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Geophys. J. Int. (2014) xxx,??–??
The Lituya Bay landslide-generated mega-tsunami. Numerical
simulation and sensitivity analysis
J.M. Gonz´
alez-Vida1, J. Mac´
ıas2, M.J. Castro2, C. S´
anchez-Linares2, M. de la Asunci´
on2
and S. Ortega-Acosta3
1Dept. Applied Mathematics, Universidad de M´
alaga, 29080, M´
alaga. Spain
2Dept. Mathematical Analysis, Universidad de M´
alaga, 29080, M´
alaga. Spain
3Laboratoy of Numerical Methods, Universidad de M´
alaga, 29080, M´
alaga. Spain
Received 2014 June ; in original form
SUMMARY
The Lituya Bay 1958 landslide generated mega-tsunami is simulated using HySEA-Landslide
model, a recently developed finite volume Savage-Hutter Shallow Water coupled numerical
model. Two factors are crucial if the main objective of the numerical simulation is not only to
reproduce tha maximal run-up, but also to obtain an precise recreation of the known trimline
of the 1958 mega-tsunami of Lituya Bay. First the accurate reconstruction of the initial slide.
Then the choice of a suitable coupled landslide-fluid model able to reproduce how the energy
released by the landslide is transmitted to the water and then propagated. Nevertheless, fixed the
numerical model, the choice of parameters appears to be a point of mayor importance. The key
role of parameters in determining model capability to accurately reproduce the observed data,
leads us to perform a sensibility analysis. Based on public domain topobathymetric data, and
from one of the main papers about this event by Miller, an approximation of Gilbert Inlet topo-
bathymetry was set up and used for the numerical simulation of the mega-event. Once optimal
model parameter were set, comparisons with observational data were performed in order to
validate the numerical results. The resulting numerical simulation succeeded in reproducing
the main features of 1958 Lituya Bay mega-tsunami.
Key words: Landslide generated tsunamis – Lituya Bay – 1958 Lituya Bay tsunami – numer-
ical model – model validation – numerical simulation
1 INTRODUCTION
Tsunamis are mostly generated by bottom displacements due to
earthquakes. However, landslides either submarine or subaerial can
also trigger devastating tsunami waves. For tsunami simulation the
most critical phases are generation and arrival to coast and inunda-
tion. Propagation over deep basins can be perform using the NLSW
equations or even the linear ones, most effort must be put on not to
be too diffusive. In the other hand, when facing landslide generated
tsunamis matters get more complicated. Generation phase become
critical and complex effects between landslide and water flow must
be taken into account. But it is, with no doubt, the case of subaerial
landslide generated tsunamis where modeling and numerical im-
plementation is more critical, owing to these phenomena produce
more complex flow configurations, larger vertical velocities and ac-
celerations, cavitation phenomena, dissipation, dispersion and the
complex coupled interaction between landslide and water flow. It
is evident that shallow water models cannot take into account and
reproduce all these phenomena, as vertical velocities or cavitation.
Nevertheless, we will show that they can be useful and able to re-
produce the main features (from a tsunami researcher point of view)
of such complex events, as runup or main leading waves. Therefore,
the aim will not be to accurately reproduce the evolution of the dis-
placed solid material or its final location, but the wave propagation,
runup and flood areas it produces.
Among all the examples of subaerial landslide generated
tsunamis, the Lituya Bay 1958 event occupies a paradigmatic place
in the records, being the larger ever recorded tsunami wave and
representing a scientific challenge its accurate numerical simula-
tion. Fritz et al. (2001) lab experiments. A number of works have
focused their efforts in trying to numerically reproduce Fritz (2001)
experiments (Mader and Gittings, 2002; Abadie et al., or S´
anchez-
Linares, 2011, using HySEA model). Detailed numerical simula-
tions of the real event in the whole Lituya Bay with a precise re-
construction of the bottom bathymetry and sourrounding topogra-
phy are limitted (citas...). As far as we know, this is the first
The aim of this work is to produce a realistic and detailed sim-
ulation of the Lituya Bay 1958 Mega-tsunami. HySEA-Landslide
model, developed by the EDANYA group, is used for this simula-
tion and a detailed real scale three-dimensional benchmark exper-
iment of Lituya Bay studying the tsunami generation, propagation
and runup in several relevant areas is performed. Here we show how
a Savage-Hutter model for the slide material coupled with Shallow
Water equations for the water flow can suitably reproduce the main
features of such an extreme event.
2J.M. Gonz´
alez-Vida et al.
