mesoscale gravity waves

Mesoscale Mesoscale Gravity WavesGravity Waves

MEA 444MEA 444

January 20, 2005January 20, 2005

OutlineOutline Gravity Wave Theory OverviewGravity Wave Theory Overview Numerical Model DescriptionNumerical Model Description Synoptic OverviewSynoptic Overview

Uccellini and Koch (1987) Synoptic Uccellini and Koch (1987) Synoptic PatternPattern

Surface & 300mbSurface & 300mb Generation MechanismsGeneration Mechanisms

Moist ConvectionMoist Convection Geostrophic AdjustmentGeostrophic Adjustment Shearing InstabilityShearing Instability

Mesoscale Gravity WavesMesoscale Gravity Waves

As defined by Uccellini and Koch 1987:As defined by Uccellini and Koch 1987: Either a singular wave of depression or Either a singular wave of depression or

a wave packet with these a wave packet with these characteristics:characteristics: Horizontal wavelengthHorizontal wavelength 50-500 km50-500 km Wave periodWave period 1-4 hours1-4 hours Surface Pressure PerturbationSurface Pressure Perturbation 0.2-12 0.2-12

mbmb

Rossby Adjustment Rossby Adjustment TheoryTheory

Internal Gravity WavesInternal Gravity Waves Wave disturbances in which the restoring force of Wave disturbances in which the restoring force of

buoyancy acts on parcels displaces from hydrostatic buoyancy acts on parcels displaces from hydrostatic equilibrium.equilibrium.

Unlike external waves, internal waves can propagate Unlike external waves, internal waves can propagate vertically.vertically.

Vertical wind shear can also destabilize parcels.Vertical wind shear can also destabilize parcels. Coriolis effects can alter wave frequency and phase Coriolis effects can alter wave frequency and phase

characteristics if period of wave is long enough (gravity-characteristics if period of wave is long enough (gravity-inertia waves)inertia waves)

Wave TiltWave Tilt

Note: Note: 0''* pu

Wave GroupsWave Groups

Vertical PropagationVertical Propagation

a means exists to a means exists to prevent energy prevent energy loss:loss: Wave ductingWave ducting Wave over-Wave over-

reflectionreflection

a means exists to a means exists to provide wave provide wave energy:energy: Shearing instabilityShearing instability Wave-CISKWave-CISK

Mesoscale gravity waves will become Mesoscale gravity waves will become incoherent quickly due to incoherent quickly due to vertical energy propagation unless:vertical energy propagation unless:

Wave DuctWave Duct

Highly reflective wave duct created by Highly reflective wave duct created by combined temperature structure and combined temperature structure and critical levels (Lindzen and Tung 1976)critical levels (Lindzen and Tung 1976)

Phase speed of a ducted wave relative to the Phase speed of a ducted wave relative to the mean flow:mean flow:

nND

C DUCTnDUCT

211

,

*Note: Duct properties determine wave phase speed.*Note: Duct properties determine wave phase speed.n = order of wave moden = order of wave mode

Wave Duct RequirementsWave Duct Requirements

Requirements for highly Requirements for highly reflective wave duct:reflective wave duct: Statically stable lower Statically stable lower

layerlayer Duct thick enough to Duct thick enough to

accommodate λaccommodate λzz/4 for /4 for given Cgiven CDUCTDUCT..

No critical level in duct No critical level in duct which could absorb wave which could absorb wave energy.energy.

Critical level with low Ri Critical level with low Ri in upper layer with in upper layer with conditional instability.conditional instability.

Event OverviewEvent Overview At 1700 UTC on 12 At 1700 UTC on 12

December 2002, a large December 2002, a large amplitude gravity wave amplitude gravity wave developed over central developed over central Texas.Texas.

It accompanied a It accompanied a cyclone toward the East cyclone toward the East Coast, and in the Coast, and in the process it reorganized process it reorganized precipitation into band-precipitation into band-like formations and like formations and produced gusty surface produced gusty surface winds, ranging from 20 winds, ranging from 20 to 35 msto 35 ms-1-1, across the , across the southeastern U.S.southeastern U.S.

