# Evidence of Ocean Waves Signature in the Space–Time Turbulent Spectra of the Lower Marine Atmosphere Measured by a Scanning LiDAR

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Campaign

#### 2.1. Test Site

^{®}Scan 100S depicted in Figure 1, from the research laboratory in Hydrodynamics, Energetics and Atmospheric Environment (LHEEA), was deployed to explore micro-scale wind–wave interactions close to the water surface by performing horizontal scans at a height of 18 m above the mean sea level (MSL). The sLiDAR was installed 100 m from the coastline in the peninsula of Le Croisic (France), on the balcony of a seafront villa with a clear view to the North Atlantic ocean from 135° to 260°. The location of Le Croisic is shown in Figure 2a, with the wind rose obtained for 2008–2017 from [59], giving the prevailing wind direction (WD) of south-west and north-east. The test site is mostly a suburban area, composed of low-rise buildings and parks with a south-western rocky coastline, aligned with an 110°–290° axis for nearly 10 km, as pictured in Figure 2b. Directly to the north-east of the sLiDAR’s position (47°17${}^{\prime}$8.6${}^{\u2033}$ N, −2°31${}^{\prime}$1.5${}^{\prime \prime}$ E), the Penn-Avel park is a densely forested area with tall vegetation of approximately 10 m in height. The local ground is around 8 m above the MSL with a mean slope of 8% down to the water in the south-west direction.

#### 2.2. sLiDAR Technology and Experimental Setup

#### 2.2.1. Technology and Challenges

#### 2.2.2. Calibration and Configuration

#### 2.3. Environmental Description and Test-Case Selection

#### 2.3.1. Meteocean Conditions

#### 2.3.2. Test Cases

## 3. Data Treatment and Analyses

#### 3.1. Energy Density Functions

#### 3.2. Two-Dimensional Fourier Transform

## 4. Results

#### 4.1. Radial Wind Speed Fluctuations

#### 4.2. One-Dimensional Turbulent Spectra

#### 4.3. Two-Dimensional Turbulent Spectrum

#### 4.3.1. Resultant Single-Sided Spectrum

#### 4.3.2. Opposing Directions and the Four-Quadrant Spectrum

#### 4.4. Rising Wind and Diminishing Sea-State

## 5. Discussion

#### 5.1. Deviations from the Taylor and Random Sweeping Hypotheses

#### 5.2. Coherence and Correlation in a Space–Time Perspective

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

1D | One-dimensional |

2D | Two-dimensional |

ABL | Atmospheric Boundary Layer |

CNR | Carrier-to-noise-ratio |

EDF | Energy Density Function |

ESDU | Engineering Sciences Data Unit |

f-LOS | fixed LOS |

FT | Fourier Transform |

FFT | Fast FT |

LiDAR | Light Detection and Ranging System |

LHEEA | Laboratory in Hydrodynamics, Energetics and Atmospheric Environment |

LOS | Line of Sight |

MABL | Marine ABL |

MSL | Mean Sea Level |

PPI | Plan Position Indicator |

RWS | Radial Wind Speed |

sLiDAR | scanning LiDAR |

SST | Sea Surface Temperature |

TI | Turbulence Intensity |

TKE | Turbulent Kinetic Energy |

UTC | Universal Time Coordinated |

WA | Wave Age |

WBL | Wave Boundary Layer |

WC | Wave-Coherent |

WD | Wind Direction |

WI | Wave-Induced |

WS | Wind Speed |

WWIII | WAVEWATCH III |

## Appendix A. Data Quality and Filter

#### Appendix A.1. Carrier-To-Noise Ratio

**Figure A1.**Cumulative distributions of Carrier-to-Noise-Ratio (CNR) occurrences below the threshold. Cases 01 and 02a depicted with full or limited f-LOS range.

#### Appendix A.2. Spike Detection and Removal

**Figure A2.**The full blue line exemplifies a time-series of ${u}_{R}(x,t)$. For spike detection, the full orange line is the low-frequency estimate ${u}_{\alpha}(x,t)$. For reconstruction, the yellow dotted line is the high-frequency estimate ${u}_{\beta}(x,t)$. The spike value is identified by a purple dot, then replaced by the green dot below.

#### Appendix A.3. Signal Reconstruction

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**Figure 1.**The sLiDAR on the balcony of a seafront villa at Le Croisic, France. Radial Line-Of-Sight (R, LOS), and vertical (z) axis. Roll ($\psi $), pitch (elevation angle $\theta $), and yaw (azimuth angle $\varphi $) angular movements.

