# Source Selection and Their Activity Rate

Finn Løvholt, Roberto Basili, Andrea Rovida, Stefano Lorito, Fabrizio Romano, Mathilde B Sørensen, Carl B Harbitz, Jacopo Selva, Raphaël Paris, Anita Grezio, et al.

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Finn Løvholt, Roberto Basili, Andrea Rovida, Stefano Lorito, Fabrizio Romano, et al. Source Selection and Their Activity Rate. Sørensen, M. Probabilistic Tsunami Hazard and Risk Analysis. A cookbook, 14, Springer, pp.87 - 156, 2026, 10.1007/978-3-031-98115-9_3. hal-05530586

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Chapter 3
Source Selection and Their Activity Rate

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Finn Løvholt, Roberto Basili, Andrea Rovida, Stefano Lorito,
Fabrizio Romano, Mathilde B. Sørensen, Carl B. Harbitz,
Jacopo Selva, Raphaël Paris, Anita Grezio, and Cléa Denamiel

**3.1 Introduction**

This chapter presents several methods to conduct tsunami source selection proce-
dures (we note that modeling of the mechanics of tsunami sources are included in
Chap. 4). The chapter is subdivided into four sections comprising the most frequent
tsunami sources, namely Earthquake sources, Landslides sources, Volcanic sources,
and Atmospheric sources. Volcanic sources may also be linked to landslides and

F. Løvholt (✉)
Offshore Energy, Norwegian Geotechnical Institute, Oslo, Norway
e-mail: finn.lovholt@ngi.no

R. Basili · A. Rovida · S. Lorito · F. Romano
Istituto Nazionale di Geofisica e Vulcanologia, Roma, Italy
e-mail: roberto.basili@ingv.it

A. Rovida
e-mail: andrea.rovida@ingv.it

S. Lorito
e-mail: stefano.lorito@ingv.it

F. Romano
e-mail: fabrizio.romano@ingv.it

M. B. Sørensen
Department of Earth Science, University of Bergen, Bergen, Norway
e-mail: mathilde.sorensen@uib.no

C. B. Harbitz
Natural Hazards, Norwegian Geotechnical Institute, Oslo, Norway
e-mail: carl.bonnevie.harbitz@ngi.no

J. Selva
Dipartimento di Scienze della Terra, dell' Ambiente e delle Risorse (DiSTAR) , Università di
Napoli Federico II, Naples, Italy
e-mail: jacopo selva@unina.it
atmospheric pressure disturbances, and in these cases the source description is given
only in the landslide or atmospheric related sections. The main ingredients that are
identified for these types of sources are listed in Table 3.1. The selection process
follows three main steps, of which the general workflow is displayed graphically in
Fig. 3.1. These steps include the following operations:

Step 1 consists of the selection of the potential source areas and the selection of the types of sources that may impact the selected target areas. It includes a qualitative analysis of the source areas relevant to the hazard or risk analysis to be conducted.

Step 2 represents the source parameterisation. It consists of defining the source position, density, parameter selection and variability (e.g., in space and size), and is applied only to the source(s) selected in step 1. This can be used to model the variability of the sources.

Step 3 defines a finite list of individual scenarios and quantifies the probability of occurrence or the mean annual rate of occurrence in the reference time window (the exposure time) for each individual source. It is applicable mostly only to probabilistic methods (see Chap. 2).

This Chapter describes the different sources in separate subsections: Earthquake sources (Sect. 3.2), Landslide sources (Sect. 3.3), Volcano sources (Sect. 3.4), and Atmospheric sources (Sect. 3.5). Each subsection presents the different methods available for each of the steps (1, 2, 3) described above.

For each source type, a synthesis of the methods is presented in a table, which provides a summary of the method descriptions, requirements, and uncertainty treatment. Finally, Sect. 3.6 provides very brief remarks about pros and cons of the various methods in order to help users select the appropriate models.

## 3.2 Earthquake Sources

Earthquakes represent the main cause of tsunamis globally, and are hence the tsunami source analysed the most, with a large body of literature covering seismic PTHA (SPTHA; e.g., Geist and Parsons 2006; Grezio et al. 2017). Much of the techniques and treatment of earthquake sources used in SPTHA originate from Probabilistic Seismic Hazard Analysis (PSHA, Cornell 1968). Over time these have been adapted

R. Paris
CNRS, IRD, OPGC, Laboratoire Magmas et Volcans, Université Clermont Auvergne, Aubière, France
e-mail: raphael.paris@uca.fr

A. Grezio
Istituto Nazionale di Geofisica e Vulcanologia, Bologna, Italy
e-mail: anita.grezio@ingv.it

C. Denamiel
Division of Marine and Environmental Research, Ruđer Bošković Institute, Zagreb, Croatia
e-mail: cdenami@irb.hr
<table><caption>**Table 3.1** Source parametrization and rates</caption><thead><tr><th></th><th></th></tr></thead><tbody><tr><td>What does the ingredient describe?</td><td>The process of defining and selecting tsunami sources and quantifying their future probability of occurrence</td></tr><tr><td>Definitions of the ingredient</td><td>This process typically consists of:<br>The selection of source types, e.g. earthquakes, landslides, volcanoes, atmospheric sources<br>The selection of the source zones and/or of the volcanoes and, for each of them, the type(s) of volcanic source<br>The definition of source parameterization and variability in each of the source zones<br>The quantification of the probability of occurrence and/or of annual rates of the individual sources</td></tr><tr><td>What is/are the metric(s) used for measuring/evaluating the ingredient?</td><td>(Initial) source position, geometry, kinematics, material parameters, and size of each source<br>Annual rates or probabilities of occurrence of individual sources in the exposure time (for each combination of the source parameters)</td></tr><tr><td>Possible uses/applications of the ingredient</td><td>Source model for hazard analysis</td></tr><tr><td>Possible multi-hazard dimensions/applications?</td><td>Yes, by combining source models for several types of hazards (earthquake hazard, landslide hazard, volcano hazard, atmospheric hazards). It is stressed that most tsunamigenic events are also a hazard per se (e.g. landslides, volcanic explosions) or generate other hazards (e.g. seismic ground shaking, volcanic tephra fall), thus adding additional impacts to the tsunami impact<br>Cascading hazards examples: Landslides triggered by earthquakes or volcanic activity. Climate effects—e.g. enhancing probability of slope failure, climate hazard influencing intensity and probability of atmospheric sources</td></tr><tr><td>Possible time-dependent/ dynamic dimensions</td><td>Earthquake rates (temporal probability of occurrence) can be significantly time-dependent, for example following a large earthquake<br>Landslide slope failure linked to precipitation and seasonal variation (winter, summer)<br>Life-cycles and states of volcanoes (quiescence, unrest, eruptions phases)<br>Atmospheric sources are fully dynamic and time-dependent (i.e., continuous variations in time and space)</td></tr></tbody></table>

(continued)
<table><caption>**Table 3.1** (continued)</caption><thead><tr><th></th><th></th></tr></thead><tbody><tr><td>List of the available methods to be described below</td><td><strong>Earthquakes:</strong><br>Seismicity Rates and mechanisms based on past seismicity<br>Seismicity Rates and mechanisms based on tectonics<br>Logic trees and ensemble modelling, non-structured expert judgment or structured expert elicitation methods, to quantify epistemic uncertainty<br>Scenarios compatible with historical events or plausible due to different tectonic settings<br><strong>Landslides:</strong><br>Methods based on past landslide data—basing the hazard on analysis of past events. Depending on the data availability, they can be both local and regional<br>Methods based on slope stability models—they are often more heuristic, although they can be mixed with past landslide frequency information, based on expert judgment, and therefore often most appropriate for local hazard analysis<br><strong>Volcanoes:</strong><br>Selected scenarios compatible with historical events or plausible due to tectonic and volcanic settings<br>For eruptive tsunamis, all methods for eruption forecasting and volcanic hazards, including event trees, belief networks, expert elicitations, Markov chains, stratified sampling, based on past data and/or on monitoring<br>For non-eruptive tsunamis, there are no consolidated methods; methods strongly vary on the source type and its triggering conditions<br>To quantify epistemic uncertainty, Bayesian methods, logic trees, ensemble modelling, and different flavours of expert elicitation can be used<br><strong>Atmospheric:</strong><br>Methods based on the type of atmospheric sources: weather or acoustic<br>Methods based on the spatial scale: local or global<br>Methods based on the type of study: forecast, climate or hazard assessment</td></tr></tbody></table>

for use in SPTHA, for example the generation of empirical scaling relations that focus on subduction zones, or the adaptation of stochastic slip models for use on complex subduction zone geometries. Regardless of the specific approach and techniques used, the first step for an earthquake tsunami hazard or risk assessment is generally to set up a (probabilistic) earthquake model.
<figure><img src="image_3.png" /><figcaption>**Fig. 3.1** Workflow for the source selection, parameterisation, and rate quantification</figcaption></figure>

### 3.2.1 Short Description of the Earthquake Source Selection Method

Earthquakes occur due to the reactivation of pre-existing faults (Sibson 1985). By knowing faults, one can predict the locations, mechanisms, and rates of future earthquake ruptures. At the global scale, most earthquakes occur along plate boundaries (Fig. 3.2). On the other hand, oceanic and continental plate interiors account for less than 4% of all global seismicity (Kagan et al. 2010). According to the plate boundary model by Bird (2003), plate boundaries comprise 278,000 km in length, 77% (213,000 km) of which is offshore.

There are three main types of plate boundaries: (i) transform, where two plates slide past each other; (ii) divergent, where plates move away from each other; and (iii) convergent, where plates move towards each other. In the case where one plate sinks below the other, it is referred to as a subduction. Subduction zones cover more than 60,000 km of the total convergent plate boundary length (Bird 2003; Berryman et al. 2015; Hayes et al. 2018; Hasterok et al. 2022).

Earthquake activity rates can be expressed with a magnitude-frequency distribution (MFD). Two methods exist to estimate MFDs: one assumes a constant seismicity rate, and the other constant seismic moment rate (Youngs and Coppersmith 1985).
<figure><img src="image_4.png" /><figcaption>**Fig. 3.2** Map of tectonic plate boundaries (data from Bird 2003) overlain by earthquake epicentres from the global centroid moment tensors (data from Ekström et al. 2012), color-coded based on the faulting mechanisms</figcaption></figure>

The first requires earthquake catalogues and fault association strategies; the second needs geologic/geodetic fault slip rates (Fig. 3.3).

<figure><img src="image_5.png" /><figcaption>**Fig. 3.3** Schematic showing the effect of varying the upper bound magnitude on the magnitude-frequency distribution (i.e. the annual number of earthquakes above a particular magnitude, in this example, magnitude 4) of two alternative approaches: (left) constant seismicity rate, if the number of earthquakes in the historical seismicity record is assumed to be a constraint on the activity rate, and (right) constant seismic moment rate, if the fault slip rate is the principle constraint on the activity rate. (Redrawn from Youngs and Coppersmith 1985). Notice that the tick marks on the Y axis are in base-10 logarithmic scale</figcaption></figure>
For earthquake sources, the main steps in tsunami source characterization follow the three basic steps outlined in Fig. 3.1. Step 1 is related to defining potential earthquake sources, either based on faults, earthquake catalogues or other sources. Step 2 links these sources to specific potential earthquake scenarios, either as fault sources, area sources, or gridded sources. Step 3 defines the occurrence probabilities of the potential scenarios. Available methods for each of those steps will be described in the following sections.

### 3.2.2 Step 1: Basis for Source Selection

#### Fault sources

Subduction zones are usually considered the main tsunami hazard drivers, and are often the only seismic source type considered in SPTHA, especially at large-scale (González et al. 2009; Davies et al. 2018). SPTHA at the regional scale tends to also consider crustal intraplate and other plate-boundary fault sources (Horspool et al. 2014; Basili et al. 2021a, b).

Subduction zones (Fig. 3.4) include structures that generate different earthquake types (Satake and Tanioka 1999). The slab interface, or megathrust, where the two plates are in contact, generates the largest and thus most relevant earthquakes for SPTHA, but also ruptures originating on the megathrust and propagating in the wedge (Clift and Vannucchi 2004) on splay faults branching upward from the interface may be important (van Zelst et al. 2022). Intraslab earthquakes are of more limited interest to SPTHA, except for relatively shallow earthquakes (Yeh et al. 1995), or outer-rise earthquakes generated where the subducting plate is bent upward (Chapple and Forsyth 1979).

Crustal faults occur on all types of plate boundaries. Although plate boundaries are prominently elongated features, the deforming area around them can be as wide as a few hundred kilometres, as in the case of back-arc basins or collision zones. These deforming areas host the majority of active crustal faults, but not all of them can be defined in sufficient detail for SPTHA (Basili et al. 2013). Additionally, crustal faulting can occur far away from plate boundaries. Depending on the level of knowledge of faults, hazard modelers may resort to different strategies for source parameterization (see Step 2).

#### Earthquake catalogues

Earthquake catalogues provide crucial information on earthquake sources. They commonly include the occurrence time, hypocentre location, and size of past events. For the size, the moment magnitude ($M_w$) scale is commonly used for seismic and tsunami hazard analyses due to its direct link to the size of the earthquake rupture. Instrumental recordings from global seismometer networks have been used to systematically assess earthquake parameters since the 1960s (e.g., International Seismological Centre 2023; Storchack et al. 2017; Storchack et al. 2020; Ekström
<figure><img src="image_6.png" /><figcaption>**Fig. 3.4** Schematic block model of a subduction zone showing typical locations of different earthquake types and their fault sources</figcaption></figure>

et al. 2012). However, instrumental catalogues have limited temporal coverage, so pre-instrumental earthquake data from historical documents are used to extend earthquake catalogues back in time. A quantitative estimate of the ground shaking at a site is obtained by comparing the effects of an earthquake on humans, buildings, and the environment with typical earthquake effects described in macroseismic scales (see overviews by Musson et al. 2010; Musson and Cecic 2012). Spatial distributions of macroseismic intensity data are then used to estimate earthquake locations and sizes (e.g., Musson and Cecic 2012; Bakun and Wentworth 1997; Gasperini et al. 1999, 2010; Provost and Scotti 2020). Harmonized earthquake catalogues combining instrumental and macroseismic data are common in Europe and worldwide (e.g., Fäh et al. 2011; Grünthal and Wahlström 2012; Manchuel et al. 2018; Rovida et al. 2020; Felzer and Cao 2008; Beauval et al. 2013; Zare et al. 2014; Mikhailova et al. 2015; Brax et al. 2019; Sawires et al. 2019). For SPTHA, large-scale catalogues can be compiled by merging existing regional catalogues and harmonizing magnitudes (Grünthal and Wahlström 2012; Albini et al. 2013, 2014).

### 3.2.2.1 Other Data Sources

Robust seismicity forecasts for hazard analysis should rely on multiple data sources in addition to fault locations and earthquake catalogues (Gerstenberger et al. 2020; Grezio et al. 2017; Behrens et al. 2021). Including faults and their slip rates could help reduce the uncertainty at long average return periods. Palaeoseismological (hardly available for offshore faults) and paleotsunami observations can help extend the analysis in the past to improve the occurrence rate forecast of future earthquakes and large tsunamis. Geodetic strain rates and geodetically constrained coupling, even
if covering only tens of years, with stationarity assumptions, can introduce further
constraints (Wang et al. 2012).

