Tuesday, November 30, 2010

Heavy Rain in the East

Today finds some very wet weather on the eastern coast of the US.  Here's the national radar mosaic from early this afternoon:
Fig 1 -- Base reflectivity radar mosaic for 1946Z, Nov 30, 2010. From the College of DuPage website. 
There's a large area of precipitation extending all the way from the middle Atlantic states down to the Gulf Coast.  There are even tornado watches for parts of the southeast.  Pretty potent system.  It seems even more so when you look at the surface map from 12Z this morning:
Fig 2 -- Sea-level pressure (contoured) and temperature (shaded) from the RUC analysis at 12Z, Nov 30, 2010.  From the HOOT website.
There's a very deep surface low that's pretty obvious over western Lake Superior at this point.  By this analysis, the minimum closed contour of pressure is 998 mb--fairly strong.  We can also see the sharp cold front associated with this low in three ways on the map above:
  1. Since one of the "adages" I mentioned in an earlier post was that pressure tends to fall as a cold front approaches and then rise again in its wake, we can conclude that a cold front tends to lie in a local pressure trough.  We can see an elongation on the contours around the low pressure center along a line stretching from near Chicago, though Indiana and down into northern Alabama.  We would suspect that some sort of boundary would like in this pressure trough.
  2. There is a shift in the winds along that same line.  To the west, winds are out of the west and become more northwesterly to northerly the further south you go.  To the east, winds are generally southerly.  This implies an area of convergence in the winds along that line. Convergence like that is typically associated with a front.  But, in connection with our first observation above, if there is a low pressure trough along that same boundary, since air tends to flow from areas of high pressure to low pressure, we would expect winds to head toward our trough.  Thus, this convergence makes even more sense.
  3. There is a strong temperature gradient across the front, particularly to the south.  Since the technical definition of a front is a strong gradient in potential temperature, this is the surest sign we have a front there.
However, one thing I would point out is how weak the temperature gradient gets once we get close to the low.  In fact, you've got similar temperatures surrounding the low itself--the temperature gradient doesn't really sharpen up until you get into Illinois and points south.  This make me think that the low is beginning to get occluded (which often occurs as a cyclone becomes stacked in the vertical).  To see our vertical support, let's look at the winds aloft:
Fig 3 -- 300 mb wind and height analysis from 12Z, Nov 30, 2010.  From the HOOT website.
Once again, a nice jet streak overhead, though this is just behind the front.  We are all the way up at 300 mb, though, so the thermal gradients may tilt with height causing the jet to be back over Illinois instead of directly over the front.  Our surface low is still located over the "exit" region of this rather cyclonically curved jet (it's even over the left exit region, which is better for divergence).  So we can still infer that the surface low is still being supported by the winds aloft.  However, note how the real core of the jet streak--where the strongest winds are--is down over Missouri, Arkansas, Oklahoma and Texas.  It's not coincidental that our strongest temperature gradients are further south.  But we also saw in our surface analysis that temperature gradients seemed to be weakening around the surface low.  This might explain why the jet seems so much weaker and less organized further north.

So what can we conclude about this cyclone, then?  Considering the weakening temperature gradients around the low over western Lake Superior, stronger temperature gradients further south, and consequently the better upper air support further south, I might suspect that the northern low is going to slowly weaken in favor of a stronger low somewhere further south.

Now this was at 12Z--what has happened since then?  Here's a look at the pressure falls as of 20Z this afternoon:
Fig 4 -- 3-hour pressure falls and wind vectors as of 20Z, Nov 30, 2010.  From the College of DuPage website.
The problem with using the pressure falls map this far north is that there are very sparse observations over northern Ontario and northwestern Quebec.  Therefore it's difficult to tell what the low is doing as it moves into that part of Canada.  However, we can see a general area of pressure rises over Minnesota and Wisconsin associated with the low passing by them earlier.  What's interesting is the elongated area of pressure falls along the eastern slopes of the Appalachians--somewhat further south than we'd expect given the typical storm track.  This is probably pressure falls in association with the cold front approaching (remember the front lies in a pressure trough).  Yet, in the absence of a strong signal for where the  surface low is going to move--could this also indicate some cyclogenesis further south?  Perhaps.  We'd have to wait and see.

Of course, one thing that this cyclone is definitely doing is bringing a lot of rain. However, it's not just along the cold front as we can see in the radar image back in figure 1.  So, what is providing the lift in that broad region?  The answer is isentropic lift.  When air moves, it tends to want to do so without gaining or losing any energy, or rather it moves isentropically--keeping the same entropy.  This means that the air may rise or sink depending on whatever path satisfies this condition.  We measure the entropy by using potential temperature which accounts for the energy in both the actual temperature and the pressure.  Two parcels of air at the same potential temperature have the same entropy.  Therefore, a map of a constant potential temperature surface is an isentropic map.  Since parcels want to conserve their entropy, if a parcel starts out at a certain potential temperaure, it wants to stay at that potential temperature as it moves around. Therefore, we can start inferring how air is going to move based on the structure of isentropic surfaces.

Below is the 300 Kelvin Isentropic surface from 12Z this morning.
Fig 5 -- 300K Isentropic Surface with heights and winds from 12Z, Nov 30, 2010.  From the HOOT website.
This shows the contours of height (in terms of presure level) of the 300K isentropic surface.  Remember, if air starts on this surface, it wants to stay on this surface.  Green shading indicates moisture at this level, and the wind barbs are wind along this level.

Take a look at what's happening in the southeast and on the east coast.  Note now the pressure contours decrease as you go further north.  Since pressure decreases with height in the atmosphere, this implies that the isentropic surface is higher off the ground to the north and closer to the ground to the south.  Also note the winds in this area.  They are all blowing from south to north in a region with lots of moisture.  We can conclude that there is very moist air on this surface being advected from south to north.  But as it moves north, this air must follow the surface.  Since the surface is getting higher as we move north, the air must be rising too.  This is a phenomenon known as isentropic lift--and there's a lot of it going on in the eastern US.  That's what's causing the precipitation to form over such a large area and to be so heavy--lots of isentropic lift.

Of course, once air becomes saturated it doesn't follow potential temperature surfaces anymore, but once the air is saturated--we're getting condensation and rain.  So it still gives a good solid reasoning behind all the rain in the eastern US...

Sunday, November 28, 2010

Snow in VCP 31

Back from my Thanksgiving break trip to Portland, Oregon.  I've had a few requests to talk a bit more about weather radar interpretation.  Radar interpretation has long been an area of interest of mine, and I worked in that area of study for the past two years.  So today I'm going to look at some snow observations with radar.

