Category Archives: jet streak

Deep Cyclogenesis and the Utility of Potential Vorticity “Thinking”

In terms of the unstable stratification of a fluid, different types of cyclogenesis can manifest itself in the mid-latitude westerlies.  It is the forecasters responsibility to understand what is happening from a full “3-Dimensional” aspect.  Our atmosphere does not work on 2-D surfaces or only at 500 hpa, 700 hpa, 850 hpa, etc.  A continuous spectrum of differing types of cyclogenesis exists with examples including open wave upper disturbances over intense low level baroclinic zones, wave deamplification, deep tropospheric cyclogenesis over moist low level baroclinic zones, etc.  Understanding the type of “potential” cyclogenesis is a key to understanding how the eventual baroclinic system will develop.  Models are not the answer–they are just the guidance tool to provide the meteorologist with the details needed to assess the state of the atmosphere.  Let’s move on.

NOTE:  All images below can be enlarged by clicking them.

A tropospheric deep, “vertically stacked” cyclone is currently rapidly developing over the northern plains.  As per usual, this type of cyclogenesis was not particularly well modeled by the numerical guidance as it is deepened faster and stronger than progged.  The resultant surface low is much farther west and “bent-back” into the low level thermal gradient.

12Z GFS model progs from a couple days ago at 500 hpa with the forecast time of 18Z Saturday:

And the surface pressure/theta-e fields:

Compare to the current 18Z analysis at 500 hpa:

The European 48 HR forecast (left panel is the ensemble mean, right is the operational) performed better, but it was also too weak and was an open wave aloft.

Which shows up much better in the surface fields.  48 hr ECMWF forecast:

12Z analysis today:

Note how the low is “bent-back” and much farther W than progged with a deeper surface low and stronger cold side gradient.  These type of forecast changes have significant effects on the eventual forecast.  If the forecaster simply “responds” to each model forecast as it continually changes, then their forecast will never be right if the models are constantly playing catch-up to observations!  Most importantly–the high impact effects of the storm won’t be relayed to the public in a timely manner.

Watch the progression of the 54 HR GFS forecast to the eventual analysis at 18Z Saturday.  Note how the position of the low changes from southern Canada north of the Great Lakes to central North Dakota .  Also note how much deeper the surface low is as well as the strength of the mass fields owing to the increased pressure gradient (as well as increased vertical momentum transport/mixing).  This is all in a period of 2.5 days of GFS model runs (dProg/dT):

If the forecaster were to simply take each individual GFS forecast verbatim, the forecast would have been a miserable bust with a large number of “jumps” in the forecast.  Both are very undesirable.

In previous blogs I took the time to explain baroclinic cyclogenesis from a standpoint of Quasigeostrophic Theory.  However, in the past 5 months, I have forced myself to learn Isentropic Potential Vorticity, and I have learned its great utility in the forecast process as a result.  I am still learning IPV, but I have seen the high usability of IPV in terms of the type of “cyclogenesis” as it is a more “natural” way to view the 3-Dimensional atmosphere and the resultant flows of baroclinic systems.

Isentropic Potential Vorticity is a pretty broad topic which would take far too long to even try and explain, but what IPV does is essentially explain the “dynamical tropopause” based on potential vorticity identified by the PV gradient on isentropes where PV (image courtesy of RAMMB) is defined as

with units of 10-6 m-2 s-1 K kg-1.

In other words, PV is the mathematical dot product of isentropic absolute vorticity and static stability.  PV is conserved and the quantity can only be changed by changes in static stability and/or friction.  The beauty of IPV is the “invertibility principle” researched and discovered by Hoskins (Hoskins, B.J., M.E. McIntyre, and A.W. Robertson, 1985: On the use and significance of isentropic potential vorticity maps.)  The invertibility principle itself is a rather long and complicated mathematical formulation, but in short, it allows for the calculations of all major meteorological quantities such as winds, heights, temperature, etc. as well as the plotting of PV maps on various surfaces (isentropes, pressure surfaces, etc.)  One variation on the use of  Potential Vorticity is the “Dynamic Tropopause”, or DT.  Typically the Dynamic Tropopause is defined as the 1.5/2 PV surface where PVU’s are “Potential Vorticity Units” (although it can vary between 1-5 PVU’s).  This is typically the “zone” between tropospheric and stratospheric air.  A “positive” PV Anomaly can therefore be defined as a local minimum in the tropopause and an area of cyclonic vorticity.  Morgan and Gammon (see references below) discuss the usage of the dynamic tropopause,

This analysis (here referred to as a tropopause map) exploits the rather simple distribution of tropospheric PV: as will be demonstrated in the next section, isentropic gradients of PV are concentrated at the tropopause. Tropopause maps are a compact way to represent this distribution. Thus, the essential character of the upper-tropospheric PV may be depicted on a single chart, rather than several isentropic maps.”

