This review presents modelling techniques and processes that govern landslide tsunami generation, with emphasis on tsunamis induced by fully submerged landslides. The analysis focuses on a set of representative examples in simplified geometries demonstrating the main kinematic landslide parameters influencing initial tsunami amplitudes and wavelengths. Scaling relations from laboratory experiments for subaerial landslide tsunamis are also briefly reviewed. It is found that the landslide acceleration determines the initial tsunami elevation for translational landslides, while the landslide velocity is more important for impulsive events such as rapid slumps and subaerial landslides. Retrogressive effects stretch the tsunami, and in certain cases produce enlarged amplitudes due to positive interference. In an example involving a deformable landslide, it is found that the landslide deformation has only a weak influence on tsunamigenesis. However, more research is needed to determine how landslide flow processes that involve strong deformation and long run-out determine tsunami generation.

Applying probabilistic methods to infrequent but devastating natural events is intrinsically challenging. For tsunami analyses, a suite of geophysical assessments should be in principle evaluated because of the different causes generating tsunamis (earthquakes, landslides, volcanic activity, meteorological events, and asteroid impacts) with varying mean recurrence rates. Probabilistic Tsunami Hazard Analyses (PTHAs) are conducted in different areas of the world at global, regional, and local scales with the aim of understanding tsunami hazard to inform tsunami risk reduction activities. PTHAs enhance knowledge of the potential tsunamigenic threat by estimating the probability of exceeding specific levels of tsunami intensity metrics (e.g., run‐up or maximum inundation heights) within a certain period of time (exposure time) at given locations (target sites); these estimates can be summarized in hazard maps or hazard curves. This discussion presents a broad overview of PTHA, including (i) sources and mechanisms of tsunami generation, emphasizing the variety and complexity of the tsunami sources and their generation mechanisms, (ii) developments in modeling the propagation and impact of tsunami waves, and (iii) statistical procedures for tsunami hazard estimates that include the associated epistemic and aleatoric uncertainties. Key elements in understanding the potential tsunami hazard are discussed, in light of the rapid development of PTHA methods during the last decade and the globally distributed applications, including the importance of considering multiple sources, their relative intensities, probabilities of occurrence, and uncertainties in an integrated and consistent probabilistic framework.

Abstract. This article focuses on the effect of dispersion in the field of tsunami modeling. Frequency dispersion in the linear long-wave limit is first briefly discussed from a theoretical point of view. A single parameter, denoted as "dispersion time", for the integrated effect of frequency dispersion is identified. This parameter depends on the wavelength, the water depth during propagation, and the propagation distance or time. Also the role of long-time asymptotes is discussed in this context. The wave generation by the two main tsunami sources, namely earthquakes and landslides, are briefly discussed with formulas for the surface response to the bottom sources. Dispersive effects are then exemplified through a semi-idealized study of a moderate-strength inverse thrust fault. Emphasis is put on the directivity, the role of the "dispersion time", the significance of the Boussinesq model employed (dispersive effect), and the effects of the transfer from bottom sources to initial surface elevation. Finally, the experience from a series of case studies, including earthquake- and landslide-generated tsunamis, is presented. The examples are taken from both historical (e.g. the 2011 Japan tsunami and the 2004 Indian Ocean tsunami) and potential tsunamis (e.g. the tsunami after the potential La Palma volcanic flank collapse). Attention is mainly given to the role of dispersion during propagation in the deep ocean and the way the accumulation of this effect relates to the "dispersion time". It turns out that this parameter is useful as a first indication as to when frequency dispersion is important, even though ambiguity with respect to the definition of the wavelength may be a problem for complex cases. Tsunamis from most landslides and moderate earthquakes tend to display dispersive behavior, at least in some directions. On the other hand, for the mega events of the last decade dispersion during deep water propagation is mostly noticeable for transoceanic propagation.

