Tag Archives: cold air advection

The Froude Number and Stable Flow: Mountain Blocking

A powerful low amplitude shortwave ejected into Montana this morning in association with a 160 kt Pacific Jet.

The 0Z NAM from yesterday clearly depicts this feature:

Large scale and mesoscale ascent developed rapidly as the jet core amplifed over the region.  Note the large increase of high level moisture associated with a region of strong vertical ascent:

0545Z:

Three hours later at 0845Z:

Low amplitude intense shortwaves such as these have a tendency to develop significant upward vertical velocity/downward vertical velocity couplets which support rapid cyclogenesis and regions of strong pressure gradients over small areas (i.e. rapid intensification, or the second partial of p with respect to x, gradient of the gradient).

Note the rapid pressure rises, on the order of 8+ mb’s / 3 hours over northern MT as extreme cold air advection set in behind the front.

The surface analysis depicts the strong surface ridging associated with the extreme subsidence mainly owing to strong cold air advection behind the cold front.  Also note how surface ridging amplifies as the high pressure region interacts with the Rockies.  The Rockies “block” the subsident air from progressing westward, therefore air builds at a faster rate east of the Continental Divide resulting in stronger surface ridges:

The Great Falls sounding at 0Z shows the flow was mainly out of the N in the low levels and NW in the mid levels.

Great Falls is around 3700 feet, so in this sounding, stable N flow extended to nearly 10,000 feet, or over 6000 feet AGL.

The Belt Range south of Great Falls extends to around 6000-8000 feet and reaching top elevations greater than 9000 feet.  Also note they form a “bowl” type shape around the region.  This makes it very difficult for air to flow around the mountains.

The Froude number,

relates the inertial forces to the gravitational force.  Think of it as a relation of kinetic energy to potential energy where V is velocity, N is the brunt vaisala frequency, and L is the height of the mountain.  Therefore, think of it as relating KE= 1/2mv^2 to PE = mgh.  The brunt vaisala frequency is: 

Note the gravity term (remember mgh) and the static stability d-theta/d-z (the more stable the air mass is, the greater the kinetic energy will need to be for air to ascend the range).

A series of radar images shows how stable N-NW flow “bunches up” into the valley as stable flow is blocked by the mountains south of the valley.  Low level stable air builds into the valley and it acts to “uplift” air above it, much like Cold Air Damming:

Note in the surface obs the heaviest snow develops coincident with rapidly rising pressure as stable air builds into the valley while V simultaneously weakens (weak V, which means lower kinetic energy, therefore the flow can not ascend the mountain).  Note also that downslope flow into the valley was not able to kill of the qpf.  Also note the powerful cold front (green) with G into the 60s.

High res models were trying to show a large weather hole over Great Falls associated with downsloping into the valley.  A good example showing high res models can struggle mightily in compex terrain:

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Central/Northern Plains Cyclone Event (11/12-14/2010)

All Images Can Be Clicked to Enlarge

An interesting weather event is shaping up for late this week and into the weekend.  A strong PV Anomaly over the intermountain west is going to “eject” into the plains initially propagating along a quasi-stationary frontal zone over the plains before developing into a cyclone as it tracks NE.  The global numerical guidance has been very consistent modeling the general pattern that can be expected, but as always significant run-by-run (and model by model) inconsistencies and large model spreads exist.  Even as we reach the “short-term” (2-4 day forecast period), a lot of variability is still persistent amongst the models.  However, since this is partially a blog about weather forecasting, I thought it would be appropriate to actually make a weather forecast.  In reality, this is the challenge all forecasters need to make on consistent basis, but decisions still need to be made so the appropriate weather risks can be assessed and disseminated to the public (and private) in a timely manner and with sufficient lead time.

As of late this afternoon, a stationary front is parked over the southern plains with a positive tilt trough slowly propagating eastward.  The warm sector across the southern plains is moist with surface dewpoints ranging from the upper 50s to upper 60s.  Moisture is going to play a key role in the eventual cyclogenesis of the storm.

