Abstract: Tsunami inundation is rare on most coastlines, but large events can have devasting consequences for life and infrastructure. There is demand for inundation hazard maps to guide risk-management actions, such as the design of tsunami evacuation zones, tsunami-resilient infrastructure, and insurance. But the frequency of tsunami-generating processes (e.g., large earthquakes, landslides, and volcanic collapses) is usually very uncertain. This reflects limitations in scientific knowledge, and the short duration of historical records compared to the long inter-event times of dangerous tsunamis. Consequently, tsunami hazards are subject to large uncertainties which should be clearly communicated to inform risk-management decisions. Probabilistic Tsunami Hazard Assessment (PTHA) offers a structured approach to quantifying tsunami hazards and the associated uncertainties, while integrating data, models, and expert opinion. For earthquake-generated tsunamis, several national and global-scale PTHAs provide databases of hypothetical scenarios, scenario occurrence-rates and their uncertainties. Because these “offshore PTHAs” represent the coast at coarse spatial resolutions (~ 1-2 km) they are not directly suitable for onshore risk management and can only simulate tsunami waveforms accurately in deep-water, far from the coast. Yet because offshore PTHAs can use earthquake and tsunami data at global scales, they offer relatively well tested representations of earthquake-tsunami sources, occurrence-rates, and uncertainties. Furthermore, by combining an offshore PTHA with a high-resolution coastal inundation model, the resulting onshore tsunami hazard can in-principle be derived at spatial resolutions appropriate for risk management (~ 10 m) for any site of interest. This study considers the computational problem of rigorously transforming offshore PTHAs into site-specific onshore PTHAs. In theory this can be done by using a high-resolution hydrodynamic model to simulate inundation for every scenario in the offshore PTHA. In practice this is computationally prohibitive, because modern offshore PTHAs contain too many scenarios (on the order of 1 million) and inundation models are computationally demanding. Monte-Carlo sampling offers a rigorous alternative that requires less computation, because inundation simulations are only required for a random subset of scenarios. It is also known to converge to the correct solution as the number of scenarios is increased. This study develops several approaches to reduce Monte-Carlo errors at the onshore site of interest, for a given computational cost. As compared to existing Monte-Carlo approaches for offshore-to-onshore PTHA, the key novel idea is to use deep-water tsunami wave heights (modelled by the offshore PTHA) to estimate the relative “importance” of each scenario near the onshore site of interest, prior to inundation simulation. Scenarios are randomly sampled from the offshore PTHA in a way that over-represents the “important” scenarios, and the theory of importance sampling enables weighting these scenarios so as to correct for the sampling bias. This can greatly reduce Monte-Carlo errors for a given sampling effort. In addition, because importance-sampling is analytically tractable, the variance of the Monte-Carlo errors can be estimated at offshore sites prior to sampling. This helps modellers to estimate the adequacy of a proposed Monte-Carlo sampling scheme prior to expensive inundation computation. The analytical variance result also enables the theory of optimal-sampling to be applied in a way that to reduces the Monte-Carlo variance, by non-uniformly sampling from earthquakes of different magnitudes. The new techniques are applied to an onshore earthquake-tsunami PTHA in Tongatapu, the main island of Tonga. In combination the new techniques lead to efficiency improvements equivalent to simulating 4-18 times more scenarios, as compared with commonly used Monte-Carlo methods for onshore PTHA. They also enable the hazard uncertainties in the offshore PTHA to be translated onshore, where they are of most significance to risk management decision-making. The greatest accuracy improvements occur for large tsunamis, and for computations that represent uncertainties in the hazard.

In November, 2018 a workshop of experts sponsored by UNESCO’s Intergovernmental Oceanographic Commission was convened in Wellington, New Zealand. The meeting was organized by Working Group (WG) 1 of the Pacific Tsunami Warning System (PTWS). The meeting brought together fourteen experts from various disciplines and four different countries (New Zealand, Australia, USA and French Polynesia) and four observers from Pacific Island countries (Tonga, Fiji), with the objective of understanding the tsunami hazard posed by the Tonga-Kermadec trench, evaluating the current state of seismic and tsunami instrumentation in the region and assessing the level of readiness of at-risk populations. The meeting took place in the “Beehive” Annex to New Zealand’s Parliament building nearby the offices of the Ministry of Civil Defence and Emergency Management. The meeting was co-chaired by Mrs. Sarah-Jayne McCurrach (New Zealand) from the Ministry of Civil Defence and Emergency Management and Dr. Diego Arcas (USA) from NOAA’s Pacific Marine Environmental Laboratory. As one of the meeting objectives, the experts used their state-of-the-science knowledge of local tectonics to identify some of the potential, worst-case seismic scenarios for the Tonga-Kermadec trench. These scenarios were ranked as low, medium and high probability events by the same experts. While other non-seismic tsunamigenic scenarios were acknowledged, the level of uncertainty in the region, associated with the lack of instrumentation prevented the experts from identifying worse case scenarios for non-seismic sources. The present report synthesizes some of the findings of, and presents the seismic sources identified by the experts to pose the largest tsunami risk to nearby coastlines. In addition, workshop participants discussed existing gaps in scientific knowledge of local tectonics, including seismic and tsunami instrumentation of the trench and current level of tsunami readiness for at-risk populations, including real-time tsunami warnings. The results and conclusions of the meeting are presented in this report and some recommendations are summarized in the final section.

