# Shallow bathymetry from pléiades data: the case study of the Grindavik volcanic crisis

Marcello de Michele, Daniel Raucoules, Virginie Pinel, Joaquín M C Belart

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Marcello de Michele, Daniel Raucoules, Virginie Pinel, Joaquín M C Belart. Shallow bathymetry from pléiades data: the case study of the Grindavik volcanic crisis. 2024 IEEE International Geoscience and Remote Sensing Symposium, Institute of Electrical and Electronics Engineers, Jul 2024, Athènes, Greece. hal-04572360

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# SHALLOW BATHYMETRY FROM PLÉIADES DATA: THE CASE STUDY OF THE GRINDAVIK VOLCANIC CRISIS.

Marcello de Michele<fnref n="1" />, Daniel Raucoules<fnref n="1" />, Virginie Pinel<fnref n="2" />, Joaquim Belart<fnref n="3" />

## ABSTRACT

On November 10, 2023, the town of Grindavik on the Reykjanes peninsula (Iceland) was evacuated due to the propagation of a shallow magmatic fissure near the town. We programmed Pléiades images on the area via the CIEST<fnref n="2" /> initiative. Due to the vicinity of the affected area to the ocean, the lava flow might reach the water modifying submarine topography. Our goal is to test a new space-based method to measure shallow bathymetry and possible submarine lava flow volume in shallow water.

**Index Terms**— coastal bathymetry, space, Pléiades, CIEST<fnref n="2" />

## 1. INTRODUCTION

On November 10, 2023, the town of Grindavik on the Reykjanes peninsula (Iceland) has been evacuated. This decision has been taken following the identification of the propagation of a shallow magmatic fissure near the town. Due to the probable imminence of an eruption in the area, we programmed Pléiades images for 11 consecutive days via the CIEST<fnref n="2" /> initiative, a scientific exploitation channel fostered by CNES (French Space Agency) and the French national center for solid Earth (Form@ter). The conditions of low solar illumination due to the entry into the winter period in Iceland made the task uneasy. Nonetheless, two Pléiades images could provide good visibility of the area affected by the magmatic intrusion, on land and ocean (figure 1). Due to the vicinity of the affected area to the ocean, the lava flow might reach the water modifying submarine topography. The mapping of lava flows in shallow water environments represents a pivotal aspect of understanding lava volume emissions and their consequential impact on underwater geomorphology. In this study, our goal was to test a new space based method to measure shallow bathymetry and possible submarine lava flow volume in shallow water.

<figure><img src="image_2.png" /><figcaption>Figure 1. The study area in Iceland. Grindavik area from Pléiades image acquired on 19 of November 2023. The red rectangle in the Atlantic Ocean represents a histogram-stretched zoom on the swell. Image Pléiades © CNES (2023), distribution by Airbus DS.</figcaption></figure>

## 2. METHODS

Here, the method is based on the joint measurement of ocean wave celerity (c), as presented in [1], and wavelength (λ), both from space. We adapted the method called BathySent [2] to Pléiades images, to retrieve shallow bathymetry from space.

This method is based on the linear dispersion law [3], which relates water depth to ocean wave celerity and wavelength: when the water depth is less than about half the dominant wavelength, the wave celerity and wavelength decreased due to decreasing water depth (h) as the waves propagated towards the coast, as in equation (1):

$$h=\lambda/2\pi \cdot \tanh^{-1}(2\pi c^2 / g\lambda) \quad (1)$$

<footnote n="1">¹ French Geological Survey (BRGM), Orléans, France</footnote>

<footnote n="2">² National Research Institute for Sustainable Development (IRD), IsTerre, Grenoble, France</footnote>

<footnote n="3">³ National Land Survey of Iceland, Reykjavik, Iceland</footnote>
where h is the water depth and g is the standard acceleration due to gravity on Earth, equal to 9.81 m/s. Equation (1) was first used in a practical sense during the Second World War [3], and works either with two sequential images acquired within a short time interval, like in our case (i.e., shorter than the wave period), or with one image but with additional in situ measurements.