2 BACKGROUND
At 06:16 UTC on July 10, 1958, a magnitude Mw8.3earthquake
occurred along the Fairweather Fault (Alaska, USA). This quake
triggered a landslide of about 30.6 km3in Gilbert Inlet (Miller,
1960) that produced the largest tsunami ever recorded. The epicen-
ter of this quake was a scant 21 km from Lituya Bay. Intense shak-
ing lasted for 1 to 4 minutes according to two eyewitnesses that
were anchored at the entrance of the bay. According to (@warning
Citation ‘miller1960’ on page 1 undefined), between 1 and 2.5 min-
utes after the earthquake a large mass of rock slid from the northeast
wall of Gilbert Inlet. It is probable that this entire mass of rocks, ice
and soil plunged into Gilbert Inlet as a unit. This landslide produced
the sudden displacement of a large volume of water as the slide
was plunged into Gilbert Inlet causing the largest tsunami ever evi-
denced. The upper limit of destruction by water of forest and vege-
tation (known as trimline) extended to a maximum of 524 m above
mean sea level on the spur southwest of Gilbert Inlet (Figure ??).
Maximum inundation distance reached to 1,400 m on flat ground at
Fish Lake on the north side of the bay, near its entrance.
In order to understand the evolution of the giant wave, a rough
model at a 1:1,000 scale was constructed at the University of Cali-
fornia (R.L. Wiegel in (@warning Citation ‘miller1960’ on page 2
undefined)). If the slide occurred as a unit and rapidly, they con-
cluded that a sheet of water washed up the slope opposite the land-
slide to an elevation at least three times the water depth while, at
the same time, a large wave, several hundred feet high, moved in
southwards direction, causing a peak rise to occur in the vicinity
of Mudslide Creek. According to (@warning Citation ‘miller1960’
on page 2 undefined), this peak reached 204 m (580 ft) (see Figure
??).
Several authors do not agree about the typology of the slide
mass movement, in fact Miller discusses it, by setting this event
near the borderline between a landslide and a rockfall following
the classifications of (@warning Citation ‘sharpe1938’ on page 2
undefined);(@warning Citation ‘varnes1958’ on page 2 undefined)
while in (@warning Citation ‘pararas1999’ on page 2 undefined)
it is classified as subaerial rockfall. Nevertheless, as we will see in
next sections, inn (@warning Citation ‘frit2001’ on page 2 unde-
fined) and (@warning Citation ‘fritz2009’ on page 2 undefined),
the authors proposed a landslide typology, in fact, they show that,
based on the generalized Froude similarity, they are able to repro-
duce this event using a two-dimensional scaled physical model of
the Gilbert Inlet. A pneumatic landslide generator was used to gen-
erate a high-speed granular slide with density and volume based on
(@warning Citation ‘miller1960’ on page 2 undefined) impacting
the water surface at a mean velocity of 110 m/s. The experimental
runup matches the trimline of forest destruction on the spur ridge
in Gilbert Inlet.
3 AREA OF STUDY
Lituya Bay (Figure ??), located within Glacier Bay National Park,
on the northeast shore of the Gulf of Alaska, is a T-shaped tidal in-
let, with almost 12 km long and width ranging from 1.2 to 3.3 km
except at the entrance, which is around 300 m wide. The north-
eastward stem of the bay cuts the coastal lowlands and the foothills
flanking the Fairweather Range of the St. Elias Mountains. Around
the head of the bay the walls are steep fjord-like and rise to ele-
vations ranging from 670 m to 1,040 m in the foothills inmediately
to the north and south, and more than 1,800 m in the Fairweather
Range. In 1958 maximum depth of the bay was 220 m and the sill
depth, at the entrance of the bay was of only 10 m. At the head
of the bay, the two arms of the T are the Gilbert (northern arm)
and Crillon (southern arm) Inlets, are part of a great trench that
extends tens of kilometers to the northwest and southeast on the
Fairweather fault. Cenotaph Island divides the central part of the
bay in two channels of 640 m and 1,290 m, respectively.
3.1 Coastal morphology
The shores around the main part of the bay are mainly rocky
beaches that rise steeply near to the shoreline. There are two ad-
joining lands rising away from the beach at rates ranging from less
than 30 m in a horizontal distance of 2 km, around Fish Lake, to
170 m in a horizontal distance of 370 m at The Paps (see Figure
??).
Prior to the 1958 wave low deltas of gravel had built out
into Gilbert Inlet at the southwest and northeast margins of the
Lituya Glacier front. Figure ?? (taken from (@warning Citation
‘miller1960’ on page 2 undefined)) shows the Lituya glaciers evo-
lution from 1854 until 1936.
According to (@warning Citation ‘miller1960’ on page 2 un-
defined), and as has been evidenced in several graphical documents,
the delta on the northeast side of Gilbert Inlet completely disap-
peared, and the delta on the southwest side was much smaller. To
recreate the scenario previous to the event used in the numerical
simulation presented here, shorelines, deltas and the glacier front
inside Gilbert Inlet before 1958 has been taken from Miller’s re-
construction (see Figure ??).
