# Transformation of Infragravity Waves during Hurricane Overwash

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Field Observations

#### 2.1. Study Sites

#### 2.2. Instrumentation

#### 2.3. Overview of Storm Impacts

#### 2.4. Groundwater Effects and Bed Level Change at PT-1

## 3. Methods

#### 3.1. Wave Statistics

#### 3.2. Spectral Estimation

#### 3.3. Multitaper Bispectral Estimation

## 4. Results

#### 4.1. Surf Zone Wave Fields

#### 4.2. IG Wave Transformation during Overwash

## 5. Discussion

#### 5.1. Cross-Barrier Changes in IG Energy during Overwash

#### 5.2. Importance and Origin of VLF Variability

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Zero-Level Bicoherence for the Multitaper Method

**Figure A1.**(

**a**) the 95% significance level for zero bicoherence as a function of degrees of freedom for the adaptive (circle) and non-adaptive (x) multitaper bispectral estimator (MBE). Theoretical significance levels are represented by solid lines for time-bandwidth products $NW$ = 2, 3, 5 with $K=2NW$ tapers, as is the 95% confidence bound (dashed) for the traditional segment-averaged technique detailed by Haubrich [51]; (

**b**) quantile–quantile plot of ${\widehat{b}}_{mt}^{2}({f}_{1},{f}_{2})$ using the adaptive MBE for $NW=3$ ($K=6$) versus a theoretical gamma distribution (equivalently a scaled ${\chi}_{2}^{2}$ distribution) and (

**c**) the maximum-likelihood estimate fit of a gamma distribution (parameters in Table A1).

**Table A1.**Gamma distribution parameters ($\alpha $, $\beta $) for theoretical and maximum-likelihood estimates (MLE) of ${\widehat{b}}_{mt}^{2}({f}_{1},{f}_{2})$ with confidence limits (CL) for two example time-bandwidth products $NW$.

$\mathit{NW}$ | ${\mathit{\alpha}}_{\mathit{theor}}$ | ${\mathit{\beta}}_{\mathit{theor}}$ | ${\mathit{\alpha}}_{\mathit{MLE}}$ [95% CL] | ${\mathit{\beta}}_{\mathit{MLE}}$ [95% CL] |
---|---|---|---|---|

