METEOTSUNAMI OCCURRENCE AND PROPAGATION IN THE NORTHEASTERN GULF OF MEXICO By MATLACK E. GILLIN A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2017
2017 Matlack E. Gillin
To my wife, Bethany, for her stea dfast support and encouragement
4 ACKNOWLEDGMENTS I would like to acknowledge the support I have received from my advisor, Dr. Arnoldo Valle Levinson, and my committee member Dr. Maitane Olabarrieta. I also acknowledge Dr. Charles and Lucinda Carlson for accepting me as their own son and loving me despite my shortcomings. And lastly, I would like to thank my parents, Jeanne M. Huffman and James J. Gillin for providing me ever y opportunity to succeed in my upbringing.
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF FIGURES ................................ ................................ ................................ .......... 6 ABSTRACT ................................ ................................ ................................ ..................... 7 CHAPTER 1 I NTRODUCTI ON ................................ ................................ ................................ ...... 9 2 METHODS ................................ ................................ ................................ .............. 13 3 RESULTS ................................ ................................ ................................ ............... 17 January 15, 2016 ................................ ................................ ................................ .... 17 January 17, 2016 ................................ ................................ ................................ .... 22 4 DISCUSSION ................................ ................................ ................................ ......... 51 5 CONCLUSION ................................ ................................ ................................ ........ 56 LIST OF REFERENCES ................................ ................................ ............................... 57 BIOGRAPHIC AL SKETCH ................................ ................................ ............................ 60
6 LIST OF FIGURES Figure page 2 1 Locations providing data for this study. ................................ .............................. 16 3 1 De tided, filtered signal at 7 stations. ................................ ................................ 27 3 2 Atmospheric conditions on January 15 th 2016. ................................ .................. 28 3 3 Meteotsunami signal on January 15, 2016. ................................ ....................... 29 3 4 January 15, 2016 wavelet analysis ................................ ................................ ..... 30 3 5 Sketch of convection cells in the area behind a cold front together with a theoretical surface elevation response. ................................ .............................. 35 3 6 Filtered East West wind record at PCB on January 15 th 2017. .......................... 36 3 7 Wavelet analysis of wind signal on Januar y 15, 2016 from PCB. ...................... 37 3 8 Wavelet coherence analysis of wind signal on January 15, 2016 from PCB. Arrows indicate the phase difference between the two signals. .......................... 38 3 9 Spatial representation of the Froude number for the mes o scale convective system on January 15, 2016. ................................ ................................ ............. 39 3 10 Atmospheric conditions on January 17 th 2016. ................................ .................. 40 3 11 Meteotsunami signal on January 17, 2016. ................................ ........................ 41 3 12 January 17, 2016 wavelet analysis ................................ ................................ ..... 42 3 13 Filtered East West wind record at PCB on January 17 th 2017. .......................... 47 3 14 Wavelet analysis of wind signal on January 17, 2016 from PCB. ....................... 48 3 15 Wavelet coherence analysis of wind signal on January 17, 2016 from PCB. Arrows indicate the phase difference between the two signals. .......................... 49 3 16 Spatial representation of the Froude number for the atmospheric system on January 17, 2016. ................................ ................................ .............................. 50
7 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering METEOTSUNAMI OCCURRENCE AND PROPAGATION IN THE NORTHEASTERN GULF OF MEXICO By Matlack E. Gillin December 2017 Chair: Arnoldo Valle Levinson Major: Coastal and Oceanographic Engineering Meteotsunamis occur globally but have only recently gained attention in the Gulf of Mexico. Records from NOAA sensors and additional instruments were used to examine water levels and atmospheric pressure forcing in the northeastern Gulf of Mexico from December 2015 to February 2016. This analysis identified two meteotsunam i events both of which were produced by an oscillatory pressure signal Continuous Wavelet Transform analysis of water level and atmospheric pressure showed a remarkably similar structure in the frequency domain during both meteotsunamis. This qualitative ly suggested a dependence of water level on atmo spheric pressure. Additional wavelet coherence analysis showed that coherency existed between wind oscillations associated with convective cells a nd the meteotsunami water level. This indicated that both atmo spheric pressure and wind play ed a role in meteotsunami generation. Vector addition using atmospheric pressure peaks and troughs yielded the speed and direction of these atmospheric disturbances. The velocity of these disturbances was used, along with the shallow water wave approximation, to identify the location of atmosphere ocean resonance and the approximate position where these meteotsunamis became free waves. T his technique
8 can be complemented with numerical modeling to quantify the wave conditions re quired to reproduce the coastline signals. This will allow future research to determine the required meteotsunami amplification in the resonance region.
