Jeremy A. Gibbstwister.caps.ou.edu/.../chapter4_presentation4.pdf · Squall Lines: Development of Supercell Lines I Most often, squall lines are composed of ordinary cells. I But

Convective Dynamics

Jeremy A. Gibbs

University of Oklahoma

[email protected]

March 12, 2015

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Overview

Squall Lines3D EvolutionDevelopment of Supercell LinesDynamicsRKW TheoryEarly 2D EvolutionRear-Inflow JetModel Simulations

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Squall Lines: 3D Evolution

I The two-dimensionalevolution described for theearly-to-mature phases of asquall line generally appliesto the middle portion ofmost squall lines.

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I However, significantthree-dimensional mesoscaleflow features can evolve atthe ends of a squall line orat breaks within the line,which can significantly alterthe subsequent evolution ofthe system.

I The most prominent ofthese features is a set ofmid-level mesoscale vortices,referred to as “line-end” or“bookend” vortices.

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I Viewing all levels of thestorm, the structure of thesystem during its symmetricphase (early in theevolution) is characterizedby low-level divergent flowwith the cold pool,symmetric line-end vorticesat mid-levels, and therear-inflow jet concentratedbetween the vortices.

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I Aloft, we find divergentflow, with weaker vortices ofopposite rotational senseabove the mid-level vorticesat the northern and southernends of the system.

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I During the asymmetricphase (later in theevolution), a dominantcyclonic vortex is evident atmid-levels, while both thelow-level and upper-leveldivergent outflows turnanticyclonically.

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Squall Lines: Development of Supercell Lines

I Most often, squall lines are composed of ordinary cells.

I But occasionally, when the environment exhibits strongvertical wind shear at both lower (0-3 km AGL) and upperlevels (3-6 km AGL), a squall line may also be composed ofsupercells.

I During the early stages of such systems, supercells often maybe spread along the entire extent of the line.

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I However, the circulations of these supercells are often quicklydisrupted as cells interact with each other along the line.

I Due to cell interactions, certain locations within a line may befavored for supercell development and maintenance,depending on the shape and orientation of the environmentalshear profile relative to the orientation of the squall line.

I In any scenario, new convective cells may also be triggeredalong the spreading cold pool between the supercells, makingcell interactions even more complicated.

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Figure: April 28, 2014 at 2044 UTC 10 / 82

Squall Lines: Physical Processes Responsible for Dynamics

We have described the observed features and evolution of squalllines. Questions remain, as to:

I Why does the strength and longevity of a squall line dependon the strength of environmental vertical wind shear?

I What produces the mesoscale pressure patterns observed withsquall lines?

I How is a rear-inflow jet generated, what controls its strength,and what impact does it have on squall line strength andevolution?

I How does the Coriolis force impact squall line evolution?

I How can we better anticipate whether an squall line is apt toproduce severe weather?

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Squall Lines: Equations to be Used

I The fundamental equations for understanding convectivemotions are the horizontal and vertical momentum equations.

I The horizontal momentum equations relate horizontalaccelerations to horizontal pressure gradients and Coriolisforcing, while the vertical momentum equation relates verticalaccelerations to buoyancy forces and vertical pressure gradientforces.

I Also useful are the vorticity equations that can be derivedfrom the momentum equations. One example is they -component of vorticity equation we presented earlier whendiscussing gust front circulations.

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Squall Lines: RKW Theory on Cold Pool

When discussing the multicell storms, we discussed how theinteraction between the system-generated cold pool and theambient low-level shear strongly modulates the tendency togenerate new cells in multiple cell systems. In a homogeneousenvironment, the strongest, most long-lived multiple cell systemsoccur in environments characterized by strong, low-level verticalwind shear.

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Rotunno, Klemp, and Weisman, (1988) proposed that the optimalcondition for the generation of new convective cells is when thereis a balance between the horizontal vorticity produced by the coldpool and the opposite horizontal vorticity associated with theambient low-level vertical wind shear on the downshear flank of thesystem

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Knowledge of the processes underlying cold pool/shear interactionsis also critical for understanding the strength, longevity, andevolutionary character of long-lived squall lines.