**Figure 2.**sLiDAR position denoted by a red dot and water depth displayed by the colormap. (

**a**) Location of Le Croisic on the French west Atlantic coast. The wind rose for Le Croisic was taken from the Global Wind Atlas [59], covering the period 2008–2017. (

**b**) View of Le Croisic peninsula, with the Plan Position Indicator (PPI) scans for WD determination in the black sector, and staring mode measurements’ lines (f-LOS) for Case 01 (blue) and Cases 02[a–c] (red) in dashed lines. Oceanic conditions were estimated from the HOMERE hind-cast database. The hind-cast grid is depicted by its nodes in yellow dots; probing was performed in the node depicted in magenta.

**Figure 3.**Evolution of wind and sea-state quantities around Cases 01 (left) and 02[a–c] (right). (

**a**,

**b**) Horizontal Wind Speed (WS) and Wind Direction (WD). Wave model (WWIII) hind-cast: (

**c**,

**d**) the significant wave height (${H}_{s}$) and peak period (${T}_{p}$); (

**e**,

**f**) the wave peak direction (${\alpha}_{w}$) and directional spreading (${\beta}_{w}$).

**Horizontal lines**in (

**a**,

**b**,

**e**,

**f**) denote the sLiDAR fLOS-aligned directions ${\varphi}_{L}$ and ${\varphi}_{L}-180$°.

**Vertical lines**denote the initial, middle and final moments of the selected periods.

**Figure 4.**10-min records of the Radial Wind Speed (RWS) from (

**a**) Case 01, and (

**b**) Case 02a. Mean RWS in dash-dotted lines. Peak wave phase and group velocities (${c}_{p}$ and ${c}_{g}$) slopes as dashed and dotted lines, respectively, dashed lines being distant by ${T}_{p}$ (Table 3). An indicative value of 0.5 RWS is provided for comparison in (

**a**).

**Figure 5.**(

**a**,

**c**) Wave-number k and (

**b**,

**d**) frequency f dependent 1D turbulent spectra ${E}_{{u}_{R}^{\prime}{u}_{R}^{\prime}}$; for (

**a**,

**b**) Case 01, and (

**c**,

**d**) Case 02a. Observed 10-min spectra in light grey, and the 3-h average in black full lines. The Engineering Sciences Data Unit (ESDU) reference is given in black dashed lines. Vertical blue lines stand for the wave peak scales ${k}_{p}$ and ${f}_{p}$, and green lines show the filter scales ${k}_{\gamma}$ and ${f}_{\gamma}$, for wave-number and frequency spectra, respectively.

**Figure 6.**Wave-number–angular-frequency 2D turbulent spectra ${E}_{{u}_{R}^{\prime}{u}_{R}^{\prime}}(k,w)$, for (

**a**) Case 01 and (

**b**) Case 02a. The mean RWS velocity is depicted by a black full line, and the wave velocity as dashed lines for $d=[14,22,30]$ m. The wave peak scale (${L}_{p},{T}_{p}$) is denoted by a star. The sLiDAR filter wave-length is given in the green dashed vertical lines.

**Figure 7.**Four-quadrants (${Q}_{\pm \pm}$) of the Energy Density Function (EDF) of ${u}_{R}^{\prime}{u}_{R}^{\prime}$, referred to by negative and positive wave-numbers ${k}_{\pm}$ or angular-frequencies ${w}_{\pm}$. (

**a**) Case 01 with waves and wind aligned in the same direction (Ocean to land) in quadrants ${Q}_{++}$ and ${Q}_{--}$. (

**b**) Case 02a with the wind aligned in the opposite direction (Land to ocean) in quadrants ${Q}_{+-}$ and ${Q}_{-+}$.

**Figure 8.**RWS contours for Case 02b. Mean RWS and peak wave phase velocity slopes as dash-dotted and dashed lines, respectively. Dashed lines are at a distance of ${T}_{p}$.

**Figure 9.**1D frequency dependent spectra for Case 02b. Observations of 10-min spectra in light grey, the 3-h average in black full lines, and the ESDU reference in black dashed lines.

**Figure 10.**Wave-number–angular-frequency 2D turbulent spectra ${E}_{{u}_{R}^{\prime}{u}_{R}^{\prime}}(k,w)$, for diminishing WA scenarios in (

**a**) Case 02b and (

**b**) Case 02c. The lines denote the characteristic scales described for Case 02a in Figure 6b.

**Figure 11.**One quadrant (${Q}_{++}$) of the wave-number–angular-frequency 2D turbulent spectrum ${E}_{{u}_{R}^{\prime}{u}_{R}^{\prime}}(k,w)$ for Case 02c. The lines denote the characteristic scales described in Figure 6.

**Figure 12.**Spectral valley (dashed) and ridges (dotted), observed in the 2D turbulent spectra of Case 01 in Figure 6. Here adapted: axes and color ranges.