9 CHAPTER 1 INTRODUCTION tsunami research developed, this understanding was forced to shift due to the acknowledgment of submarine landslides, volcanic eruptions, and even me teorite impacts as generation mechanisms for common tsunamis. Beginning in 1996, however, the study of meteorological tsunamis, or meteotsunamis, has become prevalent within the tsunami community [Rabinovich and Monserrat, 1996]. Natural Hazards dedicated its entire October, 2014 issue to this phenomenon. Meteotsunamis develop from an atmospheric pressure disturbance that causes a perturbation in water level. This water level perturbation amplifies due to resonance effects [Monserrat et al., 2006]. Meteotsu namis have likely existed for centuries and have been assigned regional names such as rissaga in the dragging et al., 2008; Asano et al., 2012]. In 1978, Vela Luka, Croatia was hit with an estimated 6m high wave that devastated the local town, causing the equivalent of $27 million worth of damage [Monserrat et al, 2006]. In 2006, Ciutadella Harbor in Menorca, Sp ain, was inundated with a wave of approximately 4 m, destroying more than 40 boats and causing an estimate $30 million euros of damage [Monserrat et al, 2006]. And in the U.S., a strong southward propagating storm system passed over Daytona Beach, FL in 19 92, generating a meteotsunami of
10 approximately 3 m. This event caused injuries to 75 people and damaged 12 vehicles [Churchill et al., 1995; Sallenger et al., 1995]. A meteotsunami has the same spatial and propagation characteristics of a seismically generated tsunami but differs in generation mechanism. These long waves (wavelengths > 20 times water depth) have periods of a few minutes to a few hours (typically not mo re than 3 hours) [Monserrat et al, 2006]. An important characteristic of meteotsunamis is that, due to their extensive wavelength, they behave as shallow water waves in coastal regions. As such, the speed of these waves is a function of the water depth. T he depth dependent phase speed of meteotsunamis means that resonance will occur in an area where depth remains largely constant. In 2006, Monserrat et al. posited four meteotsunami generation requirements. The first of these requirements is the presence o f a 2 6 hPa pressure change This pressure change could be caused by an isolated pressure jump [ Hibiya and Kajiura, 1982; Vilibic et al., 2004, 2005] or by a train of atmospheric gravity waves [Gossard and Munk, 1954; Monserrat et al., 1991a; Garcies et al., 1996]. The second requirement is that the atmospheric disturbance must propagate in resonance with the shallow water wave celerity This resonance is most often associated with Proudman resonance, where the atmospheric disturbance translational speed equals the celerity of long ocean waves [Proudman, 1929]. Other means of resonance include Greenspan resonance and shelf resonance. In Greenspan resonance the alongshore component of the atmospheric disturbance velocity equals the celerity of the j th
11 mod e of edge waves [Greenspan, 1956]. In shelf resonance, the atmospheric disturbance and associated ocean wave have periods and/or wavelengths equal to the resonant period and/or wavelength of the shelf region [Monserrat et al, 2006]. These resonance effects are best understood by using the Froude number, Fr, where Fr = U a / C where U a is the speed of the atmospheric disturbance and C is the shallow water wave celerity. Maximum resonance occurs as the Froude number approaches 1. The third requirement for meteotsunami generation is that the resonant atmospheric disturbance propagates toward a semi enclosed basin, such as a harbor. This requirement, however, was challenged by showing that a strong convective system propagating seaward could cause a wave that reflected off the shelf, back toward the coast Lastly, in order for a meteotsunami to demonstrate deva stating effects, embayment resonance must occur, where the period of the incoming meteotsunami matches the resonant peri od of the associated embayment. In 2004, de Jong and Battjes found that meteotsunami generation is more sensitive to wind oscillations associated with convective systems than to a moving atmospheric pressure disturbance These results were shown in the North Sea when analyzing low frequency waves in vicinity of Port of Rotterdam, Netherlands. Convective systems exist when a cold front mov es over an area of warm water, causing an unstable lower atmosphere. This causes warm air at the sea surface to ascend. Movement of warm air into the atmosphere draws air underneath these convective cells to fill the void. If the air is sufficiently moist,
12 condensation can cause a release of latent heat that increases the rate of airflow. Narrow bands of clouds occur in these areas of convection, which correspond to areas of precipitation and are visible on radar reflectivity imagery. The northeastern Gulf of Mexico has recently received attention as a region of meteotsunami genesis [Olabarrieta et al., 2016] because of its shelf like bathymetry and propensity for cyclogenesis activity The frequent west to east propagation of storm systems in the northeaste rn Gulf of Mexico during winter favors the incidence of meteotsunami events at the coast. Increased incidence of meteotsunamis seems to coincide with El Nio episodes. This correlation motivated the exploration of meteotsunami incidence during the 2015 201 6 El Nio. The purpose of this study is to analyze the role of atmospheric forcing on meteotsunami generation and to characterize the spatial structure of meteotsunami waves in the northern Gulf of Mexico These two objectives were achieved with a series o f water level and atmospheric measurements along the northwestern coast of Florida, between Pensacola and Apalachicola Bays.
