Monday, February 28, 2011

Why divergence aloft leads to rising motion

Last night was quite the night for severe weather--several quasi-linear convective systems moved across the southern US.  There's another moderate risk out for today in the central Appalachians associated with this same powerful cyclone.  I didn't even mention the snowfall potential on the northern side of the cyclone...  Lots going on with this one.

But today I wanted to cover a more fundamental topic that I've been asked a lot of questions about.  Three readers of this blog have sent me messages asking this fundamental question--

Why does horizontal divergence aloft lead to rising motion?  Why can't air also come down from above?

This is a very good question--admittedly one that also bothered me when I was first learning about these patterns during my undergraduate days.  So today I thought I'd try to explain what's going on aloft when we see divergence and convergence.

One area everyone seems to be able to agree on is what happens at the surface when we have horizontal divergence or convergence.  Take divergence at the surface, for example.  If air is spreading apart, it creates a semi-vaccuum, or area of lower pressure in the middle of the area where the air is spreading out.  As the saying goes, nature abhors a vacuum and tries to fill it.  It's simply a matter of air moving from higher to lower pressure.  Since the ground is below and air doesn't come out of the ground, the only way to fill that semi-vacuum left by the diverging air is to bring more air down from above.  So divergence at the surface leads to downward motion.
Fig 1 -- Divergence at the surface leads to downward motion.  Simple conservation of mass.
Likewise we can have a similar argument for horizontal convergence at the surface.  If all this air is coming together, it's going to increase the pressure in the area where the air is converging.  This makes that pressure higher than the surrounding ambient pressure and the atmosphere will want to try to evacuate air out of the area of convergence to try and equalize things again.  Since the solid ground is below and air can't be forced into the ground, then the air has to go up.  Therefore, we see that horizontal convergence at the surface leads to rising motion.
Fig 2 -- Horizontal convergence at the surface leads to upward motion.
So all is well and good at the surface where we have the solid ground serving as a boundary to prevent fluid motion in one direction.  Therefore, by default, the air will have to move in the other direction.  But what about aloft at the jet stream level?  There's no solid ground up there... 

Most of our primary jet streams (and, consequently, most of our convergence and divergence aloft) occur at or just below the tropopause level (for reasons that would make another good blog post sometime later).  The tropopause is the boundary between the lowest level of the atmosphere, the troposphere, and the next highest layer, the stratosphere.  We see this level all the time on our vertical soundings as a kink in the temperature profile.
Fig 3 -- Sample sounding from KILX at 00Z, Sunday, Feb. 27, 2011.
Our temperature trace on these vertical soundings is given by the red line.  With some minor exceptions (they're actually very important exceptions, but not for the scope of this particular post) we see that the temperature tends to decrease with height--this makes sense.  It gets colder the further up we go in the atmosphere.  At least, it does until we hit the level of the tropopause.  Right at about 200mb on the sounding above, the lapse rate (that is, the rate at which temperature is changing with height) suddenly makes nearly a right angle.  Instead of cooling with height, we see that the temperature almost remains the same (remember on these kinds of skew-T vertical charts that the temperature lines are slanted 45 degrees to the right...) or even warms slightly.  The rate of temperature change is much less than it was below.  That abrupt transition of the temperature curve marks the level of the tropopause.

Why does the temperature stop cooling off at that level?  Above the tropopause lies the stratosphere and within the stratosphere is the ozone layer.  Most of us learn in elementary or high school that the ozone layer helps block the harmful UV radiation from the sun (hence why the ozone hole is/was such a big issue).  Ozone blocks that UV radiation by absorbing it.  As the layer absorbs radiation, it gets warmer.  So all that ozone up in the stratosphere is why temperatures don't cool off with height up there.  Kind of amazing that we can see that so clearly on our temperature profiles.

Also, notice on the above sounding that I've circled the maximum wind speed in the wind barbs on the right.  Note that the maximum winds occur right around the tropopause level or just below it.  So, as I said, when we talk about the jet stream aloft, we're usually talking about right up under that tropopause level.

Now this abrupt change in the lapse rate at the tropopause signifies another property of the tropopause and the stratosphere above it.  Because temperatures tend to stay the same or even warm a bit with height, this layer is what we call statically stable.  Static stability is directly linked to vertical motion.  Vertical motion tends to be dampened or inhibited in areas of high static stability.  In areas of low static stability (or, what we usually would call relatively unstable areas), it's a lot easier for there to be vertical motions.  Because the air tends to warm a bit with height above the tropopause, it tends to be far more stable than air throughout the troposphere below where the air tends to cool off with height.  I could spend another entire blog post explaining why this is, so I'm just going to leave it at that for now.  The key link is--stratosphere=>stable=>limited vertical motion.  And also troposphere=>less stable=>more possibility of vertical motion.

