Hybrid modeling of the mega-tsunami runup in Lituya Bay after half a century

Abstract

The largest mega-tsunami dates back half a century to 10 July 1958, when almost unnoticed by the general public, an earthquake of M w 8.3 at the Fairweather Fault triggered a rockslide into Lituya Bay. The rockslide impact generated a giant tsunami at the head of Lituya Bay resulting in an unprecedented tsunami runup of 524 m on a spur ridge in direct prolongation of the slide axis. A forest trim line and erosion down to bedrock mark the largest runup in recorded history. While these observations have not been challenged directly, they have been largely ignored in hazard mitigation studies, because of the difficulties of even posing - much less solving - a well-defined physical problem for investigation. We study the mega-tsunami runup with a hybrid modeling approach applying physical and numerical models of slide processes of deformable bodies into a U-shaped trench similar to the geometry found at Lituya Bay.

Full text

Hybrid modeling of the mega-tsunami runup in Lituya Bay after half
a century
Robert Weiss,
1
Hermann M. Fritz,
2
and Kai Wu¨nnemann
3
Received 20 February 2009; revised 1 April 2009; accepted 10 April 2009; published 9 May 2009.
[1] The largest mega-tsunami dates back half a century to
10 July 1958, when almost unnoticed by the general public,
an earthquake of M
w
8.3 at the Fairweather Fault triggered a
rockslide into Lituya Bay. The rockslide impact generated a
giant tsunami at the head of Lituya Bay resulting in an
unprecedented tsunami runup of 524 m on a spur ridge in
direct prolongation of the slide axis. A forest trim line and
erosion down to bedrock mark the largest runup in recorded
history. While these observations have not been challenged
directly, they have been largely ignored in hazard mitigation
studies, because of the difficulties of even posing – much
less solving – a well-defined physical problem for
investigation. We study the mega-tsunami runup with a
hybrid modeling approach applying physical and numerical
models of slide processes of deformable bodies into a
U-shaped trench similar to the geometry found at Lituya
Bay.
Citation: Weiss, R., H. M. Fritz, and K. Wu¨nnemann
(2009), Hybrid modeling of the mega-tsunami runup in Lituya Bay
after half a century, Geophys. Res. Lett., 36, L09602, doi:10.1029/
2009GL037814.
1. Geographical and Geological Setting
[2] Lituya Bay is a T-shaped tidal inlet cutting through
coastal lowlands and foothills of the Fairweather Range on
the Pacific south coast of Alaska (Figure 1). The bay fills
and slightly overflows a glacially carved depression with
characteristic submarine contours [Miller, 1960]. The pro-
nounced U-shaped trench with steep side walls and a broad
flat seafloor is 12 km long, up to 3.3 km wide and 220 m
deep. The Gilbert and Crillon inlets at the head of the bay
are part of a great trench that extends to the northwest and
southeast as a topographic expression of the Fairweather
transform fault.
[
3] Giant waves have likely occurred in Lituya Bay at
least five times in the past two centuries as a result of the
interplay between the geological and climatic setting [Miller,
1960]. Evidence of extreme wave-runup heights in 1853 or
1854, 1936 and 1958 have each been identified by sharp
trim lines of chopped trees to elevations above 100 m.
Two additional giant waves may have occurred in 1874
and 1899. These are not typical landslide waves as often
occur in other Alaskan fjords [Plafker, 1969; Synolakis
et al., 2002].
[
4] On 10 July 1958 beginning at 6:16 UTC intense
shaking from an M
w
8.3 earthquake [Tocher and Miller,
1959] caused 6.4 m horizontal and 1 m vertical tectonic
movement. An estimated rockslide volume of about 30 
10
6
m
3
was released on the northeast wall of the Gilbert
Inlet up to an elevation of 915 m on a slope averaging
40 degrees (Figure 2). The slide material was composed of
amphibole and biotite schist. The initial slide geometry is
assumed to be a prism spanning 730 m to 915 m in width
and a thickness of 92 m normal to the slope. The lower
extent of the initial landslide position remains undefined.
The slide length was estimated to 970 m with a center of
gravity at 610 m elevation [Slingerland and Voight, 1979;
Miller, 1960]. The landslide sheared off and washed away
up to 400 m of ice from the Lituya Glacier front resulting in
a vertical ice wall perpendicular to Gilbert Inlet. The
landslide impact generated tsunami produced unprecedented
runup heights of 524 m on a headland in slide axis
prolongation and 208 m on the south shore of Lituya Bay.
The only other two landslide tsunami events known to
produce runup heights exceeding 200 m are Vajont reser-
voir in 1963 [Mu¨ller, 1964, 1968] and Spirit Lake in 1980
[Voight et al., 1981, 1983].
