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CITATION Geist, E.L., and P.J. Lynett. 2014. Source processes for the probabilistic assessment of tsunami hazards. Oceanography 27(2):86–93, http://dx.doi.org/10.5670/oceanog.2014.43.

DOI http://dx.doi.org/10.5670/oceanog.2014.43

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DOWNLOADED FROM HTTP://WWW.TOS.ORG/OCEANOGRAPHY SPECIAL ISSUE ON UNDERSEA NATURAL HAZARDS Source Processes for the Probabilistic Assessment of Tsunami Hazards

BY ERIC L. GEIST AND PATRICK J. LYNETT

ABSTRACT. The importance of tsunami hazard assessment has increased in recent years as a result of catastrophic consequences from events such as the 2004 Indian Ocean and 2011 Japan tsunamis. In particular, probabilistic tsunami hazard assessment (PTHA) methods have been emphasized to include all possible ways a tsunami could be generated. Owing to the scarcity of tsunami observations, a computational approach is used to define the hazard. This approach includes all relevant sources that may cause a tsunami to impact a site and all quantifiable uncertainty. Although only earthquakes were initially considered for PTHA, recent efforts have also attempted to Regional wavefield of tsunami from Currituck landslide at include landslide tsunami sources. Including these sources into PTHA is considerably three time steps. Evident in this more difficult because of a general lack of information on relating landslide area simulation is a secondary wave that refracts up the continental and volume to mean return period. The large variety of failure types and rheologies slope and toward shore north associated with submarine landslides translates to considerable uncertainty in of the Currituck landslide. determining the efficiency of tsunami generation. Resolution of these and several other LD wave: Leading depression wave. LE wave: Leading elevation wave. outstanding problems are described that will further advance PTHA methodologies From Geist et al. (2009) leading to a more accurate understanding of tsunami hazard.

time = 7 minutes time = 16 minutes time = 55 minutes 300

250 LE wave 8

200 6

150 refracted 4 phase

100 2 y (km) 50 broadside 0 phase LD wave (m) Amplitude 0 –2

–50 –4

–100 –6

0 50 100 150 200 250 0 50 100 150 200 250 0 50 100 150 200 250 x (km) x (km) x (km)

86 Oceanography | Vol. 27, No. 2 INTRODUCTION The most common application is using deterministic analysis, probabilistic Recent events such as the 2004 Indian a pre-specified design probability analysis directly incorporates different Ocean and 2011 Tōhoku tsunamis, to determine the exceedance value sources of uncertainties into the among many others, have demonstrated at that probability (Figure 1a). For construction of the hazard curve. In the tremendous destructive nature of tsunami hazards, the hazard value of this article, we review the framework tsunamis as they impact coastlines. interest is typically runup (runup is a of PTHA that was established using Traditionally, tsunami hazards have measurement of the maximum height just earthquake sources and discuss been assessed deterministically using the of the water that the tsunami pushed recent advances in the methodology for concept of a maximum credible event or onshore observed above a reference including landslide sources. worst-case scenario. There is, however, sea level; see http://walrus.wr.usgs.gov/ no single accepted way of determining tsunami/basics.html), although other PTHA FRAMEWORK this scenario. In some cases, the physi- impact metrics such as current speed or PTHA was developed by adapting a cally largest earthquake or landslide is momentum flux can also be considered. long-standing probabilistic method for used to assess the tsunami hazard at a A less common application of the hazard determining ground motion exceedance coastal site, whereas in other approaches, curve is using a pre-specified tolerance caused by earthquakes: probabilistic the largest historical event is defined as level to determine the probability of seismic hazard analysis (PSHA) (Cornell, the worst-case scenario. Furthermore, exceedance from the hazard curve 1968). The main differences between the deterministic scenario is created (Figure 1b). For example, engineers PSHA and PTHA relate to which sources under an implicit assumption of a min- may be interested in the probability are considered and how the hazard is imum likelihood, though the likelihood that a sea wall of a certain height will calculated for earthquakes and tsunamis. limit is often not explicitly stated. For be overtopped by a tsunami. Finally, For PTHA, it is important to consider example, tsunami hazards from asteroid probabilistic inundation maps can also large tsunamigenic earthquakes, includ- impacts are rarely considered, owing to be constructed by calculating the hazard ing those at far distances, as well as other the long mean return period associated at a specific design probability over a tsunami sources such as submarine land- with this source. Finally, uncertainty given region (González et al., 2009), slides and volcanic processes that can associated with these scenarios is often useful for setting flood insurance rates rapidly displace the water column. For not rigorously defined or used in deter- (e.g., at 1% annual probability of exceed- PSHA, it is more important to consider ministic hazard assessments. To address ance). With information regarding vul- a wider range of earthquake magnitudes, these problems, tsunami hazards have nerability and exposure of a community, including small events, close to the site recently been assessed probabilistically. hazard curves permit a risk calculation. of interest. For the hazard calculation, While these assessments are resource Ideally, historical data from a nearby empirical attenuation relations are intensive compared to deterministic water level station could be used to used in PSHA that relate earthquake assessments, they provide a systematic construct a hazard curve. However, parameters to ground motion, whereas method for defining the hazard for a there are few locations in the world physics-based numerical hydrodynamic probability of interest specific to appli- where there is a sufficiently long record models are used in PTHA so that less cations such as tsunami preparedness, of tsunami observations. A computa- uncertainty can be expected, given determining flood insurance rates, and tional method, termed probabilistic sufficiently accurate input data. In this impact on infrastructure. tsunami hazard analysis (PTHA; Geist regard, PTHA shares some similarities In contrast to deterministic analysis and Parsons, 2006), is therefore required with probabilistic storm surge forecasts that estimates the severity of natural to construct the tsunami hazard curve. that also rely on numerical modeling hazard as a single value, the primary These methods require specifying all (e.g., Resio et al., 2009). result from probabilistic analysis is a relevant tsunami sources that may There are four basic steps in hazard curve that plots the probability affect the site, performing numerical conducting PTHA (Figure 2, middle): that a given severity will be met or hydrodynamic modeling for each (1) specification of source parameters, exceeded. The hazard curve can be source, and aggregating the results to including rate of occurrence, (2) choice used in two different ways (Figure 1). form the hazard curve. In contrast to of probability model that describes

