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Comparisons of Numerical Models on Formationof Sediment Deposition Induced by Tsunami Run-Up
Paper:
Comparisons of Numerical Models on Formation of SedimentDeposition Induced by Tsunami Run-Up
Ako Yamamoto∗1,†, Yuki Kajikawa∗2, Kei Yamashita∗3, Ryota Masaya∗4,
Ryo Watanabe∗4, and Kenji Harada∗5
∗1Forestry and Forest Products Research Institute
1 Matsunosato, Tsukuba, Ibaraki 305-8687, Japan†Corresponding author, E-mail: [email protected]
∗2Social Systems and Civil Engineering, Tottori University, Tottori, Japan∗3International Research Institute of Disaster Science (IRIDeS), Tohoku University, Miyagi, Japan
∗4Civil and Environmental Engineering, Graduate School of Engineering, Tohoku University, Miyagi, Japan∗5Center for Integrated Research and Education of Natural Hazards, Shizuoka University, Shizuoka, Japan
[Received May 25, 2021; accepted August 31, 2021]
Tsunami sediments provide direct evidence of tsunami
arrival histories for tsunami risk assessments. There-
fore, it is important to understand the formation pro-
cess of tsunami sediment for tsunami risk assessment.
Numerical simulations can be used to better under-
stand the formation process. However, as the forma-
tion of tsunami sediments is affected by various con-
ditions, such as the tsunami hydraulic conditions, to-
pographic conditions, and sediment conditions, many
problems remain in such simulations when attempting
to accurately reproduce the tsunami sediment forma-
tion process. To solve these problems, various numeri-
cal models and methods have been proposed, but there
have been few comparative studies among such mod-
els. In this study, inter-model comparisons of tsunami
sediment transport models were performed to improve
the reproducibility of tsunami sediment features in
models. To verify the reproducibility of the simula-
tions, the simulation results were compared with the
results of sediment transport hydraulic experiments
using a tsunami run-up to land. Two types of ex-
periments were conducted: a sloping plane with and
without coverage by silica sand (fixed and movable
beds, respectively). The simulation results confirm
that there are conditions and parameters affecting not
only the amount of sediment transport, but also the
distribution. In particular, the treatment of the sed-
iment coverage ratio in a calculation grid, roughness
coefficient, and bedload transport rate formula on the
fixed bed within the sediment transport model are con-
sidered important.
Keywords: tsunami sediment transport, hydraulic exper-
iment, numerical simulations, model comparisons
1. Introduction
Tsunamis running up the coast or land carry a large
amount of sediment and seawater. This event was ob-
served as a “black tsunami” off the coastal areas of the
Sanriku region after the 2011 Tohoku Earthquake. In gen-
eral, the sediment contained in tsunami waves remains
after the seawater recedes and is widely distributed in
flooded areas [1]. The materials carried and deposited by
the tsunami are called tsunami sediments. They can be
preserved for a long period if the environment after their
deposition is not disturbed; thus they provide direct evi-
dence of the history of tsunami strikes in coastal areas [2–
4].
Several tsunami researchers have developed numerical
models. However, the formation of tsunami sediment fea-
tures is a complex physical phenomenon and is affected
by various factors, such as the characteristics of the in-
coming tsunami, topographic conditions, and condition(s)
of the sand(s) (grain size and specific gravity) comprising
the sediments. Owing to this, many challenges remain
in reproducing this phenomenon using numerical simula-
tions [5, 6].
Therefore, the purpose of the study was to clarify the
specific factors affecting the reproducibility of the spa-
tial distribution of sediment deposition. The investiga-
tion was based on various numerical simulations target-
ing hydraulic experiments on the formation mechanisms
of sediment deposits on land, as induced by tsunami
run-ups. This paper summarizes the contents of the
“Tsunami Hackathon” (https://tsnmhack.github.io/), held
by the Japan Society of Civil Engineers (JSCE) for three
days from September 1, 2020.
2. Method
Several teams participated in the project of “Tsunami
Hackathon,” and each team verified the reproducibility of
Journal of Disaster Research Vol.16 No.7, 2021 1015
https://doi.org/10.20965/jdr.2021.p1015
© Fuji Technology Press Ltd. Creative Commons CC BY-ND: This is an Open Access article distributed under the terms of
the Creative Commons Attribution-NoDerivatives 4.0 International License (http://creativecommons.org/licenses/by-nd/4.0/).
Yamamoto, A. et al.
Fig. 1. Experimental facility.
Fig. 2. Measurement points.
numerical simulations using their own models. This was
done based on the distribution of sand deposited in a hy-
draulic experiment that investigated the formation mech-
anism of sedimentary sand formed on land by tsunamis.
As preliminary public data, the teams were provided with
drawings of the channel, time series data of the water level
and flow velocity, and silica sand particle size distribution
data. No specification was made on how to input the ex-
ternal force conditions or how to handle the grain sizes of
the sand (uniform sand or mixed sand). Each team sub-
mitted the spatial distribution of the sand deposits, as ob-
tained from numerical calculations for comparison.
2.1. Experimental Setup
A schematic of the channel is presented in Fig. 1. The
experimental facility was a two-dimensional (2D) tsunami
wave-generating channel at Shizuoka University, Japan.
The channel consisted of a water storage tank and a wa-
terway section from the upstream side. A tsunami-like
bore was generated by rapidly opening the gate of the wa-
ter storage tank. The water storage tank was 4.5 m long,
1.4 m wide, and 0.5 m deep, and was connected to a hor-
izontal bed section of the channel across the gate. The
horizontal bed was 7.0 m long, 0.5 m wide, and 0.5 m
deep. The initial water depths in the tank and the water-
way were 0.3 m and 0.1 m, respectively. To stabilize the
flow from the water storage tank through the gate, fan-
shaped guides with a radius of 0.45 m were installed at
the two corners of the gate side in the water storage tank.
The waterway consisted of a horizontal, slope, and hor-
izontal sections from the upstream side, thereby assum-
ing the topographical conditions of a tsunami run-up to
land. The downstream end of the onshore horizontal sec-
tion was set upright with an impermeable wall surface. In
the fixed-bed experiment, the water level was measured
using an ultrasonic wave height meter, and the flow veloc-
ity was measured using an electromagnetic velocity me-
ter and propeller velocity meter. The locations where the
measurement devices were installed are shown in Fig. 2.
The velocity at Gate +9 m could not be measured in the
measurement range of the propeller velocity meter used in
the experiment; therefore, no data were available. In the
movable bed experiment, the water level and flow velocity
were measured immediately downstream of the gate. Sil-
ica sand with an adjusted grain size was used for the mov-
ing bed slope. The grain size distribution of the mixed
silica sand is shown in Fig. 3. Moreover, to capture the
deposited sand, a “Sand catcher,” as shown in Fig. 4, was
used to measure the amount of sand deposited on land.
The distribution of tsunami sediments was measured after
the tsunami had calmed down. The amount of sand was
1016 Journal of Disaster Research Vol.16 No.7, 2021
Comparisons of Numerical Models on Formationof Sediment Deposition Induced by Tsunami Run-Up
0.0
10.0
20.0
30.0
40.0
-1.0 0.0 1.0 2.0 3.0 4.0
Mass
(wt%
)
grain size,
(a) Each grain size distribution
0.010.020.030.040.050.060.070.080.090.0
100.0
0.01 0.1 1
Cu
mu
lati
veM
ass
(wt%
)
grain size(mm)
(b) Cumulative mass distribution
Fig. 3. Grain size distribution of silica sand.
measured as the amount of sand deposited per 0.2×0.2 m,
with a measurement section every 0.2 m. These data were
used as comparison data for numerical calculations.
2.2. Numerical Simulation
This study was conducted at the “Tsunami Hackathon,”
held online from September 1 to 3, 2021. The contes-
tants were divided into three calculation teams, and nu-
merical simulations were conducted for the experimen-
tal results (water level, flow velocity, and sediment dis-
tribution) described in Section 2.1. To evaluate the per-
formance of each model and make them more accurate
when reproducing the experiments, each team used dif-
ferent governing equations, numerical schemes, sediment
transport models, and calculation conditions for its sim-
ulations. The computational conditions for each team
over the three days are listed in Table 1. The non-
hydrostatic equations (fully three-dimensional (3D) and
2D non-hydrostatic) and nonlinear shallow water equation
were used as the governing equations for the tsunami flow.