3.2 Bathymetry: USGS Survey’s data
According to (@warning Citation ‘miller1960’ on page 2 unde-
fined), examination of Lituya Bay bathymetry was the first step
in determining whether the volume of water was sufficient to ac-
count for the 524 m wave. Bathymetric surveys made in 1926 and
1940 (U.S. Coast and Geodetic Survey, 1942), show that the head
of Lituya Bay is a pronounced U-shaped trench with steep walls
and a broad, flat floor sloping gently downward from the head of
the bay to a maximum depth of 220 meters just south of Cenotaph
Island. From there, the slope rises toward the outer part of the Bay.
At the entrance to the Bay, the minimum depth is only 10m at mean
lower low water level. The outer portion of Lituya Bay is enclosed
by a long spit named La Chaussee Spit, with only a very narrow
entrance of about 220-245 m kept open by tidal currents. The tide
in the bay is diurnal, with a mean range of 2 m and a maximum
range of about 4.5 m (U.S. Coast and Geodetic Survey, 1959). The
U-shape of the bay and the flatness of its floor indicate that exten-
sive sedimentation has taken place. The thickness of the sediments
at the Gilbert and Crillon inlets is not known either, but believed to
be substantial due to terminal moraine deposition during different
brief glacial and interglacial episodes.
The bathymetric data used here were obtained from the Na-
tional Ocean Service: Hydrographic Surveys with Digital Sound-
ing. In particular, data from Survey ID: H08492, 1959, were used
as referece bathymetry. This survey is the nearest in date and with
enough data to have a good representation of the entire Lituya Bay
seafloor. Data from Survey ID: H04608,1926, the closer previous
to the event, were also used to reconstruct Gilbert Inlet bathymetry
previous to the 1958 tsunami. This survey has not enough resolu-
tion to provide a acceptable bathymetry for our study in the whole
Numerical simulation of The Lituya Bay landslide-generated mega-tsunami 3
Figure 1. An example figure spanning two-columns in which space has been left for the artwork.
bay, nevertheless it provides enough data and interesting informa-
tion of the pre-tsunami bathymetry in the Gilbert Inlet. In Figures
??.a and ??.b it is shown the original 1959 bathymetry and 1926
reconstructed bathymetry, respectively. The mass volume differ-
ence between these two bathymetries in Gilbert Inlet area is about
31 ×106m3, that is, very close to the slide volume estimated by
(@warning Citation ‘miller1960’ on page 2 undefined).
4 TSUNAMI SOURCE
The dimensions of the landslide on the northeast wall of Gilbert
Inlet were determined with reasonable accuracy by (@warning Ci-
tation ‘miller1960’ on page 3 undefined), but the thickness of the
slide mass normal to the slope could be estimated only roughly
from available data and photographs. The main mass of the slide
was a prism of rock that was roughly triangular in cross section,
with dimensions from 730 m to 915m along the slope, a maximum
thickness of about 92 m normal to the slope and a center of grav-
ity at about 610 m elevation: From these dimensions the volume of
the slide estimated by (@warning Citation ‘miller1960’ on page 3
undefined) was of 30.6×106m3.
To locate and reconstruct the volume of the slide mass the
following procedure was implemented: First, based on aerial pho-
tos and data provided by (@warning Citation ‘miller1960’ on page
3 undefined), the perimeter of the slide was determined. Then, an
approximate centroid for the formerly defined surface was consid-
ered drawing two lines, one horizontal and another one vertically
projected on the surface. The surface centroid was located at 610 m
high, defining the upper bound for the mass slide. The volume of
the reconstructed slide was of 30.625 ×106m3, which matches ac-
curately with Miller’s estimation. The three criteria we tried to ful-
fill in order to reconstruct the slide geometry where: (1) to place it
in its exact location (projected area); (2) keep an approximate loca-
tion for the centroid, also in height; and (3) to recover an accurate
volume for the numerical slide.
4.1 Landslide setup
In order to reproduce the main features of the slide impact, H. Fritz
and collaborators designed a pneumatic landslide generator. They
intend to model the transition from rigid to granular slide motion.
Thus, at the begining, the granular material is impulsed until the
landslide achieves 110 m/s, that it is the approximated impact ve-
locity between the slide and the water surfece estimated by Fritz et
al., assuming free fall equations for the centroid of the slide. From
this instant, the slide is supposed to behave as a granular medium.
In this work, we have followed the same idea: assuming that
110 m/s is a good approximation for the impact velocity of the slide,
an initial velocity for the granular layer has been estimated so that
the computed impact velocity is approximately 110 m/s. This is a
critical point for the performance of the simulation, in order to re-
produce the dynamic of the impact, the generation of the tsunami,
the propagation and the runup on different areas of the domain.
Thus, for example, starting from rest, gave an impact velocity of
approximately 67 m/s.
