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Coastal Engineering 140 (2018) 306–315
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Coastal Engineering
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Energy Grade Line Analysis of Tsunami run-up on the Sendai Plain after the
2011 Tohoku earthquake
Tsuyoshi Tadaa,∗,1, Yoshihisa Miyataa,1, Richard J. Bathurstb,1
Department of Civil and Environmental Engineering, National Defense Academy, 1-10-20 Hashirimizu, Yokosuka, 239-8686, Japan
GeoEngineering Centre at Queen's-RMC, Department of Civil Engineering, Royal Military College of Canada Kingston, Ontario, K7K 7B4, Canada
Energy grade line analysis
2011 Tohoku earthquake
Database measurements
Sendai plain
Energy Grade Line Analysis (EGLA) of tsunami run-up has been proposed as a simple tool to predict inundation
heights and tsunami loads. A large database of more than 500 inundation measurements collected on the Sendai
Plain on the east coast of Japan after the Tohoku earthquake of 2011 provided the writers the opportunity to
evaluate the accuracy of the general EGLA method and to make adjustments to fit the model to the Sendai Plain.
Refinements to the EGLA model included a correction for the influence of large linear topographic obstructions
on tsunami flows in order to achieve better agreement with measured inundation heights. The study illustrates
that inundation height predictions are sensitive to the choice of Froude number parameter and land use
roughness coefficients. An important outcome of this study is a site-specific tool for probabilistic prediction of
inundation heights over the Sendai Plain that is of value for tsunami counter measure planning including design
of tsunami resistant structures.
1. Introduction
tsunami loads. This is the motivation for the current study.
Tsunamis can cause significant loss of life and property. During the
2011 Tohoku earthquake2 tsunami, more than18,000 persons were lost.
The total land area along the Pacific coast of Japan affected by the
tsunami was 561 km2 and much damage was done to industrial installations, power and transportation infrastructure (The, 2011 Tohoku
Earthquake Tsunami Joint Survey Group, 2011; Mori and Takahashi,
2012; Mori et al., 2011). One area that was damaged was the Sendai
Plain. This event has put renewed focus on tsunami countermeasure
strategies to minimize property loss and to protect human life (Coleman
et al., 2011; Monastersky, 2012). Countermeasures that have been
discussed include establishment of warning and evacuation systems,
and land use control (FEMA P-646, 2012). Disaster prevention/mitigation schemes based on “multiple defense” have also been proposed
(Cyranoski, 2012; Central Disaster Management Council of Japan,
2011). These multiple defenses consist of a seawall followed by restricted land use, strengthened buildings and elevated embankments.
Tsunami-proof structures used as evacuation facilities are also part of
the planning. A necessary prerequisite for effective tsunami counter
measure planning, including design of tsunami-resistant structures, is
satisfactory predictions of the flooded area, inundation heights and
2. Background and objectives
The general approaches for tsunami inundation prediction are based
on 1) analytical or semi-analytical solutions and 2) numerical hydrodynamic models. The former offer the advantage of simplicity at the
cost of accuracy and range of application as a result of the simplifying
assumptions required to obtain an analytical solution (Peregrine and
Williams, 2001; Carrier et al., 2003; Yeh, 2006). The latter approaches
offer better accuracy and wider range of application. Titov and
Synolakis (1998) developed a numerical simulation method that was
va1idated against large-scale laboratory experimental data. Their
method was used for run-up analyses of the 1993 tsunami in Okushiri
(Japan), the 1994 tsunami in the Kuril Islands (Russia) and the 1996
event in Chimbote (Peru). Goto et al. (2013) carried out a preliminary
survey of the Sendai Plain shortly after the 2011 tsunami and compared
measured run-up data to predictions using a 2D numerical model. The
disadvantage of numerical hydrodynamic models is that they require
initial and boundary conditions, such as wave source characteristics,
friction between tsunami and the land surface, and land boundary
Corresponding author.
E-mail addresses: (T. Tada), (Y. Miyata), (R.J. Bathurst).
All three authors contributed equally to this paper.
official name given by the Japan Meteorological Agency (JMA) is "2011 off the Pacific Coast of Tohoku Earthquake".
