In this paper, we present new results on the potential La Palma collapse event, previously described and studied in

The signal is then propagated with two different Boussinesq models: FUNWAVE-TVD and Calypso. An overall good agreement is found between the two models, which secures the validity of the results. Finally, a detailed impact study is carried out on La Guadeloupe using a refined shallow water model, SCHISM, initiated with the FUNWAVE-TVD solution in the nearshore area.

Although the slide modeling approach applied in this study seemingly leads to smaller waves compared to former works, the wave impact is still very significant for the maximum slide volume considered on surrounding islands and coasts, as well as on the most exposed remote coasts such as Guadeloupe. In Europe, the wave impact is significant (for specific areas in Spain and Portugal) to moderate (Atlantic French coast).

Recent catastrophes due to exceptionally strong tsunamis

This volcano (CVV) has drawn a strong interest among the scientific community since the first alarming work published on that case

Computations performed by

One of the goals of the TANDEM program was also the comparison of the models developed or used by the different partners of the project for operational forecasts in order to assess potential discrepancies. Here, we take the opportunity of this La Palma case study to compare the results obtained with two Boussinesq models after long-distance propagation (Sect.

The model used for wave source computations is the Navier–Stokes multi-fluid model THETIS already described in

The

THETIS belongs to the immiscible multiphase full Navier–Stokes type of solver. It has been validated against several benchmark cases involving tsunamis generated by 2D and 3D solid blocks

As previously mentioned, the tsunami sources proposed in

Cross section of the 80 km

Sketch of the experiment performed in

In the numerical model used in the present paper, the slide is modeled as a fluid with a Newtonian rheology. A simulation with a

The space and time steps are

For the first experimental case, presented in

Free-surface elevation at the gauges for the experiment (blue dashed line) and the simulations of the first case presented in

The first benchmark case was also simulated with the

The experiment presented in

To extrapolate these results for the La Palma computations, the following reasoning is adopted. First, it is assumed that the real slide is well represented by the granular medium used in the experiment. This approach is not deterministic as there are important differences between this experiment and the real case, but at least it may be considered as a better assumption than the worst case scenario presented in

Second, the 2D cross section of the La Palma slide in

The equivalent viscosity for the real case is then obtained by scaling the optimal viscosity obtained after calibrating the model against the experiments. Froude and Reynolds numbers should be the same at reduced and real scales, leading to

Based on these hypotheses, simulations were performed with three initial slide volumes corresponding to 20, 40 and 80 km

As noted in the original THETIS simulations presented in

Taking the result from the THETIS model after 300 s of simulated time, which is when several wave fronts have already propagated away from the generation site, integrating velocity over depth, we transfer the state of the model to the Boussinesq wave model FUNWAVE-TVD (see Sect.

After this filter is applied, local Boussinesq wave modeling is conducted on a 500 m resolution bathymetric grid taken from Global Multi-Resolution Topography (GMRT)

After this initial phase of propagation, the results of wave elevation and horizontal velocity are transferred to larger-scale simulations to predict propagation and impact on various coastlines, as detailed in Sect.

As dispersive effects are expected to play a significant role in this case

FUNWAVE-TVD is the most recent implementation of the Boussinesq model FUNWAVE

In the framework of the US NTHMP program, FUNWAVE-TVD has been validated for both tsunami propagation and coastal impact through an important set of analytical, laboratory and field benchmarks

The simulation of the propagation of the tsunami to the coastlines was performed with nested grids (Figs.

Computational domains for Calypso at 2 km (A) resolution in black, FUNWAVE-TVD at 2.7 km (B), 930 m (C) and 310 m (D) resolutions in red, and SCHISM at variable resolution (E) in green. Bathymetric contours range from

Computational domains for Calypso at 500 m (F), 125 m (G) and 32.5 m (H and I) resolutions in black and FUNWAVE-TVD at 450 m (J), 110 m (K) and 20 m (L) resolutions in red. After the

Calypso is a code developed by CEA and used for tsunami propagation

Four levels of nested grids are used in this computation (Figs.

In the simulation performed, the offshore propagation was simulated by using the Boussinesq model to take into account the dispersive effects in the Atlantic Ocean, and then NSW equations are solved in the daughter grids in order to reduce the computation time.

The first synthetic gauge (Gauge 1), located west in the vicinity of the Canary archipelago, is used to analyze the wave at the beginning of the event.