Two teams mainly used the nonlinear shallow water equa-
tion, but used different numerical models, computational
conditions, and sediment transport models; they were des-
ignated as Team A and Team B (initially, Team A used the
fully 3D non-hydrostatic equation). The sediment trans-
port model (STM) proposed by Takahashi et al. [7] was
used by Team B. The third team, Team C, used the same
STM as Team B for the sediment transport model, but
used different governing equations (2D non-hydrostatic
equations) and other conditions. The details of each team
are presented below.
Fig. 4. Sand capture device (Sand catcher).
2.2.1. Team A
First, the 3D Reynolds-averaged Navier–Stokes equa-
tion model (3D RANS model), using the Cartesian coor-
dinate system, was adopted for the governing equations
of tsunami flow. Furthermore, the fractional area/volume
obstacle representation (FAVOR) method [8], which can
impose boundary conditions smoothly at complex bound-
aries, was introduced into the governing equations. The
standard k-ε turbulence model was adopted to evaluate
the eddy viscosity coefficient (the FAVOR method was
introduced therein). The effects of including suspended
sediments in a flow were not considered in the turbulence
model. At the wall boundaries, the frictional resistance
was given according to the logarithmic law, and the tur-
bulent quantities were given by the wall functions. The
bedload and suspended load were considered in the sed-
iment transport calculations. The bedload transport rate
per unit width qB was calculated using the equation pro-
posed by Ashida and Michiue, as follows [9]:
qB = 17τ∗32
(
1−Kcτ∗,c
τ∗
)(
1−√
Kcτ∗,cτ∗
)
√
sgd3, (1)
where s is the specific gravity of sand in water (= σ/ρ −1), σ is the density of the sediment, ρ is the fluid density,
g is the gravitational acceleration, d is the sediment diam-
eter, τ∗ and τ∗,c are the non-dimensional tractive and criti-
cal tractive forces, respectively, and Kc is the slope factor.
Yoshii et al. [10] reported that the prediction using Ashida
and Michiue’s formula was in good agreement with the
measured bedload data of a sediment transport experi-
ment based on a tsunami. The suspended load transport
rate considering the deposit rate per unit area qsu was es-
timated using the formula proposed by Itakura and Kishi,
Journal of Disaster Research Vol.16 No.7, 2021 1017
Yamamoto, A. et al.
Table 1. Summary of model setups (RANS: Reynolds-averaged Navier–Stokes; WENO: weighted essentially non-oscillatory;
C-HSMAC: highly simplified marker-and-cell method on collocated grid system).
Team A B C
Case A1-1 A1-2 A2-1 A2-2 A3-1 A3-2 B1 B2 B3 C1 C2 C3-1 – C3-3
Governingequation
Non-hydrostaticEquation (3D
RANS)
Non-linear Shallow Water Equation(2D)
Non-linear Shallow WaterEquation (2D)
Non-linear Shallow WaterEquation (2D, NEOWAVE
without non-hydrostatic term)(Yamazaki et al., 2009 and 2011)
Numerical scheme Collocated grid Regular grid Staggered grid Staggered grid
WENO scheme,hybrid scheme,
C-HSMACmethod
WENO scheme, TVD Runge–Kuttamethod
Leap-frog methodMomentum Conserved
Advection scheme (Stelling andDuinmeijer, 2003)
Time step 0.001 s 0.001 s 0.005 s
Grid size 0.02 m 0.01 m 0.05 m 0.05 m
Sand grain size 0.25 mm mixed 0.25 mm 0.25 mm mixed 0.25 mm 0.25 mm
Manning’sroughnesscoefficient
0.0125 0.01370.0116 (B2: Set at each
grain size)Table 3
Transport formulafor bed- and
suspended loads
Ashida andMichiue (1972),Itakura and Kishi
(1980)
Ashida and Michiue (1972),Itakura and Kishi (1980)(A2-2: Ikeno et al., 2009)
STM (Takahashi et al.,2000)
B2: Takahashi et al. (2011)
STM (Takahashi et al., 2000)(C2-C3: Modified in Tab. 3)
Settling velocity Rubey (1933) Rubey (1933)Rubey (1933) with hinderingeffect (Richardson and Zaki,
1954)
Saturatedsuspended loadconcentration
No 0.01 Sugawara et al. (2014)
Critical frictionvelocity
Iwagaki (1956)modified
Egiazaroff (1972)
Iwagaki (1956)(A3-1: Iwagaki, 1956 and Tsuchiya,
1956)Iwagaki (1956) Iwagaki (1956)
Porous ratio 0.4 0.4 0.4
Incident wave Dam break Measured water level Dam break
as follows [11]:
qsu = K
(
α∗σ −ρ
σ
gd
u∗Ω−w0
)
−w0cb, . . . (2)
Ω =τ∗B∗
∫ ∞
α ′ξ
1√
πexp
(
−ξ 2)
dξ
∫ ∞
α ′
1√
πexp
(
−ξ 2)
dξ+2
τ∗B∗
−1. . (3)
Here, w0 is the settling velocity of the sediment as given
by Rubey’s formula [12], u∗ is the friction velocity, cb
is the suspended sediment concentration near the bed,
α ′ = B∗/τ∗− 2, α∗ = 0.14, K = 0.008, and B∗ = 0.143.
Itakura and Kishi’s formula has been widely used in river
research. Rubey’s formula was used to calculate the set-
tling velocity and is expressed as follows:
w0√sgd
=
√
2
3+
36ν2
sgd3−
√
36ν2
sgd3, . . . . . (4)
where ν is the kinematic viscosity of water. Moreover,
the FAVOR method was also introduced into the sedi-
ment continuity equations, and the saturated suspended
load concentration was not considered in the models of
Team A.
A collocated grid system was adopted for the computa-
tional grids of the tsunami flow. The fifth-order weighted
essentially non-oscillatory (WENO) scheme [13] was ap-
plied to discretize the advective terms of the momen-
tum equations, and the hybrid scheme [14] was applied
to discretize the k-ε equations and suspended sediment
transport equation. The highly simplified marker-and-cell
method on the collocated grid system [15] was applied
to calculate the non-hydrostatic pressure field. Details of
this model are provided in another study [16]. Moreover,
in the calculation of the sediment transport on the fixed
bed, the sediment was assumed to be deposited on the en-
tire surface of the calculation grid if even a small amount
of sand existed in the grid. In addition, the sediment trans-
port rate was estimated to be no larger than the amount of
sediment in the grid. The calculations were performed
under uniform and mixed sand conditions, with the uni-
form sand having a grain size of 0.25 mm, and the mixed
sand having a distribution of five grain sizes (0.596, 0.421,
0.298, 0.212, and 0.150 mm), as shown in Fig. 3. The re-
sults for the uniform grain size and mixed sand are shown
as A1-1 and A1-2, respectively.
Next, the governing equations of the tsunami flow were
changed to a 2D nonlinear shallow water model (2D
model); the FAVOR method was introduced therein. Re-
garding sediment transport, the topography change model
considering the bedload and suspended load was used, as
in the first day. Moreover, in the calculation of the sus-
pended load transport rate, both Itakura and Kishi’s for-
mula and the formula of Ikeno et al. [17] were used. The
suspended load transport rate considering the deposit rate
per unit area qsu proposed by Ikeno et al. [17] is as fol-
1018 Journal of Disaster Research Vol.16 No.7, 2021
Comparisons of Numerical Models on Formationof Sediment Deposition Induced by Tsunami Run-Up
lows:
qsu = Λ
(
ν2
sgd3
)0.2{
(
w0√sgd
)0.8
(τ∗− τ∗,c)
}2√
sgd
−w0cb. . . . . . . . . . . . . . . . (5)
Here, Λ is a coefficient. Ikeno et al. derived Eq. (5) from
a dimensional analysis and suggested that the coefficient
Λ = 0.15, in correspondence with their tsunami experi-
ment. The calculations were conducted under uniform
sand conditions. In the calculations using the 2D model,
an exponential distribution was assumed for the vertical
distribution of the suspended load concentration to eval-
uate the suspended sediment concentration near the bed
cb. A regular grid system was adopted as the computa-
tional grid, the fifth-order WENO scheme was applied to
discretize the advection terms of the governing equations,
and the third-order total variation diminishing Runge–
Kutta method [18] was applied to the time integration.