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Figure: Schematic diagram showing how a buoyant updraft may beinfluenced by environmental wind shear and/or a cold pool.

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(a) - With no environmental shear and no cold pool, the axis ofthe updraft produced by the thermally created, symmetric vorticitydistribution is vertical.

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(b) - With a cold pool, the distribution is biased by the negativevorticity of the underlying cold pool, causing the updraft to tiltover the cold pool.

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(c) - With environmental shear and no cold cool, the distribution isbiased toward positive vorticity, causing the updraft to leandownshear.

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(d) - With both a cold pool and shear, the two effects may negateeach other and promote an erect updraft.

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RKW looked for a quantitative criterion for the low-level shearneeded to balance a cold pool.

RKW also set out to distinguish the physical difference between acold pool spreading into a no-shear environment from that in anenvironment with low-level shear.

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Recall that the equation governing vorticity in the y -direction is

dη

dt= −

∂B

∂x,

which may be expanded as

∂η

∂t= −

∂(uη)

∂x−∂(wη)

∂z−∂B

∂x,

where

η =∂u

∂z−∂w

∂x

is vorticity and B is the total buoyancy.

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Next, we fix ourselves in a reference frame moving with the edge ofthe cold air. We then integrate the previous equation from a pointto the left, x = L, to a point to the right, x = R, of the cold-airedge, and from the ground to some level, z = d .

∂

∂t

∫ R

L

∫ d

0ηdzdx︸︷︷︸

tendency

=

∫ d

0(uη)Ldz︸︷︷︸

flux at left

−∫ d

0(uη)Rdz︸︷︷︸

flux at right

−∫ R

L(wη)ddx︸︷︷︸

flux at top

−∫ d

0(BL − BR)dz︸︷︷︸

net generation

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Assumptions

I a steady balance, so ∂/∂t = 0

I negligible buoyancy of air approaching cold pool, so BR = 0

I far away from the edge of the cold air, η ≈ ∂u/∂z

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Applying assumptions yields

0 =

(u2L,d

2−

u2L,0

2

)−

(u2R,d

2−

u2R,0

2

)

−∫ R

L(wη)ddx +

∫ d

0BLdz

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Next, we consider a situation where the cold air is stagnant(relative to the cold-air edge), so that uL,0 = 0, and restricted to aheight, z = H, where H < d . Applying these assumptions leads to

0 =u2L,d

2−

(u2R,d

2−

u2R,0

2

)−∫ R

L(wη)ddx +

∫ H

0BLdz

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Consider a situation with low-level shear (panel d earlier).

RKW looked for the optimal state where the low-level flow isturned by the cold pool in such a way as to exit as a verticallyoriented jet.

Thus, we set uL,d , uR,d , and∫ RL (wη)ddx = 0.

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The result is then∆u = c ,

where∆u = uR,d − uR,0 = −uR,0

and

c2 = 2

∫ H

0(−BL)dz = 2g

−∆θ

θ0H = 2g

∆ρ

ρ0H

→ c =

√2gH

∆ρ

ρ0

which is exactly the density current propagation speed we derivedearlier!

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Therefore the optimal condition obtained based on RKW’s vorticitybudget analysis says that the shear magnitude in the low-levelinflow should be equal to the cold pool propagation speed.

Physically, this means that the import of the positive vorticityassociated with the low-level shear just balances the net buoyancygeneration of negative vorticity by the cold pool in the volume.

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I The relative balancebetween the cold poolgenerated horizontalvorticity and the ambientshear can be quantified viathe ratio c/∆u.

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I In this ratio, c representsthe strength of the cold poolcirculation, given by thetheoretical speed ofpropagation.

I ∆u represents the strengthof the circulation associatedwith the ambient shear,given by the magnitudedifference between thecomponent of ambient windperpendicular to the coldpool at the surface, U1, andat 2.5 km AGL, U2.