Large Amplitude Gravity Large Amplitude Gravity Wave Defn.Wave Defn.

Bosart et al. (1998) defined a large Bosart et al. (1998) defined a large amplitude gravity wave as one which amplitude gravity wave as one which displayed:displayed: Amplitudes of 3-6 hPaAmplitudes of 3-6 hPa Wavelengths of 100-200 kmWavelengths of 100-200 km Phase speeds of 15-35 msPhase speeds of 15-35 ms-1-1

Durations of at least 2-3 hours.Durations of at least 2-3 hours.

Observations – PressureObservations – Pressure

Observations - Wind Observations - Wind ProfilerProfiler

Observations - PressureObservations - Pressure

Observations - Wind Observations - Wind ProfilerProfiler

Observations - PressureObservations - Pressure

UK87 Synoptic PatternUK87 Synoptic Pattern

Uccellini and Koch Uccellini and Koch (1987) found a (1987) found a common synoptic common synoptic pattern among pattern among gravity wave events:gravity wave events: 300 mb ridge axis to 300 mb ridge axis to

the northeastthe northeast 300 mb inflection axis 300 mb inflection axis

to the southwestto the southwest Surface warm or Surface warm or

stationary front to the stationary front to the southsouth

In Addition….In Addition….

Uccellini and Koch (1987) noted that Uccellini and Koch (1987) noted that the synoptic pattern was not the synoptic pattern was not sufficient by itself for gravity wave sufficient by itself for gravity wave development.development.

There also needed to be a jet streak There also needed to be a jet streak propagating away from the upper-propagating away from the upper-level trough and toward the level trough and toward the inflection axis in the height field.inflection axis in the height field.

Lower LevelsLower Levels

The key element The key element in the lower in the lower levels of the levels of the atmosphere was atmosphere was the baroclinic the baroclinic zone located zone located along the Gulf along the Gulf Coast, extending Coast, extending eastward from eastward from southern Texas.southern Texas.

850 mb Temperature (C), Height (m), Wind (m/s)850 mb Temperature (C), Height (m), Wind (m/s)

300 mb300 mb The ridge/trough The ridge/trough

amplification amplification resulting in increased resulting in increased flow curvature.flow curvature.

Inflection axis in the Inflection axis in the height field over height field over central Texas.central Texas.

Propagation of a jet Propagation of a jet streak toward streak toward northeastern Texas northeastern Texas and away from the and away from the trough axis.trough axis.

300 mb Isotachs (kts), Height (m), Wind (m/s)300 mb Isotachs (kts), Height (m), Wind (m/s)

Just To Note…..Just To Note…..

The gravity wave developed in a region The gravity wave developed in a region with:with: Surface warm front to the southSurface warm front to the south 300 mb ridge axis to the northeast300 mb ridge axis to the northeast 300 mb inflection axis to the southwest300 mb inflection axis to the southwest Jet streak propagating away from 300 mb Jet streak propagating away from 300 mb

troughtrough Thus, it satisfied the Uccellini and Koch Thus, it satisfied the Uccellini and Koch

(1987) gravity wave synoptic situation.(1987) gravity wave synoptic situation.

Gravity Wave GenerationGravity Wave Generation

Three gravity wave generation Three gravity wave generation mechanisms were examined:mechanisms were examined: Moist ConvectionMoist Convection Geostrophic AdjustmentGeostrophic Adjustment Shearing InstabilityShearing Instability

Moist ConvectionMoist Convection

There is still no real consensus as to There is still no real consensus as to what role moist convection plays in what role moist convection plays in gravity wave formation.gravity wave formation. Some have shown that convection is an Some have shown that convection is an

important source for gravity wave important source for gravity wave generation (Lin and Goff, 1988; Powers generation (Lin and Goff, 1988; Powers and Reed, 1993)and Reed, 1993)

Others found that gravity waves can Others found that gravity waves can trigger convection. (Zhang and Fritsch, trigger convection. (Zhang and Fritsch, 1988)1988)


Moist convection seems to have Moist convection seems to have played two roles in the gravity wave played two roles in the gravity wave generation:generation: Altering of the synoptic environment Altering of the synoptic environment

which increased the upper-level which increased the upper-level divergence and enhanced the divergence and enhanced the geostrophic adjustment process.geostrophic adjustment process.

