Linear Hodos and Storm-Relative Helicity

[Bob Hartig]

Life used to be a lot easier for me. A nice, sexily curved hodograph and decent CAPE meant tornadoes. Give me southeasterly winds at the surface veering with height and I'm out looking for swirlies. On the other hand, winds generally aligned from bottom to top mean a straight-line wind event. Simple, right?

Maybe from a ground-relative perspective. But thinking from a storm-relative perspective can mess with my head. As the proud owner of some pricey and ultra-cool RAOB software, I can click a "storm-relative" button and suddenly get an entirely different wind profile. Suddenly surface winds that were coming from the southwest and were boringly aligned with mid- and upper-level winds are coming out of the southeast and even the east. That helps to explain how a linear hodograph can yield tornadic 1km and 3km SRH values (and, conversely, why what at first glance appears to be a decent wind profile can sometimes surprise me with wimpy SRHs). But practically speaking, what am I supposed to make of that? All my instincts say that no way is a linear setup going to produce tornadoes. But the helicities say otherwise, and from the storm's perspective, the setup is NOT linear.

Moreover, linear hodos tend to produce storm splits, engendering right-movers that can boost mediocre helicity across the tornadic threshhold, right?

So, for you met-wizards in the crowd, my question is, Do decent SRHs trump a linear hodograph/linear ground-relative winds? I get that there are two kinds of straight hodographs: one that shows indisputably undirectional winds, and the other that actually indicates directional shear with height. I'm talking about the second kind. If the answer is what I think it should be, then it goes against the grain of my intuition. But then, I'm a storm chaser, not a storm.

 

[STexan]

That level of consideration is to high for my pay grade and experience ... i just follow the biggest line of chasers to find tornadoes ... works 21% of the time

 

[Patrick Marsh]

Storms don't care how the helicity is generated, as long as it is there. Storm-relative helicity generated from a straight-line hodograph is treated the same by the atmosphere as storm-relative helicity generated from a curved hodograph. Another way to think of it

250 m2/s2 of SRH from a straight-line hodograph == 250 m2/s2 of SRH from a curved hodograph.

 

[Jeff Snyder]

Life used to be a lot easier for me. A nice, sexily curved hodograph and decent CAPE meant tornadoes. Give me southeasterly winds at the surface veering with height and I'm out looking for swirlies. On the other hand, winds generally aligned from bottom to top mean a straight-line wind event. Simple, right?

It's important to remember that a veering wind profile (e.g. southeasterly surface winds, southerly 850 mb winds, southwesterly 500 mb winds) does not mean that the hodograph isn't straight. In other words, you can easily have a straight-line hodograph in an environment of a veering vertical wind profile. The hodograph will always be straight, however, if the wind profile is unidirectional. With a straight-line hodograph, the vertical shear vector is also straight at all levels. The linear term of the perturbation pressure equation subsequently results in perturbation pressure maxima and minima centers being vertical aligned (in other words, the perturbation high at low levels is beneath the perturbation high at upper levels in the upshear side of the updraft). When a hodograph curves in a typical clockwise pattern, the pressure perturbation extrema rotate with height. The result of this is a perturbation high on the right flank at low levels and a perturbation low on the same flank at mid- or upper-levels. This creates an upward-directed vertical perturbation pressure gradient force, enhancing the updraft. On the left flank, meanwhile, the opposite occurs, and the downward-direct vertical perturbation pressure gradient force weakens the updraft. The net result is the commonly-observed rightward deviant motion ("turning right").

Why did I spend a paragraph to explain this? Well, with a straight-line hodograph, storm motion for a simple non-supercell tends to be along the hodograph. The storm-relative wind at all levels is then also along the hodograph. Since the local vorticity vector is normal/perpendicular to the hodograph, this means that the local vorticity vector is also normal/perpendicular to the storm relative wind. In this case, there is no streamwise vorticity (all vorticity is crosswise), and the storm-relative helicity is 0. SRH may increase if a storm splits, and other forces act to force a storm righward (and leftward) of the hodograph. When this happen, the storm-relative wind has a component along the vorticity vector -- there is some streamwise vorticity, and there is now some SRH.

