# Transformation of Infragravity Waves during Hurricane Overwash

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## 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] |

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**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% |

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**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