Actual generation of the gravity wave .Actual generation of the gravity wave .


Precipitation developed over southern Precipitation developed over southern Texas just before 1200 UTC.Texas just before 1200 UTC.

Sutcliffe’s Self-Sutcliffe’s Self-DevelopmentDevelopment

As time progressed, As time progressed, a pattern of Sutcliffe’s a pattern of Sutcliffe’s Self-Development Self-Development Concept developed.Concept developed. Latent heat releaseLatent heat release Pressure ridge increasePressure ridge increase Slowed ridge progressionSlowed ridge progression Trough deepeningTrough deepening Increased flow curvatureIncreased flow curvature Jet streak acceleration Jet streak acceleration

due to mass evacuationdue to mass evacuationMoist convection resulted in increased upper-level Moist convection resulted in increased upper-level curvature in the flow and along-stream flow accelerations curvature in the flow and along-stream flow accelerations toward northeastern Texas.toward northeastern Texas.

Moist Convection Moist Convection GenerationGeneration

Wave generation occurred Wave generation occurred as the intensifying as the intensifying convection encountered the convection encountered the low-level statically stable low-level statically stable air just west of Austin, TX.air just west of Austin, TX.

Since the convection Since the convection displaced air parcels displaced air parcels vertically, the atmosphere vertically, the atmosphere was "out of balance" was "out of balance" because a component of because a component of the displacement was the displacement was horizontal due to horizontal due to convection. convection.

Thus, the large amplitude Thus, the large amplitude gravity wave developed in gravity wave developed in an attempt to restore the an attempt to restore the atmosphere to balance.atmosphere to balance.

Balanced FlowBalanced Flow Within a balanced flow system, cross-stream Within a balanced flow system, cross-stream

ageostrophic motions are directed toward the ageostrophic motions are directed toward the anticyclonic (right) side of a jet, which creates the anticyclonic (right) side of a jet, which creates the upper-level of the thermally indirect circulation upper-level of the thermally indirect circulation perpendicular to the jet exit region. perpendicular to the jet exit region.

This cross-stream arrangement, determined by the This cross-stream arrangement, determined by the equation dV/dt = fVequation dV/dt = fVagag x k, is the result of air parcel x k, is the result of air parcel deceleration in the jet exit region, causing kinetic deceleration in the jet exit region, causing kinetic energy to be converted into available potential energy to be converted into available potential energy. energy.

Unbalanced FlowUnbalanced Flow When the cross-stream ageostrophic motions in the jet When the cross-stream ageostrophic motions in the jet

exit region are directed toward the cyclonic (left) side of exit region are directed toward the cyclonic (left) side of the jet, it implies that air parcels are actually accelerating the jet, it implies that air parcels are actually accelerating in the leftward cross-stream direction rather than in the leftward cross-stream direction rather than decelerating in the rightward cross-stream direction.decelerating in the rightward cross-stream direction.

Therefore, the air parcels unable to accomplish the Therefore, the air parcels unable to accomplish the energy conversions required to maintain the atmosphere energy conversions required to maintain the atmosphere in a state of balance. in a state of balance.

Vag

Geostrophic AdjustmentGeostrophic Adjustment Uccellini et al. (1984) found Uccellini et al. (1984) found

that unbalanced ageostrophic that unbalanced ageostrophic motions occurred in a case in motions occurred in a case in which a jet streak approached a which a jet streak approached a mass ridge as a jet propagated mass ridge as a jet propagated downstream from the location downstream from the location of the geostrophic jet. of the geostrophic jet.

Thus, an air parcel in the exit Thus, an air parcel in the exit region of the geostrophic jet region of the geostrophic jet found itself in the entrance found itself in the entrance region of the actual jet. region of the actual jet.