The 0Z upper air map depicts the positive tilt trough:

The 0Z 500 hpa analysis depicts a strong vorticity maxima at the base of the trough:

The NAM 0Z analysis also depicts this clearly in its shaded vorticity fields:

A strong PV anomaly is positioned over the 4-corners with tropopause heights as low as 500 hpa.

The interaction of this strong vorticity maxima/PV anomaly with the warm and moist air mass in the warm sector is likely going to result in a strong cyclogenesis event.

This graphic shows the surface low track of each numerical model analyzed at 12Z yesterday morning (11/11/2010).  It is easy to see the model guidance has significant spreads in both surface low intensity and surface low track.  Note the NAM track in green and the GFS in red.

The 18Z NCEP guidance converged a bit, but the spread is still significant amongst the NAM/GFS.

The Short Range Ensemble Guidance is not much better:

The first 24-36 hours of the forecast is generally pretty clear as all guidance has the upper PV anomaly ejecting into the southern plains and lifting NE along the front.

At 12 hours, (12Z) note the still positive tilt to the trough.  The PV anomaly remains at the base of the upper trough.

Of course, positive tilt troughs are not very conducive to surface cyclone development.  Under this configuration, most of the the time the main belt of westerlies would cut off as the cold air remains well to the north.  Almost all vorticity associated with this trough is due to shear vorticity on the downstream side of the trough.  Cyclonic vorticity advection is minimal ahead of the trough (therefore height falls are not induced…see last post for the QG Chi equation) with any relative vorticity advection offset by planetary vorticity advection on the backside of the trough.

Note that the main jet level winds are on the downstream portion of the positive tilt trough.  Once again, from the thermal wind relation, strong jet level winds reside over regions of enhanced thermal gradients:

What would eventually happen is the trough would slowly “de-amplify” with time as the jet stream propagated northward with weak surface development.  The leftover baroclinic zone over the plains would moderate with time leaving (resulting in a weakening horizontal thermal gradient) an area of enhanced shear vorticity aloft over the region.

With this system though, a couple things are different.  First, as the main belt of westerlies cuts off, cold air advection behind the stationary front ceases to exist.  Weak warm air advection along the stationary front continues as air (on the warm side of the front) weakly advects NE due to the pressure gradient developed by the departing cyclone well into Canada.

Note that, at 850 hpa, cold air advection slackens on the cold side of the stationary front and warm air advection begins to dominate along the warm side as air continues to advect NE in association with the departing cyclone (blue line).  Our stationary front has now developed into a warm front (see inside the red circle).

The front begins to propagate northward as a result of this flow configuration.  Subtle height rises develop aloft due to the weak low level warm air advection decreasing with height (QG Chi equation).

BY 21Z, note that a weak downstream ridge axis has developed in association with the differential warm air advection.  Also note the existence of the upstream shortwave.  Kicker trough?

Why do cutoff lows “kick-out” with an approaching upstream “kicker” shortwave?  There are  a number of differing reasons, but I find the QG approach simplistic and succinct.  (To help differentiate…kicker is the shortwave that “kicks-out” the cutoff low, the cutoff low that “kicks-out” is the kickee).  Note with the incoming  kicker shortwave heights have fallen upstream of the main trough.  This acts to “flatten” the upper level height field in between the kicker and kickee (in between the two systems).  Going back to the QG Chi equation we love so much:

the amount of planetary vorticity advection by the geostrophic wind decreases (remember that f decreases equatorword) on the backside of the main trough (the kickee).  Note in the 12Z upper level height map the trough is advecting increasingly large values of f.  By 21Z (the previous image), with the approach of the shortwave trough upstream, the ridge (over the intermountain west) has flattened and now little to no f is being advected on the backside of the cutoff low.  Heights do not fall on the upstream side, and the small amount of cyclonic vorticity advection on the front portion of the kickee results in slow height falls downstream which results in forward propagation.  The cutoff has now been “kicked-out”.