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I As an example, if ∆θ = −4within a 1.5 km deep coldpool (h = 1.5), c would beabout 20 ms−1.

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I c/∆u = 1 represents theoptimal state for deep liftingby the cold pool, with valuesless than 1 signifying thatthe ambient shear is toostrong relative to the coldpool. Values greater than 1signify that the cold pool istoo strong for the ambientshear.

I c/∆u can also be used tounderstand thetwo-dimensional evolution ofa squall line, providing cluesto help us anticipate itsstrength and longevity.

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I Since potential temperatureperturbations within thecold pool can be directlyrelated to the hydrostaticpressure change within thecold pool, the speed of thecold pool (c) can becalculated by measuring thechange of pressure as thecold pool passed overhead,instead of measuring thechange of temperature.

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I This method has anadvantage over using thetemperature perturbationmethod since the pressurechange at the surfacerepresents the integratedaffects over the depth of thecold pool. Thus, one doesnot have to know the depthof the cold pool (h) to makethe calculation.

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I Again using our example ofa cold pool with a 4 Kpotential temperature deficitover 1.5 km, we can see thatit translates to a pressureexcess of ∼ 2 mb. When wecalculate the speed of thecold pool, c , for an observedpressure change of ∼ 2 mb,we again get 20 ms−1.

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Consider the simple case of a two-dimensional cold pool spreadingin an environment with little or no vertical wind shear. From theperspective of horizontal vorticity, a cold pool in the absence ofstrong ambient vertical wind shear tends to drag air up, over, andbehind the leading edge of cold air.

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If there is an optimal amount of ambient, low-level vertical windshear, such that the horizontal vorticity associated with it balancesthe opposite horizontal vorticity produced on the downshear side ofthe spreading cold pool, a more vertically oriented and deeperupdraft will be produced due to the interacting vorticities.

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If the horizontal vorticity associated with the ambient vertical windshear is stronger than that produced by the cold pool, then airparcels lifted at the leading edge of the cold pool will be tilteddownshear. They will not be lifted as much as when a vorticitybalance is in place.

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I The shear layer that is mostimportant for determining thedepth and strength of lifting at theleading edge of the cold pool is theone coinciding with the depth ofthe cold pool, usually from thesurface to about 1.5-2 km AGL.

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I However, shear over a deeper layerabove the cold pool alsocontributes to some degree. Forinstance, deeper shear may help tomaintain deeper, more uprightlifting in a case where c/∆u > 1.For this reason, we use 0-3 km AGLto define the effective shear layer.

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I Similarly, if the shear reversesabove the cold pool, as in ajet-type wind profile, the updraftcurrent aloft may tilt back over thecold pool, despite a favorablec/∆u balance at lower levels.

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Squall Lines: Cold Pool/Shear Interactions Summary

I The system-generated cold pool and the ambient low-levelshear strongly modulate the tendency to generate new cells inmultiple cell systems, including multicell squall lines.

I The deepest updrafts occur when the horizontal vorticitygenerated along the cold pool’s leading edge is nearly equal inmagnitude to, and has rotation of opposite sense to thehorizontal vorticity associated with the low-level vertical windshear.

I When the low-level wind shear is weak and is associated withweaker horizontal vorticity than the cold pool, the updraft atthe leading edge of the cold pool is tilted upshear and is notas deep and strong as when they are in balance.

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I When the low-level wind shear is stronger and is associatedwith stronger horizontal vorticity than the cold pool, theupdraft at the leading edge of the cold pool is tilted downshearand is not as deep and strong as when they are in balance.

I This cold pool/low-level shear relationship can be quantifiedas a ratio of the speed of the cold pool, c , over the value ofthe line-normal low-level vertical wind shear, ∆u.

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I c/∆u = 1 represents the optimal state for deep lifting by thecold pool.

I c/∆u < 1 signifies that the ambient shear is too strongrelative to the cold pool.

I c/∆u > 1 signifies that the cold pool is too strong for theambient shear.

