Resonant interaction between an atmospheric gravity wave and shallow water wave along Florida's west coast

ABSTRACT

On 25 March 1995, a large solitary wave, seemingly from nowhere, washed ashore along the normally tranquil Gulf Coast of Florida from Tampa Bay to south of Naples. On this Saturday morning, many beachgoers and coastal residents saw either a large wave, a surge, or a seiche. The wave was typically described as 3 m or greater, breaking between 0.5 and 3 km offshore, and taking 120-180 s to arrive at the shore. Just prior to the wave's arrival at the beach, witnesses reported a rapid runout of water, then a huge IS-25-m runup of water onto the beach corresponding to a 2-3-m vertical run-up height. Some people reported several smaller waves. This was likely due to local effects. This wave was generated and amplified by a large-amplitude atmospheric gravity wave transiting southeastward over the eastern Gulf of Mexico. The atmospheric gravity wave and the water wave moved over a channel of water depth sufficient to maintain the waves in phase allowing resonation of the shallow water wave. Surface winds appeared to have a negligible affect, increasing only slightly (3-5 m s^sup -1^) along the path of the atmospheric gravity wave and opposing propagation of the water wave.

1. Introduction

On 25 March 1995, an unusual wave moved over the Gulf of Mexico from the northwest at 25 m s-' and surged onto the beaches of western peninsular Florida. This rapidly moving wave rushed onshore from near the mouth of Tampa Bay southward for over 200 km (Fig. 1). More than 30 reports were received by the Tampa Bay National Weather Service Office from beachgoers who witnessed the wave. Several people reported seeing the huge wave offshore stretching to the horizon. A boat captain, about 13 km offshore and near the 10-m isobath, reported seeing a line of clouds about 1 km wide followed 15 min later by a single 3-m wave moving toward the southeast. The wave was generally described as 3 m or greater, breaking between 0.5 and 3 km offshore, and arriving at the shore within 120-180 s. Just prior to the wave's arrival at the beach, witnesses reported a rapid runout of water, then a huge 15-30-m runup of water onto the beach corresponding to a vertical height of 2-3 m. The runup caused people to flee as it carried jellyfish and stingrays onto the beach. The wave washed a boat ashore, nearly capsized another, and washed a man into the strong current of Stump Pass. Some people reported several smaller waves. Two tide gauges measured an oscillation in water heights for over 3 h after the wave passed. This peculiar water wave was generated by an atmospheric gravity wave. The atmospheric gravity wave emanated from a thunderstorm complex over southeast Texas 12 h earlier as a jet streak propagated toward an upper-tropospheric ridge axis. The path of the atmospheric gravity wave was tracked by surface pressure observations and barograph charts. A cloud band associated with the atmospheric gravity wave was tracked using satellite and radar. This atmospheric gravity wave moved offshore of the Florida Panhandle over the open Gulf of Mexico waters, spawning a shallow water wave. The two waves moved over a channel of water depth that maintained the waves in phase allowing resonation of the shallow water wave. Surface winds increased only slightly (3-5 m s^sup -1^) along the path of the atmospheric gravity wave (from Texas to Florida) and were opposing the propagation of the wave. Therefore, the shallow water wave was formed primarily by the rapidly moving (25 m s^sup -1^) pressure perturbation associated with the atmospheric gravity wave. This single wave moved at a speed over twice that of a typical wind wave.

2. Atmospheric gravity wave development and propagation

Large-amplitude gravity waves result in abrupt pressure perturbations that generally have wave lengths in the 100-400-km range. The term "gravity wave" is derived from the effect of "reduced gravity" or buoyancy acting as a restoring force on parcels displaced from hydrostatic equilibrium. In a study of thirteen atmospheric mesoscale wave disturbances, Uccellini and Koch (1987) found gravity waves as singular or traveling in packets with periods of 14 h, horizontal wavelengths of 50-500 km, surface pressure perturbations amplitudes of 0.2-7.0 mb, and lasting over 9 h. Common characteristics among the disturbances were a strong thermal inversion in the lower troposphere behind a cold front and a jet streak propagating toward a ridge axis in the upper troposphere, resulting in an increase of upper-level divergence and an abrupt geostrophic adjustment. A stable layer is necessary for maintenance and propagation of gravity waves within the atmosphere; otherwise the energy is rapidly dissipated. The atmosphere above the stable layer must be at least conditionally unstable, and, within this conditional layer, a critical level must exist where wind speed equals the phase speed of the gravity wave. The conditionally unstable layer must have a low (less than 1) bulk Richardson number (BRN) with high shear. The conditionally unstable layer provides strong reflectance for perturbations with long wavelengths (Lindzen and Tung 1976).

Development of the 24-25 March 1995 atmospheric gravity wave was similar to cases described above. On the evening of 24 March, a jet streak propagated toward a ridge axis in the upper troposphere over Texas. At the same time, a band of thunderstorms developed over east Texas. Uncertainty exists as to which mechanism (thunderstorm, unbalanced geostrophic flow, or both) spawned the atmospheric gravity wave, but the gravity wave emanated from the region of moderately strong thunderstorms over east Texas. Geostationary Operational Environmental Satellite (GOES) 0100 UTC 25 March 1995 IR satellite imagery (Fig. 2) shows the line of convective clouds associated with the gravity wave over east Texas and northwest Louisiana. Figure 2 also shows clouds along a stationary front across the Gulf of Mexico from south Texas to south Florida.