This led to unbalanced This led to unbalanced ageostrophic winds in the exit ageostrophic winds in the exit region of a geostrophic wind region of a geostrophic wind maximum, as defined by the maximum, as defined by the cross-stream ageostrophic flow cross-stream ageostrophic flow directed toward the cyclonic directed toward the cyclonic side of the jet. side of the jet.

V g

V

VagФ

Ф-1

Ф+1

Geostrophic AdjustmentGeostrophic Adjustment

Uccellini et al. (1984) also found Uccellini et al. (1984) also found Rossby numbers of Ro > 0.9 located in Rossby numbers of Ro > 0.9 located in the exit region of the geostrophic jet.the exit region of the geostrophic jet.

Zack and Kaplan implemented a Zack and Kaplan implemented a nonlinear balance equation (NBE = nonlinear balance equation (NBE =

) and found that ) and found that “significantly” large values (~10“significantly” large values (~10-8-8 s s-2-2) ) indicated the location of gravity wave indicated the location of gravity wave genesis.genesis.

0),(2 2 uvuJf 0),(2 2 uvuJf

uvuJf 2),(2

Ageostrophic MotionsAgeostrophic Motions Separation occurred Separation occurred

between the actual between the actual and geostrophic jets and geostrophic jets as the actual jet as the actual jet propagated propagated downstream of the downstream of the trough axis. trough axis.

Conforming to the Conforming to the Uccellini et al. (1984) Uccellini et al. (1984) study, ageostrophic study, ageostrophic flow became oriented flow became oriented toward the cyclonic toward the cyclonic side of the side of the geostrophic jet exit geostrophic jet exit region as the speed of region as the speed of the actual jet the actual jet increased.increased.

Rossby NumberRossby Number

Similar to the Similar to the findings of findings of Uccellini et al. Uccellini et al. (1984), the (1984), the region of region of unbalanced unbalanced flow produced flow produced values of Ro > values of Ro > 0.9.0.9.

Nonlinear BalanceNonlinear Balance The nonlinear The nonlinear

balance equation balance equation did indicate the did indicate the region of gravity region of gravity wave genesis, wave genesis, although it seemed although it seemed to do a better job to do a better job in pinpointing the in pinpointing the location of the location of the wave after wave after formation had formation had occurred.occurred.

Shearing InstabilityShearing Instability

Shearing instability has been found to Shearing instability has been found to be a likely generation mechanism in an be a likely generation mechanism in an environment with strong vertical environment with strong vertical shear, such that Ri < 1/4, at an shear, such that Ri < 1/4, at an altitude where the wave propagation altitude where the wave propagation speed matches the wind speed, also speed matches the wind speed, also known as the critical level known as the critical level (Miles(1961); Howard (1961); Einauldi (Miles(1961); Howard (1961); Einauldi and Lalas (1973); Gossard and Hooke and Lalas (1973); Gossard and Hooke (1975)).(1975)).

Shearing InstabilityShearing Instability

Wave phase Wave phase speed of 15 speed of 15 to 20 msto 20 ms-1-1..

Wind Wind velocity of 15 velocity of 15 to 20 msto 20 ms-1-1 between between 600-550 mb.600-550 mb.

Thus, critical Thus, critical level is level is between between 600-550 mb.600-550 mb.Since Ri < ¼ at the critical level, it can be assumed Since Ri < ¼ at the critical level, it can be assumed

that shearing instability was present at wave genesis.that shearing instability was present at wave genesis.

ConclusionsConclusions The large amplitude gravity wave that The large amplitude gravity wave that

developed at 1700 UTC on 12 December developed at 1700 UTC on 12 December 2002 adhered to the common gravity 2002 adhered to the common gravity wave synoptic pattern prescribed by wave synoptic pattern prescribed by Uccellini and Koch (1987).Uccellini and Koch (1987).

Upon examination of the various wave Upon examination of the various wave generation mechanisms, it was shown generation mechanisms, it was shown that moist convection, geostrophic that moist convection, geostrophic adjustment and shearing instability were adjustment and shearing instability were all present in the region of gravity wave all present in the region of gravity wave genesis over central Texas. genesis over central Texas.