# Infragravity Wave Oscillation Forecasting in a Shallow Estuary

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data Acquisition

#### 2.2. Data Preparation

#### 2.3. Signal Processing

#### 2.4. Machine Learning

## 3. Results

#### 3.1. Infragravity Correlations and Orbital Velocities

#### 3.2. Infragravity Predictions

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

NOAA | National Oceanic and Atmospheric Administration |

CDIP | Coastal Data Information Program |

## References

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**Figure 1.**(

**Left**): Locations for the study area, analyzed NOAA tide gauge (circle) and wave stations (triangles). (

**Right**): Study area and ADV locations within the Seal beach estuary. On the bottom right corner are wave heights for station 46253 during 2021 (https://www.ndbc.noaa.gov/, accessed on 12 March 2024). Maps extracted from https://earthexplorer.usgs.gov/, accessed on 12 March 2024.

**Figure 3.**(

**a**) Water level time series for one 16-min ADV burst and (

**b**) its associated frequency spectrum. (

**c**) Principal axes flow velocity time series for the same 16-min ADV burst and (

**d**) the associated frequency spectrum. The vertical dashed red lines represent the IG frequency band limits.

**Figure 4.**(

**a.1**) Normalized IG significant wave height (${H}_{s,IG}$) and IG $STE$ temporal distribution for the analyzed water level ADV recordings at ADV 1 in 2020 and (

**a.2**) 2021. (

**b.1**) Significant wave height and peak period from the offshore nearest buoy, 46,256 in 2020 and (

**b.2**) 2021. (

**c.1**) Mean wave direction recorded by the buoy 46,256 in 2020 and (

**c.2**) 2021. (

**d.1**) Mean tidal water levels over each burst at ADV 1 in 2020 and (

**d.2**) 2021. (

**e.1**) Wind speed magnitude and direction in 2020 and (

**e.2**) 2021. (

**f.1**) Atmospheric pressure in 2020 and (

**f.2**) 2021.

**Figure 5.**(

**a**) Correlation coefficients for the 2020 and 2021 ADV deployments. ${H}_{s}{T}_{p}^{2}$, where ${H}_{s}$ and ${T}_{p}$ are the significant wave height and peak period for the considered NOAA wave buoys (subindices: 1–46,253, 2–46,256 and 3–46,222); d is the hourly tidal water level at Long Beach Harbor tide station. For all the obtained correlations, the obtained P value lies below 0.001. (

**b**) RFR feature importance, Table 1.

**Figure 6.**(

**a.1**) Spectrogram associated with the CDIP buoy 46,256 during the observational periods of 2020 and (

**a.2**) 2021. (

**b.1**) Calculated estuarine IG significant wave height at ADV 1 during the 2020 observational period and (

**b.2**) during the 2021 observational period. (

**c.1**) Offshore significant wave height for the three considered NOAA buoy stations during the 2020 observational period and (

**c.2**) during the 2021 observational period. (

**d.1**) Tidal and orbital velocities recorded by ADV 1 during the 2020 observational period and (

**d.2**) during the 2021 observational period.

**Figure 7.**(

**a.1**) Estuarine IG spectral energy for the observational period of 2020. (

**a.2**) Total IG energy per burst from ADV 1. (

**b**) Average energy per burst related to the tidal water level for both studied ADVs during the observational period of 2020. (

**c**) Average frequency energy spectrum for ebbing and flooding stages at ADV 2. (

**d**) Average frequency energy spectrum for the 20% highest and 20% lowest observed water levels for ADV 2.

**Figure 8.**(

**a**) Average frequency spectrum for the all the 2020 and 2021 analyzed recordings at ADV 1. The extracted IG sub-bands are highlighted in gray. (

**b**) Calculated Pearson linear correlation coefficients between the $STE$ of different IG wave sub-bands and different variables, including offshore wave conditions and water levels for the recordings during 2020 and (

**c**) 2021.

**Figure 9.**IG significant wave height predicted values by the RFR and SVR algorithms against the actual values. The line in red represents the best fit.

**Figure 10.**(

**a**) SVR and (

**b**) RFR algorithms applied first to a dataset constructed with the 2020 and 2021 observational periods in grey and to a dataset composed by both observational periods together with different prediction time windows. The circles represent outliers.

**Table 1.**Features utilized as input of the ML algorithm. $Are{a}_{spec}$ stands for the area under the wave frequency energy spectrum associated with the wave buoy recordings and ${M}_{wd}$ is the mean wave direction.

Buoy 46,256 | Tide Station | Met. Station |
---|---|---|

${H}_{s}{T}_{p}^{2}$ (ms^{2}) | OWL (m) | ${p}_{atm}$ (Pa) |

${M}_{wd}$ (Deg) | ${w}_{mag}$ (m/s) | |

$Are{a}_{spec}$ | ${w}_{dir}$ (Deg) | |

${F}_{p,swell}$ (Hz) | ||

$Kurtosis$ | ||

$Skewness$ |

**Table 2.**Final ML IG oscillation regression results after the application of hyperparameter grid search and k-fold technique. The features are listed in Table 1.

${\mathit{R}}^{2}$ | $\mathit{MSE}$ (m^{2}) | |
---|---|---|

SVR | 0.575 | 2.094 $\times {10}^{-6}$ |

RFR | 0.643 | 1.864 $\times {10}^{-6}$ |

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## Share and Cite

**MDPI and ACS Style**

Gomez, B.; Giddings, S.N.; Gallien, T.
Infragravity Wave Oscillation Forecasting in a Shallow Estuary. *J. Mar. Sci. Eng.* **2024**, *12*, 672.
https://doi.org/10.3390/jmse12040672

**AMA Style**

Gomez B, Giddings SN, Gallien T.
Infragravity Wave Oscillation Forecasting in a Shallow Estuary. *Journal of Marine Science and Engineering*. 2024; 12(4):672.
https://doi.org/10.3390/jmse12040672

**Chicago/Turabian Style**

Gomez, Bernabe, Sarah N. Giddings, and Timu Gallien.
2024. "Infragravity Wave Oscillation Forecasting in a Shallow Estuary" *Journal of Marine Science and Engineering* 12, no. 4: 672.
https://doi.org/10.3390/jmse12040672