I This balance is significant for anticipating the strength andlongevity of an squall line

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Early 2D Evolution - Phase 1: Initiation

I Initially, a series of convective cellsdevelops along some pre-existinglinear forcing feature.

I Since these convective cells arebuoyant, horizontal vorticity isgenerated equally on all sides ofthe cells.

I In the absence of vertical windshear, this would produce anupright circulation.

I However, since there is verticalwind shear, the additive influenceof the horizontal vorticityassociated with the shear on thedownshear side of the cells causesthem to lean downshear.

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Early 2D Evolution - Phase 2: Strong Cells

I Once the system begins to producerainfall and a cold pool forms, thecold pool circulation is ofteninitially weak relative to theambient shear, with subsequentcells continuing to leanpredominately downshear, like theinitial cell.

I However, over time, the sequenceof new cells continues to strengthenthe cold pool, and unless theambient shear is exceptionallystrong, the cold pool circulationeventually becomes strong enoughto balance the horizontal vorticityassociated with the ambient shear.

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Early 2D Evolution - Phase 2: Strong Cells

I With this balance (c/∆u = 1) inplace, the strongest and deepestlifting is produced along the leadingedge of the cold pool. Often, it isduring this stage that the mostintense and erect convective cellsare observed along the squall line,with new cells regularly beingtriggered as old cells decay.

I Because the cells characteristicallymove at the same speed as the gustfront in this stage, the convectiveline remains relatively narrow.

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Early 2D Evolution - Phase 3: Tilting Upshear

I As the cold pool continues tostrengthen, the cold poolcirculation often eventuallyoverwhelms the ambient verticalwind shear vorticity (c/∆u > 1).Cells begin to tilt upshear andadvect rearward over the cold pool(relative to the gust front).

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I During this stage, the squall linetakes on the appearance of aclassic multiple cell system, with asequence of cells that initiate atthe leading edge, then mature anddecay as they advect rearward overthe cold pool. The leading-lineconvective cells usually become lessintense during this phase becausethe lifting at the leading edge isnot as strong or deep as it is duringthe stage of optimal balance.

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I The rearward advecting cellsproduce an expanding region oflighter precipitation extendingbehind the strong, leading-lineconvection. This rearwardexpansion of the rainfield createsthe trailing stratiform precipitationregion associated with matureMCSs. It is in this phase that thesystem begins to take on amesoscale flow structure, includingthe development of a mid-levelmesolow and rear-inflow jet.

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Early 2D Evolution - Evolution Timeframe

I The period over which thisevolution takes place depends onboth the strength of the cold poolas well as the magnitude of thelow-level vertical wind shear, andcan vary from 2-3 hours to over 8hours in some cases.

I In general, for midlatitudeconditions (which produce fairlystrong cold pools) a∆u ≤ 10 ms−1 produces thisevolution over a 2-6 hour period,while ∆u ≥ 20 ms−1 slows theevolution to between 4-8 hours.

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Early 2D Evolution - Shear Orientation

I It’s important to remember that fora squall line the only component oflow-level shear that contributes tothe c/∆u balance is thecomponent perpendicular to squallline orientation.

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Early 2D Evolution - Shear Orientation

I If we had southwesterly shear, asquall line oriented from northwestto southeast (top) would feel thefull effects of the shear, while asquall line orientednortheast-southwest (bottom)would evolve as if there were nolow-level shear at all. However, thecells at the ends of the squall linedo not necessarily follow this rulebecause they can interact with theshear more like isolated cells.

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Rear-Inflow Jet: Pressure Field

I As the squall line continuesto evolve in its maturestage, the spreading of theconvective cells rearwardtransports warm air aloft aswell. In addition, the deeperportion of the surface coldpool also extends rearward,in response to the rearwardexpanding rainfield.

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I A pool of warm air aloft overa cold pool at the surfaceproduces lower pressure atmid levels and higherpressure at the surface. Theflow field responds bydiverging at the surface andconverging at mid levels.