### 3.2.3 Step 2: Source Parameterisation

**Fault sources**

Fault-source modelers use 3D surfaces to represent subduction interfaces or crustal faults and simplify fault surfaces by reducing them to a down-dip planar shape or oriented rectangle. Stochastic distributions of fault positions may be used in cases with limited fault knowledge. Although 3D fault modelling is desirable (Tonini et al. 2020; Serra et al. 2021; Gómez de la Peña et al. 2022), rectangular faults are often used due to computational requirements. The spatial heterogeneity of fault dislocation is modelled by distributing different slip vectors onto the fault surface (González et al. 2009; Davies and Griffin 2018, 2020; Basili et al. 2021a, b). Dutta et al. (2021) showed that models of earthquake ruptures using planar faults can be affected by substantial bias and that simultaneous inversion of fault geometry and slip can solve the problem (LeVeque et al. 2016). Hence, the combination of fault geometry and slip distribution also affects the reconstruction of past earthquake ruptures.

**Area sources**

Area sources (or seismogenic zones) are 2D polygons with vertical boundaries extending to the bottom of the seismogenic layer. Area sources are regions with spatially uniform seismicity in terms of earthquake occurrence rates, magnitude distribution, maximum magnitude, expected rupture mechanism, and other relevant parameters. Despite criticism of the reliability of the underlying assumptions (Woo 1994), area sources have been conveniently used in PSHA to complement the limited knowledge about seismogenic faults often encountered even in tectonically active regions. The concept of area sources has also been adopted in PTHA (Sørensen et al. 2012; Salazar-Monroy et al. 2021).

**Gridded sources**

Gridded sources are another strategy to address the possible lack of knowledge of individual seismogenic faults. Differently from area sources, gridded sources are a geometrically regular subdivision of the seismic source domain (squares or rectangles) used to accommodate irregular distributions of earthquake occurrence rates, maximum magnitude, and rupture mechanisms (Necmioglu and Özel 2015; Basili et al. 2021a, b).
### 3.2.4 Step 3: Probabilistic Treatment

#### General concepts

In earthquake hazard analyses, seismicity is often assumed to follow a stationary Poisson process, with earthquake activity rates defined by a MFD. The exponential Gutenberg-Richter (G-R) model (Gutenberg and Richter 1944, 1949) is the most common MFD, but other shapes are used such as the maximum magnitude and characteristic earthquake models (Bommer and Stafford 2009). The G-R model gives the annual number of earthquakes of a given magnitude as a function of two parameters, the a-value describing the overall level of seismicity and the b-value describing the relation between small and large magnitudes. The Poisson model assumes constant earthquake occurrence rates and does not account for earthquakes triggering other earthquakes. Time dependent models like the ETAS (Ogata 1998) and Brownian Passage Time (BPT; Ellsworth et al. 1999; Murru et al. 2016) have been developed to address these limitations. Renewal models, such as the BPT, have also been used in SPTHA (Goda 2020).

There is significant uncertainty associated with earthquake sources, their activity rates, and the probabilistic framework, which can be addressed using logic trees, Bayesian inference, or expert elicitation (Geist and Parsons 2006; Annaka et al. 2007; Grezio et al. 2010; Selva et al. 2010; Neri et al. 2008; Selva et al. 2012a, b; Basili et al. 2021a, b).

#### Seismicity-based earthquake rate forecasting

MFDs related to specific areas can be derived from earthquake catalogues, which contain records of past earthquakes. A complete catalogue, containing all the earthquakes above a given magnitude, is needed for accurate estimates. Observation gaps may exist due to a seismic network's limitations or historical factors, particularly for smaller events or earthquakes at sea. Figure 3.5 shows that global earthquake catalogues contain significantly fewer earthquakes when one goes back in time, demonstrating that also large historical events of interest for SPTHA might be missing from global and regional catalogues (e.g., Kagan 2003; Hough 2013; Albini et al. 2013, 2014). It is thus important to account for catalogue completeness when defining seismicity rates.

Statistical methods to determine catalogue completeness often assume a stationary seismogenic process (Stepp 1972; Grünthal et al. 1998; Mulargia and Tinti 1985; Rotondi et al. 1994; Albarello et al. 2001; Rotondi and Garavaglia 2002; Wössner and Wiemer 2005; Hakimhashemi and Grünthal 2012). Statistical methods are not suitable for estimating the completeness time of the rarest and largest earthquakes. In these cases, historical methods assess completeness by evaluating the likelihood of earthquakes of a given impact at a locality being unreported by historical sources (Ambraseys and Melville 1982; Stucchi et al. 2004; Albini and Rovida 2018; Albini 2020).

To calculate earthquake probabilities, events below the completeness magnitude and older than the completeness time are excluded. Traditional seismicity-based
<figure><img src="image_7.png" /><figcaption>**Fig. 3.5** Global distribution of M7 + earthquakes according to the Global Historical Earthquake Catalogue—GHEC v1.0 (Albini et al. 2013) in different time periods (between 1000 and 1903)</figcaption></figure>

earthquake rate forecasting for PSHA (e.g., Cornell 1968) also requires the removal of dependent events (such as foreshocks, aftershocks and swarm events) to comply with the Poisson process assumption. Various methods exist for identifying dependent events based on time and space windows (Gardner and Knopoff 1974; Reasenberg 1985).

The upper bound (or maximum) magnitude of the MFD can be estimated using statistical methods. The classical G-R distribution assumes an infinite upper bound, with the maximum magnitude obtained by extrapolating the MFD to larger magnitudes until the frequency becomes negligible for a practical application. However, the finiteness of fault systems and the energy available for generating earthquakes requires modifications of the MFD at larger magnitudes. The truncated or tapered MFDs are common modifications of the classical G-R distribution (e.g., Kagan 2002a). In some practical applications, this upper limit has been estimated from the magnitude of the largest observed earthquake in the region under study plus a conservative factor or on a statistical basis with confidence intervals (e.g., Kagan 2002a; Bird and Kagan 2004; Kagan et al. 2010). However, the upper limit is hardly testable (Holschneider et al. 2014). It is important to note that the choice of the maximum magnitude and the functional form of the truncation or tapering of the distribution can affect the hazard estimation.

## Seismic-moment-based earthquake rate forecasting

This method relies on the seismic moment conservation principle by equating the geologic or geodetic moment rate to the seismic moment rate, such that
$$ \dot{m}_s = \chi \dot{m}_g = \chi \mu LW \dot{S} $$

where $\dot{m}_s$ is seismic moment rate, $\dot{m}_g$ is geologic/geodetic moment rate, $\chi$ is seismic efficiency or long-term coupling, $\mu$ is rigidity, $L$ and $W$ are fault length and width, respectively, and $\dot{S}$ is slip rate for crustal faults or convergence rate for subduction interfaces.

Different methods use various constraints to convert moment rate estimates into a convenient MFD. The first constraint is the MFD upper bound, which can be obtained in this case also by calculating the magnitude corresponding to the largest earthquake rupture that the fault source can host based on empirical scaling relations, or with methods described in the previous section. The conversion between earthquake magnitude and the seismic moment is readily obtained by the classic relation

$$ M_w = \log_{10}(M_0) / 1.5 - 6.07 $$

where $M_w$ is the magnitude and $M_0$ is the seismic moment in Nm (Kanamori and Brodsky 2004).

For various MFD forms, one must opt for the decay of the large-size end of the distribution (Utsu 1999) between the truncated and the tapered models (Anderson and Luco 1983; Kagan 2002b; Bird and Kagan 2004).

In most MFDs, the b-value controls the power-law part for small and moderate earthquakes, and the universal estimation of b ~ 0.95 can be used if seismicity data is unavailable (Kagan 1999, 2002a; Bird and Kagan 2004; Kagan et al. 2010). Different formulations can be used to calculate the a-value (Anderson and Luco 1983; Kagan 2002b). The characteristic earthquake model requires an additional parameter that determines the upper end of the exponential part of the distribution (Youngs and Coppersmith 1985). The MFD is transformed into the non-cumulative form and discretized into magnitude bins. Different MFD forms can affect the annual rates of moderate-to-large earthquakes, as shown in Fig. 3.6.

## Individual earthquake ruptures

The final step in the source characterization is to define individual earthquake ruptures (with an associated occurrence probability) that can form the basis of tsunami modelling. Each earthquake rupture must be defined with location, fault dimensions and average displacement. Individual earthquakes can be defined by modelling all possible events on a fault, or within an area or a volume, and partitioning among them the total earthquake rate. Examples include systematic sampling of the earthquake parameter space (e.g., Horspool et al. 2014; Davies et al. 2018; Basili et al. 2021a, b), and Monte Carlo methods to create synthetic source catalogues spanning a given amount of time (Sørensen et al. 2012), or even a combination of the two as in a recently proposed stratified importance sampling approach (Davies et al. 2022).

The generalized functional form between the most commonly measured rupture dimensions (length, width, area, and average displacement) and moment magnitude ($M_w$) is
<figure><img src="image_8.png" /><figcaption>**Fig. 3.6** Diagrams showing the effect on the MFD of adopting different typical forms (left panel is cumulative and right panel is incremental) based on the seismic-moment balancing. YC85 (red) is the characteristic earthquake model (Youngs and Coppersmith 1985), AL83 (blue) is the exponential truncated model (Anderson and Luco 1983), and KA02-TGR (green) is the exponential tapered model (Kagan 2002b). The three models balance the same moment rate ($M_s = 5.6E + 19 Nm$) and use the same maximum magnitude in the truncated case and corner magnitude in the tapered case ($M_{w} = 8 \pm 0.25$) and slope of the power law part ($b = 1$)</figcaption></figure>

$$log_{10}(X) = a + bMw$$

where X is the rupture dimension under consideration, and a and b are coefficients empirically derived from observed ruptures. Such scaling relations for subduction interface, or megathrust, earthquakes significantly differ from those for crustal fault earthquakes (Fig. 3.7).

Comparing several different scaling relations, Skarlatoudis et al. (2016) found that the rupture areas of subduction interface earthquakes are about 1.7 times larger, and their average slip is about 0.4 times smaller than those of crustal earthquakes with the same seismic moment. Different scaling also exists for crustal fault earthquake ruptures of different slip types (Blaser et al. 2010). This highlights the importance of using appropriate scaling relations when modelling individual ruptures, as they can result in different seafloor deformation.

To predict future rupture mechanisms, geologic and geodetic information, or statistics of past earthquakes, can be used. Crustal fault sources are typically reported with a rake value associated with fault geometry (strike and dip) derived from geologic information. For subduction interfaces, the rake is often conservatively assumed to be 90° (pure reverse mechanism), or derived from the local mean direction of plate convergence (relative motion of the upper and lower plates). In areas
<figure><img src="image_9.png" /><figcaption>**Fig. 3.7** Comparison between subduction interface (solid lines) and reverse crustal fault (dotted lines) earthquake rupture scaling relations between rupture area (A) and earthquake moment magnitude (left panel) and mean slip (D) and earthquake moment magnitude (right panel). WC94 (Wells and Coppersmith 1994), BL10 (Blaser et al. 2010), LE14 (Leonard 2014), TH17 (Thingbaijam et al. 2017), MU08 (Murotani et al. 2008), MU13 (Murotani et al. 2013), ST10 (Strasser et al. 2010), GO16 (Goda et al. 2016), SK16 (Skarlatoudis et al. 2016), AH17 (Allen and Hayes 2017). Only BL10 for subduction interface earthquakes falls within the range of crustal fault relations, though with a different slope. Notice that the average displacement for WC94, BL10, and ST10 was derived from the seismic moment</figcaption></figure>

without known faults, the faulting mechanism can be derived from focal mechanism statistics (e.g. Taroni and Selva 2021), which includes all angles but cannot distinguish between the two auxiliary nodal planes.

A few studies treat slip probability as non-uniform on the fault plane (Davies 2019; Scala et al. 2020), such as in subduction interfaces where depth-dependent features of rigidity and shallow slip amplification effects enhance tsunami hazard (Murphy et al. 2016). Most SPTHA studies model slip distribution as a stochastic process (see Chapter 4), whereas they rarely include additional complexity such as laterally varying seismic coupling in the seismic model (Behrens et al. 2021).

### 3.2.5 Summary Table

See Table 3.2.
<table><caption>**Table 3.2** Summary table: earthquake source selection</caption><thead><tr><th>Short description of method</th><th></th></tr></thead><tbody><tr><td>Theoretical/mechanical background for the method(s)</td><td><ul><li>Earthquakes occur on faults most of which are along active plate boundaries but also within the plate interiors</li><li>The earthquake MFD has an exponentially decreasing part controlled by the rate of relatively small earthquakes and a more undefined tail controlled by the behaviour of large earthquakes</li><li>The characteristics of individual earthquakes depend on the local structure, pre-stress, and frictional states</li><li>Not all the faults can be known, so earthquakes may be initially assumed to occur everywhere; yet large earthquakes are more frequently observed on principal faults and subduction zones</li></ul></td></tr><tr><td>Short outline of how the method(s) works</td><td><ul><li>The first step of the definition of the source model for a SPTHA is to select both local and distant sources that are potentially relevant to the target area, based on the basin shape, known faults, past seismicity and tsunami</li><li>In SPTHA two typologies of faults are considered, that is subducting plate interface and crustal faults</li><li>Then, for each typology, different approaches can be used for the parameterisation of the sources (fault, area, gridded sources)</li><li>Different approaches can also be used to parameterise the MFD of the earthquakes (seismicity- or seismic moment-based)</li></ul></td></tr><tr><td>How is/are the output(s) of the method(s) represented?</td><td>List of potential future earthquake ruptures within a chosen range of magnitude or seismic moment, including their geographic location and depth, orientation (strike and dip), sense of movement (rake), size (length and width, or area and aspect ratio, and slip), frequency (e.g., yearly number of events), and probability. The granularity of these parameters depends on the discretization type and level of each rupture</td></tr><tr><td>In what way do(es) the method(s) take into account time-dependent/dynamic aspects?</td><td>A time-dependent model is sometimes considered based on recent earthquakes at a specific location</td></tr><tr><td>Do(es) the method(s) use parallelisation, machine learning, surrogate models, advanced simulation schemes, other computational reduction strategies (e.g. cluster analysis, etc.)?</td><td>We are at the dawn of using AI for preparing input data, for example regarding the construction of earthquake catalogues</td></tr></tbody></table>

