Dr. Steven Koch, NCSU, Hugh D. Cobb, III and Neil A. Stuart, WFO Wakefield 

General Information

Amplitudes of 1-15 hPa/MB and Wavelengths of 50-500 KM (Uccellini and Koch, 1987) Periods of 1-4 HR

Most likely energy source mechanisms are latent heat release in deep convection and shear instability in which waves can extract energy from the Jet Stream when vertical wind shear is sufficiently strong to reduce the Richardson number below 0.25. Alternatively wave energy loss can be prevented by an efficient wave duct, which appears to be the most prevalent of the three mechanisms described. 

Strongest upward motions with Gravity Waves occur just following the surface pressure trough and lead to maximum precipitation rates just ahead of the ridge.

Gravity waves typically form within or near the back edge of a precipitation shield.

Recent studies indicate that Gravity Waves may occur as frequently as 34% of the time in the Central US during the Winter months.

Current poor understanding of gravity waves and acknowledged skepticism of their existence stems from the fact that it is both difficult and tedious to conduct a study of even a single event. In addition forecasters have often been mislead by the existence of large scale gravity waves in 2 noteworthy events.

• Rapid pressure falls associated with a strong gravity wave mislead forecasters into believing that secondary cyclogenesis was taking place along a coastal front (Bosart and Seimon, 1988).
• Schneider (1990) presented a case which occurred in Illinois in December 1987 in which the minimum pressure associated with one of the wave troughs was lower than that of the synoptic scale cyclone through which it passed. The isallobaric fall region associated with the wave was noted by forecasters, who lacking knowledge of the wave, mistakenly attempted to correct the model forecasts of the track.

• 5 MIN sampling by ASOS - The availability of high temporal resolution data from ASOS is an important factor  in the determination of whether an operational detection of gravity waves is feasible.
• ASOS data is expected to meet that need. ASOS allows for the automated bandpass filtering of digital pressure time series data.
• 6 MIN Wind Profiles
• WSR-88D VWP/VAD winds

Strategy for the Operational Detection of Gravity Waves

In order for gravity wave detection to be incorporated into the forecast process, forecasters need a systematic approach to diagnose favorable conditions for gravity waves. There are 4 steps within the gravity wave detection flowchart for forecasters to focus on in diagnosing gravity waves. These are....

• Surface/upper air analyses to diagnose the synoptic pattern favoring gravity waves
• Mesoscale model diagnostics to determine if an unbalanced flow exists or if there is a wave ducting mechanism present
• Automated ASOS gravity wave detection system
• The use of WSR-88D Data/GOES Imagery

• A diffluent region bounded by a 300 MB Ridge Axis to the east and a 300 MB trough axis to the west
• Bounded by inflection axis to the southwest
• A surface Warm front to the south of the region favoring Gravity Waves

An upper level Jet streak propagating out of the mean trough and toward the downstream ridge axis away from the geostrophic jet max and nearing the inflection axis
• The propagation of the jet streak downstream of the geostrophic wind maximum at the base of the trough produces divergent ageostrophic flow which is in an unbalanced state, where the cross contour flow is directed in the opposite sense one would normally see in quasi-geostrophic theory. The flow is directed toward lower heights in the exit region of the geosptrophic wind maximum.

Mesoscale model diagnostics to determine the existence of Unbalanced Flow and Wave ducting mechanisms
Van Tuyl and Young determined that gravity-inertia waves are preferentially generated just downstream of a jet core when the flow is unbalanced in the sense that the Lagrangian-Rossby number which measures the relative importance of the parcel acceleration to the coriolis acceleration is larger than 0.5. The simplified version of the Lagrangian-Rossby number is defined by the following equation

where V_ag  is the transverse ageostrophic component of the geostrophic wind. Large parcel divergence and Ro_L  greater than 0.5 have been shown to occur as a jet streak approaches a highly diffluent area in mesoscale model simulations.

The existence of large parcel divergence violates the nonlinear balance equation.

      1             2              3         4

where the terms are the Laplacian of geopotential (1), the Jacobian of the winds (2), the vorticity term (3) and the beta effect term (4).  
Gravity waves are often seen emanating from these regions of diagnosed imbalance.

Click here for a schematic of the key points a forecaster must consider to determine unbalanced flow and evaluate wave ducting mechanisms

The Role of Wave-Ducting Processes in Gravity Wave Maintenance

Click here to access a prototype sounding which illustrates the wave ducting mechanism.