Personally, although SRH is SRH, I'd rather chase a storm in an environment of a curved hodograph over one with a straight hodograph. If a hodograph has significant clockwise curvature, right-movers tend to be preferred over left-movers. This may mean fewer supercells and fewer storm interactions as the left-movers weaken/dissipate. If the hodograph is straight, left-movers acquire negative SRH and right-movers acquire positive SRH, and there are more opportunities for storm interactions and collisions (all other things being equal).

It's also important to remember that SRH, by definition, depends upon the storm motion. For the same hodograph, two storms moving in two different directions or with two different speeds may have significantly different SRH. The forces contributing to a storm's motion may be quite complicated, and a storm motion that deviates significantly from "expected" storm motion (e.g. if there's an OFB boundary around and storm motion isn't quickly across the boundary) may yield significant enhanced SRH.

 

[Bob Hartig]

Thanks for your answers, Pat and Jeff. In a nutshell, what I get is that a clockwise-curving hodo favors right-movers over left-movers; hence, less cell competition than with a straight hodo in which both splits fare equally well and storm collisions are normative. However, either hodo is capable of producing ambient helicity, which can be further enhanced (or, presumably, reduced) by an individual storm's motion. So, for example, if a RAP forecast sounding indicates that I can expect 1km SRH of 200 m2/s2 at a given location, then I can conclude, assuming that other ingredients are in place, that the potential for tornadoes will exist regardless of whether the hodo is curved or linear. This being said, though, there are reasons--some of which are obvious at a glance--why curvy is better. (That's not the main reason why guys love curves, but it helps. )

In case anyone wonders why all of this matters from a practical standpoint, it depends on where you live. If Tornado Alley is your home, then you might not even bother with a straight hodo because you get your share of the beautifully swept-out kind in conjunction with loaded-gun soundings. But if you live elsewhere, you become more likely to look for other less-apparent options that just might produce within reach of a day trip. When you're used to dining on rib-eye, you may scoff at hamburger, but a hungry man will be glad to get a hot dog.

 

[Rob H]

It's important to remember that a veering wind profile (e.g. southeasterly surface winds, southerly 850 mb winds, southwesterly 500 mb winds) does not mean that the hodograph isn't straight. In other words, you can easily have a straight-line hodograph in an environment of a veering vertical wind profile.

Very informative post, but you lost me on this part. The only way I can imagine a veering wind profile producing a "straight line" would be is if speed magnitude is extremely low between two points. Is this what you meant, or is there some other subtlety I'm failing to grasp here?

edit:
1) Surface = 5kt southeasterly
2) 850 = 5kt southerly
3) 500 = 60kt southwesterly

Even though you have directional shear, in the absence of speed shear you end up with a fairly linear looking hodograph. Is this the scenario you were alluding to?

double edit: Eh... I was really overthinking things. Thanks for the explanation, Jeff.

 

[Jeff Snyder]

Very informative post, but you lost me on this part. The only way I can imagine a veering wind profile producing a "straight line" would be is if speed magnitude is extremely low between two points. Is this what you meant, or is there some other subtlety I'm failing to grasp here?

edit:
1) Surface = 5kt southeasterly
2) 850 = 5kt southerly
3) 500 = 60kt southwesterly

Even though you have directional shear, in the absence of speed shear you end up with a fairly linear looking hodograph. Is this the scenario you were alluding to?

Hi Rob,

A straight hodograph (e.g. a wind shear or vorticity vector that does not rotate with height) can result from a vertical wind profile that looks, qualitatively, very "classic". For example, below is a little graphic I made for a different post/topic, but it'll work okay here:

Let's just look at the red hodograph plot. This hodograph shows 30 kt southerly surface winds, 40 kt southwesterly 3 km winds, and 60 kt west-southwesterly 6 km winds. So, the winds veer with height, and they also increase in speed, things that we'd typically say would be very good for supercells. Heck, we could even move that surface wind over to the left by using, for example, a 40 kt southeasterly surface wind. The result would be the same, however -- a straight hodograph with no SRH for storms with initial motion along the hodograph. Now, after 45-60 minutes, a storm may split, and the right-mover may end up with a storm motion near the red star (e.g. nearly NE at ~35 kts). Now, there IS some SRH > 0 m2/s2 for that storm (the 0-3 km SRH is proportional (twice) the area shaded in red), and that storm may acquire a more robust mesocyclone. Likewise, the left split may end up being NNE at 45 kts, it will ingest parcels with negative SRH, and that storm may acquire a mesoanticyclone.

