Chapter 2 – tsunami dynamics, forecasting, and mitigation

Chapter 2 – tsunami dynamics, forecasting, and mitigation Chapter 2 – tsunami dynamics, forecasting, and mitigation Chapter 2 – tsunami dynamics, forecasting, and mitigation Chapter 2 – tsunami dynamics, forecasting, and mitigation Chapter 2 – tsunami dynamics, forecasting, and mitigation Chapter 2 – tsunami dynamics, forecasting, and mitigation Chapter 2 – tsunami dynamics, forecasting, and mitigation

Tsunami Dynamics,

Forecasting, and Mitigation

Utku Kaˆno
glu1and Costas Synolakis2,3

1

Department of Engineering Sciences, Middle East Technical University, Ankara, Turkey,2Viterbi School of Engineering, University of Southern California, Los Angeles, CA, USA,3Technical University of Crete, Chania, Greece

ABSTRACT

Tsunamis had been earlier believed as extremely rare events, yet about one event peryear has been reported in the past two decades, making them a more common extremehazard After the 2004 Indian Ocean tsunami, the need for substantial improvements intsunami real-time and long-term forecasting capabilities, education, and development oftsunami-resilient communities became evident Thereafter, there were substantial ad-vances in tsunami science, i.e., significant advancements in warning methodologies,predisaster preparedness, and basic understanding of related phenomena The 2011Japan tsunami, broadcasted live to a stunned world audience, underscored the difficulties

of implementing theoretical advances in applied hazard mitigation Japan is possibly themost tsunami-ready nation on the Earth Nonetheless, the size of the 2011 earthquakewas largely unexpected and, in many instances, the floods penetrated several times thedistances that had been anticipated in pre-event planning Three years later, Japan is stillrecovering A need exists for acquainting the broader scientific community on advances

in prediction and mitigation in hopes that applied disaster preparedness improves

2.1 INTRODUCTION

After the December 26, 2004, Indian Ocean (Boxing Day) tsunami,Huppertand Sparks (2006) wrote “It is likely that in the future, we will experienceseveral disasters per year that kill more than 10,000 people.” Their assessmentwas not far off, unfortunately, to wit the March 11, 2011, Japan tsunami (theGreat East Japan Earthquake Disaster) that alone resulted in more than 20,000casualties Tsunamis and other coastal disasters have killed over 200,000 sinceBoxing Day 2004 Coastal communities are now extensively developed centers

of substantial commercial activities that are also at risk

Coastal and Marine Hazards, Risks, and Disasters http://dx.doi.org/10.1016/B978-0-12-396483-0.00002-9

Tens of millions of people live in high-risk coastal communities around theworld, and hundreds of thousands of tourists are at high-risk beaches at anygiven time This appears yet another case of what Jackson (2006)has calledfatal attraction; earthquakes occur in places where they would likely causemore casualties compared to earlier times because in some places the avail-ability of water is linked to underlying faults and because many rural com-munities have grown much larger with mostly poor building standards.Furthermore, geological hazards such as tsunamis are not only threats tothe countries in whose territories they originate but also can cause wide-scaledevastation across national boundaries, as dramatically shown during the 2004Boxing Day tsunami which impacted at least 16 countries directly and touristsfrom many other countries (Synolakis and Kong, 2006) Among the casualtiesduring the 2004 disaster were 428 Swedish people, out of a population ofabout 10 million.

The word tsunami made its grand debut in most world languages with theDecember 26, 2004 event Yet the first historical inference of coastal inundation bytsunamis refers to the eruption of the Thera volcano in the Eastern Mediterranean(Marinatos, 1939), now believed to have occurred around 1620 BC Thisprecipitated the demise of the Minoans in Crete Island (Bruins et al., 2008).Referred to as tidal wave in English, the exact translation of tsunami from theJapanese is harbor wave Probably, early observations of these unusual waves byeyewitnesses were in ports, as harbors were centers of commercial activity and thepoints of contact with the sea In Japan, where historic records exist since the ninthcentury AD, these motions were often associated with tsunamis, hence the name It

is not uncommon that a relatively small tsunami entering a port or harbor cantrigger substantial water level oscillations and reach substantial heights, and watermotions can persist for hours, as most recently observed in many harbors along theJapanese coast, as well harbors in the Pacific coast of the United States after the

2011 Japan tsunami (Figure 2.1)

Tsunamis are generated by impulsive geophysical events of the seafloorand of the coastline, such as earthquakes and submarine and subaerial land-slides Volcanic eruptions and asteroid impacts are less common but morespectacular tsunami-generation mechanisms (Gisler, 2009; Morrison, 2006).Tsunamis are high-impact, long-duration disasters and often entail substantialhuman drama, as outlined in the Hollywood movie The Impossible They arelong waves with small steepness and evolve substantially, through spatial andtemporal spreading from their source region, as suggested in the map of energypropagation of the Boxing Day tsunami (Titov et al., 2005a) (Figure 2.2); alsoseeFigure 2.3for the March 11, 2011, tsunami (Tang et al., 2012)

The determination of the terminal effects of tsunamis as they strikeshorelines and coastal structures remains one of the quintessential problems intsunami hazard mitigation Since the Boxing Day tsunami, a new science oftsunami forecasting has emerged (Bernard and Robinson, 2009) The firstextensively tested real-time forecasting methodology is now officially in use

FIGURE 2.1 Significant tsunami currents were observed in many harbors during the March 11,