By 0Z, the downstream ridge has continued to amplify and a lead shortwave at the base of the trough has now developed as large values of cyclonic vorticity are being advected with increasing height falls:

Now the feedback process begins as warm air advection continues in the warm sector.  In a moist system such as this, diabatic affects can be significant as warm and moist air condenses and releases latent heat, especially along the warm front.  This process can act to increase the along-front thermal gradient therefore acting in a frontogenetic manner.  Moreover, the release of low level latent heat due to condensation can act to decrease the static stability of the atmosphere.

In the omega equation, note the location of the static stability parameter in the various RHS forcing terms:

Low static stability acts to enhance the cyclogenesis process during the initial stages of development.

Without considering every forecast hour, skipping ahead to hour 33, the NAM now features a significantly amplified upper ridge downstream and the lead shortwave has now taken on a negative tilt.

Both the NAM/GFS are illustrating an upper level jet coupling combined with the significant low level warm air advection/diabatic heating and subsequent upper level height rises ahead of the main shortwave.  It is likely mesoscale jet circulations will play a prominent role in enhancing divergence (and vertical ascent) and the subsequent cyclogenesis process as well as strong convection along the cold front.  Rapid cyclogenesis and occlusion is likely with this system.


What does this all mean?  First the significant model differences.  The 0Z guidance is in and the spread remains signficant.

The NAM is a significant outlier with its significantly farther W track while the GFS is on the opposite end of the spectrum.   Interestingly, it seems with increasing resolution of the numerical model being considered, the farther W its surface low track is.  After the NAM, the ECMWF (blue) is next followed by all the other global models (CMC, NOGAPS, UKMET, GFS).

Even the 21Z SREF spread is rather large:

Once again though, it seems the W tracks are dominated by higher resolution guidance while the farther E tracks are dominated by the RSM (pink/red), a variant of the GFS used for the SREF data.

It should also be mentioned the GFS and the rest of the global guidance has continued to shift westward with time to match the higher resolution mesoscale models.  First, consider the size of this storm.  In terms of the Rossby Number R, it is rather small compared to a typical synoptic scale system which yields larger values of R:

QG theory works nicely with large synoptic systems, but as R increases, sub-synoptic scale forcing becomes more prominent in the development of the system.  Numerous studies have shown this…and various omega equations have been developed to account for sub-synoptic scale forcing.  Mesoscale circulations are more prominent, and often times the higher resolution models can more effectively forecast these systems.

Lets just illustrate this with a simplistic comparison by arbitrarily choosing the 700 hpa pressure level.

First the 0Z NAM @ 33 hours:

and the GFS at the same time:

A couple things worth noting.  First, the NAM 700 hpa heights are much lower than the GFS.  The low level mass response is stronger in the NAM than GFS, and the low is displaced slightly farther W.  It is common for rapidly developing cyclones to develop farther W than expected.  Why?  It mostly relates to the position of the warm front and zone of warm air advection.  Think of the propagation of a surface low.  The region of surface low pressure will propagate towards the region of strongest surface pressure falls.  It makes sense then that developing surface lows propagate along the surface warm front.  From our earlier discussion, remember rapid cyclogenesis results in more amplified upstream ridging owing to thermal advection/diabatic heating in the warm sector.  Also remember differential cyclonic vorticity advection (along with mesoscale jet circulations), which is a dominant forcing method aloft, results in vertical motion fields which are displaced farther W from the surface low.  Therefore, as surface occlusion begins, low level warm air advection decreases (and subsequent differential warm air advection decreases) resulting in less height rises upstream of the shortwave.  Differential vorticity advection and forced ascent become stacked with the surface low and intensification slows significantly (surface low can still deepen due to forced ascent above the surface but still below the level of non-divergence…in other words, baroclinic processes may still result in forced ascent in the low levels above the surface occlusion…hence why surface lows still deepen after occlusion).  This also results in a much slower track.