The NOAA NEXRAD radar network has a set of protocols for how the radars scan the environment.  Each WSR-88D radar (this is their model name--it stands for Weather Surveillance Radar-model 1988 Doppler) has a set of nine pre-defined scanning "patterns" it can use to scan.  These patterns define a series of elevation angles, or "tilts", the speed at which the antenna rotates and the length of radar pulse that is used.  These are called "Volume Coverage Patterns" or VCPs.  The nine available VCPs can further be subdivided into "precipitation" and "clear air" VCPs.  When no precipitation is expected, the radar doesn't need to scan as frequently or with as much vertical resolution, but it does need to be sensitive to pick up any small disturbances in the atmosphere that could signal the beginning of precipitation. So clear air VCPs tend to take longer to complete, have fewer elevation tilts, but have more sensitive pulse patterns.

The vast majority of the time, when there's no precipitation going on, the radar will be left in VCP 32--one of two clear-air VCPs.  (The 3 in the number represents clear-air mode and the 2 represents the "number 2" pulse pattern).  Take a look at a map of what VCP all the radars were in this afternoon.
Fig 1 -- CONUS NEXRAD VCP status from 2048Z, Nov 28, 2010.  From the WDSS-II website.
Most of the radars in the eastern half of the country are in VCP 32.  This is very normal, and is usually the case when not much is going on with the weather.

But what about where things are going on?  Currently the biggest weather story is areas of snow associated with a shortwave moving through Montana eastern Idaho and northern Utah.  Some of the heaviest snows are occurring in central Montana, between Billings and Helena.  But look at the status map above--both the Billings and the Great Falls radars are in VCP 31.  But--31 (since it begins with a number 3) is a clear-air mode VCP.  Why are we using a clear-air VCP when precipitation is falling?

Let's take a step back and look at what these clear-air VCPs are like.  Below is a diagram of the scanning pattern of VCPs 31 and 32.
Fig 2 -- Scanning pattern of NEXRAD radars in clear-air mode.  From the NEXRAD Radar Operations Center website.
In the chart above, the radar would be located in the lower left corner.  As we go out in range from the radar, we move to the right.  Each color represents a different "tilt" of the radar--the radar dish will make on complete circle at each tilt before moving up to the next highest tilt.  After it finishes the highest tilt, the radar goes back down to the lowest tilt and starts all over again.  The red numbers at the right of the chart represent the elevation angle in degrees of the center of the beam.  The radar beam spreads out as it moves away from the radar--that's why the colored wedges spread out.  On the left we can see the height above ground.  Anywhere in white is not scanned by the radar.  You can immediately see some of the difficulties with this scanning pattern.  The area directly over the radar is not scanned at all.  This region is referred to as the "cone of silence".  In a clear-air pattern like this one, the cone of silence is particularly large.  During severe thunderstorm events on the plains, thunderstorms can often top out at over 50,000 feet tall.  According to this chart, we wouldn't even begin to scan the tops of these thunderstorms (in clear air mode) until we got over 80 miles from the radar.  That's a huge area of no good coverage.

However, if we're not expecting deep thunderstorms, all we're really concerned about is what's near or falling toward the ground.  Therefore all we need are these low elevation angles, and that's why clear-air mode VCPs only have low-level elevation angles.  There are other differences in clear-air mode.  For instance, the radar antenna spins much more slowly than in precipitation mode.  This allows us to spend a longer time looking at things and increases the accuracy of measurements.  However, the trade off is that the radar takes a much longer time to finish a full cycle of elevation tilts--10 minutes in clear air mode as opposed to four and a half minutes in the fastest precipitation mode VCP.

What about the difference between VCP 31 and VCP 32?  VCP 32 uses "short" pulses and VCP 31 uses "long" pulses.  A doppler radar doesn't scan with a continuous beam of energy.  It uses short pulses of emissions to measure both velocity and reflectivity.  For a given volume of space, the radar takes the average return of several of these pulses to obtain the reflectivity measurement for that area.  How long each pulse lasts has an effect on these measurements.  A longer pulse length (leaving the beam "on" for longer during each pulse) allows for a lot more energy to interact with each volume of space and, by taking a longer time, increases our sampling of reflectivity and in turn provides a much more accurate and more sensitive reflectivity measurement.  Basically, a longer pulse length (like in VCP 31) gives a much more accurate, much more coherent, much more sensitive reflectivity measurement, particularly in areas of low reflectivity to begin with.  Here's an example of the VCP 31 image of snow from Billings, Montana.
Fig 3 -- Base Reflectivity from Billings, Montana, KBLX radar, 2019Z, Nov 28, 2010.
Note how much structure and detail can be seen in that reflectivity image.  This comes from the lowest tilt (0.5 degrees).  The details of bands of snow and regions of enhanced snowfall really show up in this image.  Since snow in general has a much lower reflectivity than rain, the more sensitive scanning strategy of VCP 31 picks it up much better and with more detail than we would see if we used a "precipitation" mode VCP.

So why don't we use VCP 31 more often?  If longer pulses provide a better reflectivity measurement, why would we ever use shorter pulses (like in VCP 32)?  Unfortunately longer pulses have a trade-off.  It turns out (for some rather technical reasons) that the longer the pulse time, the less accurate the velocity measurements become.  For a given pulse length, there's a maximum unambiguous velocity that can be detected called the Nyquist velocity.  If velocities become larger than the Nyquist velocity, the radar (as it's designed) can't tell what the correct velocity should be (though we can make a good guess based on continuity with the surrounding field, and there are algorithms that do this).

For VCP 31, the Nyquist velocity happens to be about 11.5 meters per second, or about 26 miles per hour.  This is incredibly low when we start looking at wind speeds.  We regularly see winds of well over 26 miles per hour at just  a few hundred feet above the surface.  Take a look at the velocity image that corresponds with the above reflectivity image.
Fig 4 -- Base Velocity from Billings, Montana, KBLX radar, 2019Z, Nov 28, 2010.
Remember in radar velocity images that cool colors (green) indicate places where wind is blowing toward the radar and warm colors (red) indicate places where air is blowing away from the radar.  Notice how we generally have cool colors to the north and warm colors to the south, indicating air blowing from the north to the south.  But what about these blobs of the opposite color in the middles of these regions?  Is there really this big jet of air moving the opposite direction in the middle of the general flow?  Not at all!  These are areas where the wind velocity exceeds the Nyquist velocity and the radar has incorrectly assigned velocity values for that region.  Any time you see these random large blobs moving in the opposite direction as the surrounding flow, you must suspect that the velocity is exceeding the Nyquist velocity.  When the radar mis-assigns these values, it's called "velocity aliasing".

