# Identifying 2010 Xynthia Storm Signature in GNSS-R-Based Tide Records

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## Abstract

**:**

## 1. Introduction

^{−1}and pressure down from ~1000 to 977 hPa that were recorded by meteorological stations during high spring tide were responsible for a huge storm surge along the coast of the Bay of Biscay [14,17]. For example a surge of 1.53 m was recorded at La Rochelle tide gauge (8.01 m above the hydrographic zero). Such a high tide level was never recorded since the set-up of this tide gauge in 1997. The surge was also greater than the largest recorded at Brest tide gauge (1.42 m) during the last 150 years [13]. For this reason, the densification of sensors and observations is crucial in establishing a well-structured surveillance and warning system to ensure the safety of populations. Currently, tide gauges that now used radar technique to measure the tides along the French coast ensured long-term monitoring. They are more and more co-located with either GNSS geodetic receivers or Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) space geodesy system to separate the changes in Sea Surface Height (SSH) from crustal motions (e.g., Wöppelmann et al., 2006 [18]).

## 2. Study Area

## 3. Datasets

#### 3.1. GNSS Data

#### 3.2. Tide Gauge Data

#### 3.3. Meteorological Data

^{−3}is density of seawater; and, g = 9,81 cms

^{−2}is the mean acceleration of gravity [32].

#### 3.4. Significant Wave Height Data

## 4. Methods

#### 4.1. Inversion of the SNR Data

#### 4.2. Analysis of the GNSS-R-Based Water Levels

#### 4.2.1. Singular Spectrum Analysis

#### 4.2.2. Continuous Wavelet Transform

## 5. Results

#### 5.1. GNSS-R SSH Time Series Analysis Using the SSA Method

#### 5.2. GNSS-R SSH Time Series Analysis Using CWT Method

## 6. Discussion

#### 6.1. The Accidental Tide Gauge and More

- -
- the presence of several buildings, dikes, which mask part of the GNSS satellite and are likely to cause parasite multi-paths (more than one reflection), and
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- the presence of boats in the bay that are likely to also cause other parasite multi-paths.

- -
- many other GNSS geodetic stations from permanent networks around the world can also be used as accidental tide gauges to complement or improve the existing tide gauge networks,
- -
- GNSS geodetic stations offer the opportunity to record other geophysical phenomena such SWH (e.g., Roussel et al., (2015) [22]) or surge or inverted barometer (this study), and
- -
- if located on a better environment as the top of a hill or a mast, better accuracy can be reached (e.g., 0.12 m see [47]). The choice of the location and the altitude of deployment can be facilitated by the use of dedicated softwares, such as GNSS Reflected Signals Simulations (GRESS) [48] or the GPS tool box [49], which provide a simulation of the position of the reflection points depending on the location of the GNSS geodetic station.

#### 6.2. The Choice of the SSA and CWT for Separating Tides from Other Geophysical Parameters

#### 6.3. The Complementarity Between SSA and Inverse CWT (iCWT) to Separate Tides from Other Geophysical Signals

#### 6.4. Is Each SSA Mode Related to a Single Geophysical Phenomena?

_{atmos}(R = 0.70, Figure 5b). A wavelet cross-correlation (XWT) and a liner correlation between RC3 and the sum of the surge and h

_{atmos}were performed (Figure 8a,b), respectively. Higher correlations were found over a long time period. Very high correlations are observed between the two variables for periods that are higher than two weeks. High correlations were found on the periods 4–8 days before and after the Xynthia storm and 2–4 days during the Xynthia storm. High correlations are also found on smaller periods (from 4 h to two days) during storm occurrences. The XWT confirms that the Xynthia storm was the more energetic event that occurred during the observation period. Temporal correlation between RC3 and the sum of the surge and of the IB exhibits larger values than the correlation with either the surge or the IB at all of the time scales (0.77 against 0.72 and 0.70 between January and March 2010, 0.75 against 0.7 and 0.62 before the storm, 0.82 against 0.77 and 0.73 during Xynthia, 0.73 against 0.71 and 0.74 after the storm for the sum of the surge and IB, the surge, IB, respectively). As the surge and IB are strongly related, RC3 can be seen as the signature of the storm on the GNSS-R SSH signal.