(continued)
<table><caption>**Table 3.2 (continued)**</caption><tr><td>What are the pros and cons and peculiarities of this specific method(s)? Are there known shortcomings / benefits of the method(s)? In what cases is this method(s) a good/poor choice</td><td><ul><li>The method overcomes to some extent the scarcity of tsunami data by recurring to tsunamigenic seismic source analysis and numerical tsunami modelling</li><li>Nonetheless, the tails of the magnitude-frequency earthquake distributions remain largely unconstrained, as well as the frequency of specific slip distributions at a given locality (e.g. shallow slip probability/tsunami earthquakes)</li><li>The stationarity of the seismic process is a convenient working hypothesis in a regime of large uncertainty regarding its time-dependent features; yet it would be in principle better to constrain the modelled future occurrence with the past local seismicity</li><li>The seismicity-based and the seismic moment-based models are not necessarily consistent with one another</li></ul></td></tr><tr><td>Data and technical requirements for method</td><td></td></tr><tr><td>What input data does the method(s) use?</td><td><p>The source selection uses as input data</p><ul><li>Earthquake catalogues including historical events</li><li>Geometry of the subduction plate interfaces</li><li>Crustal fault sources</li><li>Area sources</li><li>Gridded sources</li></ul><p>The source parameterization uses as input data</p><ul><li>Rectangular geometry for crustal sources whose sizes depend on the earthquake moment magnitude and empirical scaling relations</li><li>Faulting mechanism and slip vector</li><li>Geometry of the subduction plate interface opportunely meshed in a discrete number of elementary sub-faults</li></ul></td></tr><tr><td>What are the technical requirements?</td><td><ul><li>The earthquake catalogues have to be complete and declustered to not contain foreshocks and aftershocks if assuming that the seismicity follows a Poisson process</li><li>The distribution of the seismicity in the area sources has to be uniform</li><li>The regions containing the seismic events in the gridded sources have to be regular (square, rectangular)</li></ul></td></tr><tr><td>Are HPC computing resources necessary, would absence of these compromise the use?</td><td>No</td></tr><tr><td>Is the method(s)/ workflow(s) available as a git/software/jupyter notebook?</td><td>No</td></tr></table>

(continued)
<table><caption>**Table 3.2 (continued)**</caption><thead><tr><th colspan="2">Treatment of uncertainties for the method</th></tr></thead><tbody><tr><td>Is the method(s) itself deterministic or uncertainty based?</td><td>Generally (but not always) the fault/source characterization is deterministic while the characterization of its behaviour (mechanism, recurrence) is uncertainty based</td></tr><tr><td>Which are potential sources of uncertainties? Which parameters are used to characterize them?</td><td>Unknown or never-observed earthquake sources, variability in the realization of earthquakes from known sources</td></tr><tr><td>How are uncertainties quantified for the identified parameters? Are there significant correlations between different uncertain parameters?</td><td>The uncertainties are characterized based on consistency with observations of past events and geology/seismotectonics, as well as based on the assumed theoretical framework (e.g. functional form of the MFD relation, depth-dependency of the slip occurrence)</td></tr><tr><td>Is the method(s) able to digest and propagate uncertainty in input (previous ingredient) and propagate it to the output (next ingredients)? Does the assessment of this ingredient require uncertainty propagation? If yes, how are uncertainties propagated?</td><td>Yes, in principle uncertainty in input can be propagated. For example, when assigning different weights to alternative models</td></tr><tr><td>What are the consequences of lack of data in input or for boundary conditions, or for characterizing certain parameters?</td><td>Potentially missing important sources of hazard, with consequent underestimation of the total hazard, or large uncertainty stemming from unconstrained parameters</td></tr><tr><td>What are the consequences of ignoring or poorly treating uncertainties?</td><td>Potentially missing important sources of hazard, with consequent underestimation of the total hazard, or a sense of false precision if the natural variability is not explored sufficiently</td></tr></tbody></table>

## 3.3 Landslide Sources

### 3.3.1 Short Description of Method

Identification and demarcation of landslide sources in tsunami hazard analysis involve large uncertainty, both with respect to volumes and rates. Landslide source treatment depends on the expected type of landslide from subaerial slides, volcano sector or flank collapses, slump-like submarine landslides, or long run-out giant submarine slides (Fig. 3.8). As landslides are not tied to tectonic structures as earthquakes and volcanoes are, they can in principle happen everywhere where there is enough material to be released on a slope. Another reason for the large uncertainty is that acquiring all data needed for a broad landslide source probability identification is often not feasible. This uncertainty in forecasting landslide volume probability is a direct reason for the Landslide Probabilistic Tsunami Hazard Assessment (LPTHA)
being relatively sparsely developed and used, and that consequently past hazard anal-
yses have still often turned to the credible worst case scenario method (e.g. Tinti et al.
2008; Harbitz et al. 2014b; Grilli et al. 2017). Both the amount of data and the under-
standing of the local or regional slope stability conditions for large landslides are
imperative for the source selection methodology. In order to place landslide sources
into a probabilistic framework, several simplifying steps are necessary for compu-
tational feasibility. Only a few examples of LPTHA exist to date (e.g. Lane et al.
2016; Løvholt et al. 2020). In these examples, the hazard based on averaged rates is
aggregated, but the hazard uncertainty is not quantified as for the more sophisticated
hazard aggregation procedures used for SPTHA (e.g. Selva et al. 2016).

Landslide source parameterisation for PTHA follows three steps, where Step 1 mostly concerns how the available data can be used to set up a synthetic scenario database, while Steps 2 and 3 concern building the database of scenarios setting source parameters and rates, respectively. Because the first step is mostly a qualitative assessment where the strategy for selecting sources is chosen, the feasibility and strategies for Steps 2 and 3 will be assessed already in this first step.

Broader discussions encompassing the uncertainty and maturity of landslide
tsunami hazard analysis methods are found in Behrens et al. (2021), Geist and Lynett
(2014a), Harbitz et al. (2014a), and Løvholt et al. (2020). There is presently no single
streamlined and complete LPTHA method. While various building blocks exist, all

<figure><img src="image_10.png" /><figcaption>**Fig. 3.8** Different types of landslides that may generate different types of waves. **a** Subaerial landslides, including rockslides and volcano flank collapses, that generate impulsive short-crested waves. **b** Submarine debris flows, often involving large volumes that can reach long run-out distances on gentle slopes. **c** Rotational slumps, short run-out and duration, can generate higher and shorter waves than debris flows. **d** Retrogressive landslides, where the failure process takes place in a staged fashion, implying that the landslide volume is not mobilized in the same instance</figcaption></figure>
these blocks have not been tested and combined into a single and complete LPTHA. For the family of methods described here, it is assumed that the sources are meant to be used for simulation-based PTHA, where many different synthetic sources serve as input to numerical tsunami simulations that again provide the aggregated probabilities (frameworks FW1A and FW1B as described in Chap. 2). In cases where sufficient data (of either slope stability evaluation or past relevant landslide data) do not exists, establishing temporal source probabilities may not be feasible. The rigor of the analysis may then be reduced by removing the temporal part of the hazard analysis, and further by reducing the number of scenarios spanning the epistemic uncertainties related to e.g. modelling landslide dynamics. Hence, the same methods may also be used in scenario-based methods not considering probabilities.

### 3.3.2 Step 1: Basis for Source Selection and Area Demarcation of Sources

LPTHA and related landslide source selection mainly follow two alternative pathways: (i) determining the hazard and sources based on occurrence of past events, and (ii) determining the sources based on slope stability analyses. For method (ii), the slope stability methods may also be mixed with information from past events. Below, these two pathways are discussed in brief.

#### Landslide sources and rates based on past events

Similar to the approach for earthquakes, statistics of past landslide events can be used to establish source rates. Such methods have the benefit that they are independent of the local trigger. First, an area covering a source region must be defined. This can either be a confined region with homogeneous deposits (e.g. Cook Strait New Zealand, Lane et al. 2016), or broader regions that cover a wider range of source types (e.g. Mediterranean, Urgeles and Camerlenghi 2013). The simplest possible way of establishing source probabilities is to assume that the rates of past events can be used to represent present-day source probabilities.

For this type of source treatment, a comprehensive record of past events is necessary, including assessment of the completeness of the record (e.g. Geist and Parsons 2014b). Acquiring such landslide data requires many years of expensive offshore operations that are normally results of investigations for other purposes, e.g. oil and gas field exploration or seabed mapping carried out by governmental organizations. As such data are available only in a few places (e.g. Mediterranean Sea, USA, New Zealand, Norway), the method based on past data is not applicable for all regions worldwide. MFD curves for landslide sources relate the landslide volumes with their frequency of occurrence. Dating information can be used to bring these MFD curves from relative rates to annual source rates. Alternatively, time periods encompassing geological age ranges can be used (e.g., if the past landslides cannot be dated but interpreted to a given geological time such as the Pleistocene). On the other hand,
this would typically imply a broader uncertainty range due to the date being more imprecise. Sedimentation rates and thickness of deposits can often constrain uncertainties to some degree, and most often only the geologically youngest deposits most representative for today's situation (e.g. late Pleistocene, ice age) are used. Available age dating may have influence on the confidence in rate estimation (e.g. Geist et al. 2013).

## Landslide sources and rates based on slope stability evaluations

Geotechnical or engineering geology-based source estimation implies knowledge of the triggers and geological structures (either soil thickness distribution or fracture compositions) and may sometimes be tied to assessments of more semi-probabilistic or heuristic nature as the rate in this case cannot be tied to statistical landslide data. As for the statistical source model explained above, slope stability methods require elaborate data, but the investigations are on a more local level. Slope stability evaluation constitutes a large discipline on its own, and we will hence limit the discussion only to methods that have already been used for geohazard evaluations related to landslide tsunamis. These methods are divided into engineering geology methods used for unstable rock slopes, and geotechnical methods for soils. To an extent, they are also validated based on regional landslide statistics and probability parameters are therefore not always transferable from one geographical location to another. These two different branches are described individually below.

### Source determination for unstable rock slopes

We here follow the Norwegian risk categorisation method for rock slopes (Hermanns et al. 2012, for a full description see NGU 2012), applicable both for risk related to direct landslide run-out and risk related to secondary impacts such as tsunamis (outputs of the Hermanns et al. 2012 method are used in Løvholt et al. 2020). The classification scheme is related to single rock slopes and translates different observables of the slope to an index-based hazard classification scheme ("very low" to "very high" hazard). The rockslide hazard indexes are in turn translated to annual probabilities as the risk scheme is linked to the legislation (while in reality they are based on a structured expert judgment scheme, which implies that the rate estimation is based on expert judgement). The different indexes are partly tuned to comply with regional statistics of past landslides when a large body of unstable slopes is considered. The following unstable slope parameters are taken into account in the complex scheme that is briefly schematised in the following: (i) development of the back scarp of the slope (degree of opening of the back scarp fracture), (ii) identification and dip angle of potential failure surfaces/initial glide planes, (iii) degree of motion on the slope that has already taken place, (iv) kinematic slope failure feasibility, which takes into account the different faults' orientation and potential of failure, (v) expression/characteristics of basal failure surface (morphologic expression), (vi) rate of present-day displacement, (vii) change in rate of displacement (acceleration), (viii) change of rate in rock fall activity, (ix) presence of other post-glacial (geologically recent) events.
Applying this scheme necessitates close and detailed monitoring of the rock slope, including local field surveys as well as long-term monitoring of displacements and rock falls. It is also beneficial to carry out a geophysical mapping of the substructure. Consequently, the scheme is mainly applicable to a single or a few slopes encompassing a limited sized region, and hence for source characterisation for local LPTHA only. In cases where such information is not available, it might be necessary to carry out the hazard analysis without addressing annual probabilities (i.e. only relative probabilities). This classification scheme estimates both the average return period and the uncertainty of a potential slope failure of the entire volume but does not provide an MFD curve as the assessment for each slope only concerns a single-source volume. On the other hand, information from several slopes can be combined to build a set of synthetic sources (Løvholt et al. 2020).

## Source determination for soils and submarine landslides

We here refer to the method outlined by Carlton et al. (2019), also described by Løvholt et al. (2022). The starting point for this method is based on the infinite slope stability analysis, which provides only point values for the static Factor of Safety (FoS), or seismically induced failures linked to the Probabilistic Seismic Hazard Analysis (PSHA). In the former case, the spatial distribution of FoS forms the background for setting up maps for setting both slope areas and thicknesses in a non-probabilistic manner. In the absence of geophysical data, the pure infinite slope FoS can hence be used to make a screening of source areas and volumes prone to landsliding and provide input to non-probabilistic scenario-based methods. Yet, this might often lead to conservative or biased probability estimates as uncertainties related to volumes are large and return periods are unconstrained. On the other hand, if combined with geotechnical and geophysical information, PSHA outputs allow for earthquake-related strain-rate maps to be linked to probability of failure (in the case of earthquake triggered landslides). This implies that the possibility of estimating source probabilities should be considered already in this first step. The method can be supplemented with local slope stability analyses for increased sophistication. This method requires extensive input data including geophysical characterisation of the substructure, typically combined with geotechnical Cone Penetration Tests (CPT) or laboratory tests to quantify the geo-technical strength properties used to establish input parameters to the landslide model in LPTHA. As these methods necessitate different submarine operations for acquiring the field data even for a limited source area, they are often local in nature. They can work in a semi-probabilistic fashion but can further be combined with statistical information of past landslides to form the input to a fully probabilistic source description, unless slope failure can be linked to seismic triggering and PSHA. A preliminary attempt to demonstrate such a method is described in more detail by Løvholt et al. (2022).
### 3.3.3 Step 2: Source Parameterisation

The slope stability methods described above yield areas for potential slope failure as well as potential failure depth. The rock-slope engineering-geology based method will typically give a single volume as input to the initial condition in a landslide dynamics model, which so far has not been associated with an uncertainty. The infinite slope method returns an area and a depth profile that may be used to form the input for several source volumes but can be supplemented by local slope stability analyses to further constrain the volumes. The actual interpretation of the unstable slopes involves expert judgment, and often the logically connected potentially unstable slopes are used to set up volumes that consist of almost the whole unstable area (see e.g. examples in Carlton et al. 2019).

In most cases, the volumes obtained from slope stability analyses will be direct initial conditions in numerical landslide simulations. Examples are complex worst-case connected polygons (e.g. Carlton et al. 2019) forming source grids that may be used in a similar fashion as unit sources in earthquakes (e.g. Løvholt et al. 2022). Because landslide tsunami generation is time dependent and involves tsunami generation away from the initial failure area, simple unit sources including linear superposition (that are popular for earthquakes) can most often not be employed for landslides, implying that all the source realizations must be modelled separately (see e.g. Løvholt et al. 2022).

Another potentially useful way of setting up initial source geometries that has not been employed so far in PTHA, is using scaling laws that connect the landslide source area to the volume, in order to establish ratios between the landslide area and the slide thickness (Urgeles and Camerlenghi 2013; Zengaffinen-Morris et al. 2022). The scaling relationships also include uncertainty in the initial geometry of the landslide. On the other hand, it is purely statistical of nature, and will not take into account local slope conditions even though site-to-site variability is expected.

