Multicell SquallLine Structure as a Manifestation of Vertically Trapped Gravity Waves

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Multicell Squall-Line Structure as a
Manifestation of Vertically Trapped Gravity Waves

• Ming-Jen Yang and Robert A. House Jr.Mon. Wea.
  Rev., 123, 641-661

Hsiao-Ling Huang 2003/12/29
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Introduction

• Byers and Braham(1949) identified three stages in
  the evolution of an ordinary cell the cumulus
  stage (updraft alone), the mature stage (updraft
  and downdraft), and the dissipating stage
  (downdraft alone).
• Fovell and Ogura(1988) individual cells moved
  rearward relative to the gust front as they aged,
  transporting hydrometeors in their updrafts into
  the trailing portion of the storm, and the new
  cells cutting off the moisture supply of the
  older cells.
• The gravity wave structure excited by convection
  of the squall line system(1985/06/1011), which
  is the focus of this study.

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Numerical model and initial conditions

• Numerical model
• Compressible nonhydrostatic cloud model,
  microphysical bulk parameterization, ice-phase
  microphysics is included.
• Both 2D and 3Dversions of the model.
• 2D simulationgrid points 455 (H) 62
  (V)domain 4814 km(H)21.7 km(V)

314 km
2250 km
2250 km
Fine mesh1 kmStretch grid is 1.0751
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• 3D simulationgrid ?x ?y 2 km (H), 31
  points (V)domain 240 km(x)60 km(y) 21.7 km(z)

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• Initial conditions

1985/06/10/2331 UTC Enid(END), Oklahoma. T, TD,
u, v 1985/06/10/2330 UTC Pratt(PTT), Kansas.
Low-level moisture
1985/06/1011
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A 5-km deep, 170-km-long cold pool of ?T -6 K
and ?qv -4 g kg-1 ------2D simulation?T -10
K and ?qv -6 g kg-1 ------3D simulation
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2D simulation results
Mesoscale structure
Intense precipitation cells at the leading edge
and much weaker precipitation in the trailing
stratiform region.
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2D simulation
Dual-Doppler radar analysis of Biggerstaff and
Houze (1993)
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2D simulation
Dual-Doppler radar analysis of Biggerstaff and
Houze (1993)
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Transient convective structure
w, qra, qsn
w, p
w, u
w, ?
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bight band
M
M
Dual-Doppler radar analysis
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Gravity wave interpretation
The traditional multicell model would suggest
that the spreading cold outflow of an old cell
enhances convergence, which then triggers the
formation of a new cell. The period for the
regeneration of gravity wave updrafts is 12-14
min, which is the same as the generation period
of precipitation cells in the surface rainfall
rate field.
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Convective cell trajectories(updraft)
The convective updraft cells always propagate
rearward relative to the gust front, regardless
of the direction of the airflow in their near
environments. The updraft cells move at
velocities significantly different from the
airflow in their near surroundings.
The air-parcel trajectories(airflow)
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vertical velocity z 5.25 km t 10-11 h
A property of a vertically propagating gravity
wave.
vertical velocity x 18 km t 10-11 h
A Characteristic of trapped waves.
A gravity wave structure different from those
above the tropoausevertically trapped gravity
waves.
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Three-dimensional simulation results
3 D , Z 6.3 km , t 5 h
2 D , t 11 h
w, qra, qsn
The heavy line is the surface gust front
determined by the ? -1
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3 D , Z 0.7 km , t 5 h
3 D , Z 11.9 km , t 5 h
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Linear theory presentation of model gravity waves
p nondimensional pressure N
Brunt-Väisälä(bouyancy) frequency cs
basic-state sound speed
are functions of z Q the latent heating
produced by convection.
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To remove the effect of the decrease in density
with height by defining new variables (Bretherton
1966)
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when cs ?8, then (10) can be written in a simpler
form,
and eliminate
A1
A2
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Taking ,we can eliminate
with the aid of (12) to yield a single equation
for
We obtain a single equation for
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Substitution of (14) into (13)
l2 is called the Scorer parameter (Scorer 1949)
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Discussion
Linear theory result
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Characteristics of trapped waves in the simulated
squall line
The leading portion of the simulated squall
linehorizontal wavelengths ? 16 20 km,
storm-relative phase speeds c -20 -25
ms-1,the main gravity wave periods T ?/c
10.7 16.7 min. The trailing stratiform
region(with weaker amplitudes) horizontal
wavelengths ? 25 35 km, storm-relative
phase speeds c -30 -40 ms-1. The period of
convective cells are the same as the gravity wave
periods.
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Trapping mechanisms
l2 gt k2 ---a vertically propagating wave.
l2 lt k2 ---a trapped wave.
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The waves become trapped in the mid- to upper
troposphere because of the strong decrease of
Scorer parameter with height as a result of
strong vertical wing shear and the reduced static
stability aloft. Waves are trapped in lower
levels because of the rigid ground.
Trapping of gravity waves in the troposphere is
not a result of the strong static stability in
the lower stratosphere.
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Conclusion

• The old cell dissipates when a new cell appears
  ahead if it along the gust front and cuts off
  the old cells supply of moisture and buoyant
  air.
• The convectional interpretation of the cutoff
  process is actually a gravity wave phenomenon.
  Updraft cells behind this low-level leading edge
  updraft are transient gravity wave features.
• Convective cells in the troposphere exhibit a
  quadrature relationship between the w and p (or
  u) fields that indicates they are vertically
  trapped gravity waves(mid- to upper-troposphere).

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• In the trailing stratiform region, the amplitudes
  of these gravity waves become weaker, but their
  wavelengths become longer with faster phase
  speeds.
• The gravity wave explanation for the
  multicellular structure of thunderstorms and
  squall lines may lead to a new understanding of
  convective momentum transport.

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