From a detailed analysis of the bathymetry surveys available
for this study, an unexpected shifted location of the slide deposit on
the floor of the Gilbert Inlet (see Figure ??.a), with a larger deposit
concentration to the south part of the inlet was observed. The obser-
vation of this fact made us to consider a slide initial velocity vector,
vs, slightly shifted to the south, with modulus closed to 80 m/s (see
Figure ??). Thus, with this initial condition, the model reproduces
both the runup on the spur southwest of Gilbert Inlet and a giant
wave traveling into the bay with enough energy to accurately re-
produce the effects of the wave along the Lituya Bay.
5 MODEL DESCRIPTION AND NUMERICAL SCHEME
Coulomb-type models for granular driven flows have been inten-
sively investigated in the last decade, following the pioneering
work of Savage-Hutter (@warning Citation ‘savage1989’ on page
3 undefined), who derived a shallow water type model including
a Coulomb friction term to take into account the interaction of
the avalanche with the bottom topography. This model has been
extended and generalized by a number of authors. In this frame-
work, EDANYA group has implemented a finite volume numerical
model for the simulation of submarine landslides based on the two-
layer Savage-Hutter model introduced in (@warning Citation ‘fer-
nandeznieto2008’ on page 3 undefined) that takes into account the
movement of the fluid inside which the avalanche develops. This
model is useful for the generation and evolution of tsunamis trig-
gered by both submarine and aerial landslides.
This section describes the system of partial differential equa-
tions modelling landslide generated tsunamis based on layered
average models. The 2D HySEA-Landslide model, is a two-
dimensional version of the model proposed in (@warning Citation
‘fernandeznieto2008’ on page 3 undefined) for 1D problems, where
local coordinates are not considered.
4J.M. Gonz´
alez-Vida et al.
5.1 Simplified Two-layer Savage-Hutter type model
Let us consider a layered medium composed by a layer of inviscid
fluid with constant homogeneous density ρ1(water), and a layer of
granular material with density ρsand porosity ψ0. We assume that
both layers are immiscible and the mean density of the granular
material layer is given by ρ2= (1 −ψ0)ρs+ψ0ρ1. The system of
PDE describing the coupled two-layer system writes as:
8
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:
∂h1
∂t +∂ q1,x
∂x +∂ q1,y
∂y = 0
∂q1,x
∂t +∂
∂x q2
1,x
h1
+g
2h2
1!+∂
∂y „q1,x q1,y
h1«=−gh1
∂h2
∂x +gh1
∂H
∂x +Sf1(W)
∂q1,y
∂t +∂
∂x „q1,x q1,y
h1«+∂
∂y q2
1,y
h1
+g
2h2
1!=−gh1
∂h2
∂y +gh1
∂H
∂y +Sf2(W)
∂h2
∂t +∂ q2,x
∂x +∂ q2,y
∂y = 0
∂q2,x
∂t +∂
∂x q2
2,x
h2
+g
2h2
2!+∂
∂y „q2,x q2,y
h2«=−grh2
∂h1
∂x +gh2
∂H
∂x +Sf3(W) + τx
∂q2,y
∂t +∂
∂x „q2,x q2,y
h2«+∂
∂y q2
2,y
h2
+g
2h2
2!=−grh2
∂h1
∂y +gh2
∂H
∂y +Sf4(W) + τy
(1)
In these equations, subscript 1refers to fluid upper layer, and
subscript 2to the lower layer composed of the fluidized material.
i-th layer thickness at point (x, y)∈D⊂R2at time t, where
Dis the horizontal projection of domain occupied by the fluid,is
denoted by hi(x, y, t).H(x, y)indicates the depth of non erodi-
ble bottom measured from a fixed reference level at point (x, y),
and qi(x, y, t) = (qi,x (x, y, t), qi,y (x, y, t)) is the flow of the i-th
layer at point (x, y) at time t, that are related to the mean velocity
of each layer (ui(x, y, t)) by qi(x, y, t) = hi(x, y , t)ui(x, y, t),
i= 1,2. The value r=ρ1/ρ2denotes the ratio between the con-
stant densities of the two layers (ρ1< ρ2). Note that H(x, y)does
not depend on t, that is, the non-erodible bottom topography does
not change through the simulation although bottom may change
due to second layer movement. Figure ?? shows graphically the re-
lationship between h1,h2and H. Usually, h1+h2=Hat rest or
they represent the mean sea level.
The terms Sfi(W),i= 1,...,4, model the different effects
of dynamical friction, while τ= (τx, τy)is the Coulomb friction
law. Sfi(W),i= 1,...,4, are given by:
(Sf1(W) = Scx(W) + Sax(W)Sf2(W) = Scy(W) + Say(W)
Sf3(W) = −r Scx(W) + Sbx(W)Sf4(W) = −r Scy(W) + Sby(W)
Sc(W) = `Scx(W), Scy(W)´parameterizes the friction be-
tween the two layers, and is defined as:
(Scx(W) = mf
h1h2
h2+rh1
(u2,x −u1,x)ku2−u1kScy(W) = mf
h1h2
h2+rh1
(u2,y −u1,y)ku2−u1k
where mfis a positive constant.