Received 20 March 2018; Received in revised form 24 June 2018; Accepted 12 August 2018
Available online 13 August 2018
0378-3839/ © 2018 Elsevier B.V. All rights reserved.
Coastal Engineering 140 (2018) 306–315
T. Tada et al.
Fig. 1. Location of Sendai Plain study area.
and Naito et al. (2016) using sites in Oregon and Hawaii, respectively.
Kriebel et al. (2017) compared predictions using EGLA with the results
of Monte Carlo simulations using the program COULWAVE (Lynett
et al., 2002; Park et al., 2013). Kriebel et al. (2017) concluded that the
EGLA approach is conservative (i.e., overestimates maximum inundation depth and maximum velocity). The need to investigate the veracity
of the EGLA method against real-world scenarios with physical data
was noted by Naito et al. (2016). Carden et al. (2015) compared EGLA
predictions against measurements of flow depths and velocities recorded at five different locations in the Tohoku area after the 2011
However, for the design of a multiple defense systems extending
over large urban areas located on tabular topography a simple analytical model with a minimum number of input parameters is likely the
only practical methodology. Such an approach is the Energy Grade Line
Analysis (EGLA) method that is described in Chapter 6 of ASCE standard ASCE/SEI 7-16 (2017). Greater detail and explanation of the
general approach can be found in the paper by Kriebel et al. (2017)
where the EGLA approach is called the Energy Method (EM).
Earlier efforts to calibrate and investigate the accuracy of the EGLA
based on numerical modelling have been described by Weibe (2013)
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T. Tada et al.
(caption on next page)
Coastal Engineering 140 (2018) 306–315
T. Tada et al.
Fig. 2. Land use and survey points on Sendai Plain.
conducted by a collaboration of 64 research institutes located in Japan
(Mori and Takahashi, 2012). The original survey comprised of measurements of inundation and run-up heights located with longitude and
latitude co-ordinates. A total of 2700 run-up heights and 3200 inundation heights were collected by Mori and Takahashi (2012) for the
larger Tohoku target area which includes the Sendai Plain. The original
locations of survey points for the Sendai Plain are shown in Fig. 2.
The Sendai site was revisited by the first author and the database of
measurements described above was reexamined (Tada et al., 2018).
Some original data points were removed as shown in Fig. 2. These include spot measurements representing flow conditions that were influenced by proximity to local obstructions such as buildings, bridge
columns, soil structures (e.g., embankments), and trees. The EGLA
model in this paper is based on energy dissipation due to friction;
hence, those data where deviations from macroscale area roughness are
relatively large were removed. Obstructions of the type described above
are expected to generate locally reduced inundation distances on the
Sendai Plain (Goto et al., 2013). The influence of the two rivers shown
in Fig. 2 was also removed as were a number of small channels. Clearly
a river offers a preferential path for tsunami flows to penetrate inland.
Original measurements taken on dyke and road embankment slopes
were also excluded.
Initial reports of inundation heights of 12 m or more close to the
shoreline have since been discounted by Japanese coastal engineers.
Tada et al. (2018) also removed some anomalous flow depth records
that were due to splash-up marks and errors in inundation heights due
to misinterpretation of topographic elevations at observation points.
Table 1 summarizes the number and type of observations that have
been removed from the original database for the Sendai Plain. Fig. 3
shows removed data and the final data points used in this study (Tada
et al., 2018).
The writers located the measurement co-ordinates for the filtered
Table 1
Summary of observations at survey points for Sendai Plain.
Inundation height
Run-up height
Unobstructed (used)
Obstructed (removed)
From original database from Mori and Takahashi (2012).
Tohoku earthquake tsunami including one location on the Sendai Plain.
In this study, EGLA predictions for 64 transects of the Sendai Plain
are compared to a large database of inundation heights recorded at
more than 500 locations after the 2011 Tohoku earthquake tsunami.
The Froude number parameter α and Manning's n in the EGLA equations are then adjusted to improve the agreement with measured data.
The important outcomes from this study are 1) lessons learned to improve the accuracy of the EGLA approach and, 2) a site-specific prediction tool for tsunami counter measure planning for the Sendai Plain.