Once the geometries of the sources have been set up, the landslide parameters must be associated to each scenario (how to select source models is outlined further in Chap. 4). In Lane et al. (2016), the landslide scenario is modelled as initial conditions, based on a set of overall (non-local) Computational Fluid Dynamics (CFD) simulations that take into account only the water depth, volume, and slope, and therefore do not necessitate further parameterisation. In Løvholt et al. (2020), the landslide kinematics (run-out distance, velocity, and frontal area of the landslide) is subject to epistemic uncertainty, and parameter values for these will need to be built into the model. In Carlton et al. (2019), each scenario must be associated with rheological parameters for each landslide scenario by combining geophysical information with CPT data (see Løvholt et al. 2022 for more details).
### 3.3.4 Step 3: Probabilistic Treatment

Where a sufficient record over a defined time window of past (large volume) landslides is available, statistical methods can be used to set up MFDs for the landslide sources, relating either the landslide volume or the landslide area (see further discussion below) to the occurrence rate. The modeller then needs to assess how well the past record can be used to represent today's situation. Maximum Likelihood methods (Geist and ten Brink 2019) can be used for setting up the rate functions, both for the median and the mean rates as well as for the uncertainty in the rates. Typically, these rate functions are nonlinearly tapered in the tail, examples of MFD functions include for instance tapered Pareto functions.

For forecasting the source probabilities, Poissonian (stationary) processes are normally assumed. As a first pass, the same MFD can be assumed homogeneous over an entire region to set up the source rates using the landslide volume only as the input. Yet, it has been demonstrated by submarine landslide data statistics (Løvholt et al. 2022) that the relative landslide volume distribution with slope is non-uniform, i.e., there is a tendency that the smaller-volume landslides are more frequent for steeper slopes, and that larger volumes have a higher relative frequency at lower slope angles. In addition, different regions can have different MFD's, for instance it has been observed that landslides are more frequent but have smaller maximum volumes in seismically active regions (Urgeles and Camerlenghi 2013; ten Brink et al. 2016). Hence, it is possible that the rate should use at least a two-parameter function consisting of both the volume and the slope angle. Further complexity such as correlation of rates with faults can be examined, and it is also possible to compartmentalize source subregions within a greater area, to increase the granularity and the realism in the source rates. Yet, it is stressed that in the LPTHA applications carried out to date (e.g. Lane et al. 2016), only regional one-parameter rates have been considered. A principle sketch of such cumulative curve showing the relative frequencies of different landslide volumes is shown in Fig. 3.9. In this example, age constraints (see e.g. Urgeles and Camerlenghi 2013; Geist and Parsons 2014b) from the landslide database are needed to convert these statistics into a MFD relating the volume to the frequency of occurrence.

Once the volume vs rate information is established, it can be embedded into the scenario probability estimation. The most basic steps for setting up the hazard aggregation (summing and ranking probabilities of the tsunami exceeding a given height) are discussed below. In the probabilistic methods applied in present literature, the probabilistic analysis is represented by ensembles of landslide source scenarios. Aggregation procedures such as event trees are used to discretize the source probabilities for each scenario. The main parameter (top branch) is the landslide volume or location. Below, we present some examples of how the probabilities are interpreted.

**Volume discretization:** Lane et al. (2016) and Løvholt et al. (2022) investigate different synthetic scenario volume probabilities for submarine landslides. For feasibility, only three different volumes are considered. Rough discretisation representing wide volume ranges are necessary for feasibility purposes. It is ensured that the
<figure><img src="image_11.png" /><figcaption>**Fig. 3.9** A generic sketch of a cumulative MFD of landslide volumes. The dotted line indicates the distribution of data, and the dashed line a fit to the largest landslide volumes. For the smallest landslide volumes there is typically an area where landslides are under-sampled. Examples of such empirical MFD curves can be found in Zengaffinen-Morris et al. (2022), and Geist and ten Brink (2019)</figcaption></figure>

summed rates over the whole set of ensemble scenarios’ discrete realizations are equal to the sum of empirical rates. In this way only landslide volumes in the range of past slope failures are included in the analysis. As noted above, this omits modelling potentially larger and less probable/more consequential events.

**Uncertainty treatment of the landslide kinematics:** In Løvholt et al. (2020), uncertainties are discretized in an event tree that includes velocity, run-out distance, and frontal areas (see recipe R8). These represent kinematically prescribed landslide dynamics quantities (elaborated further in Chapter 4.3). They are obtained by combining landslide run-out observations, calibrating the model towards past tsunamis, and numerical modelling. A high degree of expert judgment is used to set up parameter values and conditional probabilities in the assessment for each parameter in the event tree branch.

**Uncertainty treatment of the landslide soil properties:** In Løvholt et al. (2022), a similar uncertainty treatment is set up, but now using soil parameters as input to landslide dynamics models rather than prescribed kinematics. The parameter values are established based on landslide run-out calibrations using in-situ soil properties for the initial yield strength on the average depth of the soil profile as input.

**Some potential future improvements:** It is noted that the models outlined above all assume time independent rates. On the other hand, it is likely that the tsunami hazard is linked to time-dependent features, such as short-term climatic drivers (e.g. rainfall increasing slope instability) or more slowly time-variable triggers (e.g. earthquake cycles, glacial cycles, volcanic unrest), and these are not embedded into the
source models reviewed here. It is further stressed that release of unstable slopes can involve time dependent volume release such as retrogressive failure that can significantly influence the tsunami-genesis reducing the effective volume or even splitting into several independent tsunami events. As such, it has been demonstrated that these effects can influence tsunami-genesis for Holocene slides such as Storegga and Trænadjupet (Løvholt et al. 2017). The time separation between individual volume releases may also imply that individual retrogressive volumes act as separate tsunami-genic events, as observed for e.g. for the ancient Canary Island slope failures (e.g. Masson et al. 2006).

### 3.3.5 Summary Table

See Table 3.3.

<table><caption>**Table 3.3** Summary table: landslide source selection</caption><thead><tr><th></th><th></th></tr></thead><tbody><tr><td>Short description of methods</td><td></td></tr><tr><td>Theoretical/mechanical background for the methods</td><td>Evidence and data describing past landslides and their statistics, slope behaviour, geology and geophysics of the substrata, related to possible instabilities that may indicate a potential for future tsunamigenic landslides</td></tr><tr><td>Short outline of how the methods work</td><td>The method gives lists of synthetic scenarios and rates. There are two main classes of methods, both can be combined with event tree analysis:<ul><li>Methods based on past landslide data—source selection methods are sparsely available and mostly prototypical</li><li>Methods based on slope stability models—they are often more heuristic, where the rates used in the analysis are often based on expert judgment, and often appropriate for local hazard analysis. Regional statistics of past landslides are still used to calibrate model probabilities. Volumes are taken from unstable slope information</li></ul></td></tr><tr><td>How are the output(s) of the methods represented?</td><td>A set of landslide sources / synthetic databases. For each landslide source in the database: Initial position, lateral source extent and thickness, landslide parameters (kinematics or material properties), as well as related conditional probabilities</td></tr></tbody></table>

(continued)
<table><caption>**Table 3.3 (continued)**</caption><tr><td>In what way do the methods take into account time-dependent/dynamic aspects?</td><td>Although subaerial slope failures are linked to precipitation and season (winter, summer), this is not yet accounted for in presently available models</td></tr><tr><td>Do the methods use parallelisation, machine learning, surrogate models, advanced simulation schemes, other computational reduction strategies (e.g. cluster analysis, etc.)?</td><td>No, but future applications will likely soon include this due to the fast acceleration of AI based methods</td></tr><tr><td>What are the pros and cons and peculiarities of these methods? Are there known shortcomings/benefits of the methods? In what cases are these methods good/poor choices?</td><td>The methods require large amounts of data in order not to have excessive uncertainty bounds, with less data, uncertainties are pronounced. Not all steps are tested operationally, and the examples of use are so far limited. Severe lack of data may imply inaccurate source representation for probabilistic analysis as well as excessive uncertainties</td></tr><tr><td colspan="2">Data and technical requirements for method</td></tr><tr><td>What input data does the method(s) use?</td><td>Depending on the method, one or more of the following is needed to decide on source model selection:<ul><li>Databases of landslides</li><li>Age date constraints on the landslide data</li><li>Earthquake soil or rock displacements from PSHA</li><li>Soil parameters and seismic information, information about basal layers</li><li>Data from slope stability investigations, scheme for slope stability evaluation, or aggregated slope stability data</li></ul></td></tr><tr><td>What are the technical requirements?</td><td>Step 1—mostly qualitative, assessing how available data can be used to constrain sources in hazard analysis<br>Step2—high-quality slope stability analysis can sometimes require rigorous processing of geophysical data. Past data for calibration can help constraining the analysis, this is linked to the source modelling (Sect. 4.3)<br>Step 3—is mostly statistically based with few technical requirements</td></tr><tr><td>Are HPC computing resources necessary, would absence of these compromise the use?</td><td>No</td></tr></table>

(continued)
<table><caption>**Table 3.3 (continued)**</caption><tr><td>Is the method(s)/workflow(s) available as a git/software/jupyter notebook?</td><td>No</td></tr><tr><td colspan="2">Treatment of uncertainties for the method</td></tr><tr><td>Are the method(s) itself deterministic or uncertainty based?</td><td>The single source representation has deterministic characteristics. On the other hand, each source output can be associated with different probabilities</td></tr><tr><td>Which are potential sources of uncertainties? Which parameters are used to characterize them?</td><td>The main sources of uncertainties are:<ul><li>Poor/limited information of past events</li><li>Projections of past statistics into today's situation</li><li>Sparse material data or spatial representation of the ground properties determining failure probability and volumes</li><li>Limited knowledge of the landslide mechanisms</li></ul>Parameters that can describe the uncertainties are:<ul><li>Landslide volumes/frontal areas, run-out distance, soil properties</li><li>Landslide kinematics and run-out from past model hindcasts</li></ul></td></tr><tr><td>How are uncertainties quantified for the identified parameters? Are there significant correlations between different uncertain parameters?</td><td>Parameters such as landslide kinematics and run-out are associated with different weights representing the epistemic uncertainty. There are few / no examples with uncertainty treatment for the aggregated hazard. Representations of parameterised landslide kinematics (impact velocity and run-out distance) have been used. There can be internal correlations between these kinematic parameters</td></tr><tr><td>Are the methods able to digest and propagate uncertainty in input (previous ingredient) and propagate it to the output (next ingredients)?</td><td>The uncertainty, if included, is only aggregated to the mean hazard in the presently available workflows</td></tr><tr><td>What are the consequences of lack of data in input or for boundary conditions, or for characterizing certain parameters?</td><td>Large uncertainties in the models. Potential under / overestimation of large impact components of the hazard curve. If too little data is present, exhaustive probabilistic analysis may not be feasible</td></tr><tr><td>What are the consequences of ignoring or poorly treating uncertainties?</td><td>Limited understanding of the hazard</td></tr></table>
## 3.4 Volcanic Sources

### 3.4.1 Short Description of the Method

What we commonly define as a “volcanic tsunami” is a tsunami generated by either eruptive processes, rapid ground deformation or flank instability at volcanoes (Day et al. 2015; Paris 2015). Following this definition, volcanic tsunamis represent about 5% of all listed tsunamis during the four last centuries (NCEI global tsunami database 2023). Historical examples and theoretical studies on tsunami generation have made it possible to distinguish different types of volcanic tsunamis (Fig. 3.10).

A large variety of volcanic sources may generate tsunamis (Begét 2000; Day et al. 2015; Latter 1981; Kienle et al. 1987; Paris 2015; Grezio et al. 2017) but they are grouped in eruptive (strictly connected to eruption dynamics) and non-eruptive sources (related to the structure of the volcanic edifice and to the existence of specific triggering phenomena). Eruptive tsunamis are generated directly by eruptions, including underwater explosions, pyroclastic flows, collapse of the eruptive column, caldera collapse, and atmospheric acoustic-gravity waves created by major explosions. Non-eruptive volcanic tsunamis are instead related to subaerial and submarine landslides, debris flows (e.g. lahars), or even volcanic earthquakes. All those source mechanisms have different characteristics in terms of duration, volume, mass flux, and energy, which has consequences on the waves generated and the methods used to simulate them. The volcanic tsunami dynamics clearly highlight two substantial features, both for the eruptive and the non-eruptive tsunamis: the multi-hazard character (as most of the triggering events may represent a potential hazard independently from the tsunami) and the time-dependent elements (as triggering conditions are strongly related to life-cycles of volcanoes, e.g. quiescence,

<figure><img src="image_12.png" /><figcaption>**Fig. 3.10** Different types of volcanic tsunamis, i.e. tsunamis generated by volcano activity and instability (updated from Paris et al. 2014)</figcaption></figure>
unrest, eruptions), which are also related to other external and potentially time-
varying phenomena, like rainfall, strongly varying in the short-term (e.g., seasons)
as well as in the long-term (e.g., climate change).

The volcanic source and estimation of the rate of occurrence is the first step in the hazard assessment, and it consists of the identification and quantification of the annual rates of all the potential volcanic sources of tsunamis that may affect a pre-selected target location. The general workflow graphically reported in Fig. 3.1 fully applies to volcanic sources. For volcanic sources, Step 1 consists of the selection of the potential source volcanoes or volcanic areas, and the selection of the types of sources to be considered for each volcano; Step 2 is applied only to the selected source(s), and encompasses the definition of the source variability (in space and size) to explore the natural variability of the important parameters for tsunami generation, and the kinematics or dynamics of the selected types of sources; and Step 3, applicable only to probabilistic methods, defines a specific list of individual scenarios and quantifies their probabilities or their mean annual rates of occurrence in the exposure time.

The final result of the volcanic source and rate estimation is the definition of a (potentially very long) list of possible sources, described by their characteristics like size, position, geometry, etc., and, for each source, a quantification of the probability of occurrence in the time frame selected for the hazard/risk assessment. This list is typically provided as input to tsunami generation and propagation models (Chap. 4), to complete the hazard quantification. In deterministic scenario-based approaches, Step 3 is omitted, and a list of individual sources is defined directly in Step 2, while a probabilistic quantification of annual rates is omitted.

In general, methods differ significantly for eruptive and non-eruptive tsunamis.
The former is connected to the eruption forecasting, both in the characterization of
the position of the events (vent opening) and in the constraining of source size (erup-
tion magnitude or size). The latter is instead more related to the specific triggering
phenomena, which may or may not be influenced by ongoing volcanic phenomena
during unrest or eruptions (e.g. heavy rains, new material available for lahars just
after the eruptions, increased seismicity and deformation, or hydrothermal alteration
of materials for slope instability).

Most existing volcanic hazard quantifications are focused on single volcanoes (e.g., Neri et al. 2015) rather than on target areas, and they rarely include tsunami hazards. Considering that a few volcanic phenomena may propagate far from the source (typically tephra fall and tsunamis, Selva et al. 2019), a full volcanic tsunami hazard and risk quantification should define firstly the list of volcanoes that may potentially trigger a tsunami in a target area (IAEA 2016; Grezio et al. 2017; Behrens et al. 2021). However, given that each volcano has its own peculiarities, each source requires a volcano-specific analysis to be constrained (see next section) and sometimes specific sources may require computationally expensive procedures to model the tsunami generation and propagation process (see Sect. 4.3). Consequently, the exploration of the sources in volcanic probabilistic applications may be reduced. In the volcanic hazard literature, there are only a few examples of multi-volcano hazard or risk quantifications (Loughlin et al. 2015; Jenkins et al. 2022), also due to the substantial lack of homogeneous methods to quantify annual rates or probabilities
for the different volcanic systems (Selva et al. 2022). Other methods range from the selection of one or few fully parameterized reference scenarios to a few examples of full exploration of the parameter space (Paris et al. 2019b; Grezio et al. 2020). The former approach is based on fully parametrizing a short list of scenarios, which allows skipping the quantification of the probability of each individual scenario (discussed in Step 3) but prevents the quantification of source uncertainty. Single scenarios are usually defined through expert opinion, guided by past occurrences or by geological and structural maps to identify the relevant position and size of sources.