Sa(W) = `Sax(W), Say(W)´parameterizes the friction
between the fluid and the non-erodible bottom, and is given by a
Manning law
(Sax(W) = −gh1
n2
1
h4/3
1
u1,x ku1kSay(W) = −gh1
n2
1
h4/3
1
u1,y ku1k
where n1>0is the Manning coefficient.
Sb(W) = `Sbx(W), Sby(W)´parameterizes the friction be-
tween the granular and the non-erodible bottom, and as in the pre-
vious case, is given by a Manning law:
(Sbx(W) = −gh2
n2
2
h4/3
2
u2,x ku2kSby(W) = −gh2
n2
2
h4/3
2
u2,y ku2k
where n2>0is the corresponding Manning coefficient.
Note that Sa(W)is only defined where h2(x, y, t)=0. In
this case, mf= 0 and n2= 0. Similarly, if h1(x, y, t) = 0 then
mf= 0 and n1= 0.
Finally, τ= (τx, τy)is defined as follows:
Si kτk ≥ σc⇒8
>
>
<
>
>
:
τx=−g(1 −r)h2
q2,x
kq2ktan(α)
τy=−g(1 −r)h2
q2,y
kq2ktan(α)
If kτk< σc⇒q2,x = 0, q2,y = 0
where σc=g(1 −r)h2tan(α), where αis the Coulomb friction
angle.
System (??) can written as a system of conservation laws with
source terms and nonconservative products (ref)
In the next section, the finite volume scheme used to discretize
system (??) is described. As friction terms are semi-implicitly dis-
cretized, we first consider that SF(W)=0. Then, the way those
terms are discretized is described.
5.2 Numerical scheme
To discretize system (??), the domain Dis divided into Lcells
or finite volumes Vi⊂R2,i= 1,...,L, which are assumed to
be closed polygons. We assume here that the cells are rectangles
with edges parallels to Cartesian axes. Given a finite volume Vi,
Ni⊂R2is the center of Vi,ℵiis the set of indices jsuch that
Vjis a neighbor of Vi,Γij is the common edge of two neighboring
volumes Viand Vj, and |Γij|is its length; ηij = (ηij,x , ηij,y )is
the unit normal vector to the edge Γij and pointing towards Vj(see
Figure ??).
We denote by Wn
ian approximation of the solution average
over the cell Viat time tn:
Wn
i∼
=1
|Vi|ZVi
W`x, y, tn´dx dy
where |Vi|is the area of cell Viand tn=tn−1+ ∆t, where ∆tis
the time step.
Let us suppose that Wn
iit is known. Thus, to advance in time,
a family of one-dimensional Riemann problems projected in the
normal direction to each edge of the mesh Γij is considered. Those
Riemann problems are approximated by means of IFCP numeri-
cal scheme (see (@warning Citation ‘fernandeznieto2011’ on page
4 undefined)). Finally, Wn+1
iis computed by averaging these ap-
proximate solutions. The resulting numerical scheme writes as fol-
lows:
Wn+1
i=Wn
i−∆t
|Vi|X
j∈ℵi
|Γij | F −
ij (Wn
i, W n
j, Hi, Hj)(2)
To define F−
ij (Wn
i, W n
j, Hi, Hj)the following notation has
been considered:
5.3 Wet/dry fronts
The numerical scheme described above, when applied to wet-dry
situations, may produce incorrect results: The gradient of the bot-
Numerical simulation of The Lituya Bay landslide-generated mega-tsunami 5
tom topography generates spurious pressure forces and the fluid can
artificially climb up slopes. In (@warning Citation ‘castro2005’ on
page 4 undefined), to avoid this problem, a modification of the nu-
merical scheme is proposed. Here the same strategy is used to cor-
rect the proposed numerical scheme to suitably deal with wet-dry
fronts. With this strategy, spurious waves reflection in the coast are
avoided and a more realistic simulation of the flooded areas is ob-
tained. Moreover, transitions between sub and supercritical flows,
that appears continuously in simulations as the one presented here,
which further complicate matters, are also suitably treated.
5.4 Boundary conditions at the coasts
The implementation of the wet-dry front treatment in the numer-
ical scheme results in not having to impose boundary conditions
at the coasts. Coastline becomes a moving boundary, computed by
the numerical scheme. Depending on the impact wave character-
istics or the water retraitment movement, the computational cells
are filled with water or they run dry, respectively. Consequently, no
specific stabilization model technique is either required.