2. Experiments
[5] Based on generalized Froude similarity, Fritz et al.
[2001] built a 2D physical model of the Gilbert inlet scaled
at 1:675. The prototype unit volume of the slide was
determined to 37.2  10
3
m
3
/m based on a volume of
30.6  10
6
m
3
spread over an average width of 823 m. The
bathymetry and topography are simplified in the laboratory
by headlands with slope angles (a and b) of 45 degrees and
maximum uniform water depth (h) of 122 m at prototype
scale. The short tsunami propagation distance combined
with the confining wall formed by the Lituya Glacier may
justify a simplified two-dimensional approach given the
limited space for 3D spreading (Figure 2) [Fritz et al.,
2009].
[
6] The Lituya Bay rockslide w as modeled with an
artificial granular material (PP-BaSO
4
) matching the density
of the prototype schist. Given the unit volume, the slide
mass per unit width is m
0
= 98.5  10
3
t/m. The slide
granulate, initially contained in the slide box, is accelerated
by a pneumatic landslide generator to control landslide
dynamics and impact characteristics. Two laser-distance
sensors measure granular slide profiles before impact. A
laser-based digital PIV-system provides instantaneous
velocity vector fields in the slide impact and runup areas
providing insight into the kinematics of wave generation and
GEOPHYSICAL RESEARCH LETTERS, VOL. 36, L09602, doi:10.1029/2009GL037814, 2009
1
Department of Geology and Geophysics, Texas A&M University,
College Station, Texas, USA.
2
Civil and Environmental Engineering, Georgia Institute of Technology,
Savannah, Georgia, USA.
3
Museum fu¨r Naturkunde, Leibniz Institute, Humboldt University of
Berlin, Berlin, Germany.
Copyright 2009 by the American Geophysical Union.
0094-8276/09/2009GL037814
L09602 1of6

runup (Figure 3) [Fritz et al., 2003]. A capacitive wave gauge
is installed at a distance of 885 m from the slide impact along
with two runup gauges on the headland. In the physical
model, the slide mass is accelerated up to a prototype impact
velocity v of 110 m/s, which corresponds to an estimated free-
fall velocity with the centroid situated at 610 m elevation
[Law and Brebner, 1968; Noda, 1970], resulting in an impact
slide Froude number F = v/(gh)
0.5
= 3.18.
3. Hydrocode Modeling
[7] We adapted the multi-material hydrocode iSALE
(Impact Simplified Arbitrary Lagrangian Eulerian) [e.g.,
Wu¨nnemann et al., 2006, and references therein] to simulate
the Lituya Bay rockslide and tsunami. iSALE is a multi-
material, finite-difference hydrocode for simulating fluid
flows and deformations of solid bodies at subsonic and
supersonic speeds. A full description of the code is beyond
the scope of this paper and we refer to the manual of the
original code by Amsden et al. [1980] and more general
literature on hydrocode modeling, see, e.g., Pierazzo and
Collins [2004], Benson [1992] and Anderson [1987].
[
8] The basic approach of the algorithm used in iSALE is
to deform a regular grid of computational cells in a
Lagrangian step according to the velocity field computed
at the grid nodes. The deformed grid is then remapped (at
the end of each time step) onto the original orthogonal mesh
by advecting cell-based quantities (density, energy, momen-
tum) through cell boun daries. The overall method applied
then corresponds to an Eulerian solution scheme, where the
computational mesh is fixed in space and material flows
through it. To accurately simulate the movement of more than
one material in an Eulerian mesh, where material is fluxed
through a stationary mesh, requires the tracking of interfaces
between two materials within one cell (mixed cell). For
general information on interface tracking techn iques see,
e.g., Benson [2002].
[
9] The equations for conservation for mass, momentum,
and energy are solved by using a first-order upwind (full
donor cell) advection scheme. The material is treated
compressible, therefore an equation of state (EoS) is re-
quired to compute pressure as a function of density and
internal energy. Because compression is small (velocities
are much smaller than the speed of sound in the material),
we used, for simplicity, the Tillotson EoS [Tillotson, 1962]
for water, and granite for the slidebody and slope (for EoS
parameters see, e.g., Melosh [1989]).
[
10] To calculate the deviatoric stress tensor and its effect
on the velocity field, iSALE employs a deviatoric stress
model similar to that described by Collins et al. [2004] and
Ivanov et al. [1997]. In each time step, the second invariant
of the stress tensor in a cell is compared to the yield strength
of the material. Where the invariant exceeds the yield
envelope stresses are modified accordingly to meet the yield
strength of the material again.