The details of the model can be found in the correspond-
ing reference [19]. The results obtained by using Itakura
and Kishi’s formula and the formula of Ikeno et al. are
shown as A2-1 and A2-2, respectively.
Finally, to solve the problem of estimating the sedi-
ment transport rate on a fixed bed, the calculation of the
non-dimensional critical tractive force and the formula for
the bedload transport rate on a fixed bed were modified.
Iwagaki’s formula [20], which is applicable to a mov-
able bed, was applied to a fixed bed area to estimate the
non-dimensional critical tractive force. Herein, Team A
attempted the calculation using Tsuchiya’s formula [21],
which can be applied to the smooth surface of a fixed bed.
In contrast, Ashida and Michiue’s formula has been ap-
plied to calculate the bedload transport rate, assuming that
there is a sufficient amount of sand in the calculation grid,
not only on the movable beds but also on the fixed beds.
Ashida and Michiue’s formula [9], which is applicable to
a fixed bed, is introduced as follows:
qB =β ′
µ ′f
f
(
u∗d
ν
)
τ∗
(
1−Kcτ∗,c
τ∗
)(
1−√
Kcτ∗,cτ∗
)
u∗d, (6)
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
u
u∗=
u∗z
ν:
u∗d
ν≤ 6.83,
u
u∗=
1
0.4ξ
(
1
2−
√
ξ 2 +1
4
)
+2.5 ln(
2ξ +√
4ξ 2 +1)
+6.83 :u∗d
ν> 6.83,
. . . . . . (7)
ξ = 0.4(u∗z
ν−6.83
)
, . . . . . . . . . . . (8)
where u∗ is the friction velocity, β ′ is the constant of pro-
portionality, µ ′f is the dynamic friction coefficient of sand
on a fixed bed with a smooth surface, β ′/µ ′f is the exper-
imental constant (≈ 1.0), u is the velocity at height z, and
f (u∗d/ν) is the value of u/u∗ at the height z = d.
The tsunami flow was calculated using the 2D model,
and the suspended load transport rate was calculated us-
ing Itakura and Kishi’s formula for uniform sand. Eqs. (1)
and (2) were applied to the movable and fixed bed ar-
eas, respectively. The results from using both Iwagaki’s
and Tsuchiya’s formulas for the estimation of the non-
dimensional critical tractive force are denoted as A3-1,
and the results from only using Iwagaki’s formula are de-
noted as A3-2.
2.2.2. Team B
First, the 2D model was used to calculate the tsunami
propagation, and the leapfrog method on a staggered grid
system was adopted for the discretization of the govern-
ing equations. The STM proposed by Takahashi et al. [7]
was used to calculate sediment transport. The bedload and
suspended load transport rate formulas derived by Taka-
hashi et al. [7] are expressed as follows:
qB = a (τ∗− τ∗,c)32
√
sgd3, if τ∗ > τ∗,c, . . . . (9)
qsu =
{
b (τ∗− τ∗,c)2√
sgd−w0C, if τ∗ > τ∗,c,
−w0C, if τ∗ ≤ τ∗,c.(10)
Here, a and b are the coefficients of the bedload and
suspended load transport rates, respectively. The non-
dimensional critical tractive force τ∗,c was estimated using
Iwagaki’s formula [20]. C is the depth-averaged concen-
tration of the suspended load. The calculation was con-
ducted under a single grain size condition from an estima-
tion of the average grain size, as shown in Fig. 3; the coef-
ficients were set to a = 21 and b = 1.2×10−2 [7]. More-
over, the saturated suspended load concentration was set
to 0.01 as a constant value. The water level measured im-
mediately downstream of the gate was used as the input
for the incident wave. The details are presented in Ta-
ble 2. This result was designated as B1.
Next, the condition of the sand grain size was changed
from a single grain size to a mixed grain size. Three grain
sizes were set, as shown in Fig. 3, and the grain sizes used
for the mixed sand were 0.250, 0.125, and 0.063 mm. The
coefficients a and b on the bedload and suspended load
transport rate formulas were interpolated from the results
of Takahashi et al. [22]. Moreover, the settling veloc-
ity, Manning’s roughness coefficient, and friction velocity
were set for each particle size. The settling velocity was
calculated using Rubey’s formula [12], and Manning’s
roughness coefficient was estimated from the Manning–
Strickler formula as follows [23]:
n =Hd
16
ψ√
g, . . . . . . . . . . . . . . (11)
ψ = 6.0+5.75 logHd
2.5dR
, . . . . . . . . (12)
where n is the Manning’s roughness coefficient, Hd is the
design water depth, and dR is the representative grain size
of the bottom material. The critical friction velocity u∗c
Journal of Disaster Research Vol.16 No.7, 2021 1019
Yamamoto, A. et al.
Table 2. Calculation condition (Team B).
B1 B2 B3
Number of grids 52 × 2200 30 × 553
Grid interval 0.01 m 0.05 m
Time interval 0.001 s
Calculation time 60 s
Input dataMeasured water level (Fromthe gate +1 m)
Dam break
Grain size 0.250 mm0.250 mm0.125 mm0.063 mm
0.250 mm
Settling velocity 0.0332 m/s0.0332 m/s0.0117 m/s0.0035 m/s
0.0332 m/s
Manning’sroughness coefficient
0.01160.01160.01070.0098
0.0116
Critical frictionvelocity
0.0142 m/s0.0142 m/s0.0101 m/s0.0071 m/s
0.0142 m/s
was determined as follows:
u∗c =√
τ∗,csgd. . . . . . . . . . . . . (13)
As in the first experiment, the measured water level just
downstream of the gate was used as the input wave. This
result is presented in Section B2.
Finally, the condition of the grain size used in the sed-
iment transport model was changed back to the single
grain size of the first run, and the input wave was changed
to a dam break. In addition, the grid size was changed
because the computation became unstable owing to the
generation of waves with sudden changes. The details are
presented in Table 2 and the result is designated as B3.
2.2.3. Team C
First, to simulate tsunami and sediment transport, a
coupled model [24] was used. This model comprised
the NEOWAVE model [25, 26] based on the vertical in-
tegral non-hydrostatic equation [27] and the STM [7].
In general, the momentum conserved advection (MCA)
scheme [28] implemented in NEOWAVE approximates
wave-breaking and hydraulic jumps as bores and consid-
ers energy dissipation without using empirical indices to
conserve the flow. The volume and momentum are con-
served. The governing equations for fluid and sediment
transport, as defined on a spherical coordinate system, are
discretized on a staggered grid; however, in this study,
they were transformed into a Cartesian coordinate system
for the laboratory experiments. The hydrostatic flow was
calculated without considering the non-hydrostatic pres-
sure term. A dam break was used as the wave-making
method. The obtained results are denoted as case C.
In the model, the settling velocity, w0, in Eq. (10) was
replaced with w0(1−C/Cr)5 to consider the hindering ef-
fects [29], where Cr is the reference concentration. Man-
ning’s roughness coefficient ns for evaluating τ∗ could be
set separately from that for the tsunami flow, that is, n.
The roughness coefficients, n and ns, were set from the
Manning–Strickler equation based on the sand grain size.