One proxy that meteorologists use to measure stability is a quantity called potential temperature (another good topic for another blog post).  It turns out as air moves around in the atmosphere, it likes to keep the same potential temperature.  Therefore, if the potential temperature gradient with height is very strong (if the contours are very close together), as air moves around it is forced to stay very close to the same potential temperature value it started with.  If the gradient of potential temperature is weaker (if the contours are further apart), the air has a bit more freedom of how it can move around.

Fig 4 -- Comparison of very stable and less stable environments.  Air parcels want to stay at the same potential temperature (the same value of theta in the above images).  If the air is stable, the theta gradient is very strong (the top panel) and the parcel does not have a lot of potential for vertical motion.  If the air is less stable, the theta gradient is weaker (the bottom panel) and the air parcel has a larger potential for vertical motion.
Below is an averaged vertical cross section across the northern hemisphere of potential temperature.  Notice how below around 200mb the potential temperature gradients are pretty weak.  But suddenly, right at around the 150-200mb levels, we start seeing lots and lots of potential temperature contours--potential temperature is increasing rapidly with height.  This is another way we see the tropopause--it's the level where we start seeing a very strong potential temperature gradient.  A strong potential temperature gradient means strong static stability.

Fig 5 -- Vertical cross section of potential temperature across the northern hemisphere from July 18, 2010.  Latitude increases as you go to the right.  The troposphere is marked by very weak potential temperature gradients whereas the more stable stratosphere above has very strong potential temperature gradients (tightly packed contours).

So hopefully by now I've managed to convince you that at and above the tropopause the air is very stable.  Because the air is so stable, vertical motions are inhibited.  But you've probably actually seen this particular phenomenon yourself.  Ever look at a big thunderstorm with its anvil cloud shape?  Why is it shaped like an anvil?  Because as all that air rushes upward in the thunderstorm, eventually it hits the tropopause.  When it hits the tropopause, the strong stability reduces the vertical motion.  There's still all that air lifting in the updraft below, though.  So what does the air do?  It spreads out.
Fig 6 -- Schematic of a thunderstorm anvil cloud overlayed on a photo taken by the author in Anchorage, Alaska, during the summer of 2010.
So you can literally see the abrupt transition between the less stable air below and the very stable air above the tropopause as the level where the thunderstorm anvil spreads out!  All because the strong static stability above the tropopause works against vertical motion, forcing the air to go somewhere else instead of up.  Therefore, the air spreads out instead.

But this gets us back to our fundamental question of what happens with divergence and convergence in the jets aloft.  Take divergence for example.  The original question posed was why divergence aloft didn't mean downward motion from above to fill the void being left by the diverging air.
Fig 7 -- Why can't we see downwward motion and upward motion if we have divergence in the jet stream winds aloft?
The above schematic would make perfect sense--except for the fact that our jet stream winds and their associated divergence (or convergence) almost always occur just below the tropopause.  We now know that the tropopause and the air above it is statically stable (it tends to warm with height) and therefore it inhibits vertical motions.  Therefore, any vertical motion above the tropopause will be zero or very, very small in comparison to the vertical motion possible in the less stable troposphere below.  Thus we assume that the dominant vertical motion by far will be upward motion from below.
Fig 8 -- Vertical motions of any kind are dampened or inhibited by the stable air above the tropopause.  The vertical motion of air in the troposphere below is much greater.
Therefore we get our final model of what we expect to see with divergence aloft--strong upward motion from below to compensate for the diverging air above.
Fig 9 -- Final model showing why we expect upward motion from below as the main compensator for divergence aloft.
If we look at convergence aloft, we see a similar story.  Any vertical motion above the tropopause, no matter the direction, will be inhibited--the primary compensation left has to be motion below in the less stable troposphere.  Thus, we see downward motion below as a response to convergence aloft.
Fig 10 -- Final model for what happens in response to convergence aloft.  Downward motion below is the favored response.
Whew.  That was a long post.  But I hope it has helped to explain that burning question about how the atmosphere responds to convergence and divergence in the upper level jets.  This discussion also brought up a whole lot of other topics for other, future blog posts...

Thanks to my blog readers who asked me questions about this topic!  I'm very grateful for your interest and I have a lot of fun trying to compose these responses.  So, keep your questions coming!

1 comment:

  1. Hi Luke,
    Thanks bro for the wonderful blog post.
    It is clear and I like the way you use simple English language.It helps a lot.

    Lee kee