2011, tsunami (Top left) View of whirlpool at Port of Oarai, Japan, taken from helicopter approximately at 17:54 (local time), i.e., 3 h 8 min after the earthquake; (bottom left) numerical results of Lynett et al (2012) for the fluid speed of the tsunami in the Port of Oarai; after the 2011 Japan tsunami (top right) surge jetting in to the inner harbor of Crescent City, California; and (bottom right) Pillar Point Harbor, south of San Francisco, which experienced counterrotating eddies in the inner and outer basins After Lynett et al (2012)

FIGURE 2.2 Global maximum tsunami heights of the Boxing Day tsunami computed from numerical model of Method of Splitting Tsunami (MOST) ( Titov and Gonza´lez, 1997 ), after 44 h

of propagation Inset shows distribution of the slip among four subfaults (from south to north:

21 m, 13 m, 17 m, and 2 m) which provides best fit for satellite altimetry data and correlates well with seismic and geodetic data inversions, and the computed wave heights in the Bay of Bengal Wave amplitudes, directionality, and global propagation patterns appear primarily determined by the orientation and intensity of the offshore seismic line source and subsequently by the trapping effect of midocean ridge topographic waveguides Contours show computed tsunami travel times Circles denote the selected tide gauge stations where amplitudes of tsunami are given in three range categories After Titov et al (2005a)

Time after earthquake (h)

0.75 1 1.25 1.5 1.75

−200

−100 0 100 200

Time after earthquake (h)

21401 SE of Iturup Island, Russia

Observation MOST model

FIGURE 2.3 (Top) Deep-ocean Assessment and Reporting of Tsunamis (DART) measurements used by the United States National Oceanic and Atmospheric and Administration (NOAA) Center for Tsunami Research (NCTR) for the inversion of the March 11, 2011, Japan tsunami and the resulting waveforms at DARTs after the inversion (Middle) Global maximum wave amplitudes for the source identified by the NCTR in real time Inset shows the resultant unit sources After Tang

et al (2012) (Bottom left) Initial tsunami source defined by the NCTR in real time for the event Comparison of computed tsunami maximum wave amplitudes on land based on (bottom center) tsunami source constrained from DART measurements and (bottom right) the US Geological Survey (USGS) finite fault model source with measured tsunami heights and runup values (black lines, red dots, and blue dots denote computed MOST model maximum wave amplitudes (m), observed tsunami heights (m), and observed runup values (m), respectively) Although computed MOST model maximum wave amplitudes are given by Wei et al (2013) , the observed tsunami heights and runup values are given by Mori et al (2011)

by tsunami warning centers (Vasily Titov, personal communication, June 8,2013) and is rapidly becoming web-based (Burger et al., 2013) This tech-nology is based on real-time data assimilation from measurements fromtsunamographs: deep-ocean buoys also known as DARTs (Tang et al., 2012;Wei et al., 2008) Measurements from tsunamographs are used to better definethe seafloor displacement that triggered the tsunami Such hydrodynamic in-versions are now as standard as seismic inversions New markers have emergedthat help to identify paleotsunamis and thus better infer the mechanisms ofpaleoearthquakes High-end computational tools now allow for inundationpredictions, even from submarine landslides New analytical results helpexplain the scaling of vexing tsunami evolution problems Most coastlines ofhighly developed nations along the Pacific now have inundation maps forpre-event planning (seesection 2.4.1), as do at-high-risk cities in Indonesia,such as Padang Several communities, including several in the United States,have earned the coveted tsunami-ready designation With the exception of theMediterranean, all the at-risk world oceans and seas are now covered with rapidwarning procedures.

Tsunami studies are multi-disciplinary, at the cross-roads of geology,geophysics, geography, oceanography, coastal engineering, mathematics, andsocial science Once initial conditions, offshore bathymetry, and onshoretopography are known, the evolution of a tsunami can be calculated fairlyaccurately, at least until the time of its maximum inland penetration Un-certainties arise in the specification of the initial condition, assessing the repeatinterval of the phenomenon, and in developing mitigation measures, particu-larly given the variability of the human response In addition, the long duration

of tsunamis with multiple waves attacking target coastlines challenge rescueefforts, and might cause secondary effects such as fire, nuclear accidents(Satake, 2013), and debris flows (Lebreton and Borrero, 2013)

In early tsunami studies, none of the analytical or numerical results forpredicting inundation had been validated with data from laboratory experi-ments, and no realization existed of the scales of tsunamis of geophysicalinterest Up until the 1970s, no numerical computations existed, and tsunamiswere studied as idealized periodic waves generated by uniform seafloor dis-placements Most studies were analytical, and results were either in terms ofcomplex formulas or asymptotics, yet they revealed little of the underlyingphysics and were of equally little practical interest

The analytical results remained disjointed from the laboratory experiments,possibly because of the different ranges in wave steepness that analysis andexperiments were referring to, the latter having been undertaken with farsteeper waves than the former No realization existed of what tsunamisresembled, beyond that they were long water waves Even empirical re-lationships did not exist to relate the size of the wave offshore to the runupwith inundation, and, what can one only still describe as confusion, remained

as to the order of approximations used in the different analytical approaches

Worse, the few historic photos of advancing tsunamis from the 1946 Aleutianand 1983 Japan Sea events were interpreted as suggestive of advancing tur-bulent bores, i.e., fluid structures notoriously difficult for computations Mostpeople who watched live footage from the 2011 Japan tsunami can visualizetsunamis better than the few tsunami experts in the early 1980s could.Beginning in the 1980s, detailed modeling tools and high-resolution,small-scale laboratory experiments become available Many of the existingresults were synthesized into powerful analytical and numerical tools, andthen validated with laboratory experiments, thus setting the stage for theadvances in the now widely used tsunami forecast models (FMs) The 1990sshowed rapid progress toward a more realistic understanding of the entiretsunami evolution process from generation to runup Not only did large-scalelaboratory data become available (Briggs et al., 1995; Liu et al., 1995) butalso tsunamis started to be reported at a rate of almost one per year,debunking their extreme hazard status, at least for moderate events Post-tsunami surveys started being carried out after every event, and observationshelped to motivate advances.