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I The flow that converges infrom the rear of the systemat mid levels is known as therear-inflow jet (RIJ). Theconvergence from the frontof the system tends to beblocked by the updraft, somost of the flow convergesin from the rear of thesystem.

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Rear-Inflow Jet: Horizontal Vorticity

I From the horizontal vorticityperspective, the horizontalbuoyancy gradientsassociated with the backedge of the warm air aloftand back edge of the coldpool at the surface generatea vertically stackedhorizontal vorticity couplet.This couplet is responsiblefor the generation of therear-inflow jet.

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Rear-Inflow Jet: Strength

I Since the rear-inflow jet isgenerated in response to thehorizontal buoyancy gradients atthe back edge of the system, thestrength of the rear-inflow jet isdirectly related to the strength ofthose buoyancy gradients, bothaloft and within the cold pool. Thestrength of these buoyancygradients is directly related to therelative warmth of the air withinthe front-to-rear (FTR) ascendingcurrent, as well as the relativecoolness of the surface cold pool.

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I The potential temperature excesswithin the FTR ascending currentis directly related to thethermodynamic instability of theair mass.

I If the maximum temperatureexcess for a surface parcel risingthrough the atmosphere is only 2◦

C, then one could expect amaximum of 2◦ C of warmingwithin the FTR current.

I Likewise, if the maximumtemperature excess for the risingsurface parcel was 8◦ C, then onecould expect up to 8◦ C ofwarming within the FTR current.

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I The strength of the cold pool isalso directly related to thethermodynamic instability in theenvironment. The potential coolingwithin the cold pool increases forboth increasing lapse rates as wellas increasing dryness (and thelowness in θe) at mid levels.

I In general, the potential strengthof the rear-inflow jet increases forincreasing amounts of instability(CAPE) in the environment.

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I The magnitude of the vertical windshear is yet another contributor tothe strength of the rear-inflow jet.

I Stronger shear tends to strengthenthe RIJ by producing enhancedlifting at the leading edge of thesystem, which leads to a stronger,more continuous FTR ascendingcurrent.

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I The result is that more warm air istransported aloft, enhancing thegeneration of horizontal vorticity,which enhances the magnitude ofthe RIJ. A strong FTR current alsotends to lead to a stronger coldpool as well, since strongerconvection leads to strongerdowndrafts.

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Rear-Inflow Jet: Affecting Squall Line Evolution

Generally, the rear-inflow jet entrains additional mid-level dry airinto the rainy downdraft, further strengthening the cold pool. Twooverall scenarios may then evolve.

I Descending RIJ

I Elevated RIJ

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Descending Rear-Inflow

I If the buoyancy gradientsassociated with the warm air aloftare weaker than those associatedwith the rear flank of the coldpool, then the rear-inflow jetdescends and spreads along thesurface further back in the system.

I In this case, the negative horizontalvorticity associated with therear-inflow jet is of the same signas that being produced by theleading edge of the cold pool.

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Descending Rear-Inflow

I The resultant vorticity interactionmakes the effective c/∆u ratioeven larger, forcing the system totilt even further upshear andcontinue to weaken.

I This is the most commonlyobserved scenario, occurring inenvironments with relatively weakshear and/or weak CAPE.

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Elevated Rear-Inflow

I If the buoyancy gradients aloft arestrong relative to the cold poolbelow, the rear-inflow jet tends toremain more elevated and advancescloser to the leading edge of thesystem.

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I The horizontal vorticity producedby the speed shear below therear-inflow jet is now of the samesign as the environmental shear.The resultant vorticity interactionthen reduces the net impact of thecold pool circulation, bringingc/∆u closer to the optimal ratio of1, enhancing the leading-lineconvective updrafts and creating amore vertically erect structure.

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I This scenario occurs inenvironments with relatively strongshear and/or large CAPE and isespecially associated with thedevelopment of severe bow echoes.

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Rear-Inflow Jet: Strength Limits

I Observations and modeling studiessuggest that rear-inflow jets vary instrength from a few ms−1 for weaksystems, to 10-15 ms−1 formoderately strong systems, to 25to 30 ms−1 for the most severesystems such as bow echoes. TheseRIJ strengths are relative to stormmotion, i.e., actual ground-relativewinds may be much stronger.