The idea behind the method is that the CCDs on a push broom sensor can not physically co-exist on the same spot on the focal plane. Therefore, there exist a time lag between the acquisitions of the different spectral bands, as the sensor travels at the speed of 7 km/s, depending on the sensor. This time lag can be used as a crucial variable for the measurement of ocean wave celerities [1]. In a recent past, we developed the method to work with Sentinel 2 data, exploiting the time lag between two Sentinel 2 spectral bands, acquired quasi-simultaneously, from a single satellite dataset [2]. Here, we adapted the method to be used with Pléiades data, acquired during the Grindavik eruptive crisis, via the activation of the CIEST² initiative. The Pléiades satellites are a constellation of optical Earth observation platforms, developed through a cooperation between CNES and Airbus Defence and Space. Operating at a sun-synchronous orbit around 700 kilometers above the Earth's surface, these satellites employ cutting-edge optical instruments to capture high-resolution imagery with exceptional precision. With a maximum ground resolution of 70 centimeters (panchromatic) and 2 meters (multispectral), the Pléiades satellites allows rapid repositioning and imaging of specific targets with stereoscopic view. In disaster management scenarios, the Pléiades satellites play a pivotal role by swiftly delivering pre and post-event images, enabling timely support to emergency response efforts. In our study, Pléiades dataset is acquired on 19 November 2023. The time lag between the acquisition of the panchromatic band and the blue band of Pléiades satellite is 0.16 seconds (CNES, pers. Comm.). Our idea is to calculate shallow bathymetry before and after the eruption to measure volume changes due to underwater lava flows. Here, we show an attempt to measure the pre-eruptive coastal bathymetry from space, before winter in Iceland.

Here, we propose a complementary, rapid, approach to retrieve coastal bathymetry –particularly adapted when the need of the project is to retrieve shallow coastal morphology in the presence of a monochromatic swell.

Our approach stems from the observation that conventional statistical cross-correlation approaches to measure c [1,4] works well in the presence of monochromatic swell. Therefore, instead of utilizing multiple (c,λ) combinations within the same resolution cells, to expedite processing, we implemented a two-step procedure based on the direct measurement of c and the wave period. First, we employed the statistical correlator implemented in the COSI-CORR software [4] to retrieve one value of c within each resolution cell, at each step of a grid. This techniques generates localized, sub-sampled waves offsets and their corresponding waves celerities is calculated by dividing the offset by the

time lag that exists between acquisitions in Pléiades bands during a single pass of the satellite.

The wave celerities were computed from smaller sub-images based on a grid defined by the sampling step, which determined the resolution of the final bathymetric map. Then, we measured λ at large by visual inspection. Surely, in a future step, there will be rooms for automating this procedure. Afterwards, for each sub images, we calculated the waves period (T = λ/c). Finally, we solve the linear dispersion relation as a function of T, for each (c,T) pairs independently, to find h (equation 2, figure 2) :

$$h=cT/2\pi \cdot \tanh^{-1}(2\pi c / gT) \quad (2)$$

where λ at large is 78.5; c_λ is 11.25 m/s. So T = (λ / c_λ) = 6.97 sec.

<figure><img src="image_3.png" /><figcaption>Figure 2. Coastal water depth in the Grindavik area from Pléiades images, 19 November 2023. The color bar is from 4 m depth to 28 m depth. Image Pléiades © CNES (2023), distribution by Airbus DS.</figcaption></figure>

## 3. RESULTS AND PERSPECTIVES

Our results suggest that the low solar illumination angle, typical for winter time in Iceland, is pretty favorable to image the ocean swell. Therefore, we could calculate a shallow bathymetry map, from 4 to 28 meters depth (figure 2). We found this method stable for fast processing as it does not
depend on the square of celerity ($c^2$) shown in equation (1).
Therefore, this method might be suitable for shallow
morphology mapping.

This method has high potential for mapping morphological
changes of shallow bathymetry, which could be particularly
useful in the case of a shallow sub-aerial or shallow
submarine volcanic eruption, where the lava delta may extend
hundreds of meters beyond the old shoreline. This method
might be employed as a bridge in the gap that typically
remains between multi-beam bathymetric surveys and the
land. We plan to crossCompare our results with future field-
based bathymetric surveys. Furthermore, we will be waiting
for suitable light conditions in Iceland, next spring, to acquire
a new Pléiades dataset.

4. ACKNOWLEDGEMENTS

We thank Emilie Bronner and Claude Boniface (CNES) for
providing Pléiades data via the CIEST² initiative and the
Form@ter center. Pléiades images are distributed by Airbus
DS.

5. REFERENCES

[1] M. de Michele, S. Leprince, J. Thiébot, D. Raucoules and R. Binet, “Direct measurement of ocean waves velocity field from a single SPOT-5 dataset”, Remote Sens. Environ., 119, 266–271, 2012.

[2] M. de Michele, D. Raucoules, D. Idier, F. Smai and M. Foumelis, “Shallow Bathymetry from Multiple Sentinel 2 Images via the Joint Estimation of Wave Celerity and Wavelength”, Remote Sens., 13, 2149, 2021.

[3] W. W. Williams, “The determination of gradients on enemy-held beaches”, The Geographical Journal, 109(1/3), 76–90, 1947.

[4] S. Leprince, S. Barbot, F. Ayoub, and J.-P. Avouac, “Automatic and precise orthorectification coregistration, and subpixel correlation of satellite images: Application to ground deformation measurements”, IEEE Transactions on Geoscience and Remote Sensing, 45, 1529–1558, 2007.