Oceanography | June 2014 87 source occurrence in time (most often owing to the natural variability of analysis (Parsons and Geist, 2009; Poisson, as described below), (3) hydro- tsunami evolution (aleatory uncertainty). Grezio et al., 2010). dynamic modeling for each source The latter is directly integrated into A perhaps subtle assumption in many location and set of source parameters to the hazard curve through a defined probabilistic analyses of tsunamis and compute tsunami hazard characteristics probability distribution that models the other natural hazards is that events are at a site, and (4) aggregation of the uncertainty. The former is incorporated random in time and unrelated to one modeling results and incorporation of through the use of logic trees (Figure 2, another, termed a Poisson process. The uncertainty. It is easy to see, with the bottom). Each branch of the logic tree time between tsunami events in such a number of sources involved and the is a separate calculated hazard curve process follows an exponential distri- many possible combinations of source that is weighted according to a specific bution. Accordingly, the hazard curve parameters, that the computational subjective (i.e., expert consensus) or represents the probability that one or load associated with PTHA can become objective (i.e., normal distribution) more tsunamis will meet or exceed the a major obstacle in performing the scheme. The final hazard curve is corresponding runup on the horizontal analysis. There are several methods for defined as the median or some other axis over a given exposure time (T) given decreasing the computational load. First, fractile of the ensemble hazard curves by P(R ≥ R0) = 1 – exp(–λT), where λ is usually there is a primary parameter, from the logic tree. the rate of occurrence of these tsunamis such as earthquake magnitude, that has Data available from nearby water level and is constant with time. For tsunamis a dominant effect on the tsunami hazard stations and other observations can be and other floods, annualized probabili- at a site. Other parameters scale with the used to check the PTHA calculations. ties are often considered (exposure time primary parameter, reducing the range Tsunami observations may be censored T of one year). For small values of λT, of parameters that need be considered. at low runups and undersampled at high P approximately equals λ and hazard In addition, random sampling of possible runups (Geist and Parsons, 2006). With curves are often calculated in terms of λ parameter combinations (Monte Carlo this in mind, if the empirical hazard rather than P. The exceedance rate λ is simulation) can decrease the computa- curve results in higher hazard values critically dependent on the probability tional workload. for a given probability than the PTHA model chosen for the tsunami sources Throughout the analysis, different hazard curve, then there is a problem in step 2 of PTHA (Figure 2, middle), causes of uncertainty in the calculation with which sources are included and the with the Poisson model being a common are tracked (Figure 2, top). A distinction validity of assumptions used in PTHA. starting model. is made between uncertainty in our The available data can also be used to The choice of design probability knowledge of parameters or processes fill in the PTHA calculations for rare depends on the particular application (epistemic uncertainty) and uncertainty or unknown sources using Bayesian of PTHA. For determining flood zones for insurance purposes, an annual (a) (b) probability of 1% and, less often, 0.2% is considered (Burby, 2001). The mean P(R > R0) P(R > R0) return period is given by 1/ λ and these designs are often termed the 100- and 500-year floods, although these terms design often generate confusion in the public probability P that is caused by not understanding the