Large tsunamis occur infrequently but have the capacity to cause enormous numbers of casualties, damage to the built environment and critical infrastructure, and economic losses. A sound understanding of tsunami hazard is required to underpin management of these risks, and while tsunami hazard assessments are typically conducted at regional or local scales, globally consistent assessments are required to support international disaster risk reduction efforts, and can serve as a reference for local and regional studies. This study presents a global-scale probabilistic tsunami hazard assessment (PTHA), extending previous global-scale assessments based largely on scenario analysis. Only earthquake sources are considered, as they represent about 80% of the recorded damaging tsunami events. Globally extensive estimates of tsunami run-up height are derived at various exceedance rates, and the associated uncertainties are quantified. Epistemic uncertainties in the exceedance rates of large earthquakes often lead to large uncertainties in tsunami run-up. Deviations between modelled tsunami run-up and event observations are quantified, and found to be larger than suggested in previous studies. Accounting for these deviations in PTHA is important, as it leads to a pronounced increase in predicted tsunami run-up for a given exceedance rate.

The NEAM Tsunami Hazard Model 2018 (NEAMTHM18) is a probabilistic hazard model for tsunamis generated by earthquakes. It covers the coastlines of the North-eastern Atlantic, the Mediterranean, and connected seas (NEAM). NEAMTHM18 was designed as a three-phase project. The first two phases were dedicated to the model development and hazard calculations, following a formalized decision-making process based on a multiple-expert protocol. The third phase was dedicated to documentation and dissemination. The hazard assessment workflow was structured in Steps and Levels. There are four Steps: Step-1) probabilistic earthquake model; Step-2) tsunami generation and modeling in deep water; Step-3) shoaling and inundation; Step-4) hazard aggregation and uncertainty quantification. Each Step includes a different number of Levels. Level-0 always describes the input data; the other Levels describe the intermediate results needed to proceed from one Step to another. Alternative datasets and models were considered in the implementation. The epistemic hazard uncertainty was quantified through an ensemble modeling technique accounting for alternative models’ weights and yielding a distribution of hazard curves represented by the mean and various percentiles. Hazard curves were calculated at 2,343 Points of Interest (POI) distributed at an average spacing of ∼20 km. Precalculated probability maps for five maximum inundation heights (MIH) and hazard intensity maps for five average return periods (ARP) were produced from hazard curves. In the entire NEAM Region, MIHs of several meters are rare but not impossible. Considering a 2% probability of exceedance in 50 years (ARP≈2,475 years), the POIs with MIH >5 m are fewer than 1% and are all in the Mediterranean on Libya, Egypt, Cyprus, and Greece coasts. In the North-East Atlantic, POIs with MIH >3 m are on the coasts of Mauritania and Gulf of Cadiz. Overall, 30% of the POIs have MIH >1 m. NEAMTHM18 results and documentation are available through the TSUMAPS-NEAM project website (http://www.tsumaps-neam.eu/), featuring an interactive web mapper. Although the NEAMTHM18 cannot substitute in-depth analyses at local scales, it represents the first action to start local and more detailed hazard and risk assessments and contributes to designing evacuation maps for tsunami early warning.

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Regional and global tsunami hazard analysis requires simplified and efficient methods for estimating the tsunami inundation height and its related uncertainty. One such approach is the amplification factor (AF) method. Amplification factors describe the relation between offshore wave height and the maximum inundation height, as predicted by linearized plane wave models employed for incident waves with different wave characteristics. In this study, a new amplification factor method is developed that takes into account the offshore bathymetry proximal to the coastal site. The present AFs cover the NorthEastern Atlantic and Mediterranean (NEAM) region. The model is the first general approximate model that quantifies inundation height uncertainty. Uncertainty quantification is carried out by analyzing the inundation height variability in more than 500 high-resolution inundation simulations at six different coastal sites. The inundation simulations are undertaken with different earthquake sources in order to produce different wave period and polarity. We show that the probability density of the maximum inundation height can be modeled with a log-normal distribution, whose median is quite well predicted by the AF. It is further demonstrated that the associated maximum inundation height uncertainties are significant and must be accounted for in tsunami hazard analysis. The application to the recently developed TSUMAPS-NEAM probabilistic tsunami hazard analysis (PTHA) is presented as a use case.