### 3.4.2 Step 1 Basis for Source Selection and Constraining the Area of Sources

The first steps for the volcanic source and rate estimation consists of the selection of the volcanoes and, for each volcano, the type(s) of source(s) to be considered.

Once one (or more) volcano is selected, the relevant tsunami-generating phenomena should be identified, among all the potential types of sources that may generate tsunamis at volcanoes. The volcano is often preselected due to its relevance or relatively high potential tsunami generation. This selection is usually based on qualitative considerations regarding the main types of sources, for example the explosivity of eruptions, the main character (dilute vs dense) of pyroclastic flows, the presence of significant slopes or submerged part of the edifice, the depth of potential submarine sources, etc.

To select volcanoes and typologies of sources, we may define the following procedures with increasing level of completeness:

1. Preselected volcano, preselected type of source: a model considering, at a preselected volcano, a specific source typology and exploring its variability (in size and location);

2. Preselected volcano, all types of sources: a model considering, at a preselected volcano, all potential source typologies and exploring, for each of them, their natural variability;

3. All volcanoes and preselected type of source: a model exploring the entire natural variability of one preselected type of source, including all potential volcanoes that may generate tsunamis reaching the target area;

4. All volcanoes and all types of sources: a model exploring the entire natural variability of the sources that may generate a volcano tsunami reaching the target area, including all the volcanoes in the area and all potential source typologies.

In all cases, the output of these procedures is a list of volcanoes and potential types of sources for the subsequent steps toward hazard and risk quantification. The selection is based on databases of active volcanoes or volcanic areas, local records of past eruptions and past tsunamis, as well as the existing theoretical knowledge about potential sources of tsunamis (e.g. tsunami records at global scale). In some cases,
the selection may be driven by the present state of the volcano (e.g. during volcanic unrest), which may lead to some time-dependency.

To our knowledge, all existing examples of volcano source tsunami hazard quantification are limited to point 1 above involving qualitative and deterministic procedures, which restrict the exploration of the natural variability of the sources and the potential uncertainties. In fact, considering only an inadequate number of potential sources (in terms of volcanoes, source typologies or limited natural variability) implies that we adopt a strong filter to potential tsunami sources, with possible substantial biases in the volcanic hazard and risk quantifications. While standard Volcano Probabilistic Tsunami Hazard Assessment (VPTHA) procedures may account for the full natural variability of the selected sources (e.g. Paris et al. 2019b; Grezio et al. 2020), we are not aware of formal or quantitative procedures to select which volcanoes should be included in a complete VPTHA, as well as which types of sources should be considered the most important at each volcano. This represents an important gap in VPTHA that should be resolved in the future (Behrens et al. 2021). So far, this selection is qualitative, that is, based either on a specific interest (e.g., needs for the building of a dedicated warning system, like in Stromboli), or on the availability of all the required input information (size variability and probability).

### 3.4.3 Step 2 Source Parameterisation

The goal of this step is to establish the parameters describing individual sources selected in Step 1, and to define their range of variability to describe the variability of the tsunami generation process. This is often done by defining a list of fully parameterized individual scenarios that are defined by combining the expert judgment with the analysis of past data, both from the specific volcano and from analogous situations. The specific source parameters selected to describe source models are position, size, duration, and geometry of the possible sources and are different for each source typology.

Probabilistic hazard quantification requires the definition of a range of variability for each source parameter. Ranges covering the entire natural variability are typically set from structural considerations and from the analysis of past activity, in the target volcano or from analogous volcanoes (e.g. Tierz et al. 2019), including local records of past eruptions and tsunamis, records from similar volcanoes, geological and geophysical maps used to identify ranges for vent location, extension and volume of potential sources for collapse. For eruptive phenomena, the main parameters to describe the source are the vent location and a measure of the energy of the eruption (magnitude, volcanic explosivity index, etc., e.g. Newhall and Hoblitt 2002) and may be linked to the standard volcanic hazard. Unknown or never-observed sources, limited knowledge on the structure of the volcano, or other limitations of this type may lead to an underestimation of the ranges, in particular of their upper limits, and this should be possibly included in the epistemic uncertainty quantification.
Once ranges are defined for all the specific source parameters, a list of scenarios may be produced sampling each parameter a large number of times. To make the evaluation of the tsunami propagation computationally feasible, the trade-off between full exploration and computational feasibility should be solved (e.g. as for earthquake tsunamis, Lorito et al. 2015; Selva et al. 2016; Davies and Griffin 2020). For this reason, the definition of the list of individual scenarios from the parameter ranges is discussed in Step 3.

In principle, the definition of the range of natural variability of the individual sources is not time-dependent. However, significant structural changes in the volcano may strongly impact the ranges, for example when a large eruption occurs. In this case, new edifices and caldera depressions may be formed, obviously changing the potential range of tsunamigenic sources. Also, variations in the state of the volcano (e.g. quiescence, unrest, eruption) and the occurrence of other phenomena (in the short-term the increasing of flank deformation, rapidly accumulated material on the flanks, heavy rainfall, regional tectonic earthquakes, or in the long-term extreme weather conditions due to climate change, land use changes, deforestation, modifications of soil conditions) may alter the conditions for the occurrence of the different sources. However, in those cases the temporal variability may be treated by decoupling the ranges of parameters from the probabilistic assessment of occurrences (Paris et al. 2019b) or introducing time-dependence in the probability of individual sources (e.g. Selva et al. 2014).

The actual discretization of the parameter space is very different for the different types of sources, which are consequently treated separately in the following subsections.

## Landslides and debris flows

Flank instability of volcanoes has been widely documented. Volcano flanks display a broad variety of instabilities, from rock falls, cliff collapses and small landslides (with volumes typically in the order of $10^5–10^6 \text{ m}^3$) to large debris avalanches (with volumes that may range up to order of e.g. $10^8–10^9 \text{ m}^3$). As for landslide sources in general (Sect. 3.3), the main source parameters are the volume of the landslide Froude number (and maximum velocity), relative thickness, mass flux and volume and, for submarine sources, its initial acceleration (Fritz 2004; Viroulet et al. 2013; Yavari-Ramshe and Ataie-Ashtiani 2016; Lee 2022; Ward 2001; Grilli and Watts 2005; Løvholt et al. 2015).

Volcano flanks are particularly unstable, and this instability is the result of both endogenous (structural discontinuities, hydrothermal alteration, and magmatic intrusions inside the edifice, rapid growth by accumulation of tephra and lava flows) and exogenous factors (earthquake, tectonic uplift, weather and climatic event, sea level variations).

Many volcanoes are entirely (volcanic seamounts) or partly (volcanic islands) submarine or sub-lacustrine. As for subaerial landslides, the volumes implied by submarine landslides range from small-scale ($10^5–10^6 \text{ m}^3$) events (e.g. collapses of coastal lava deltas, landslides in submarine canyons) to massive collapses on the submarine flanks of ocean islands (up to $10^7–10^9 \text{ m}^3$ or more). The number of
tsunamis generated by submarine landslides on volcanoes is probably underestimated due to a lack of observations and data. For this reason, there are few unequivocal historical examples such as Ritter Island 1888 (Johnson 1987; Ward and Day 2003; Karstens et al. 2019), and the more recent examples of Stromboli 2002 (Bonaccorso et al. 2003) and Anak Krakatau 2018 (Muhari et al. 2019; Grilli et al. 2021).

The triggering processes at volcanoes may be particularly complex, making their probabilistic quantification challenging (see Step 3). On the contrary, in terms of tsunami generation, there is no specific difference between landslides observed on the flanks of volcanoes and other landslides, despite each event having its own structural setting, lithology and rheology (see Sect. 3.3).

## Pyroclastic flows

Pyroclastic flows are hot mixtures of gas and particles generated by volcanic eruptions, particularly in the case of a dome collapse or a plume (eruptive column) collapse. Pyroclastic flows can generate tsunamis, as demonstrated by recent examples at Montserrat in 2003 and Stromboli in 2019 (Pelinovsky et al. 2004; Herd et al. 2005; Selva et al. 2022), but the conditions required to generate a tsunami and the mechanisms of interaction between the flow and the water are still poorly understood due to lack of observations and the absence of physical models.

The dense basal component of the pyroclastic flow is the main source of tsunami, but other phenomena such as steam explosion, flow pressure and shear, and pressure impulse could theoretically generate small waves (Watts and Waythomas 2003). The important parameters controlling the generation of a tsunami by pyroclastic flows are the flow volume and mass flux, together with the flow density and permeability (ash-rich flows being more tsunamigenic because of their low permeability), the angle of incidence, and the transport distance from the eruptive vent (Watts and Waythomas 2003; Maeno and Imamura 2011; Bougouin et al. 2020; Grezio et al. 2020). High-velocity pyroclastic flows with a bulk density near or even below that of water may generate waves, irrespective of their temperature (Bougouin et al. 2020; Freundt 2003).

## Caldera collapse

Large explosive eruptions may result in the collapse of the central part of the edifice, thus forming a caldera. In case of an underwater eruption, the caldera collapse produces subsidence of the water surface that initiates the propagation of a leading trough. The amplitude of the water subsidence depends not only on the volume and geometry of the collapse, but above all on its duration (Gray and Monaghan 2003; Maeno et al. 2006; Ulvrova et al. 2016).

Large collapses lasting just a few minutes are theoretically tsunamigenic but probably unrealistic. Indeed, based on recent examples, the duration of a caldera collapse during an explosive eruption typically lasts more than 30 min (Stix and Kobayashi 2008). There are different types of geometries and collapse mechanisms (Roche et al. 2000; Stix and Kobayashi 2008). Consequently, there is no unequivocal example of a tsunami generated by a caldera collapse. Other phenomena such as underwater explosions, eruptive column collapse and pyroclastic flows may generate
tsunamis during an explosive caldera-forming eruption, which makes it difficult to determine the source of the tsunami(s), as illustrated by the near-field tsunami that impacted the Tonga Islands during the 2022 eruption of Hunga Tonga–Hunga Ha’apai volcano (Omira et al. 2022).

## Underwater explosion

The theory of water waves generated by underwater explosions is well documented, and has been applied to nuclear, chemical and volcanic explosions (Le Méhauté 1971; Duffy 1992; Le Méhauté and Wang 1996; Egorov 2007). After an underwater volcanic explosion and while different jet flows of fragmented lava and gas are ejected, the development of a water crater might be initiated, depending on water depth and energy of explosion, which are the two main input parameters for initiating wave generation. Subsequent expansion, rise and gravitational collapse of the crater create two successive bores followed by a number of smaller undulations propagating radially from the source. In theory, all volcanic eruptions above 500 m water depth are potentially tsunamigenic, but in reality, only a few such events are significant.

The variability of the sizes and positions of potential underwater volcanic explosions is controlled by the natural variability of eruptive scenarios. Vent position forecasts control the spatial extent to be considered for sources, which in turn is typically controlled by structural considerations like caldera borders or volcanic apron (e.g. Scandone et al. 1991; Orsi et al. 1995; Selva et al. 2012a, b; Connor et al. 2019; Cañón-Tapia 2022). The sizes of the tsunami-generating explosions are instead related to the expected variability of eruption size at the volcano, which strongly varies from volcano to volcano. Explosion energy may be roughly related to eruption size measures like explosivity or magnitude, and even to geometrical observables of past eruptions like crater radius (Torsvik et al. 2010; Ulrova et al. 2016; Paris et al. 2019b).

## Collapse of eruptive column

An eruption column or eruption plume is a cloud of volcanic tephra (mostly ash) suspended in gasses emitted during an explosive eruption, potentially up to 40–50 km altitude. When the material (i.e., the tephra) in the column can no longer be supported by convection, it falls under gravity, forming pyroclastic flows on the flanks of the volcano. The intensity of the collapse is variable from one eruption to another and, for stable plumes, it may evolve as a function of the buoyancy ratio (Carazzo et al. 2015).

If the eruption comes from a small island or a shallow-water volcano, the eruptive column may collapse directly into the water. Pyroclastic flows resulting from the collapse are then subaqueous and the collapse itself becomes the main source of tsunami. Although there is abundant literature on eruptive column collapse in volcanology, it is not commonly addressed as a source of volcanic tsunami. However, this neglected mechanism may have played a role in the generation of near-field tsunami during explosive eruptions such as Krakatau 1883 and Hunga Tonga-Hunga Ha’apai 2022. The main input parameters influencing tsunami generation by an eruptive column collapse are the mass flux at the impact, the duration of the collapse, the
water depth, and the sea floor geometry (e.g., the presence of a submerged volcanic cone beneath the impact might change the geometry of the initial waves).

### Atmospheric forcing following a large explosion

The atmospheric acoustic-gravity waves that are produced during a major volcanic explosion can generate a tsunami. This rare phenomenon was first documented for the 1883 eruption of Krakatau (Press and Harkrider 1966; Pelinovsky et al. 2005) and extremely well recorded for the 2022 eruption of Hunga Tonga-Hunga Ha'apaii volcano in the Tonga Islands. Tsunamis generated by such an atmospheric forcing represent the only type of volcanic tsunamis that may have a global reach.

The largest explosive eruptions generate a broad range of waves in the atmosphere, including acoustic-gravity waves that may reach the ionosphere (Astafyeva et al. 2022). Among these different types of atmospheric waves, compressional surface-guided Lamb waves traveling at the speed of sound can produce long-period waves in the ocean (Kubota et al. 2022; Omira et al. 2022). The tsunami generation and propagation processes are similar to other atmospheric sources, as discussed in Sects. 3.5 and 4.5.

### Volcano-tectonic earthquake

Although earthquakes are often mentioned as a source of tsunami preceding or during a volcanic eruption, historical examples are poorly documented because the distinction between tectonic earthquakes, volcanic earthquakes, or other source mechanisms of tsunami (e.g., landslide) is often unclear. Among all kinds of earthquakes related to volcanic and magmatic processes, only volcano-tectonic (high-frequency) earthquakes can involve ground deformation large enough to generate a tsunami. Volcano-tectonic earthquakes result from the accumulation of stress induced by magma ascent. They are characterized by seismic swarms at shallow depth (<10 km), with magnitudes typically lower than $M_w = 6$, thus generating very small-magnitude tsunamis, if any (Paris 2015).

Two special cases are mentioned here. First, earthquakes with magnitude $M_w > 6$ on large reverse faults at the base of the oceanic shield volcanoes (e.g., Hawaii) can produce tsunamis, as demonstrated by the 1975 Kalapana earthquake at Kilauea volcano, Hawaii (Ando 1979; Ma et al. 1999; Day et al. 2005). Second, earthquakes with magnitude $M_w < 6$ resulting from trapdoor faulting of submarine caldera floor can generate small-amplitude tsunamis, as frequently observed around the Sumisu caldera, Japan (Sandanbata et al. 2022). Tsunami generation and propagation for volcano-tectonic earthquakes is similar to other earthquake sources, as discussed in Sects. 3.3 and 4.3.

