Positive Vorticity Advection (PVA)

I'm still trying to wrap my mind around PVA and its importance in initiating convection. That is when I try and picture it, I guess I still don't understand it correctly. (e.g. I know that PVA is coupled some how with divergence in the exit region of a wave (trough) thus resulting in vertical motion) I wonder if anyone has any input on this matter? :confused:
Thanx
 
Well, when you're looking for vertical motion, you want to look at DIFFERENTIAL PVA (or differential NVA)! Per the QG approximation, vertical motion is a function of thermal advection (warm-air advection causes upward motion; cold-air advection results in subsidence) and differential vorticity advection (positive vorticity advection increasing with height causes upward motion, as does negative vorticity advection decreasing with height!) . Generally, flow in the low-levels, while highly-curved, is weaker than flow aloft. Meanwhile, it's typical for upper-level flow to be quite strong but also less curved. Vorticity is comprised of that from shear and that from curvature, and the mid-levels tend to have the highest vorticity since there can be both significant shear vorticity and curvature vorticity. So, with all this in mind, most folks look at a 500mb vorticity map, and note that where positive vorticity is being advected, there is probably upward motion. Likewise, as a vorticity maximum is moving away, there is probably downward motion. Not that this is technically not correct -- you really need to make sure that vorticity is becoming more cyclonic/positive faster with height (i.e. PVA is stronger aloft than in the low-levels).

The vertical motion associated with exit and entrance regions of jet streak is another process altogether (though it can certainly reinforce or weaken vertical motion tendencies caused by DPVA or DNVA). You should be able to find information on this easily on Google (there's a Habyhints about this) -- just search for "Transverse circulation". Note that the typical "quadrant model" of vertical motion in a jet streak is valid for straight jet streaks. As jet streaks become more curved, you'll often see enhanced vertical motion on one side of the jet streak and reduced (or even reversed) vertical motion on the opposite side after differential vorticity advection effects are accounted for. In addition, the ageostrophic wind equation has other terms that can yield in vertical motion (for example, ageostrophic curvature divergence aloft downstream of a trough axis and upstream of a ridge axis, maximized at the inflection point).

"Regular" vorticity advection (as opposed to differential VA) is tied to height tendency (height falls or rises), as is differential thermal advection.
 
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Jared: Frankly you should do some serious reading of books or at least a good internet search if you want to get a good handle on the subject, including digging into the mathematics. Its not an easy subject. However, here's a watered-down way to look at it:

Vetrical motion at some level requires convergence somewhere below that level and divergence above. This is required by mass continuity--the rising air has got to come from somewhere and has to go somewhere!

Cyclonic Vorticity Advection; CVA (it is NOT PVA, remember our good friends down south of the equator, we wouldn't want to confuse them too!) is a means of implicitly diagnosing that divergence aloft. A parcel exiting a trough is entering an environment with less curvurture (it's leaving the most curved part, therefore there is CVA). By conservation of angular momentum, to remain in equilibrium with its environment, the parcel has to somehow lose some of its vorticity. It can do this by "diverging": the common example given to students is an ice skater speading their arms to lose the spin.

So, CVA 'means' divergence, which 'means' upward motion. With the right thermodynamics, you can get convection.
As Jeff poits out, it much more complicated than that, since among other things i've totally ignored thermal advection. But that's it in a nutshell. hope it helps-S
 
Yeah that helps guys, so say a shortwave is digging out and with an accompanying vort max. The divergence in the exit region is alone capable of enough forced lift to set things in motion(giving the right ingrediants of course) ?

Thanx guys
 
I'm not sure what you mean by "exit region"... Typically, when one uses exit or entrance region to describe a jet feature, it's in terms of a jet streak (e.g. the left-exit region of the jet streak). For a straight upper-level jet streak, there is divergence (and assumed uperward motion) in the left-exit and right-entrance regions, and convergence (and assumed subsidence) in the right-exit and left-entrace regions. If a vort max is approaching, you could also see vertical motion owing to DIFFERENTIAL positive vorticity advection [again, PVA, or CVA, alone does not cause divergence or convergence and implied vertical motion -- you need to look at how the CVA/PVA changes with height].

So, let's say that there's a curved jet streak that's rounding the base of a progressive trough. In the left-exit region of that jet streak, there is upper-level divergence (and implied upward motion) from transverse circulation (it's the inertial-advective wind, technically); in the right-exit region, there is upper-level convergence (and implied downward motion). Now, if you add to that large-scale upward motion from DPVA, you could very well see enhanced upward motion in the left-exit region (up+up) and weaker downward motion (or neutral vertical motion) in the right-exit region (where the upward motion from DPVA may act to negate the downard motion from transverse circulation effects in the right-exit region of the jet streak). This can become very complex ,however, since there could be upward motion in the right-exit region of the curved jet streak downstream of a trough axis from warm-air advection as well (which isn't uncommon since there is a enhancement of the low-level flow towards the trough axis owing to the transverse circulation under the exit region of the jet streak).

