Jet Streaks

GEOG 451 Dynamic Meteorology Ball State University

Presented by Kelly Boyd December 12th 2011

Summary of My Lecture • Review of basic concepts of jet streaks

– Definition and characteristics • Dynamic equations that explain jet streaks

– Jetogentic functions • Cross-Jet Ageostropic term and Coriolis term

– Vertical motions of jet streaks – Propagation over a distance per time

• Why jet streaks are important in weather forecasting – Produces heavy snowfall events in the winter – Severe weather events in the spring/summer/fall

• climatology of jet streaks • (case study by Clark et al. 2009)

Jet Streaks (J.S.) • An area of a jet stream with maximum winds

– Basic forcing mechanism are thermal winds • Winds that usually blow >160 knots • High level located around 300-250mb level • 250-1000 km in length • 50 to 200 km in width

– Evolve over a scale of a few hours to days • Propagation over an area is slower than the speed of the

winds within a jet streak • J.S. can be found in both the Polar and Subtropical jets

Forcing Mechanism of Jet Streaks • A strong/large temperature gradient at the surface is

usually a sign of jet streaks aloft around the 300mb level

Jet Streaks Continued – J.S. can not only advect temperatures and humidity but also itself – Strong influence on mesoscale systems and deep moist convection – Most jet streaks have strong PVA (created by vorticity shear)

Image Source: Matt Eastin Ph.D. from UNC Geography Dept.

Jet Streak Wind Velocity • Like all theoretical winds aloft, velocity within a jet

streak (the real wind, M in the diagram) can be calculated by first computing the: – Geostrophic wind component (Vg) or (G in the diagram) – Agestrophic wind component (Va) or (Vag in the diagram )

M = Vg (G) + Vag (Vg) Image From: Stull, R., 2000: Meteorology for Scientist and Engineers, pg. 292

The “four quadrant’’ model

Jetogenetic Function • A quantitative kinematic process to measure jet

streaks intensity – The rate of change of the intensity of the jet streak

following air-parcel motion – Either intensifying or weakening

– 𝛻2 is the 3D Laplacian of the horizontal wind speed as a f(time)

• (AKA complex advection) – J is a unit-less #

( )uDtDJ 2∇−=

Source: Bluestein, H. B., 1986: Fronts and jet streaks: A theoretical perspective, pg. 203

Measuring a Jet Streak • The best way to represent a jet streak’s intensity in a

coordinate system is one in which an air parcel moves along a jet streaks same frame of reference – (Eulerian or Lagrangian?)

• The formula assumes: – 𝛻𝑢 = 0 in the center of the jet streak (advection WRT u is not

changing) – The jet streak is oriented E to W (zonally) – Jetogenesis /Jetolysis is measured along or near a jet axis

yvvfJ a ∂∂

−∇−= β220

Cross-Jet Ageostrophic Term Coriolis Term

Source: Bluestein, H. B., 1986: Fronts and jet streaks: A theoretical perspective, pg. 203

Cross Jet Ageostrophic Term

• The dominate of the two terms (in mid latitudes) – Again 𝛻2is the Laplacian operator (complex advection WRT “va”) – 𝑣𝑎 is the ageostrophic component of the wind in the y-direction

• A jet streak will increase in magnitude if va is maximized along the jet axis

avf 20∇−

Arrows represent Va Winds Red arrows = Jetogenesis Blue arrows = Jetolysis Jetogenesis (J > 0) Jetolysis (J < 0)

Image Source: Matt Eastin Ph.D. from UNC Geography Dept.