With hindsight, no critical mass of scientists studying tsunamis existed untilthe early 1990s The growth was precipitated through a series of landmarkworkshops which allowed for identification of the show stoppers and, later, forintermodel comparison (Synolakis and Okal, 2005) The first took place in TwinHarbors, Catalina Island, California, in 1990 This workshop brought togetherapplied mathematicians and coastal engineers, and was geared more towardunderstanding the state-of-the-art of tsunami hydrodynamics with the emphasis

on how to best validate numerical and analytical tools, then under development(Liu et al., 1991) The main conclusions were that the shallow water model wasadequate for applications of geophysical interest and also that there was apervasive need for laboratory data for long waves propagating in two directions

to allow further progress in computational models No realization existed of theimportance of the initial condition, or of how an appropriate one could be derivedfrom geological or geophysical considerations, and the solitary wave modelremained the standard All this was to change

The deficiencies of threshold models1triggered rapid development of dimensional numerical inundation models, i.e., models that include shorelinemotions in the tsunami evolution calculations Comparisons between field dataand model predictions are referred to as model verification and are a crucialpart of any scientific modeling effort Without comparison to real-world data

two-no basis exists to accept the predictive capability of any model To underlinethis process, another workshop was organized at Friday Harbor, Washington,

in 1995 (Yeh et al., 1996) The focus was the validation and verification of

1 Refers to the models that interrupt the computation at some threshold offshore location, such as

at 10 m water depth.

computational codes to predict runup and inundation A conspicuous teristic of almost all models presented was their gradual evolution fromthreshold one-dimensional propagation models, to one-dimensional inundationmodels, to threshold two-dimensional models, to two-dimensional inundationmodels This evolution over a 10-year period allowed modelers to identifynuances and artifacts The 1995 Friday Harbor workshop showed that givenreasonable initial data, the predictions of runup heights were correct to the firstorder, and therefore attention shifted to defining realistic initial conditions forthe computations.

charac-In 1995, the Workshop on Seafloor Deformation Models took place inSanta Monica, California (Synolakis et al., 1997) There was then wideconsensus that the seismic moment, the hypocentral location, and the dip andstrike angles are reliably determinable in the short term for first-orderinitialization of hydrodynamic computations, and these estimates are suffi-cient for differentiating between small and large events Eddie Bernard andFrank Gonza´lez presented NOAA’s plans for the development of network ofinstruments to record the free-field signature of tsunamis in the deep ocean.These are tsunamographs, also now known as DARTs

The quest for more realistic initial conditions was catapulted by the 1998Papua New Guinea (PNG) tsunami, whose trigger, although controversial atfirst, was finally shown to have been a submarine landslide Another work-shop took place in 2000 at the University of Southern California, LosAngeles, California, to discuss submarine mass failures and their conse-quences A companion North Atlantic Treaty Organization-sponsoredAdvanced Research Workshop on Underwater Ground Failures on TsunamiGeneration, Modeling, Risk and Mitigation took place in Istanbul, Turkey, in

2001 with similar objectives but wider international representation (Yalciner

et al., 2003)

In summary, at the dawn of the twenty-first century, the tsunami munity had grown by a factor of two within a decade, and sufficient under-standing existed of tsunami sources and computations to start developinginundation maps for emergency preparedness The development of tsunamihydrodynamics and tectonic tsunamis is discussed bySynolakis and Bernard(2006) and by Shuto (2003)with a historical point of view Synolakis andKaˆno
glu (2009)discuss tsunami science from the perspective of development

com-of validated and verified numerical models Here, we will provide a briefsummary of different visualizations of tsunamis, then proceed to discussnumerical codes

2.2 SIGNIFICANT ADVANCES IN TSUNAMI SCIENCE

BEFORE THE 2004 BOXING DAY TSUNAMI

As with all incompressible fluid motions, the evolution of tsunamis can

be described by approximations of the NaviereStokes equations Even

when these three coupled nonlinear differential equations are mated,2exact solutions are only possible for a few idealized initial wave-forms These exact solutions are very useful in helping to validatenumerical models and to understand the underlying phenomenology Lab-oratory experiments that establish the ground truth are equally useful and offundamental importance in benchmarking numerical procedures (Synolakis

approxi-et al., 2008)

Before discussing the now-standard computations of tsunami impacts, webriefly describe what we feel were five seminal advances in the past threedecades; the calculation of the directivity of tsunamis and experiments withidealized seafloor deformations resulting the establishment of the solitarywave model, the analytical results and experiments with solitary wave runup,the demise of the solitary wave model and the realizations that the front wave

in a tsunami train is dipole shaped, development of large-scale laboratory andfield benchmark tests, and the realization of tsunami generation by landslidesresulted from moderate earthquakes