I mentioned that there are some algorithms that try and fix that by guessing at the correct velocity measurement.  If we try applying one of these algorithms to the image above, we get this:
Fig 5 -- Base Reflectivity from Billings, Montana, KBLX radar, 2019Z, Nov 28, 2010. With velocity dealiasing applied.
Note how the algorithm has fixed much of the velocity field so that the colors are more coherent.  There's still an area to the south of the radar (the green blob in the middle of the red) where the algorithm didn't quite work.  It's an improvement, but it's not perfect.

So... in summary:

  • NEXRAD radars have nine different scanning patterns or VCPs, separated into clear air and precip modes.
  • Clear air VCPs are more sensitive and scan more slowly, but they have fewer elevation angles and take much longer to complete a full scan than precipitation VCPs.
  • Longer pulses mean more sensitive reflectivity measurements, but much lower maximum unambiguous velocities.
  • When velocities exceed the maximum unambiguous velocity (the Nyquist velocity), the radar can misinterpret the true wind velocity which results in velocity aliasing.
  • Algorithms can try to correct velocity aliasing, but they don't always get it right
So this is why we use clear-air mode VCP 31 for snow--its enhanced reflectivity measurements due to the longer pulses give us a better idea about the structure of snowfall, particularly since snow has such a low reflectivity to begin with.  Since we aren't worried about having fast updates (there are no fast-developing convective storms) and we're also not worried about very accurate velocity measurements, we can sacrifice time and velocity measurements to get the good reflectivity provided by VCP 31.

There's a whole lot more about choosing the correct VCP for the situation--after all, there are nine total.  I'm sure in future blog posts I'll talk about other VCP differences.

Tuesday, November 23, 2010

After the Snow Falls...

The snow and wind have finally stopped here in Seattle.  In fact, today looks like a gorgeous day outside--I've never seen the sky this blue out here, as a matter of fact.  Bright, sunny, though still very chilly.  Temperatures are only in the mid-20s for much of the Puget Sound region.

So how bad was it?  I measured the snow accumulation outside my house.
That's about four inches of snow outside my place.  (Note how I used an official NOAA Office of Education ruler to make this measurement--therefore this must be a very official measurement...regardless of there being a fence nearby...).  How did things pan out last night?
Fig 1 -- 24 hour meteogram from the top of the UW Atmospheric Sciences building as of 2047Z, Nov 23 2010.
The most recent time on the above meteogram is to the right.  I described meteorgrams in a previous blog post, but remember that meteorgrams are just several time series charts of how a particular meteorological variable has changed over time at a certain place.  This one starts at the left early yesterday afternoon and this afternoon is on the right.  In the first panel, we see that winds all night were pretty strong--in the 10-20 knot range with frequent gusts over 20 knots.  Winds were also rather steady out of the north, as we can see in the second panel.  Our temperatures hit a low of near 20 degrees last night, which, combined with the strong winds has caused a lot of freezing on the roadways and making travel treacherous.  (In fact, the University of Washington cancelled classes today, so I get an unexpected day off...).

Snowfall amounts are difficult to measure from an automated station, and the one on the roof of the atmospheric sciences building isn't really equipped for that.  However, some snow apparently did melt and fall into the rain gauge (they may have a heated rain gauge, actually...I'll have to check on that...).  However, I suspect this is just random snow melting into the rain gauge.  I'm guessing this because the precipitation amounts (the second panel from the bottom) have continued to increase slowly during the day today even though there definitely has been no new snowfall.  So, I wouldn't trust the precipitation measurements from this plot.

As this cyclone has been departing, you can see in the pressure plot (the third from the bottom) that our pressures have been steadily rising.  This points to high pressure and widespread subsidence building in, which suppresses vertical motion in the atmosphere.  This is why the skies are so clear--it's more difficult to form clouds without some kind of lifting mechanism.  You can see for yourself how clear it is in the last panel of the meteogram, which is showing incoming solar radiation.  On a completely clear day you'd expect to see a nice sinusoidal curve of the shaded region which shows increasing solar radiation as  the sun climbs higher in the sky in the morning and decreasing solar radiation as the sun goes down in the evening.  You can see that so far today we have a nearly perfect sinusoidal curve, meaning very clear skies.  Compare that to yesterday on the left hand side of the plot where all the thick clouds kept us from getting much solar radiation at all.  Remember--clouds don't block out ALL the solar radiation--otherwise it would be completely dark on a cloudy day.  Some still gets through--though not much.

Another view of the clear weather over Washington:
Fig 2 -- Visible satellite image of Washington state from GOES-W for 2045Z, Nov 23, 2010.  From the College of DuPage  website.
There are still some low clouds over much of the eastern part of Washington and out over the Pacific.  But in general--all the white and lighter grays you see across the Cascades, the Olympics and the Puget Sound lowlands--that's all snow.  It didn't miss anyone, so it seems.  The bright spot southeast of Seattle, by the way, is the snow cap on Mount Rainier...

Well, now the next question is--where is this storm moving next?
Fig 3 -- Objective surface analysis from 20Z, Nov 23, 2010.  From the HOOT website.
The low pressure center this afternoon had already moved to somewhere in the southern Idaho/northern Utah area (it's difficult to get an exact fix because of the difficulties of dealing with pressure in the mountains--more on that in another blog).  This storm has lost none of its potency--my friend Joe in Salt Lake City has been talking about the blizzard warnings going up for that area today.  Not the best environment to being trying to fly in.

However, I think this system is only going to deepen as it moves out over the Rockies and into the plains and midwest.  Models also agree with this conclusion, but how can we see that now?
Fig 4 -- 500mb wind analysis for 18Z, Nov 23, 2010.  From the HOOT website.
Based on a model-derived upper air analysis for this afternoon, we can see the deep 500 mb trough over northern Idaho.  Remember that troughs tend to be associated with colder air (cooling the air in a column compresses it, causing the depth of the column to shrink--and therefore the heights to fall).   But in a more obvious way of looking at it, just look at how cold we got in Seattle as this trough came through.  Anyhow, this trough is moving slightly south and east and bringing its cold air with it.  As this cold air moves south and east, it's going to encounter the much warmer air over Texas and the southwest.  This is going to strengthen the temperature gradient at lower levels as the trough heads in that direction.  Remember our thermal wind argument--what happens to the winds aloft as the temperature gradient below increases?
Fig 5 -- ECMWF 24 hour forecast of 500 mb geopotential heights and winds for tomorrow morning at 12Z.  From the HOOT website.
You can see in this ECMWF model projection how much winds have increased to the southeast of the trough--where the temperature gradients will probably be the strongest.  Another wonderful example of the thermal wind in action (at least according to the models). We now have a jet streak that is somewhat cyclonically-curved with an exit region over the high plains.  We know what tends to happen under the exit regions of cyclonically-curved jet streaks--surface cyclogenesis.  Aiding this spin-up will be the fact that the low pressure center will be coming off of the high terrain of the Rockies to the lower terrain of the plains. Without getting into the very technical details of this, in fluid dynamics if you stretch a rotating column of fluid, the column will rotate even faster.  As our surface cyclone moves from higher to lower terrain, the depth of the column (in our case, the distance from the ground to the tropopause) will increase as the terrain drops down--stretching the column.  This means that the circulation around the low pressure center should increase  (further strengthening the cyclone).