### 3.4.4 Step 3 Probabilistic Treatment

The goal of this step is to evaluate the probabilities of occurrence or the annual rates for a list of individual scenarios that cover the natural variability of the selected
tsunami sources. The parameters and the ranges provide the input to the probability
evaluation made in Step 3 (Fig. 3.1).

The list of individual scenarios is provided as input to tsunami generation and propagation models (Sect. 4.4), while the probability of occurrence or the annual rate of each scenario is provided as input to hazard aggregation (Grezio et al. 2017; Basili et al. 2021a, 2021b). This step is typically skipped when non-probabilistic scenario-based methods are selected (e.g. FW1D in Sect. 2.2; see Fig. 3.1), with the consequence that the potential impact of some representative scenarios is evaluated without accounting for uncertainty or quantifying the likelihood of such events.

The output of this step is a list of scenarios with the associated probabilities of occurrence or annual rates in the exposure time. The list may be defined to cover the source space and, subsequently, quantify their probability of occurrence (e.g. Selva et al. 2016), or sampling from scenario probabilities, generating synthetic catalogues (e.g. Davies 2019). To quantify the epistemic uncertainty, multiple lists of probability of occurrence or annual rates may be provided (Selva et al. 2016; Basili et al. 2021a, 2021b). In this case, such multiple lists should be accompanied by a weight defining the subjective credibility of each list. This information may provide input models for the quantification of epistemic uncertainty, such as logic trees or ensemble modelling (Budnitz et al. 1997; Geist and Parson 2006; Bommer and Scherbaum 2008; Marzocchi and Jordan 2014; Marzocchi et al. 2015, 2021; Selva et al. 2016).

For eruptive tsunamis, eruption forecasting methods may be adopted to quantify
the spatial and magnitude variability of the sources including statistical tools like
event trees, belief networks, expert elicitations, Markov chains, stratified sampling,
or other statistical techniques that sample probability distributions based on past data
or tracking observations (Newhall and Hoblitt 2002; Aspinall et al. 2003; Marzocchi
et al. 2008; Marzocchi and Bebbington 2012; Newhall and Pallister 2015; Hincks
et al. 2014; Tierz et al. 2017; Sandri et al. 2017; Bebbington et al. 2019; Bebbington
and Jenkins 2022; Selva et al. 2015; Neri et al. 2015; Grezio et al. 2020). Spatial
distributions of vent opening are often modelled with spatial kernels or other methods
based on the hierarchization of tracking features (e.g. Scandone et al. 1993; Selva
et al. 2012b; Connor et al. 2019; Cañón-Tapia 2022). Due to the cascading process
from volcanic initialisation to tsunami impact, linking tsunami hazard to the standard
eruption forecasting methods requires the definition of a direct connection between
typical size metrics for volcanic eruptions and potential sizes for the tsunami sources
(Paris et al. 2019).

Several models for eruption forecasting and volcanic hazard are available as
open software or in open-source codes (e.g. https://theghub.org/groups/v/), without
specific finalizations for tsunamis.

For eruptive phenomena and for consequent tsunamis it is common to only quan-
tify the conditional hazard, that is the probabilistic hazard conditional to the occur-
rence of an eruption (Biass et al. 2016, 2012; Jenkins et al. 2012; Sandri et al. 2017;
Selva et al. 2018; Paris et al. 2019). On the one hand, this simplifies the computation,
as it removes the eruption forecasting from the hazard quantification, concentrating
on the natural variability of the sources when an eruption occurs. On the other hand,
this conditional hazard may provide fundamental information to decision makers for planning interventions in case of eruption, like for example for the definition of evacuation areas and evacuation routes (e.g., DPC 2016). However, this choice complicates the comparison between the quantified hazard and the other hazards in a multi-hazard risk perspective as return period computation is omitted.

For non-eruptive sources during volcanic quiescence periods, the procedures discussed in Sects. 3.2, 3.3 and 3.5 may be applicable and the sources can be treated as standard non-volcanic sources. For flank collapses and landslides many of the methods developed for standard landslides may be applicable (see Sect. 3.3), even if the initial conditions may suddenly change due to the eruptive processes and the largest landslides are often related to the increase of volcanic activity or major eruptions (e.g., debris avalanches). Non-eruptive tsunami sources during the unrest episodes, that are periods with an increased volcanic activity with respect to the background, may be connected to both eruption forecasts and related hazards (e.g. Hincks et al. 2014; Tonini et al. 2016).

Forecasting of non-eruptive tsunamis generated at volcanoes is linked to the ability to forecast the occurrence of the source during the life cycles of volcanoes (which include quiet periods as well as unrest and eruptions). To this end, the statistics of the source and the triggering conditions are usually analysed through specific statistical models (e.g., Tierz et al. 2017). Spatial distributions are often studied through susceptibility studies (e.g. Masson et al. 2006). For non-eruptive events there are potential complexities due to the interaction between phenomena within the multi-hazard context of volcanoes. For example, landslides on the flanks of a volcano may occur independently of an eruption, because old eruptive material can be mobilized even years after the last eruption due to external triggers like heavy rainfall or tectonic earthquakes (Tinti et al. 1999; Lenti et al. 2015a, b). Such movement may be favoured during both eruptive and non-eruptive unrest periods because of deformation or alteration of materials in connection with degassing, hydrothermal changes, and local seismicity (Tommasi et al. 2018; Lenti et al. 2015a, b; Paparo et al. 2017; Ripepe et al. 2009, 2015, 2021; Selva et al. 2020). Due to the large variety of such phenomena, a link must be established between the volcanic phenomena and the occurrence (and the size) of the volcanically induced tsunami sources.

In Fig. 3.11, we report a possible event tree that may be adopted for the quantification of the time-varying probability of tsunami sources of volcanic origin, adapting the Bayesian Event Tree evaluation scheme (Marzocchi et al. 2008, 2010; Selva et al. 2014). At node 1, the event tree describes the three main states at which a volcano may be: quiescence, unrest or eruption. These states are connected to significantly different probabilities of occurrence of the sources, as well as significantly different approaches to quantify them (Marzocchi et al. 2008, 2010; Selva et al. 2014). At nodes 2, the main potentially tsunamigenic volcanic phenomena are listed, and each of them is generically parameterized through area of potential occurrence (node 3) and size (node 4). Node 5 deals with the forecast of the occurrence of the tsunami generation, while nodes 6 and 7 are targeted to the quantification of the related hazard curve (Marzocchi et al. 2010; Selva et al. 2014).
<figure><img src="image_13.png" /><figcaption>**Fig. 3.11** Bayesian Event Tree for Volcanic Tsunami Hazard. The combination of all nodes is possible: arrows indicate potential paths which involve different volcanic states (node 1), phenomena (node 2), source position and size (nodes 3 and 4), and tsunami generation (node 5). In these examples, only the blue arrows indicate the path of a possible scenario generating a tsunami (node 5) and leading to the evaluation of the hazard curve at all targets (nodes 6 and 7)</figcaption></figure>

The complex relationship between the different volcanic phenomena also highlights the potential for significant time-dependencies, single sources being potentially connected to the volcano state (e.g. quiescence, unrest, eruption) and to the occurrence of other volcanic or non-volcanic phenomena (e.g. deformation, degassing, rainfall, etc.). For the eruptive sources, specific time-dependency may be accounted for by switching from long-term assessment based on past data to short-term assessment based on monitoring and/or weather forecast (Marzocchi et al. 2008; Selva et al. 2014), accounting for potential changes in regime when the probability of eruption is evaluated (De la Cruz-Reyna 1993; Bebbington 2010, 2013, 2014; Selva et al. 2022). Other dependencies may be accounted for through networks or Markov chains that account for the concatenation of events (Tierz et al. 2017; Bebbington and Jenkins 2019, 2022). In general, these methods treat temporal variability by decoupling the selection of the list of scenarios from the probabilistic assessment and introducing time-dependence in the probability of individual sources.

The main inputs to probability assessments are local records of past eruptions or tsunamis and observed past unrest episodes. Geological data and maps may also play an important role, especially for determining the spatial probability, due to the relative paucity of data or lack of knowledge that affect most, if not all, individual volcanoes. An important input to probabilistic quantifications is provided by other volcanoes, especially by the so-called analogous volcanoes, that is, volcanoes that show similar dynamics to the target one (Marzocchi et al. 2008; Tierz et al. 2019). Another important contribution in this sense is provided by expert opinion, often collected through formalized expert elicitations (Aspinall 2006, 2010; Aspinall et al. 2003; Selva et al. 2012a; Aspinall and Woo 2014; Tadini et al. 2022). These approaches are of course subject to large epistemic uncertainty. In volcanology, such uncertainty is often treated by adopting Bayesian models (Aspinall 2006; Marzocchi et al. 2008; Aspinall and Woo 2014), but also methods collecting alternative implementations like logic trees or ensemble modelling have been proposed (IAEA 2012, 2016; Marzocchi et al. 2021).
The final list of scenario probabilities may be produced by discretizing the param-
eter space or sampling from the probability of each scenario (e.g. Basili et al. 2021a;
Davies et al. 2022). In the former, the definition of the list is independent from the
probability definition, while in the latter they are connected and must be performed
simultaneously (Selva et al. 2016; Davies et al. 2022). When a predefined discretiza-
tion is adopted, multiple statistical models may be defined independently and equally
applied to all defined sources, simplifying the treatment of epistemic uncertainty
(Selva et al. 2016). However, this typically leads to a large number of scenarios
to be modelled individually, thus necessitating strategies to reduce the computa-
tional effort (Molinari et al. 2016; Basili et al. 2021a). Differently from seismic
sources, the nonlinear hydrodynamics often characterizing volcanic tsunamis near
the source do not allow for strategies based on linear superposition of unit sources.
Hence, ad hoc strategies may be adopted to define representative individual scenarios.
The sampling approaches may help significantly to reduce the required number of
scenarios. However, if the statistical model changes, the list of scenarios must be
resampled, implying new simulations to be performed (Davies et al. 2022).

**3.4.5 Summary Table**

See Table 3.4.

**3.5 Atmospheric Sources**

**3.5.1 Short Description of the Method**

Atmospheric sources usually generate tsunamis (hereafter referred to as meteotsunamis) that are typically an order of magnitude smaller than those triggered by other sources. They can be separated in two categories: weather and acoustic sources (Fig. 3.12). As illustrated in the schematic given in Fig. 3.12, weather-related events are directly connected to mesoscale atmospheric processes (Monserrat et al. 2006) while acoustically driven events result from the generation of planetary acoustic-gravity waves after an explosion (e.g., volcanic eruption, asteroid impact/bolide explosion). Both categories of events have the potential to generate strong surface pressure (and wind, e.g., Linares et al. 2016) disturbances inducing meteotsunamis.

The uncertainty linked to weather-related events is possibly the lowest of the entire
suite of tsunami sources as it highly depends on both the relatively well constrained
weather conditions (Denamiel et al. 2019a) and the geomorphology of the coastal
areas (Pattiaratchi and Wijeratne 2015; Rabinovich 2020). Impact of weather-related
events is mostly local as it depends on the ability of harbours and bays to amplify
the offshore waves, and so-called hotspot locations—where the intensity and the
<table><caption>**Table 3.4** Summary table: volcanic sources</caption><thead><tr><th>Short description of method</th><th></th></tr></thead><tbody><tr><td>Theoretical/mechanical background for the methods</td><td><ul><li>All offshore and near shore volcanoes may in principle generate tsunamis</li><li>Multiple volcano-related phenomena may be tsunamigenic, during eruptions or independently from eruptions</li><li>There is a large variability of potential scenarios</li><li>Hazard is time-dependent due to the complex connections between the different volcanic phenomena during quiescence, unrest, and eruption phases</li><li>Except for large explosions or collapses, volcano tsunamis are generally dispersive with relatively short wavelengths; consequently, they are often local</li></ul></td></tr><tr><td>Short outline of how the methods work</td><td><ul><li>In step 1, a single volcano is often pre-selected; only recently, multi-volcano analyses start being discussed</li><li>The typology of sources selected at each volcano is typically pre-selected, based on experience or recent history. Existing methods are mainly qualitative</li><li>In step 2, single scenarios are usually defined through expert opinion. In probabilistic methods, ranges are set mainly from structural considerations and past activity</li><li>In step 3, source probability is often computed conditional to eruption, while unconditional probabilities or annual rates are rarely evaluated</li><li>For eruptive tsunamis, methods for eruption forecasting and volcanic hazards are used, including event trees, belief networks, expert elicitations, Markov chains, stratified sampling, based on past data or on monitoring</li><li>For non-eruptive tsunamis, there are no consolidated methods; methods strongly vary on source type</li><li>Epistemic uncertainty is quantified with Bayesian methods, logic trees, ensemble modelling, and different flavours of expert elicitations</li></ul></td></tr></tbody></table>

(continued)

frequency of such events is known to have devastating effects—have already been identified (Vilibić et al. 2021). Consequently, two main uncertainties are related to
<table><caption>**Table 3.4 (continued)**</caption><tr><td>How are the output(s) of the methods represented?</td><td><ul><li>In step 1, a list of volcanoes and source typology(-ies) is provided</li><li>In step 2, the range of variability of source parameters is provided</li><li>In step 3, a list of individual scenarios and respective probability of occurrence or annual rate in the exposure time is provided</li></ul></td></tr><tr><td>In what way do the methods take into account time-dependent/dynamic aspects?</td><td><ul><li>The selection of sources may depend on the present state of the volcano (e.g. quiescence/ unrest/eruption)</li><li>Structural changes (e.g. due to large eruptions) may induce a significant change in the parameters ranges</li><li>Other temporal modulations are due to changes in the state of the volcano or to other phenomena (flank deformation, rapidly accumulated material on flanks, heavy rains, tectonic earthquakes, climate change, land-use changes, etc.)</li><li>Probability of occurrence is strongly time-dependent at all scales, from regime changes (tens of years), to changes in the volcanoes' states (months), to quicker dynamics like heavy rain (days)</li></ul></td></tr><tr><td>Do the methods use parallelisation, machine learning, surrogate models, advanced simulation schemes, other computational reduction strategies (e.g. cluster analysis, etc.)?</td><td>Not in present applications</td></tr><tr><td>What are the pros and cons and peculiarities of these methods? Are there known shortcomings / benefits of the methods? In what cases are these methods good/poor choices?</td><td><ul><li>Step 1 is qualitative. The development of more quantitative tools is required in the future</li><li>In step 2, the analysis of single scenarios may be important as a preliminary step toward the selection of the type of source, or to provide an exemplificative description of the phenomena to decision makers</li><li>For hazard/risk purposes, the selection of single scenarios is more subjective than the definition of a range of possible scenarios covering the expected natural variability. The definition of proper ranges allows quantifying the effective natural variability</li><li>Different methods exist for Step 3, with specific pros and cons, as discussed in the main text</li></ul></td></tr><tr><td>Data and technical requirements for method</td><td></td></tr></table>