13 CHAPTER 2 METHODS Water level data were obtained from December 2015 to February 2016 at 3 C TD locations (P1, P3 and P4; P2 was not recovered) and 4 NOAA stations (Figure 2 1). A CTD Diver instrument recorded conductivity, temperature, and depth every 2 minutes. Station P1 was located approximately 10 kilometers east of the Destin inlet, P3 was approximately 5 kilometers east of the Panama City inlet, and P4 was located approximately mid way between Panama City Beach and Port St. Joe. NOAA stations at Pensacola (PSC), Panama City Beach (PCB), Panama City (PC) and Apalachicola (ALC) provided water level, barometric pressure, wind, and temperature data at 6 minute intervals. All CTD and NOAA water level signals were first de tided using t he U Tide program [Codiga, 2011] Once the tidal signal was removed, a band pass PL66TN filter was applied with a window period of 0.25 6 hours to remove other low frequency oscillations and high frequency contributions from wind waves. The signals at PCL, PCB, PC, and ALC were then line arly interpolated to provide 2 minute interval spacing to match the CTD records. The threshold to identify meteotsunamis was a value of 5 standard deviations (5 ) from the mean filtered records. This threshold was higher than that suggested by Monserrat e t al, 2006 but lower than the threshold of 6 suggested by Olabarietta et al, 2016. Next an amplitude threshold was established of 30cm (e.g. Rabinovich and Monserrat 1996), to clearly separate a meteotsunami signal from the invers e barometer effect. Th is ensured that spurious meteotsunami signals were not included in the data analysis. Once these metrics were applied to all water level records, events
14 were identified coinciding at 3 or more sites. T his allowed for description of the progression of movem ent of water level fluct uations in a meteotsunami event. Each of the 4 NOAA signals was high pass filtered with a PL66TN filter using a cutoff period of 6 hours to remove low frequency oscillations. Unlike the water level signals, the high frequency atmos pheric pressure signal was preserved to compare the role of isolated pressure jumps to that of atmospheric gravity waves. In reality, this analysis was limited due to the 6 minute sampling period Morlet Continuous Wavelet Transform analysis was performed on the de tided, filtered water levels to show the structure of the meteotsunami signal in the frequency domain and how that structure changed over time [Morlet et al., 1982]. The same analysis was used on the filtered atmospheric pressure records to deter mine if the frequency structure of the water level and atmospheric pressure were related. Additionally, low frequency wind variations associated with convective systems have been shown to affect meteotsunami growth [de Jong and Battjes, 2004]. Using wind d ata provided by the NOAA buoys at PCB and ALC, continuous wavelet transform analysis was used to determine the frequency structure of these low frequency wind oscillations. A 100m resolution grid of the Gulf of Mexico coastline was obtained from NOAA, alon g with a 0.05 resolution bathymetry grid. Additionally, radar reflectivity images were obtained from the NOAA Level III NEXRAD database. The speed and direction of the atmospheric disturbance associated with each
15 event was determined with vector addition, assuming that the atmospheric disturbance moved as a plane wave at a constant speed Because meteotsunamis are a product of resonance, a Froude number analysis was conducted to determine the potential location of this resonance. As discussed in Chapter 1 meteotsunamis have periods ranging from minutes to hours and, as such, always behave as shallow wat er waves in the coastal region [Monserrat et al, 2006] Using the shallow water wave celerity approximation of where C is the shallow water wave c elerity, g is the gravitational acceleration and h is the local water depth, one can see that meteotsunami wave speed is a function of depth. With this in mind, the bathymetry mentioned above was used to create a spatial representation of the Froude number for each event.
16 Figure 2 1: Locations providing data for this study. NOAA sites are shown as red triangles and CTD locations are shown as red circles. Henceforth, Pensacola will be referred to as PSC, Panama City Beach will be referred to as PCB, Panama City will be referred to as PC, and Apalachicola will be referred to as ALC.