In the Caribbean Sea, the tsunami wave features close to the Guadeloupe archipelago will be detailed. The latter is located 16

In Europe, the following synthetic gauges are used (Figs.

Guadeloupe archipelago and locations of gauges 8 and 9 and of the cities of Bouillante, Le Gosier, Le Moule and Desirade.

Values of Manning coefficient as a function of land use in Guadeloupe.

Summary of locations of numerical output (see Fig.

Summary of grid characteristics (see Fig.

Independent of the wave signal quality, an accurate assessment of the impact of a given tsunami also requires refined computations on nested refined grids including local friction coefficients and an accurate knowledge of the bathymetry and the topography. In the present study, this extensive work was performed in La Guadeloupe. For this archipelago, the transoceanic propagation is performed using the code FUNWAVE-TVD, while nearshore propagation and inundation are carried out with SCHISM.

Semi-implicit Cross-scale Hydroscience Integrated System Model (SCHISM)

A hot start is made from the wave train of the FUNWAVE-TVD grid over the SCHISM unstructured grid at

Figures

Snapshots of slide upper free surface, thickness and corresponding water-free surface for the inviscid case

Snapshots of slide upper free surface, thickness and corresponding water-free surface for the present study (i.e., viscous slide with a viscosity of 2

The bulge, which was very developed in the previous case (Fig.

THETIS 3D computations for 80 km

THETIS 3D computations for 80 km

As a consequence of lower velocity and slide cross-section reduction, the wave train generated is significantly less energetic than in the inviscid case (Figs.

For this volume, after almost 10 min of propagation, the leading wave, which was previously about 80 m high, only reaches

THETIS 3D computations for the 80 km

Figure

Nevertheless, there is a significant variation in wave amplitude depending on the slide volume considered (Fig.

Taking the THETIS solution (Fig.

THETIS 3D computations for 20 km

The effect of the filtering can be seen clearly in Fig.

Region around Cumbre Vieja volcano after 5 min of simulated time with THETIS for the 80 km

The potential dispersive character of the wave train can be assessed by investigating the frequencies present in the wave spectrum. To that purpose, the wave signal close to the source in the direction of the maximum wave energy and the associated Fourier transform is presented in Fig.

Surface elevation (m;

The resulting wave elevation and velocity fields (e.g., Fig.

Region around the Canary Islands 20 min after the beginning of the event (after 5 min of simulated time with THETIS and 15 min of simulated time with FUNWAVE-TVD) during the 80 km

Figure

Surface elevations (m) (left column) and Fourier transforms (right column) for the 80 km

Near Guadeloupe (Fig.

The frequency content of the wave signal for the 80 km

The wave train generated by the 20 km

Surface elevations (m) (left column) and Fourier transforms (right column) for the 20 km

Comparison of the surface elevation (m) and the associated periods computed by a Fourier transformation

Figure

Figures

Maximum surface elevations (m) computed by FUNWAVE-TVD for the 80 km

Maximum surface elevations (m) computed by FUNWAVE-TVD for the 80 km

Territories close to the generation area are highly affected. The first locations impacted are the other surrounded Canary Islands, nearby archipelagos (Madeira Island, Cape Verde) and west Africa, especially the western Sahara (Dakhla city – 100 000 inhabitants) and specific parts of Morocco through refraction on shallower part of the local bathymetry (Agadir, Essaouira and Safi – 800 000 inhabitants overall). In the latter areas, the waves are larger than 5 m.

The wave propagating toward Europe is obviously less energetic than in the western direction on which the main part of the energy is focused (Fig.

Figure

Maximum surface elevation computed with Calypso for the 80 km

For the Guadeloupe archipelago, Fig.

Flood map showing the maximum water level reached during the 80 km^{®} software by Esri. ArcGIS^{®} and ArcMap™ are the intellectual property of Esri and are used herein under license. Copyright © Esri. All rights reserved.

