A Look At Hodographs, Helicity, and Supercells

by Jon Davies

Storm Track, Jan/Feb 1994

Just what is a hodograph? And what does it have to do with thunderstorm rotation or potential for tornadoes? Tim asked me to write this article to give interested storm enthusiasts a better idea of how wind profiles impact supercell thunderstorm formation and forecasting tornadoes. He also asked me to try to explain things in general terms, without being too picky or too scientific. So, here goes...

One way to visualize a hodograph is to imagine yourself several miles up in the atmosphere looking down from a stationary position directly above the location from which a weather balloon is released. If a solid line were traced out by the balloon as it ascended, this "curvy/wavy line" you would see from your position looking directly down would essentially be the "hodograph", a pattern traced out by the balloon as it encountered different winds at different levels as it rose toward you. A hodograph, then, is one way of representing graphically the vertical pattern or profile of winds measured from a specific location during a certain time.

One can plot up a rough hodograph by using the wind speed and direction information from several points or levels in the vertical. For example, if one has the observed wind data for several levels from a weather balloon sounding (such as, surface: 160 deg at 15 kts, 925mb: 190 deg at 35 kts, 850mb: 210 deg at 40 kts, 700mb: 220 deg at 35 kts, and 500mb: 240 deg at 45 kts), each level can be plotted as a vector "arrow" drawn from the center (origin) of the hadograph diagram showing a magnitude and direction of force (wind speed and direction) applied by the wind at that level. The tips of the vectors can then be connected by a line to form a rough hodograph:

For a number of years, meteorologists have recognized that supercell thunderstorms (storms that have a persistent rotating updraft) are associated with environments that contain a certain general type of wind profile. This wind profile is represented by a hodograph that loops or curves clockwise, such as the hodograph at right. The reason why this type of wind profile can induce rotation on a thunderstorm updraft is not simple, and here we will only try to touch on visualizing the process in a general way.

In the hodograph example at right, the wind at the ground is from a southeasterly direction, but as we ascend cend through 850mb (roughly 5000 ft above sea level), the winds become stronger and come from an increasingly westerly direction. The wind at 700mb (roughly 10,000 ft above sea level) is even more westerly, although speed drops off a little. With this type of wind profile, if we had some way of suspending or "floating" a giant football several thousand feet in diameter above the ground, we would see the football begin to spin and move northward, similar in some ways to a spiraling football thrown in a northerly direction by a quarterback. In other words, the forces applied to the football by the wind profile would cause it to spin, and in this way we can therefore say that the wind profile contains some amount of "spin".

What might happen if a thunderstorm were to develop within this wind profile containing "spin"? Let's visualize one of our spinning footballs being pulled into an organized thunderstorm updraft. The football, initially spinning along a horizontal axis, would probably be turned on its side and end up spinning along a vertical axis as it was accelerated upward into the storm updraft. In other words, the "spin" would be "tilted" into the updraft, causing the updraft itself to begin rotating.

While this is far from a perfect analogy (air is a compressible "invisible" fluid, not solid like a football), it does allow us to put together a mental picture of how a thunderstorm updraft might begin to rotate as it "ingests" and tilts the "spin" present in a wind profile represented by a clockwise looping hodograph.

Apart from just looking at hodographs to see if they loop nicely, how might one go about assessing from hodograph to hodograph the amount of apparent potential for rotation in a given wind profile? Dr. Robert Davies-Jones at the National Severe Storms Laboratory has developed a computation that is useful for assessing the amount of "spin" available for tilting to initiate rotation in an updraft. This computation is called helicity. Without getting into a technical physical discussion, helicity amounts to an area "underneath" or "enclosed to the right" of a hodograph shape, which we can measure for comparing hodographs to see if one wind profile has more helicity than another.

One fly in the ointment here is that the amount of helicity depends on a storm's motion. The storm's movement "creates" additional wind from the storm's point of view, the same way driving your car with the windows down makes it "windy" inside the car, even on a calm day. Obviously, we don't know a storm's movement in advance of when it forms. However, because helicity is a fairly conservative quantity (meaning it doesn't vary that much with relatively small changes in the wind profile or storm motion), we can make an educated guess regarding storm motion and calculate a rough "potential" helicity for a wind profile based on this assumed storm motion.

There are a number of ways one can come at calculating an estimated storm motion for a given wind profile. One simple way for a storm enthusiast to make a very rough but quick and workable guess is simply to average the values of wind direction and wind speed for the wind profile points you have available. With the hodograph/wind profile on the previous page, we have data through mid- levels(500mb or roughly 18000 ft above sea level), and can average direction (160+190+210+220+240 divided by 5 = 204 deg) and speed (15+35+40+35+45 divided by 5 = 33 kts), coming up with a rough guess of 205 deg at 33 kts. (It would be more reliable to have wind data at least up through 25,000 to 30,000 ft, or 400 to 300mb.) Because supercells tend to move to the right of this mean wind due to strong and continuous updraft development on the storm's right (south) flank, it is good to add 20 or 30 degrees to the right of this averaged wind direction, and slow the speed of movement down some, say, to 75% of our averaged wind speed. Adding 30 degrees to our mean wind, and slowing it down by 25% gives us 235 deg at 25 kts for our guess at storm motion for supercells that might develop in our example wind environment.