5.5 Friction terms discretization
In this section the numerical scheme when the friction terms
SF(W)are discretized is presented. First, the terms Sf1(W),
Sf2(W),Sf3(W)ySf4(W)are discretized semi-implicitly; next
the Coulomb friction term τwill be discretized following (@warn-
ing Citation ‘fernandeznieto2008’ on page 5 undefined). The re-
sulting numerical scheme is a three-step method, where in the first
step, the IFCP scheme is used and then in the other two steps, the
dynamical and static friction terms will be discretized. The three-
step method will be denoted as follows:
Wn
i→Wn+1/3
i→Wn+2/3
i→Wn+1
i
The resulting scheme is exactly well-balanced for the station-
ary water at rest solution (q1=q2=0and µ1and µ2constant).
Moreover, the scheme solves accurately the stationary solutions
corresponding to q1=q2=0,µ1constant and ∂xµ2<tan(α)
and ∂yµ2<tan(α), that is an stationary water at rest solution for
which the Coulomb friction term balances the pressure term in the
granular material.
5.6 Model setup
Landslide initial conditions have been described in Section ??.
Initially water is at rest, and according to (@warning Citation
‘miller1960’ on page 5 undefined), an initial level of 1.52 m have
been taken.
A 4 m ×7.5 m rectangular grid with 3,650 ×1,271 =
4,639,150 cells has been taken in order to perform the simulation.
A high efficient GPU based implementation of the numerical
scheme presented before has been developed in order to be able
to compute high accuracy simulations in reasonable computational
time.
The numerical simulation shown here covers a real time pe-
riod of 10 minutes. 14,516 time iterations were performed to evolve
from initial conditions to final state the 10 minutes later. This re-
quired a computational time of
1,528.83 s (approx 25.5 min), which means 44 millions of compu-
tational cells processed per second in a nVidia GTX480 graphic
card.
6 PARAMETER SENSITIVITY ANALYSIS
To overcome the uncertainty inherent to the choice of model pa-
rameters and in order to produce a numerical simulation as close as
possible to the real event, a sensitivity analysis has been performed.
To do so, the three key parameters: (1) Coulomb friction angle, α,
(2) the ratio of densities between the water and the mean density
of the slide, r, and, (3) the friction between layers mf, have been
retained as varying parameters for this sensitivity analysis. The val-
ues for these three parameters have been moved over the following
ranges of reasonable values:
α∈[10o,16o]r∈[0.3,0.5] mf∈[0.001,0.1].
Four criteria were selected in order to get the optimal parameters:
•the runup on the spur southwest of Gilbert Inlet had to be the
closest to the optimal 524 m,
•the wave moving southwards to the main stem of Lituya bay
had to cause a peak close to 208 m in the vicinity of Mudslide
Creek,
•the simulated wave had to break through the Cenotaph Island,
opening a narrow channel through the trees (@warning Citation
‘miller1960’ on page 5 undefined),
•the trimline maximum distance of 1,100 m from high-tide
shoreline at Fish Lake had to be reached.
Hundred of simulations have been performed in order to find
the optimal values for the parameters verifying in the best possible
way the four conditions mentioned above.
Finally the optimal parameters found were:
α= 13o, r = 0.44, mf= 0.08.
Setting the three parameters to the values given above, simu-
lation satisfied the previous four criteria with very good accuracy,
more precisely:
(i) the runup in Gilbert Inlet reached 523.85 m;
(ii) the runup peak in the vicinity of Mudslide Creek reached a
height close to 200 m;
(iii) the wave produced a narrow channel crossing through
Cenotaph Island and, finally,
(iv) the runup reached more than 1,100 m distance from high-
tide shoreline in Fish Lake area.
Figure ?? shows graphically the four items above.
Next section describes in some detail the numerical experi-
ment performed with the optimal set of parameters.
7 MODEL RESULTS
Sensibility analysis provided us the optimal set for the three key pa-
rameters considered. In this section model results correponding to
that simulation are presented, first studying the main characteristics
of the giant wave generated in Gibert Inlet and then describing its
evolution through the main stem of Lituya Bay. Finally, inundation
details will be presented, by comparing the numerical simulation
runup with the real trimline observed in several areas of interest.
7.1 Giant wave generation and evolution in Gilbert Inlet. t: 0
s-39s
After the landslide is triggered, the generated wave reaches its max-
imum amplitude, 272.4m, at t= 8 s (Figure ??.b). The wave is
6J.M. Gonz´
alez-Vida et al.
spreading in southwards direction while its amplitude in decreas-
ing (Figures ??.c, ??.d). 22 s after triggering, the wave hits the bot-
tom of southwest spur of Gilbert Inlet. At t= 39 s the maximum
523.9m runup is reached (Figure??.f).