1 The fact that impacts from tsunamis originating far-field were localized,and at times appeared capricious, was first explained byBen-Menahem andRosenman (1972) They used linear theory to calculate the two-dimensional radiation pattern from an underwater moving source andshowed that tsunami energy radiates primarily in a direction normal to therupturing fault The concept of source directivity predated the identification

of the 1700 Cascadia earthquake by Satake et al (1996) and helped toexplain far-field effect of the 1755 Lisbon (All Saints’ Day) tsunami, as acombination of source directivity and focusing by irregular bathymetry(Woods and Okal, 1987; Satake, 1988) Okal et al (2003)reported fieldobservations of the 1946 Aleutian tsunami in the far-field, and concludedthat a large slow earthquake and a landslide must have occurred concur-rently to have caused the observed far-field distribution and near-fieldrunup Emile Okal used classic directivity arguments to show that the

2004 Boxing Day tsunami was caused by a long fault, in the early event days, when there were two competing scenarios for the fault motion.Directivity arguments are not helpful in estimating the coastal impact oftsunamis, beyond identifying qualitatively areas that may be at higher riskthan others To understand the shape of the waves on the free water surfacegenerated by impulsive motions, Hammack (1973, 1972) used a novelgeneration method where one end of a laboratory channel had a shortsection that could be impulsively lifted or dropped He measured preciselythe evolution of the resulting waveforms over a constant depth Hammackthen related the initial wave to the wave motion at large distances, and

post-2 Peregrine (1966) provided a comprehensive exposition of the orders of approximation through a perturbation expansion.

predicted that certain initial conditions would generate a series of solitarywaves at infinity.

It was thus clear, or so it seemed, that solitary waves were an appropriatemodel for tsunamis at least in the far-field, given that most seafloor dis-turbances would cause waves which eventually would become solitary.This was a great conceptual advance, and triggered a race between Caltech,Stanford, and Massachusetts Institute of Technology to find how solitarywaves evolved over the continental shelf; seeGoring (1978) andMadsenand Mei (1969) The stage was thus set for the calculation of the tsunamirunup, the most relevant parameter for estimating impacts

The runup (R in Figure 2.4) is the maximum elevation with respect tothe initial shoreline that the wave reaches The region between themaximum runup and the initial shoreline is the inundation An inundationdepth is the overland flow depth reached as the tsunami evolves overinitially dry land, and of course it is time dependent Measurements offlow depths after a tsunami usually identify the maximum flow depthreached at that location

2 To calculate the evolution of a solitary wave and its runup, Synolakis(1987, 1986)solved the boundary value problem of the nonlinear shallowwater wave (NSW) equations He defined the latter as a long waveevolving over constant depth and then climbing up a sloping beach(Figure 2.4) His work resulted in the following scaling lawdnow known

as the runup law,

R=d ¼ 2:831pffiffiffiffiffiffiffiffiffifficotbðH=dÞ5 =4:The coefficient in this equation was calculated analytically Synolakisproceeded with experiments at the Caltech Laboratory, then directed byProfessor Fred Raichlen, to measure solitary wave runup.Synolakis (1987,1986)compared the analytical predictions with laboratory measurementsand found excellent agreement (Figure 2.5)

Synolakis (1987, 1986) introduced a solution to the seminal nonlineartransformation developed by Carrier and Greenspan (1958) which

FIGURE 2.4 Definition sketch for the canonical problem, i.e., evolution of a long wave over a constant depth first, and then climbing a sloping beach.

FIGURE 2.5 (Left) Laboratory data for maximum runup of nonbreaking waves climbing up different beach slopes: 1:19.85 ( Synolakis, 1986 ); 1:11.43, 1:5.67, 1:3.73, 1:2.14, and 1:1.00 ( Hall and Watts, 1953 ); and 1:2.75 ( Pedersen and Gjevik, 1983 ) Solid line represents the runup law (Right) Maximum runup of solitary waves over a 1:19.85 sloping beach in nonbreaking and breaking regimes ( Synolakis, 1986 ).

transformed the NSW equations into a single linear equation solvable withstandard methods He proceeded to calculate the nonlinear evolution forcomplex spectral distributions, such as those of solitary waves, through theentire runup and rundown process for the canonical problem, and thusdemonstrated what is now known as the runup invariance, i.e., for the sameinitial condition, linear and nonlinear theories predict mathematicallyidentical results Then laboratory data and his analytical solutions remainthe standard for benchmarking numerical codes (Synolakis et al., 2008).Despite the availability of analytical results and small-scale laboratorymeasurements, in the early 1990s, there were not even one-dimensionalcodes that would reliably predict runup Although large-scale, two-dimensional experiments had been planned, and were in fact just starting atthe Waterways Experiment Station in Vicksburg, Mississippi, tsunamisstarted being reported more frequently than before These reports, oftenassociated with descriptions of the resulting human drama, intensified theneed for quality benchmark data, but also changed the focus from solitary

to dipole-shaped N-wave, i.e., wave which has depression and elevationparts

3 The September 1, 1992, Nicaragua tsunami launched a scientific decade

of modern tsunami observations and surveys More scientists pated in this survey than any other before 2004 Beginning in 1992, post-tsunami surveys have been carried out by the highly interdisciplinaryInternational Tsunami Survey Teams (ITSTs), immediately following eachevent (Synolakis and Okal, 2005) The ITST scientists measured runup,overland flow depths, inundation distances, and on-occasion water cur-rents, and they interviewed eyewitnesses to obtain information about thetiming of the tsunami arrival and the community response Three distinctfeatures were observed during the Nicaragua tsunami:

partici-One, the parent earthquake was clearly a tsunami earthquake,3 and thewave it triggered killed more than 160 people Tsunami earthquakes hadbeen studied by Newman and Okal (1998) who introduced a slownessparameter,Q ¼ log10(EE/M0), where EEis the estimated energy carried byhigh-frequency seismic body waves and M0is seismic moment measured

on long-period surface waves This parameter can be determined in realtime and defines how slow an earthquake is, i.e., whether it is unusuallyefficient in generating tsunamis

Two, the wave, despite having been generated very close to the shore,featured remarkable directivity in its impact At El Transito, the mostdevastated site, runup values ranged up to 11 m; in the adjoining beach

3 A tsunami earthquake is a seism whose tsunami has far greater amplitude than expected from its conventional magnitude, and its characteristic slow motion is often reported as not felt by eyewitnesses ( Okal, 1993; Kanamori, 1972 ).