This all adds up to what could be a powerful storm for the upper midwest.  We'll be watching in the days to come to see just how bad it gets.

Monday, November 22, 2010

Tornado and Snow

Well--quite the day.  And at least from the Seattle end of things, it's just beginning...

But first--unfortunately, this morning's tornado possibility in northern Illinois verified.  A strong tornado formed just east of Rockford, Illinois, and caused significant damage in the town of Caledonia.  This same supercell produced additional tornadoes along its path as it moved across northern Illinois and southern Wisconsin.  I grew up riding my bike through Caledonia all the time--I can only hope that there are no fatalities and that the damage isn't too bad. Tornado watches continue along this frontal boundary as it pushes east, so we're not out of it yet...

I'm still trying to get some radar images from the Milwaukee radar as the tornado strengthened.  I was watching as this went on but was unable to grab any screen captures.  There was a loosely-defined hook structure in the reflectivity field.  However, the true strength really came through in the velocity field.  It should be noted that these storms were moving northeast at almost 50 knots--fast movement can often mask internal rotation signatures.  This is why it's always important to use storm-relative velocity fields when trying to assess rotation..

I also wanted to update the snow situation.  We're looking at winter storm warnings throughout the Puget Sound region, with strong northerly winds and snow expected to continue this evening.  Here are the surface observations for western Washington from
Fig 1 -- Surface Observations from 100Z, Nov 22 2010.
The lowest pressure currently observed is just under 1000 mb, which is stronger than we were expecting from our models.  The low pressure center is actually on the western side of the Olympic Mountains and slowly tracking southeast.  However, note this isn't very well reflected in the wind field--we can see that the winds along the coast are indeed curving counter-clockwise around the low like we'd expect.  But--the winds throughout Puget Sound are very strong and out of the north.  This is opposite of what we'd expect for being on that side of the low.  So what's going on?

Take a look at the wind profiler images for the lowest 3.5 km for the last day or so.  Particularly focus on the most recent four profiles (the four left-most profiles).
Fig 2 -- Wind profiler history for the lowest 3.5 km at Sand Point.  Current as of 200Z, Nov 23, 2010
The labels at the bottom are of the form date/Zulu-time.  Notice how we had relatively light winds until 2300Z.  Then the winds became northerly near the surface while the winds aloft stayed relatively out of the west-southwest.  As the hours have gone on since then, we see that the layer of northerly winds has gotten deeper and deeper with southwesterly winds aloft.  This represents a strong wedge of cold air that's moving south across the Puget Sound region near the surface.  Aloft, we still see westerly to southwesterly flow--which is more the direction we'd expect from having a low-pressure to the west-southwest of the area!

Why is this important?  Because a setup like this is going to enhance snowfall amounts across the Puget Sound region.  We have a wedge of cold air moving in at the surface, but above the low-pressure center is still advecting in moist air that's coming in off the Pacific Ocean.  As this moister air is lifted over the cold wedge, we'll see the moisture condense out and more precipitation.  Furthermore, since the air new the surface is getting so much colder (cold air advection associated with the northerly winds), that precipitation is going to fall as snow--and any liquid near the surface will soon be frozen.  I believe that we're seeing an area of enhanced isentropic lift in association with this cold wedge coming south--a topic I'll get into in a later blog.

In the meantime, time to stay indoors and stay warm in Seattle tonight!

Seattle Snow and Illinois Tornado Watch

Quite the day of contrasts here--I wasn't sure what exactly I should focus on.  On one hand, I live in Seattle now, and Seattle is currently having their first significant snowfall in two years.  On the other hand, I'm from northern Illinois which is now under an unusually late-season tornado watch.  So, we'll briefly look at a little bit of both.
After reading several different articles from various people over the last few days about how it was definitely not going to snow in the Seattle lowlands today, I was pleasantly surprised to find a half-inch of snow on the ground outside my house this morning--with the snow still coming down.  The weather service, for their part, did a pretty good job at calling this, actually.  In spite of some model evidence to the contrary, they decided to err on the side of caution and it's looking like this has paid off. Continuing that trend we now have a winter storm warning for tonight.

Let's take a look at the general weather setup across the US right now.  Here we have the HPC's objective analysis for the surface from this morning.
Fig 1 -- 1500Z, Nov. 22, 2010 Surface Objective Analysis from the Hydrometeorological Prediction Center
Though it's difficult to glean relative strengths from this map, we can see our two lows of interest--one just off the Washington coast and one over northern Missouri.  Based on what I talked about in my last blog post, are these lows in positions favorable for strengthening?
Fig 2 -- 1500 Z Nov. 22, 2010 RUC 500 mb geopotential height and wind analysis
Both lows are located under the exit regions of jets aloft (there might be some debate over whether these are actually "cyclonically curved" or straight jets, but in general the lows are not that far out of good position). So, we can conclude that in general these lows should be deepening.  Another product we can look at with respect to the strength (and also movement) of surface cyclones is by looking at observations of 3-hour pressure falls.
Fig 3 -- 3-hour pressure changes and wind vectors from 18Z, Nov 22, 2010
Solid contours surround areas of increasingly negative pressure changes, and therefore these are areas where the surface pressure has fallen over the past three hours.  Dashed contours surround areas where the pressure has risen over the past three hours.  This graphic really makes our areas of interest stand out.  We're limited off the coast of Washington because there are very, very few observations over the ocean.  However, even on the Washington coast there have been significant pressure falls over the last three hours.  Oddly enough, though, there area areas of pressure rises to the east of the Cascades on this graphic.  With a strengthening pressure gradient as the low moves onshore, we can expect some pretty strong winds tonight in the Puget Sound area, which is exactly what's being forecast.

Over the midwest, though, we see an interesting feature in the pressure changes--a sort of couplet, with an area of strong pressure rises over the Kansas City area and an area of strong pressure falls over central Wisconsin.  If you go back to figure 1 above (the HPC analysis) you'll see that the surface low-pressure center is right between the two (keep in mind that the HPC analysis above is from three hours before the pressure change map).  This couplet of pressure rises--pressure falls shows us how the low pressure center is moving.  As the low center approaches, we'd naturally expect pressures to be falling.  As the low moves away, you'd expect pressures to rise again.  Therefore, a good way of finding the direction of movement of a low pressure center is to draw a line from the center of the pressure rises to the center of the pressure falls.  The low should roughly follow that line.  We see above that this means our low pressure center is going to be moving through eastern Iowa and into central Wisconsin.