**Table 1.**Staring mode scans for Case 01 (f-LOS 01) and Cases 02[a–c] (f-LOS 02); and PPI mode scans for the reconstruction of the wind speed (WS) and wind direction (WD). The elevation angle is $\theta =$ 0° and the gate length ${L}_{\gamma}=$ 25 m.

Scan | ${\mathit{\varphi}}_{\mathit{L}}$ | Rot. Speed | Gate Spacing | First Gate | Last Gate | Acc. Time | Duration |
---|---|---|---|---|---|---|---|

(°) | (°s${}^{-1}$) | (m) | (km) | (km) | (s) | (s) | |

f-LOS 01 | 221.8 | 0 | 10 | 1.00 | 2.00 | 1.00 | 600 |

f-LOS 02 | 221.8 | 0 | 10 | 0.75 | 1.75 | 0.25 | 600 |

PPI | [154–199] | 3 | 25 | 0.50 | 1.75 | 1.00 | 16 |

**Table 2.**Summary of the wind parameters for each test case. Date and time; f-LOS total average radial wind speed (RWS) ${U}_{R}$, wind direction (WD), turbulence intensity (TI), air–sea temperature difference $\Delta T$, and the bulk Richardson number $Ri{}_{b}$.

Case ID | Day | Start Time | ${\mathit{U}}_{\mathit{R}}$ | WD | TI | $\mathit{\Delta}\mathit{T}$ | $\mathbf{Ri}{}_{\mathit{b}}$ |
---|---|---|---|---|---|---|---|

(UTC) | (m s${}^{-1}$) | (°) | (%) | (°C) | (Stability) | ||

01 | 12 November 2020 | 11:10:32 | 4.12 | 212 | 8.6 | 1.4 | 0.04 (Stable) |

02a | 4 November 2020 | 07:10:24 | 4.29 | 60 | 10.0 | −6.2 | −0.17 (Unstable) |

02b | 4 November 2020 | 19:41:19 | 5.31 | 51 | 13.7 | −4.6 | −0.09 (Unstable) |

02c | 5 November 2020 | 04:44:30 | 6.93 | 56 | 12.1 | −7.2 | −0.08 (Unstable) |

**Table 3.**Summary of the sea-state parameters for each test case. Wave age (WA); significant height ${H}_{s}$, wave peak period ${T}_{p}$ and length ${L}_{p}$, phase and group velocities ${c}_{p}$ and ${c}_{g}$, mean wave direction ${\alpha}_{w}$, and directional spreading ${\beta}_{w}$.

Case ID | WA | ${\mathit{H}}_{\mathit{s}}$ | ${\mathit{T}}_{\mathit{p}}$ | ${\mathit{L}}_{\mathit{p}}$ | ${\mathit{c}}_{\mathit{p}}$ | ${\mathit{c}}_{\mathit{g}}$ | ${\mathit{\alpha}}_{\mathit{w}}$ | ${\mathit{\beta}}_{\mathit{w}}$ |
---|---|---|---|---|---|---|---|---|

(m) | (s) | (m) | (m s${}^{-1}$) | (m s${}^{-1}$) | (°) | (°) | ||

01 | 3.0 | 1.3 | 10.1 | 127 | 12.5 | 9.4 | 241 | 26 |

02a | −3.1 | 1.0 | 13.5 | 181 | 13.5 | 11.4 | 247 | 30 |

02b | −2.5 | 0.7 | 13.2 | 177 | 13.4 | 11.3 | 249 | 46 |

02c | −1.9 | 0.6 | 12.5 | 166 | 13.3 | 11.0 | 219 | 71 |

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## Share and Cite

**MDPI and ACS Style**

Paskin, L.; Conan, B.; Perignon, Y.; Aubrun, S. Evidence of Ocean Waves Signature in the Space–Time Turbulent Spectra of the Lower Marine Atmosphere Measured by a Scanning LiDAR. *Remote Sens.* **2022**, *14*, 3007.
https://doi.org/10.3390/rs14133007

**AMA Style**

Paskin L, Conan B, Perignon Y, Aubrun S. Evidence of Ocean Waves Signature in the Space–Time Turbulent Spectra of the Lower Marine Atmosphere Measured by a Scanning LiDAR. *Remote Sensing*. 2022; 14(13):3007.
https://doi.org/10.3390/rs14133007

**Chicago/Turabian Style**

Paskin, Liad, Boris Conan, Yves Perignon, and Sandrine Aubrun. 2022. "Evidence of Ocean Waves Signature in the Space–Time Turbulent Spectra of the Lower Marine Atmosphere Measured by a Scanning LiDAR" *Remote Sensing* 14, no. 13: 3007.
https://doi.org/10.3390/rs14133007