Tag Archives: chi equation

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) .

Advertisements

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.


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):

Continue reading


%d bloggers like this: