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Mesoscale
Gravity Waves
MEA 444
January 20, 2005
Outline
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Gravity Wave Theory Overview
Numerical Model Description
Synoptic Overview
Uccellini and Koch (1987) Synoptic Pattern
 Surface & 300mb
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Generation Mechanisms
Moist Convection
 Geostrophic Adjustment
 Shearing Instability
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Mesoscale Gravity Waves
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As defined by Uccellini and Koch 1987:
Either a singular wave of depression or a wave
packet with these characteristics:
Horizontal wavelength
 Wave period
 Surface Pressure Perturbation
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50-500 km
1-4 hours
0.2-12 mb
Rossby Adjustment Theory
Internal Gravity Waves
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Wave disturbances in which the restoring force of buoyancy acts
on parcels displaces from hydrostatic equilibrium.
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Unlike external waves, internal waves can propagate vertically.
Vertical wind shear can also destabilize parcels.
Coriolis effects can alter wave frequency and phase characteristics
if period of wave is long enough (gravity-inertia waves)
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Wave Tilt
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Note:
u* ' p'  0
Wave Groups
Vertical Propagation
Mesoscale gravity waves will become incoherent
quickly due to vertical energy propagation unless:
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a means exists to prevent
energy loss:
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Wave ducting
Wave over-reflection
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a means exists to provide
wave energy:
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Shearing instability
Wave-CISK
Wave Duct
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Highly reflective wave duct created by combined
temperature structure and critical levels (Lindzen and
Tung 1976)
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Phase speed of a ducted wave relative to the mean flow:
CDUCT ,n
D1 N DUCT
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1 2  n 
n = order of wave mode
*Note: Duct properties determine wave phase speed.
Wave Duct Requirements
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Requirements for highly
reflective wave duct:
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Statically stable lower layer
Duct thick enough to
accommodate λz/4 for given
CDUCT.
No critical level in duct which
could absorb wave energy.
Critical level with low Ri in
upper layer with conditional
instability.
Event Overview
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At 1700 UTC on 12
December 2002, a large
amplitude gravity wave
developed over central Texas.
It accompanied a cyclone
toward the East Coast, and in
the process it reorganized
precipitation into band-like
formations and produced
gusty surface winds, ranging
from 20 to 35 ms-1, across
the southeastern U.S.
Large Amplitude Gravity Wave Defn.
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Bosart et al. (1998) defined a large amplitude
gravity wave as one which displayed:
Amplitudes of 3-6 hPa
 Wavelengths of 100-200 km
 Phase speeds of 15-35 ms-1
 Durations of at least 2-3 hours.
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Observations – Pressure
Observations - Wind Profiler
Observations - Pressure
Observations - Wind Profiler
Observations - Pressure
UK87 Synoptic Pattern
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Uccellini and Koch (1987)
found a common synoptic
pattern among gravity
wave events:
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300 mb ridge axis to the
northeast
300 mb inflection axis to
the southwest
Surface warm or stationary
front to the south
In Addition….
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Uccellini and Koch (1987) noted that the
synoptic pattern was not sufficient by itself for
gravity wave development.
There also needed to be a jet streak propagating
away from the upper-level trough and toward
the inflection axis in the height field.
Lower Levels
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The key element in
the lower levels of
the atmosphere was
the baroclinic zone
located along the
Gulf Coast,
extending eastward
from southern Texas.
850 mb Temperature (C), Height (m), Wind (m/s)
300 mb
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The ridge/trough
amplification resulting in
increased flow curvature.
Inflection axis in the
height field over central
Texas.
Propagation of a jet
streak toward
northeastern Texas and
away from the trough
axis.
300 mb Isotachs (kts), Height (m), Wind (m/s)
Just To Note…..
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The gravity wave developed in a region with:
Surface warm front to the south
 300 mb ridge axis to the northeast
 300 mb inflection axis to the southwest
 Jet streak propagating away from 300 mb trough
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Thus, it satisfied the Uccellini and Koch (1987)
gravity wave synoptic situation.
Gravity Wave Generation
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Three gravity wave generation mechanisms were
examined:
Moist Convection
 Geostrophic Adjustment
 Shearing Instability
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Moist Convection
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There is still no real consensus as to what role
moist convection plays in gravity wave
formation.
Some have shown that convection is an important
source for gravity wave generation (Lin and Goff,
1988; Powers and Reed, 1993)
 Others found that gravity waves can trigger
convection. (Zhang and Fritsch, 1988)
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Moist Convection
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Moist convection seems to have played two roles
in the gravity wave generation:
Altering of the synoptic environment which
increased the upper-level divergence and enhanced
the geostrophic adjustment process.
 Actual generation of the gravity wave .
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Moist Convection
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Precipitation developed over southern Texas just before
1200 UTC.
Sutcliffe’s Self-Development
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As time progressed,
a pattern of Sutcliffe’s
Self-Development
Concept developed.
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Latent heat release
Pressure ridge increase
Slowed ridge progression
Trough deepening
Increased flow curvature
Jet streak acceleration
due to mass evacuation
Moist convection resulted in increased upper-level
curvature in the flow and along-stream flow accelerations
toward northeastern Texas.
Moist Convection Generation
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Wave generation occurred as
the intensifying convection
encountered the low-level
statically stable air just west of
Austin, TX.
Since the convection displaced
air parcels vertically, the
atmosphere was "out of
balance" because a component
of the displacement was
horizontal due to convection.
Thus, the large amplitude
gravity wave developed in an
attempt to restore the
atmosphere to balance.
Balanced Flow
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Within a balanced flow system, cross-stream ageostrophic
motions are directed toward the anticyclonic (right) side of
a jet, which creates the upper-level of the thermally
indirect circulation perpendicular to the jet exit region.
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This cross-stream arrangement, determined by the
equation dV/dt = fVag x k, is the result of air parcel
deceleration in the jet exit region, causing kinetic energy to
be converted into available potential energy.
Unbalanced Flow
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When the cross-stream ageostrophic motions in the jet exit
region are directed toward the cyclonic (left) side of the jet, it
implies that air parcels are actually accelerating in the leftward
cross-stream direction rather than decelerating in the rightward
cross-stream direction.
Therefore, the air parcels unable to accomplish the energy
conversions required to maintain the atmosphere in a state of
balance.
Vag
Geostrophic Adjustment
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Uccellini et al. (1984) found that
unbalanced ageostrophic motions
occurred in a case in which a jet
streak approached a mass ridge as a
jet propagated downstream from
the location of the geostrophic jet.
Thus, an air parcel in the exit region
of the geostrophic jet found itself
in the entrance region of the actual
jet.
This led to unbalanced ageostrophic
winds in the exit region of a
geostrophic wind maximum, as
defined by the cross-stream
ageostrophic flow directed toward
the cyclonic side of the jet.
Ф-1
Ф
Ф+1
f  2 J (u, v)   2  u  0
Geostrophic Adjustment
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Uccellini et al. (1984) also found Rossby
numbers of Ro > 0.9 located in the exit region
of the geostrophic jet.
Zack and Kaplan implemented a nonlinear
balance equation (NBE = f  2J (u, v)   2  u )
and found that “significantly” large values
(~10-8 s-2) indicated the location of gravity wave
genesis.
Ageostrophic Motions
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Separation occurred
between the actual and
geostrophic jets as the
actual jet propagated
downstream of the
trough axis.
Conforming to the
Uccellini et al. (1984)
study, ageostrophic flow
became oriented toward
the cyclonic side of the
geostrophic jet exit
region as the speed of
the actual jet increased.
Rossby Number
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Similar to the
findings of Uccellini
et al. (1984), the
region of
unbalanced flow
produced values of
Ro > 0.9.
Nonlinear Balance
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The nonlinear
balance equation did
indicate the region of
gravity wave genesis,
although it seemed to
do a better job in
pinpointing the
location of the wave
after formation had
occurred.
Shearing Instability
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Shearing instability has been found to be a likely
generation mechanism in an environment with
strong vertical shear, such that Ri < 1/4, at an
altitude where the wave propagation speed
matches the wind speed, also known as the
critical level (Miles(1961); Howard (1961);
Einauldi and Lalas (1973); Gossard and Hooke
(1975)).
Shearing Instability
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Wave phase
speed of 15 to
20 ms-1.
Wind velocity
of 15 to 20 ms1 between 600550 mb.
Thus, critical
level is between
600-550 mb.
Since Ri < ¼ at the critical level, it can be assumed
that shearing instability was present at wave genesis.
Conclusions
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The large amplitude gravity wave that developed
at 1700 UTC on 12 December 2002 adhered to
the common gravity wave synoptic pattern
prescribed by Uccellini and Koch (1987).
Upon examination of the various wave
generation mechanisms, it was shown that moist
convection, geostrophic adjustment and
shearing instability were all present in the region
of gravity wave genesis over central Texas.