2 | 1 | 0.00130 | 0.99 [0.98 1.01] | 0.00135 [0.00133 0.00137] |

3 | 1 | 0.00058 | 0.99 [0.97 1.00] | 0.00060 [0.00058 0.00061] |

## References

- Sallenger, A.H., Jr. Storm impact scale for barrier islands. J. Coast. Res.
**2000**, 16, 890–895. [Google Scholar] - Holland, K.T.; Holman, R.A.; Sallenger, A.H. Estimation of overwash bore velocities using video techniques. In Coastal Sediments; American Society of Civil Engineers: Reston, VA, USA, 1991; pp. 489–497. [Google Scholar]
- Hoekstra, P.; Haaf, M.T.; Buijs, P.; Oost, A.; Breteler, R.K.; van der Giessen, K.; van der Vegt, M. Washover development on mixed-energy, mesotidal barrier island systems. In Proceedings of the Coastal Dynamics 2009: Impacts of Human Activities on Dynamic Coastal Processes; World Scientific: Singapore, 2009; pp. 1–12. [Google Scholar] [CrossRef]
- Matias, A.; Ferreira, Ó.; Vila-Concejo, A.; Morris, B.; Dias, J.A. Short-term morphodynamics of non-storm overwash. Mar. Geol.
**2010**, 274, 69–84. [Google Scholar] [CrossRef] - Sherwood, C.R.; Long, J.W.; Dickhudt, P.J.; Dalyander, P.S.; Thompson, D.M.; Plant, N.G. Inundation of a barrier island (Chandeleur Islands, Louisiana, USA) during a hurricane: Observed water-level gradients and modeled seaward sand transport. J. Geophys. Res. Earth Surf.
**2014**, 119, 1498–1515. [Google Scholar] [CrossRef] [Green Version] - Engelstad, A.; Ruessink, B.; Wesselman, D.; Hoekstra, P.; Oost, A.; van der Vegt, M. Observations of waves and currents during barrier island inundation. J. Geophys. Res. Ocean.
**2017**, 122, 3152–3169. [Google Scholar] [CrossRef] [Green Version] - Lashley, C.H.; Bertin, X.; Roelvink, D.; Arnaud, G. Contribution of Infragravity Waves to Run-up and Overwash in the Pertuis Breton Embayment (France). J. Mar. Sci. Eng.
**2019**, 7, 205. [Google Scholar] [CrossRef] [Green Version] - Huntley, D.; Guza, R.; Bowen, A. A universal form for shoreline run-up spectra? J. Geophys. Res.
**1977**, 82, 2577–2581. [Google Scholar] [CrossRef] - Guza, R.; Thornton, E.B. Swash oscillations on a natural beach. J. Geophys. Res. Ocean.
**1982**, 87, 483–491. [Google Scholar] [CrossRef] - Ruggiero, P.; Holman, R.A.; Beach, R. Wave run-up on a high-energy dissipative beach. J. Geophys. Res. Ocean.
**2004**, 109. [Google Scholar] [CrossRef] [Green Version] - Senechal, N.; Coco, G.; Bryan, K.R.; Holman, R.A. Wave runup during extreme storm conditions. J. Geophys. Res. Ocean.
**2011**, 116. [Google Scholar] [CrossRef] [Green Version] - Hughes, M.G.; Aagaard, T.; Baldock, T.E.; Power, H.E. Spectral signatures for swash on reflective, intermediate and dissipative beaches. Mar. Geol.
**2014**, 355, 88–97. [Google Scholar] [CrossRef] [Green Version] - Ruessink, B. Observations of turbulence within a natural surf zone. J. Phys. Oceanogr.
**2010**, 40, 2696–2712. [Google Scholar] [CrossRef] [Green Version] - Fiedler, J.W.; Brodie, K.L.; McNinch, J.E.; Guza, R.T. Observations of runup and energy flux on a low-slope beach with high-energy, long-period ocean swell. Geophys. Res. Lett.
**2015**, 42, 9933–9941. [Google Scholar] [CrossRef] [Green Version] - Inch, K.; Davidson, M.; Masselink, G.; Russell, P. Observations of nearshore infragravity wave dynamics under high energy swell and wind-wave conditions. Cont. Shelf Res.