A single grain size d50 was used. The equivalent rough-
ness ks was set to ks = 2.5d50 (cases C1, C2, and C3-1) or
ks = 5.0d50 (cases C3-2–C3-3). The critical friction ve-
locity was estimated using Iwagaki’s formula. Moreover,
the prediction formula proposed by Sugawara et al. [30]
was used to evaluate the saturated suspended load concen-
tration Cs in the sediment transport model, as follows:
Cs =1
s
esn2sU3
D43 w0 − esn2
sU3. . . . . . . . . . (14)
Here, D is the total water depth, U is the depth-averaged
horizontal flow velocity, and es = 0.025 is the efficiency
coefficient. The maximum value of the suspended load
concentration Cmax = 0.377 is based on observations by
Xu [31, 32]. The Cr mentioned above was assumed to be
Cmax.
As described below, the water level fluctuation and to-
tal amount of sand deposits simulated on the first day were
generally reasonable. Therefore, we considered that there
was an issue in modeling the sediment transport in the
fixed-bed section and examined the direction of improve-
ment by changing the parameter settings and algorithms
in the fixed-bed section. First, to improve the topographic
continuity at the connection between the movable bed and
fixed floor, we adjusted the connection shape to a slope to
make it closer to the actual experimental conditions. Next,
based on the Rouse number of the fixed-bed section, it
was determined that bedload transport was the predomi-
nant sediment transport mode, so the amount of sediment
entrainment from the fixed-bed section was changed to
zero to match the sediment transport mode in the experi-
ment. In addition, the effect of reducing the amount of bed
load sand was examined by focusing on the sediment cov-
erage of the fixed bed, as shown in the video. The cover-
age on the fixed bed A was assumed to be A = 0.2 and was
multiplied by the bedload rate formula in Eq. (9) as the co-
efficient. However, to avoid calculation instability caused
by discontinuous changes in the amount of bedload trans-
port between the movable bed and fixed bed sections, the
two sections were smoothly connected so that the cover-
age ratio A was set from 1.0 to 0.2. The simulated results
are denoted as C2.
Finally, to verify the effectiveness of the MCA scheme
in reproducing the tsunami run-up, the condition without
the MCA scheme was also examined (case C3-1). The
second validation of the sediment transport model (C2)
showed that it was able to reproduce the distribution trend
and total amount of sediment in the fixed bed, but the
result was an underestimation. Therefore, a sensitivity
analysis of the coverage and Manning’s roughness coeffi-
cient was conducted to investigate the effect of coverage
and/or terrestrial roughness on the sedimentation distri-
bution. The coverage (A) was varied from 0.15 to 0.3
(case C3-2), and the roughness coefficient (nsl) on the
land for the estimation of τ∗ was varied from 0.0 to 0.014
(case C3-3); however, n = 0.014 for tsunami flow and
ns = 0.014 on the movable bed. The details are presented
in Table 3.
1020 Journal of Disaster Research Vol.16 No.7, 2021
Comparisons of Numerical Models on Formationof Sediment Deposition Induced by Tsunami Run-Up
Table 3. Calculation condition (Team C).
C1 C2 C3-1 C3-2 C3-3
MCA scheme√ √
No√ √
Manning’s
roughness
coefficient
n = ns = 0.012 n = ns = 0.014
n = 0.014
ns = 0.014 (< 11 m)
= 0−0.014 (≥ 11 m)
Sediment
entrainment
With sediment
entrainment
With sediment entrainment (< 11 m)
Without sediment entrainment (≥ 11 m)
Coverage A A = 1.0A = 1.0 (< 11 m)
= 0.2 (≥ 11 m)
A = 1.0 (< 11 m)
= 0.2 (≥ 11 m)
A = 1.0 (< 11 m)
= 0.15−0.3 (≥ 11 m)A = 1.0
n: for tsunami flow, ns: for τ∗ in sediment transport model
(a) Water level (b) Velocity
Fig. 5. Time series data of water level and velocity in the hydraulic experiment.
3. Result
3.1. Hydraulic Experiment
Figure 5 shows the results for the water level and flow
velocity at each measurement point in the fixed-bed exper-
iment. A rapid increase in the water level and velocity was
observed with the arrival of waves at each site. The water
level reached a maximum of approximately 0.08 m at the
junction of the fixed and movable beds, and the flow ve-
locity reached a maximum of approximately 2.5 m/s. The
run-up waves that reached the wall at the downstream end
of the channel were reflected by an upright impermeable
wall. Therefore, a return flow in the upstream direction af-
ter the arrival of the first wave was observed at each site.
Fig. 6 shows the amount of sand deposited at the horizon-
Fig. 6. Distribution of the amount of sand deposited in the
hydraulic experiment.
Journal of Disaster Research Vol.16 No.7, 2021 1021
Yamamoto, A. et al.
Fig. 7. Time series data of water level (Team A).
tal section of the terrestrial area in the movable bed exper-
iment. The distribution of the deposited sand exceeded
40 g near the shoreline and decreased slowly toward the
downstream wall. The total amount of sand deposited in
the land area was 1041.4 g.
3.2. Numerical Simulation of Hydraulic Experi-
ments
3.2.1. Team A
The results for the water level and flow velocity from
A1 are shown in Figs. 7 and 8, respectively. The arrival
time of the first wave at each measurement point was gen-
erally reproduced by the 3D RANS model for the water
level and current velocity. The wave height was larger
than the experimental value at the arrival time of the first
wave at the measurement point near the downstream end
wall; however, it was generally consistent at the other
points. As shown in Fig. 9, a large amount of sand was
deposited near the downstream end wall, and a smaller
amount of sand was deposited from the shoreline to the
middle of the channel. By comparing the results from the
A1-1 uniform grain size and the A1-2 mixed sand, it can
be confirmed that the A1-2 mixed sand condition tends
to deposit sediments slightly closer to the middle of the
channel.
The calculated results for the water level and veloc-
ity by the 2D model of A2 are shown in Figs. 7 and 8,
in which the results from the 3D RANS model are al-
ready indicated. Comparing the results of each model,
although some differences were observed after the con-
vergence of the first wave among the models, no signifi-
cant differences were observed in the arrival time of the
Fig. 8. Time series data of velocity (Team A).
Fig. 9. Comparison of the distribution of the amount of sand
deposited (Team A).
first wave and wave height. In other words, the numer-
ical simulations of this phenomenon showed that the 3D
flow did not develop in most areas, except near the down-
stream end wall, where the vertical flow was dominant.
Regarding the amount of sediment deposition, as shown
in Fig. 9, even after changing both the flow model and the
suspended sediment transport equation, more sand tended
to deposit near the downstream end wall, and the sediment
deposition from the shoreline to the middle of the channel
could not be reproduced. However, it can be confirmed
that the result from A2-1 (using Itakura and Kishi’s for-
mula) tended to indicate deposition of more sand in the
1022 Journal of Disaster Research Vol.16 No.7, 2021
Comparisons of Numerical Models on Formationof Sediment Deposition Induced by Tsunami Run-Up
middle of the channel than the result from A2-2 (using
the formula of Ikeno et al.).
As shown in Fig. 9, similar to A2, both A3-1 and A3-2
did not show any improvements in the tendency of sedi-
ment deposition near the downstream end wall. However,
it was possible to reproduce the tendency for sand to ac-
cumulate in the middle of the channel, where it had pre-
viously not accumulated. By comparing the results from
A3-1, in which Iwagaki’s and Tsuchiya’s formulas were
used for the non-dimensional critical tractive force, with
the result from A3-2 in which only Iwagaki’s formula was
used, it can be seen that the reproducibility of A3-2 was
improved. This is because Tsuchiya’s formula is applica-
ble to smooth surfaces, although it can be used in fixed
beds. The smooth surface condition did not completely
satisfy the conditions of the present experiment. There-
fore, A3-2 was considered to have better reproducibility
than A3-1. Moreover, from a comparison of A2-1, which
uses Eq. (1), and A3-2, which uses Eq. (1) and Eq. (2), it
can be seen that it is necessary to apply the sediment trans-
port rate formula according to the fixed bed, as shown in
Eq. (2) when estimating the sediment transport rate in a
fixed bed. However, the situation in which sediment de-
position did not appear near the shoreline could not be im-
proved despite various examinations. Although the calcu-
lation of amount of sediment deposition with mixed sand
instead of uniform sand under the condition of A3-2 was
conducted, there was no significant difference in the cor-
responding results. When the results of Team A were ex-
amined, reproduction of the amount of sediment deposi-
tion near the shoreline and near the downstream end wall
remained an issue.
