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We present a database of pre-calculated tsunami waveforms for the entire Mediterranean Sea, obtained by numerical propagation of uniformly spaced Gaussian-shaped elementary sources for the sea level elevation. Based on any initial sea surface displacement, the database allows the fast calculation of full waveforms at the 50 m isobath offshore of coastal sites of interest by linear superposition. A computationally inexpensive procedure is set to estimate the coefficients for the linear superposition based on the potential energy of the initial elevation field. The elementary sources size and spacing is fine enough to satisfactorily reproduce the effects of M> = 6.0 earthquakes. Tsunami propagation is modelled by using the Tsunami-HySEA code, a GPU finite volume solver for the non-linear shallow water equations. Like other existing methods based on the initial sea level elevation, the database is independent on the faulting geometry and mechanism, which makes it applicable in any tectonic environment. We model a large set of synthetic tsunami test scenarios, selected to explore the uncertainty introduced when approximating tsunami waveforms and their maxima by fast and simplified linear combination. This is the first time to our knowledge that the uncertainty associated to such a procedure is systematically analysed and that relatively small earthquakes are considered, which may be relevant in the near-field of the source in a complex tectonic setting. We find that non-linearity of tsunami evolution affects the reconstruction of the waveforms and of their maxima by introducing an almost unbiased (centred at zero) error distribution of relatively modest extent. The uncertainty introduced by our approximation can be in principle propagated to forecast results. The resulting product then is suitable for different applications such as probabilistic tsunami hazard analysis, tsunami source inversions and tsunami warning systems.

This paper is devoted to benchmarking the Multilayer-HySEA model using laboratory experimental data for landslide-generated tsunamis. This article deals with rigid slides, and the second part, in a companion paper, addresses granular slides. The US National Tsunami Hazard and Mitigation Program (NTHMP) has proposed the experimental data used and established for the NTHMP Landslide Benchmark Workshop, held in January 2017 at Galveston (Texas). The first three benchmark problems proposed in this workshop deal with rigid slides. Rigid slides must be simulated as a moving bottom topography, and, therefore, they must be modeled as a prescribed boundary condition. These three benchmarks are used here to validate the Multilayer-HySEA model. This new HySEA model consists of an efficient hybrid finite-volume–finite-difference implementation on GPU architectures of a non-hydrostatic multilayer model. A brief description of model equations, dispersive properties, and the numerical scheme is included. The benchmarks are described and the numerical results compared against the lab-measured data for each of them. The specific aim is to validate this new code for tsunamis generated by rigid slides. Nevertheless, the overall objective of the current benchmarking effort is to produce a ready-to-use numerical tool for real-world landslide-generated tsunami hazard assessment. This tool has already been used to reproduce the Port Valdez, Alaska, 1964 and Stromboli, Italy, 2002 events.

The final aim of the present work is to propose a NTHMP-benchmarked numerical tool for landslide-generated tsunami hazard assessment. To achieve this, the novel Multilayer-HySEA model is validated using laboratory experiment data for landslide-generated tsunamis. In particular, this second part of the work deals with granular slides, while the first part, in a companion paper, considers rigid slides. The experimental data used have been proposed by the US National Tsunami Hazard and Mitigation Program (NTHMP) and were established for the NTHMP Landslide Benchmark Workshop, held in January 2017 at Galveston (Texas). Three of the seven benchmark problems proposed in that workshop dealt with tsunamis generated by rigid slides and are collected in the companion paper (Macías et al., 2021). Another three benchmarks considered tsunamis generated by granular slides. They are the subject of the present study. The seventh benchmark problem proposed the field case of Port Valdez, Alaska, 1964 and can be found in Macías et al. (2017). In order to reproduce the laboratory experiments dealing with granular slides, two models need to be coupled: one for the granular slide and a second one for the water dynamics. The coupled model used consists of a new and efficient hybrid finite-volume–finite-difference implementation on GPU architectures of a non-hydrostatic multilayer model coupled with a Savage–Hutter model. To introduce the multilayer model more fluidly, we first present the equations of the one-layer model, Landslide-HySEA, with both strong and weak couplings between the fluid layer and the granular slide. Then, a brief description of the multilayer model equations and the numerical scheme used is included. The dispersive properties of the multilayer model can be found in the companion paper. Then, results for the three NTHMP benchmark problems dealing with tsunamis generated by granular slides are presented with a description of each benchmark problem.

The 1958 Lituya Bay landslide-generated mega-tsunami is simulated using the Landslide-HySEA model, a recently developed finite-volume Savage–Hutter shallow water coupled numerical model. Two factors are crucial if the main objective of the numerical simulation is to reproduce the maximal run-up with an accurate simulation of the inundated area and a precise recreation of the known trimline of the 1958 mega-tsunami of Lituya Bay: first, the accurate reconstruction of the initial slide and then the choice of a suitable coupled landslide–fluid model able to reproduce how the energy released by the landslide is transmitted to the water and then propagated. Given the numerical model, the choice of parameters appears to be a point of major importance, which leads us to perform a sensitivity analysis. Based on public domain topo-bathymetric data, and on information extracted from the work of Miller (1960), an approximation of Gilbert Inlet topo-bathymetry was set up and used for the numerical simulation of the mega-event. Once optimal model parameters were set, comparisons with observational data were performed in order to validate the numerical results. In the present work, we demonstrate that a shallow water type of model is able to accurately reproduce such an extreme event as the Lituya Bay mega-tsunami. The resulting numerical simulation is one of the first successful attempts (if not the first) at numerically reproducing, in detail, the main features of this event in a realistic 3-D basin geometry, where no smoothing or other stabilizing factors in the bathymetric data are applied.