A deep vertical PV anomaly aloft and a strong potential temperature (theta-e) gradient in the low levels can be favored regions of deep and rapid cyclogenesis owing to a number of factors including moist latent heat release, stratospheric intrusions/tropopause folding, and upper level frontogenesis.  This characterization of the baroclinic atmosphere is referred to as the “Eady model representation”, and it should be noted here that PV usage does not describe the baroclinic atmosphere differently than the various forms of the Quasigeostrophic set of equations, it just uses a different approach (all rely on the N-S equations).

I have found a mixture of the Quasigeostrophic “thinking” combined with “PV thinking” to be optimal in assessing the baroclinic environment and the potential types of cyclogenesis.  For instance, one may want to assess the potential for a deep stratospheric intrusion (a deep vertical PV anomaly)/upper level cold front to interact with a low level baroclinic zone which can incite rapid positive feedback cyclogenesis under the right conditions.  Assessing the Dynamic Tropopause in such situations is crucial in understanding this potential for deep tropospheric cyclogenesis.  It can be shown that a deep DT/upper level cold front will enhance the vertical wind field aloft.  Consider the thermal wind equation:

which essentially states that a deep vertical layer of air consisting of  a strong horizontal thermal gradient through the depth results in increasing geostrophic winds with height.

Think of an upper level cold front cross section:

This is one way to “visualize” the 3-D atmosphere is through the superpositioning of a strong upper level cold front/DT/PV anomaly over a low level baroclinic zone, rapidly resulting in an increase in the vertical depth of the baroclinic zone as the upper anomaly progresses over a low level baroclinic zone.  It becomes obvious that jet streaks are an atmospheric response to propagating PV anomalies in the upper atmosphere.  Therefore the upper level wind fields are strongly influenced by PV anomalies, and the resultant divergent mesoscale jet circulations that develop are simply a response to the anomaly.  This is why rapidly “bombing” surface lows often feature strongly curved and/or coupled jet streaks aloft.

The February 1, 2011 “Groundhogs Day Blizzard” and the coupled jet streak and strongly divergent mesoscale circulation:

400-250 Potential Vorticity:

Also note the WV imagery and the direct “coupling” of the low level deep, moist convection “feeding” directly into the divergent portion of the upper level jet streak.  This is a classic feature in rapidly developing storms, and it can be considered the “warm conveyor belt” typical in synoptic storms.  Once again, it can be shown with PV thinking that low level and deep, moist baroclinic zones with a deep upper level PV anomaly can incite rapid and deep cyclogenesis driven strongly by moist latent heat release and decreased static stability.

It has been studied and shown in numerous studies that the release of latent heat in the low levels can have an enormous contribution to the omega equation vertical forcing (sometimes greatly larger than all the other terms combined):

Often times the influence of diabatic effects (red arrow) is often considered small (and all together dropped) from the omega equation.  However, it has been shown to play a significant role in rapid deepening and can strongly influence potential self-development/mutual development/positive feedback effects on the cyclogenesis process (for more information on self devolopment/rapid cyclogenesis, see : https://pantherfile.uwm.edu/roebber/www/pubs/R93.pdf).  Also note the static stability parameter (in green…the sigma characters) plays a prominent role in all the major forcing terms of the omega equation.  In other words, low static stability plays a major role in rapid development (hence why the most intense lows often have very warm and moist warm sectors.  Also note PV thinking/Eady model development also make use of low level static stability contributions. http://journals.ametsoc.org/doi/pdf/10.1175/1520-0493(1986)114%3C1019%3ATPIOUU%3E2.0.CO%3B2

Note the deep Dynamic Tropopause and the very high values of 925 theta-e for the February 1, 2011 event.  One can imagine how the overlaying of a cold anomaly over a warm and moist baroclinic zone can result in extremely low static stability (and possibly static instability):