Moreover, it is not fully clear why this phenomenon
could not be reproduced by the analysis using the 3D
model. Although not taking the saturated suspended load
concentration into account in the model might be one of
the causes, the most likely cause is the setting of grid
spacing in the vertical direction. In calculations of A1-1
and A1-2, the vertical grid spacing was set to 0.005 m.
However, the flow depth at the time of tsunami run-up on
the slope was quite low, and the vertical grid spacing of
0.005 m may have made the grid too coarse for the 3D
model to calculate the friction velocity from the near-bed
velocity. Therefore, it is necessary to improve the sedi-
ment transport model as well as the 2D model and exam-
ine the setting of the vertical grid spacing in more detail
for the 3D model.
3.2.2. Team B
The results for the simulated water level and velocity
from B1 are shown in Figs. 10 and 11. It was confirmed
that the calculated arrival time of the first wave and wave
height generally coincided with the experimental data in
terms of the water level and current velocity. However,
after the passage of the first wave, a large, reflected wave
was generated from the tank side upstream of the chan-
nel, and a run-up phenomenon of the reflected wave to
the land area occurred. A comparison of the distribution
of the weight of the deposited sand is shown in Fig. 12.
The weight of the deposited sand was almost the same, ex-
cept near the downstream end wall. However, large scour-
ing (which was not observed in the experiment) occurred
near the horizontal and slope areas of the land area at the
transition point between the movable and fixed beds. The
time series of the topography at this point showed that a
strong return flow occurs at the convergence of the first
wave, resulting in significant scouring. One of the rea-
sons for this was that the scouring depth limit was not set
in the model. In addition, the amount of sand deposited
near the downstream end of the wall was larger than the
actual amount. In the experiment, the amount of deposited
sand decreased as it approached the downstream side wall.
However, in the numerical calculation, it increased as it
approached the wall. This was because the model used
for the calculation was a 2D model, and therefore, verti-
cal turbulence was not reflected in the calculation. The
velocity of the flow at this point decreases rapidly with
the wall impact and is considered to have accelerated the
sand deposition.
In B2, only the sand grain size condition in the sedi-
ment transport model was changed to mixed sand. There-
fore, the results for the water level and flow velocity did
not change significantly from the results of B1, as shown
in Figs. 10 and 11. The results for the amount of sand de-
posited in B2 are shown in Fig. 12. The amount of sand
deposited was more consistent with the experimental data
from near the shoreline to the horizontal area relative to
the amount of sand deposited in B1. However, the amount
of sand near the downstream end of the wall was not im-
proved by the calculation considering the mixed sand.
The distribution of each grain size shows that medium-
to coarse-grained sand is abundantly distributed. In con-
trast, the amount of fine-grained sand, which is relatively
easy to transport, is small along the shoreline and near the
wall. This is because strong reflected waves are generated
at the downstream wall, and the waves carry away easily
transportable fine-grained sand.
As a result of B3, although the generation of the re-
flected waves is not completely suppressed, as shown in
Figs. 10 and 11, the wave height of the second wave,
which had been a problem thus far, is slightly improved.
As shown in Fig. 12, the amount of sand deposited in the
horizontal section of the land area increased significantly
near the downstream end of the wall, and the sand near
the shoreline was discharged with the convergence of the
waves. This is in contrast to the previous results. Fig. 11
indicates that the discharge of sediment near the shoreline
in this case was also caused by the predominance of nega-
tive velocities owing to the development of local scouring
at the time of the convergence of the first wave at the tran-
sition between the fixed and movable beds.
During the three-day verification, the reproduction of
the water level and velocity in the second wave was im-
proved by changing the input wave to the dam break.
However, the phase tended to be delayed toward the tip of
the run-up. Therefore, further improvement is needed to
accurately reproduce the amount of deposited sediment.
Journal of Disaster Research Vol.16 No.7, 2021 1023
Yamamoto, A. et al.
Fig. 10. Time series data of water level (Team B).
This is important to address the wall and the switching
point from the fixed bed to the moving bed, where ver-
tical turbulence is especially likely to occur. Moreover,
the calculation time for B3 was shorter than that for B1
and B2, which were conducted under the condition of a
smaller grid size. In this context, it can be confirmed that
the calculation of B3 can be performed stably. As the dis-
tribution of fine sediment at each site was obscured by
increasing the grid size, it was necessary to use different
grid sizes, depending on the required accuracy.
3.2.3. Team C
From C1, it can be seen that the reproductions of the
water level and flow velocity at each location were gener-
ally consistent, as shown in Figs. 13 and 14. However, as
shown in Fig. 15(a), the amount of sand deposited tended
to be unevenly distributed around the upper end of the
wall, indicating that the depositional distribution differed
greatly from the experimental results.
As a result of C2, it was confirmed that the distribution
and total amount of sand deposited in the terrestrial area
were generally good, as shown in Fig. 15(a). The Rouse
number of the fixed bed at 15 m from the gate was gener-
ally 1 during the rising period of the upwelling wave and
exceeded 2.5 in the subsequent flow. In other words, it
was inferred that the flow field was dominated by bedload
transport. Although the experimental video image of the
flow over the fixed bed shows suspended transport, it cap-
tured the advection of the sediment entrainment from the
moving bed at the beginning of the run-up, which implies
that occurrence of resuspension from the bottom was dif-
ficult. To make the model consistent with this sediment
Fig. 11. Time series data of velocity (Team B).
(a) Experiment, B1, B2, and B3
(b) Three grain size in B2
Fig. 12. Comparison of the distribution of the amount of
sand deposited (Team B).
transport field, the hoisting rate on the fixed bed was set
to 0. From the experimental images released on the first
day, the coverage of the deposited sediment was clearly
smaller than 1. Considering that there is a correlation
1024 Journal of Disaster Research Vol.16 No.7, 2021
Comparisons of Numerical Models on Formationof Sediment Deposition Induced by Tsunami Run-Up
Fig. 13. Time series data of water level (Team C).
between the coverage ratio and the reduction rate of the
amount of bedload rate [33], the effect of the coverage ra-
tio was investigated by assuming that the coverage ratio
of the sediment in the fixed bed was 0.2. As a result, it
was found that the amount of deposited sand reproduced
the trend of the sand volume decrease from the shoreline
to the wall, as well as the experimental results. The re-
sult of C2 suggests that the sedimentation distribution can
be improved by considering the sediment transport at the
fixed bed.
As a result of C3, it was confirmed that the phase of the
wave was significantly delayed compared to the experi-
mental value when the MCA scheme was not considered
(case C3-1), as shown in Figs. 13 and 14. In addition, the
phase difference became larger at the top of the run-up.
It was shown that the MCA scheme can reproduce waves
close to the experimental values, even on a dry bed. How-
ever, the model with the non-hydrostatic pressure term
did not show any significant changes (the test case is not
shown in Tables 1 and 3). This suggests that the influ-
ence of the non-hydrostatic pressure term was small in
this case. From the results of C2, it can be seen that sedi-
ment deposition is affected by varying the coverage of the
sediment in the fixed bed area. Therefore, in addition to
C2 in Fig. 15(a), which was conducted with a coverage ra-
tio of 0.2, the results from varying the coverage ratio in the
range of 0.15 to 0.3 (C3-2) show that the overestimation
of the amount of sand deposited near the berm decreases,
and the amount of sand deposited near the wall tends to
increase. However, there are still some problems in re-
producing the amount of sand deposited near the halfway
point and downstream end wall. In addition, the effect
Fig. 14. Time series data of velocity (Team C).
(a) Experiment, C1, C2 and C3-3 with nsl = 0.0065 (nsl :
roughness coefficient on the land (mixed bed) for τ∗)
(b) Sensitivity analyses of nsl in C3-3 (nsl : roughness coeffi-
cient on the land (mixed bed) for τ∗)
Fig. 15. Comparison of the distribution of the amount of
sand deposited (Team C).
