A Closer Look at Damaging Surface Winds Timothy A. Coleman and Kevin R. Knupp The University of Alabama in Huntsville AMS 12th Conference on Mesoscale Processes 8 August 2007 Associated with Gravity Waves

1. Introduction Numerous ducted gravity waves of significant amplitude (> 3 hPa) are detected in surface observations across the U.S. annually. Sometimes, these waves produce significant surface winds (> 25 m s -1 ). In these cases, wind damage often occurs Therefore, understanding the dynamics and environment of gravity waves which cause wind damage is important.

2. Review of Gravity Waves Idealized plane gravity waves, traveling upward and to the right Air parcel displacements are perpendicular to wave motion, so waves are transverse

2. Review of Gravity Waves Similar waves, traveling downward and to the right

2. Review of Gravity Waves Most waves causing wind damage at the surface are ducted gravity waves. Wave reflection may occur at the ground, or in layers with rapid vertical variation in Scorer parameter (l 2 ), given by: So, vertical decreases in static stability, or changes in the wind shear profile, may cause wave reflection.

2. Review of Gravity Waves Wave reflection region due to change in static stability Stable layer below 2 km, neutral in the 2-3 km layer Wave reflection would occur near 2 km Vertical profiles of  (left) and Scorer parameter (right)

2. Review of Gravity Waves Wave reflection region due to change in wind shear profile Constant wind speed (7.5 m s -1 ), but large directional shear (90 degrees per km) in the 0-2 km layer Wave moving northward would encounter a “wave-relative jet” near 1 km, resulting in wave reflection. Hodograph (left) with wave motion, vertical profile of Scorer parameter (right)

2. Review of Gravity Waves If wave reflection occurs ¼ of a vertical wavelength above the surface, then the incident and reflected waves will constructively interfere, causing wave ducting Vertical motion maximized at top of duct, horizontal motion maximized near surface.

3. Factors Affecting Surface Winds in Gravity Waves Impedance relation (e.g., Gossard and Munk 1954; Gossard and Hooke 1975) relates wind perturbation (u’) to pressure perturbation (p’) and intrinsic phase speed (c-U): The actual wind is the vector sum of the background wind U and the wind perturbation u’: So, surface wind depends on the amplitude of the wave (p’), the intrinsic phase speed, and the background wind.

3. Factors Affecting Surface Winds in Gravity Waves Impedance relation may be derived by linearizing the horizontal momentum equation for a sinusoidal disturbance in wind and pressure New impedance relation for winds at surface currently being tested at UAH maintains first-order non-linear terms Assuming w=0 at surface, and that u = U + u’

3. Factors Affecting Surface Winds in Gravity Waves Integrating with respect to t and solving for p’ yields If one removes the non-linear term on the RHS, the original impedance relation is obtained. However, quadratically solving the non-linear equation for u’ yields

3. Factors Affecting Surface Winds in Gravity Waves Basic phase relationship between p’ and u’ essentially not affected.

3. Factors Affecting Surface Winds in Gravity Waves Classical impedance relationship

3. Factors Affecting Surface Winds in Gravity Waves New non-linear impedance relationship

3. Factors Affecting Surface Winds in Gravity Waves Wind speeds with new impedance relationship are lower in wave trough

3. Factors Affecting Surface Winds in Gravity Waves Wind speeds with new impedance relationship are higher in wave ridge.

3. Factors Affecting Surface Winds in Gravity Waves In trough, nonlinear acceleration to the right decreases the wind speed. In ridge, acceleration to right increases wind speed.

3. Factors Affecting Surface Winds in Gravity Waves Comparison of classical vs. non-linear impedance relation to observed winds in 13 actual gravity wave cases Non-linear impedance relation wins in 8 cases, classical wins in 3, and there are 2 ties (errors within 5% of each other)

3. Factors Affecting Surface Winds in Gravity Waves RMS error is also lower for non-linear impedance model Improvement of 28%.

4. Case Study – Moderate Surface Winds Birmingham, AL 14 April 2007 Gravity wave ridges are moving in same direction as low level flow However, waves moving rapidly NE (c-U=23.5 m s -1 ) Pressure perturbations small (1.3 hPa)

5. Case Study – Moderate Surface Winds Pressure perturbations simply too small.

6. Case Study – Moderate Surface Winds Huntsville, AL 10 May 2006 Larger amplitude gravity wave trough (3.5 hPa), moving fairly slowly (c-U=14 m s -1 ) However, wave trough moving with the wind, so fairly large perturbation winds (u’=-20 m/s) oppose background wind

6. Case Study – Moderate Surface Winds Time-to-space conversion of VAD wind profile reveals significant wind perturbations, but in the opposite direction of mean winds So, actual winds not that high. Actual wave-normal wind u Perturbation wave-normal u’

7. Case Study – High Surface Winds St. Louis, MO 28 April 1996 Similar amplitude gravity wave trough (4 hPa) But, this wave moving in opposite direction of background wind, so perturbation winds add to actual wind speed Wind gusts near 30 m s -1 in STL (Gaffin 1999)

7. Case Study – High Surface Winds u (m/s) u’ (m/s)

8. Case Study – High Surface Winds Birmingham, AL 22 February 1998 Large-amplitude wave trough moving NE through state of Alabama (p’=-7.5 hPa) Even though wave moving fairly quickly and background wind is only weakly opposite wave motion (U=-6.2 m s -1 ), large pressure perturbations still produced very high winds over large area, causing damage.

8. Case Study – High Surface Winds

Gravity waves occur frequently, and occasionally produce damaging winds. Situations conducive to high surface winds include slow- moving waves, large wave amplitudes (large pressure perturbations) Also, for wave troughs, background headwinds; and for wave ridges, background tailwinds New non-linear impedance relationship shows promise, must be improved to include friction and w’ terms, and tested further 9. Conclusions and Future Work