Eric L. Geist ([email protected]) is Research Geophysicist, US Geological Survey, Menlo Park, CA, USA. Patrick J. Lynett is R0 R tolerance R level Associate Professor, Department of Civil and Environmental Engineering, University of Figure 1. Schematic tsunami hazard curve showing different applications: (a) exceedance runup R( 0) determined from design probability, and (b) probability (P) determined from specified tolerance level. Southern California, Los Angeles, CA, USA.

88 Oceanography | Vol. 27, No. 2 random nature of the hazard (Bell and earthquake statistics and plate tectonic significantly lower, although not zero Tobin, 2007). For example, there is a 63% models is currently the best method for if various uncertainties are considered chance of the 100-year flood occurring constraining the rate of occurrence for because earthquakes larger than the in any given 100-year time period. In megathrust tsunamis (Bird and Kagan, characteristic magnitude do not exist, by other cases, such as for ground motion 2004). Devastating tsunamis have been definition. For example, the mean return from earthquakes (Frankel et al., 2000), historically generated on faults other period for magnitude 9 earthquakes the design is a specific probability over than subduction megathrusts, such as along the northern Cascadia subduction a period of time, such as the 5% in faults along the outer trench slope and zone is approximately 500–540 years. 50 years event that is equivalent to an outer rise of subduction zones and in the (Atwater and Hemphill-Haley, 1997). annualized rate of 1/974.8 years. For back arc, although it is even more diffi- PTHA analysis at an annual design nuclear applications, the annual design cult to assign slip rates to these faults. probability of 0.2% for coastal sites in the probability can be as low as 10–4 to 10–6 A long-running controversy in Pacific Northwest would be higher under (Nicholson and Reed, 2013). seismology that affects PTHA is how the characteristic hypothesis compared earthquake magnitudes are distributed to the Gutenberg-Richter hypothesis, EARTHQUAKE SOURCES along a fault zone (Parsons et al., 2012). but lower for a design probability of Earthquake sources considered for The characteristic earthquake hypothesis 0.1%. One of the significant advantages PTHA are located primarily along is that the largest earthquakes that occur of PTHA analysis, however, is that both subduction zones. Here, the world’s along an individual fault or fault segment hypotheses can be considered sources of largest earthquakes occur on the are of similar magnitude throughout epistemic uncertainty and included in a interface fault that separates the time. The competing hypothesis is that logic-tree framework. The occurrence of downgoing plate from the overriding earthquake magnitudes are distributed the 2011 Tōhoku earthquake is seen by plate, often termed the “megathrust.” according to a power-law relationship many as a refutation of the characteristic The geometry of these massive faults (termed the Gutenberg-Richter rela- hypothesis (see Opinion by Kagan et al., can be defined from geophysical tionship) that is tapered at the highest 2012), and at the very least demonstrates methods and the precise location of magnitudes. For the characteristic the difficulty in assigning a maximum instrumentally recorded earthquakes model, at design probabilities less than magnitude using the characteristic (Hayes et al., 2012). Although relative but near the mean recurrence rate of the model (Geist and Parsons, 2014). plate convergence rates and slip rates on characteristic earthquake, the contribu- specific faults can be determined using tion to the overall hazard will be higher LANDSLIDE SOURCES modern geodetic methods, a significant than for the Gutenberg-Richter rela- For landslide-generated tsunamis, source of uncertainty is how much tionship. For lower design probabilities, specification of the seafloor time history, of the slip on megathrusts is released the contribution to the overall hazard which is used to force generation of seismically. A combination of both under the characteristic hypothesis is the ocean surface wave, is a difficult

Figure 2. (middle) General Identification of Significant Sources of Uncertainty steps in probabilistic tsunami hazard analysis (PTHA). (top) Throughout the spec- ification of tsunami sources, Source Probability Generation & Aggregation probability models, and Parameters Models Propagation Models tsunami simulations, various Specifies geometric Gives the probablitiy that Calculates the tsunami Determines the hazard epistemic and aleatory parameters and long- each source will occur in a wave height at the site for curve for each branch of term rates of occurrence. specified time span. each source. the logic tree. uncertainties are identified. (bottom) Epistemic uncertainty is included in a logic tree and a hazard Development and Calculation of all Logic Tree Branches curve is computed for each logic tree branch during the aggregation phase.