(continued)
<table><caption>**Table 3.4 (continued)**</caption><tr><td>What input data does the method(s) use?</td><td><ul><li>Local records of past eruptions and tsunamis</li><li>Records from analogous volcanoes</li><li>Databases of active volcanoes or volcanic areas (mainly step 1)</li><li>Theoretical knowledge about potential sources of tsunamis (mainly step 1)</li><li>Geological and geophysical maps, to identify ranges for vent location, the extension and the volume of potential sources for collapse (mainly step 2)</li><li>Monitored past unrest episodes</li><li>Expert opinion</li></ul></td></tr><tr><td>What are the technical requirements?</td><td>None</td></tr><tr><td>Are HPC computing resources necessary, would absence of these compromise the use?</td><td><ul><li>The lack of sufficient computing resources may be one of the reasons to select a scenario-based deterministic approach</li><li>The technique adopted at step 3 to define the list of scenarios to be propagated should be selected based on the available computational resources</li></ul></td></tr><tr><td>Is the method(s)/ workflow(s) available as a git/ software/jupyter notebook?</td><td>Several tools for eruption forecasting and volcanic hazard are available as free software or open-source codes</td></tr><tr><td>Treatment of uncertainties for the method</td><td></td></tr><tr><td>Are the method(s) itself deterministic or uncertainty based?</td><td><ul><li>Step 1: methods are usually deterministic</li><li>Step 2: methods based on one or few scenarios are deterministic, while the definition of ranges for all source parameters enables the uncertainty quantification</li><li>Step 3: methods are uncertainty based</li></ul></td></tr><tr><td>Which are potential sources of uncertainties? Which parameters are used to characterize them?</td><td><ul><li>In step 1, the existence of unknown or never-observed types of sources</li><li>In step 2, the existence of unknown or never-observed sources, limited knowledge of the structural conditions of the volcano, or other uncertainty of this type, may lead to underestimation of the ranges, especially of their upper limits</li><li>In step 3, the paucity of data or lack of knowledge may lead to non-univocal definition of probability distributions, leading to large epistemic uncertainty</li></ul></td></tr></table>

(continued)
<table><caption>**Table 3.4 (continued)**</caption><tr><td>How are uncertainties quantified for the identified parameters? Are there significant correlations between different uncertain parameters?</td><td><ul><li>Uncertainties in parameter ranges (step 2) or probabilistic formulations (step 3) are treated through an ensemble of alternative formulations, managed through logic Trees, ensemble models or Bayesian models</li><li>Significant correlations among parameters and their uncertainty may exist; they are usually treated as conditional/stratified sampling and through the use of multivariate statistics</li></ul></td></tr><tr><td>Are the methods able to digest and propagate uncertainty in input (previous ingredient) and propagate it to the output (next ingredients)? Does the assessment of this ingredient require uncertainty propagation? If yes, how are uncertainties propagated?</td><td><ul><li>The expert selection in step 1 does not propagate uncertainty; to this end, new techniques should be developed in the future</li><li>Ranges defined through single or few scenarios do not propagate uncertainty, while the definition of full ranges allows for it</li><li>The uncertainties in source definitions and statistical properties can be treated by quantifying and propagating epistemic uncertainty</li></ul></td></tr><tr><td>What are the consequences of lack of data in input or for boundary conditions, or for characterizing certain parameters?</td><td><ul><li>Paucity of data or scarce knowledge of the volcano may lead to ignoring important sources and underestimating variability ranges</li><li>Paucity of data increases the epistemic uncertainty in probabilistic quantifications</li></ul></td></tr><tr><td>What are the consequences of ignoring or poorly treating uncertainties?</td><td><ul><li>Missing sources or underestimation of ranges may lead to significant underestimation of the hazard</li><li>The subjective definition of one or few scenarios introduces uncontrolled biases in hazard quantification</li><li>The scarce exploration of epistemic uncertainty does not allow the communication of existing constraints in hazard quantification</li></ul></td></tr></table>

such events: (1) the detection and proper modelling of the weather sources (e.g., location, speed, period, intensity) and (2) the impact of climate change.

Acoustically driven events can have worldwide impacts but are extremely rare. They are thus associated with larger uncertainties with respect to their intensity and rate. Despite being potentially more destructive than the weather-related sources (Denamiel et al. 2023), they have not yet been widely studied. Consequently, the uncertainty linked to acoustically driven events is not well known but is yet directly tied to the explosive volcanic eruptions and asteroid impacts/bolide explosions uncertainty.

At present, Atmospheric Probabilistic Tsunami Hazard Assessment (APTHA) remains sparsely developed as only one study has produced an assessment for weather
<figure><img src="image_14.png" /><figcaption>**Fig. 3.12** Summary of the atmospheric sources and the generation mechanisms leading to atmospherically-driven tsunamis or meteotsunamis</figcaption></figure>

related events (Geist et al. 2014c). On the contrary, most of the efforts in this field have evolved around early warning systems. However, several avenues have already been explored for the identification and modelling of the atmospheric sources. The following subsections present the different atmospheric sources as well as a family of methods specifically implemented for the quantification of atmospherically-driven tsunamis or meteotsunamis.

### 3.5.2 Step 1: Basis for Source Selection

#### Weather sources

Historically, weather-related meteotsunamis are defined as long waves in the tsunami frequency range driven by atmospheric disturbances (Monserrat et al. 2006). More generally, Non-Seismic Sea-Level Oscillations at Tsunami Timescales (NSLOTT) are generated worldwide through the transfer of energy from atmospheric waves to background ocean long waves (Vilibić and Šepić 2017). However, extreme NSLOTTs, or meteotsunamis that are, associated with flooding, structural damages,
and human losses, only occur when two conditions are fulfilled. First, the transfer of energy must be increased by offshore resonance (Vilibić 2008) obtained either when the speed of the atmospheric waves is equal to the tsunami long wave speed (i.e., Proudman resonance; Proudman 1929) or when the speed of the atmospheric waves is equal to the speed of the edge waves along a coastline (Greenspan resonance; Greenspan 1956). Second, the offshore ocean long waves must be amplified nearshore, for example through shoaling and harbour resonance (Pattiaratchi and Wijeratne 2015; Rabinovich 2020). In practice, this means that weather related meteotsunamis mostly occur (1) in known hotspots (e.g., Balearic Islands, Adriatic Sea in the Mediterranean region or Great Lakes in the USA; see Fig. 3.13) favorable to the nearshore amplification of the long waves (Vilibić et al. 2016, 2021) and (2) during weather events generating atmospheric waves at a speed triggering the Proudman or Greenspan resonances.

## Acoustic sources

Recently, the concept of atmospherically driven tsunamis has been extended to long waves generated by acoustic-gravity waves (Matoza et al. 2022; Amores et al. 2022; Harrison 2022; Adam 2022; Wright et al. 2022; Omira et al. 2022). These planetary meteotsunami waves spread with much greater speeds than tsunamis (Satake et al. 2020; Adam 2022) as they mostly occur during very large volcano explosions or asteroid impacts/bolide explosions capable of generating atmospheric acoustic-gravity waves with speeds far greater than the local shallow water propagation speed of tsunamis given by $\sqrt{gH}$ where g is the gravity and H is the local water depth. Their existence has been first hypothesized after the catastrophic eruption of the

<figure><img src="image_15.png" /><figcaption>**Fig. 3.13** Locations where weather related meteotsunami events are either suspected (in green) or known (in red) to have occurred until 2015. The sizes of the markers are related to the intensities of the events. The Mediterranean region, where most of these events occurred, is highlighted with a dotted box. Adapted from Vilibić et al. (2016), licensed under CC-BY 4.0</figcaption></figure>
Krakatau volcano in 1883 (Press and Harkrider 1966; Self and Rampino 1981) and fully confirmed with the explosive eruption of the Hunga Tonga-Hunga Ha'apai (HTHH) volcano in 2022 (e.g., Wright et al. 2022; Omira et al. 2022). This event was exceptionally well observed by satellites and recorded worldwide by thousands of microbarographs, seismometers, and tide-gauges. Based on the known meteotsunami generation mechanisms, the two processes that can amplify the acoustically driven planetary meteotsunami waves are the deep-ocean Proudman resonance and the inverse barometer effect which implies that larger meteotsunami waves should be generated by larger pressure disturbances driven by acoustic-gravity waves:

$$ \xi = \frac{1}{\rho g} \Delta P $$

where $\xi$ is the sea surface elevation, $g$ is the gravity, $\rho$ is the density and $\Delta P$ is the pressure disturbance. Consequently, simple numerical experiments dividing the speed of the HTHH Lamb waves by a factor 1.5 to reach the deep-ocean Proudman resonance at a speed of about 212 m/s (Experiment P; Fig. 3.14) or multiplying their amplitude by 10 to increase the inverse barometer effect (Experiment A; Fig. 3.14), lead to meteotsunami surges above 1 m (and up to 10 m) along more than 7% of the worldwide coastlines while they did not even reach 1 m during the HTHH event (Denamiel et al. 2023; see Fig. 3.14).

### 3.5.3 Step 2: Source Characterization

#### Weather sources

In contrast to the other tsunami sources, meteotsunamis are driven by atmospheric patterns and mesoscale conditions that can potentially be forecasted with numerical models. The following section is thus describing the different atmospheric sources driving meteotsunamis, at different locations of the world, and for different synoptic conditions, instead of their parameterization.

At the synoptic scale, strong mid-troposphere jets are the main atmospheric pattern causing meteotsunami events worldwide (Zemunik et al. 2022). Such events were recorded in the USA (e.g., Thomson et al. 2009), in the Mediterranean Sea (e.g., Jansà et al. 2007; Zemunik et al. 2021), in the northeast Atlantic basin (e.g., Tappin et al. 2013; Sibley et al. 2016) and in Japan (e.g., Tanaka 2010). Other recurrent synoptic patterns include (1) an inflow of warm and dry air in the lower troposphere, (2) instability of the mid-troposphere, (3) weak surface cyclones, and (4) winds that increase from the surface towards the upper levels. However, in some regions of the world, meteotsunamis may be accompanied by other atmospheric patterns depending on the mesoscale processes driving the events.

The most common mesoscale processes driving meteotsunamis are (1) atmospheric Mesoscale Gravity Waves (MGWs), (2) convective storms, (3) frontal
<figure><img src="image_16.png" /><figcaption>**Fig. 3.14** Modelled meteotsunami surges, as cumulative density functions (top panel) and distributions by coastal sub-domains (bottom panel), obtained under deep-ocean Proudman resonance conditions (Experiment P) and tenfold amplification of the Lamb wave amplitudes (Experiment A) in the atmosphere. Adapted from Denamiel et al. (2023)</figcaption></figure>

passages/squall lines and (4) tropical cyclones. Atmospheric MGWs may be gener-
ated by unbalanced jet streaks through the so-called spontaneous balance adjustment
(Ruppert et al. 2022) and can interact with fronts and organized precipitation. They
can cause rapid surface pressure oscillations > 5 hPa in less than an hour and can drive
meteotsunamis (Bechle et al. 2016; Dusek et al. 2019). For example, Sheremet et al.
(2016) measured a meteotsunami driven by atmospheric MGWs generated by a strong
cold front that passed over the northeastern Gulf of Mexico on 7 March 2008. During
this event, the MGWs induced rapid surface pressure falls of ≥ 10 hPa (including a
fall of 6.7 hPa in 10 min), rapid wind vector changes (e.g., 17 m/s in 25 min), and
high wind gusts (e.g., 20 m/s). Individual convective storms can be generated locally
in unstable atmospheric situations and are typically associated with surface pressure
perturbations that, when propagating at appropriate speeds, can cause meteotsunamis
(e.g., Belušić et al. 2009). Concerning the squall lines, or lines of thunderstorms, they often form along or ahead of cold fronts and can extend laterally for hundreds of kilometres. Long-lived strong squall lines, also called “derechos” (Spanish for ‘straight’), can travel many hundreds of kilometres and are associated with air pressure disturbances that can generate meteotsunamis through Proudman resonance. An example of such an event occurred on 13 June 2013 in the northeastern United States where waves impacted the New Jersey and southern Massachusetts coasts, despite clear skies and calm weather. Wertman et al. (2014) demonstrated that the waves had been generated by a derecho that had passed through the area hours earlier. Finally, during tropical cyclones, the generation of meteotsunamis can be driven by either tropical cyclone rainbands—i.e., the regions of heaviest precipitation outside of the tropical cyclone eyeball—that can develop squall-line-like characteristics or by atmospheric internal gravity waves produced in the stratosphere and the lower troposphere. Shi et al. (2020) studied tropical cyclones driving meteotsunami events in the Gulf of Mexico between 1998 and 2018. They found that Hurricane Harvey (2017) produced the largest observed meteotsunami: a single-peak wave with a maximum elevation of 0.78 m.

### Acoustic sources

Catastrophic events such as volcano explosions (Choi et al. 2003) or asteroid impacts/bolide explosions (Chapman and Morrison 1994; Morgan et al. 2022; deGroot-Hedlin et al. 2011) can generate atmospheric waves (Matoza et al. 2022; see Fig. 3.12) including acoustic-gravity waves (Yeh and Liu 1974) and the most prominent Lamb waves (Lamb 1911; Bretherton 1969). Lamb waves propagate horizontally in the atmosphere with a speed close to the mean sound speed (about 318 m/s; Dragoni and Santoro 2020) and can circle the globe multiple times (Press and Harkrider 1966; Amores et al. 2022). They are associated with surface pressure oscillations of several hectopascals (hPa) per minute (Press and Harkrider 1966; Harrison 2022) and their energy is dissipated towards the thermosphere (Forbes et al. 1999) via the ionosphere. Additionally, during the first hours after the explosive eruption of the Hunga Tonga–Hunga Ha’apai volcano in 2022, several Internal Gravity Waves (IGWs)—likely generated by the complex eruption sequence and traveling with speeds between 240 and 270 m/s—were recorded by seismo-acoustic and satellite observations (Matoza et al. 2022; Wright et al. 2022). The speed of these IGWs is thought to be largely controlled by the vertical profile of the temperature perturbation introduced by the eruption (e.g., Lashkin and Cheremnykh 2023). This suggests that under favourable conditions (e.g., a steeper initial temperature anomaly profile above the tropopause), large amplitude waves with speeds favourable to Proudman resonance can be generated (Denamiel et al. 2023).

