Why do supercells move to the right?

[AtticaFanatica]

Most single- and multi-celled convective storms will move in the direction of the mean wind. Conversely, a ubiquitous observation of supercells is that they “move to the right.” In other words, in the Northern Hemisphere, the storm tends to move to the right of the density-weighted mean horizontal wind.

This post will attempt to answer a basic question: Why is it that supercells tend to move to the right?

However, in answering this question, one learns most of the important aspects of supercell dynamics.

The Short Answer

“Linear” and “non-linear” effects that lead to upward-directed perturbation pressure gradient forces on particular flanks of the storm updraft (the main area of rising air that drives the supercell).

The Long Answer

The explanation for why supercells move to the right is actually rather complicated for two reasons. 1) The math involved starts to get a bit complex and 2) there is still considerable and spirited debate in the research community as to what mechanism is most responsible for supercell propagation and maintenance. As a result, I will avoid complicated math in favor of simplified physical explanations and I will present both mechanisms as, ultimately, they are both important.

The two main mechanisms are both dynamic in nature (i.e., they involve the pressure field). Right off the bat, you might be thinking, “What about buoyancy?”; after all, buoyancy is extremely important since it is buoyancy that drives the initial updraft and leads to a storm. However, while buoyancy continues to be important as a supercell updraft progresses, upward motion due to buoyancy is usually collocated with the center of the main updraft. To get an updraft to propagate, to move in a certain direction, you need upward motion to occur on a particular side of the updraft, else the updraft simply moves with the mean wind.

In other words, the updraft is continually regenerating on a particular outer flank and simultaneously dissipating on the opposite flank. (This is known as continuous propagation, compared to discrete propagation, which arises from separate unique updrafts.) Wherever the updraft is regenerating is the direction it’s going to move in (ignoring for a moment simple advection by the mean wind). This is where the pressure gradient forces come into play (i.e., air flowing from high to low pressure), it turns out that upward motion tends to occur on the sides of updrafts such that the updraft’s motion bends to the right in the Northern Hemisphere. How does that happen?

For the sake of completeness, I will include the equation that these explanations rely on:

α₀∇²p' = −[(∂u'/∂x)² + (∂v'/∂y)² + (∂w'/∂z)²] − 2(∂u'/∂y ∂v'/∂x + ∂w'/∂x ∂u'/∂z + ∂w'/∂y ∂v'/∂z) − 2[∂w'/∂x∂U/∂z + ∂w'/∂y ∂V/∂z] + ∂B/∂z

And fortunately, we won’t go any deeper than that mathematically.

As I mentioned, there are two main dynamic effects that play a large part in this process of updraft propagation. Let’s look first at the nonlinear effects. The nonlinear effect essentially leads to relatively low pressure in areas of enhanced local rotation (vorticity). We know that all supercells have mesocyclones, which is just a fancy term for an updraft that is rotating cyclonically. The cyclonic rotation comes about by the tilting of horizontal vorticity (horizontal spin, which exists due to vertical wind shear) by the updraft into the vertical to create vertical rotation. It turns out that the strongest rotation in the updraft generally occurs at midlevels in the storm, say about 4 km above the surface, with somewhat weaker rotation closer to the surface. Because the nonlinear term dictates that the stronger the rotation, the lower the relative pressure, it ends up that the midlevels of the storm updraft have relative low pressure and the low levels of the storm updraft have somewhat higher pressure due to weaker rotation. This leads to an upward-directed pressure gradient force that helps, along with the buoyancy forcing, to sustain the upward motion in the updraft. Nonlinear effects tend to dominate in supercells that arise in environments with straight hodographs. This leads me to take a somewhat brief tangent to explain what is going on, but it is important in understanding the dynamics of supercells.

An important concept in severe convection is vertical wind shear, which I think most people have a solid grasp of. The most popular way to display what the environmental wind shear is at a particular location is to use a hodograph, which simply plots the east-west (u component) and north-south (v component) wind on a graph. The wind at each height is plotted and the points connected by a line. An example below:

One of the many convenient features of the hodograph is that determining the shear vector at a particular height is pretty simple. The shear vector is just the line running tangent to the hodograph at a particular height:

It turns out that the shear vector is rather important in supercell dynamics and connects back to the linear and nonlinear dynamic pressure effects. It has been shown that when you have wind shear such that there is a constant shear vector, the shear vector points in the same direction at every height, like this:

then you will likely have splitting supercells, a right mover with a cyclonically-rotating updraft that is located to the right of the shear vector and a left mover with an anticyclonically-rotating updraft that is located to the left of the shear vector in mirror image form. In addition, the right and left movers will move normal (at a 90° angle) to the shear vector in opposite directions:

It is the nonlinear term that plays a large part in causing the right movers to move/regenerate to the right of the shear vector (and the left movers to move/regenerate to the left of the shear vector) in cases with no curvature in the hodograph. [Precipitation plays a large role in this too, but I’d rather not get into that.] Updrafts that move to the right of the shear vector also tend to be updrafts that move to the right of the mean wind, thus it can be seen how the nonlinear term allows supercells to move to the right, particularly in cases of straight hodographs. It is also important to note that even as you add curvature to the hodograph, the nonlinear term still plays a large part in the movement of the updraft because as long as there is a rotating updraft, there will be nonlinear effects acting to cause upward motion on the flank of the updraft such that the updraft will move approximately normal to the environmental shear vector. The combination of upward motion due to the nonlinear effects and upward motion due to buoyancy sustain the updraft; the rising air will continue to tilt horizontal vorticity into vertical vorticity allowing the updraft to rotate cyclonically. The proponents of the nonlinear term advocate that it is the term most essential to understanding supercell dynamics and that the rotation in the supercell’s updraft is the dominant mechanism responsible for the storm’s propagation through the nonlinear term. In other words, updraft rotation leads to storm propagation. I should mention that there are many that would take issue with the above argument, particularly the part in bold. I’ll get back to that, but now on to linear effects.

While the concept of the nonlinear term is pretty simple: low pressure at the location of maximum rotation (it’s actually more complicated, but it’s really not necessary to go much deeper into it to get the basic understanding), the linear term requires a bit more work to get a physical explanation. Atmospheric modeling studies confirmed that splitting supercells come about in environments with straight hodographs. However, it has been observed in the Northern Hemisphere that there are far more right-moving supercells with cyclonically-rotating updrafts than there are left-moving supercells with anticyclonically-rotating updrafts. It turns out that as more and more clockwise curvature is added to hodographs, the right mover is strengthened and the left mover is weakened. Eventually as one models a hodograph with a large amount of clockwise curvature (like in the first hodograph example above), there is no left mover at all and only a strong right mover. Likewise, as one adds counter-clockwise curvature to the hodograph, the left mover is strengthened and the right mover is weakened. In other words, hodograph curvature favors one of the splitting supercells over the other. This modeling result is supported by observations, in that we see mostly right movers and most supercell hodographs have clockwise curvature. What is it about curvature in the hodograph that leads to strong right movers?

In short, it turns out that the linear effects are enhanced by adding curvature to the hodograph. As with the nonlinear effects, the linear effects create areas of locally high and low pressure, thus creating pressure gradient forces, some of them in the vertical. These vertical pressure gradient forces act to enhance updrafts in some areas and weaken the updraft in other areas, allowing the updraft to propagate in a particular direction. However, in this case, the location of the low and high pressures depends not on the rotation in the storm’s updraft, but in the location of the shear vectors, introduced above. It turns out that, due to linear effects, perturbation low pressures are found downshear of a storm’s updraft at a given height and high pressures are found upshear of a storm’s updraft at a given height. Downshear is similar to downstream, and refers to the location where the shear vector is pointing to. Upshear is similar to upstream, and refers to the location where the shear vector is coming from. The best way to understand this is just to do an example. Using the hodograph above repeated below:

You can see that there are three distinct wind shear vectors: at the surface, at midlevels and at upper-levels. We can use this hodograph, which is simplified but roughly represents what we see in supercell cases, to examine how the linear effect would cause a supercell to bend to the right. We have southerly shear at the surface, westerly shear at midlevels, and northerly shear at upper levels. Using our rule established above, at the surface, downshear is north and upshear is south since the shear vector is pointing from south to north. As a result, the linear term leads to relatively low pressure to the north and relatively high pressure to the south of the updraft. Similarly at midlevels, there is low pressure to the east and high pressure to the west and at upper levels, low pressure to the south and high pressure to the north. Looking at all of this together, we see something interesting: to the south of the updraft, there is high pressure at the surface and low pressure at upper levels, meaning there is an upward-directed pressure gradient force to the south of the updraft:

Upward motion will be enhanced to the south of the updraft causing the updraft to move more toward the south, to the right of the mean winds, which are generally from the south and west. The mean winds will still play a part in moving the updraft, so in this case, the updraft wouldn’t move due south, but it would move more toward the south than one would expect just by looking at the average winds. Also, don’t forget that even with a curved hodograph, the nonlinear effects still play a part in the updraft’s propagation, though that part diminishes in importance as the hodograph becomes more curved. It should also be mentioned that in the example above, upward motion is weakened (suppressed) to the north because of a low at the surface and a high at upper levels; this leads to a downward-directed pressure gradient force in that location.