17 CHAPTER 3 RESULTS Usin g the metrics described in Chapter 2, three meteotsunami events were identified between December 14, 2015 and February 16, 2016. Figure 3 1 shows the water level signal at all 7 stations for each of these three events. Of note, stations Pensacola, Panama C ity, and Apalachicola demonstrate damped meteotsunami signals because they are located inside estuaries. The third event, February 16 th occurred as the instruments began to cease recording, resulting in incomplete data for that event. This also prevent ed analysis of the frequency signal using a Morlet Wavelet due to the cone of influence collapsing. As such, the event on February 16 th 2016 is not analyzed further in this paper. January 15, 2016 On January 15, 2016 a meso scale convective system ( MCS ) d eveloped in the northwest Gulf of Mexico. As is common with most winter storms in this area, the storm had a general west to east propagation. The radar reflectivity imagery can be seen in Figure 3 2 a c. The associated atmospheric pressure signal, obtaine d from stations PCB and ALC, is shown in Figure 3 2.d and 3 2. e. Both signals are high pass filtered with a 6 hour cutoff period. As the system passed over stations PCL and P1, no clear squall line was yet present. At about 0730, a north south squall line began to emerge over Panama City with an apparent west to east propagation. The intensity of this squall line continued to increase as the storm moved eastward, resulting in a maximum intensity over ALC. As it passed over station PCB, the system showed a m a ximum pressure change of ~3.5 hPa over ~36 mins. The pressure change also occurred in the
18 form of an oscillatory motion, instead of the often cited instantaneous jump in meteotsunami generation [Choi et al, 2008]. As the atmospheric system developed and p assed over ALC, it then displayed a maximum pressure change of ~4 hPa over ~36 mins. The nature of the pressure change at ALC is characteristic of a n a brupt pressure change, typically associated with a well developed squall line. When standardized over a 1 0 minute interval the values for pressure ch ange at PCB and ALC were 0.97 hPa /10mins and 1.11 hPa /10mins, respectively. As seen in Figure 3 3 the first station to show a water level signal meeting the criteria for a meteotsunami event (5 sigma or greater and at least 30 cm in heig ht) was P3 at ~1006 UTC with a wave height of ~30 cm. The next stat ion was P4 at ~1032 UTC with a wave height of ~74 cm. The third and final station to demonstrate the characteristics of a meteotsuna mi was PCB at ~1124 UTC with a wave height of ~32 cm. Fluctuations are visible at each of the other four stations but do not meet the criteria for a meteotsunami event and are not considered in data analysis moving forward. To better understand the relationship between the behavior of a n atmospheric disturbance and sea level response, a simple comparison of atmospheric pressure and water level is insufficient. Continuous Wavelet Transform analysis was conducted on both the atmospheric pressure signal and the water level signal at each of these 3 applicable stations. The results of thes e analyses are shown in Figure 3 4 When comparing the atmospheric pressure signal at PCB to the signal at ALC, the general frequency structure of the signal
19 changed little as the system propagated from one location to the other. At PCB, maximum energy occurred with a period of ~2.2 hours at ~1000 UTC. At ALC, maximum energy occurred with a period of ~2 hours at approximately 1030 UTC. As seen in Figure 3 4.d and 3 4 .e, the amplitude of the pressure change in creased as the system propagated from PCB to ALC and the period associated with maximum energy decreased. Wavelet analysis of the water level at PCB reveals maximum energy with a period of ~2 hours starting at 1100 UTC and lasting until 1400 UTC. Although the structure of the atmospheric pressure signal and water level signal are similar, there is a the time lag of approximately 2 hours that occurred between the two different signals as they arrived at PCB. This time lag suggests that the wave separated fro m the atmospheric disturbance at some point offshore and slowed due to shoaling. At P3, maximum energy occurred with a period of ~2.2 hours at 1500 UTC. The time lag between maximum energy at PCB and P3 (approximately 5 km apart) suggests that interference potentially due to refraction, may be masking the first arrival of the wave at P3. Sheremet et al. (2016) showed that constructive interference is possible due to refraction. As such, one can surmise that deconstructive interference is also possible. Whe reas the signal at PCB dissipated after a few hours, the signal at P3 continued with similar energy to the leading edge. Occasional peaks of energy can be identified later that day with shorter periods of ~20 minutes, ~60 minutes, and ~100 minutes. Lastly, at P4, a leading edge of high energy appears at 0900 while the signal continued in the range of periods from 0.5 hrs to 2 hrs. This interval of high
