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The Beta Effect

By: Lee Grenci 2:51 PM GMT on July 27, 2013

Yesterday I talked about the steering of tropical cyclones by the mean wind in a steering layer determined by the system's minimum central pressure (revisit the relevant graphic). For strong hurricanes, the steering layer spans a large portion of the troposphere. For example, the steering layer for a hurricane with minimum central pressure between 940 mb and 949 mb spans from 850 mb (roughly 5000 feet) to 250 mb (roughly 35000 feet). The mean wind in this layer (the "steering wind") accounts for roughly 80% to 90% of the hurricane's motion.

As I briefly mentioned yesterday, about 10% to 20% of the storm's motion arises from the Beta effect. You might think that forecasting the track of tropical cyclones would thus be "child's play." But modeling the Beta effect isn't easy. The Beta effect gets even more complicated when tropical cyclones are moving briskly and undergoing rapid changes in intensity. Lesson learned: Predicting the tracks of tropical cyclones, though forecasters continue to improve, is not an exact science. Sometimes, it's far from it.

Hurricanes moving due westward tend to drift northwestward in time. Why? Stay tuned.

What is the Beta effect? For starters, let's agree to restrict our discussion to the Atlantic Ocean in the Northern Hemisphere. In a nutshell, the Beta effect arises from the variation of the Coriolis parameter with latitude. This variation of the Coriolis parameter is the primary reason why hurricanes forming at low latitudes tend to drift northwestward (see schematic above) from their westward track (for simplicity, I'm assuming here that the mean wind in the deep steering layer blows from east to west across the Atlantic Ocean).

Before we delve into the nuts and bolts of the Beta effect, I need to make sure that all my readers are on the same page with regard to some of the basic concepts about vorticity that are relevant to this discussion. First, vorticity is simply the measure of the spin around an axis. For the most part, synoptic meteorologists are interested in the spin around the local vertical, which is simply a line drawn from a point on the earth's surface to the center of the earth (here's an idealized schematic of a few local verticals, courtesy of A World of Weather: Fundamentals of Meteorology). This "vertical vorticity" (spin around a local vertical) is not fast by most standards. For sake of comparison, the vertical vorticity of a tornado with a diameter of 100 meters is roughly 10,000 to 100,000 times greater than the vertical vorticity that's relevant in synoptic meteorology. Nonetheless, such seemingly slow spin plays a pivotal role in weather.

An idealized schematic showing a 500-mb ridge (left) and a 500-mb trough (right). 500-mb height lines are the thin, dark contours, and the capsule-shaped features represent air parcels. Note how an air parcel moving through the ridge gains anticyclonic spin (negative relative vorticity) and an air parcel moving through the trough gains cyclonic spin (positive relative vorticity). Courtesy of A World of Weather: Fundamentals of Meteorology.

There are two sources of vorticity that weather forecasters weigh. The first is relative vorticity, which is generated by the curvature of isobars or height contours on a constant pressure surface. For example, an air parcel shaped like a Tylenol capsule acquires relative vorticity as it simply flows through 500-mb troughs and ridges (check out this idealized schematic above, courtesy of A World of Weather: Fundamentals of Meteorology). To get your bearings, the contours that form the ridge and trough are 500-mb height lines. At any rate, air parcels acquire cyclonic vorticity (by convention, a positive number) as they round the bend in the trough, and anticyclonic vorticity (negative relative vorticity) as they negotiate the curve in the ridge.

Horizontal wind shear produces anticyclonic relative vorticity in a 500-mb ridge (left) and cyclonic relative vorticity near the base of a 500-mb trough (right). Courtesy of A World of Weather: Fundamentals of Meteorology.

Horizontal wind shear, which is the change in wind speed and/or wind direction over a horizontal distance, is also a source of relative vorticity. In the idealized schematic above, air parcels appear as little fans. The green vectors represent the wind (the longer green vectors correspond to faster winds). And so, you can get the sense that horizontal wind shear in troughs and ridges cause the fans to rotate, creating cyclonic vorticity in the trough and anticyclonic vorticity in the ridge.

The second type of vertical velocity is planetary vorticity (alternatively, earth vorticity), which is spin around a local vertical induced by the rotation of the earth (check out the idealized schematic below, courtesy of A World of Weather: Fundamentals of Meteorology). Note that earth vorticity increases with increasing latitude. In other words, earth vorticity at the equator is zero, and earth vorticity at the North Pole is a maximum. The relatively small values of earth vorticity in the Tropics accounts for the reason why tropical cyclones must form a minimum distance of 500 kilometers (about 300 miles) from the equator (in order to develop a cyclonic circulation). There are exceptions to this rule, of course...Typhoon Vamei in 2001, for example.

Earth vorticity increases from zero at the equator to a maximum at the North Pole. Courtesy of A World of Weather: Fundamentals of Meteorology.