**2017**, 138, 19–31. [Google Scholar] [CrossRef] - Bertin, X.; Martins, K.; de Bakker, A.; Chataigner, T.; Guérin, T.; Coulombier, T.; de Viron, O. Energy transfers and reflection of infragravity waves at a dissipative beach under storm waves. J. Geophys. Res. Ocean.
**2020**, 125, e2019JC015714. [Google Scholar] [CrossRef] - Bertin, X.; Olabarrieta, M. Relevance of infragravity waves in a wave-dominated inlet. J. Geophys. Res. Ocean.
**2016**, 121, 5418–5435. [Google Scholar] [CrossRef] [Green Version] - Bertin, X.; Mendes, D.; Martins, K.; Fortunato, A.B.; Lavaud, L. The closure of a shallow tidal inlet promoted by infragravity waves. Geophys. Res. Lett.
**2019**, 46, 6804–6810. [Google Scholar] [CrossRef] - Mendes, D.; Fortunato, A.B.; Bertin, X.; Martins, K.; Lavaud, L.; Silva, A.N.; Pires-Silva, A.A.; Coulombier, T.; Pinto, J.P. Importance of infragravity waves in a wave-dominated inlet under storm conditions. Cont. Shelf Res.
**2020**, 192, 104026. [Google Scholar] [CrossRef] - Roelvink, D.; Reniers, A.; Van Dongeren, A.; de Vries, J.v.T.; McCall, R.; Lescinski, J. Modelling storm impacts on beaches, dunes and barrier islands. Coast. Eng.
**2009**, 56, 1133–1152. [Google Scholar] [CrossRef] - McCall, R.T.; De Vries, J.V.T.; Plant, N.; Van Dongeren, A.; Roelvink, J.; Thompson, D.; Reniers, A. Two-dimensional time dependent hurricane overwash and erosion modeling at Santa Rosa Island. Coast. Eng.
**2010**, 57, 668–683. [Google Scholar] [CrossRef] - Baumann, J.; Chaumillon, E.; Bertin, X.; Schneider, J.L.; Guillot, B.; Schmutz, M. Importance of infragravity waves for the generation of washover deposits. Mar. Geol.
**2017**, 391, 20–35. [Google Scholar] [CrossRef] - Battjes, J.; Bakkenes, H.; Janssen, T.; Van Dongeren, A. Shoaling of subharmonic gravity waves. J. Geophys. Res. Ocean.
**2004**, 109. [Google Scholar] [CrossRef] [Green Version] - Van Dongeren, A.; Battjes, J.; Janssen, T.; Van Noorloos, J.; Steenhauer, K.; Steenbergen, G.; Reniers, A. Shoaling and shoreline dissipation of low-frequency waves. J. Geophys. Res. Ocean.
**2007**, 112. [Google Scholar] [CrossRef] [Green Version] - De Bakker, A.; Tissier, M.; Ruessink, B. Shoreline dissipation of infragravity waves. Cont. Shelf Res.
**2014**, 72, 73–82. [Google Scholar] [CrossRef] - Henderson, S.M.; Bowen, A. Observations of surf beat forcing and dissipation. J. Geophys. Res. Ocean.
**2002**, 107, 14. [Google Scholar] [CrossRef] - Henderson, S.M.; Guza, R.; Elgar, S.; Herbers, T.; Bowen, A. Nonlinear generation and loss of infragravity wave energy. J. Geophys. Res. Ocean.
**2006**, 111. [Google Scholar] [CrossRef] [Green Version] - Thomson, J.; Elgar, S.; Raubenheimer, B.; Herbers, T.; Guza, R. Tidal modulation of infragravity waves via nonlinear energy losses in the surfzone. Geophys. Res. Lett.
**2006**, 33. [Google Scholar] [CrossRef] [Green Version] - Ruju, A.; Lara, J.L.; Losada, I.J. Radiation stress and low-frequency energy balance within the surf zone: A numerical approach. Coast. Eng.
**2012**, 68, 44–55. [Google Scholar] [CrossRef] - Guedes, R.; Bryan, K.R.; Coco, G. Observations of wave energy fluxes and swash motions on a low-sloping, dissipative beach. J. Geophys. Res. Ocean.