[
11] The yield strength in the slide body is calculated by a
simple Drucker-Prager strength model with zero cohesion,
in which the yield strength Y is a linear function of pressure
Figure 1. Lituya Bay, Alaska satellite image (August 2001, Landsat) with superimposed 1958 landslide scar at the head of
the bay and forest trimline of tsunami runup after Miller [1960]. Note the forest destruction to a maximum runup elevation
of 524 m on a spur ridge and a maximum inundation distance of 1100 m from high-tide shoreline at Fish Lake.
L09602 WEISS ET AL.: THE 1958 LITUYA BAY TSUNAMI RUNUP MODELING L09602
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p: Y = C + mp (m is coefficient of internal friction and C =0
is cohesion). A Drucker-Prager material model appropri-
ately represents the behavior of granular material such as
gravel. For the rigid slopes and the basement we assumed an
infinite cohesion to avoid any movement or deformation
during the slide process. Water behaves like an inviscid
fluid in our model.
[
12] iSALE is validated against experimental studies of
hypervelocity impacts and other hydrocodes [Pierazzo et al.,
2008] and used successfully in modeling of meteorite impact
wave generation studies [Weiss et al., 2006; Wu¨nnemann
et al., 2007].
[
13] The general model setup is described in detail by,
e.g., Wu¨nnemann and Lange [2002]. iSALE supports two
different geometries: a Cartesian and a Cylindrical grid. For
two-dimensional computations, without radial spreading of
waves, the Cartesian coordinate system is used for the
modeling on prototype scale (Figure 2). Assuming a con-
stant volume of the slide body as in the laboratory experi-
ments, three parameters, (i) initial velocity, (ii) density, and
(iii) friction, constrain the wave generation. In order to match
the experimental data, an initial velocity is introduced to
meet the impact velocity of 110 m/s. The grains have a
density of r
g
= 2640 kg/m
3
, but the slide impact density is set
to the bulk density of the granular material, r
s
= 1610 kg/m
3
,
by introducing a porosity of 39%. iSALE supports treatment
of porosity as a function of volumetric strain [Wu¨nnemann
et al., 2006]; however, in our models we kept the porosity
constant at 39% during the slide process. Measured internal
friction coefficient of the granular material range between
0.9–1.0 [Fritz, 2002]. The friction coefficient of the slide
body in the model was set to m = 0.4 which corresponds to
the bed friction coefficient between the slope and the slide
body in the experiments. In the current version of iSALE it
is possible to use different internal friction coefficients for
the slope and the slide body, but the code does not allow for
specifying friction coefficients for interfaces between mate-
rials, e.g., slope and slide. For the dynamics of the slide
body it appears to be more important to match the bed
friction. Although the too small internal friction coefficient
of the slide body may enhance deformation of the body
during slide and impact into the water.
4. Results
[14] The time series of free surface elevations recorded by
the wave gauge documents the generation of a single impulse
wave which reaches its maximum 16 s after the impact at
152 m, propagating towards the headland (Figure 4). The
second crest after 48 s represents the wave reflection from
the head wall. Various empirical and theoretical predictive
relationships for the landslide-generated tsunami amplitude
Figure 2. Trimlines carved by tsunami in 1958: (a) NE_view of Lituya Bay from Cenotaph Island to Gilbert Inlet with
landslide scar at the head of the bay and trimlines of destructed forest with 524 m runup on spur ridge. (b) NW_view of
Gilbert Inlet with landslide scar, post_event Lituya Glacier front, forest destruction and soil erosion down to bedrock
(Photos: courtesy of USGS). (c) Gilbert Inlet illustration showing landslide dimensions, impact site and tsunami runup to
524 m on spur ridge directly opposite to landslide impact. Direction of view is north and the front of Lituya Glacier is set to
1958 post slide position. Illustration background is synthesized from two aerial photos recorded in 1997.
L09602 WEISS ET AL.: THE 1958 LITUYA BAY TSUNAMI RUNUP MODELING L09602
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were compared with the Lituya Bay benchmark experiment
[Fritz et al., 2004]. The solutions by Hall and Watts [1953]
and Synolakis [1986, 1987] for solitary wave runup on
impermeable slopes match the experimentally measured
wave runup and the observed elevation of forest destruction
in Lituya Bay with predictions of R = 526 m and R = 493 m
based on experimentally measured incident wave parameters
H = 162 m and h = 122 m [Fritz et al., 2001]. This confirms
the 160 m wave height by Slingerland and Voight [1979]
inferred from back calculation from the runup. The wave
height of the measured solitary-like wave exceeds solitary
wave breaking criteria H/h = 0.83 [Tanaka, 1986]. Con-
sequently, the leading wave does collapse into a bore in
exp eriment s without the headland providing sufficient
propagation distance for wave evolution [Fritz et al.,
2003]. However the solitary-like wave in Gilbert Inlet
does not extensively break due to the short propagation
distance and the steep headland slope [Jensen et al.,
2003].