20 energy occurred from 0900 UTC to 1100 UTC, at which point high energy only persisted in the range of 1 hr to 2 hrs until 1300 UTC. Later in the day, intervals of high energy were present in bands at 1 h ou r periods and 0.5 h ou r periods while original high energy periods of ~2 hours disappeared. A relationship is evident between the frequency structure of the at mospheric pressure signal and the frequency structure of the water level signal. Wavelet coherence was used to quantify this relationship, but yielded little to no co herence (results not shown). This lack of coherence suggests that another mechanism during this event leads to meteotsunami generation. De Jong and Battjes ( 2004 ) provide a sketch to describe the mechanisms of low frequency (0.1 2.0 m Hz) wind oscillations associated with convective cells as seen in Figure 3 5. The wind records from PCB were ana lyzed to determine if the behavior of the wind played a role. The high pass filtered east component of the wind is shown for January 15 th in Figure 3 6 Wavelet analysis explored the frequency structure of these wind oscillations (Figure 3 7 ). The wind fre quency structure behaves similarly to both the atmospheric pressure signal and the water level signal, but shows no time lag. In this case, the wavelet coherence (Figure 3 8 ) between water level and eastward wind is more revealing than the wavelet coherence between water level and atmospheric pressure. Coherence > 0 .8 exists at periods between 2 and 4 hours for the duration of the event. The wind signal leads the water level signal by approximately 90 180 degrees, wh ich corres ponds to a lead time of 0.5 to 2 hour s
21 To quantify the speed and direction of the atmospheric disturbance, a version of vector addition was used. Other methods have been proposed such as tion Function Method (Monserrat & Thorpe, 199 2). The Isochronal Method assumes a plane wave and uses a least squares regression to minimize the difference between expected and calculated atmospheric disturbance propagation. The Cross Correlation Function M ethod allows for an atmospheric disturbance to be dispersive, meaning that different frequency bands within the system can move in different directions and at different speeds. In this way, one can analyze multiple independent aspects of one storm system a nd isolate only the frequency band(s) that are needed. A third method exists which u ses radar reflectivity to create normal vectors from the line of maximum reflectivity and, using time lapse imagery, calculates the speed of this line. The applicability of this last method will be challenged in Chapter 4 of this paper. Using vector addition and assuming that the atmospheric disturbance associated with the MCS on January 15, 2016 traveled as a plane wave at constant speed it traveled at 18.5 m/s with a dire ction of 118 T. As noted before, meteotsunami waves, by virtue of their wavelength, travel as shallow water waves. As such, their celerity is a function of water depth. In order for the Froude number associated with this atmospheric disturbance to equal 1 the shallow water wave celerity must also equal 18.5 m/s, yielding a resonance depth of ~ 35 m. Using a bathymetry grid of the northern Gulf of Mexico, I identified the 35m isobath and those isobaths that would yield a Froude number
22 of 0.85 and 1.15. Reso nance decreases rapidly outside of +/ 5%, but for a spatial representation an d conservative analysis, +/ 15% was used [Proudman, number is shown in Figure 3 9 Again, using th e assumption of a plane wave without lateral constraints, a vector indicating the propagation direction can be applied to the spatial representation of the Froude number. This allowed elucidation of the maximum distance at which resonance would occur and t he point at which resonance would cease. Upon resonant cessation, the resulting wave would become free. Based on this analysis, the maximum distance that resonance could have occurred during the January 15 th event is 88 km. The wave then must have separate d from the atmospheric disturbance at a location just south of the Panama City Inlet. At this point, it became free to propagate in the same direction as the atmospheric disturbance before undergoing refraction and shoaling effects. January 17, 2016 Two da ys after the January 15 event, a similar event occurred in which a MCS passed over the northeastern section of the Gulf of Mexi co from west to east. Figure 3 10 a c show s the radar reflectivity images for this system. The associated atmospheric pressure si gnal, obtained from stations PC B and ALC, is shown in Figure 3 10.d and Figure 3 10 .e. In contrast to the January 15 th event, this system did not appear to have a well developed squall line associated with it. Rather, it contained a swath of radar reflectivity values that were more uniform than on January 15 th This poses a
23 challenge when attempting to locate the section of the system in which an atmospheric pressure disturbance would exist (typically one can assume it exists at the squall line). Although no such line is visible, the magnitude of pressure change is greater at both PCB and ALC than on January 15 th The maxi mum pressure change at PCB is 4.2 hPa in ~24 mins while the maximum pressure change at ALC is 4 hPa in ~42 mins. When standardized over a 10 minute interval, these pressure changes at PCB and ACL equate to 1.75 hPa/10mins and 0.95 hPa /10mins, respectively. Comparing this to the event on January 15 th the rate of pressure change is 56% higher at PCB while the rate of pressure change at ACL is 14% lower on January 17 th than it was on January 15 th This analysis demonstrates a weakening of the pressure disturb ance as it propagates eastward, in contrast with the January 15 th atmospheric disturbance, which strengthened over time. Also of note, the initial N wave structure of the atmospheric pressure signal at PCB changes to a nearly solitary atmospheric pressure signal at ALC. This unique behavior may affect the resonance process for meteotsunami generation, but has not been simulated in numerical models. The trough of the atmospheric pressure signal is eliminated as it passes over ALC, suggesting that multiple at mospheric pressure signals with different frequencies are moving within the system at different speeds, causing constructive or deconstructive interference. This behavior has been shown to exist and is the basis for the Isochronal Method for quantifying th e speed and