Playa Hermosa, even the beach umbrellas had been left standing Clearly,two-dimensional computations at a resolution of at least 50 m are likelynecessary to resolve such differences Not only were inundation modelsabsent then but also such resolutions were not possible then with ordinarycomputers in reasonable times.

Three, the earthquake-triggered tsunami manifested itself first with ashoreline recession, which was the only precursor for the coastal residents.Sadly, they did not identify it as a tsunami, since the shaking from the

M0¼ 3.4  1027dyn cm parent earthquake was not felt by most coastalresidents queried during the subsequent field survey

This last observation led to a paradigm change, i.e., considering N-wave as

an appropriate initial condition for tsunami modeling instead of solitarywaves (Tadepalli and Synolakis, 1994) Tsunamis that cause the initialshoreline to retreat are now known as leading depression N-waves (LDNs)

In less than 1 year after the 1992 Nicaragua tsunami,Tadepalli and olakis (1994) presented analytical results that showed that LDNs hadhigher impact than their mirror images, leading elevation N-waves (LENs).Tadepalli and Synolakis (1994) derived asymptotic results for differentfamilies of N-waves and showed that LDNs always runup higher than theircompanion LENs LDNs had been believed hydrodynamically unstable;the crest was supposed to quickly overtake the trough Controversy ensueddespite additional reports of LDNs striking the south coast of Java (1994),Mindoro Island (1994), Shitokan Island (1994), and Manzanillo (1995)

Syn-In 1996, Tadepalli and Synolakis further refined the N-wave model andsuggested an explanation to reconcile the reports of receding shorelineswith prevailing inverse-scattering-based theory and the resulting solitarywave paradigm (Tadepalli and Synolakis, 1996) First, they showed thatN-waves were one particular solution of the parent equations of motionwhen forcing the linear shallow water wave (LSW) equation with a step-function motion They then showed N-waves of geophysical scaleswould have to evolve more than once around the perimeter of the Earth, toreach the idealized infinity of inverse scattering theory, i.e., trains of sol-itary waves They suggested that because of the nature of the dipolarseafloor deformation in subduction zones, LDNs would strike the adjacentshoreline, while LENs would move toward the open ocean The fact thatthe near-field manifestation of a tsunami is an LDN was finally settled inthe 2004 Boxing Day tsunami (Satake, 2007), with hundreds of de-scriptions from eyewitnesses confirming it

4 Before anyone had the chance to absorb the impacts of the Nicaraguatsunami, a 5.1 1027dyn cm earthquake triggered a tsunami on December

12, 1992, in the eastern part of Flores Island, Indonesia Runup heightsranged from 5 to 26 m along the coast This event is mostly remembered bythe catastrophe in the conical-shaped volcanic Babi Island located betweenthe epicentral region and Flores Island, about 5 km directly north of Flores

coast The tsunami attacked from the north of Babi, yet the impact washigher on the lee side of the island, destroying two fishing villages nor-mally protected from swell waves (Yeh et al., 1994) (Figure 2.6) Thisraised some controversy as to whether the enhanced runup was due to someunidentified circular island effect or reflection of the tsunami off Flores.

By serendipity, as a result of the 1990 Catalina workshop, large-scaleexperiment had already been planned to measure the interaction of soli-tary waves with a conical island A series of laboratory tests were under-taken for a laboratory model of a 7.2-m-base-diameter island with a slopeangle of 14 (Kaˆno
glu and Synolakis, 1998; Kaˆno
glu, 1998; Briggs et al.,1995; Liu et al., 1995) (Figure 2.6) Solitary waves of different crestlengths were generated and their runup were measured These experimentsappear to be the first laboratory visualization of a tsunami catastrophe overrealistic two-dimensional bathymetry and topography

The experiments demonstrated that once the wave hits the circular island,the crest splits into two waves that propagate around the island having theircrest perpendicular to the shoreline and collide behind it, in a spectaculardemonstration of constructive interference (Yeh et al., 1994) The experi-mental data set has been used extensively for benchmarking of numericalcodes (Titov and Synolakis, 1998), as described inSynolakis et al (2008).Further, Kaˆno
glu and Synolakis (1998) were able to compute the runuparound a conical island using entirely analytical tools, based on theSynolakis (1987) methodology, thus verifying the applicability of lineartheory even in the two-dimensional problem

On July 12, 1993, the Hokkaido-Nansei-Oki earthquake (M0¼ 4.7 

1027dyn cm) generated a tsunami that devastated the island of Okushiri,west of Hokkaido Field measurements identified extreme runup value of

33 m at a river gully near Monai, and currents ranging to up 18 m/sec Thewave overflowed a 7-m-high protection wall and destroyed the town ofAonae High-resolution seafloor bathymetry before and following the eventallowed meaningful identification of the seafloor deformation Titov and

FIGURE 2.6 (Left) Catastrophe on the back side of Babi Island ( Yeh et al., 1994 ) (Right) Top view

of the laboratory manifestation of a solitary wave attacking a conical island to model the catastrophe

in Babi Island in 1992 ( Kaˆno
glu and Synolakis, 1998; Kaˆno
glu, 1998; Briggs et al., 1995; Liu et al.,

1995 ) Top shows back of the island with respect to incoming wave in both insets.

