Mesoscale Gravity Waves MEA 444 January 20, 2005

Outline Gravity Wave Theory Overview Gravity Wave Theory Overview Numerical Model Description Numerical Model Description Synoptic Overview Synoptic Overview Uccellini and Koch (1987) Synoptic Pattern Uccellini and Koch (1987) Synoptic Pattern Surface & 300mb Surface & 300mb Generation Mechanisms Generation Mechanisms Moist Convection Moist Convection Geostrophic Adjustment Geostrophic Adjustment Shearing Instability Shearing Instability

Mesoscale Gravity Waves As defined by Uccellini and Koch 1987: As defined by Uccellini and Koch 1987: Either a singular wave of depression or a wave packet with these characteristics: Either a singular wave of depression or a wave packet with these characteristics: Horizontal wavelength km Horizontal wavelength km Wave period1-4 hours Wave period1-4 hours Surface Pressure Perturbation mb Surface Pressure Perturbation mb

Rossby Adjustment Theory

Internal Gravity Waves Wave disturbances in which the restoring force of buoyancy acts on parcels displaces from hydrostatic equilibrium. Wave disturbances in which the restoring force of buoyancy acts on parcels displaces from hydrostatic equilibrium. Unlike external waves, internal waves can propagate vertically. Unlike external waves, internal waves can propagate vertically. Vertical wind shear can also destabilize parcels. 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) Coriolis effects can alter wave frequency and phase characteristics if period of wave is long enough (gravity-inertia waves)

Wave Tilt Note: Note:

Wave Groups

Vertical Propagation a means exists to prevent energy loss: a means exists to prevent energy loss: Wave ducting Wave ducting Wave over-reflection Wave over-reflection a means exists to provide wave energy: Shearing instability Wave-CISK Mesoscale gravity waves will become incoherent quickly due to vertical energy propagation unless:

Wave Duct Highly reflective wave duct created by combined temperature structure and critical levels (Lindzen and Tung 1976) Highly reflective wave duct created by combined temperature structure and critical levels (Lindzen and Tung 1976) Phase speed of a ducted wave relative to the mean flow: Phase speed of a ducted wave relative to the mean flow: *Note: Duct properties determine wave phase speed. n = order of wave mode

Wave Duct Requirements Requirements for highly reflective wave duct: Requirements for highly reflective wave duct: Statically stable lower layer Statically stable lower layer Duct thick enough to accommodate λ z /4 for given C DUCT. Duct thick enough to accommodate λ z /4 for given C DUCT. No critical level in duct which could absorb wave energy. No critical level in duct which could absorb wave energy. Critical level with low Ri in upper layer with conditional instability. Critical level with low Ri in upper layer with conditional instability.

Event Overview At 1700 UTC on 12 December 2002, a large amplitude gravity wave developed over central Texas. 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. 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. Bosart et al. (1998) defined a large amplitude gravity wave as one which displayed: Bosart et al. (1998) defined a large amplitude gravity wave as one which displayed: Amplitudes of 3-6 hPa Amplitudes of 3-6 hPa Wavelengths of km Wavelengths of km Phase speeds of ms -1 Phase speeds of ms -1 Durations of at least 2-3 hours. Durations of at least 2-3 hours.

Observations – Pressure

Observations - Wind Profiler

Observations - Pressure

Observations - Wind Profiler

Observations - Pressure

UK87 Synoptic Pattern Uccellini and Koch (1987) found a common synoptic pattern among gravity wave events: Uccellini and Koch (1987) found a common synoptic pattern among gravity wave events: 300 mb ridge axis to the northeast 300 mb ridge axis to the northeast 300 mb inflection axis to the southwest 300 mb inflection axis to the southwest Surface warm or stationary front to the south Surface warm or stationary front to the south