Offshore Probabilistic Tsunami Hazard Assessments (offshore PTHAs) provide large-scale analyses of earthquake-tsunami frequencies and uncertainties in the deep ocean, but do not provide high-resolution onshore tsunami hazard information as required for many risk-management applications. To understand the implications of an onshore PTHA for the onshore hazard at any site, in principle the tsunami inundation should be simulated locally for every scenario in the offshore PTHA. In practice this is rarely feasible due to the computational expense of inundation models, and the large number of scenarios in offshore PTHAs. Monte-Carlo methods offer a practical and rigorous alternative for approximating the onshore hazard, using a random subset of scenarios. The resulting Monte-Carlo errors can be quantified and controlled, enabling high-resolution onshore PTHAs to be implemented at a fraction of the computational cost. This study develops novel Monte-Carlo sampling approaches for offshore-to-onshore PTHA. Modelled offshore PTHA wave heights are used to preferentially sample scenarios that have large offshore waves near an onshore site of interest. By appropriately weighting the scenarios, the Monte-Carlo errors are reduced without introducing any bias. The techniques are applied to a high-resolution onshore PTHA for the island of Tongatapu in Tonga. In this region, the new approaches lead to efficiency improvements equivalent to using 4-18 times more random scenarios, as compared with stratified-sampling by magnitude, which is commonly used for onshore PTHA. The greatest efficiency improvements are for rare, large tsunamis, and for calculations that represent epistemic uncertainties in the tsunami hazard. To facilitate the control of Monte-Carlo errors in practical applications, this study also provides analytical techniques for estimating the errors both before and after inundation simulations are conducted. Before inundation simulation, this enables a proposed Monte-Carlo sampling scheme to be checked, and potentially improved, at minimal computational cost. After inundation simulation, it enables the remaining Monte-Carlo errors to be quantified at onshore sites, without additional inundation simulations. In combination these techniques enable offshore PTHAs to be rigorously transformed into onshore PTHAs, with full characterisation of epistemic uncertainties, while controlling Monte-Carlo errors. Appeared online in Geophysical Journal International 11 April 2022.

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. Appeared online in Front. Earth Sci., 05 March 2021.

Tsunamis are unpredictable and infrequent but potentially large impact natural disasters. To prepare, mitigate and prevent losses from tsunamis, probabilistic hazard and risk analysis methods have been developed and have proved useful. However, large gaps and uncertainties still exist and many steps in the assessment methods lack information, theoretical foundation, or commonly accepted methods. Moreover, applied methods have very different levels of maturity, from already advanced probabilistic tsunami hazard analysis for earthquake sources, to less mature probabilistic risk analysis. In this review we give an overview of the current state of probabilistic tsunami hazard and risk analysis. Identifying research gaps, we offer suggestions for future research directions. An extensive literature list allows for branching into diverse aspects of this scientific approach. Appeared online in Front. Earth Sci., 29 April 2021

At far-field coasts the largest tsunami waves often occur many hours after arrival, and hazardous waves may persist for more than a day. To simulate tsunamis at far-field coasts it is common to combine high-resolution nonlinear shallow water models (covering sites of interest) with low-resolution reduced-physics global-scale models (to efficiently simulate propagation). The global propagation models often ignore friction and are mathematically energy conservative, so in theory the modelled tsunami will persist indefinitely. In contrast, real tsunamis exhibit slow dissipation at the global-scale with an energy e-folding time of approximately one day. How strongly do these global-scale approximations affect nearshore tsunamis simulated at far-field coasts? To investigate this issue we compare modelled and observed tsunamis at sixteen nearshore tide-gauges in Australia, which were generated by the following earthquakes: Mw 9.5 Chile 1960; Mw 9.2 Sumatra 2004; Mw 8.8 Chile 2010; Mw 9.1 Tohoku 2011; and Mw 8.3 Chile 2015. Each historic tsunami is represented with multiple earthquake source models from the literature, to prevent bias in any single source from dominating the results. The tsunami is simulated for 60 hours with a nested global-to-local model. On the nearshore grids we solve the nonlinear shallow water equations with Manning-friction, while on the global grid we test three reduced-physics propagation models which combine the linear shallow water equations with alternative treatments of friction: 1) frictionless; 2) nonlinear Manning-friction; and 3) constant linear-friction. In comparison with data, the frictionless global model works well for simulating nearshore tsunami maxima for ~ 8 hours after tsunami arrival, and Manning-friction gives similar predictions in this period. Constant linear-friction is found to under-predict the size of early arriving waves. As the simulation duration is increased from 36 to 60 hours, the frictionless global model increasingly over-estimates the observed tsunami maxima; whereas both models with global-scale friction perform relatively well. The constant linear-friction model can be improved using delayed linear-friction, where propagation is simulated with an initial frictionless period (12 hours herein). This prevents the systematic underestimation of early nearshore wave heights. While nonlinear Manning-friction offers comparably good performance, a practical advantage of the linear-friction models in this study is that their solutions can be computed, to high accuracy, with a simple transformation of frictionless solutions. This offers a pragmatic approach to improving unit-source based global tsunami simulations at late times.