Regarding the 20 km

The main goal of the present study was to improve the state of the art for the potential La Palma tsunami source and to use this new proposed scenario to perform an impact assessment for Europe and, particularly, for French territories. Such high return period events with potentially catastrophic consequences are particularly important to study as accurately as possible since, due to the difficulty in assessing their precise return period, they often serve as a reference for hazard mitigation studies

The first result of the present work is the new tsunami source computed by Navier–Stokes simulation (for the initial 5 min), ad hoc filtering and Boussinesq wave propagation (for the following 15 min). As stressed previously, this source is more realistic than that considered in

The second result is a presumably better impact assessment in Europe generally and a new detailed impact assessment for France and Guadeloupe. Considering a credible yet extreme 80 km

Regarding the physics of the problem and the modeling strategy, the analysis of the wave signal obtained with FUNWAVE-TVD close to the source confirmed the presence of high frequency waves prone to dispersion at the depths encountered in this area of the Atlantic Ocean. Hence, physically, dispersion is expected, and, theoretically, an appropriate Boussinesq modeling is required. The results obtained with FUNWAVE-TVD appear consistent with what is physically expected: high frequency waves progressively disappearing from the spectra during the propagation. The comparison between FUNWAVE-TVD and Calypso, which showed good agreement, allowed us to simultaneously validate the models and secure the results obtained (even though some discrepancies remain in the low-frequency band). The methodology of performing transoceanic simulations in Boussinesq mode and shifting to NSW mode in the nearshore area is also validated through the good match observed in Fig.

Of course there are some limitations in this study which may provide the basis for future improvements.
First, this study should not be considered as a hazard assessment stricto sensu because the return period aspect is not considered, and the sensitivity in the landslide parameters is not covered extensively. For a review of probabilistic tsunami hazard analysis (PTHA) methods, the reader is referred to

Second, we used a glass-beads-based experiment

The present work did not explicitly take into account the possibility of a retrogressive scenario. Whether the flank collapse occurs en masse or in successive stages is obviously crucial in terms of wave generation. In this study, we proposed several slide volume scenarios which can be used for a crude assessment of the wave reduction in case the collapse occurred as several separate events with no interactions between the successive slides (e.g., the 20 km

On the other hand, the extreme scenario of 450 km

The wave generated by a potential Cumbre Vieja volcano flank collapse and its impact on Europe and Guadeloupe was studied in this work. The source computation used an improved characterization of the slide rheology compared to previous works. Moreover, the subsequent propagation was performed using different models, which allows for a model comparison in a real configuration. The main conclusions of the work performed are the following.

The new wave source is reduced by half compared to previous estimations mainly due to the larger value of slide viscosity used in this work.

The wave impact is still very significant on nearby areas and on more remote coasts, such as Guadeloupe, located in the path of the maximum wave energy for the maximum slide volume considered here (i.e., 80 km

In Europe, the impact may be considered as moderate to significant in the most exposed areas, such as some areas in Portugal and Spain, and weak to moderate along the French Atlantic coast.

The tsunami source calculated in this paper after 15 min of propagation in FUNWAVE-TVD and proposed to the community in the SEA scieNtific Open data Edition (SEANOE) repository is dispersive, and therefore we recommend using appropriate models (e.g., Boussinesq models) to propagate further this source in future studies.

The comparison of the Boussinesq models (i.e., FUNWAVE-TVD and Calypso) mutually validates the models in this particular case and secures the results obtained. This comparison also stresses the importance of model resolution and the possibility to turn off the dispersive terms in the model after a certain distance of propagation.

The new calibrated source (after filtering and propagation in the Boussinesq model) for the La Palma tsunami is made available through the SEANOE portal (

SA carried out THETIS simulations of the CVV slide and the associated wave and LC the simulations of the benchmark cases (Viroulet et al., 2013; Grilli et al., 2017). JH post-processed the THETIS results and conducted the initial FUNWAVE-TVD simulations. AP (Paris), PH and AP (Poupardin) carried out the Calypso simulations, RP and SLR the FUNWAVE-TVD simulations at large scale and for the impact assessment, GA and YK the SCHISM simulations for transoceanic propagation (not shown here) and the evaluation of the impact on Guadeloupe, and RA the Telemac2D simulations at large scale (not shown here). Global analysis of the results was carried out by SA with the help of AP (Paris), PH, JH and GA. SA prepared the initial draft with input from all the coauthors. Substantial revision work was ensured by SA with contributions from all coauthors and especially AP (Paris), JH and GA. JH and SA prepared the data for the repository on SEANOE.

The authors declare that they have no conflict of interest.

This work has been performed in the framework of the PIA RSNR French program TANDEM and as a part of the project C3AF. Part of this work was supported by the Laboratoire de Recherche Conventionné (LRC) CEA-Ecole Normale Supérieure (ENS) Yves Rocard.

This research has been supported by the ANR (grant no. ANR-11-RSNR-00023-01), the ERDF and the Guadeloupe region (C3AF grant).

This paper was edited by Maria Ana Baptista and reviewed by three anonymous referees.