Journal of Disaster Research Vol.16 No.7, 2021 1025
Yamamoto, A. et al.
Fig. 16. Comparison of the total amount of sand deposited
in each case (C3-2: A = 0.2, C3-3: nsl = 0.0065).
of Manning’s roughness coefficient on the land nsl on
the sediment distribution in the sediment transport model
was investigated, as shown in C3-3 (coverage ratio of 1).
As a result, when the roughness coefficient was set to 0,
the tendency of sediment accumulation near the shoreline
and decreasing inland could be reproduced, as shown in
Fig. 15(b). By gradually increasing the roughness, the
amount of sand near the shoreline decreased to a value
close to the experimental value, and the sand distribution
gradually shifted to the downstream end wall. Based on
the bedload formula, the relationship between coverage A
and the roughness coefficient of the mixed field consist-
ing of the fixed and movable beds, αns, is appropriated
to O(A1/2) ∼ (α), where α is the correction coefficient.
In other words, the results of the sensitivity analysis in
Fig. 15(b) reflect coverage A, and the reduced roughness
coefficient αns is interpreted to represent the spatiotem-
porally averaged coverage A. The sensitivity analyses im-
ply that an appropriate reduction of Manning’s roughness
coefficient, which corresponds to an equivalent roughness
coefficient, could be an effective method for obtaining a
simple estimation of sediment transport in a mixed field
of fixed and movable beds.
4. Discussion
In the examinations, although there were some cases
with a phase delay of the first wave, in general, all teams
were able to reproduce the experimental waves. Fig. 16
shows the total amount of sediment deposited as per the
results of each model over three days. All team models
were able to reproduce the total amount of sediment de-
posited on land over three days. However, the distribu-
tion of sediment in the land area remained an issue for
each team. Although the distribution of sediment near the
transition between the movable and fixed beds showed a
tendency to improve, it was difficult for all teams to repro-
duce the amount of sediment near the downstream wall.
To discuss the cause of the increased sediment depo-
sition near the downstream side wall, the calculation re-
sults were examined separately for the bedload and sus-
pended load. All teams examined the bedload and sus-
pended load separately, and bedload deposition was found
to be dominant near the transition between the movable
and fixed beds. In addition, it was confirmed that the
sediments around the wall were formed by bed- and sus-
pended loads. This was also confirmed by the results
for C1, C2, and C3-3 of Team C. C2 without sediment
entrainment significantly improved the distribution trend
compared with C1, which overestimated the amount of
sand deposited near the wall. The variation of nsl in C3-3
plays a role in controlling the bedload rate on the fixed
bed. The result (Fig. 15(b)) implied that the entrained
sediment at the slope settled before reaching the down-
stream end wall and that the bedload transport drove the
sediment to the wall side. As nsl can be associated with
the coverage, it is expected that the amount of sand de-
posited near the wall would be smaller because nsl is
larger around the shoreline area where the coverage and
the amount of sand deposited are larger, and nsl is smaller
near the wall where they are smaller. Therefore, the accu-
racy of the distribution may be improved if coverage A can
be expressed as a function of the amount of sand deposited
at each calculation grid. Moreover, in the 2D calculation,
a comparison was performed between a case in which the
distribution of suspended load concentration in the verti-
cal direction was assumed to be an exponential function,
and a case in which the distribution was assumed to be
constant. The results showed that the amount of deposited
sediment near the wall tended to increase more when as-
suming a constant distribution. This result suggests that it
is difficult to reproduce the phenomenon induced by 3D
flow in 2D calculations.
In addition, our study suggests that the reproducibility
of the total amount of sediment in the run-up area can be
improved by properly setting the sediment coverage ratio
in the calculation grid, roughness coefficient, and bedload
transport rate formula, even in the 2D numerical model.
As can be seen from the calculated result C2 indicated in
Fig. 15(a) by Team C, the result of the sediment distribu-
tion is dramatically improved by considering the sediment
coverage ratio in a grid. Therefore, we concluded that
the most important factor in reproducing this phenomenon
with numerical simulations is the consideration of the sed-
iment coverage ratio in a calculation grid. Next, from the
analyses by Team C, in which the sediment coverage ratio
was fixed and the roughness coefficient on the fixed bed
was changed, as shown in Fig. 15(b), and the results in
Section 3.2.3, it can be seen that the change in the rough-
ness coefficient on the fixed bed also affects the calculated
results. In particular, the result for nsl = 0.0065 was the
closest to the experimental data. However, nsl = 0.0065
was too small, even if the experimental channel bed had
a smooth surface. Therefore, we concluded that the set-
tings of the roughness coefficient on the fixed bed can-
not affect the calculated results as much as the considera-
tion of the sediment coverage ratio. Finally, as mentioned
in the results of Section 3.2.1, from the simulated result
A3 shown in Fig. 9 from Team A, it was found that the
1026 Journal of Disaster Research Vol.16 No.7, 2021
Comparisons of Numerical Models on Formationof Sediment Deposition Induced by Tsunami Run-Up
change in the bedload transport rate formula on the fixed
bed also improved the calculated result. However, no dra-
matic improvement was achieved, and the experimental
data could not be sufficiently reproduced. Therefore, we
have identified that the effect of changing the bedload
sediment transport formula for the calculated results was
smaller than the effect of setting the roughness. More-
over, the simulated result B2 indicated in Fig. 12(a) from
Team B shows the mixed sand result, but there was no
dramatic change from B1, that is, the uniform sand result.
Therefore, the effect of the mixed sand was considered to
be small within the scope of the experimental conditions
covered in this study. According to the above results, to
reproduce this phenomenon by numerical simulation, the
following factors are considered to have an impact on the
results: (1) whether or not the sediment coverage ratio in a
calculation grid is taken into consideration, (2) the setting
of the roughness coefficient on the fixed bed, and (3) the
selection of the bedload transport rate formula.
Furthermore, as the computational load for the 2D cal-
culations was small, the results can be shown and dis-
cussed based on a relatively short time (e.g., three days
in this study). As this advantage is effective in emergency
situations requiring immediate results, it is necessary to
continue working on improving the reproducibility of the
phenomenon. Therefore, it is expected that a new 2D
model for accurately reproducing this phenomenon will
be developed in the future. This can be achieved by lo-
cally incorporating a 3D model approach into a 2D model
while simultaneously examining the above three factors
and the vertical grid spacing of the 3D model.
5. Conclusion
In this study, three teams conducted several numeri-
cal simulations using various numerical models, aiming
to reproduce sediment deposition on land, as induced by
a tsunami run-up. With respect to the tsunami flow, all
teams were able to reproduce the experimental data. How-
ever, in terms of the distribution of the sediment deposits,
the initial calculations showed that each team had prob-
lems near the switching point between the movable and
fixed beds and near the downstream wall. Therefore, to
solve these problems, each team conducted various ex-
aminations by changing the bedload transport rate for-
mula, sediment coverage ratio in a grid, roughness, and
other parameters. Consequently, it was found that the phe-
nomenon could be reproduced with some accuracy by a
2D model into which the above changes had been intro-
duced. However, the sediment deposition near the down-
stream end wall generated by the 3D flow could not be
reproduced by a 2D model.
A detailed investigation using a 3D flow model will
be necessary to clarify the phenomenon of sedimentation
near the downstream end wall. However, from the view-
point of practicality, the reproduction of the phenomenon
using a 2D model is desired. Hence, we expect to de-
velop a new 2D model for accurately reproducing this
phenomenon by locally incorporating a 3D model into a
2D model.
Acknowledgements
This study was made possible with the support of the Coastal En-
gineering Committee of the JSCE. The experimental work was
supported by JSPS KAKENHI Grant Number 17H02060. We
would also like to express our gratitude to Dr. Yoshinori Shigihara
of the National Defense Academy for his advice on writing this
paper and thank him for this opportunity.
References:[1] T. Abe, K. Goto, and D. Sugawara, “Relationship between the
maximum extent of tsunami sand and the inundation limit of the2011 Tohoku-oki tsunami on the Sendai Plain, Japan,” SedimentaryGeol., Vol.282, pp. 142-150, doi: 10.1016/j.sedgeo.2012.05.004,2012.