It should come as no surprise, looking at the model data, that the Groundhogs Blizzard eventually “bombed” faster than any model projections which had profound effects on the track of the low, the resultant mass fields/wind fields, and the distribution of the precipitation.  It should be noted this event had “several” model solutions ranging from a very weak and “flat” track with the NAM and a moderately NW curving “non-linearly” developing low (GFS/ECMWF) to a strongly curved and intensely bombing low (RGEM).  Understanding model bias and understanding the situation at hand is crucial to understanding the forecast potential.  In this case, the usually “amped” NAM was being influenced significantly by “convective feedback” owing to “overcooked” convection and the mass release of unrealistic latent heat into the upper troposphere.  This warming of the upper levels crippled the model dynamic fields resulting in the unusual “flat” and weak track the NAM developed.

Hard to see here, but the NAM progged a “flat” and weak surface low track–much weaker than all other guidance.  Note the very high values of anticyclonic vorticity ahead of the 500 hpa shortwave–a response to the significant deep, moist convection the NAM was developing ahead of the wave.  Also note in the last frame the eastward “jump” the low takes–a sign of the significant issues the NAM was having in terms of the development of this system.  In reality–the low tracked much farther NW and was much more intense than the NAM projected, and the NAM remained too weak through the entire event.

In reality, as shown above, deep convection can play a strong role in rapid development owing to a strongly divergent mesoscale jet circulation and a direct “coupling” of the low level deep, moist convection feeding into the circulation.

As will be shown in later posts, many different types of cyclogenesis occur spanning a continuous spectrum from deep and bombing non-linear cyclogenesis to steady-state open waves (shallow cyclogenesis) and the resultant low level cyclogenesis.

A good example of shallow cyclogenesis is a classic Alberta Clipper with an open wave aloft and strong cyclogenesis in the low levels–a result of the “shallow” nature of the PV maxes aloft and shallow but intense low level baroclinic zones.  Also note the rather “steady” linear development of the cyclone (compare to a deep tropospheric bombing cyclone).  This is typical in Alberta Clippers owing both to the aforementioned shallow PV anomaly but also due to the significant lack of moist processes (latent heat release in the low levels).

Click the link for an animation of a classic Alberta Clipper developing from Canada to the East Coast:

http://www.meteo.psu.edu/~gadomski/NARR/2007/us0222j3.php

Getting back to the current northern plains storm, why does all this matter?

Note the GFS forecast from the 28th of April, 2011 at 12Z (same as the first plot above with the weak overall solution) featured a deep PV anomaly plotted on pressure surfaces for the 24 hour forecast (note the scale on right–dark blue is a deeper PV anomaly–and we are referencing the anomaly over the intermountain W):

There was significant potential for deep cyclogenesis given the warm sector in place even though the eventual GFS forecast was weak (seen above).  How does this play into the forecast process?  Does the forecaster take the model verbatim and run with it?  If one looked at surface fields alone, it would not be in any way obvious anything special was going to happen.  However, the forecaster had other available guidance (the ECMWF…and the Canadian to a degree) suggesting potential for a more significant event (let us ignore the GFS ensemble suite for now to use this as a case example).  Understanding the type of cyclogenesis is absolutely crucial to being able to identify where the model solutions may potentially “bust”.  Moreover, using such a “dynamic” assessment of the atmosphere, one can apply model bias as well as forecaster “experience” in such a situation to add significant benefit to the forecast.  Models are tools–they are NOT the solution, and using models as solutions only will result in bad forecasts and very significant busted forecasts during high impact events.  Let us continue.

By the 29th of April at 00Z (12 hours later), the 12 hour forecast panel suggests an even farther S and slightly broader DT.

The result, owing to stronger cross barrier flow across the Rockies, was an increase in low level warm air advection across the warm sector due to increased lee side troughing (which can be described through the conservation of potential vorticity as well as through quasigeostrophic theory by setting a lower boundary condition and deriving a new set of equations).