The reason the linear effect is not as pronounced when there is little or no curvature is that a straight hodograph means the shear vector points in the same direction at all heights, so the low and high pressures are at the same location at all heights leading to weak vertical pressure gradient forces. As curvature is added to the hodograph, it necessitates shear vectors pointing in different directions at different heights leading to highs and lows in different locations at different heights. Thus, there are more/stronger vertical pressure gradient forces to help propagate the updraft.

The proponents of the importance of the linear term advocate a somewhat different way to explain it, however. As mentioned above, an updraft’s rotation comes about from the tilting of horizontal vorticity (horizontal spinning) into the vertical by the updraft leading to vertical spinning. If there is an updraft and cyclonic vertical vorticity (cyclonic spinning) in the same location, then there will be a cyclonically-rotating updraft, the normal scenario for a supercell thunderstorm. In other words, a positive correlation between vertical velocity and vertical vorticity (spinning) is an ideal setup for a supercell updraft. It turns out that in the Northern Hemisphere, storms that move to the right of the shear vector will tend to have cyclonically-rotating updrafts due to the positive correlation between upward motion and cyclonic vertical vorticity. If you’ve made it this far, this is not a surprising result as we’ve already established that above. However, the proponents of the linear term arrive at this result differently than the proponents of the nonlinear term. The proponents of the linear term argue that such a correlation is maximized when storm-relative winds (the movement of the winds relative to the motion of the storm) are moving in the same direction as the vorticity (i.e., the velocity vector and vorticity vector point in the same direction). This type of vorticity or spinning is known as streamwise vorticity. A similar quantity is known as storm-relative environmental helicity (SREH); helical flows have a lot of rotation in them. SREH can actually be calculated on a hodograph assuming one knows the motion of the storm. So, given a hodograph, which contains the environmental winds at several heights and given the motion of the storm, one can determine how much SREH there is in the environment and therefore, how likely it is for there to be a cyclonically-rotating updraft given a storm. Generally, the more SREH, the greater the likelihood of rotating supercells. Typically, SREH is measured in the lowest 1 km or 3 km above ground level. Let’s look at the same example hodograph. With winds from the SE, SW, S, and W through most of the atmosphere, one might expect a storm motion toward the NE or ENE, a common storm motion. However, now we know that linear effects mean there is a component of storm motion toward the south. This would likely lead to a storm motion toward the E or SE instead of toward the NE or ENE. For the sake of argument, let’s specify a storm motion of toward the E at 15 mph. Now, we can use our hodograph to plot out how much SREH there is between the surface and 3 km.

I should note that another great aspect of hodographs is that one can easily determine the storm-relative winds at any height. Simply plot the motion of the storm, the “X” in the example above, and connect that X to the environmental winds at a height; the line that connects the two represents the speed and direction of the storm-relative winds at that height (for example, in this case, the storm-relative surface winds are from the SE at about 25-30 mph). Back to the diagram above, you’ll notice something interesting. What happens if our storm moves even more to the right? Let’s say it’s now moving ESE at a similar speed:

It now has more SREH (a greater blue area in the hodograph). This occurs because the storm motion bending more to the right leads to stronger storm-relative winds (for example, the line connecting the storm motion to the surface winds is longer, meaning stronger surface storm-relative winds). The stronger storm-relative winds means more streamwise vorticity and, as the graph shows, more SREH. This means a better chance of rotating updrafts in any storm that forms.

The advocates of the linear effects or, equivalently the helicity approach, believe that the nonlinear term is not the most essential aspect of supercell dynamics and stress that both effects are crucially important to understand a supercell’s behavior in all types of wind shear. As shown in the examples above, an important parameter in determining the linear effects is the storm motion. Changing the motion of the storm can change the amount of SREH and streamwise vorticity dramatically because both rely on the storm-relative winds. Yet, it is these very quantities in the helicity approach that are used to determine storm rotation. So the storm’s unique propagation characteristics determine its ability to derive rotation through the amount of streamwise vorticity and SREH available. In other words, storm propagation leads to updraft rotation. Again, there are those that would argue that the above is not the best way to view supercell dynamics.