As part of the current study, the original database of measurements
collected by Mori and Takahashi (2012) soon after the tsunami was also
reexamined and anomalous data removed. This database is now available for future studies.
3. Post-event survey database for Sendai Plain
The Sendai Plain study area is shown in Fig. 1 and was heavily
damaged by the 2011 Tohoku earthquake tsunami. The terrain is generally flat and landuse is relatively homogeneous as shown in Fig. 2.
These conditions make the Sendai Plain an attractive location to investigate the Energy Grade Line Analysis (EGLA) method.
The post-event survey of the 2011 Tohoku earthquake tsunami was
Fig. 3. Corrected survey data used in this study (data from Tada et al., 2018).
Coastal Engineering 140 (2018) 306–315
T. Tada et al.
Fig. 4. Energy grade line analysis EGLA (ASCE/SEI 7-16, 2017).
Fig. 5. Transects used in current study.
range of inundation limits was 2800–5300 m in the updated database.
The maximum and average ground elevation above topographic sea
level (i.e., sea level at time of tsunami) were 6.7 m and 1.4 m, respectively, based on measurements made at the filtered observation points
used in the current study.
Table 2
Manning's roughness coefficient, n for Energy Grade Line Analysis (ASCE/
SEI 7-16, 2017).
Description of frictional surface
Coastal nearshore bottom friction
Open land or field
All other cases
Buildings of at least urban density
0.025 to 0.03
4. Analysis method
The Energy Grade Line Analysis (EGLA) method was used in this
study (Fig. 4). The details of the method can be found in the paper by
Naito et al. (2016). The method is based on the energy equation for onedimensional steady state flow. The solution for inundation height, I can
be solved at the end of each increment of distance, x using a conventional first-order forward difference approximation. Increments of distance (Δx) start from the maximum inundation limit distance xR from
the shoreline following thetransect oriented perpendicular to the
shoreline. The numerical formulation includes an approximation to the
Froude number expressed as:
Table 3
Manning's roughness coefficient, n for different land use types in
Japan (Kotani et al., 1998).
Land use category
Residential land (high density)
Residential land (medium density)
Residential land (low density)
Factory and other land
Forest land
Others (vacant lots, green spaces, etc.)
Fr = α (1 − x / xR)1/2
The dissipation of energy over each increment of distance is equated
to an estimate of surface roughness for that increment quantified by
Mannings's n.
A total of 64 transects were used in this study at the locations shown
in Fig. 5. The starting point for each transect was taken at the Sendai
Bay shoreline and the endpoint was taken at the corresponding run-up
observation point. The length of the transects matches the inundation
limits noted above. The elevation profile for each transect was taken
from the digital elevation map (DEM) for the study area that is available
from the Geospatial Information Authority of Japan (http://www.gsi. The increment of distance was taken as
Δx = 25 m. The recorded run-up heights were within 1 m of the DEM
elevations, hence z(xR) was taken as the DEM elevation at the location
data on digital topographic maps to determine the topographic elevation and distance of each measurement point from the shoreline. Using
the sea level at the time of tsunami as datum, the inundation height
(I = h + z = maximum water height above sea level over the inundation distance) and run-up height, R (height above sea level at inland
limit of tsunami) shown in Fig. 4 were computed at each measurement
location. The filtered data were then mapped to the topographic data to
establish the distances between measurement points and the shoreline
identified in Fig. 1 and observation point elevations. The maximum runup height was 4 m and the maximum inundation height was 11 m. The
Coastal Engineering 140 (2018) 306–315
T. Tada et al.
Fig. 6. Projection of measurement point on transect.
elevation extended horizontally to find the inundation limit.
In this study we introduce an alternative approach which is to reduce the elevation of the topographical obstruction to less than the
predicted hydraulic height. The correction is carried out as follows:
Table 4
EGLA scenarios.
Parameter set
EGLA Method 1
EGLA Method 2
n from Table
α = 1.3
n from Table
α = 1.0
n from Table 3
Residential land (low density)
n = 0.03
α = 1.0
1. Define the topographic data for the transect.
2. Begin EGLA from inundation limit towards the shoreline.
3. If the topographic height of an obstruction is greater than the predicted hydraulic height, the elevation of the obstruction is reduced
to the elevation at the previous calculation step. Go back to step 2.