24 On January 17 th the first station meeting the aforementioned criteria for water level signal was P1 (as measured at time of peak w ater level) at 0850 UTC with a wave height of ~38 cm. The signal then appeared to propagate eastward from this location. The next station to show maximum wave height was PCB at 0928 UTC with a wave height of ~33 cm. Following PCB were P3 and P4 which exhibited the signal simultaneously with wave he ights of ~44 cm and ~60 cm, respectively. The January 17 th water levels are shown in Figure 3 11 As was the case on January 15 th a wavelet analysis was conducted on both the atmospheric pressure signal and water level signal associated with the January 1 7 th event. These an alyses are shown in Figure 3 12 a e. The frequency structure of the atmospheric pressure signal at PCB shows an initial high energy band arriving at approximately 0400 UTC with a dominant period of ~2 hours. By 0800 UTC, this structure h as changed to a maximum energy contribution from a dominant period of ~2.5 hours but notably higher energies across the energy spectrum from ~10 minutes to ~3 hours. By ~1800 UTC, all energies above the 95% confidence limit have dissipated. The ALC structu re is similar in that it also shows an initial high energy contribution from a period of ~2 hours, occurring at approximately 0600 UTC. This main contribution from a period of ~2 hours persists until approximately 1000 UTC, where it then dissipates. Wavele t analyses of the water levels at PCB P3, and P4 (shown in Figure 3 12 c e) tell a similar story. Most notably, the water level frequency structure at PCB shows a leading edge of high energy at approximately 0600 UTC with a dominant period of ~2.5 hours, followed shortly thereafter by a relatively uniform
25 distribution of high energy from periods of 1 hour to 2.5 hours. Moreover, a simple visual comparison between the two shows a remarkably similar structure between the atmospheric pressure signal and water level signal at PCB. At P3, wavelet analysis of the water level signal shows a similar overall structure to PCB, but identifying a leading edge of high energy is difficult due to the spread of high energies over different frequencies. The maximum energy a t P3 occurs at approximately 1000 UTC with a dominant period of ~2.5 hours. Lastly, at P4, water level wavelet analysis shows higher energies across the entire time window, with maximum energy occurring at approximately 0800 UTC with dominant periods of ~1 .2 hours and ~2.5 hours. By 1500 UTC these high energy bands have dissipated into lower energy, broad spectrum contributions. The high pass filtered wind signal, shown in Figure 3 13 reveals oscillatory motion with smaller amplitudes than on January 15 th When converted into frequency space, one can see that the frequency structure of the wind oscillations does not appear in sync with the water level or atmosp heric pressure signal (Figure 3 14 ). Maximum energy occurs at ~0600 with a period close to 3 hour s. From here, no discernable behavior exists. Wavelet coherence was then used to quantitatively analyze the relationship (or lack thereof) between water level and wind oscillations The result, shown in Figure 3 15 is somewhat surprising and shows signifi cant coherence (>.8) in periods between 1.5 and 2.5 hours for the duration of the event. The wind signal leads the water level signal by ~135 also corresponding to a lead time of between 0.5 and 1 hour. Just as was shown in the January 15 th analysis, the role of wind oscillations cannot be
26 neglected in studying the relationship between meteotsunami waves and atmospheric forcing. Applying the same method used to analyze the January 15 th atmospheric disturbance speed and direction, the January 17 th system moved at 35.6 m/s with a direction of 113.5 T. For resonance to occur, this atmospheric disturbance speed corresponds to a resonance depth of ~100 m. As before, the 100 m isobath was identified and is shown as a spatial representation of the Froud e number in Figure 3 16 This event produced a free wave just south of P1. While the January 15 th event did not produce a signal at P1 meeting meteots unami criteria, the January 17 th system did. This is expected due to the wave becoming free at a more west ward location than the January 15 th system.
27 Figure 3 1: De tided, filtered signal at 7 stations. Wave heights are offset by multiples of 50 cm. The stations are in order from west to east, such that a signal propagating to the right as the y axis decreases represents a n eastward propagation. The events of January 15, January 17, and February 16 are highlighted in red.
28 Figure 3 2: Atmospheric conditions on January 15 th 2016. Radar reflectivity imagery from NOAA Level III NEXRAD at a) 0730 UTC, b) 0900 UTC, and c) 1030 UTC. d) High passed atmospheric pressure signal at PCB and e) high passed atmospheric pressure signal at ALC.
29 Figure 3 3 : Meteotsunami signal on January 15, 2016. Data has been de tided and band pass filtered with a window of 0.25 6 hrs.
30 Figure 3 4 : January 15, 2016 w avelet analysis of a) atmospheric pressure sign al from PCB, b) atmospheric pressure sign al from ALC, c) w ater level signal from PCB, d) water level signal from P3, and e) water level signal from P4. Periods greater than 3 hours have been grayed out to indicate that they are outside of the meteotsunami frequency band.
31 Figure 3 4: Continued
32 Figure 3 4: Con tinued
33 Figure 3 4: Continued
34 Figure 3 4: Continued
35 Figure 3 5: Sketch of convection cells in the area behind a cold front together with a theoretical surface elevation response.
36 Figure 3 6: Filtered East West wind record at PCB on January 15 th 2017.
37 Figure 3 7: Wavelet analysis of wind signal on January 15, 2016 from PCB. Periods greater than 3 hours have been grayed out to indicate that they are outside of the meteotsunami frequency band.