7.2 Wave evolution
t:30s-2m
While the maximum runup on the east side of Gilbert head
is reached, the southern propagating part of the initial wave, with
more than 100 m high, moves in a south-west direction, hitting the
south shoreline of the Bay after 35 s (Figure ??.a, ??.b), causing a
maximum runup close to 180 m to occur in the vicinity of Mudslide
Creek at t= 70 s (Figure ??.c, ??.d). In the meanwhile, part of the
water reaching the maximum runup area over Gilbert head retreats
back down and part flows over the Gilbert head, inundating the
observed affected area to the south of Gilbert head.
t:2m-3m
While the initial wave moves through the main axis of the
Lituya Bay to Cenotaph Island, a larger second wave appears as
reflection of the first one from the south shoreline (Figure ??.c,
??.d). Both waves swept both shorelines in their path. In the north
shoreline the runup reaches between 50-80 m height (??.e) while in
the south shoreline the runup reaches between 60-150 m height.
The first wave reaches Cenotaph Island after 2min and 5s
with a mean amplitude close to 20 m (Figure ??.e,f) flooding over
more than 650 m from the most eastern prominence of the island
and about 700 m from the little cape, slightly southwards. About
25 seconds later, a second wave with approximately 32 m height
hits the east coast (Figure ??.g, ??.h).
t:3m-5m
After hitting Cenotaph Island, the wave is splitted in two parts,
one advancing in the shallow channel north of the island and other
one traveling through the deeper channel south of the island. Waves
higher than 25 m hit the north shoreline area in front of Cenotaph
Island causing large extension runups (above 1km inland from the
coastline) in the east area near Fish Lake. In the south shoreline in
front of Cenotaph Island, larger waves with 40-50m of amplitude
hit the coast, penetrating around 1 km inland the flat areas located
east of the Paps.
t:5m-8m
Large inundated areas were formed both around Fish Lake,
in the north shoreline, as in the flat areas surrounding the Paps
while the main wave reaches the narrow area near La Chausse Spit.
During this time, the wave amplitude is larger than 15m, indeed
over 20 m in the north shoreline. At 5m50 s the wave reaches La
Chausse Spit, passing over it to the sea and partially reflecting a
wave inside the bay.
7.3 Inundation assessment
In this section the maximum runup extension is compared with the
real trimline drawn by Miller. Figure ?? depicts the total extension
of the runup and the maximum height of the inundation along the
runup area. The trimline determined by Miller (Figure ??) is su-
perimposed in pink. We will assess numerical runup with mapped
trimline dividing our analysis in several areas of interest.
7.3.1 Gilbert Inlet
As it has been shown, in Gilbert Head, the maximum runup (523.9
m) is reached on the east slope. Furthermore, the runup is extended
oblique-to-slope on the western face of Gilbert Head. Runup ex-
tension and trimline coincide quite accurately in this sector (Figure
??). There is a large runup extension over the Lituya Glacier from
its shoreline up to more than 2km over the glacier. Finally it can be
observed a good concordance between trimline and runup on the
east slope of Gilbert Inlet where the slide was initially located.
7.3.2 North Shoreline
There is a good agreement between the inundated area and the real
trimline around the east part of the north shore due to the higher
slopes. Good concordance between trimline and runup in the north
shoreline of La Chausse Spit is also found.
7.3.3 Fish Lake area
The agreement around the flat areas surrounding Fish Lake is good.
In this case, inundation extension includes vicinity areas of Fish
Lake under 40 m height. In order to achieve a better agreement be-
tween runup and trimline, probably it would be necessary to con-
sider a map of drag friction indicating different friction coefficiens
depending of the type of vegetation or soil.
The runup underestimates the trimline over steeper slopes in
the east third of the south shores. Moreover, the numerical model
provides mean runup heights around 100 m while mean trimline
heights are over 140 −190 m around this sector (xxxxx comprobar
xxxxx). There is a good agreement both in The Paps shores as in
the south shoreline in front of La Chausse Spit.
7.3.4 East area of The Paps
Around the central third of the south shoreline the agreement be-
tween runup and trimline is not so accurate. On the flat east area
near The Paps a large inundation occurs, ocupying the flooding area
a sector under 30 −40 m height. As already mention, it would be
necessary to consider a map of drag frictions in order to achieve
more precise results over this area.
7.3.5 Cenotaph Island
One of the items to be checked in the sensitivity analysis presented
in Section ?? was related with flooding in Cenotaph Island. There-
fore a good agreement is expected in this area. In fact the trimline
and the runup are close in the island as can be observed in Figure
??.
7.3.6 La Chausse Spit
As has been described before, La Chausse Spit was completely cov-
ered by the water from minute 6and during more than 90 seconds.
Trimlines around La Chausse Spit are in good agreement with com-
puted runups.
Numerical simulation of The Lituya Bay landslide-generated mega-tsunami 7
8 DISCUSSION
8.1 Potential sources of error
HySEA-Landslide model has been tested against analytical so-
lutions and laboratory measurements of (@warning Citation
‘fritz2009’ on page 6 undefined) (article in progress).