In order to have sufficient wave ducting you need the following mechanisms

• There must be a layer of static stability defined as the duct depth near the surface (D₁)
• There must not be a critical level (Zc) within the lower stable layer, which would lead to absorption of wave energy. The critical level is defined as the level where the wind speed in the  direction of wave propagation is equal to the wave phase speed.
• The stable layer must have sufficient depth to contain 0.25 of the wavelength corresponding to the phase speed
• There must be a layer of conditional instability (D₂) above the stable layer. This "reflecting layer"  prevents the wave from propagating its energy out of the stable duct layer.

Where the terms are the wave phase (1) and the ducted phase speeds divided by the Brunt-Vaisala frequency number (2).

The efficiency of a ducting mechanism must also be taken into consideration through the Duct factor equation.  

 
where....

p1=lowest pressure level taken at or near the ground (typically 950 mb, the default value) - Potential temperature @ p1 used
p2=pressure level of top of low-level stable duct layer (default = 800 mb, but adjustable, depending upon inspection of soundings for the day) - Potential temperature @ p2 used
p3=pressure level of bottom of conditionally unstable layer (default = 800 mb, but often higher is better, depending upon inspection of soundings for the day) - Equivalent Potential temperature @ p3 used
p4=pressure level of top of conditionally unstable layer (often the tropopause, or use 400 mb default) - Equivalent Potential temperature @ p4 used

The reasoning behind this easily calculated parameter is than an efficient duct, according to the linear theory of Lindzen and Tung (1976) is one in which there exists a conditionally unstable layer (800-400 mb) above a very stable surface based layer (950-800 mb).    

Schneider (1990) and Koch and O'Handley (1997) found that maximum wave amplitude occurs in regions where weak mid-level static stability overlaid a strong stable layer. Rapid amplification of a wave occurred as it entered a region of highly stable cold air damming east of the Appalachians (Bosart and Seimon, 1988).

The Automated ASOS Gravity Wave Detection System

The unbalanced flow diagnostics and ducting analysis serves a dual purpose of refining the predicted area for mesoscale gravity wave activity and establishing a "confidence level" (an increased probability of significant and long-lasting wave activity when all the test results are positive).  Having been alerted to the likelihood of a gravity wave event, the forecaster should look to an automated gravity wave detection system which incorporates digital, high temporal resolution data from ASOS. The availability of this data is a very important factor in determining whether operational gravity wave detection is feasible. 

Click here to access the schematic describing the Automated ASOS Gravity Wave Detection System

The use of WSR-88D/GOES Imagery
 
Forecasters should monitor available WSR-88D/GOES imagery for the development and  intensification of convective elements and precipitation bands as well as changes to existing cloud structures.

Gravity waves can affect an existing cloud pattern in several ways as they propagate through.....

• Modulate the cloud pattern with the development of wave cloud formations
• The wave and cloud can propagate in tandem with little affect on the overall cloud pattern

Results from several studies (Zhang and Fritsch, 1988, Schneider, 1990 and Powers and Reid, 1993) indicated that convection was essential for the development, maintenance and amplification of gravity waves.

Results in a separate study (Bosart and Seimon, 1988) of a wave depression forming behind a squall line in an area of strong static stability, concluded that gravity waves shared similarities with wake lows associated with convective systems.  

Interactions between Gravity Waves and Convection

Wave CISK Theory - Organized convection is forced by convergence associated with a gravity wave, while latent heat release within the convection provides a source of wave energy. Convection amplifies the wave trough by compensating subsidence and enhances the wave ridge by evaporative cooling of precipitation.

Wave CISK theory also states that the strongest convective vertical motions must also exist at the wave critical level instead of midway through the stable layer so the gravity wave and the convective system move in tandem.
 

References for additional reading on this topic

"Operational Forecasting and Detection of Mesoscale Gravity Waves", by Steve Koch and Christopher O'Handley Weather and Forecasting, June 1997 pp. 253-281.

"A case study of an Unusually Intense Atmospheric Gravity Wave", by Lance Bosart and A. Seimon. Monthly Weather Review, Vol. 116, pp. 1857-1886.

"The Synoptic Setting and Possible Energy Sources for Mesoscale Wave Disturbances", by Louis Uccellini and and S. Koch. Monthly Weather Review, Vol. 115, pp. 721-729.