**2013**, 118, 3651–3669. [Google Scholar] [CrossRef] - de Bakker, A.; Herbers, T.; Smit, P.; Tissier, M.; Ruessink, B. Nonlinear infragravity-wave interactions on a gently sloping laboratory beach. J. Phys. Oceanogr.
**2015**, 45, 589–605. [Google Scholar] [CrossRef] [Green Version] - De Bakker, A.; Tissier, M.; Ruessink, B. Beach steepness effects on nonlinear infragravity-wave interactions: A numerical study. J. Geophys. Res. Ocean.
**2016**, 121, 554–570. [Google Scholar] [CrossRef] [Green Version] - Herbers, T.; Russnogle, N.; Elgar, S. Spectral energy balance of breaking waves within the surf zone. J. Phys. Oceanogr.
**2000**, 30, 2723–2737. [Google Scholar] [CrossRef] - Morton, R.A. Texas barriers. In Geology of Holocene Barrier Island Systems; Springer-Verlag: Berlin/Heidelberg, Germany, 1994; pp. 75–114. [Google Scholar]
- Morton, R.A.; Miller, T.L.; Moore, L.J. National Assessment of Shoreline Change: Part 1: Historical Shoreline Changes and Associated Coastal Land Loss along the US Gulf of Mexico; U.S. Geological Survey Open-file Report 2004-1043; U.S. Geological Survey: Reston, VA, USA, 2004.
- Blake, E.; Zelinsky, D. Hurricane Harvey. NOAA, National Hurricane Center Tropical Cyclone Report. 2018. Available online: https://www.nhc.noaa.gov/data/tcr/AL092017_Harvey.pdf (accessed on 25 July 2018).
- USACE; JALBTCX; NOAA; National Ocean Service; Office for Coastal Management (OCM). 2016 USACE NCMP Topobathy Lidar DEM: Gulf Coast (TX); NOAA’s Ocean Service, OCM: Charleston, SC, USA, 2017. [Google Scholar]
- Turner, I.L.; Nielsen, P. Rapid water table fluctuations within the beach face: Implications for swash zone sediment mobility? Coast. Eng.
**1997**, 32, 45–59. [Google Scholar] [CrossRef] - Turner, I.L.; Masselink, G. Swash infiltration-exfiltration and sediment transport. J. Geophys. Res. Ocean.
**1998**, 103, 30813–30824. [Google Scholar] [CrossRef] - Horn, D.P. Measurements and modelling of beach groundwater flow in the swash-zone: A review. Cont. Shelf Res.
**2006**, 26, 622–652. [Google Scholar] [CrossRef] - Sous, D.; Lambert, A.; Rey, V.; Michallet, H. Swash—Groundwater dynamics in a sandy beach laboratory experiment. Coast. Eng.
**2013**, 80, 122–136. [Google Scholar] [CrossRef] - Sous, D.; Petitjean, L.; Bouchette, F.; Rey, V.; Meulé, S.; Sabatier, F.; Martins, K. Field evidence of swash groundwater circulation in the microtidal rousty beach, France. Adv. Water Resour.
**2016**, 97, 144–155. [Google Scholar] [CrossRef] [Green Version] - Guza, R.; Thornton, E.; Holman, R. Swash on steep and shallow beaches. In Proceedings of the 19th International Conference on Coastal Engineering, Houston, TX, USA, 3–7 September 1984; pp. 708–723. [Google Scholar] [CrossRef]
- Thomson, D.J. Spectrum estimation and harmonic analysis. Proc. IEEE
**1982**, 70, 1055–1096. [Google Scholar] [CrossRef] [Green Version] - Raubenheimer, B.; Elgar, S.; Guza, R.T. Estimating Wave Heights from Pressure Measured in Sand Bed. J. Waterw. Port Coast. Ocean. Eng.
**1998**, 124, 151–154. [Google Scholar] [CrossRef] - Bronez, T.P. On the performance advantage of multitaper spectral analysis. IEEE Trans. Signal Process.
**1992**, 40, 2941–2946. [Google Scholar] [CrossRef] - Rahim, K.J.; Burr, W.S.; Thomson, D.J. Applications of Multitaper Spectral Analysis to Nonstationary Data. R Package Version 1.0-14. Ph.D. Thesis, Queen’s University, Kingston, ON, Canada, 2014. [Google Scholar]
- Collis, W.; White, P.; Hammond, J. Higher-order spectra: The bispectrum and trispectrum. Mech. Syst. Signal Process.