### 3.5.4 Step 3: Probabilistic Treatment

#### Weather sources
No accurate APTHA has been achieved for meteotsunami events. Consequently, their probability of occurrence or their annual rates—including also the impact of climate change on the atmospheric tsunami sources—has yet to be defined. However, several methods accounting for the uncertainty, linked to the difficulty to accurately model the atmospheric conditions driving meteotsunami events, are currently developed, mostly for operational purposes (i.e., within early warning systems). To this date, the probabilistic treatment of the atmospheric sources is thus only applied to a few methods: (1) “Synoptic Index”, (2) “Deterministic Atmospheric Model”, (3) “Synthetic Catalogue” and (4) “Climate Uncertainty”. The derivation of synoptic indices follows the findings of Lorenz (1956, 1969) who argues that two relatively similar atmospheric synoptic situations are likely to produce similar local effects. Synoptic indices have only been successfully automatized and implemented for operational meteotsunami forecasting in the Balearic Islands, Spain (Ramis and Jansà 1983). However, they have recently been derived worldwide and strong connections between meteotsunami events and synoptic patterns have been found along most of the world’s coastlines (Zemunik et al. 2022). The advantage of the approach is that no additional numerical cost is required, as synoptic indices—identifying meteotsunami events up to a week in advance—can be derived and used with relatively coarse weather models (30–80 km in resolution) provided by many weather services. The major drawback is the impossibility to quantify the intensity of the events mostly related to mesoscale processes. Consequently, the implementation of (sub)-kilometre-scale deterministic models is an unavoidable necessity. To this date, this method have only been operationally implemented in the Balearic Islands (Renault et al. 2011) and the Adriatic Sea (Denamiel et al. 2019a, 2019b). In both systems the meteotsunami-genic disturbances triggering the event mode of the early warning systems are always detected but not necessarily their exact location, speed, period, etc. However, even for a 3-day simulation, running sub-kilometre scale models has been proven to have a prohibitive numerical cost and, for the Adriatic Sea, the operational forecasting service was discontinued.

Both “Synoptic Index” and “Deterministic Model” methods are by nature deter-
ministic but probabilistic treatment can be obtained by implementing ensemble
modelling using several numerical models in order to partially account for the known
uncertainty of global and regional models (i.e., the difficulty to simulate the precise
location and intensity of extreme events). Additionally, weather related meteotsunami
events are driven by atmospheric conditions highly influenced by ongoing global
warming. Deriving APTHA for weather related events thus requires accounting for
the impact of climate change on the recurrence and intensity of the meteotsunami-
genic disturbances. However, little is still known about this issue as presently only
two studies have been published on the subject. One used the synoptic index-based
approach in the Balearic Islands (Vilibić et al. 2018) and found that meteotsunami
occurrences could increase by one third under extreme warming conditions (Repre-
sentative Concentration Pathway RCP 8.5 scenario). The other used the pseudo-
global warming (PGW) downscaling approach (Schär et al. 1996; Denamiel et al.
2020a) for half a dozen meteotsunami events in the Adriatic Sea (Denamiel et al.
2022) and found a strong impact of climate warming on the spatial variability of the
meteotsunami intensity under RCP 8.5 scenario. However, both studies were carried
out with a single Regional Climate Model (RCM) and for a single climate scenario,
and thus do not account for the climate uncertainty.

In the “Climate Uncertainty” method, to limit the numerical cost of APTHA
for weather related events, the “Synoptic Index” method can be applied to extract
the potential meteotsunami events from ensembles of global climate models and
(sub)-kilometer-scale atmosphere–ocean models. Then, the “Deterministic Atmo-
spheric Model” method can be used to simulate the mesoscale behaviour of these
potential events in order to only select those leading to meteotsunamis. Finally, as
meteotsunamis can be categorized as rare events, synthetic catalogues—based on the
simplification and parametrization of the meteotsunamigenic disturbances and the
generation of thousands of conditions—can be directly used for uncertainty quan-
tification. Currently, such a catalogue approach has only been used in the northeast
U.S. (Geist et al. 2014c) to derive APTHA, but without accounting for the impact
of climate change, and in the Adriatic Sea (Denamiel et al. 2019b, 2020b, 2021) to
account for the uncertainty in meteotsunami simulations. The main advantage of the
approach is that it is inherently probabilistic, but it uses simplistic representations
of the meteotsunamigenic disturbances that might not fully reflect the complexity of
the atmospheric signal.

Acoustic sources

The detection and modelling of the atmospheric acoustic-gravity waves are currently
at their exploratory stage as most studies have only focused on the recent Hunga
Tonga-Hunga Ha'apai volcano eruption. But as these events are extremely rare,
only the systemic reproduction of past events and the forecast of potential events
could allow better understanding of the acoustic-gravity wave-driven atmosphere-
ocean dynamics and the quantification of the uncertainties linked to the transfer of
energy from the explosive process (volcanic eruption or asteroid impact/bolide explo-
sion) to the acoustic-gravity wave initial conditions used in the atmospheric model.
This would involve the use of both (1) “Deterministic Atmospheric Model” method
that can produce the worldwide atmospheric response after a volcanic explosion or
an asteroid impact/bolide explosion and (2) “Synthetic Catalogues” allowing uncer-
tainty quantification depending on the location and intensity of the acoustically driven
events. As the speed of the acoustic-gravity waves depends on the Earth’s surface
temperature, climate change might impact acoustically driven events. Consequently,
proper APTHA should in principle also account for climate uncertainty. Finally, it
is important to note that, in contrast to other tsunami sources, inland volcanic explo-
sions or asteroid impacts/bolide explosions (e.g., Tunguska explosion; Chyba et al.
1993) can also produce worldwide meteotsunamis.

**3.5.5 Summary Table**

See Table 3.5.
<table><caption>**Table 3.5** Summary table: atmospheric sources</caption><thead><tr><th colspan="2">Short description of methods</th></tr></thead><tbody><tr><td>Theoretical/mechanical background for the methods</td><td>Two categories of atmospheric tsunamis (or meteotsunamis): (1) weather related events driven by mesoscale processes and (2) acoustically driven events generating planetary acoustic-gravity waves after a volcanic explosion or an asteroid impact/bolide explosion</td></tr><tr><td>Short outline of how the methods work</td><td>Types of weather related events: (1) mesoscale gravity waves, (2) squall lines/derechos and (3) hurricanes<br/>Types of acoustic-gravity waves during acoustically driven events: (1) Lamb waves that can circle the globe several times and (2) internal gravity waves near the epicentre</td></tr><tr><td>How are the output(s) of the methods represented?</td><td>Type of studies (methods) using probabilistic treatment: (1) for weather related events: forecast from synoptic to local scales (synoptic index and operational forecast), climate warming impact from synoptic to local scales (climate model) and stochastic hazard assessments at local scale (synthetic catalogue) and (2) for acoustically driven events: remains to be performed</td></tr><tr><td>In what way do the methods take into account time-dependent/dynamic aspects?</td><td>Fully integrated for all atmospheric sources which highly vary in time (at both weather and climatic scales) and space (local, synoptic, and global scales)</td></tr><tr><th colspan="2">Data and technical requirements for method</th></tr><tr><td>What input data does the method(s) use?</td><td>Weather related events: (1) hotspot location database and (2) mesoscale atmospheric process identification (i.e., observation and/or modelling)<br/>Acoustically driven events: (1) explosive volcano/asteroid impact/bolide explosion location database and (2) acoustic-gravity wave identification (i.e., observation and/or modelling)</td></tr><tr><td>What are the technical requirements?</td><td>Step 1—mostly qualitative, assessing what is the source category and identifying hotspot locations for hazard analysis<br/>Step 2—Characterizing the different atmospheric sources<br/>Step 3—Probabilistic treatment based on the mesoscale processes/worldwide acoustic-gravity waves depending on the type of study to perform (forecast, climate, hazard assessment)</td></tr><tr><td>Is the method(s)/ workflow(s) available as a git/software/jupyter notebook?</td><td>No</td></tr></tbody></table>

(continued)
<table><caption>**Table 3.5 (continued)**</caption><thead><tr><th colspan="2">Treatment of uncertainties for the method</th></tr></thead><tbody><tr><td>Is the method(s) itself deterministic or based on uncertainty quantification (UQ)?</td><td>The identification of the category of atmospheric source (weather or acoustic) and the types of sources (e.g., derecho, Lamb wave, etc.) as well as the choice of the type of studies are all deterministic. Uncertainty quantification can be obtained with ensemble modelling and synthetic catalogues</td></tr><tr><td>Which are potential sources of uncertainties? Which parameters are used to characterize them?</td><td>The main sources of uncertainties are: (1) poor/ limited/sparse observational dataset and (2) limited knowledge of the mesoscale atmospheric processes/acoustic-gravity waves The parameters describing the uncertainties are: (1) for weather related events: direction, start location, amplitude, speed, period, etc. and (2) for acoustically driven events: initial condition at the epicentre and the Earth's surface temperatures</td></tr><tr><td>What are the consequences of lack of data in input or for boundary conditions, or for characterizing certain parameters?</td><td>Incapacity to properly identify the atmospheric process driving the meteotsunami events and improper modelling strategies</td></tr><tr><td>What are the consequences of ignoring or poorly treating uncertainties?</td><td>Lack of accuracy of the forecasts (false alarms/ missed events) and the climate projections</td></tr></tbody></table>

## 3.6 Choosing What Method to Use

### 3.6.1 Earthquake Sources

The main drivers in the choice of the method are the instrumental coverage, historical investigations, and availability of earthquake catalogues inherited from previous efforts. Time and budget constraints control the level and granularity of the specific investigations (e.g. merging and harmonizing seismic catalogues for large regions is needed for PTHA). Regarding faults, the availability of offshore survey data to characterize the faults in detail is a first order factor in the choice of the method. PTHA projects often rely on existing fault compilations derived from literature data. Again, the choices of the project managers are controlled by time and budget constraints for detailed analysis at the scale of the single structure/system, versus the availability of fault catalogues inherited from previous projects.

The use of earthquake catalogues tends to locate future earthquakes near the locations of past earthquakes and to overlook potential sources with long recurrence intervals (in the so-called silent regions) and, in general, the larger earthquakes. The use of faults tends to locate earthquakes near known faults, but not all faults can be known with all the necessary parameters. The partition of the total moment rate into
earthquakes of different sizes also depends on seismicity rate parameters such as the b-value.

Regarding the source parameterization, it is important to find the optimal trade-off between precision and accuracy. If the variability regarding, for example, the possible earthquake locations is too large, the precision can be reduced; however, if the parameter range is too narrow, there is a risk of low accuracy (bias). A similar reasoning can be applied for the MFD and time-dependence, in the sense that the more sophisticated the approach, the more data is needed to constrain it.

Dynamically consistent models of the seismic cycle are rarely used but there are promising examples. Time-dependent models are used infrequently given that simpler methods are often considered more reliable, at least on the tsunami time scales that are longer than those of the earthquakes.

## 3.6.2 Landslides

Available data dictates the method selection and whether a rigorous probabilistic analysis is at all possible. In areas with a relatively high amount of past large landslides, a source inventory based on past data can be established. Dating or geological time information must be available to constrain the time envelope of the events, otherwise uncertainties can be excessive. Slope-stability information gives more information about the present day situation and may hence be preferred when available. However, this approach implies that a relatively broad regional analysis of the slope movements is available, otherwise certain source areas may be overlooked. A difficulty with the slope-stability based models is that the probability of occurrence can not always be tied to the statistics of past events, unless statistical information of past landslides or probability models linking the trigger to potential slope failure and trigger is available (e.g. earthquake triggers and PSHA). Without any data constraining the volume and frequency of the landslide, either past landslides (or landslide tsunamis), or slope stability data, it is not possible to perform a probabilistic analysis or a source sensitivity analysis bounded by the data. A simpler conditional probabilistic analysis can be carried out instead. Carrying out a deterministic scenario analysis without uncertainty treatment is not recommended as the hazard is likely to be strongly biased on the chosen event.

## 3.6.3 Volcanoes

The driving issues that control the selection of one specific approach are (i) the computational need of the simulations (Sect. 4.4) and/or the availability of HPC resources; and (ii) the difficulty of defining the potential ranges of parameters and their probability of occurrence.
Probabilistic methods are often avoided also due to the difficulty in constraining ranges and spatio-temporal probabilities for many of the potential volcanic sources (e.g. Esposti-Ongaro et al. 2021). To this end, a few past events are often selected, typically choosing a few past scenarios in hindcasting mode. As discussed in Chap. 2, all the approaches selecting few scenarios typically imply a few tsunami simulations and allow skipping the quantification of the probability of each individual scenario (see also Step 3 in Sect. 3.4), simultaneously solving both the computational and lack of knowledge issues, and strongly simplifying the entire workflow. However, single scenarios can hardly represent the natural variability, preventing the possibility to fully quantify the hazard.

Sometimes, a few scenarios roughly covering the spatial or size variability are proposed (e.g. Tinti et al. 2011; Zaniboni et al. 2013; Necmioglu et al. 2023; Selva et al. 2019). This approach again does not allow for a full exploration of uncertainty, but at least may be considered as a preliminary step toward the probabilistic hazard, to quantify the potential of a given type of source. For example, this may provide quantitative information to feed a tool for the selection of a volcano and/or a typology of source (see Step 1 in Sect. 3.4). This information may thus feed probabilistic methods (like for example event trees), allowing an advanced exploration of source variability, as required for full hazard and risk quantifications.

The selection of a full probabilistic method allows for a full quantification of the natural variability, allowing to fully quantify hazard and risk. However, it implies the need of linking a forecast model for the source to an efficient tsunami modelling. The event tree technique has been successfully applied to this end, at least for tsunamis generated by eruptive events. Also, the treatment of time-dependency and the potential for multiple hazards acting at the same time are fundamental for all volcanic sources (e.g. IAEA 2008). This may be treated by considering, at least, the state of the volcano and potential changes of it (Marzocchi and Bebbington 2012; Selva et al. 2022). Tools like event trees have been explicitly designed to this end (Newhall and Hoblitt 2002; Newhall and Pallister 2015; Marzocchi et al. 2008, 2010). Other methods are instead devoted to treating the forecasts within a specific period, e.g. an unrest, like for example Belief Networks (e.g. Aspinal and Woo 2014, Hincks et al. 2014). In all cases, the use of expert elicitation is often recommended to treat difficult-to-constrain problems, at least to reach a consensus among experts over the results (Aspinall et al. 2002; Neri et al. 2008; Selva et al. 2012a, b).

In any case, considering the difficulty of selecting the source and to define the effective range of variability and rates, whatever is the probabilistic approach selected to explore aleatory uncertainty, methods explicitly treating epistemic uncertainty (like logic trees, ensemble, or Bayesian methods) are highly recommended.

### 3.6.4 Atmospheric Sources

For meteotsunamis, the selection, characterization, detection and modelling of the atmospheric sources is mostly straightforward and only depends on (1) the category
of events (i.e., weather or acoustic sources), (2) the location and, hence, the type of synoptic conditions (e.g., strong mid-troposphere jets) and/or of mesoscale atmospheric processes (e.g., mesoscale gravity waves, derechos, hurricanes, etc.) driving the weather related events or the type of acoustic-gravity waves during acoustically driven events and (3) the kind of study (e.g., forecast, climate change, hazard assessments, etc.). It should be noted that, to this date, APTHA is at its very early stage and that more advanced methods are expected to be developed and implemented in the next decade with the integration of meteotsunami sources within the wider tsunami community. Consequently, the focus in meteotsunami research is presently mostly oriented towards forecasting and hindcasting (understanding past events), and long-term hazard analysis still in its infancy. Yet, several of the methods discussed above comprise possible building blocks that likely can be combined to perform future probabilistic analysis.

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