4. Continue incremental calculations until the shoreline is reached.
The rationale for this approach was the observation that flows were
observed to go around obstacles such as berms and road embankments
using culverts and underpasses during the Sendai Plain event.
Table 2 reproduces recommended Manning's roughness parameter n
found in the ASCE/SEI 7-16 (2017) guidelines. In Japan, the n values
recommended by Kotani et al. (1998) are prescribed by the Ministry of
Land, Infrastructure, Transport and Tourism of Japan (2012). These
values are shown in Table 3. Based on land use in the study area the
of the run-up observation point and corrections such as the Extended
EGLA method adopted by Naito et al. (2016) were not required.
Strategies to correct for topography features that project above the
run-up elevation or inundation depth are necessary using the EGLA
model. For example, if the topographic elevation is greater than the
run-up elevation, ASCE/SEI 7-16 (2017) recommends that the elevation
of the topographic feature be taken as the run-up elevation and this
a) Scenario A
b) Scenario B
c) Scenario C
d) Scenario D
Fig. 7. Example of predicted energy grade line and inundation heights, and measured inundation heights along example transect.
Coastal Engineering 140 (2018) 306–315
T. Tada et al.
a) Scenario A
b) Scenario B
c) Scenario C
d) Scenario D
Fig. 8. Comparison of predicted and measured inundation heights.
slope is 1∕100 or milder. This value has been justified due to bores that
can develop at the tsunami wave front particularly for shallow nearshore bathymetry. Bathymetric gradients for Sendai Bay are shallow at
1/100 out to 500 m and about 1/200 thereafter to about 5000 m.
Carden et al. (2015) assumed α = 1.3 based on ASCE/SEI 7-16 (2017)
recommendations. However, video recordings showed that bores at the
front wave did not appear at locations where inundation heights were
greatest. Some video recordings showed that the water level gradually
rose over several minutes after the front of the wave reached the
shoreline. Hence, the highest watermarks were not always marked by
the bore at the front of the tsunami. For this reason, a Froude number of
α = 1 was judged to be more applicable for the Sendai Plain analyses to
A total of 451 unobstructed inundation height measurements
(Table 1) were projected onto the nearest of 64 transects as shown in
Fig. 6. The projection distance varied from zero to 900 m with most
points within 100 m of the transect line.
Table 5
Summary of bias statistics where bias is the ratio of measured to predicted
inundation height.
Number of data points
Bias statistics
Spearman's ρ
Note: Calculations with 17 data points correspond to example transect.
Calculations with 451 data points correspond to data points from all 64
At level of significance of 5%.
5. Results and discussion
value of 0.04 corresponding to residential land (low density) may be
too high. For this reason analyses were also carried out using n = 0.03
for this land use category.
In ASCE/SEI 7-16 (2017) guidelines the Froude number coefficient
in Equation (1) is taken as α = 1.3 when the nearshore bathymetric
Four different scenarios were investigated to evaluate EGLA method
accuracy using the adjustment for obstructions recommended in ASCE/
SEI 7-16 (2017) guidelines (EGLA Method 1) and the alternative
treatment proposed by the authors to better match observations made
Coastal Engineering 140 (2018) 306–315
T. Tada et al.
Fig. 9. Characteristics of model bias for predicted inundation heights using Scenario D.
Fig. 10. Probability of exceedance of predicted inundation height using Scenario A, B, C and D.
Coastal Engineering 140 (2018) 306–315
T. Tada et al.
6. Conclusions
during the Sendai Plain tsunami inundation in the vicinity of linear
obstacles (EGLA Method 2). The latter approach was examined using
different choices of Froude number and Manning's roughness coefficient
identified in parameter sets 1, 2 and 3 in Table 4. Parameter set 2 uses n
values recommended in current Japanese practice. Parameter set 3 replaces the value of n = 0.04 with n = 0.03 for the low density residential land use category.
The results of analyses are shown in the plots of Fig. 7 for the example transect identified in Fig. 5. A total of 17 measurement points
were projected onto this transect. These measurement points were located within 250 m of each side of the transect. These plots show that
Scenario A gives the poorest agreement between predicted and measured inundation heights. Fig. 7a (Scenario A) shows the location and
height of a highway embankment at about 3200 m from the shoreline.