Oceanography | June 2014 89 task. Submarine mass movements can piece, not as a group of smaller, spatially landslide-generated tsunamis into PTHA take a wide variety of forms, such as and temporally separated segments), is the understanding of local sources translational slides, rotational slumps, and “fast” (meaning that the time scale with significant heterogeneity in their and debris flows, and each will have of motion of the movement is on the spatial geometry and time evolution. different tsunamigenic efficiency. Here, order of the generated wave period) This would be classified for the most part efficiency is a measure of the transfer of (e.g., Lynett and Liu, 2002). Note that as epistemic uncertainty, driven by our the energy of the mass movement into the discussion above details efficiency lack of understanding of how small-scale free ocean surface waves. In general, the and does not address tsunami potential, spatial and temporal details generate most efficient mass movements are those which is a function of the efficiency and and evolve. If this heterogeneity can be that are “shallow” (meaning the hori- is also closely related to metrics such as quantified, as it can to a reasonable extent zontal length scale of the slide is much landslide volume and mass discharge for earthquake sources, and coupled with greater than the local depth), “coherent” rates (Harbitz et al., 2006). statistical information about local slope (meaning that the mass fails as a single A great challenge to including stability mechanisms and landslide prob- ability of occurrence, then proceeding with a PTHA is justified. For landslides, this is a great challenge. Furthermore, the mean return periods of submarine landslides in a given area, which are integral to PTHA, are often accompanied by leading order imprecision and uncer- tainty. Figure 3 provides an example methodology for integration of landslides in PTHA, focusing only on modeling the landslide time history. Note that Figure 3 represents an expansion of detail for the “generation and propagation” box shown in Figure 2 associated with landslide tsu- namis. The first pieces of information are functional relations between the mean return period and both slide volume and horizontal slide area. Note that slide area is equally important, as without this piece of information it is not possible to estimate slide thickness, which largely controls the generated wave height (e.g., Lynett and Liu, 2005). Alternatively, relating slide volume to slide area (and/or maximum slide thickness), when used in conjunction with a slide volume to return period relationship, would close this problem. These relations come from statistical data from previous landslides, geophysical information, and geotechnical samples. Currently, these Figure 3. Example procedure tree for the inclusion of slide variability and uncertainty into a PTHA. Note that this flowchart represents an expansion of detail for the “generation and propagation” box types of data are sparse, so only limited shown in Figure 2. information is available for building these

90 Oceanography | Vol. 27, No. 2 starting-point relationships. evolution model for a translational slide with justification, to the generality given With these relationships in hand, (solid body motion) is established in the here. These simplifications will often however, they can be sampled to arrive literature, the same cannot be said for exist in the description of the failure at a set of landslide volume + thickness any of the other “types” of motion, such types/rheological models and distri- combinations. For each member of as rotational slumps, creeping slides, butions of the parameters that govern the set, a distribution of possible slide and debris flows. With the parameters them. Our current state of knowledge time histories should be determined. necessary for the failure model provided, of wave and landslide coupling may The first step in this procedure is for the slide time history can be imported not justify a confident simplification the user to decide how to describe the into the hydrodynamic model, and a to these models/parameters, and, motion (Figure 3). There are two main single realization can be generated. In hence, the current preference is for a categories of choice (which could also a Monte Carlo analysis, this procedure highly conservative landslide source be combined into a single category, if is repeated until enough realizations estimate with a deterministic modeling desired): (1) specify the failure type, or are generated so that distributions can approach. Likewise, the computational (2) specify the rheological model. In be constructed for whichever tsunami cost for a PTHA-with-landslides, driven the “Specify Failure Type” route, a set impact metric is under analysis. by the high computational cost of of different types of failure mechanisms Instead of choosing the “failure type” three-dimensional/dispersive models are included, such as rotational slides, route, it is possible to specify a set of often needed for accurate physical translational slides, block slides, debris different rheological models. Here, representation of the slide and waves flows, and avalanches. These slide slide motion is not specified a priori; (e.g., Abadie et al., 2012), is significant motions are defined as “prescriptive,” rather, the landslide motion is a function and may only be justified for sites where meaning that their temporal and spatial of an initial condition, boundary a tsunami from a local landslide controls evolution profiles are known a priori. conditions, and a set of differential the design hazard level. Lastly, the reader Each of these different types will yield equations to evolve the material in time. is directed to Geist and ten Brink (2012) different tsunamigenic efficiencies as well Rheological models are meant to cover for a more complete and comprehensive as different generated wave properties. the full spectrum of materials relevant review of the challenges in landslide This step represents a branching logic to landslides, from fluids to solids and tsunami modeling related to PTHA. tree, and thus a weighting factor must elastic to viscous materials. Similar be assigned for each different type. The to the “failure type” approach, the OUTSTANDING PROBLEMS variety and number of types can likely be range and weightings of the employed In addition to the challenge of including reduced based on site-specific conditions, rheological models are location specific. landslide sources, as well as volcanic and indeed the weighting factors must Rheological models tend to be more sources (Paris et al., 2014), into PTHA, be location specific as well. Once a type complex and computationally costly than there are general issues that need to be is chosen, the parameters that govern its the “prescriptive” models and require addressed to improve the accuracy of evolution must be selected. With a trans- calibration of numerous submodels, such PTHA in the future. These issues include lational landslide, for example, its initial as closure equations for yield stress or incorporating (1) extreme sources not motion would likely follow solid body basal friction. Furthermore, each sub- represented in the historical or recent (block) motion, and therefore parameters model contains a handful of material and geological record, (2) time-varying such as drag coefficient, added mass, and empirical parameters, and a distribution rates of recurrence for tsunami sources, material density must be given (Enet and for each needs to be constructed. and (3) dependencies among different Grilli, 2007). These parameters, which are Note that the methodology outlined models of source occurrence. In each location specific, should be selected from in Figure 3 is simply one suggestion for case, resolving these issues will rely distributions created for each parameter; a probabilistic analysis incorporating on a variety of statistical and other though such information could likely be landslides—an analysis procedure that methodologies used the in the assess- generated, it is not currently known to is currently not well defined. Alternative ment of other natural hazards, such as formally exist for submarine landslides. methods are certainly viable, and storm-surge forecasting. It is also worth noting that while the significant simplifications may be made, For the case of incorporating extreme