This specific figure also shows that SRH may increase if surface winds are actually weaker. The blue hodograph plot shows the same 3 km and 6 km winds, but the surface winds are only 1/2 of what they are in the red plot (e.g., 10 kts now). Despite weaker surface winds, the hodograph now has greater curvature, and the area swept out by the hodograph (i.e. the blue shading) is even greater than the red shading associated with the stronger surface winds. Indeed, for the storm motion marked by the blue star, the blue hodograph actually has more SRH than the red one (given storm motion at the red star). This digresses from the main point of the thread, however.

 

[Stan Rose]

why is your red line curved (sfc to storm)?

 

[Jeff Duda]

Maybe from a ground-relative perspective. But thinking from a storm-relative perspective can mess with my head. As the proud owner of some pricey and ultra-cool RAOB software, I can click a "storm-relative" button and suddenly get an entirely different wind profile. Suddenly surface winds that were coming from the southwest and were boringly aligned with mid- and upper-level winds are coming out of the southeast and even the east.

If it helps you understand what the storm relative wind basically means, picture the storm having zero motion. The storm relative wind profile is what the wind profile would be for that storm. Imagine riding your bike northward in a wind field that is from the due west. You will experience a bit of a headwind since there will be a northwesterly you-relative wind. That's like saying if you stopped completely, there would be a northwest wind.

 

[Andy Wehrle]

Thanks, Jeff...aside from answering Bob's question, I think I just finally grasped how to read a hodograph after eight years as a member of ST and my eyes glazing over halfway through most posted "explanations."

 

[Bob Hartig]

If it helps you understand what the storm relative wind basically means, picture the storm having zero motion. The storm relative wind profile is what the wind profile would be for that storm. Imagine riding your bike northward in a wind field that is from the due west. You will experience a bit of a headwind since there will be a northwesterly you-relative wind. That's like saying if you stopped completely, there would be a northwest wind.

I get the storm-relative concept, Jeff, and I get how a straight hodo can produce SRH provided it's not purely unidirectional. The thing that I've had a hard time wrapping my mind around has been seeing straight hodos producing tornadic SRHs and curved hodos producing sub-tornadic helicity, particularly in the low levels. Not that I don't understand how it works; there's just something in me that sees it as counterintuitive. Flipping the setting from ground-relative to storm-relative on my RAOB hodograph module and watching the vertical wind profile switch from southwesterly 850 mb winds to southeasterly or easterly has been hard for me to digest, even though I get the storm-relative concept. It's not so much the change in direction of the wind at various levels as much as its implications in terms of what is potentially tornadic and what isn't from a surface-relative perspective.

What also plays with my mind is thinking about calm ambient surface winds. Let's say that a surface-based storm is heading east at 35 knots. 850 mb winds are blowing from the south at 30 kts, and the the winds veer with height and speed shear increases. But at the surface, winds are calm. From my perspective, there's no inflow; yet from the storm's perspective, it's getting inflow from the east at 35 knots. What kind of low-level helicity does that kind of scenario generate?

I don't know how realistic this scenario is, since to my thinking, in real life a surface-based storm will generate its own surface-relative inflow. But from a forecasting point of view, it seems to me that a storm could fire up in conditions with wimpy surface winds, and yet from a storm-relative perspective, surface winds could be strong and low-level helicity substantial.

This speculation is actually a question. Have I articulated my reasoning clearly, and does it make sense? Because I'd love to get some input on it.

UPDATE: Now that I think of it, I think it's time I dug a little deeper into my RAOB software. I should be able to create some models that will answer my own questions. I think I already know the answer, but I wonder how practical it is in real life.

 

[Jeff Snyder]

why is your red line curved (sfc to storm)?

Hi Stan -- If you are referring to the bottom edge of the textured red surface (connecting the red star representing storm motion to the SFC wind vector), then it really should be straight. I don't remember why it was curved to begin with, but I know it was an issue with the graphics program I was using at the time. So, it really should be straight between the storm motion vector (red star) and the surface wind vector ("SFC").

 

[Stan Rose]

Yes, thanks, just making sure i wasn't seeing imaginary curves...