Synolakis (1997)were able to successfully model the extreme runup Here,

it became clear that the details of the timing of seafloor deformation were not

as important as some believed, at least compared to a fairly accuratedescription of the seafloor deformation Numerical modeling of the eventshowed that a resolution of 5 m was necessary to predict the extreme runup.Modeling of this event has become another benchmark test for modelvalidation

5 The PNG tsunami on July17, 1998, resulted in over 2,100 fatalities, despitethe relatively small size of the parent earthquake It changed tsunamiscience on a scale analogous to what the 2004 megatsunami did Excep-tional runup heights, reaching 15 m at Arop, but concentrated on a 25-kmstretch of coastline, were measured byKawata et al (1999) The excessiveamplitude and concentration of the runup were incompatible with anymodeling based on the excitation of the tsunami by a seismic dislocationand eyewitness reports generally indicated that the tsunami had arrived atleast 10 min later than predicted by all acceptable models of propagation(Synolakis et al., 2002) In addition, the earthquake was not a tsunamiearthquake Finally, Okal (2003) identified the hydroacoustic record inWake Island which demonstrated beyond doubt the characteristic signature

of the landslide through comparisons with the acoustic signatures at thesame locale from the earthquake and its main aftershock

Kawata et al (1999)proposed that an underwater landslide generated thetsunami Later, a number of hydrographic surveys (e.g.,Sweet and Silver,

2003) identified a 4 km3slump contained in a bowl-shaped amphitheater,located 25 km away from the coast Numerical modelings that used thelandslide as the source of the tsunami successfully modeled the runupalong the Sandaun coast (Synolakis et al., 2002; Heinrich et al., 2000) As aresult, hazard posed by relatively moderate, approximately magnitude 7level, earthquakes started being reexamined (Borrero et al., 2004; Bardet

et al., 2003; Borrero et al., 2001) for their submarine landslide-generationpotential

By the end of the 1990s, no analytical results existed for waves generated

by submarine landslides, and empirical formulas produced vastly differentpredictions for the initial wave height, even for the same slide geometry.Conceptually, the physical problem is challenging for it involves a time-dependent boundary Although a forcing term can be included in theshallow water wave equations with small additional computational cost,the timescale of the landslide motion remains undefined If the slide is veryclose to the initial shoreline, the computations become more evolved,because now not only the shoreline but also the seafloor moves in the sameregion To provide an analytical benchmark problem for numerical codes,Liu et al (2003)developed an analytical solution for a subaerial landslidethat starts moving from the shoreline Again, this solution has become abenchmark for validating numerical codes (Synolakis et al., 2008)

By the 2004 Boxing Day tsunami, substantial advances had been achieved

in the development of benchmarked numerical codes California was the first

to have started producing inundation maps for emergency planning (Eisner

et al., 2001), and soon thereafter most Pacific states of the United States werefollowing Landslide tsunamis had started being considered, and increasedemphasis was given to documenting and understanding tsunamis in the past

The 2004 Boxing Day tsunami prompted hundreds of photos, some found

in cameras that were washed by the tsunami In many of these photos peopleappear to pose in front of the advancing wavefront, which at the time of thepicture taking was offshore This was perplexing, why did these people not runaway as they saw the tsunami advancing, and instead think they had the time totake pictures? One remarkable observation whose usefulness was not entirelyrecognized until these pictures were examined is the acceleration of thewavefront past the initial shoreline As shown in Synolakis (1987), in theevolution of the front of the solitary wave, the wave first slows down as itclimbs up the sloping beach, due to the reduction in depth; recall that thewave celerity czpffiffiffiffiffiffiffiffiffiffiffighðxÞ, where h(x) is the changing depth Once the wavehits the initial shoreline, it slows down, but accelerates again, before decel-erating to its ultimate on-land penetration point, the maximum wave runup.This appears to happen even far inland, for different reasons

In a video taken near the Grand Mosque in Aceh, one can infer that thewavefront first moved at speeds less than 8 km/h, then accelerated to 35 km/h(Fritz et al., 2006) The same phenomenon is probably responsible for themesmerization of victims during tsunami attacks, first noted in a series ofphotographs of the 1946 Aleutian tsunami approaching Hilo, Hawaii Thewavefront appears slow as it propagates initially past the shoreline, leading to

a sense of false security; it appears as if humans can outrun it, and then thewavefront accelerates rapidly as the main disturbance arrives A series of three

photographs from the 1995 Manzanillo tsunami taken by a survivor whichshow three men being unable to outrun a very thin wavefront underscores thispoint (Borerro et al., 1997).