Coriolis Term

• Often small in magnitude (sometimes neglected)

– Remember , 𝛽 = 𝑑𝑑𝑑𝑑

~10−11𝑚−1𝑠−1 (very small)

– 𝜕𝑣𝜕𝑑

is the wind speed over a poleward distance towards the poles

• When taken into effect (usually in wx. models): – Jeteogenesis -occurs wherever the meridional wind decreases as

one moves northward – Jetolysis -occurs wherever the meridional wind increases as on

moves northward

yv∂∂

− β2

Source: Bluestein, H. B., 1986: Fronts and jet streaks: A theoretical perspective, pg. 203

Vertical Motion of Jet Streaks • Can be determined using a simplified vorticity equation:

• Thus, the vorticity change through time can be measured by a parcel of air moving through the jet streak – Assuming a jet streak in the N.H.

• Used in wx. models

( )Div−≈DtDζ

Image Source: Matt Eastin Ph.D. from UNC Geography Dept.

Easier Equation for Vertical Motion • To find mid-level vertical velocity (wmid) below a left exit

region and right entrance region of a J.S.

– We can derive an Wmid equation using the 2D continuity equation and equation of ageostrophic wind velocity (W.R.T. East-West)

– where U is the velocity of the wind through the J.S. core – ΔU is the change in wind speed from the center of the J.S. to the

exit region – f is the Coriolis parameter – Δx is the E-W distance of the jet streak – Δy is the N-S distance of the jet streak (width) – Δz is the vertical thickness at the core of the jet streak

Formula From: Ronald Stull, 2000 Meteorology for Scientist and Engineers, pg. 292

𝑤𝑚𝑚𝑑 =𝑈 ∙ ∆𝑈𝑓 ∙ ∆𝑥

∙∆𝑧∆𝑦

Example • Suppose a jet streak of width of 1000 km has a core wind

speed of 50m/s that decreases eastward to 25 m/s across a distance of 1000 km. If the jet region is 5km thick, find the mid-level vertical velocity.

• This answer is fairly large compared to average V.V. values • A value such as this can drastically intensity a cyclone (both

in synoptic and mesoscale)

𝑤𝑚𝑚𝑑 =(50 𝑚−1𝑠−1) ∙ (25 𝑚−1𝑠−1)

(10−4𝑠−1) ∙ (106𝑚)∙

5𝑘𝑚1000 𝑘𝑚

= 0.0625 𝑚−1𝑠−1

Formula From: Ronald Stull, 2000 Meteorology for Scientist and Engineers, pg. 292

Detecting Vertical Motion of J.S.

Image Source: Matt Eastin Ph.D. from UNC Geography Department

Background of Vertical Propagation • The movement and direction of a jet streak/stream can be

determined by quasi-geostrophic analysis through the height tendency equation with geostrophic coordinates:

• It is calculated by eliminating the ageostrophic vertical motion (omega) between the Q-G thermodynamic equation and the Q-G vorticity equation

• Q-G height tendency equation involves the time derivative of the height field (chi)

• Helps predict the movement of jet streaks/streams in wx. models

𝛻2 +𝑑02

𝜎𝜕2

𝜕𝜕2𝜒 = −𝑓0𝑉𝑔 ∙ 𝛻𝜂𝑔 +

𝑑02

𝜎𝜕𝜕𝜕

𝑣𝑔 ∙ 𝛻𝜕𝜕𝜕𝜕

Source: Bluestein, H. B., 1986: Fronts and jet streaks: A theoretical perspective, pg. 208-209

A.) 3D Laplacian of height tendency

B.) Advection of absolute geostrophic vorticity WRT geostrophic wind

C.) Vertical variation of geostrophic thickness advection

Propagation of Jet Streaks • For simplicity, we will assume the jet streak is at the 300 mb level

aloft dropping the temperature advection term (C) (Why assume?): – If B is positive, then A is positive

• There is a height fall (PVA) – If B is negative, then A is negative

• There is a height rise (NVA)

𝛻2 +𝑓02

𝜎𝜕2

𝜕𝜕2𝜒 = −𝑓0𝑉𝑔 ∙ 𝛻𝜂𝑔

Image Source: Matt Eastin Ph.D. from UNC Geography Dept.