Reviewing the parts in bold, you can now see where there is disagreement. The proponents of the helicity/linear effects approach argue that the environment drives the storm’s propagation and through that propagation, the storm derives its rotation. The proponents of the nonlinear/wind shear approach argue that the environment drives the storm’s rotation and through that rotation, the storm propagates in a particular direction.

To sum it up:

1) Do you think a storm propagates in a certain direction because of the storm’s rotational characteristics? If so, you favor the nonlinear effects/vertical wind shear approach.

or

2) Do you think a storm derives its rotation from its propagation characteristics? If so, you favor the linear effects/helicity approach.

Admittedly, the above questions are intentionally obtuse. You don’t have to fall into one camp or the other. Both descriptions have strengths and both have weaknesses. For example, in the helicity approach, one caveat is that a storm motion has to be assumed, yet determining storm motion just from a hodograph is very difficult to do leading some to wonder if the assumption of a pre-determined storm motion is the right way to approach the problem. Likewise, in the wind shear approach, there are some major simplifications and assumptions made in the mathematics to arrive at the locations of lows and highs. There are several caveats and assumptions like the ones above within each argument. It would take me quite a while to get through them all.

You also may be asking, “What does it matter?” Well, one reason that supercells are able to last for long periods of time is that the updraft and downdraft(s) are displaced from each other. Most storms die off when the rain-driven downdraft falls into the updraft killing the updraft and killing the storm. The ability of supercells to keep the downdraft(s) and the updraft separated means the storms can last much longer. Even the maintenance aspect of supercells can be addressed using both methods. Taking into account nonlinear effects, the ability of the storm to rotate leads it to propagate off the shear vector allowing the updraft and downdraft to stay in different locations. The helicity approach argues that highly helical flows, in addition to having more streamwise vorticity, are more stable and delay energy cascading (another subject entirely), thus allowing supercells to persist longer.

Regardless of which way you prefer to describe it, these are the most important aspects of supercell dynamics. Both the linear and nonlinear effects lead to pressure gradient forces that allow supercells to move in a direction different than that of the mean wind and that of the mean wind shear vector.

Questions, comments, criticisms welcome.

Selected sources:

Rotunno, R., and J.B. Klemp, 1982: The Influence of the Shear-Induced Pressure Gradient on Thunderstorm Motion. Mon. Wea. Rev., 110, 136–151.

Weisman, M.L., and J.B. Klemp, 1984: The Structure and Classification of Numerically Simulated Convective Storms in Directionally Varying Wind Shears. Mon. Wea. Rev., 112, 2479–2498.

Davies-Jones, R., 1984: Streamwise Vorticity: The Origin of Updraft Rotation in Supercell Storms. J. Atmos. Sci., 41, 2991–3006.

Rotunno, R., and J. Klemp, 1985: On the Rotation and Propagation of Simulated Supercell Thunderstorms. J. Atmos. Sci., 42, 271–292.

Weisman, M.L., and R. Rotunno, 2000: The Use of Vertical Wind Shear versus Helicity in Interpreting Supercell Dynamics. J. Atmos. Sci.,57, 1452–1472.

Davies-Jones, R., 2002: Linear and Nonlinear Propagation of Supercell Storms. J. Atmos. Sci., 59, 3178–3205.

All of the above publications can be accessed for free if you're interested in learning more: http://ams.allenpres...t=search-simple

[AtticaFanatica]

This is a re-post from 2 years ago (damn, 2 years). I spent a lot of time on it and was afraid I'd lose it.

[yoda]

Wow... I am going to have to re-read all this info... but its EXCELLENT INFO. Thanks for the awesome post Attica

[Sickman]

This is a re-post from 2 years ago (damn, 2 years). I spent a lot of time on it and was afraid I'd lose it.

I know I remembered this post from Eastern.

It's an awesome read, and I thank you for re-posting this here.

[Road Runner]

, God, I love the way you write. You and Clark are so good.

[Srain]

Awesome Attica! I remember the 'read'.

[CoastalWx]

Hey great stuff Attica. Awesome read.

[AtticaFanatica]

Correction: the helicity plots should specify that SREH is -2 times the area swept out, not 2.

[baroclinic_instability]

"It now has more SREH (a greater blue area in the hodograph). This occurs because the storm motion bending more to the right leads to stronger storm-relative winds (for example, the line connecting the storm motion to the surface winds is longer, meaning stronger surface storm-relative winds). The stronger storm-relative winds means more streamwise vorticity and, as the graph shows, more SREH. This means a better chance of rotating updrafts in any storm that forms."