This feature is largely responsible for the poor agreement noted above.
The better agreement between measured and predicted inundation
heights in the remaining figures is ascribed to the alternative treatment
of topographic projections proposed by the writers.
Fig. 8 shows measured versus predicted inundation heights using all
451 measurement points projected onto all 64 transect lines. The visual
impression is that Scenario B gives better agreement than Scenario A,
but both Scenarios C and D give similar and better agreement than
Scenario B. However, a quantitative assessment of relative accuracy can
be carried out using bias analysis where bias is the ratio of measured to
predicted inundation height. Bias statistics are summarized in Table 5
for each EGLA scenario using the example transect line with 17 data
points and all 451 measurement points from all 64 transects. Scenarios
with mean (average) of bias values close to one and smaller coefficient
of variation (COV) of bias values are more accurate. Based on the values
shown in Table 5, the average accuracy of the four scenarios in this
study and the spread in their accuracy improves in the order of Scenario
A, B, C and D. Another desirable feature of any model approach is that
here are no undesirable dependencies (correlations) between bias and
predicted inundation height. If there are, then model accuracy varies
with magnitude of predicted inundation height. Potential dependencies
of this type are quantified here using Spearman's rank correlation test
which is a measure of the strength of the monotonic relationship between data pairs. The results of this test are also shown in Table 5. The
dependency test for Scenario D with 451 data points was very close to
the 5% level of significance criterion and thus bias values and predicted
inundation heights are judged to be practically uncorrelated for both
Scenario C and D. Fig. 9a confirms, at least visually, that there is no bias
dependency with inundation height.
Fig. 9 shows Scenario D plots of bias values against normalized
distance from shoreline (Fig. 9a), distance from transect line (Fig. 9b)
and elevation discrepancy (Fig. 9c). Spearman's correlation tests
showed that in each of these plots the model accuracy was uncorrelated
with the independent parameter at or about a level of significance of
5%. According to the EGLA formulas, greater elevation leads to higher
water level and thus a positive correlation must be expected in Fig. 9d.
On the other hand, a negative correlation is expected according to 1D
open channel flow theory with the condition Fr < 1. A Spearman's
correlation coefficient of +0.22 between bias and elevation discrepancy was computed for the data in Fig. 9d at a level of significance
of 5%. Hence, it can be argued that the former case dominates.
A corollary benefit of bias analysis is that bias values can be used
directly to quantify the probability of predicted inundation heights
exceeding measured values using different modelling scenarios.
Probability of exceedance plots are shown in Fig. 10. The plots show
that the probability of exceedance is 2.5%, 7.4%, 23% and 29% for
Scenarios A, B, C and D, respectively. Hence, the current ASCE/SEI 7-16
(2017) approach (Scenario A) is the most conservative for design.
Scenario D proposed by the writers is the least conservative but most
accurate for the site-specific Sendai Plain topography and land use.
This paper describes one of the largest databases of tsunami inundation measurements collected to date. This database has provided
the writers the opportunity to evaluate the accuracy of the general
EGLA method and to make adjustments to fit the model to a particular
site (i.e., the Sendai Plain on the east coast of Japan). For example, the
paper describes a new approach to correct for the influence of topographic obstructions on tsunami flows in order to achieve better
agreement with measured inundation heights. The study illustrates that
inundation height predictions are sensitive to the choice of Froude
number parameter and land use roughness coefficients. Finally, an
important outcome of this study is a site-specific tool for probabilistic
prediction of inundation heights over the Sendai Plain that is of value
for tsunami counter measure planning including design of tsunami resistant structures.
The authors wish to thank The 2011 Tohoku Earthquake Tsunami
Joint Survey (TTJS) Group, Japan, for permission to use their data for
this study. The authors are also grateful for funding awarded by the
Japan Ministry of Education, Culture, Sports, Science and Technology
(Grant-in-Aid for Scientific Research (B) No. 24360195) to carry out
this study including support for the third author to work on this project
while on sabbatical in Japan.
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