The air mass north of the front provided a strong wave duct for maintenance of the gravity wave. The 1200 UTC 25 March 1995 Tampa, Florida, sounding (Fig. 3) and other soundings near the track of the gravity wave from Slidell, Louisiana, and Tallahassee, Florida, (not shown) were similar with a strong inversion from the surface to around 850 mb. The inversion was partially due to radiational cooling and partially due to weak subsidence behind the front. Because of the radiational cooling, some fog developed under the inversion that morning. Winds within the inversion layer were from the northeast at 3-5 m s^sup -1^ across the southeastern United States. The atmosphere had a BRN of zero. Above 850 mb, the atmosphere was conditionally unstable with northwest winds 20-30 m s^sup -1^ in phase with the gravity wave through almost 300 mb. The soundings indicate a channel and phase speed for the propagation of the atmospheric gravity wave over a broad area. A critical level above the duct in which the wind velocity is approximately equal to the phase velocity of the gravity wave is necessary for gravity wave maintenance (Gossard and Hooke 1975; Einaudi et al. 1978). In this case, the critical level was around 525 mb, where northwest winds at 25 m s^sup -1^ correspond to the velocity of the gravity wave. Koch and O'Handley (1997) showed that gravity wave motion could be estimated (+/- 20 deg, +/- 5 m s^sup -1^) by using the average wind vector in the conditionally unstable layer, which is true in this case with the average wind from 3000 at 20.6 m s^sup -1^.

National Data Buoy Center 42036 was the only sensor array over the Gulf of Mexico in the path of the gravity wave. At that time, the buoy only recorded measurements hourly and, therefore, the presence of the wave was not detected. Uncertainty exists regarding winds over the eastern Gulf. As the atmospheric gravity wave moved over the Gulf from the Florida Panhandle and back onshore near Tampa Bay, the winds increased slightly, but were southeast-opposing wave movement.

Pressure jumps on surface observations and barograph traces from Texas to Florida confirmed the presence of the rapidly moving gravity wave. Pressure measurements from Egmont Key (Fig. 4), near the mouth of Tampa Bay, show a common trend in other barograph traces along the path of the gravity wave. The pressure perturbation and corresponding cloud line moved across the Florida Panhandle, then south over the west Florida continental shelf waters, with the eastern edge of the gravity wave brushing the coastline. Isochrones (Fig. 5) show the path of the atmospheric gravity wave. Gravity wave speed and pressure trends were deduced from satellite imagery, barographs, pressure jump remarks on surface observations, and automated pressure readings in 6- and 10-min increments.

Clouds and precipitation develop in the area of strongest upward vertical motion following the surface pressure trough (Koch and O'Handley 1997). In this case, an arch-shaped cloud band, approximately 2.5 km high (based on IR satellite and radar data), developed and moved with the gravity wave. GOES 1100 UTC 25 March 1995 IR satellite imagery (Fig. 6) shows the cloud band associated with the gravity wave and the clear area behind the cloud band associated with compensating subsidence.

3. Water wave development and propagation

Churchill et al. (1995) and Sallenger et al. (1995) described a shallow water wave on 3 July 1992 in the Daytona Beach area along Florida's east coast that was forced by a combination of a pressure preturbation and wind associated with a squall line. This wave, reported up to 6 m high, moved southward at 14 m s^sup -1^ and struck at night with a vertical runup height of about 2.5 m. If people and automobiles had not been on the beach that evening, this might have gone unnoticed. Churchill et al. (1995) derived a formula for development of the wave based on wind and pressure effects but could not estimate a wave of sufficient height to account for the observed wave. Significant differences exist between the 1992 Daytona Beach wave and the wave presented in this paper. The Daytona Beach wave had significant wind forcing (13 vs 3-5 m s^sup -1^ and opposing the wave propagation), a much slower wave speed (14 vs 25 m s^sup -1^), affected a much smaller area (20 vs 200 km), and transited shallower water (20 vs 60 m).