With the exception of recent tsunamis in the Solomon Islands, it is notcommon that two tsunamis triggered by comparable earthquakes strike thesame region within a 5-year period This happened in PNG in 1998 and

2002 Based on the measured differences between the 1998 and 2002 namis, Okal and Synolakis (2004)fitted Gaussian distributions to the long-shore runup measurements from real events and the computed runup valuesover idealized geometries using MOST to augment the historic data set.They defined two dimensionless parameters, one each for tectonic andlandslide tsunamis These invariants characterize the tsunami source, land-slide versus dislocation, yet they are largely independent of the exact pa-rameters describing the respective sources Hence, they showed that theseinvariants can be used as discriminants to identify the nature of the tsunamisource

tsu-This analysis was useful, because coseismic landslides are not uncommon,yet it had been very difficult to differentiate from seismic recordings alonewhether the main tsunami was triggered by the earthquake or the landslide, asthe PNG slide demonstrated This is even more so for studies of paleo-tsunamis The geosciences have several scaling laws to allow for quantification

of parameters that are otherwise grueling to infer

Note that one fundamental observation linking the tsunami source withinundation, although never published as such, is George Plafker’s Whilesurveying the aftermath of the 1964 Great Alaskan tsunami (Pararas-Carayannis, 1972), Plafker proposed that the maximum runup locally does notexceed twice the height of deformed seafloor offshore (Plafker, 1965; Plafker

et al., 1969) This is now referred to as the Plafker rule, and has largelywithstood the test of time, after being unrecognized for three decades(Synolakis and Okal, 2005) The Okal and Synolakis (2004) parameter isprecisely what the empirical Plafker rule suggests The 2004 tsunami did notcontradict this rule, even at Longa near Banda Aceh

It is instructive here to briefly discuss the history of landslide experiments,

at least from the point of view of classical hydrodynamics Wiegel (1955)performed landslide experiments using a wedge-shaped block sliding down aplane beach and, measuring the waves propagation offshore, concluded thatonly about 1 percent of the slide energy is converted to energy in the generatedwave However, his emphasis was on the shape of the wave moving offshore

In an effort to better understand the generation and runup of waves fromsubmarine and subaerial slides, Raichlen and Synolakis (2003) conductedlarge-scale experiments at Oregon State University, Corvallis, Oregon(Figure 2.7) FollowingWiegel (1955)’s experiments, they first used a vertical-face wedge block, and then semispherical and rectangular boxes of equalvolume in the wave tank with the depth of 2.44 m Two configurations of the

wedge on the slope were used, one with the front face of the wedge verticaland another with the wedge turned end-for-end so that for this orientation thetop and front faces were neither horizontal nor vertical By varying the weight

of the blocks, Raichlen and Synolakis (2003) were able to vary the initialacceleration, whereas the initial position varied from totally aerial to totallysubmerged After its release, the sliding wedge generated a leading positiveseaward propagating wave, but the water surface above the wedge is depressedand causes the shoreline to retreat first The experiments revealed a depressionforming over the wedge as the motion begins For the aspect ratio of theirboxes, they observed that wave generation became inefficient as the submer-gence of the blocks exceeded one block height The results from theseexperiments defined one of the four benchmark problems in the 2004 National-Science-Foundation-supported Catalina workshop (Liu et al., 2008), and havesince been used as another benchmark test for hydrodynamic model validation(Synolakis et al., 2008)

These experiments were the reality check and validation exercise of the fullDNS solution of Liu et al (2005) (Figure 2.7) However, hydrodynamiccomputations of the evolution of the free surface motions from landslide wavesare very challenging The seafloor is continuously deforming, and the impact

of the solid slide with the water surface during subaerial generation maytrigger local breaking Breaking can also happen if the slide moves rapidly and

if it is located very close to the surface Further, the wedge geometry used inthe experiments has sharp corners which trigger further instabilities, even infull DNS of the parent NaviereStokes equations of motions Hence, not onlyextreme near-shore or onshore landslide tsunami generation in the laboratoryremains a vexing calculation but also simulations of prototype landslides areeven more difficult, for the timing of the slide remains an important but poorlyunderstood parameter, exquisitely dependent on several constitutive parame-ters of the slide material

In terms of the work in deformable slides, Fritz (2002) investigatedtsunamis generated by granular subaerial landslides in a two-dimensional,physical laboratory model, at the Swiss Federal Institute of Technology.The landslide material in the experiment matched the rockslide character-istics Hermann Fritz and his collaborators determined that the relevantparameters for free surface wave generation were the granular slide mass,the slide impact velocity (vs), the still water depth (h), and the slide thickness(Fritz et al., 2003a,b) Most of the impulse waves were located in the in-termediate water depth regime, yet the propagation velocity of the leadingwave crest closely followed the theoretical approximations for solitarywaves, which are long waves The slide Froude number (F¼ vs=pffiffiffiffiffigh

, where

g is the gravitational acceleration) was identified as the dominant parameter.The physical model results were then compared to the giant rockslidegenerated impulse wave which struck the shores of the Lituya Bay, Alaska,

in 1958 (Miller, 1960) That slide produced runup in excess of 400 m along

the steep fjord walls A cross-section of Gilbert Inlet was rebuilt at smallscale and the measured wave runup matched the trimline of forest destruc-tion (Fritz et al., 2001) The Lituya Bay experiments highlighted the for-mation of an impact crater, as the slide plunged into the fjord, thusincreasing the water displacement The runup measurements revealed a shortpropagation distance and runup of a solitary wave exceeding the breakinglimit by a factor of 1.5, likely due to the narrow Gilbert inlet and the steepheadland Recently, Mohammed and Fritz (2012) conducted three-dimensional experiments on tsunami generation by subaerial landslides inthe tsunami wave basin of the Network for Earthquake Engineering Simu-lation at Oregon State University in Corvallis, Oregon, USA They used anovel pneumatic landslide generator and showed a sequence of the wavegeneration by landslide impact (Figure 2.7) They characterized the landslide

by its volume, front velocity, length, thickness, and width on the hillslope atimpact They determined that 1e15 percent of the landslide kinetic energy atimpact is converted into the wave train energy They also determined that thewave amplitudes, periods, and wavelengths are related to the landslide pa-rameters at impact with the landslide Froude number being a dominantparameter This experimental data set on tsunamis generated by three-dimensional, deformable, granular landslides could serve validation of nu-merical models