**1998**, 12, 375–394. [Google Scholar] [CrossRef] - Elgar, S.; Guza, R. Observations of bispectra of shoaling surface gravity waves. J. Fluid Mech.
**1985**, 161, 425–448. [Google Scholar] [CrossRef] - Birkelund, Y.; Hanssen, A.; Powers, E.J. Multitaper estimators of polyspectra. Signal Process.
**2003**, 83, 545–559. [Google Scholar] [CrossRef] - Haubrich, R.A. Earth noise, 5 to 500 millicycles per second: 1. Spectral stationarity, normality, and nonlinearity. J. Geophys. Res. Ocean.
**1965**, 70, 1415–1427. [Google Scholar] [CrossRef] - Kim, Y.C.; Powers, E.J. Digital Bispectral Analysis and Its Applications to Nonlinear Wave Interactions. IEEE Trans. Plasma Sci.
**1979**, 7, 120–131. [Google Scholar] [CrossRef] - Birkelund, Y.; Hanssen, A. Multitaper estimators for bispectra. In Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics, Caesarea, Israel, 16 June 1999; pp. 207–211. [Google Scholar]
- Stockdon, H.F.; Holman, R.A.; Howd, P.A.; Sallenger, A.H., Jr. Empirical parameterization of setup, swash, and runup. Coast. Eng.
**2006**, 53, 573–588. [Google Scholar] [CrossRef] - Bertin, X.; de Bakker, A.; Van Dongeren, A.; Coco, G.; Andre, G.; Ardhuin, F.; Bonneton, P.; Bouchette, F.; Castelle, B.; Crawford, W.C.; et al. Infragravity waves: From driving mechanisms to impacts. Earth-Sci. Rev.
**2018**, 177, 774–799. [Google Scholar] [CrossRef] [Green Version] - Billson, O.; Russell, P.; Davidson, M. Storm Waves at the Shoreline: When and Where Are Infragravity Waves Important? J. Mar. Sci. Eng.
**2019**, 7, 139. [Google Scholar] [CrossRef] [Green Version] - Lippmann, T.; Herbers, T.; Thornton, E. Gravity and shear wave contributions to nearshore infragravity motions. J. Phys. Oceanogr.
**1999**, 29, 231–239. [Google Scholar] [CrossRef] - Tucker, M. Surf beats: Sea waves of 1 to 5 min. period. Proc. R. Soc. Lond. A
**1950**, 202, 565–573. [Google Scholar] [CrossRef] - Guza, R.; Thornton, E.B. Observations of surf beat. J. Geophys. Res. Ocean.
**1985**, 90, 3161–3172. [Google Scholar] [CrossRef] - Elgar, S.; Herbers, T.; Guza, R. Reflection of ocean surface gravity waves from a natural beach. J. Phys. Oceanogr.
**1994**, 24, 1503–1511. [Google Scholar] [CrossRef] - Sheremet, A.; Guza, R.; Elgar, S.; Herbers, T. Observations of nearshore infragravity waves: Seaward and shoreward propagating components. J. Geophys. Res. Ocean.
**2002**, 107, 10-1. [Google Scholar] [CrossRef] - List, J.H. A model for the generation of two-dimensional surf beat. J. Geophys. Res. Ocean.
**1992**, 97, 5623–5635. [Google Scholar] [CrossRef] - Masselink, G. Group bound long waves as a source of infragravity energy in the surf zone. Cont. Shelf Res.
**1995**, 15, 1525–1547. [Google Scholar] [CrossRef] - Janssen, T.; Battjes, J.; Van Dongeren, A. Long waves induced by short-wave groups over a sloping bottom. J. Geophys. Res. Ocean.