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Rear-Inflow Jet: Strength Limits

I Weisman (1992) quantified thedependence of rear-inflow jetstrength on vertical wind shear andbuoyancy for numerically simulatedconvective systems and confirmedthat rear-inflow strength increasesfor increasing CAPE and increasingvertical wind shear.

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Rear-Inflow Jet: Large-Scale Causes

I Imagine a synoptic pattern like thisidealized scenario that is commonlyassociated with severe squall linesincluding bow echoes (Johns,1993). For a squall line developingin the brown threat area, we cansee that stronger flow in the regionof the polar jet would enhance therear-inflow jet associated witheither the squall line or anembedded bow echo developing inthe northern portion of the area.

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Rear-Inflow Jet: Large-Scale Causes

I Additionally, if the mid-levelstorm-relative winds aresignificantly stronger behind asquall line, these enhanced windscan also contribute to thegeneration of the rear-inflow jet,especially when the squall line isexpanding rearward to produce alarge stratiform precipitationregion.

I Of course, enhancements in thelarge-scale wind field behind thesquall line need not be present forthe production of a significantrear-inflow jet.

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Rear-Inflow Jet: Summary

I During the mature stage of an MCS, the convective cellsspread rearward transporting warm air aloft. The surface coldpool also extends rearward due to the rearward expandingrainfield.

I The juxtaposition of the warm air aloft over a cold poolproduces lower pressure at mid levels, leading to mid-levelconvergence. The flow that converges in from the rear of thesystem at mid levels is known as the rear-inflow jet.

I The formation of the RIJ can also be explained by thehorizontal buoyancy gradients at the back edge of the system,which generate a vertically stacked horizontal vorticity coupletthat induces the rear-inflow jet.

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I The strength of the RIJ is directly related to the strength ofthose buoyancy gradients, i.e., the relative warmth of the FTRcurrent and the relative coolness of the cold pool.

I The RIJ strength is also affected by the strength of thevertical wind shear. Stronger shear produces enhanced liftingat the leading edge of the system, which leads to a strongerFTR current and enhanced warm pool.

I In weak shear, lower CAPE environments, the warm pool alofttends to be weaker than the cold pool. In this case, the RIJdescends further back in the system.

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I In stronger shear/higher CAPE environments, the warm poolaloft tends to be comparable to the cold pool. This keeps theRIJ elevated until much closer to the leading line convection.This is usually the case with severe bow echoes.

I Storm-relative RIJ strengths vary from a few ms−1 for weaksystems, to 10-15 ms−1 for moderately strong systems, to 25to 30 ms−1 for the most severe systems, such as bow echoes.

I In general, RIJ strength increases for increasing CAPE andincreasing vertical wind shear.

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Model Simulations of Quasi-2D Squall Lines

I Simulations are presented which characterize a weak-shearscenario, a strong-shear scenario, and a scenario with strongshear at 45◦ to the line. The amount of CAPE for all was2200 J/kg.

I The weak-shear simulation is run in an environment with 10ms−1 of shear over the lowest 2.5 km AGL, with constantwinds above 2.5 km, and demonstrates a squall line that tiltsupshear and weakens by 3-4 h into its evolution.

I The stronger-shear simulation is run in an environment with20 ms−1 of shear over the lowest 2.5 km AGL, anddemonstrates a squall line which maintains its strengththrough the full 6 h of the simulation.

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Model Simulations of Quasi-2D Squall Lines

Horizontal cross section at .5 km. The fields shown includereflectivity, storm relative winds, and an updraft contour wherew > 1.5 ms−1 (in yellow). Spacing for wind vectors is 6 km.

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Documents

Jeremy A. Gibbstwister.caps.ou.edu/.../chapter4_presentation4.pdf · Squall Lines: Development of Supercell Lines I Most often, squall lines are composed of ordinary cells. I But