So--more snow in Seattle?  It's difficult to tell because we lack a really good measure of moisture aloft.  There are no soundings over the Puget Sound region (the nearest are at Quilute out on the other side of the Olympics on the coast and way over in Spokane) so trying to figure out where our moisture is aloft is difficult.  We could try a water vapor image...
Fig 4 -- GOES-W water vapor channel from 1830Z, Nov. 22, 2010
We do see moisture "aloft" but it's difficult to see much in the way of structure.  We can see the subsidence (and consequent drying) associated with that jet streak coming in from the northwest, so at least that lends some validity to our upper-air map above.  However, there is no organized source of moisture (like a so-called "atmospheric river") fueling the cyclone from the south.  There's definitely still moisture there, though, and so if models are showing more snowfall this afternoon and tonight (which they are)...no reason to doubt that...

However, in the midwest, we DO have a sounding in the middle of our area of interest.  One thing I want to point out is how quickly the lower troposphere can change in advance of this cyclone.  This is this morning's 12Z sounding out of Davenport:
Fig 5 -- 12Z sounding from KDVN, from the SPC website.
This sounding is a tour of different layers all stacked in a fun way.  From the surface up to around 900 mb there was a strong inversion--the atmosphere was almost isothermal (at the same temperature) through that entire layer.  From 850 mb to 700 mb, the atmosphere becomes dry adiabatic--a highly unstable layer.  Above 850 mb, the profile becomes moist adiabatic (good for heavy rain if there's moisture--which there is).  The entire boundary layer up to 850 mb is saturated, so naturally once we get to the unstable dry adiabatic layer there's a healthy amount of CAPE.  However, to get more severe convection, we'd have to be able to draw on more of that boundary layer moisture which means breaking that strong surface inversion. But six hours later---
Fig 6 -- 18Z sounding from KDVN, from the SPC website.
  Wow!  Talk about some warming.  Two things helped here--there's a fair degree of warm-air advection in the area (winds are strong out of the south throughout the state of Illinois) and that helped to warm things up considerably.  More importantly, though,not only did warm air get advected north, but moisture as well.  This has allowed us to not only erode the inversion, but also to stay saturated as well--a rare combination!  Note we are now nearly dry adiabatic from the surface up to 800, with a (much smaller) inversion, above which we have another dry adiabatic layer and then a conditionally unstable layer all the way up to the tropopause.  Wich such steep lapse rates and saturation near the surface, CAPE values are naturally high--2411J/kg of surface based CAPE in this sounding.  Very unstable, very primed for severe weather.

However, to get tornadic weather, you need healthy amounts of wind shear as well.  Clearly this is not lacking in the sounding above.  South-southwesterly winds slightly veering with height (another sign of warm-air advection!) and increasing in speed from 10 knots at the surface to 50 knots around 850 mb.  That's both directional and speed shear.  Excellent environment for maintaining discrete storms with rotation capabilities.  No wonder the SPC is putting out tornado watched.

As of 1930Z, the radar looked like this:
Fig 7 -- Radar image from KDVN, VCP 212, 1923Z, Nov 22, 2010.
Based on where the wind shift is in the surface observations, the cold front still seems to be the primary lifting mechanism.  But, if the 18Z Davenport sounding is indicative of the airmass over Illinois and southern Wisconsin, I wouldn't be surprised if more discrete storms popped up ahead of the front this afternoon.  Those storms could be somewhat intense.  Also note that even with the front as the forcing, the storms are remaining independent so far and not conglomerating into a big line.  This is due to the extraordinary wind shear which is helping to keep the updrafts separate.

Exciting afternoon in the world of weather!

Saturday, November 20, 2010

Why this morning's low-pressure center is a dud for Washington

All the buzz up here in Seattle right now is on the possibility of lowland snow (that is, snow in the city itself and not just up in the mountains) for Sunday and Monday.  But, as I was asked recently, this morning there appeared to be a storm sitting off the coast of Washington today--so, why aren't we concerned about it?

Currently, there is indeed an upper-level trough whose axis lies just off the coast of western Washington.  Note the jet streaks on either side of the trough in the image below.
Fig 1 -- 300mb geopotential height and winds from 12Z, Nov 20, 2010.  From the HOOT website.
Now if we examine a very low-level chart, we notice that there is a low-level cyclone also situated just off the Washington coast:
Fig 2 -- 925mb geopotential height and dewpoint depressions from 12Z, Nov 20, 2010.  From the HOOT website.
Notice how the 925mb low is directly beneath the upper-level trough.  If you remember one of my blog posts from last week, you might recognize this situation as being a stacked low.  Stacked lows are weakening systems (since they tend to lack strong temperature gradients near their centers).  To confirm this, take a look at this morning's sounding out of Quileute (on the Washington coast):
Fig 3 -- Sounding from Quileute, WA (KUIL) 12Z, Nov 20, 2010.  From the HOOT website.
We see a low tropopause height of around 450 mb, but this makes sense as Quileute is near the deepest part of the upper-level trough.  Within the troposphere (under the tropopause), we see little in the way of organized directional wind shear--winds are generally out of the southeast at all levels.  This is another indication of a stacked low--if the trough aloft and the cyclone at the surface were displaced at all, we'd expect winds to be changing direction with height.

So what do we expect to happen?  Well, in a stacked low situation, we would not expect the low-level cyclone to be strengthening in its current location.  So we have to re-examine our analyses and try and figure out where would be a better spot for low-level cyclogenesis.

My very first blog post talked about diagnosing upper-level divergence (and consequently rising motion and usually cyclogenesis at the surface) using  jet streaks.  Back then I talked about how in cyclonically-curved jet streaks, we typically saw upper-level divergence in the exit region of the jet--where air is leaving the jet streak.  Let's try applying this to our 300 mb map above.

Fig 4 -- 300 mb geopotential height and winds from 12Z, Nov 20, 2010.  Annotated with a basic jet-streak analysis.
Above I've annotated the 300 mb map, drawing a long red arrow along the axis of the cyclonically-curved jet streak and using the default cloud-thought-bubble shape to outline the exit region of the jet in brown.  This is the area where we'd expect to find the most divergence aloft.  Remember--divergence aloft leads to rising motion which leads to lower pressure below as air lifts out of the levels below.  We'd expect better chances of cyclogenesis (i.e. falling surface pressure) down in that region, off the coast of southern Oregon and northern California.  Also notice that if we had a surface low develop there, the lower-and upper-level cyclone/trough centers would no longer be stacked.  So, if we were to make a prediction, based solely on analysis--without using any model output at all so far, we would predict that our weakening surface low off the Washington coast would be replaced by a strengthening surface low off the coast of northern California.