**2003**, 108. [Google Scholar] [CrossRef] - Guerin, T.; de Bakker, A.; Bertin, X. On the Bound Wave Phase Lag. Fluids
**2019**, 4, 152. [Google Scholar] [CrossRef] [Green Version] - Freilich, M.H.; Guza, R.T.; Whitham, G.B. Nonlinear effects on shoaling surface gravity waves. Philos. Trans. R. Soc. Lond. Ser. Math. Phys. Sci.
**1984**, 311, 1–41. [Google Scholar] [CrossRef] - Herbers, T.; Burton, M. Nonlinear shoaling of directionally spread waves on a beach. J. Geophys. Res. Ocean.
**1997**, 102, 21101–21114. [Google Scholar] [CrossRef] - Biésel, F. Équations générales au second ordre de la houle irrégulière. La Houille Blanche
**1952**, 3, 372–376. [Google Scholar] [CrossRef] [Green Version] - Longuet-Higgins, M.S.; Stewart, R. Radiation stress and mass transport in gravity waves, with application to ‘surf beats’. J. Fluid Mech.
**1962**, 13, 481–504. [Google Scholar] [CrossRef] - Hasselmann, K. On the nonlinear energy transfer in a gravity-wave spectrum Part 1. General theory. J. Fluid Mech.
**1962**, 12, 481–500. [Google Scholar] [CrossRef] - Masuda, A.; Kuo, Y.Y. A note on the imaginary part of bispectra. Deep. Sea Res. Part A Oceanogr. Res. Pap.
**1981**, 28, 213–222. [Google Scholar] [CrossRef] - Oltman-Shay, J.; Howd, P.; Birkemeier, W. Shear instabilities of the mean longshore current: 2. Field observations. J. Geophys. Res. Ocean.
**1989**, 94, 18031–18042. [Google Scholar] [CrossRef] - Haller, M.C.; Putrevu, U.; Oltman-Shay, J.; Dalrymple, R.A. Wave group forcing of low frequency surf zone motion. Coast. Eng. J.
**1999**, 41, 121–136. [Google Scholar] [CrossRef] - Shi, L.; Olabarrieta, M.; Nolan, D.S.; Warner, J.C. Tropical cyclone rainbands can trigger meteotsunamis. Nat. Commun.
**2020**, 11, 678. [Google Scholar] [CrossRef] - Olabarrieta, M.; Valle-Levinson, A.; Martinez, C.J.; Pattiaratchi, C.; Shi, L. Meteotsunamis in the northeastern Gulf of Mexico and their possible link to El Niño Southern Oscillation. Natural Hazards
**2017**, 88, 1325–1346. [Google Scholar] [CrossRef] [Green Version] - Tissier, M.; Bonneton, P.; Ruessink, B. Infragravity waves and bore merging. In Proceedings of the Coastal Dynamics 2017, Helsingor, Denmark, 12–16 June 2017; pp. 451–460. [Google Scholar]
- García-Medina, G.; Özkan-Haller, H.; Holman, R.A.; Ruggiero, P. Large runup controls on a gently sloping dissipative beach. J. Geophys. Res. Ocean.
**2017**, 122, 5998–6010. [Google Scholar] [CrossRef] - Elgar, S.; Sebert, G. Statistics of bicoherence and biphase. J. Geophys. Res. Ocean.
**1989**, 94, 10993–10998. [Google Scholar] [CrossRef] - Elgar, S.; Guza, R.T. Statistics of bicoherence. IEEE Trans. Acoust. Speech Signal Process.
**1988**, 36, 1667–1668. [Google Scholar] [CrossRef] - Birkelund, Y.; Hanssen, A.; Powers, E.J. Multitaper estimation of bicoherence. In Proceedings of the 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing, Salt Lake City, UT, USA, 7–11 May 2001; Volume 5, pp. 3085–3088. [Google Scholar] [CrossRef] [Green Version]
- Thomson, D.J. Multi-window bispectrum estimates. In Proceedings of the Workshop on Higher-Order Spectral Analysis, Vail, CO, USA, 28–30 June 1989; pp. 19–23. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) location map of both field sites in relation to Hurricane Harvey’s track with relevant storm locations denoted in hours relative to hurricane landfall. (

