Abstract. 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.

Tsunamis pose a hazard that may strike a coastal population within a short amount of time. To effectively forecast and warn for tsunamis, extremely fast simulations are needed. However, until recently such urgent tsunami simulations have been infeasible in the context of early warning and even for highresolution rapid post-event assessment. The implementation of efficient tsunami numerical codes using Graphical Processing Units (GPUs) has now allowed much faster simulations, which have opened a new avenue for carrying out simulations Faster Than Real Time (FTRT). This paper discusses the need for urgent computing in computational tsunami science, and presents workflows for two applications, namely FTRT itself and Probabilistic Tsunami Forecasting (PTF). PTF relies on a very high number of FTRT simulations addressing forecasting uncertainty, whose full quantification will be made more and more at reach with the advent of exascale computing resources.

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In seismically active regions with variable dominant focal mechanisms, there is considerable tsunami inundation height uncertainty. Basic earthquake source parameters such as dip, strike, and rake affect significantly the tsunamigenic potential and the tsunami directivity. Tsunami inundation is also sensitive to other properties such as bottom friction. Despite their importance, sensitivity to these basic parameters is surprisingly sparsely studied in literature. We perform suites of systematic parameter searches to investigate the sensitivity of inundation at the towns of Catania and Siracusa on Sicily to changes both in the earthquake source parameters and the Manning friction. The inundation is modelled using the Tsunami-HySEA shallow water code on a system of nested topo-bathymetric grids with a finest spatial resolution of 10 m. This GPU-based model, with significant HPC resources, allows us to perform large numbers of high-resolution tsunami simulations. We analyze the variability of different hydrodynamic parameters due to large earthquakes with uniform slip at different locations, focal depth, and different source parameters. We consider sources both near the coastline, in which significant near-shore co-seismic deformation occurs, and offshore, where near-shore co-seismic deformation is negligible. For distant offshore earthquake sources, we see systematic and intuitive changes in the inundation with changes in strike, dip, rake, and depth. For near-shore sources, the dependency is far more complicated and co-determined by both the source mechanisms and the coastal morphology. The sensitivity studies provide directions on how to resolve the source discretization to optimize the number of sources in Probabilistic Tsunami Hazard Analysis, and they demonstrate a need for a far finer discretization of local sources than for more distant sources. For a small number of earthquake sources, we study systematically the inundation as a function of the Manning coefficient. The sensitivity of the inundation to this parameter varies greatly for different earthquake sources and topo-bathymetry at the coastline of interest. The friction greatly affects the velocities and momentum flux and to a lesser but still significant extent the inundation distance from the coastline. An understanding of all these dependencies is needed to better quantify the hazard when source complexity increases.

This paper improves and generalizes to multi-layer systems the shallow-water solver presented in [Bermu ´dez et al., IMA J. Numer. Anal., 11, 79-97 (1991)]. The model equations are discretized in time using the method of characteristics and the Euler implicit method. The space discretization is performed using the first-order Raviart-Thomas mixed finite element. A formulation of the non-linear equations to solve at each time step that takes into account regions without water is given, and numerical results are presented in which this situation takes place for the one-dimensional case. These non-linear problems are solved by a duality technique with an automatic choice of parameters that greatly improves the convergence of the algorithm. A preconditioner has been designed for solving the linear problems that appear at each iteration of the duality method, which significantly reduces the computational cost. This is illustrated with some numerical examples. Finally, an application of the multi-layer model to a realistic geometry of the Alboran Sea is presented, giving good results from a qualitative point of view. Copyright