When you say this, it almost sounds as if, in some ways, there is a positive feedback loop going on. It reminds me of some types of intense cyclogenesis where, for instance, strong low level WAA + diabatic heating can alter the upper level height fields and increase other forcing terms such as differential vorticity advection aloft, which increases WAA, etc as well as mesoscale jet circulations, which also feedbacks to other effects and subsequent rapid occlusion and intense cyclogenesis (intense marine cyclogenesis, for instance). In this case, does strong curved hodographs, especially in the lower levels, positively feedback to other forcings such as perturbation pressures as you spoke of in the non-linear terms which then further enhances the linear term, etc etc until you have an extremely intense supercell, perhaps of the long-track/long-lived type? Or perhaps rapidly cycling systems in a manner which suggests a "limit" to intensity, much like an occlusion in synoptic systems? Either way, good information. I think it would be great if you did provide a tad more background into the equations and the individual terms and their importance.

[baroclinic_instability]

Let me reinforce what I am attempting to say, " In this case, does strong curved hodographs, especially in the lower levels, positively feedback to other forcings such as perturbation pressures as you spoke of in the non-linear terms which then further enhances the linear term, etc etc until you have an extremely intense supercell, perhaps of the long-track/long-lived type? Or perhaps rapidly cycling systems in a manner which suggests a "limit" to intensity, much like an occlusion in synoptic systems? ". What I am trying to say is, in the case of a curved hodograph (clockwise w/height) defined by strong directional and vertical shear, does, for instance, the right moving cyclonic updraft increase its storm relative flow as it continues propagating right (therefore increasing the non-linear effects) which also increases the linear effect which results in a further increased south propagation (farther right if mean wind from the west) etc etc etc.?

[AtticaFanatica]

To some degree, yeah, feedbacks are definitely involved. Any mechanism, such as larger SRH, that enhances midlevel rotation is going to enhance upward perturbation VPGF (ignoring a situation with a stronger low-level meso), which enhances vertical vorticity production and rotation through stretching, which in turn drives the non-linear effect, and so on. The contentious issue is what's driving what. As far as supercell maintenance, another argument by the SRH folks is that highly helical flows have been shown to be more stable, so that an environment with a lot of SREH is favorable for a longer-lasting, more stable system (e.g., a supercell). This hasn't been explicitly shown for supercells, but it's an idea.

Storm cycling isn't all that well understood. The seminal observational work on the subject suggests that the mean flow the meso or tornado is embedded in is important and that advection of the meso or tornado by SR winds in cases with relatively weak storm outflow can lead to rapid storm cycling. In such a scenario, increases in rear-flank outflow may help to "balance" any rearward advection and keep a meso/tornado in a vorticity-rich environment that sustains it for much longer periods of time. Then the question becomes what drives sudden changes in the strength of rear-flank outflow.

However, the seminal numerical modeling work done on the subject of storm cycling did find that storm cycling and the manner of storm cycling was at least partially dependent on the amount and distribution of vertical wind shear, so an overt connection to the SRH or vertical wind shear approach is certainly plausible as well.

[AtticaFanatica]

I think it would be great if you did provide a tad more background into the equations and the individual terms and their importance.

I'm not sure how that would translate on a message board or if anyone is really interested in that. I was basically just intending to provide a research-oriented physical explanation.

[AtticaFanatica]

Basically, the first term on the RHS of the equation (of the 4 main terms I provided) plus one part of the second term is the non-linear term (though the first part, the fluid extension term, is sometimes ignored). The 3rd term is the linear term. Once you make some assumptions (e.g., pure rotation, no deformation), most of the second term goes away. The resulting perturbation pressures for the non-linear term are negative for increases in rotation (either cyclonic or anti-cyclonic). For the linear term perturbation pressures are negative on the downshear side of the updraft as calculated from the dot product of the vertical wind shear and the vertical velocity gradient (the linear term can be rewritten as such).

[ArtRosen]

Thank you for taking the time to write this. VERY informative. I hope to see some supercells next year if I chase.

[LocoAko]

I'm not sure how that would translate on a message board or if anyone is really interested in that. I was basically just intending to provide a research-oriented physical explanation.

I'd find it interesting (or at least I'd try to understand it ) but that's just me and I don't speak for the majority I assume.

[AtticaFanatica]

Mods, not sure how you envision the Meteorology 101 forum, but I figured this might be a good thread to move there...

[HoarfrostHubb]

I had not read this before. Very understandable to a non-met, yet detailed and thought provoking