As has been explained in Section ?? the model used is a finite
volume coupled landslide-fluid model that acts as a shallow water
model when the slide layer is still or when there is not a sediment
layer in the column of water. Furthermore, a suitable and simple
treatment of the wet-dry fronts avoids spurious waves reflection in
the coast and produces a more realistic simulation of the flooded
areas. Transitions between sub and supercritical flows, that appears
continuously in simulations as the one presented here, and which
further complicate matters, are also suitably treated.
Nonetheless, as it has been mentioned before, potential source
for model errors can come from the quality of model initialization
parameters, the initial landslide conditions or the DEM and bathy-
metric data. Moreover, in real landslides, the material is not homo-
geneous, neither granular, as supposed here. Nevertheless, this type
of model can be used in practise to obtain a general information of
the generated tsunami and the flooded areas.
8.1.1 Limitations of the DEM and Digital Bathymetry
A high quality DEM is necessary to properly model tsunami wave
dynamics and inundation onshore. In this study there is an addi-
tional difficulty due to the need of good information about the topo-
bathymetric data just before the 1958 mega-tsunami in Lituya Bay.
Though we have combined the DEM based on the best avail-
able data in the region (described in Section ??), data neither of
the pre-tsunami bathymetry of the bay nor the definition of Lituya
Glacier front just before the 1958 tsunami were available with a
fine resolution and enough quality. Even more, there were only es-
timations about the volume and position of the slide that caused the
tsunami. Thus, as has been described in Sections ?? and ??, in this
study we have proposed a reconstruction of original Lituya Glacier
shoreline and Gilbert Inlet bathymetry based on the descriptions in
(@warning Citation ‘miller1960’ on page 7 undefined) and 1926 &
1959 U.S. Coast and Geodetic Surveys.
8.2 Model results
Due to the choice of optimal parameters in the sense described in
Section ?? the simulation achieves the main objectives proposed.
Section ?? presents the first stage of the tsunami dynamics in
Gilbert Inlet: Giant wave generation and the inundation induced
over the east slope of Gilbert Inlet. Later, the wave propagation
in south-west direction along the Lituya Bay is described until the
wave crosses La Chausse Spit. Model results are in good agreement
with those described in (@warning Citation ‘miller1960’ on page
7 undefined).
In a second stage an inundation assessment is performed. A
detailed description of the runup areas along the shores of the bay is
presented. In general, computed inundation areas are in very good
agreement with Miller observations. Nevertheless, model provides
larger inundation areas that the 10.35 km2between the trimlines
and the high-tide shorelines estimated by Miller. But in fact, Miller
made an estimation of the total area inundated by the wave of at
least 13 km2that is closer to the model results.
9 CONCLUSIONS AND RECOMMENDATIONS FOR
FUTURE WORK
It have been demonstrated that landslide triggering mechanism pro-
posed by (@warning Citation ‘fritz2009’ on page 7 undefined) is
crucial in order to reproduce not only the wave dynamics inside
Gilbert Inlet, but also all the tsunami dynamics produced along the
bay, including inundation effects, wave heights and several achieve-
ments observed in (@warning Citation ‘miller1960’ on page 7 un-
defined).
Impact times, wave heights, trimlines, etc. provided by the
simulation are in good agreement with the majority of observations
and conclusions described by (@warning Citation ‘miller1960’ on
page 7 undefined).
Concerning future work, uncertainty in the data (initial condi-
tion, parameters of the models, etc.) is of paramount importance in
real applications. Therefore, some information of the main proba-
bilistic moments should be provided. Uncertainty quantification is
nowadays a very active front of research and one of the most effi-
cient techniques are multilevel Monte Carlo methods. To run such
a method, first a family of embedded meshes is considered. Then, a
large enough number of samples of the stochastic terms are chosen
and, for each sample a deterministic simulation is run, finally the
probabilistic moments are then computed by a weighted average of
the deterministic computations.
Another improvement of the model will be carried out by con-
sidering shallow Bingham dense avalanche models, like those in-
troduced in (@warning Citation ‘fernandeznieto2010’ on page 7
undefined), that will be coupled with the hydrodynamic model.
We are currently working on the implementation of a model
including dispersive effects, this will allow to compare both mod-
els, with and without dispersion, and assessing the importance or
role played by dispersive terms in this kind of events. Nevertheless,
this work shows that a Savage-Hutter model coupled with shallow
water equations are sufficient to suitably reproduce the main fea-
tures of an extreme event such as the one occurring at Lituya Bay
in 1958.
ACKNOWLEDGMENTS
All the numerical experiments requiered for the development of
this research have been performed at the Laboratory of Numeri-
cal Methods of the University of Malaga. This work has been par-
tially funded by the NOAA Center of Tsunami Research (NCTR),
Pacific Marine Environmental Laboratory (U.S.A.) Contract. No.
WE133R12SE0035, by the Junta de Andaluc´
ıa research project
TESELA (P11-RNM7069) and the Spanish Government Research
project DAIFLUID (MTM2012-38383-C02-01).