So what do models say?  Here is the GFS surface pressure field at its initialization at 12Z this morning (the same time as the maps above).  Note our nice surface low centered off the coast of Washington.
Fig 5 -- GFS sea-level pressure, surface temperature and winds, analysis from 12Z, Nov 20, 2010.
Now here is the GFS's 6-hour forecast for that same model run:
Fig 6 -- GFS sea-level pressure, surface temperature and winds, 6 hour forecast valid 18Z, Nov 20, 2010.
The GFS has forecast the center of the surface low to have moved to just offshore of the Oregon-California border.  But we just predicted this above!  So you can see now why Washington shouldn't have been concerned about the low looming off of their coast.  A simple look at the upper-air analyses shows that the low was going to weaken off the Washington coast and strengthen much further south.  And this was all without looking at model data to come to that conclusion.  I find that to be pretty cool.

Thursday, November 18, 2010

A tour of GFS temperatures for the next week

Today I'm going to do a relatively simple, mostly untechnical post just talking about what the GFS model is showing for th next week.  Yes, this is a model, and we know models don't verify.  But I looking at model forecasts simply because I think our models, since they were written with rather stringently-specified physical equations, do an excellent job of really manifesting a lot of basic weather concepts.  So, even though this isn't necessarily what's happening, it's still fun to look at what physically could happen.

So it's now this Thursday--where is the cold air that was forecast to be blasting into the central US today?  It's still building across Canada:
Fig 1 -- Northern Hemispheric plot of 500 mb height (shaded) and sea-level pressure (contoured) for 12 Z, Nov. 18, 2010.  From the HOOT website.
But our once-bullish models from last week have definitely backed off with the speed at which they are advecting the colder air into the central US.  Notice on the figure above how we have a trough off the Pacific Northwest, a trough over the Canadian Maritimes, and a very broad, low-amplitude ridge between the two.  This general pattern is being forecast to hold on by both the GFS and ECMWF models until the middle of next week when the persistant troughing over the northwest finally becomes progressive and gets across the country (with a fun, deep surface cyclone according to the GFS).  As long as the central US stays under that ridging, the cold air will be held back.

The model temperature forecasts still have the central US getting colder, though the consensus is now that this really won't happen until the middle of next week.  Here's the GFS forecast for the lows this Saturday morning.
Fig 2 -- GFS forecast surface temperatures for 12Z Saturday, Nov. 20, 2010--48 hour forecast.
We can see the really cold temperatures are there, with lows in the -5 to -20 degree Fahrenheit range across much of the Canadian Prairies. Even reflected at the surface you can still see that general pattern of trough to the west, trough to the east, and ridging in between. However, note that there appears to be some convergence in the winds along a line through the Oklahoma Panhandle then stretching along the I-44 corridor through central Missouri and southern Illinois. With cold air to the north and warmer air to the south and converging winds, this hints at frontogenesis in this region.  We can even see the pressure troughing starting to occur in the pressure contours along that line.  (Remember from the last post that cold fronts tend to be associated with pressure falls...).

Sure enough, by Monday morning, we can see that there is a loosely-defined front in this region.
Fig 3 -- GFS forecast surface temperatures for 12Z Monday, Nov. 22, 2010--96 hour forecast.
We can see a nice swath of warm Gulf of Mexico air that has advected into much of the lower Mississippi River valley and into parts of the midwest, contrasting with the colder air to the north.  Very frontogenic.  However, the surface pressure field remains rather ill-defined in this area.  What's the dominant low pressure center?  Is it over western Ontario?  Or near Kansas City?  The winds to the north of this front remain relatively light, partially because of the unorganized pressure field.  As such, no strong cold air advection is occurring.  However, you can see that the cold air was begun to expand in western Canada.  It has also gotten much colder in Minnesota, the Dakotas, and even down into Colorado.  Why can't the surface pressure field organize?  Probably because there's not much support from the structure aloft:
Fig 4 -- GFS forecast for 500 mb heights and winds for 12Z Monday, Nov. 22, 2010--96 hour forecast.
At 500 mb, we can see how there is a broad jet streak along that same line where the weak frontal boundary is at the surface.  This is no coincidence--the increase in winds aloft in a direction parallel to the temperature contours is a thermal wind response (there's that term again...).  Remember from before--temperature gradients below cause winds to change aloft.  (Though, admittedly, when I've been talking about thermal wind before, I've talked about it in the opposite way--if we see winds changing with height this means a temperature gradient below...but it works both ways...) We see that thermal wind connection beautifully shown here as winds aloft increase in response to the sharpening temperature gradient at the surface.  But otherwise--there's no well-defined shortwave trough anywhere along that frontal boundary to provide the right divergence aloft to spin something up at the surface.  Thus things remain poorly defined.

By Thursday of next week, things have become much sharper.
Fig 4 -- GFS forecast surface temperatures for 12Z Thursday, Nov. 25, 2010--168 hour forecast.
Over the first half of the week, a shortwave trough became much better defined along the periphery of that broader trough and that was enough to cause surface cyclogenesis. You can see now that we now have a relatively deep surface cyclone and the front has become anything but stationary.  Lows in the 20s have pushed all the way into Texas and Louisiana with very strong 20+ knot winds immediately behind the cold frontal boundary.  New England would be seeing a whole lot of snow if this cyclone were to organize in this way.  The coldest air has also moved eastward, now centered over western Ontario and northern Minnesota.  Temperatures are cold, for sure, but this cold isn't nearly as widespread as we may have originally been thinking.

One fun feature of the above map--note how there is a corridor of relatively warmer air stretching north along the high plains just east of the Rockies.  I'm talking about the swath of slightly warmer temperatures from western Kansas and Nebraska up through eastern Montana and into Alberta and Saskatchewan.  Why is it oddly warmer there when they should be in the middle of this frigid air mass?  Take a look at the wind field.  In that area, there are very strong westerly winds being forecast.  This represents downslope flow along the eastern slopes of the Rockies.  As air runs down the slopes of the mountains, it moves from lower pressures up at the mountain tops to higher pressures down near the surface.  This means the air compresses as it sinks and when air compresses, it warms.  We typically see this kind of warming associated with downslope winds.  If you've ever heard of the warm "chinook winds" along the Colorado front range or the Alberta Rockies, this is exactly what's happening.