**b**) post-storm cross-island profiles measured proximate to both pressure transducers (PT) at Matagorda Peninsula (“MP”, the east profile bisects PT-1 and the center profile PT-2) and (

**c**) the acoustic Doppler velocimeter with co-located PT (ADV+PT) at Follets Island (“FI”). The dotted lines in the aerial subsets of (

**a**) delineate the profile locations. Elevation Z is relative to North American Vertical Datum 1988 (NAVD88) and the mean high water (MHW) is plotted for additional reference.

**Figure 2.**Hydrodynamic conditions measured during Hurricane Harvey (

**a**) offshore (data from National Data Buoy Center (NDBC) Station 42019, 82 m water depth), (

**b**–

**d**) in the backshore (PT-1) and back barrier (PT-2) at Matagorda Peninsula (MP), and (

**e**,

**f**) in the surf zone (ADV+PT) at Follets Island (FI). Bulk statistics include (

**a**) deep-water significant wave height ${H}_{0}$ and mean spectral wave period ${T}_{0}$; (

**b**–

**c**) mean spectral period ${T}_{{P}_{IG}}$ and height ${H}_{{P}_{IG}}$ of pressure head in the IG frequency band; (

**e**) incoming IG significant wave height ${H}_{IG+}$ and sea-swell significant wave height ${H}_{SS}$; (

**f**) mean water depth h; and (

**d**) pressure head referenced to NAVD88 (Z, referenced using post-storm PT elevations). The gray shaded region in (

**b**–

**d**) corresponds to the time period of overwash and Phase I and Phase II reference different periods of groundwater dynamics (see Figure 4). The difference between the dashed lines in (

**d**) denotes the estimated bed-level change at PT-1 from post-storm reconnaissance (i.e., 47 cm).

**Figure 3.**Morphological impacts at Matagorda Peninsula from Hurricane Harvey as shown through comparison of pre- and post-storm digital elevation maps (DEMs) as well as site reconnaissance photographs (I–III, taken one week after storm landfall). The pre-storm DEM was created from September 2016 LiDAR (−1 year) collected as part of the United States Army Corps of Engineers (USACE) National Coastal Mapping Program [37], and the post-storm DEM (+1 week) using images collected by an unmanned aerial vehicle (UAV) in combination with a stereo photogrammetric structure-from-motion (SfM) algorithm. The location of the berm(s) is annotated in both DEMs for interpretation of storm impacts.

**Figure 4.**(

**a**) pressure head in the backshore at Matagorda Peninsula (PT-1) for the time period when wave-like signals were observed in the sea-swell and IG frequency range (−18.8 to 9 h). The schematics show how the pressure time series are categorized within two “phases”, corresponding to the degree to which the capillary fringe influences the pressure head of surface wave and swash signals due to a decoupling of the groundwater table (WT) and sand bed. Subsets of (

**a**) are shown in (

**b**,

**e**) for Phase I, when the mean water level (MWL), WT, and sand bed are rising but at different rates and with varying time-evolution; (

**c**) a transitional period that depicts the last WT pressure signal prior to Phase II; and (

**d**) Phase II, when the sand bed is fully coupled to the WT. During Phase II, pressure head fluctuations are assumed to be hydrostatic and representative of surface waves. See text for additional interpretations.

**Figure 5.**(

**a**) time series of the instantaneous free surface elevation $\eta $ in the surf zone at Follets Island proximate to landfall, low-pass filtered to depict wave phenomena at very-low frequencies (“VLF”, 0.1–3 mHz, 5.6 min to 2.8 h periods); (

**b**) surf zone wave power spectra $S\eta \eta +$ (plotted for the IG frequency band only) from Follets Island. Multitaper spectral estimates were generated using ∼68 min records of the high-frequency free-surface elevation $\eta +$ (incoming only, $f>0.002$ Hz), a time bandwidth of 8, and 15 Slepian tapers, yielding a passband bandwidth $2W$ of 0.0039 Hz and about 28 degrees of freedom (dof) per frequency; (

**c**) the imaginary component of the bispectrum im $\left\{\widehat{B}({f}_{1},{f}_{2})\right\}$ early in the storm (−19 h) and (

**d**) proximate to hurricane landfall (−8 h), computed using 8 ∼9 min sub-records of ${\eta}^{+}$, a time bandwidth of 3, and 5 Slepian tapers yielding a passband bandwidth $2W$ of 0.0117 Hz and about 64 dof per frequency. The solid lines in (

**c**,

**d**) correspond to the frequency cutoff between IG and swell energy whereas dashed lines in (

**b**–

**d**) partition the IG frequency band into low- (0.003–0.015 Hz), middle- (0.015–0.027 Hz), and high-frequency (0.027–0.04 Hz) components. Bispectral estimates are set to zero below a bicoherence of 0.14.