Chrystal (1906), Lamb (1932), and Proudman (1952) suggested moving pressure disturbances as a cause of lake and coastal seiches. Pond and Pickard (1989) described the process for water levels adjusting to compensate for atmospheric pressure changes. As atmospheric pressure decreases, the force exerted by the water increases until the force is again in equilibrium. Krauss and Businger (1994) and Dan and Dalrymple (1984) described water wave development by a traveling air pressure fluctuation through a resonance process. The water wave amplifies when the perturbation's lower air pressure remains in phase and is aligned along the leading edge of the water wave. Therefore, water depth is important to maintain phase. For a resonant wave, where U approaches the phase speed C of a shallow water wave, where H is the water depth and U is the speed of the pressure disturbance. Therefore, in a channel of approximately 60 m, the shallow water wave will move in phase with the atmospheric gravity wave moving at 25 m s^sup -1^. When the waves are in phase, resonance occurs. In deeper water, the wave outruns the atmospheric forcing; in shallower water, the wave is slower and the atmospheric forcing outruns it. In this case, the 60-m isobath (Fig. 5) stretched along the gravity wave path for over 250 km and provided a rather long and straight fetch that directed the wave toward the west coast of Florida from about Tampa Bay south. The long wavelength of this wave caused refraction in deeper water than is typical with wind waves. This refraction allowed the wave to move onshore where the 60-m isobath paralleled the coast. Shallow water waves have wavelengths that are much longer than the water depth through which the wave propagates. Wavelength (A) is approximated by where C is the water wave phase speed and g is gravity. Therefore, in this case, the horizontal wave length of 400 m propagated through 60 m of water. The 25 m s^sup -1^ shallow water wave speed was based on automated coastal observations and over 30 eyewitness reports from beachgoers and boaters.

Sallenger et al. (1995) deduced the Daytona Beach wave height by modeling runup and provided an explanation for the wave height based largely on the process described by Dean and Dalrymple (1984). Assuming the atmospheric forcing terms are constant in time and space and moving with the wave, and the pressure disturbance moves along an isobath at the speed of the shallow water wave, wave height can be represented by where h is the height of the shallow water above or below mean water level, P is the pressure perturbation amplitude, and p is the water density. This is unbounded without frictional damping terms when U = C (at approximately 64-m depth). In this case, U approached C, producing a very large wave. The minor affect of light surface wind (35 m s^sup -1^) that was opposing wave propagation was not calculated.

Following the initial wave, a seiche occurred. Tide gauges at Naples (on the Gulf) and inside Tampa Bay at St. Petersburg measured an oscillation in water heights for over 3 h after the wave passed. Figure 7 shows the long-lasting effect of the seiche that followed the shallow water wave at Naples. Since tide gauges damp wave motion, neither tide gauge measured the shallow water wave; but the variability in water height is clearly visible. 4. Conclusions

Large wave development in the absence of wind is rare. In this case, several factors aligned to produce this large wave along Florida's west coast. First, an atmospheric gravity wave developed and an atmospheric channel was present for wave maintenance and propagation. Then the pressure perturbation associated with the gravity wave moved over water of necessary depth to keep the atmospheric and water waves in phase, resonating to produce the solitary swell. Beachgoers were caught unaware and were terrified as the wave engulfed them; it was fortunate that no one drowned. Gravity waves are not always evident until passage, but pressure remarks on surface observations and arc-shaped cloud lines on satellite images may be a clue to the presence of gravity waves.

Acknowledgments. The authors would like to thank Drs. Mark Luther and Bob Weisberg of the University of South Florida, Department of Marine Science, for input and technical advice; Mr. Bob Baker, park manager at Egmont Key State Park, for his input; Mr. Steve Gill of the National Ocean Service for data retrieval; and National Weather Service Administrative Support Assistant, Mrs. Annegret Cornell, for her superb editing skills. Finally, we would like to thank the entire staff of the Tampa Bay National Weather Service, who gathered invaluable eyewitness reports and provided technical advice and insight.

[Reference]

References

[Reference]

Chrystal, G., 1906: On the hydrodynamical theory of seiches. Trans. Roy. Soc. Edinburgh, 41 (III), 599-49. Churchill, D. D., S. H. Houston, and N. A. Bond, 1995: The Daytona Beach wave of 34 July 1992: A shallow water gravity wave forced by a propagating squall line. Bull. Amer. Meteor. Soc, 76, 21-32.

[Reference]

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[Reference]

Kraus, E. B., and J. A. Businger, 1994: Atmosphere-Ocean Interaction. 2d ed. Oxford University Press, 384 pp. Lamb, H., 1932: Hydrodynamics. Cambridge University Press, 738 pp.

[Reference]

Lindzen, R. S., and K. K. Tung, 1976: Banded convective activity and ducted gravity waves. Mon. Wea. Rev., 104, 1602-1617. Pond, S., and G. L. Pickard,1989: Introductory Dynamical Oceanography. 2d ed. Pergamon Press, 329 pp.

Proudman, J., 1952: Dynamical Oceanography. Dover, 409 pp. Sallenger, A. H., Jr., J. H. List, G. Elfenbaum, R. P. Stumpf, and M. Hansen, 1995: Large wave at Daytona Beach Florida, explained as a squall line surge. J. Coastal Res., 11, 1383-1388. Uccellini, L. W., and S. E. Koch, 1987: The synoptic setting and possible energy sources for mesoscale wave disturbances. Mon. Wea. Rev., 115, 721-729.

[Author Affiliation]

Charles H. Paxton and Daniel A. Sobien NOAA/NWS, Tampa Bay, Florida

[Author Affiliation]

Corresponding author address: Daniel A. Sobien, NWS Tampa Bay Area, 2525 14th Ave. S.E., Ruskin, FL 33570.

E-mail: dsobien@marine.usf.edu

In final form 14 September 1998.