Tuesday, November 16, 2010

Windy Western Washington

Time for me to return to Pacific Northwest weather for a day.  Unfortunately (or fortunately if you like highly dynamic weather) for us, this impending "arctic outbreak" isn't the only major pattern change going on. Here's a look at our current hemispheric plot like we've been looking at over the last several blog posts.
Fig 1 -- Northern Hemispheric plot of 500 mb heights (shaded) and mean sea-level pressure (contoured) from 12Z, Nov. 16, 2010.  From the HOOT website.
First, I'd mention that the really cold air mass is continuing to slowly move south from the pole in our direction.  But turning our attention to the northern Pacific, we can see some very broad areas of high pressure at the surface which are mostly mirrored in the 500 mb height shadings above.  With high 500 mb heights in this region, we expect the mean temperatures in the lower atmosphere to be relatively warm.  However, as cold air continues to slowly creep southward over the continent through Canada, it's going to be increasing the temperature gradient between the relatively warm ridge over the eastern Pacific and the cold continental polar air.

See the band of green shading where the heights (and consequently temperatures) rapidly change from warm (the yellows and oranges) to cold (the blues and purples)?  This is the region where we would expect to be find the strongest winds aloft, also known as the jet stream.  What have we seen that connects temperature gradients with winds aloft?  If you guessed the thermal wind, you'd be correct.  But I'm not ready to return to that topic yet...

Basically, you can see how the height (or temperature) gradient seems strongest over the Pacific Northwest, and it would only be expected to strengthen as cold air moved south.  This region is an area where shortwave storm systems are likely to form.  It only takes a small pocket of colder air perturbing that interface to start cyclogenesis at the surface and eject a shortwave.  Last night the Pacific Northwest saw one of these shortwaves move through (you can see in figure one above how the surface cyclone associated with this has already moved inland over Idaho and Montana).  While not the biggest precipitation producer, this little storm did bring some powerful winds.
Fig 2 -- 24-hour meteogram from UW rooftop weather station.  As of 1847Z, Nov 16, 2010.
The figure above is what is called a "meteogram" from the weather station on top of the University of Washington atmospheric sciences building.  It shows a time series of several different meteorological variables over the last 24 hours, with the most recent time at the right.  This allows us to see how several different variables have evolved over time and also identify any correlations between them. (Click the image to get a full-size version.)

In the top panel, we can see the wind speeds over the last 24 hours.  Note how winds remained relatively strong, varying between 10-25+ knots from 00Z to 06Z last evening (from about 4 PM to 10 PM).  Gusts were often well over 30 knots.  Strong winds like these were seen throughout the Puget Sound region and were responsible for some moderate damage and power outages last night.

Let's notice one additional thing about this data.  Many of the news sources last night were saying that the strong winds were in association with a cold front moving through as this cyclone came on shore to the north.  Is this so?  Because of the effects of mountains, wind direction is not the best indicator of frontal passages out here (take note of this, meteorology students!).  Instead, we remember two other features of fronts:
  1. A cold front typically lies within a local pressure trough such that pressure falls as the front approaches and rises after the front has passed.
  2. Fronts are technically defined as regions of strong potential temperature gradients.  But, since we're at the surface and near 1000 mb, ordinary temperature gradients will do.  So we'd look for temperatures to cool behind a cold front  Common sense.
Where do we see those two features occuring?  Right around 530Z (930 PM, PST).

This is the most likely time that the cold front passed through the area--toward the end of the time of maximum winds!  This means that these strong winds were in the warm sector of the cyclone ahead of the cold front.

Another interesting feature of this meteogram is how the temperature profile changed (or didn't).  Note in the bottom panel of these meteograms there is a "solar radiation" chart showing how much radiation was received by the sensor on the roof.  We can guess where the sun went down by seeing where that graph finally went to zero--around 100Z.  However, even though the sun went down, the temperatures did not drop much at all until the front came through four and a half hours later.  Three factors probably contributed to this:
  1. Since we've already concluded that these strong winds were in the warm sector of the cyclone, there was probably some good warm air advection going on which canceled out much of the cooling.
  2. Cloud cover over the warm sector helped to insulate the lower atmosphere so that longwave radiation from the surface did not escape to space.  This would help keep the near-surface layers from cooling significantly.
  3. The strong winds through the lower atmosphere kept the boundary layer well-mixed, preventing a strong surface inversion from forming by mixing warmer air (in terms of potential temperature) aloft down to the surface.
So what about these crazy wind directions and speeds? What caused them?  The biggest factor seems to be the interaction with the terrain, particularly the Olympic Mountains to the west.  Below is a 3-hour forecast graphic from last night's UW WRF model run.
Fig 3 -- 3-hour forecast of 950 mb temperature, MSLP, and 10 m wind barbs from UW WRF model initialized 00Z, Nov. 16, 2010.
There are two areas where winds in the Puget Sound region were particularly strong.  One was over and to the east of the Strait of Juan de Fuca  and the other was over the south Puget Sound and Seattle areas.  Why were the winds stronger in these regions?
  1. To the north, there is a relatively narrow gap over the Strait of Juan de Fuca between Vancouver Island and the Olympic Peninsula.  Both of these land masses quickly rise to mountains, and as such any westerly flow approaching them (like we see here) is going to be channeled and accelerated through the gap.  Thus we see really strong winds through the strait and any land mass downstream of that gap.
  2. As strong westerly flow approaches the Olympic Mountains, a lot of the low-level air is forced to split and go around the mountains.  On the other side (the eastern side), this creates an area of relatively low pressure (which we see very, very nicely in the figure above).  As such, once air gets around the mountains, it is accelerated toward that area of lower pressure (the air wants to fill this relative "vaccuum").  Therefore, we see strong winds across southern Puget Sound being turned from westerly to more southerly as they are accelerated by this pressure difference.
So there is a brief look at some of the details surrounding this little shortwave passage through western Washington.  With this particular upper-air setup, though, we're expecting even more action as another shortwave moves through on Wednesday...then again on Friday...then again over the weekend...  It promises to be an exciting week.

Sunday, November 14, 2010

A Closer Look at Critical Thickness

Last time I talked about the impending "arctic outbreak" that was being forecast to occur at the end of this week (I also have a brief update on that at the end of the post).  I mentioned that one product we could look at was a plot of 1000-500 mb thickness to serve as a rough guide to a dividing line between snowfall and rainfall in our precipitation.  On a side note, I also jumped ahead last week (kind of) and made a statement that for much of the upper midwest this arctic outbreak could bring the first snows for much of the upper midwest.  I neglected to look in the near term and, as many people in Minnesota, Iowa and parts of Wisconsin now have seen, the first decent snowfall occurred this weekend:

Fig 1 -- 2-day snow accumulations as of 1500Z, Nov 14, 2010.  From NCDC.
However, more of the midwest, including points east of that snow swath, could see their first snow later this week.  I based that on using an analysis product that contoured the 1000-500 mb thickness and talked about how there was this "magical" rule of thumb where the dividing line between snow and rain was typically at the 5400 m 1000-500 mb thickness contour.  However, that's not the only thickness rule of thumb that exists.  Below is a plot of critical thicknesses for several different layers (more than just 1000-500 mb) from the College of DuPage's model output.
Fig 2 -- Critical thickness analysis values from an operational WRF-NMM model at 12Z, Nov 14, 2010. From the College of DuPage website.