**Figure 6.**Pressure head P recorded over ∼2 h in (

**a**) the backshore (PT-1) and (

**b**) back barrier (PT-2) at Matagorda Peninsula during overwash. Time series are low-pass filtered (cutoff frequency of 0.003 Hz) to highlight VLF variations in pressure head. Note the different vertical plot scales in (

**a**,

**b**).

**Figure 7.**IG pressure head power spectra ${S}_{pp}$ in the (

**a**) backshore and (

**b**) back barrier during overwash at Matagorda Peninsula (−5 to 0 h), all obtained from ∼34 min records of the high-frequency pressure head ($f>0.002$ Hz). The time bandwidth of the ∼34 min multitaper spectral estimates is 5 with 9 Slepian tapers, yielding a $2W$ of 0.0049 Hz and about 16 dof per frequency. The dashed lines partition the IG frequency band into low- and high-frequency components.

**Figure 8.**The imaginary component of the bispectrum im $\left\{\widehat{B}({f}_{1},{f}_{2})\right\}$ generated using four 17 min records (zero-padded) of the high-passed pressure head as measured in the backshore at Matagorda Peninsula (PT-1) for two time periods during overwash that were deemed sufficiently stationary: (

**a**) −4 to −3 h and (

**b**) −3 to −2 h. A time bandwidth of 5 and 9 Slepian tapers were used, resulting in a passband bandwidth $2W$ of 0.005 Hz and about 64 dof per frequency. The dashed lines partition the IG frequency band into low- and high-frequency components. Bispectral estimates are set to zero below a bicoherence of 0.11.

**Figure 9.**NEXRAD radar reflectivity mosaics from NOAA depicting land-falling tropical cyclone rainbands (TCRs) offshore both field sites (

**a**) coincident with the initiation of coastal flooding in the backshore at Matagorda Peninsula (“MP”, Figure 4b) and (

**b**) just prior to the peak water level at MP (Figure 6). Atmospheric disturbances accompanying TCRs can trigger meteotsunami in the GOM, and it is hypothesized that VLF fluctuations at both field sites are meteotsunami.

**Table 1.**Mean water depth h scenarios for estimation of the cross-barrier change in IG energy flux $\Delta F$ during overwash (−4 to −3 h) given uncertainties in bed level.

Scenario | PT-1 | PT-2 | $\mathbf{\Delta}\mathit{F}$ (% Decrease between PT-1 and PT-2) | ||
---|---|---|---|---|---|

h [cm] | Total IG | High-f IG (0.01–0.04 Hz) | Low-f IG (0.003–0.01 Hz) | ||

Maximum depth | 30 | 52 | 86% | 70–71% | 95–96% |

Minimum depth | 10 | 40 | 79% | 52–56% | 92–94% |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Anarde, K.; Figlus, J.; Sous, D.; Tissier, M.
Transformation of Infragravity Waves during Hurricane Overwash. *J. Mar. Sci. Eng.* **2020**, *8*, 545.
https://doi.org/10.3390/jmse8080545

**AMA Style**

Anarde K, Figlus J, Sous D, Tissier M.
Transformation of Infragravity Waves during Hurricane Overwash. *Journal of Marine Science and Engineering*. 2020; 8(8):545.
https://doi.org/10.3390/jmse8080545

**Chicago/Turabian Style**

Anarde, Katherine, Jens Figlus, Damien Sous, and Marion Tissier.
2020. "Transformation of Infragravity Waves during Hurricane Overwash" *Journal of Marine Science and Engineering* 8, no. 8: 545.
https://doi.org/10.3390/jmse8080545