FInishing this post up, rapid intensification almost always results in a system displaced farther W.  Global guidance continues to shift W towards the higher resolution model solutions, and the high resolution models are all developing a rather significant TROWAL (Trough Of Warm Air Aloft).  This makes sense as the low level mass fields are much stronger in the high resolution models due to the increased deepening and more rapid intensification.  A strong closed low level circulation results in warm air “wrapping” around the main upper low and a region of enhanced warm air advection ascent on the north then backside of the upper low (this also enhances the development of the surface low farther W and sometimes NW).  Large TROWALS are obviously efficient snow machines in winter since the precipitation falls on the cold side of the storm (in the low levels).

Subsequently, the NAM has a much larger QPF field farther west into the cold side of the storm and a farther W track of the surface low.

With the GFS farther E and with a less defined TROWAL of QPF:

Given the information I have given and the current trends (which further support the dynamic assessment above), and without doing an in-depth analysis of the thermal fields (for brevity), it seems an early season snow event across portions of eastern MN/western WI is likely.  Track wise, I think it will be slightly farther E of the NAM but a tad farther W of the ECMWF which would take it slightly inside the SE Minn border or right along it.  I am also leaning towards the NAM intensity which would yield a mid-level TROWAL well displaced over the low level cold air.  Given this information, it is quite probable a band of accumulating snow can be expected across central and eastern MN into W Wisconsin into the Arrowhead of MN.  It most certainly will be fun to watch.

Finally, as a quick mention, it is worth noting IPV thinking yields similar conclusions.  IPV thinking also deals with the diabatic effects even though potential vorticity is being conserved along isentropic surfaces.  For instance, significant diabatic effects on the warm sector (definitely not adiabatic!) results in the destruction of the upper level vorticity (in the QG perspective…upper level height rises) with increased development of the cyclone in the low levels below the region of latent heat release (strong low level mass response) .


Incredible Jet Stream Divergence

No amount of superlatives can describe the storm taking shape over the central and northern plains.  My projections of surface intensity in the previous post were completely wrong (I believed 966 was too low).  With any sort of extreme weather system, any particular dynamic and/or kinematic field is expected to be impressive.  This storm, however, is displaying an incredible amount of jet stream divergence which shows up in spectacular fashion on satellite imagery.    Let’s take a look.

IR satellite image at 15Z with the center of the jet stream noted at 250 hpa with the red line.  The green circle denotes the upstream jet streak in excess of 160-180 knots.

12Z 300 hpa analysis with winds and divergence plotted (thanks to http://www.patricktmarsh.com/, I never knew jet stream level winds with divergence plotted existed!):

As analyzed by the 12Z GFS @ 18Z (250 hpa):

Note the increasing jet level winds on the eastern side of the upper level trough from 12Z to 18Z.  Let’s investigate further.

The 12Z HPC surface analysis has the cold front analyzed in northern CO:

Note the well defined lee cyclone in the Front Range of CO extending into New Mexico, an atmospheric response due to the cross-barrier flow blocking effect of the Rockies.  Large and long mountain ranges block the otherwise orderly flow of cold air advection, resulting in a geostrophic adjustment process.  Lee cyclogenesis acts to enhance the low-level south flow and, in the case of the US, the flow of warm and moist Gulf air northward.  The “blocking” of cold air into the plains acts to “displace” the cold air aloft from the low level warm air in the plains in the vertical.  Mentioned in the previous post as well, the thermal wind equation comes into play here.  http://amsglossary.allenpress.com/glossary/search?id=thermal-wind-equation1

The change in the geostrophic wind with height (vertical shear) is related to the thermal gradient.  The jet stream, therefore, is a manifestation of intense baroclinic zones and upper level fronts, not the other way around.

Let us put it together a little more.  Take a look at the GFS 12Z analyzed 1000-500 mb thickness fields:

The location of the surface trough is noted with the green line with strong surface ridging behind the front (as expected).

