. Same principle here: positive vorticity advection happens when the wind is bringing higher values of vorticity to a particular location.
In the above map, heights are in black (again), and vorticity is colored: green, yellow, and red for large vorticity, blue for small vorticity. Let's look at a couple of areas. One that stands out is over western Montana and Idaho, with extremely large vorticity. It's pretty easy to see (based on the heights) that the air would be spinning counterclockwise there. Conversely, over the Bahamas and Cuba, the vorticity is rather small, and the height contours imply that the air is rotating clockwise there.
Something doesn't quite make sense here. If the vorticity is the rate of spin, why isn't the vorticity negative when the air is spinning in the opposite direction?
Well, what's plotted on the map is not just the vorticity of the wind. Also added in is the spin of the Earth itself on its axis. In midlatitudes, in the units of the figure, the so-called "planetary vorticity" is about +10. It gets even bigger near the North Pole. So when the vorticity is less than +10, the air has some clockwise spin to it.
Flow curvature and the Earth's rotation aren't the only things that imply vorticity. Look over central California and Nevada, where the heights suggest a slight cyclonic curvature even though the vorticity is less than +10. What's going on there is that the wind speeds are much stronger in northern Nevada than in southern Nevada (as you can tell from the spacing of the height contours), so a propeller placed over Nevada would be spun clockwise by the stronger winds to the north. This type of vorticity, caused by cross-stream variations in wind speed, is called shear vorticity.
What's causing the rather large variation in vorticity across Virginia and North Carolina?
As for the giant "X"s and "N"s, they represent the locations of maXima and miNima of vorticity, sort of like "H"s and "L"s for pressure.
* No, it's not really illegal, but use of the word "vorticity" on air is definitely a hazard to job security. The public doesn't want to know about vorticity, they want to know whether it's going to rain.
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