A.) 3D Laplacian of height tendency

B.) Advection of absolute geostrophic vorticity WRT geostrophic wind

In this case the trough is deepening since there is PVA and the height is falling

Why J.S. are important in Severe Wx. • Jet streaks along with isotropic lift, frontogensis and

some degree of instability causes strong upward motion • Add sufficient moisture from a L.L.J. can equal a large

amount of precipitation or severe weather

Image Source: NWS Louisville: http://www.crh.noaa.gov/lmk/?n=jet_streaks

Severe Weather and Jet Streaks • Jet streaks ahead of fronts cause enhanced convection through

vertical wind shear – Cause a combination of ageostrophic circulations from jet streaks and the

front can create strong lift along the warm (unstable side of the front) – Low level jet will bring warm air/moisture into the area

Image Sources: Bluestein 1986, Fronts & jet streaks: A theoretical perspective, pg. 210 and the Louisville NWS http://www.crh.noaa.gov/lmk/?n=jet_streaks

A Climatology of J.S. & Severe Wx. • Conducted by: Clark, et al., 2009: Climatology of storm

reports relative to upper-level jet streaks. Weather Forecasting, 24, 1032-1051.

• Study and Spatial/Temporal Areas: – They examined the location of all severe wx. reports (tornado,

hail, winds) relative to any upper-level jet streaks – Mid-western U.S. From 1994 to 2004 (March to September)

• Expectations/ hypothesis : – Increased vertical shear and enhanced motion will cause greater

storm longevity and parcels being lifted to the LFC in the right entrance and left exit regions

A Climatology of J.S. & Severe Wx. • Results from Clark et al 2009:

– A total of 126,864 storm reports occurred during the ten year period of the study

– 84% were associated with upper-level jet streaks

A Climatology of J.S. & Severe Wx. • Results continued: • All reports were geo-referenced to the four quadrant model

associated with jet streaks with reference to entrance and exit quadrants

• It was found yes indeed, a majority of severe wx. reports were located in the right- entrance and along jet streaks axis in the exit region

A Climatology of J.S. & Severe Wx. • Top left: 250hPa winds &

divergence

• Top right: MSLP, 10 m height winds, divergence

• Bottom left: Surface CAPE/CIN

• Bottom right: Surface height

Summary of Lecture • Defined Jet Streaks & Forcing Mechanisms • Jet Streak Velocities • Jetogenetic Functions • Measuring Jet Streak Intensities • Jet Streak Vertical Motions • Jet Streak Propagation • How/Why Jet Streaks are Important In Severe Wx.

Questions? • Thanks for listening!

– Good luck on Finals!

Picture of a Jet Stream from Space: Via NASA

Sources: • Bluestein, H. B., 1986: Fronts and jet streaks: A theoretical perspective.

Mesoscale Meteorology and Forecasting, Amer. Meteor. Soc., 173-215. • Clark, A. J., C. J. Schaffer, W. A. Gallus, and K. Johnson-Omara, 2009:

Climatology of storm reports relative to upper-level jet streaks. Wea. Forecasting, 24, 1032-1051.

• Eastin, M. D., 2009: University of North Carolina Charlotte, Departmetn of Geography Advanced Synoptic Course, Lecture 11: Jet Streaks, Link: http://geoearth.uncc.edu/people/meastin/class/advsyn/METR4245-jets.ppt

• Holton, J. R. (2004). Synoptic-scale motions I: Quasi-geostrophic analysis, An introduction to dynamic meteorology: 4th edition (139 - 181). Burlington, MA: Elsevier Academic Press.

• NWS Louisville Website Published July 10th 2009: “Entrance of Jet Streaks” Link: http://www.crh.noaa.gov/lmk/?n=jet_streaks

• Stull, R. B., 2000: Meteorology for Scientist and Engineers. Brooks/Cole Cengage Learning., 2nd Edition, 291-293