Note that, at 12Z, the upper level cold air isotherm packing is lagging behind the low level cold air:

The effects of large scale flow blocking become much more apparent here as we put things together.  The effect of the broad and high Colorado Rockies is to block or retard the low level progression of otherwise orderly cold air advection.

BY 18Z, the region of cold air aloft has now become superimposed over the region of lower level cold air associated with the low level front, currently being blocked by the high terrain of the Rockies.

Oh, but wait.  What did the thermal wind equation state?  The picture is becoming slightly more clear now.  The juxtaposition of cold air aloft and at low levels along with the continued effect of lee cyclogenesis due to cross barrier flow results in southerly warm air advection in the low levels of the high plains.  These processes work to enhance the baroclinic zone along the mountain barrier.

18Z GFS forecast shows how much tighter the 1000-500 mb thickness field has become due to the aforementioned processes.  Also note the high-low pressure couplet that has developed across CO with the decrease in the surface pressure of the lee cyclone, now to 984 mb.  Cold bora winds downslope into the plains as the cold air “pours” over the Front Range.

As expected from the thermal wind equation, our jet stream has now become stronger on the eastward side of the curved jet stream over our now enhanced baroclinic zone across the high plains (circled).:

Also worth noting here are some of the terrain flows that can develop under such circumstances.  In the case of the Front Range, mesoscale terrain flows can develop around or over regions of decreased height in the Rockies.  Extreme pressure gradient forces are relaxed through relatively narrow regions of the terrain, resulting in terrain enhanced gradient forces.

Both the Ferris Mountains and the Laramies reach elevations above 10,000 feet with the Snowy Range (named the Medicine Bows in Colorado) extending to over 12,000 feet.  Gaps in the terrain extend down to 7500 feet in Laramie, WY before reaching approximately 4600 feet in Akron, CO.  With I-80 along southern WY being the only large scale “outlet” for subsident air over the Great Basin, winds can become rather extreme.

The obs from Akron, CO clearly show frontal passage (boxed red) with the typical pressure falls preceding the front followed by rapid pressure rises.  Of course, peak winds occur during the time period of rapid pressure rises (boxed green) and strong descent due to efficient mixing in the convective boundary layer acting in conjunction with descent on the backside of the frontal circulation (circled red).

Let’s move on.

Curved jet dynamics result in regions of strong ascent/descent (ascent on the exit region, descent on the entrance region) on the poleward (cold) side of the jet stream.

Also note the increasing amplitude of the trough and the “digging” nature of the jet.  Is this a result of QG Chi interepreted height falls associated with abnormal thermal advection patterns noted earlier?  Think about that.  Do jets “dig” or do heights fall?  I will let the readers decide.

Goes satellite derived WV winds at 18Z suggest both the NAM and GFS are under observing the jet streak winds on the downstream portion of the trough which would result in even greater values of jet divergence.  Circled isotach at 120 kts (18Z GFS peaked at 90 kts from 300-200 hpa).

This jet stream divergence was manifested in spectacular fashion on satellite imagery:

And on multi-spectral satellite imagery:

Here is an animation of the cloud patterns associated with this divergence over Colorado.  This is the best way to see the divergence pattern and associated cloud field:

Also note the “folds” oriented perpendicular to the flow (easily seen in the visible sat images).  Personally, I have no explanation for these features.  It seems plausible the N-S oriented CO Rockies have an influence, but I personally have no reasoning.  Anyone with ideas or explanations please let me know.

Update:  The expected smooth nature of the jet cloud pattern over WY is typical earlier in the day.  As the system interacts with the Front Range of Colorado, the folds seem to originate in the region where enhanced vertically propagating mountain waves often develop.  This seems like a plausible explanation, but I will have to do more of an analysis before coming to such a conclusion.