38 Figure 3 8: Wavelet coherence analysis of wind signal on January 15, 2016 from PCB. Arrows indicate the phase difference between the two signals. (Arrow pointing up indicates water level leads wind by 90 )
39 Figure 3 9: Spatial representation of the Froude number for the meso scale convective system on January 15, 2016. The blue line indicates the propagation of the atmospheric disturbance, optimized for the maximum potential resonance.
40 Figure 3 10: Atmospheric conditions on January 17 th 2016. Rada r reflectivity imagery from NOAA Level III NEXRAD at a) 0730 UTC, b) 0900 UTC, and c) 1030 UTC. d) High passed atmospheric pressure signal at PCB and e) high passed atmospheric pressure signal at ALC.
41 Figure 3 11: Meteotsunami signal on Janu ary 17, 2016. Data has been de tided and band pass filtered with a window of 0.25 6 hrs.
42 Figure 3 12 : January 17, 2016 w avelet analysis of a) atmospheric pressure sign al from PCB, b) atmospheric pressure sign al from ALC, c) water level signal from PCB, d) water level signal from P3, and e) water level signal from P4. Periods greater than 3 hours have been grayed out to indicate that they are outside of the meteotsunami frequency band.
43 Figure 3 12: Continued
44 Figure 3 12: Continued
45 Figure 3 12: Continued
46 Figure 3 12: Continued
47 Figure 3 13: Filtered East West wind record at PCB on January 17 th 2017.
48 Figure 3 14: Wavelet analysis of wind signal on January 17, 2016 from PCB. Periods greater than 3 hours have been grayed out to indicate that they are outside of the meteotsunami frequency band.
49 Figure 3 15: Wavelet coherence analysis of wind signal on January 17, 2016 from PCB. Arrows indicate the phase difference between the two signals. (Arrow pointing up indicates water level leads wind by 90
50 Figure 3 16: Spatial representation of the Froude number for the atmospheric system on January 17, 2016. The blue line indicates the propagation of the atmospheric disturbance, optimized for the maximum potential resonance.
51 CHAPTER 4 DISCUSSION Possible meteotsunami generation mechanisms relate to instantaneous pressure jumps or trains of atmospheric gravity waves [ Hibiya and Kajiura, 1982; Vilibic et al., 2004, 2005; Gossard and Munk 1954; Monserrat et al., 1991a; Garcies et al., 1996 ] In the Gulf of Mexico, it appears that the os cillatory motion seen in Figure 3 2 and Figure 3 10 is more indicative of wave trains causing meteotsunamis. The change in water surface elevation due to P roudman resonance can be given as [Proudman, 1929; Monserrat et al., 2006; Choi et al., 2008; Vilibic 2008]: ( 4 1 ) where is the water level variation due to the inverse barometer effect, is the change in atmospheric pressure, g is the acceleration of gravity, and is the density of water. The celerity is the shallow water wave celer ity, where h is the water depth and U a is the speed of the atmospheric disturbance. Rearranging, we can define the Froude number as As shown here, amplification increases as the Froude number approaches a value of 1. Additionally, as the Fro ude number approaches 1, the maximum elevation change is given by: ( 4 2 )
52 where is the distance the pressure jump travels while resonance is present and L is the horizontal scale of the pressure jump. Equation 4 2 was applied to both the January 15 th and January 17 th events to determine the maximum elevation change due to atmospheric pressure ove r the distances shown in Figure 3 9 and Figure 3 16 For both events, this approach yielded values that were one order of magnitude smaller than the water levels recorded by sensors. This discrepancy indicates that solely analyzing for atmospheric pressure is insufficient. Analytical expressions must be developed th at include resonance caused by atmospheric pressure and wind oscillations. For both of the meteotsunami events, wavelet analysis of water level and atmospheric pressure show similar frequency structures. Further analysis shows, however, that this similarit y can be misleading. Wavelet coherence, which quantitatively measures the similarity of the signals, yielded little to no coherence between the two. January 15 th wind records, when transformed into a wavelet spectrum, looked similar to the water level and atmospheric pressure signals, but only showed coherence with the water level signal January 17 th wind records do not visually resemble either the associated water level or atmospheric p ressure signals, but still show coherence with the water level signal. While this does not prove that atmospheric pressure forcing is negligible, it does allow one to conclude that wind oscillations play a role in meteotsunami amplification Again, f urther research is required to determine the balance, if any, that these two factors strike in the development of meteotsunamis.