Note the warm air surging off the high plains into KS/OK (and how much stronger it is in the 29th April, 12 Z forecast):

And explained through the Quasigeostrophic Chi equation, increased low level warm air advection (which decreases with height aloft) will drive height rises aloft:

Which I explained much more thoroughly in this post: http://jasonahsenmacher.wordpress.com/2010/11/12/centralnorthern-plains-cyclone-event-1112-142010/

Note the upper level height response manifested in increased ridging aloft over MN and into Canada (500 hpa vorticity):

By this time, it was clear to the forecaster that the potential for tropospheric deep cyclogenesis owing to the deep PV anomaly aloft, the warm anomaly in the low levels (high theta values which corresponds to high PV), and the southern trend of the upper anomaly which resulted in even richer low level warm air advection (thus strengthening the low level baroclinic zone (and the corresponding PV anomaly in the low levels).

Notice how the guidance was rapidly deepening the low/mid levels with time with the 12Z GFS forecast on the 29th (500 hpa vorticity).  Also note, in this situation, the 500 hpa level is not indicative of the region of mass divergence.  In other words, 500 hpa is typically the atmospheric pressure level often evaluated for the placement of upper level waves since the average level of non-divergence (LND) is 550-600 hpa.  In this case, the LND would likely be well above 500 hpa into the upper troposphere.  Care must be taken when evaluating upper waves as 500 hpa alone may not be representative.

Note how the superposition of the upper anomaly over the warm anomaly in the low levels results in deep and rapid cyclogenesis/height falls and the “creation” of cold air in the low levels (watch the 925 theta-e fields with time).

This can be explained through the “interaction” between the positive PV anomalies in the upper and lower levels and the stretching of vorticity through the vertical.

It is also a result of the “descent” of the upper level cold front into the lower levels of the atmosphere–and as shown earlier–can be tied directly to an increase in the upper level wind fields.  From this point, classic “mutual development”/positive feedback cyclogenesis occurs.  Deep height falls and cyclogenesis results in increased wind fields and mass transport of warm air into the warm sector as well as the development of a TROWAL as warm air is advected onto the backside of the upper low and above the descending upper level cold front.  According to the QG Omega equation, WAA will result in synoptic ascent, but this WAA through the warm sector also increases the baroclinity farther northward.  According to the thermal wind equation–an increasing thermal gradient in the horizontal results in stronger wind fields aloft.  As a result, a distinct jet coupling aloft develops which results in increased values of divergence and a stronger warm conveyor belt which drives stronger WAA which then supports greater synoptic ascent and faster low level pressure falls/mass convergence.  Horizontal confluence in the low levels increases frontogenesis values (horizontal deformation contribution)

and mesoscale ascent along the front where yellow is the axis of dilatation.  In certain cases–it has been shown that precipitation processes/moist processes associated with ascent along the front can contribute significantly to vertical forcing and associated low level pressure falls owing to latent heat release.

Note how the jet coupling aloft develops (the secondary jet especially in Canada) in response to the increasing WAA into Canada (increasing low level warm front as well) and subsequent increase in the horizontal thermal gradient:

By this point warm air advection ascent associated with the TROWAL and increasing curved jet level divergence results in a bent back surface low with a strong cold side gradient:

This is classic self development/positive feedback cyclogenesis, and there are multiple mechanisms (besides the one mentioned above) that can create positive feedback cyclogenesis.

The effect of a descending upper level cold front and deep tropospheric cyclogenesis also tends to result in very efficient mixing through contributions of strong vertical descent over the cold sector and the destruction of inversions.  This can have significant results on the overall wind fields in the low levels.

Note the deep mixed layer and extreme mixing potential in the May 1, 00Z KRAP sounding:

Positive feedback cyclogenesis can occur in many ways, but this is one example of where mutual development strongly driven by intense WAA can result in rapid cyclogenesis.

It is typical in these situations for models to be in constant “catch-up” mode and they will potentially be adjusting all the way to the final event.  Note the NAM surface fields from the day 2 forecast until analysis at 18Z April 31 (especially note the much slower/farther W track and the stronger mass fields):

While numerical models are amazing tools, the complex statistical data assimilation systems are not capable of responding to rapidly changing observations once positive feedback begins.  Moreover, models are influenced heavily by the previous analysis field, so under a situation where there is a “cascading” effect, models will always be “behind”–sometimes multiple iterations behind reality.  It is the forecasters responsibility to assess this potential as it can have massive impacts on the eventual forecast–as seen here.

The eventual storm deepened to 987 hpa, well below the 2 day model progs, and even below the current model analyses.  The low was farther west into the cold air than progged by the guidance, and the storm moved much slower.