In Addition…. Uccellini and Koch (1987) noted that the synoptic pattern was not sufficient by itself for gravity wave development. 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. 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 The key element in the lower levels of the atmosphere was the baroclinic zone located along the Gulf Coast, extending eastward from southern Texas. 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 The ridge/trough amplification resulting in increased flow curvature. The ridge/trough amplification resulting in increased flow curvature. Inflection axis in the height field over central Texas. Inflection axis in the height field over central Texas. Propagation of a jet streak toward northeastern Texas and away from the trough axis. 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….. The gravity wave developed in a region with: The gravity wave developed in a region with: Surface warm front to the south Surface warm front to the south 300 mb ridge axis to the northeast 300 mb ridge axis to the northeast 300 mb inflection axis to the southwest 300 mb inflection axis to the southwest Jet streak propagating away from 300 mb trough Jet streak propagating away from 300 mb trough Thus, it satisfied the Uccellini and Koch (1987) gravity wave synoptic situation. Thus, it satisfied the Uccellini and Koch (1987) gravity wave synoptic situation.

Gravity Wave Generation Three gravity wave generation mechanisms were examined: Three gravity wave generation mechanisms were examined: Moist Convection Moist Convection Geostrophic Adjustment Geostrophic Adjustment Shearing Instability Shearing Instability

Moist Convection There is still no real consensus as to what role moist convection plays in gravity wave formation. 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) 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) Others found that gravity waves can trigger convection. (Zhang and Fritsch, 1988)

Moist Convection Moist convection seems to have played two roles in the gravity wave generation: 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. Altering of the synoptic environment which increased the upper-level divergence and enhanced the geostrophic adjustment process. Actual generation of the gravity wave. Actual generation of the gravity wave.

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

Sutcliffe’s Self-Development As time progressed, a pattern of Sutcliffe’s Self-Development Concept developed. As time progressed, a pattern of Sutcliffe’s Self-Development Concept developed. Latent heat release Latent heat release Pressure ridge increase Pressure ridge increase Slowed ridge progression Slowed ridge progression Trough deepening Trough deepening Increased flow curvature Increased flow curvature Jet streak acceleration due to mass evacuation 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 Wave generation occurred as the intensifying convection encountered the low-level statically stable air just west of Austin, TX. 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. 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. Thus, the large amplitude gravity wave developed in an attempt to restore the atmosphere to balance.

Balanced Flow 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. 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. This cross-stream arrangement, determined by the equation dV/dt = fV ag x k, is the result of air parcel deceleration in the jet exit region, causing kinetic energy to be converted into available potential energy. This cross-stream arrangement, determined by the equation dV/dt = fV ag 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 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. 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. Therefore, the air parcels unable to accomplish the energy conversions required to maintain the atmosphere in a state of balance. V ag

Geostrophic Adjustment 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. 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. 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. 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. VgVg V V ag Ф Ф-1 Ф+1

Geostrophic Adjustment Uccellini et al. (1984) also found Rossby numbers of Ro > 0.9 located in the exit region of the geostrophic jet. 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 = ) and found that “significantly” large values (~10 -8 s -2 ) indicated the location of gravity wave genesis. Zack and Kaplan implemented a nonlinear balance equation (NBE = ) and found that “significantly” large values (~10 -8 s -2 ) indicated the location of gravity wave genesis.

Ageostrophic Motions Separation occurred between the actual and geostrophic jets as the actual jet propagated downstream of the trough axis. 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. 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 Similar to the findings of Uccellini et al. (1984), the region of unbalanced flow produced values of Ro > 0.9. Similar to the findings of Uccellini et al. (1984), the region of unbalanced flow produced values of Ro > 0.9.

Nonlinear Balance 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. 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 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 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 Wave phase speed of 15 to 20 ms -1. Wave phase speed of 15 to 20 ms -1. Wind velocity of 15 to 20 ms -1 between mb. Wind velocity of 15 to 20 ms -1 between mb. Thus, critical level is between mb. Thus, critical level is between mb. Since Ri < ¼ at the critical level, it can be assumed that shearing instability was present at wave genesis.

Conclusions 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). 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. 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.