[2] F. Nanayama, A. Makino, K. Satake, R. Furukawa, Y. Yokoyama,and M. Nakagawa, “Twenty tsunami event deposits in the past 9000years along the Kuril subduction zone identified in Lake Harutori-ko, Kushiro City, eastern Hokkaido, Japan,” Annual Report on Ac-tive Fault and Paleoearthquache Researches, No.1, pp. 233-249,2001 (in Japanese).
[3] O. Fujiwara, T. Kamataki, J. Uchida, K. Abe, and T. Haraguchi,“Early Holocene coseismic uplift and tsunami deposits recordedin a drowned valley deposit on the SE coast of the Boso Penin-sula, central Japan,” Quaternary Res., Vol.48, No.1, pp. 1-10, doi:10.4116/jaqua.48.1, 2009 (in Japanese).
[4] D. Sugawara, “Tsunami sedimentation amd deposits due to the 2011Tohoku earthquake: a review of case studies from Sendai and Hi-rota Bays,” Jour. Geol. Soc. Japan, Vol.123, No.8, pp. 781-804, doi:10.5575/geosoc.2017.0047, 2017 (in Japanese).
[5] D. Sugawara, K. Goto, and B. E. Jaffe, “Numerical mod-els of tsunami sediment transport – Current understanding andfuture directions,” Mar. Geol., Vol.352, pp. 295-320, doi:10.1016/j.margeo.2014.02.007, 2014.
[6] B. E. Jaffe, K. Goto, D. Sugawara, G. Gelfenbaum, and S. L. Selle,“Uncertainty in Tsunami Sediment Transport Modeling,” J. Disas-ter Res., Vol.11, No.4, pp. 647-661, doi: 10.20965/jdr.2016.p0647,2016.
[7] T. Takahashi, N. Shuto, F. Imamura, and D. Asai, “Modeling sedi-ment transport due to tsunamis with exchange rate between bedloadlayer and suspended load layer,” Proc. of the Int. Conf. Coastal Eng,pp. 1508-1519, doi: 10.1061/40549(276)117, 2000.
[8] C. W. Hirt and J. M. Sicilian, “A porosity technique for the defini-tion obstacles in rectangular cell meshes,” Proc. of 4th Int. Conf. onNum. Ship Hydrodyn., pp. 1-19, 1985.
[9] K. Ashida and M. Michiue, “Study on hydraulic resistance and bed-load transport rate in alluvial streams,” Proc. of the Japan Soc. ofCivil Eng., Vol.206, pp. 59-69, doi: 10.2208/jscej1969.1972.20659, 1972 (in Japanese).
[10] T. Yoshii, M. Ikeno, and M. Matsuyama, “Experimental Studyof Sediment Transport caused by Tsunami,” Proc. Coastal Eng.,Vol.55, pp. 441-445, doi: 10.2208/proce1989.55.441, 2008 (inJapanese with English abstract).
[11] T. Itakura and T. Kishi, “Open channel flow with suspended sedi-ments,” J. Hydraul. Div., ASCE, Vol.106(HY8), pp. 1325-1343, doi:10.1061/JYCEAJ.0005483, 1980.
[12] W. W. Rubey, “Settling velocities of gravel, sand, and silt particles,”Am J. Sci., Vol.25, pp. 325-338, doi: 10.2475/ajs.s5-25.148.325,1933.
[13] C.-W. Shu, “High order finite difference and finite volumeWENO schemes and Discontinuous Galerkin methods for CFD,”Int. J. Comput. Fluid D., Vol.17, No.2, pp. 107-118, doi:10.1080/1061856031000104851, 2003.
[14] S. V. Patankar, “Chapter 5: Convection and Diffusion,” S. V.Patankar, “Numerical Heat Transfer and Flow,” McGraw-Hill,1980.
[15] S. Ushijima and I. Nezu, “Computational method for free-surfaceflows on collocated grid with moving curvilinear coordinates,” J.Jpn. Soc. of Civil Eng., No.698/II-58, pp. 11-19, doi: 10.2208/jscej.2002.698 11, 2002 (in Japanese with English abstract).
[16] Y. Kajikawa and M. Kuroiwa, “Numerical simulation of 3D flowand topography change in harbor caused by Tsunami,” Proc. 10thInt. Conf. on Asian and Pacific Coasts (APAC 2019), pp. 183-190,doi: 10.1007/978-981-15-0291-0 26, 2019.
Journal of Disaster Research Vol.16 No.7, 2021 1027
Yamamoto, A. et al.
[17] M. Ikeno, T. Yoshii, M. Matsuyama, and N. Fujii, “Estimationof pickup rate of suspended sand by tsunami experiment andproposal of pickup rate formula,” J. Jpn. Soc. of Civil Eng.,Ser. B2 (Coastal Engineering), Vol.65, No.1, pp. 506-510, doi:10.2208/kaigan.65.506, 2009 (in Japanese with English abstract).
[18] S. Gottlieb and C.-W. Shu, “Total variation diminishing Runge-Kutta schemes,” Math. Comput., Vol.67, pp. 73-85, doi:10.1090/S0025-5718-98-00913-2, 1998.
[19] Y. Kajikawa and O. Hinokidani, “Development of 2-D shallow-water flow model using WENO scheme,” J. Jpn. Soc. of Civil Eng.,Ser. B1 (Hydraulic Engineering), Vol.69, No.4, pp. I 631-636, doi:10.2208/jscejhe.69.I 631, 2013 (in Japanese with English abstract).
[20] Y. Iwagaki, “(I) Hydrodynamical study on critical tractive force,”Trans. Jpn. Soc. of Civil Eng., Vol.1956, Issue 41, pp. 1-21, doi:10.2208/jscej1949.1956.41 1, 1956 (in Japanese with English ab-stract).
[21] T. Tsuchiya, “Scour limit at the downstream end of a smooth-surfaced channel bed,” Trans. Jpn. Soc. of Civil Eng., Vol.80,pp. 18-28, doi: 10.2208/jscej1949.1962.80 18, 1956 (in Japanese).
[22] T. Takahashi, T. Kurokawa, M. Fujita, and H. Shimada, “Hydraulicexperiment on sediment transport due to tsunamis with various sandgrain size,” J. Jpn. Soc. of Civil Eng., Ser. B2 (Coastal Engineer-ing), Vol.67, pp. 231-235, doi: 10.2208/kaigan.67.I 231, 2011 (inJapanese with English summary).
[23] J. T. Limerinos, “Determination of the manning coefficient frommeasured bed roughness in natural channels,” Water Supply Paper,1898-B, United States Geological Survey, doi: 10.3133/wsp1898B,1970.
[24] K. Yamashita, Y. Yamazaki, Y. Bai, T. Takahashi, F. Imamura,and K. F. Cheung, “Coupled non-hydrostatic flow and sedimenttransport model for investigation of coastal morphological changescaused by tsunamis,” 27th IUGG General Assembly, 2019.
[25] Y. Yamazaki, Z. Kowalik, and K. F. Cheung, “Depth-integrated,non-hydrostatic model for wave breaking and runup,” Int. J. Numer.Methods Fluids, Vol.61, No.5, pp. 473-497, doi: 10.1002/fld.1952,2009.
[26] Y. Yamazaki, K. F. Cheung, and Z. Kowalik, “Depth-integrated,non-hydrostatic model with grid nesting for tsunami generation,propagation, and run-up,” Int. J. Numer. Methods Fluids, Vol.67,pp. 2081-2107, doi: 10.1002/fld.2485, 2011.
[27] G. S. Stelling and M. Zijlema, “An accurate and efficient finite-difference algorithm for non-hydrostatic free-surface flow with ap-plication to wave propagation,” Int. J. Numer. Methods Fluids,Vol.43, No.1, pp. 1-23, doi: 10.1002/fld.595, 2013.