Back to the basics of vertical vorticity (I'll sometimes drop the "vertical" and simply write, "vorticity." At any rate, absolute vorticity is simply the sum of relative vorticity and earth vorticity. Okay, we're ready to delve into the Beta effect and to understand why hurricanes moving due west tend to drift northwestward with time (to see what I mean, check out the first slide of the flash animation below). As you read through the following paragraph, please revisit this flash animation, which you can advance by clicking on the forward button in the upper-right corner.

The Beta effect helps to control the movement of tropical cyclones (the mean wind in the steering layer controls 80% to 90% of the storm's movement). Explore the nifty flash animation above to see why (click on the forward button in the upper-right corner). In general, the Beta effect causes westward-moving storms to move to the right (N.H.) of the steering wind (the mean wind in the steering layer). In the absence of a steering wind, an apparently motionless hurricane will drift toward the northwest in response to the Beta effect (I'm assuming we're in the Northern Hemisphere). Courtesy of Penn State's online Certificate Program.

Okay, air parcels moving southward on the western flank of the tropical cyclone's center lose earth vorticity. On the eastern side of the storm, northward-moving air parcels gain earth vorticity (the Coriolis parameter, which depends on latitude, increases with increasing latitude). As it turns out, absolute vorticity associated with hurricanes tends to be conserved above the boundary layer. Thus, the relative vorticity of southward-bound air parcels must increase on the hurricane's western flank to offset their loss of earth vorticity. Similarly, the relative vorticity of northward-bound parcels must decrease on the eastern flank of the storm to compensate for their gain in earth vorticity. As a result, two centers of positive and negative relative vorticity form to the west and east of the hurricane's center (respectively). In response, two secondary circulations develop (cyclonic around the center of positive relative vorticity, and anticyclonic around the center of negative relative vorticity). Please note that you can't observe these circulations on satellite loops because their orders of magnitude are so much smaller than the hurricane's circulation.

Nonetheless, these circulations associated with the Beta effect are sufficiently large to cause a westward-moving hurricane to drift northwestward. Moreover, the Beta effect is the reason why tropical cyclones flirting with crossing the equator swerve to the northeast before it's too late.

To my knowledge, there haven't been any tropical cyclones that have crossed the equator, but a few have come close, particularly in the northern Indian Ocean. But is it possible, Grenci? I would answer "yes." That's because a tropical cyclone's relatively large cyclonic relative vorticity would not initially be affected by the weak change in the Coriolis force as it crossed into the opposite hemisphere (eventually, of course, the circulation of a hemisphere-swapping hurricane would become anticyclonic and dissipate). And, as I just discussed, the Beta effect works against any crossover.

A clockwise-rotating disturbance over the North Atlantic on June 26-27, 2008. Apparently, the disturbance crossed the equator from the Southern Hemisphere. Courtesy of CIMSS.

Still, I can't deny that there are equator-crossing disturbances. To see what I mean, check out case of a anticyclonically rotating disturbance that apparently originated in the Southern Hemisphere and then crossed the equator into the Northern Hemisphere on June 27, 2008 (see satellite animation above). In my opinion, some really cool stuff!

Here endeth the lesson.



The views of the author are his/her own and do not necessarily represent the position of The Weather Company or its parent, IBM.

Reader Comments

Quoting Tazmanian:

its up too the NHC if they want too re name it now the NWS in PR so it not settle the NHC will make that call later today if the storm keeps the name or not

So you think the NHC will go against NWS and against what they have done in the past?

TS Emily of 2011 springs to mind.... Was named... degenerated into a TW over Hispaniola then became a TD near the Bahamas then back to TS.
TWC has always covered storm in the East Pacific. Not nearly with the hype or involvement as storms in the Western Atlantic.
Storms possibly affecting Hawaii usually get a quick mentioning but usually not much more.
I really think the NHC has egg on their faces , never should have declassified , in the first place , Dorian was undergoing a house cleaning , he was reastablishing himself , now look at him , healthy as ever , It will be very scary when he really blows up , then for somebody BAM!
IMO..A note on naming.. If if does regenerate it will indeed be Dorian again, the 91L marker is just a place holder of sorts (INVEST) to separate it from any other invest that may pop up. It would be renamed Dorian because the origin of any new development could easily be retraced back to TS Dorian.(same vorticity and partial LLC)

2506. Grothar
Just a few models. You can pick the one that panics you the most

Quoting 2504. EyEtoEyE:
I really think the NHC has egg on their faces , never should have declassified , in the first place , Dorian was undergoing a house cleaning , he was reastablishing himself , now look at him , healthy as ever , It will be very scary when he really blows up , then for somebody BAM!

I disagree, Dorian was downgraded to a tropical wave for a short time...
2508. Grothar
Quoting 2497. mikatnight:

I've been trying to catch up, very intrigued by your forecast of movement towards the N or NW from center of Cuba north, but still no model support yet, right?