One vexing question raised by the PNG landslide wave was whether thecoastal evolution of landslide tsunamis could be effectively modeled withthe NSW equations, or whether the Boussinesq equations are necessarydtheyare computationally far more complex Landslide waves are steeper andshorter than tectonic tsunamis and disperse more rapidly.Lynett et al (2003)compared results from Boussinesq and NSW models with the field measure-ments and concluded that while the near-shore evolution was predicted to bedifferent, the runup predictions were not In this regard, and given theconsiderable known uncertainties in characterizing the landslide motion, itappears that computations with Boussinesq-type models are an overkill when

it comes to determining inundation, and likely misleading Such computationsare reminiscent of adding decimal digits in a computation where even thesignificant figures cannot be determined with certainty

The field survey of the 2010 Mentawai tsunami revealed another terintuitive observation for tsunamieisland interaction (Hill et al., 2012) Therunup behind small islands off the Mentawai in Indonesia was higher than inareas not sheltered by the islands.Stefanakis et al (2013)used active learningmethods and employed numerical solutions of the NSW equations for thebathymetry of a conical island off a shoreline with a plane beach and anincoming solitary waveform They used seven parameters to describe thephysical problem; even if they had only tried 10 values for each of the sevenparameters, they would have required 100,000 simulations to determine whichcombinations produced higher runup along the continental coastlines sheltered

coun-by the island With active learning, they only had to do 200 simulations todetermine the global maximum In none of their simulations did the islandoffer any additional protection The Economist magazine in its review of thearticle commented on the dangers of insularity, and of how mainland residentsshould be informed of the additional hazard offshore islands posed in case of atsunami attack The situation may become even worse if resonant wave in-teractions occur (Stefanakis et al., 2011).

Stefanakis et al (2011) numerically simulated the one-dimensional NSWequations to investigate the boundary value problem for plane and morecomplex bathymetries forcing with monochromatic waves, as well as virtualwave-gage recordings from real tsunami simulations They observed resonantphenomena between the incident wavelength and the beach slope, which result

in enhanced runup of nonleading waves The resonance occurs due toincoming and reflected wave interactions, and the actual amplification ratiodepends on the beach slope They suggested that these phenomena can explainwhy it is not always the first wave that causes the highest runup, as well as whythe tail of a single wave may produce leading-order runup values However,when the bathymetry is more complex, it is not clear to what extent resonance

is attributed to wave trapping and generation of harmonics Resonant anisms are not limited to the plane beach paradigm (Ezersky et al., 2013) butcan be observed in more complex bathymetries as well, thus suggesting thatlocal runup amplification is not rare

mech-An interesting question that has arisen from field surveys is whether theenhanced runup observed in theoretical investigations for one-dimensionalN-waves can explain real tsunami impacts with two-dimensional bathyme-tries Recently,Kaˆno
glu et al (2013)introduced a new analytical solution tostudy the propagation of a finite strip source over constant depth, using LSWtheory Their two-dimensional strip N-wave represents the waves generated

by tectonic seafloor displacements Kaˆno
glu et al (2013)’stwo-dimensionalsolution is not only exact but also general and allows the use of realisticinitial waveforms They showed the existence of focusing points for N-wave-type initial displacements, i.e., points where unexpectedly large wave heightsmay be observed (Figure 2.8) Focusing points exist using linear nondisper-sive, linear dispersive, nonlinear nondispersive, and weakly nonlinear weaklydispersive theories, all approximations of the parent NaviereStokes equations.They discussed geophysical implications of their solution using the July17,

1998, PNG and the July 17, 2006, Java tsunamis (Fritz et al., 2007) as amples Their results may also help to explain high runup values observedduring the March 11, 2011, Japan tsunami, which are otherwise not consistentwith existing scaling relationships They concluded that N-waves generated bytectonic displacements feature focusing points, which may significantlyamplify runup beyond what is often assumed from widely used scalingrelationships

ex-(a) Initial wave (b) Evolution (c) Overall maximum

FIGURE 2.8 (Top) Definition sketch for focusing Evolution of an N-wave source over a stant depth calculated using the MOST model: (a) initial wave, (b) evolution, and (c) maximum amplitude at each grid point for entire propagation (Middle) The July 17, 2006, Java tsunami field runup and wave height measurements ( Fritz et al., 2007 ) (red and blue dots denote observed tsunami heights (m) and observed runup values (m), respectively) (Bottom) Reverse tsunami travel time (RTTT) contours for Permisan (red filled triangle) where the runup exceeded 20 m, while runup values ranged from 5 to 7 m at the surrounding areas Three of the NCTR’s 100 by

con-50 km 2 tsunami source functions (white rectangles) are presented as a possible source mechanism considering focusing at Permisan The red arrows indicate approximate locations of two positive waves from the sides of the depression and a positive wave from the center of the elevation, which arrive simultaneously to the focusing point (red filled triangle) considering the same RTTT (44 minutes) contour After Kaˆno
glu et al (2013)