Wind gusts at Buffalo, SD were in excess of 75 MPH and many locations saw sustained winds of over 50 MPH.  Locations in ND saw significant life threatening blizzard conditions for a prolonged period of time.  Some locations saw over one foot of snow with 60+ MPH winds within the blizzard locations.

It is quite obvious that models are not the solution–they are only a tool in assessing the atmosphere.  Having a strong understanding of the processes at work is an absolute must, and understanding how numerical models simulate the atmosphere is crucial in understanding their weaknesses as well as biases.  Potential Vorticity thinking is just another tool available to the forecaster which can significantly aid in assessing atmospheric processes, and as I continue to learn, I hope to add more posts in the future as well as expand on PV/IPV topics.

As always, meteorology is a beautiful and wonderful thing when it makes sense.  Dynamic assessment allows the forecaster to “view” atmospheric flow in a more natural way.  Having this understanding no longer makes us a slave to the numerical models, but it gives us the ability to not only see “potential” but to avoid big high impact forecast busts as well.   Most importantly, it allows the forecaster to view the forecast from a different perspective.  One can fill in the “details” in their head–and it gives them the ability to analyze the things that matter and disregard the things that really don’t mean much in the end (for instance–model derived isentropic ascent/descent and model vertical velocity fields)–an important quality in these days of “too much information” and busy forecast schedules.  Knowing what to “track” and analyze and what influences baroclinic development will give the forecaster the ability to “see” potential for significant deviations in the model forecast or for things to be stronger/weaker than progged.

References:

http://onlinelibrary.wiley.com/doi/10.1034/j.1600-0870.1995.00124.x/pdf

http://journals.ametsoc.org/doi/abs/10.1175/1520-0493(1998)126%3C2555%3AUTMTDM%3E2.0.CO%3B2

http://journals.ametsoc.org/doi/abs/10.1175/2008JAS2921.1

http://journals.ametsoc.org/doi/pdf/10.1175/1520-0434(1988)003%3C0217%3ATROLHR%3E2.0.CO%3B2



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:


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) .


Weak Elevated Convective Instability Associated With Dynamic Height Falls

There is always something interesting going on in weather.  What initially may seem run-of-the-mill can become more interesting upon closer inspection.  Sunday featured a migratory baroclinic wave, cutoff from the primary westerlies, passing through the intermountain west and “ejecting” into the central plains during the afternoon.  What was particularly interesting was the interaction of a deep frontal circulation within a region of “dynamic” height falls aloft which supported the release of elevated instability.  The co-location of a mesoscale divergent jet stream aided in the rapidly increasing cloud field and elevated “gusty” virga showers.

The wave in question is quite clear in WV with the mid-level trough axis over Colorado at 12Z Sunday:

The 300 hpa upper air analysis clearly shows the upper wave and jet stream level winds as well as the large amounts of divergence (plotted yellow):

The 500 hpa analysis at 12Z.  Note the lower amplitude of the wave at 500 hpa as compared to 300 hpa (this is important!), suggesting this was largely an upper tropospheric wave.  Also note the large values of cyclonic vorticity near the base of the trough owing largely to horizontal shear (of course curvature vorticity is also present, but it does not play as large a role), simply expressed by :

in the natural coordinate system.

This is typical of low amplitude baroclinic waves owing to the amount of shear.  Why do low amplitude waves propagate at a greater speed than longwave troughs?  The rapid forward propagation of the wave is explained (compared to a longwave trough) by the dominance of cyclonic vorticity advection and subsequent height falls ahead of the shortwave trough.  Planetary vorticity advection on the backside of the wave is minimal due to the short wavelength, therefore height falls on the upstream portion of the wave are much smaller than height falls downstream.

The advection of cyclonic relative vorticity by the geostrophic wind dominates over f in the QG Chi equation regarding shortwave troughs:

And the 12Z GFS, once again, note the high values of cyclonic vorticity near the base of the shortwave:

Note the thermal pattern at 500 mb.  There is little to no cold air advection at 12Z:

Note that, by 18Z, as progged by the GFS, the cold air overspreads much of Colorado with little to no advection.  Why?  “Dynamic” height falls:

A combination of QG Chi and the hypsometric equation can help explain this.  As mentioned earlier, large values of cyclonic vorticity are being advected by the geostrophic wind near the base of the shortwave.  The more cyclonic vorticity and/or the stronger the wind, the greater the height falls.

