Tag Archives: wave

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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The Importance of Model Timing: Ohio Valley and SE Rain Event

Click on images to see an enlarged view.

The timing of upper level features in numerical models is crucial to the eventual weather patterns they subsequently simulate.  There are times, however, when the difference in timing can have significant feedback effects with errors which grow rapidly with time.  The forecast for the Ohio Valley and SE U.S. shows significant model divergence within the first 48 hours amongst the current 0Z NCEP model guidance.  The GFS is illustrating a large rain event while the NAM is much weaker with eventual cyclogenesis and keeps precipitation much farther south.  Let’s take a look why they are so different and why the current 0Z NAM is likely going to be wrong.

All numerical guidance is more or less the same by 24 hours with the large scale synoptic features.

Both feature a large scale upper trough over the central CONUS with a low amplitude shortwave embedded near the base of the trough.

Fast forward to 33 hours and things still look mostly the same.  However, upon closer inspection, it is clear the NAM has the leading shortwave at the base of the trough displaced further W than the GFS–in other words, it is slower.

The GFS, shortwave circled:

NAM:

Also note the slightly higher amounts of shear vorticity upstream of the shortwave in the NAM compared to the GFS.  Essentially the mid-level speed max is displaced farther W in the NAM.  Also note a very low amplitude and subtle downstream ridge is developing in the GFS ahead of the shortwave.  Why?

Note in the GFS 850 hpa theta-e field a large region of warm air advection has developed ahead of the upper level shortwave (circled) with a stronger low level circulation.

NAM:

Note the NAM features a much weaker wave as opposed to a developed low level circulation.  While the theta-e profile is similar to the GFS, the NAM features no warm air advection as the 850 hpa winds are mainly parallel to the theta-e gradient.  I can’t hammer the point home more, but low level warm air advection decreasing with height lends itself to upper level height rises.

Stronger cyclogenesis is a positive feedback process.  As was shown in the previous post as well, an upper level baroclinic wave interacting within a region of low level baroclinity results in developing cyclogenesis.  Vorticity advection by the geostrophic wind in a shortwave trough results in height falls aloft and forced synoptic ascent.  This forced ascent, if above the level of non-divergence, and because the atmosphere follows the laws of mass continuity, will result in a low level mass response and increasing low level convergence/cyclogenesis.  Low level diabatic heating (see the previous post for a more in-depth reasoning) mainly owing to the release of latent heat as low level moist air rises and condenses will only hasten the process–and this system has ample amounts of Gulf moisture to process.  Meanwhile, the thermal gradient in the low levels tightens and frontal boundaries become more defined owing to processes such as horizontal deformation (of the many which can result in frontogenesis).  This is all due to the increasing low level convergence/mass response to upper level forced synoptic ascent.  Mesoscale ascent/convergence along the fronts increases owing to the increasing frontal thermal gradient which results in even more low level mass convergence and increasing surface pressure falls.  Meanwhile, owing to continued synoptic ascent in the upper levels (differential cyclonic vorticity advection) and subsequent cooling, upper level heights begin to fall at a faster rate.  Because the thermal gradient in the lowel levels is tightening, the thermal wind relation

states upper level winds must increase with height.  So not only does the jet stream increase, but upper level heights continue falling at an increased rate, therefore, the amplitude is increasing.  Jet stream divergence increases due to increased cyclonic curvature in the upper level height field and a stronger jet max (as well as a shorter wavelength if the system takes on a negative tilt), therefore, stronger mesoscale ageostrophic jet circulations develop.  Cyclogenesis is now increasing rapidly; this positive feedback loop continues until the low level baroclinic zone has been sufficiently processed.

With that in mind, it is much easier to understand why timing is crucial.  In most cases, the speed of an upper level shortwave just means the timing of cyclogenesis may develop at a different time, but it will develop in a similar fashion regardless of the timing.  In this case, however, a delayed upper level response to a shortwave trough (the NAM) with the large scale trough propagating eastward will result in less warm and moist Gulf air to interact with.  That is, because the NAM is slower with the shortwave, cyclogenesis will be delayed and the positive feedback loop will not be present ( or will play a much smaller role).

Skipping ahead 6 hours, note how much things have changed.

By 39 hours, the upper level shortwave has now “ejected” into the Ohio Valley with an increasingly amplifying downstream ridge ahead of the shortwave.

The NAM, however, features a flat height field ahead of the shortwave with the shortwave much farther W.

As one would expect, the low level mass fields are completely different with the GFS developing a much more intense and deep surface low by 45 hours as deep cyclogenesis has developed strong cyclonic rotation through the depth of the troposphere.  In the mid levels, the GFS features a strong closed circulation while the NAM has a broad open wave.

NAM:

The surface fields are even more dramatic as the GFS has a strong sub 996 mb surface low while the NAM has broad and weak ~1008 mb low.

These differences result in a vastly different precipitation field:

GFS:

The differences are vast.  The GFS solution yields moderate to heavy precipitation over much of Indiana and Ohio associated with a large TROWAL (associated with the strong and deep cyclonic rotation) while the NAM is almost completely dry only 48 hours out!  You can’t really make a compromise because the solutions are so vastly different and would yield a cruddy forecast.  In my forecasting experience, when the NAM features a slower propagating low amplitude shortwave trough than the GFS, it is wrong ~ 90-95% of the time.  Under certain circumstances (as was shown with last storm…read the previous post), the NAM can be right with a slower solution under rapid cyclogenesis events.  However, those cases usually feature much more amplified and intense shortwaves and/or intense PV anomalies.  In this case, I would give the NAM a less than 10% chance of being right.  Because of that, I would simply not even include it in the forecast.  Under these circumstances, it is not unheard of for the NAM to not simulate a realistic solution until the system has already developed.  In other words, it is wrong all the way leading up to eventual cyclogenesis.  I suspect the 12Z NAM will correct a lot, but I doubt it will completely fix it.  As for the GFS, I do believe it is a bit too intense and far west with its surface low track and precipitation field, but it is most definitely the better solution.  The GEM seems like a more reasonable solution with most of the heavy precipitation staying across southern IN/OH with lighter amounts farther north.

In my experiences, the regional GEM is a far more reliable model than the NAM under most circumstances.

This post goes to show how important timing of upper level features can be on the forecast, even in the short-term (in this case only 48 hours).  It also shows how rapidly feedback effects hasten the process of cyclogenesis (IPV thinking explains this very nicely).  Most importantly, this example illustrates why forecasters must analyze both the synoptic and mesoscale features present as opposed to simply reading the model output without interpreting it.  Simply looking at model output QPF or surface fields (i.e. surface pressure fields) without considering the meteorological processes developing those fields will result in less accurate (worse) forecasts.  Learning model biases takes time and requires attention to detail.

The butterfly effect?  Chaos Theory?  Dr. Lorenz proved himself to be many years beyond that of his peers–a genius amongst geniuses.

http://eapsweb.mit.edu/research/Lorenz/Deterministic_63.pdf


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.


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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