Now, to allow us to compute a helicity value, we plot our storm motion guess as a vector arrow, starting at the center/origin of the hodograph diagram, as shown at the left. To enclose an area that represents helicity, draw two straight lines from the tip of this vector: one to the beginning of the hodograph (the point on the hodograph that represents the surface wind), and another to the point on the hodograph that represents 700mb or roughly 10,000 ft above sea level. This "pie-shaped" area represents an estimation of the helicity present in the wind profile covering the in0ow layer of a potential storm (roughly the first two miles or three kilometers above ground). Remember to consider that locations in the high plains (such as Amarillo and Goodland) are between 2500 and 5000 ft above sea level, in which case it would be best to look at helicity that extends somewhat above 700mb in order to be reasonably consistent in comparing the same general depth above the ground when looking at different hodographs.

To come up with a helicity value, all we need to do now is compute the area of our pie-shaped enclosure. Note that the hodograph diagram background we've used is made up of uneven "boxes" that result from directional lines (emanating from the diagram origin) that intersect the circles representing wind speed in knots. Although these boxes are not consistent in size, I've found (on average) that if one takes each box to represent roughly 30 m^2/s^2, and counts up the approximate number of boxes that make up the helicity "area", a storm enthusiast can make a very rough "ball park" estimate of the helicity in the wind profile for an assumed storm motion. In the example on the previous page, I count the equivalent of roughly 9 "boxes" in the pie-shaped area; 9 x 30 computes to a helicity value somewhere between 250 and 300 m^2/s^2. Of course, the helicity area can be computed much more accurately by storm enthusiasts with some background in trigonometry and computers.

When we look at helicity, we're looking at a key factor in the potential for supercells. The possibility of tornadoes is only implied because of their association with supercells. As experienced storm chasers know, probably less than 50% of all supercells produce tornadoes. Supercell-related tornado development is not really understood yet, and depends on additional factors such as downdraft orientation and mid-level wind strength, as well as localized factors that are difficult if not impossible to measure with science's current capabilities. However, with that said, when helicity is considered in combination with instability, stronger combinations of helicity and instability imply stronger potential for supercells, which in turn often implies more potential for tornadoes.

Concerning helicity guidelines, work by Dr. Davies-Jones and Don Burgess indicates that tornado-producing supercells tend to be associated with helicity values greater than roughly 150. However, as work by Bob Johns and John Hart at the National Severe Storms Forecast Center shows, the degree of instability is also important to consider. If instability is quite strong, isolated supercells that form when helicity values are only around 150 can produce strong or violent tornadoes. At the opposite end of the spectrum, very large helicity values (400 to 500 and greater) don't neccessarily mean that tornadoes will occur: among other considerations, remember that at least some instability is needed to support thunderstorms to begin with, or else helicity values are essentially meaningless.

A problem for storm enthusiasts (and forecasters) when using helicity is that wind profiles change during the day; ma ming soundings are usually not very representative of afternoon conditions. Most of us don't have real-time access to data from the new network of profilers in the central U. S. that measures wind profiles remotely and continuously by using Doppler principles. However, one source of information that I've found useful is the so-called "FD winds aloft" forecast data based on the National Weather Service's NGM forecast model. For Accu-Data users, this information is available using the following commands:

"MED FDUS11 KWBC 12z" and "MED FDUS12 KWBC 12z" accesses 6 hr forecast winds from a.m. (12z) data

"MED FDUS13 KWBC 12z" and "MED FDUS14 KWBC 12z" accesses 12hr forecast winds from a.m. (12z) data

"MED FDUS15 KWBC 12z" and "MED FDUS16 KWBC 12z" accesses 24hr forecast winds from a.m. (12z) data

Using "00z" instead of "12z" accesses data from the p.m. (00z) model run. These winds are usually available by 10:30 a.m. or p.m. CDT (9:30 a.m. or p.m. CST).

One can plot up rough hodographs using this forecast information combined with an expected estimated surface wind (the FD forecast doesn't output surface winds). If the model data is forecasting or handling a weather system welf, this information often turns out to be quite workable for assessing upcoming wind profiles over an area. At the top of the next page is a forecast hodograph from May 9th last year which saw several strong tornadoes in north-central Texas. For contrast, a forecast hodograph the next day associated with non-tornadic severe weather from the same system over the Mississippi Valley is also shown:

Note that the hodograph and helicity for the 5/9/93 case is quite similar to our earlier example. You can use the above data to check yourself on hadograph plotting, estimating storm motion and helicity.

The blank hodograph diagram below is shown so you can make copies for your own experimentation this spring. Or, you can make your own with a ruler and protractor.

Although the above material is not easy to absorb, this discussion will hopefully help weather enthusiasts have a better sense of how wind profiles are a key factor contributing to supercell thunderstorm development. And maybe it will help on a chase day forecast or two. Have fun!!