[
15] The slide body deforms in the numerical simulation
as it moves down the slope and is shown just before
impacting the water in Figure 4b (t = 4 s). The maximum
of the first peak in time series of Figure 4g corresponds to
Figure 4c (t = 19 s). Shortly after the maximum wave height
passes the tide gauge at 885 m from the headland of the
wave impact, partial breaking of the generated wave is
indicated in Fig ure 4d. The water mass runup on the
headland slope with subseq uent resurge creates the second
crest shown in Figure 4e (t = 53 s). Severe wave breaking
can be observed near the hillslope slope. In Figure 4f, the
second maximum passed and the water mass moved the
slide body moved to the west. Given the complexity of
the water movement and the nonlinearity of the generated
waves, time series of the water elevation help to evaluate
generated waves in laboratory experiments and in numer-
ical mo dels, but also serve as important validation for
numerical models. The agreement between experimental
and modeled data for the tide gauge in 885 m distance from
the impact slope is remarkable for both amplitude and
phase (Figure 4g). The maximum amplitude is A = 152 m
occurs approximately 16 s after the impact into the water.
The maximum runup of 518m mod eled with iSALE is
remarkably close to both observed and experimentally
measured runup heights of about 524 m.
5. Conclusion
[16] We studied the 1958 Lituya Bay rockslide and
tsunami numerically and by analog modeling in the labora-
tory, the latter at a scale of 1:675 using a unique pneumatic
landslide tsunami generator to control the slide impact
characteristics. To match the runup of 524 m, the slide
volume estimated by Miller [1960] was accelerated to an
impact velocity of 110m/s. The impact formed a large air
cavity and a highly nonlinear wave. Using the geometry of
the physical model at prototype scale, iSALE computed the
detailed evolution of the coupled free surface and slide
deformations. Comparisons between experimental and
modeling results show an excellent agreement, indicating
that all dominant processes are approximated adequately
raising the possibility of more advanced hazard mitigation
studies in the region. After half a century, the numerous
landslide deposits in Lituya Bay still remain to be mapped
to establish a baseline bathymetry prior to any possible
future landsl ide tsunami in Lituya Bay. With such a
bathymetry, the Lituya Bay rockslide and tsunami as well
as other extreme events can be understood with the help of
the same hybrid approach consisting of three-dimensional
Figure 3. Landslide tsunami experiment: (a) Experimen-
tal setup with pneumatic installation and measurement
systems: Laser distance sensors (LDS), capacitance wave
gages (CWG) and particle image velocimetry (PIV). (b–d)
PIV velocity vector plot sequence of two synchronized
granular slide impact experiments with juxtaposed areas of
view and up_scaled parameters: Froude number F = 3.18,
impact velocity v = 110 m/s, mass per unit width m
0
=
95.5  103 t/m
0
, water depth h = 122 m, slope angles
a = b =45°, time increment 5.19 s with the first image at
t = 2.49 s after impact. Highlighted is the flow separation
on the back of the landslide and the formation of an
impact crater [Fritz et al., 2001].
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experiments [Fritz et al., 2009] and thre e-dimensional
modeling with iSALE-3D.
[
17] Acknowledgments. H.F. was supported by the National Science
Foundation under grant CMMI-0421090. Any opinions, findings, and
conclusions or recommendations expressed herein are those of the author(s)
and do not necessarily reflect the views of the National Science Founda-
tion. The two-dimensional experiments conducted at VAW (ETH Zurich)
were supported by the Swiss National Science Foundation under grant
2100-050586.97. K.W. was supported by DFG grant WU 355/5-2 and is
grateful for the financial support by the NOAA Center for Tsunami Research
(NCTR), PMEL. R.W. thanks management and personnel of the NOAA
Center for Tsunami Research and the Pacific Marine Environmental labora-
tory for their support and guidance during his tenure at NCTR.
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
H. M. Fritz, Civil and Environmental Engineering, Georgia Institute of
Technology, Savannah, GA 31407, USA. (fritz@gatech.edu)
R. Weiss, Department of Geology and Geophysics, Texas A&M
University, College Station, TX 77843, USA. (weiszr@tamu.edu)
K. Wu¨nnemann, Museum fu¨r Naturkund, Leibniz Institute, Humboldt
University of Berlin, Invalidenstr. 43, D-10115 Berlin, Germany.
(kai.wuennemann@museum.hu-berlin.de)
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