[28] G. S. Stelling and S. P. A. Duinmeijer, “A staggered conservativescheme for every Froude number in rapidly varied shallow waterflows,” Int. J. Numer. Methods Fluids, Vol.43, No.10, pp. 1329-1354, doi: 10.1002/fld.537, 2003.
[29] J. F. Richardson and W. N. Zaki, “Sedimentation and fluidization:Part I,” Trans. Inst. Chem. Eng., Vol.32, pp. 35-52, 1954.
[30] D. Sugawara, H. Naruse, and K. Goto, “On the role of energy bal-ance for numerical modelling of tsunami sediment transport,” AGU2014 Fall Meeting, 2014.
[31] J. Xu, “Grain-size characteristics of suspended sediment in theYellow River, China,” Catena, Vol.38, No.3, pp. 243-263, doi:10.1016/S0341-8162(99)00070-3, 1999.
[32] J. Xu, “Erosion caused by hyperconcentrated flow on the LoessPlateau of China,” Catena, Vol.36, No.1-2, pp. 1-19, doi:10.1016/S0341-8162(99)00009-0, 1999.
[33] G. Tanaka and N. Izumi, “The bedload transport rate and hy-draulic resistance in bedrock chanels partly covered with gravel,”J. Jpn. Soc. of Civil Eng., Ser. B1 (Hydraulic Engineering), Vol.69,No.4, pp. I 1033-I 1038, doi: 10.2208/jscejhe.69.I 1033, 2013 (inJapanese with English abstract).
Name:Ako Yamamoto
Affiliation:Assistant Professor, National Defense Academy
Address:1-10-20 Hashirimizu, Yokosuka, Kanagawa 239-8686, Japan
Brief Career:2016- Graduate School of Society Sciences, Kansai University
2018- Forestry and Forest Products Research Institute
2021- National Defense Academy
Selected Publications:• A. Yamamoto, T. Takahashi, K. Harada, M. Sakuraba, and K. Nojima,
“Hydraulic experiment on tsunami deposits formation related with sand
grain and bore wave,” J. Jpn. Soc. of Civil Eng., Ser. B2 (Coastal
Engineering), Vol.73, pp. 367-372, 2017 (in Japanese).
• A. Yamamoto, T. Takahashi, K. Harada, M. Sakuraba, and K. Nojima,
“Validation of Sediment Transport Model Using Hydraulic Experiment
Data to Assess the Influence of Grain Size and Reflection Wave on
Tsunami Deposit,” Safety Science Review, Vol.9, pp. 3-19,
http://hdl.handle.net/10112/00017148, 2019.
Academic Societies & Scientific Organizations:• Japan Society of Civil Engineers (JSCS)
• Sedimentological Society of Japan (SSJ)
• Japanese Society of Coastal Forest (JSCF)
• Japan Geoscience Union (JpGU)
• American Geophysical Union (AGU)
Name:Yuki Kajikawa
Affiliation:Associate Professor, Social Systems and Civil
Engineering, Tottori University
Address:4-101 Minami, Koyama-cho, Tottori 680-8552, Japan
Brief Career:2006- Research Associate, Faculty of Engineering, Tottori University
2008- Assistant Professor, Graduate School of Engineering, Tottori
University
2018- Associate Professor, Social Systems and Civil Engineering, Tottori
University
Selected Publications:• “Effect of Check Dam System on Water Redistribution in the Chinese
Loess Plateau,” J. of Hydrologic Eng., Vol.18, No.8, pp. 929-940, 2013.
• “Three-Dimensional Numerical Analysis of Tsunami Runup-Induced
Local Scouring around a Cylinder,” J. Jpn. Soc. of Civil Eng., , Ser. B2
(Coastal Engineering), Vol.76, No.2, pp. I 487-I 492, 2020 (in Japanese).
Academic Societies & Scientific Organizations:• Japan Society of Civil Engineers (JSCE)
• Japan Society for Natural Disaster Science (JSNDS)
1028 Journal of Disaster Research Vol.16 No.7, 2021
Comparisons of Numerical Models on Formationof Sediment Deposition Induced by Tsunami Run-Up
Name:Kei Yamashita
Affiliation:Researcher, Division of Research for Earthquake
and Tsunami Regulatory Standard and Research
Department, Nuclear Regulation Authority
Address:1-9-9 Roppongi, Minato-ku, Tokyo 106-8450, Japan
Brief Career:2014- Postdoctoral Researcher, International Research Institute of Disaster
Science (IRIDeS), Tohoku University
2015- Assistant Professor, IRIDeS, Tohoku University
2018- Visiting Researcher, University of Hawaii
2018- Researcher, Tokushima University
2018- Associate Professor, IRIDeS, Tohoku University
2021- Researcher, Nuclear Regulation Authority
Selected Publications:• “Development of a tsunami inundation analysis model for urban areas
using a porous body model,” Geosciences, Vol.8, Issue 1, No.12, 2018.
• “Numerical simulations of large-scale sediment transport caused by the
2011 Tohoku Earthquake Tsunami in Hirota Bay, Southern Sanriku Coast,”
Coastal Engineering J., Vol.58, No.4, Article No.1640015, doi:
10.1142/S0578563416400155, 2016.
Academic Societies & Scientific Organizations:• Japan Society of Civil Engineers (JSCE)
• American Geophysical Union (AGU)
Name:Ryota Masaya
Affiliation:Telecom Business Division, Telecom and Utility
Business Sector, NTT DATA Corporation
Address:3-3-3 Toyosu, Koto-ku, Tokyo 135-6033, Japan
Brief Career:2018- Graduate School of Engineering, Tohoku University
2021- NTT DATA Corporation
Selected Publications:• “Investigating beach erosion related with tsunami sediment transport at
Phra Thong Island, Thailand, caused by the 2004 Indian Ocean tsunami,”
Natural Hazards and Earth System Sciences, Vol.20, pp. 2823-2841, 2020.
Name:Ryo Watanabe
Affiliation:Civil and Environmental Engineering, Graduate
school of Engineering, Tohoku University
Address:6-6-06 Aza-Aoba, Aramaki, Aoba-ku, Sendai, Miyagi 980-0845, Japan
Brief Career:2020- Civil and Environmental Engineering, Graduate school of
Engineering, Tohoku University
Selected Publications:• “Topographic changes caused by the 1964 Alaska Tsunami in Discovery
Bay, State of Washington, USA,” J. Jpn. Soc. of Civil Eng., Ser. B2
(Coastal Engineering), Vol.76, No.2, pp. I 433-I 438, 2020.
Academic Societies & Scientific Organizations:• Japan Society of Civil Engineering (JSCE)
Name:Kenji Harada
Affiliation:Associate Professor, Center for Integrated Re-
search and Education of Natural Hazards,
Shizuoka University
Address:836 Ohya, Suruga-ku, Shizuoka 422-8529, Japan
Brief Career:2003- Postdoctoral Fellow, Disaster Prevention Research Institute, Kyoto
University
2005- Research Scientist, Disaster Reduction and Human Renovation
Institution
2008- Assistant Professor, Saitama University
2011- Associate Professor, Shizuoka University
Selected Publications:• A. Kitamura, Y. Yamamoto, K. Harada, and T. Toyofuku, “Identifying
storm surge deposits in the muddy intertidal zone of Ena Bay, Central
Japan,” Marin Geology, Vol.426, Article No.106228, 2020.
• T. Noda, K. Yamori, and K. Harada, “Development of Disaster Response
Applications and Improvements in Regional Disaster Prevention Capacity
Based on Collaborative Information Use,” J. Disaster Res., Vol.14, No.2,
pp. 375-386, 2019.
Academic Societies & Scientific Organizations:• Japan Society of Civil Engineers (JSCE)
• Japan Society for Natural Disaster Science (JSNDS)
• Japan Association for Earthquake Engineering (JAEE)
• The Seismological Society of Japan (SSJ)
• Japan Society for Disaster Information Studies (JASDIS)
• American Geophysical Union (AGU)
• Asia Oceania Geoscience Society (AOGS)
• Japan Geoscience Union (JpGU)
Journal of Disaster Research Vol.16 No.7, 2021 1029
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