Oceanography | June 2014 91 sources for low design probabilities, 2006). In addition, there may be a long- margins have recently been considered the issue comes down to how well we term change in the rate of tsunami source for probabilistic analysis. However, there can extrapolate the historical record of occurrence, as Lombardi and Marzocchi are significant challenges in including source occurrence. The paleoseismic (2007) describe for large earthquakes. For these sources, ranging from the variety record can augment earthquake catalogs, submarine landslide sources, the effect of landslide types and rheologies to especially for subduction zones where the of climate change and glacial cycles may the need for high-dimensional occurrences of megathrust earthquakes also systematically change the occurrence hydrodynamic modeling to compute are marked by coastal subsidence and rate for these sources (Masson et al., wave heights and other impact metrics. sedimentary deposits left by the ensuing 2006; Lee, 2009), although the signif- Conducting the analyses requires sub- tsunami. Similarly, drill hole records icance of this connection is currently stantial resources, although methods are and multichannel seismic data can yield under debate (Urlaub et al., 2013). being developed to reduce the computa- information to assess that distribution of Finally, different conceptual models tional load associated with probabilistic landslide sizes in a given region. The diffi- for the occurrence of earthquakes and analysis, particularly when inundation culty with these geologic and geophysical landslides are often included in PTHA calculations are needed. Resolution of records is in assessing both the age and in a logic tree. Occurrence models several outstanding theoretical issues the size of prehistoric tsunami sources include how the sizes of the sources are will improve probabilistic tsunami and quantifying the uncertainty in both distributed and the probability model hazard analysis in the future based on of these parameters (Geist et al., 2013). for how they occur in time. In averaging focused acquisition of specific geological One of the basic assumptions for the hazard curves that result from these data sets and application of probability the probabilistic assessment of natural models in a logic tree format, these mod- methods used for other natural hazards. hazards is that the hazard rate is constant els are treated independently; each model with time. This is contradictory to well- likely represents some “true” aspect of ACKNOWLEDGEMENTS known observations that earthquakes occurrence, but is not a complete model The authors greatly appreciate con- cluster in time and space in the form of in and of itself (Page and Carlson, 2006). structive comments by Finn Løvholt, foreshock, mainshock, and aftershock A similar issue arises also in climate Jason Chaytor, Tom Parsons, and an sequences (Kagan and Jackson, 1991). change models (Dosio and Paruolo, anonymous reviewer. Landslides also appear to cluster, as 2011). Various ways of incorporating this indicated from detailed geologic studies uncertainty include Bayesian techniques REFERENCES such as in Port Valdez, Alaska, where and the use of copulas, which are Abadie, S.M., J.C. Harris, S.T. Grilli, and R. Fabre. 2012. 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