The winds at 300 hpa are on the order of 70-90 kts:

And 40-60 kts at 500 hpa:

This suggests the geostrophic wind at 300 hpa is advecting more cyclonic vorticity than at 500 hpa due to the strengthened flow aloft (I don’t have the map, but the amount of cyclonic vorticity at 300 hpa is similar to 500 hpa).  Heights are falling faster aloft than they are at lower levels (this makes more sense now…remember the higher amplitude 300 hpa shortwave compared to 500 hpa?  This implies heights must fall at a greater rate aloft than regions below with a forward propagating wave).  As a result, because the atmospheric column is shrinking from some level below 500 hpa to the upper troposphere, temperatures must cool in response, implying forced ascent.

The effects of these dynamic height falls results in cooling of the upper levels and steepened lapse rates, which can be enhanced by diurnal insolation in the lower levels.

By 18Z, note the large convective cloud field which has developed post-front over the Colorado Rockies.  Also note the plume of high cirrus associated with the divergent jet stream (green) with a crudely drawn streamline:

By 20Z, the front has progressed into the plains, but note the still cloud free region in western NE:

The 12Z GFS @ 18Z over western NE shows the influence of dynamic induced height falls in the model Skew-T.  Note the mid-level lapse rates:

BY 21Z, note the steep mid-level lapse rates and the deep cold front (red).  Also note the GFS upper level winds are mainly S-SW.

Air parcels lifted to the top of the frontal circulation will be able to ascend freely somewhere around (after calculating a crude elevated LFC) 500 hpa before reaching the Equilibrium Level near 400 hpa.  Also note the very narrow and shallow zone of CAPE–likely around 50 j/kg or less.  Note the rapid expanse of the cloud shield over western NE along with the small pockets of weak convection from 20z to 23z:

Also note the continued SE flow aloft.  The rapid expanse of the cloud field was likely enhanced by the mesoscale jet circulation.  Also note how cold the cloud temperatures are in western NE:

The 12Z GFS @ 0Z is forecasting winds at 300 mb to be nearly due SSW (180-200 degrees).  Also note the ridge axis upstream.

Air parcels exiting the jet streak would become supergeostrophic and flow to lower heights aloft, in this case towards the NW.  This enhances the ageostrophic wind field/divergence and mesoscale forced ascent.  Remember that, in the case of jet stream circulations, this must be considered in addition to the large scale synoptic vertical motion field.  Jet streaks and their associated circulations are mesoscale and are not in any way related to synoptic scale ascent and the QG equations of vertical motion (which can be shown through a scale analysis).   Note that, in the 0Z analysis, which employs upper air soundings, the flow is indeed S-SE (also indicated in the cloud flow pattern and in satellite derived winds).  In this case, the 12Z model runs were likely underestimating the strength of the jet circulation and associated vertical motion field.  While the impacts were relatively minimal here, in winter, that could result in models significantly underestimating the potential for heavy snow banding (just one of many potential high impact events), for instance.

Also worth noting here is the 18Z 300 hpa wind forecast at the same time (compare this to the 12Z forecast above).  Satellite derived winds ingested by the numerical model data assimilation systems were able to adjust the upper level wind field to the satellite observations.  This is a good example showing “off” hour runs are not worthless and can have operational significance if used intelligently by the forecaster.

A large area of showers formed over the region including heavy convective showers.

 

Surface observations suggest most of the shower activity over western NE never hit the ground and cloud bases (AGL) remained high at around 10-12000 feet.  The main effect of the showers was to enhance horizontal momentum transport downwards and increase wind gusts along the frontal circulation.  Most surface observations showed peak wind gusts with the arrival of the showers, some in excess of 40 mph, hence the name “gusty” showers.

This case is a good example of the importance of “dynamic” height falls in meteorology, especially in terms of summer convective potential when deep, moist convection is often initiated/and or enhanced by very low amplitude waves/upper level “impulses” due to cap erosion, steepening lapse rates (increased CAPE), and regions of low level mass convergence (surface based and/or elevated).  Also important is the co-location of differing meteorological circulations (e.g. mesoscale jet circulations, frontal circulations, regions of synoptic ascent, etc.), especially during winter storm events.  Being able to diagnose and forecast these regions is of utmost importance, even more so in the short-term forecast and NOWcast.


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


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