And below is their guide to what each of the contours represent (the shading is (I think, because it's not labelled) 850 mb relative humidity, a rough proxy for where precipitation may be falling):
RED = 1000-700mb 2840m Thickness ContourCYAN = 850-700mb 1540m Thickness ContourYELLOW = 1000-850mb 1300m Thickness Contour
MAGENTA = 700-500mb 2560m Thickness ContourGREEN = 850-500mb 4100m Thickness ContourWHITE = 1000-500mb 5400m Thickness Contour
 BLUE = 850mb 0 degree Isotherm

Why are these called "critical" thicknesses?  The "critical" part comes from their association with the rain-snow dividing line.  For each of these layers, empirical experience has shown that these particular thickness values usually correspond to the approximate rain-snow dividing line.  However, critical thickness values are different in different locations.  There are also many, many examples where critical thickness levels did not correspond to the actual rain-snow line.  But, in general, these provide a good first guess for estimating precipitation type.  By looking at several different layers and their critical thicknesses (like in figure 2 above), we can gain a reasonable degree of confidence about what kind of precipitation will fall.  For example, if you happen to be north of every single critical thickness line (assuming it's colder to he north, which it almost always is), you're pretty sure to receive snow.  If you're in the middle of the spread of lines, that's much less certain.

But what do these critical thickness values really mean?  Sure they came from "years of observation", but what can they tell us about the difference between rain and snow?  I mentioned in my last post that the thickness of a layer is related to the mean temperature in that layer, with a colder mean temperature corresponding to  a "thinner" thickness.  There's actually a (relatively simple) equation to describe this, known to most meteorology students as the hypsometric equation:
--From the Wikipedia page for the hypsometric equation
Where h is the thickness, R is the gas constant for dry air (287 J/kg/K), g is the acceleration due to gravity (9.81 m/s^2), and T is the mean (virtual) temperature (in Kelvin) of the layer.  P1 is the pressure at the bottom of the layer and P2 is the pressure at the top of the layer.  We know the pressures at the top and bottom of our layer and the critical thickness of the layer, so we can solve this for the mean temperature we would expect to find in each layer when the layer's thickness is at the critical thickness.  The results are shown below:
Mean Temperature Calculated from Layer Thickness
Pressure Levels (mb)
Thickness (meters)
Mean Temperature (degrees Celsius)
2840 m
-0.8 C
2560 m
-13 C
1540 m
-2 C
4100 m
-9 C
1300 m
0.4 C
5400 m
-7 C
Table 1 --Calculated mean temperatures based on layer thicknesses via the hypsometric equation.

What can we see from these numbers?  A couple things stand out:
  1. The 1000-850 mb critical thickness of 1300 m corresponds to a mean temperature of 0.4 degrees Celsius.  That's an average temperature above freezing.  This tells us that snow can fall even when the temperature is above freezing at the surface.  We see this quite often, actually, and usually the snow that falls is very wet snow.  Frozen snowflakes falling from above need time as they fall to melt, so if the layer above freezing is relatively shallow, the snowflakes simply don't have time to fully melt before they hit the ground.
  2. The mean temperature in the 700-500 layer should be cooler than -13 degrees Celsius.  This represents a temperature on the upper bound of the so-called "dendritic growth zone".  It turns out that the most vigorous production of snowflakes tends to occur where there are temperatures between -12 to -18 degrees Celsius (the exact numbers will vary depending on what study you look at or who you ask).  Therefore, it would make sense that we need to have a layer that is at least that cold to be confident in seeing snowflakes (if snow is forming).
  3. The mean temperatures never get above freezing except in the lowest layer.  This implies that if we ever see the temperature on our profile get above freezing (except for in a very near-surface layer, but even then...) we must begin to seriously question whether or not snow will fall.  A small layer above freezing may not be enough to fully melt the snow crystals.  However, a relatively deep layer above freezing will start pulling the mean values in layers spanning that particular layer closer to the freezing point.  This will in turn warm the mean temperatures in those layers beyond these "critical" values.
  4. If we actually plot these mean temperature values at the average pressure levels they represent and calculate some rough lapse rates (not shown here), we see that below ~800 mb the lapse rate represented by this profile is absolutely stable and above ~800 mb the lapse rate becomes conditionally unstable.  I believe this implies that critical thickness values may be more representative in atmospheres where the lower part of the troposphere (i.e. below ~800 mb) is statically stable, since the further our lapse rates stray from the idealized lapse rates in this profile, the less representative of the atmosphere this critical thickness idealization will be.  (I was initially dubious when I had this idea until I saw this paper by Paul Heppner (1992).  It's an excellent review of how accurate critical thickness values are based on a statistical analysis.  He also confirms a tendency for the values to be more applicable in a stable environment).
So, remember--critical thickness plots are fun tools that can help provide an initial guess at checking precipitation type.  It's always best to check multiple critical thickness values for different layers to get a clearer picture of what's going on.  And, we can see from the simple calculations above what these critical thickness values can tell us about a typical snow vs a typical rain environment.  There's a lot more analysis that could be done, but this is just a flavor of what critical thickness implies.

***UPDATE: The upcoming "arctic outbreak"***

Remember last time I mentioned how we would want to see a buildup of really cold arctic air on our side of the globe if we were to have an "arctic outbreak" here later this week?  Here is the hemispheric plot of 500 mb heights (or, in proxy form, temperature) from 48 hours ago:
Fig 3 -- Northern Hemispheric plot of 500 mb heights (shaded) and mean sea-level pressure (contoured) from 12Z, Nov. 12, 2010. From the HOOT website.
We can see that the coldest air (represented by the lowest 500 mb heights) was just about centered over the North Pole two days ago.  Now look at this morning's plot:
Fig 4 -- Northern Hemispheric plot of 500 mb heights (shaded) and mean sea-level pressure (contoured) from 12Z, Nov. 14, 2010. From the HOOT website.
The center of the cold air has shifted off the pole!  Not only that, but it has shifted toward the North American side.  Could this be the beginning of our arctic outbreak air?  Possibly.  Remember this air has a long way to go before it gets down here, and interactions with the land can warm the air considerably.  (Though this weekend's snow cover over the upper midwest won't do anything to help warm the air mass, if the snow sticks around...)