ATMO 201: Atmospheric Science

Convective: Part 2Weather Systems Fall 2015Outline:a. dynamics of rotating thunderstorms (supercells)

b. storm splitting right vs. left moversLast timeIdentified the main classifications of convective stormsLooked at how vertical wind shear affects the mode of convectionSaw how we can use a hodograph to look at the shearQuestions for todayWhat is helicity and how does it relate to convective storms?Why do updrafts rotate?Why can supercells maintain their intensity for so long?What causes storm splitting?Why do supercells move in the directions they do?

The hodographA way to visualize the vertical wind shearUsing polar coordinates, a point is plotted at the tip of the wind vector at each levelThe tangent line represents the shear vector

Storm-relative motionThe storm motion vector can also be plotted on the hodographThen, the storm-relative winds can also be plotted

cStorm-relative motionThe area signed out underneath this is the storm-relative helicityThis is often calculated from 0-1 or 0-3 km

cStorm Relative Environmental Helicity (SREH)A wind profile that maintains a single direction and increases its speed with height generates a shear vector parallel to the wind direction. This shear results in a horizontal vorticity whose axis (the vorticity vector) is perpendicular to the wind direction. We refer to this as crosswise vorticity.

Storm Relative Environmental Helicity (SREH)a wind profile whose speed remains constant, but whose direction changes with height generates a shear vector perpendicular to the mean wind.the resulting vorticity vector is parallel to the mean wind. We refer to this as streamwise vorticity in the real world, vorticity is rarely perfectly crosswise or streamwise. Thus, when we say streamwise vorticity we refer to the vector component of the vorticity that is oriented parallel to the mean flow.

Helicity - Tilting

Legend:

Pink area = updraft

Blue arrow = shear vector

Red arrow = vertical velocity gradient

Curved arrow = relative vorticity anomaly 9(Markowski and Richardson, adapted from Davies-Jones 1984)

Storm motion is off the hodographHelicity = largeUpdraft likely to rotateStorm motion is on the hodographHelicity = 0Updraft will not rotateHelicity

Helicity

HelicityTo summarize the development of midlevel rotation within a thunderstorm environment:

Initially a vorticity couplet develops owing to the tilting of environmental horizontal vorticity. This is immediately advected by the storm-relative winds such that, in the case of streamwise vorticity, the rotation and the updraft become more in phase.The wind hodographComposite hodograph of > 400 proximity soundings near cyclonic supercells in the US

Note that the storm motion is completely off the hodograph it lies to the right of the wind at all levels!

(Markowski and Richardson, adapted from Markowski et al. 2003)The wind hodograph

Wind profiler obs nearHallam, NE F4 tornado

(courtesy Matt Bunkers, NWS Rapid City)The wind hodograph

Jackson, MS 1200 UTC sounding, 27 April 2011

01-km SRH of 490 m2/s2 for right-moving storm (!!!)ExceptWeisman and Rotunno (2000) point out that supercells are also observed in environments with straight hodographsThe helicity theory would require fundamentally different dynamics for this to occurThey point out that the helicity argument assumes a priori that a steady, propagating updraft existsBetter for after the fact explanation, rather than predictionDoes the storm rotate because it propagates, or does it propagate because its rotating? Weisman and Rotunno argue that it is the latterTo understand the development and maintenance of a rotating storm, its better to consider the effects of shear on an updraftIn this theory, the formulation of the dynamics of supercells with straight vs. curved hodographs are basically the same

Weisman, Morris L., Richard Rotunno, 2000: The Use of Vertical Wind Shear versus Helicity in Interpreting Supercell Dynamics. J. Atmos. Sci., 57, 14521472.

Conceptual Model of Tornadic Thunderstorm(Lemon and Doswell 1979)

Dallas/Fort Worth tornadic supercells from 2012

20Six-state supercell, March 2006

Tuscaloosa/Birmingham tornadic supercell, 27 April 2011

(from Brian Tang, NCAR)22Supercell dynamicsUse anelastic equations (no sound waves)Also neglect friction and Coriolis (Coriolis unimportant on these scales)

Horizontal and vertical vorticity equationsCan get vertical vorticity by tilting and/or stretchingIf no vertical vorticity initially, it must be produced by tiltingNo direct baroclinic generation of vertical vorticity

Vertical vorticityHorizontal vorticityVorticity tiltingConsider an isolated updraft in unidirectional shearLinearize (11.10), assuming no vertical vorticity initially:

y

vertical perturbation pressure gradientNonlinear effectsThis spin term dominates the nonlinear pressure perturbationThis says that pressure perturbations are related to the magnitude of vorticity: there will be low pressure where the magnitude of vorticity is greatTherefore, the strong rotation in the vortex pairs induces low pressure regardless of the direction of rotation

vertical perturbation pressure gradientWeve now tilted horizontal vorticity (which exists because of the wind shear) into the verticalWe have counter-rotating vortices on the flanks of the updraftAs the cloud grows, precipitation particles grow and lead to a downdraftIn weak shear, the outflow spreads out in all directions eventually cutting off the supply of warm moist airIn strong shear:easterly storm-relative flow prevents the cold outflow from surging eastward ahead of the stormLifting pressure gradients reinforce new updraft growth on the southern and northern flanks of the storm

Storm Splitting

y

vertical perturbation pressure gradientThe low pressure induced by the counter-rotating vortices leads to two separate enhanced updrafts the storm splits!A downdraft is not even required for the storm splitting process, though it can enhance itAfter the split, one (cyclonic) supercell moves to the right, and one (anticyclonic) to the left of the windIn unidirectional shear (straight hodograph), both storms now have storm-relative helicity, which enhances the updraft rotation

STORM SPLITTING

A high perturbation pressure will exist where the shear vector points toward increasing vertical motion (and vice versa)

In the case of a clockwise-turning hodograph, the pressure perturbations (and helicity) favor the right-moving supercellstraight hodographcurved hodograph

Enhanced upward motion on downshear side: keeps storms from tilting over but doesnt have an effect on right or left sideNow, we get enhanced upward motion on the right flank (relative to the shear) the right mover is enhanced and left mover weakensstraight hodographcurved hodographRight-mover is favored!Straight vs. curved hodograph

StraighthodographCurved hodographMarkowski and Richardson, adapted from Klemp (1987)

Markowski and RichardsonStraight hodographMarkowski and RichardsonCurved hodograph

Summary shear-induced pressure gradientsIn an environment with vertical wind shear, updrafts tilt horizontal vorticity into the vertical, creating counter-rotating vorticesWhen the updraft grows, the linear effect keeps it from tilting over in the shear by enhancing upward motion on the downshear sideThe nonlinear effect leads to low pressure at both of the vortices both updrafts strengthen and the storm splitsIn an environment with a straight hodograph, the rotation in both storms is enhanced by storm-relative helicityIn an environment with a clockwise-turning hodograph, the right-moving storm is favored:Storm-relative helicity is greater, therefore greater rotationPressure perturbations favor development of new convection on right sides of updraftsStraight vs. curved hodograph

From Davies-Jones et al. (2001); also Table 8.1 in MMMConvective storm matrixhttp://www.meted.ucar.edu/convectn/csmatrix

http://www.crh.noaa.gov/images/unr/soo/scm/Hodograph_Spreadsheet.xls

Interactive hodograph spreadsheet

Time lapse photography 2005, Kevin Tory & Wesley Terwey