Looming Snowstorm and the Fujiwhara

By: 24hourprof , 4:48 PM GMT on February 08, 2013

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With an historic snowstorm looming over New England later today and tomorrow, I wanted to set the record straight with regard to the evolving interaction between the two 500-mb short-wave troughs in the southern and northern branches (see the 12Z NAM model analysis below; larger image). The explanations I heard on television have run the gamut from "merging surface lows" to a "phasing" of the 500-mb short-wave troughs.


The 12Z NAM model analysis of 500-mb heights, 500-mb absolute vorticity, and 500-mb wind barbs on February 8, 2013. Larger image. Courtesy of NCEP.

The merging of the two surface lows (12Z surface analysis) is not really feasible because the low associated with the 500-mb short-wave trough in the northern branch can't scale the Appalachians and remain intact. That's because an eastward-moving low attempting to "climb" a mountain will gain anticyclonic relative vorticity (vorticity is a measure of the rotation of an air parcel around the local vertical). For a low-pressure system whose longevity depends on maintaining or enhancing its cyclonic vorticity, gaining anticyclonic rotation while climbing a mountain means that the low will weaken dramatically. By the way, the notion of an air parcel gaining anticyclonic vorticity as it ascends a mountain is a consequence of the conservation of Ertel's Potential Vorticity, a topic which I intend to write about in a future blog.

The explanation that purports a phasing of the two short-wave 500-mb troughs is correct, although it's been my experience that most folks treat phasing as a simple merging of the two troughs. Phasing is not that simple. Indeed, two short-wave 500-mb troughs destined to phase typically perform a Fujiwhara, a cyclonic "dance" that occurs when the two short-wave troughs get sufficiently close together. I point out here that the context of a Fujiwhara typically involves tropical cyclones (when tropical cyclones get sufficiently close together, they start to cyclonically rotate about the same intermediate point). Obviously, the Fujiwhara also occurs over the middle latitudes during the phasing of two 500-mb short-wave troughs (details will be forthcoming). For the record, I have also observed the Fujiwhara in action when a 500-mb short-wave trough and a tropical cyclone get close enough to interact.

Let's assume that two short-wave 500-mb troughs get sufficiently close together to interact, and, for ease of explanation, are aligned from north to south. Check out the idealized juxtaposition of the two short-wave troughs on slide #1 from the synoptic course I used to teach at Penn State (the short-wave troughs are each designated by an "X" inside a red circle to mark the position of its vorticity maXimum). Okay, the northern short-wave trough starts to slow its eastward progression as it encounters the cyclonic circulation associated with the southern short-wave trough (see slide #2). Meanwhile, the southern-branch short-wave trough swings northeastward as it "senses" the cyclonic circulation of the northern short-wave (see slide #3). Note that the two vorticity maxima are even closer (see slide #4 below; larger image). At this point, the Fujiwhara continues, with one trough eventually emerging after this cyclonic dance comes to an end.


When two short-wave 500-mb troughs (marked by their vorticity maXimum in each case) get sufficiently close together to interact, the northern trough slows and the southern trough swings northeastward, setting the stage for the Fujiwhara to continue. Eventually, the two troughs phase. Larger image.

Look again at the 12Z NAM model analysis of 500-mb heights and absolute vorticity and note the initial positions of the two 500-mb short-wave troughs in the northern and southern branches. Now follow the progression of 500-mb NAM forecasts from 3 hours (valid at 15Z this morning) to 21 hours (valid at 09Z tomorrow morning). I'm listing them individually so you can focus more closely on the evolving interaction of the two short-waves. Can you see the Fujiwhara?

NAM Forecasts of 500-mb heights and absolute vorticity from the 12Z run on February 8, 2013:

3-hour

6-hour

9-hour

12-hour

15-hour

18-hour

21-hour

Movie

Lee

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5. WunderAlertBot (Admin)
1:13 AM GMT on February 13, 2013
24hourprof has created a new entry.
4. 24hourprof
2:26 PM GMT on February 11, 2013
Quoting NEWxSFC:
"...the notion of an air parcel gaining anticyclonic vorticity as it ascends a mountain is a consequence of the conservation of Ertel's Potential Vorticity..."

A phenomenon sometimes observed in IR imagery as the feature crosses the mountains (warming tops).


Not sure what you're driving at here. Adiabatic cooling during ascent and adiabatic warming during descent are pretty much independent of vorticity.

Any way, IR satellite imagery does not detect changes in temperature in air parcels.

Warming of mountain tops on IR imagery is likely due to solar heating or warmer clouds (cloud tops) passing over mountains. I guess I don't understand your comment.
Member Since: October 24, 2012 Posts: 88 Comments: 793
3. NEWxSFC
10:16 PM GMT on February 10, 2013
"...the notion of an air parcel gaining anticyclonic vorticity as it ascends a mountain is a consequence of the conservation of Ertel's Potential Vorticity..."

A phenomenon sometimes observed in IR imagery as the feature crosses the mountains (warming tops).
Member Since: January 5, 2013 Posts: 0 Comments: 3
2. 24hourprof
1:13 PM GMT on February 10, 2013
Quoting JNCali:
From the NOAA Glossary:
Fujiwhara Effect: A binary interaction where tropical cyclones within a certain distance (300-750 nm depending on the sizes of the cyclones) of each other begin to rotate about a common midpoint.

Read the wikipedia entry fascinating! But.. has anyone figured out what the cause of the attraction is yet?

according to the wiki entry In 1984 a study (DeMaria, Mark and Johnny C. L. Chan (August 1984). "Comments on "A Numerical Study of the Interactions between Two Cyclones". Monthly Weather Review 112: 1643) noted that: "It has not been agreed upon whether this (the attraction) is due to the divergent portion of the wind or vorticity advection"

I find it hard to believe that with Fujiwhara's observations being all the way back in 1921, that we still don't know this.. I guess it's not a priority with grants..

Thanks for the excellent(again) article!


You're a gentleman and a scholar! You're very welcome.
Member Since: October 24, 2012 Posts: 88 Comments: 793
1. JNCali
9:51 PM GMT on February 09, 2013
From the NOAA Glossary:
Fujiwhara Effect: A binary interaction where tropical cyclones within a certain distance (300-750 nm depending on the sizes of the cyclones) of each other begin to rotate about a common midpoint.

Read the wikipedia entry fascinating! But.. has anyone figured out what the cause of the attraction is yet?

according to the wiki entry In 1984 a study (DeMaria, Mark and Johnny C. L. Chan (August 1984). "Comments on "A Numerical Study of the Interactions between Two Cyclones". Monthly Weather Review 112: 1643) noted that: "It has not been agreed upon whether this (the attraction) is due to the divergent portion of the wind or vorticity advection"

I find it hard to believe that with Fujiwhara's observations being all the way back in 1921, that we still don't know this.. I guess it's not a priority with grants..

Thanks for the excellent(again) article!
Member Since: September 9, 2010 Posts: 5 Comments: 1032

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About 24hourprof

Retired senior lecturer in the Department of Meteorology at Penn State, where he was lead faculty for PSU's online certificate in forecasting.