Just a hunch ;-)
Quoting 2458. Grothar:

Actually, it is odd. I hope it is just a fluke.

Sky-Pony (mod) mentioned it as well. It is rare for models to agree on anything. But where they do agree is precisely where we should pay particularly close attention.

So in this case they all agree it will get stronger, in an approximately linear manner. Which means no RI.

Of course they all could change after they get some good Recon data later today.
new blog
2511. ACEhigh
Well well, looks like dorian took this whole dissipation thing to heart. He's baack, and with an axe to grind with the folks at the NHC. Looks like the ULL is ventilating him and if he can keep the convection going it shouldn't be that big of a problem imo. You can see he is already firing new convection, and I don't see any outflow boundaries on the rgb, there are obs of west winds in the northern islands too, think once de plane gets out there this sucker will go straight from 20% to TS. Miami nws calling for the Bermuda high to build in behind the current trough, then have its western flank eroded by the next trough midweek. If it keeps getting its act together, a hit or a close shave for somewhere on the east coast of florida looks increasingly likely. looks like the bahamas are pretty much guaranteed at least some sort of fun weather.
2512. VR46L
Quoting 2438. yonzabam:
91L is 1,300 miles from Florida. Intensity models have it as a cat 1 in 120 hours. According to the NHC, it's traveling at between 15 and 20 mph. Let's call it 17.5 mph. At that speed, it reaches Florida in 72 hours.

Either 91L's forward speed is expected to slow down considerably, or someone's pushing the wrong buttons.

The GFS had shown a stall last week of about 2 days around the Bahamas for the then Dorian
2513. pcola57
Flossie not stacked as well as yesterday..

850 mb..


In fact you can make out in this image the East and West vorticity parcels that Lee Grenci was pointing out in the above blog post..


2514. beell
Couple of buoy links. Used 20N, 60W as a rough approximation of 91L's location. The buoy NNE of Puerto Rico is close to the expected short term path of 91L. Probably too far away right now to be useful.

Both buoys reporting MSLP around 1018 mb.

Approx 285 nm WNW of 20N, 60W
Station 41043/ 170 nm NNE San Juan, Puerto Rico

Approx 120 nm NE of 20N, 60W
Station 41044/ 330 nm NE St. Martin
2515. MPI88
Quoting 2514. beell:

Both buoys reporting MSLP around 1018 mb.

Approx 285 nm WNW of 20N, 60W

That's far field pressure, those buoys are too far out right now. The HH aircraft drop-sondes are your best source at this moment.

We'll see how this develops, not much can be said now.
2516. GatorWX
This little fella is starting to impress me to be frank. I'm starting to not be sure I want to look at the satellites in the morning. For one, and this could change depending on where the ull tracks, it currently has a very nice structure developing. I think two center may have been competing, but looks to have consolidated to the ne center of convection. It certainly looks nice without a lot of clouds. Almost perfect outflow. I'm surprised it kept the show going today. With similar conditions tonight, you never know. If it doesn't fire new storms near the center soon, it could start to feel more of that shear. Most of the day it's seemed pretty nil. Bahamas and East Coast should certainly think about things.This has potential, key word, of being quite an interesting setup. I mentioned earlier the dry air south of it. It seems to have blocked that out after its consolidation process. Banding seems to be commencing. This is a tough little thing to track I tell ya. Steering was supposed to be so easy with this one.
Out of all due respect...I'm not a meteorologist but have been heavily into weather since I was 3. I have a B.S. in Geography with a remote sensing background. My swan song at 20 was figuring out how chemtrails work and being the only person to successfully forecast around them...and the meteorological community had the entire concept of chemtrails wrong...
I'm bringing evidence of a new weather modification system by our Govt that consists of 7 polar orbiting satellites that are using high frequency Microwaves to attenuate the atmosphere in order to gain a 3D image of the entire air column in terms of water vapor. The transmissions are beamed back to a NORAD office in which a 3D model is generated within 30-45 seconds. A decision is then made by the US Govt where to transmit microwaves at harmonic frequencies to target a specific layer of the atmosphere in which they can steer storms on a dime. I've documented well over 20 different events since Jan 2013 where this has happened. Shapes used by the Govt include letters, numbers, face, animals. Typically a number with the harmonic frequency used will show up to tell the meteorologist involved in this top secret project which GHz band they used. Last week over Texas July 15th several 12's appeared burned through the clouds...curly cue #2's...well defined and generated from what I believe are the 7 polar orbiting satellites involved. There was a windmill to the east side of Dorian on July 26th @ 2015UTC on the WV picture a windmill appears. Coordinates range from 16N41W northeast to 19N 38W for the blade part of the windmill then the base of the windmill extends from 17N 39W southeastward to 14N 36W. Just before the GFS opened up a sudden southward track a Capital I appeared to the northeast of Dorian. The sudden heating of the atmosphere created a mesoscale high pressure that the GFS clearly picked up on...just a few observations!