53 The Gulf of Mexico, because of its extensive shelf bathymetry, provides a unique opportunity to study meteotsunami generation and propagation. Due to the influence of El Nio in winter 2015 2016, I was able to select from at least 9 atmospheric systems that had the potential to generate meteotsunamis. Such ability is rare in the study of meteotsunamis because of their unpredictability. A number of assumptions were made to determine the time at which the meteotsunamis on January 15 th and January 17 th became free waves. The first, and most crucial, is the existence of a well structured convective system that travels as a plane (linear) wave. The atmospheric pressure and wind data presented here are fro m land based sensors at least 40 km from the location where resonance should have occurred. If atmospheric data could be obtained from the geographical resonance area, it could be different from that obtained by a land based sensor. Other authors have use d radar reflectivity values to determine the speed The methods presented in this paper challenge this ap proach. As seen on January 15 th a clear squall line develops as the system propagates westward with a maximum ra te of pressure change of 1.11 hPa /10mins. Such a squall line does not exist on January 17 th and yet the magnitude of the pressure change is ab out 50% higher. If the magnitude of the radar reflectivity value does not correspond to the magnitude of the pressure change, one should question whether the speed and direction of this squall line corresponds to the speed and
54 direction of the pressure dis turbance. Still, a limitation of the results presented in vector addition and assuming a plane wave. The 4 NOAA stations used in this study make a nearly straight line, limitin g the effectiveness of triangulation. If another sensor existed (ideally in open water), more accurate speed and direction calculations would be possible. A major limitation to this research is the absence of numerical modeling. A number of studies attempt to capture the behavior of meteotsunamis in numerical models [Vilibic et al., 2014; Whitmore and Knight, 2014], but the community has yet to provide an effective air sea coupled model that can capture the effects of resonance. The information presented in this paper should be used in the future to identify the location where a meteotsunami becomes a free wave. Using numerical modeling, one could presumably create a meteotsunami wave at this location, free of resonant forcing, that would yield the same sign al response on the coastline as the events of January 15 th and January 17 th This approach would provide a specific amplitude of the wave at the point of separation and, comparing this to the wave size at the generation point (only influenced by the invers e barometer effect), one could quantify the amplification of a meteotsunami during this period of resonance. In the future, at least 3 atmospheric pressure sensors should be deployed i n the areas described by Figure 3 9 and Figure 3 16 Atmospheric pressu re sensors will allow accurate characterizations of the geometry of an atmospheric pressure disturbance. Because meteotsunami studies use coastal sensors to
55 detect meteotsunamis, other types of forcing often muddle these signals (refraction, diffraction, s hoaling, etc.). Sensors placed in open water will allow for a more focused study of meteotsunami amplification due to resonance. As stated before, meteotsunamis can have devastating effects on coastal communities. These effects are especially intense when harbor resonance occurs. Because of this, further study should be considered to analyze the vulnerability of coastal inlets to meteotsunamis. Additionally, priority should be dedicated to develop ing a system that can accurately forecast meteotsunami events. The current limitation to this is a lack of spatial resolution for atmospheric pressure sensors. The results presented in this paper can serve as a basic characterization of conditions favorable f or meteotsunami generation (speed, direction, and amplitude of pressure disturbance). Given better spatial resolution, these conditions could be monitored in real time to suggest when coastal communities in the northeast Gulf of Mexico should expect meteot sunami activity.
56 CHAPTER 5 CONCLUSION Meteotsunamis are common in the northeastern Gulf of Mexico. The typical eastward propagation of atmospheric disturbances in the winter months makes Panama City and areas east of it particularly susceptible to these long wave phenomena. The results shown here demonstrate that meteotsunamis of over 70 cm are possible and can be caused by atmospheric disturbances in multiple types of storm structures. Meteotsunami appearance in the Gulf of Mexico is related to oscillatory m otion in atmospheric properties. In addition to the atmospheric pressure signal, coherence between the meteotsunami water level and oscillatory wind patterns indicates a relevant role of wind associated with convective systems. Lastly, t his st udy presents a novel approach, using spatial Froude number representation, to identify the physical location of resonance and the point where an atmosphere coupled wave becomes a free wave. Using this approach, future research can model a wave that starts at this location and propagates toward the shoreline, recreating a signal similar to established sensors. In this way, one can determine precisely how much amplification occurs during this resonance period, which in turn will allow for re examination of cu rrent understanding of resonant mechanics.
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60 BIO GRAPHICAL SKETCH Matlack E. Gillin received a Bachelor of Science in Ocean Engineering from the United States Naval Academy in May 2010. He was then commissioned in the United States Navy as a Nuclear Submarine Officer. He attended Navy Nuclear Propulsion Training Command in Charleston, SC and Naval Propulsion Training Unit in Ballston Spa, NY before checking on board USS MARYLAND in transitioned to Commander, Submarine Forces Atlantic in Norf olk, VA as a Submarine Watch Officer. He separated from active duty in July 2016 to pursue graduate studies at the University of Florida. He recei ved a Master of Engineering in coastal and oceanographic e ngineering in December 2017.