For what it's worth, there is also, as noted previously, upper-level divergence maximized at the inflection point downstream of a trough axis and upstream of a ridge axis caused by ageostrophic curvature divergence aloft. As an air parcel moves through the base of the trough, it must slow owing to the cyclonic curvature, which means that the winds are subgeostrophic (imagine the total wind being the sum of the geostrophic wind and the ageostrophic wind, which means that, in this case, the ageostrophic wind acts against the geostrophic wind to make a new wind weaker than the geo wind). As a parcel moves through the top of a ridge, it speeds up, which means that winds are supergeostrophic (or, the ageostrophic wind is in the same direction as the geostrophic wind). By definition, the geostrophic wind is non-divergent, so we need to look at the ageostrophic wind for divergence/convergence (and implied vertical motion). If you can imagine, there's westerly ageo wind in the base of the trough, and easterly ageo wind at the top of the ridge (assuming a normal trough-ridge wavepattern in the NH) -- therefore, there is divergence of the ageostrophic wind between the ridge and the trough. On the other side of the trough (or to the west of the trough and east of a ridge in the NH), there is ageo convergence. This helps explain, in part (since thermal and vorticity patterns also significantly influence this), why the region downstream of a trough is a preferred region for surface cyclone development, and why the region downstream of a ridge is a preferred location for surface anticyclone development.

All of the above is in context of the quasi-geostrophic approximation. Ageostrophic responses become more important when more processes are included (i.e. in the semigeostrophic approximation).
 
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Yeah that helps guys, so say a shortwave is digging out and with an accompanying vort max. The divergence in the exit region is alone capable of enough forced lift to set things in motion(giving the right ingrediants of course) ?

Thanx guys

Well, not exactly. if that were the case there would be convection occuring everywhere. It makes things more conducive to things getting going, as Jeff points out. Among other things, it can increase the instability of the air column. Usually the actual trigger is at a smaller scale, a front or convergence boundary for example. But you get the general idea.
 
Interesting discussion.
Am I correct in thinking that VA in its various guises can also help steepen the lapse rate, increasing the instability? By my understanding this can occur through the process of the air being advected when unsaturated and cooling at the DALR en masse. This in turn lowering the environmental temperature that any potential updraught is rising in to.
 
Interesting discussion.
Am I correct in thinking that VA in its various guises can also help steepen the lapse rate, increasing the instability? By my understanding this can occur through the process of the air being advected when unsaturated and cooling at the DALR en masse. This in turn lowering the environmental temperature that any potential updraught is rising in to.

DIFFERENTIAL positive vorticity advection (cylonic VA) leads up large-scale upward motion, which in turn can steepen lapse rates through mid-level adiabatic cooling. Thermal advection processes can also steepen lapse rates -- e.g. low-level warm-air advection occurring underneath mid-level cold-air advection steepens lapse rates. However, remember that thermal advection results in vertical motion as well, and the sign of the vertical motion is that which acts to neutralize the thermal advection. For example, for CAA, there is subsidence, which is a warming process; during WAA, there is upward motion, which is a cooling process. So, differential thermal advection can steepen lapse rates (and you can think of the effect of differental thermal advection in height/pressure rises and falls per the QG chi equation), but you'll often see mid-level subsidence as a result (assuming there's midlevel CAA). An 'incoming' vort max can lead to DPVA, which can result in large-scale upward motion, cooling the column in the process, and yielding steeper lapse rates (assuming WAA and/or diabatic heating in the low-levels keeps the near-surface air relatively warm and potential unstable).

Also, remember that static stability (which is proportional to the change in potential temperature with height) affects the degree of forcing caused by thermal and vorticity advection patterns. Generally, as static stability decreases, the response to a given forcing increases. For example, if the 850-500mb lapse rate is dry-adiabatic, static stability is very low, (well, zero in that case), and the upward motion from DPVA or WAA is larger than would be the case if the lapse rate was more like moist-adiabatic. If a layer of the troposphere is relatively stable, response to forcing from differential vorticity advection and thermal advection is weaker than is the case when that layer is less stable. So, a weak vort max moving at some speed may produce as strong (or stronger) forcing as (than) a stronger vort max if the first occurs with lower static stability (thereby implying stronger vertical motions from weaker forcing components).
 
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I'm still trying to wrap my mind around PVA and its importance in initiating convection.

I'm not sure this has specifically been addressed yet. I think this is an excellent question and could spark quite a debate.

Synoptic scale lift such as DPVA is supposed to be on the order of cm/sec (relatively small; I may well have my units wrong)... whereas it is the mesoscale boundaries (the famed "fronts, drylines, sea breezes, and outflow boundaries" list) that are fundamental to convective initiation. In addition to DPVA... low-level WAA, upper divergence (not easy to diagnose IMO), and high-level difluence are likewise theoretically supposed to function in "readying" the environment, making it more favorable for initiation, perhaps even helping to slowly cool capping inversions through gradual ascent.

Meanwhile... of the dozen or so clear sky busts I've had, all but 1 or 2 were entirely lacking in DPVA via incoming shortwave energy. (A few of these also involved a climatologically strong 700mb cap, but most did not.) I find this pretty interesting, but I'll leave it at that. I believe that the synoptic scale ascent mechanisms should not be underestimated w.r.t. "helping along" convective initiation.
 
I completely agree with your comments afischer... same over this side of the pond. Without at least a little DPVA, deep convection rarely occurs...
 
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