## 7. Conclusions

## Author Contributions

## Acknowledgments

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Location of the Global Navigation Satellite Systems (GNSS) receiver at the SCOA station (43°23′42.83″N, 01°40′54.05″O); (

**b**) view of the antenna TRM55971.00 set up on a roof, at 10.664 m above the sea surface (source: http://rgp.ign.fr).

**Figure 2.**The Global Navigation Satellite Systems-reflectometry Sea Surface Height (GNSS-R SSH) in Socoa and the four main components of its SSA decomposition and its associated eigenvalues (λ), expressed in % of the explained variance.

**Figure 3.**Impact of the time window size on the SSA results through comparisons with Socoa tide gauge records in terms of root mean square error (RMSE) (m) (

**a**) and correlation coefficient (R) (

**b**). The blue line corresponds to GNSS-R SSH, the red line to the 1st reconstruction mode (RC1), the purple line to the 2nd reconstruction mode (RC2) and the green line to the sum of RC1 + RC2.

**Figure 4.**The GNSS-R SSH third reconstruction mode (RC3) of the SSA (red) was compared to different environmental variables (blue): the wind force (

**a**), the IB effect (

**b**), the surge (

**c**), and the SWH measured at the Anglet buoy about 20 km from Socoa station (

**d**).

**Figure 5.**Continuous wavelet transform (CWT) of the GNSS-R SSH in Socoa from the 1st of January to the 31st of March 2010.

**Figure 6.**Tide prediction time series (blue line) using T-Tide analysis Toolbox and residual time series (red line) after removing of tidal signal. (

**a**) For tide gauge data and (

**b**) GNSS-R SSH with the smoothing applied.

**Figure 7.**Comparisons between in situ tide gauges and: (

**a**) SSH based GNSS-R data; (

**b**) sum of (RC1 + RC2) using SSA method; (

**c**) inverse CWT at 12 h frequency; and, (

**d**) inverse CWT from 6 h to 12 h frequencies.

**Figure 8.**(

**a**) Cross wavelet transform (XWT) for RC3 (SSA) and sum of the surge and ${h}_{atmos}$; and, (

**b**) Time series RC3 and the surge + ${h}_{atmos}$ from January to March 2010 at Socoa.

**Table 1.**Comparisons between in situ tide gauge records and GNSS-R SSH based data, sum of (RC1 + RC2) using the SSA method, inverse CWT at 12 h frequency, inverse CWT from 6 h to 12 h frequencies (bias, RMSE and R).

Bias (m) | RMSE (m) | R | |
---|---|---|---|

SSH GNSS-R | 0.001 | 0.30 | 0.96 |

RC1 + RC2 | 0.003 | 0.16 | 0.99 |

iCWT at 12 h | 0.005 | 0.26 | 0.99 |

iCWT from 6 h to 12 h | 0.005 | 0.25 | 0.97 |

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## Share and Cite

**MDPI and ACS Style**

Vu, P.L.; Ha, M.C.; Frappart, F.; Darrozes, J.; Ramillien, G.; Dufrechou, G.; Gegout, P.; Morichon, D.; Bonneton, P. Identifying 2010 Xynthia Storm Signature in GNSS-R-Based Tide Records. *Remote Sens.* **2019**, *11*, 782.
https://doi.org/10.3390/rs11070782

**AMA Style**

Vu PL, Ha MC, Frappart F, Darrozes J, Ramillien G, Dufrechou G, Gegout P, Morichon D, Bonneton P. Identifying 2010 Xynthia Storm Signature in GNSS-R-Based Tide Records. *Remote Sensing*. 2019; 11(7):782.
https://doi.org/10.3390/rs11070782

**Chicago/Turabian Style**

Vu, Phuong Lan, Minh Cuong Ha, Frédéric Frappart, José Darrozes, Guillaume Ramillien, Grégory Dufrechou, Pascal Gegout, Denis Morichon, and Philippe Bonneton. 2019. "Identifying 2010 Xynthia Storm Signature in GNSS-R-Based Tide Records" *Remote Sensing* 11, no. 7: 782.
https://doi.org/10.3390/rs11070782