This analysis ends here, but note this is just one explanation (also the more simplistic and less mathematical approach and reasoning) of lee cyclogenesis and further baroclinic development associated with an intense jet stream (lee troughing is possible with little to no jet stream/weak baroclinity).  Other authors have proposed a QG explanation (Bluestein uses this approach in his Synoptics in Midlatitudes) as well as potential vorticity reasoning.  In general, differing “theories” and interpretations seem to come to relatively similar conclusions (in the last 20 years at least).

Meteorology is a beautiful thing when it makes sense.

Additional reading for those interested.

http://journals.ametsoc.org/doi/pdf/10.1175/1520-0493(1989)117%3C0154:NAOTIO%3E2.0.CO;2

http://www.atm.helsinki.fi/~dschultz/pubs/19-SchultzDoswell00.pdf


First “bomb” Cyclone of Fall 2010

I have been so transfixed with the large cyclone transitioning into a vigorous shortwave trough across the western U.S. lately I had paid little attention to weather events along the east coast.  My special love for vertically propagating mountain waves, downslope windstorms, and intermountain/mountain west weather in general may have blinded me (albeit very briefly) slightly to the events along the other coast of America.  I apologize, and I ask for forgiveness from any east coasters I know.

WV imagery during the initial stages of rapid deepening:

12 hours later.  Note the rapid increase in mid-upper tropospheric moisture as the system interacts with the Gulf Stream.  Also note the rapid development of a significant “dry-slot” off the east coast–quite common in rapidly intensifying cyclones (will also go more in-depth during later posts…more complex dynamically and thermodynamically than one may think!) :

No analysis needed here (I will do a more thorough analysis of the dynamics and thermodynamics sometime this winter).  The interaction of Canadian cold air advection and the semipermanent zone of baroclinity along the Gulf Stream results in some of the most spectacular weather in the U.S. during the fall/winter.

Surface pressure falls at Portsmouth, NH.  27 mb/20 hours, and the very impressive nearly 15 mb in the last 5 hours:

The late renowned MIT professor Dr. Fred Sanders, a synoptician for whom I have the utmost respect for, was the first to “coin” the term bomb in the case of rapid marine cyclogenesis.  http://journals.ametsoc.org/doi/pdf/10.1175/1520-0493(1980)108%3C1589:SDCOT%3E2.0.CO;2

Update:

Portsmouth, NH finally reached a low pressure of 982 mb and nearly 35 mb/24 hrs.

Atmospheric Bombogenesis.  Fred Sanders would be proud.  Enjoy the spectacular satellite signature:



Cold Air Advection Over the Northern Plains

A large intrusion of cold air into the central and eastern portion of the United States this weekend ushered in the coldest air of the season across the Northern Plains and Great Lakes region.  It was slightly unusual in that there was no significant surface low/intense shortwave trough and associated sharp cold front.  What starts as a mid-upper level weakly baroclinic stationary trough centered over the Hudson Bay eventually develops into a case of lower to mid-level frontogenesis, incredible cold air advection, and synoptic subsidence incited by a low amplitude upper level wave disturbance.

Let’s investigate.

The analysis fields of the GFS on the 30th September, 12Z depict the trough over the Hudson Bay:

The upper tropospheric wave disturbance (12z) is seen here over northern Alberta:

By 0Z the 31st, the analysis fields of the NAM/GFS nicely capture the intensifying wave disturbance as it begins to interact with the larger trough over the Hudson Bay:

The disturbance is quite evident in the WV loop:

This is also captured nicely in the RUC Analysis field at 0Z.  Note the lack of a low-level wave as no low level mass response has developed at this point in time.

Since there has yet to be any low level mass response, it makes sense there is a total lack of cold air advection in the low levels (850 hpa) along the southern Canada border into northern MN:

By 18Z the 1st October, the disturbance had progressed over the Great Lakes with the weak phasing essentially complete.  Note the significant subsidence behind the wave disturbance.

Here is how the 12Z GFS has it analyzed (at 500 hpa) 6 hours later (same time as the WV image):

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