Introduction
Tsunami hazard maps and early warning systems are essential for mitigating
the consequences of catastrophic tsunami disasters. Prior to actual detection
of tsunamis, warnings can be issued based on earthquake information (e.g.,
magnitude and hypocenter location). Tsunami warning systems detect off-shore
tsunami waves and issue updated warnings to residents in coastal communities
based on the observations and modified earthquake information. In coastal
areas, people evacuate to designated high grounds and shelters following
local hazard maps and real-time instructions by emergency officers. The
importance of these tsunami risk management tools (together with hard
engineering mitigation measures) can be understood by comparing two massive
events, the 2004 Indian Ocean tsunami and the 2011 Tohoku tsunami. The
tsunami early warning systems were not deployed prior to the 2004 tsunami and
there was no tsunami protection along the coast, resulting in 230 000+
fatalities (Murata et al., 2010). On the other hand, the early warning
systems were in place and operational during the 2011 Tohoku tsunami, saving
many lives (Fraser et al., 2013).
Issuing accurate and prompt tsunami warnings to residents in coastal areas is
critically important for mega-thrust tsunamigenic earthquakes. During the
initial phase, it requires reliable estimation of key earthquake source
characteristics, such as magnitude and location. The estimation of earthquake
information is usually accurate and prompt – however, for very large
earthquakes satisfactory performance may not be achieved during the early
phase of evacuation. This can be exemplified for the 2011 Tohoku tsunami case
(Hoshiba and Ozaki, 2014). The first estimate of the Japan Meteorological
Agency (JMA) magnitude was Mj7.9 (3 min after the earthquake) and later was
updated to Mj8.4 (74 min after the earthquake). The significant
underestimation was caused by the saturation of Mj. A correct estimate of the
moment magnitude (Mw) equal to 8.8 (and eventually to 9.0) was
reached 134 min after the earthquake. It took a considerably long time to
reach the correct Mw value because seismograms recorded at
broadband stations in Japan had exceeded the maximum amplitudes of the
instruments. On the other hand, overseas agencies, such as the US Geological
Survey, obtained correct estimates of Mw about 20 min after the
earthquake using teleseismic signals recorded outside of Japan. Consequently,
tsunami warnings issued by the JMA underestimated the observed tsunamis
significantly (3 to 6 m versus 10+ m; Cyranoski, 2011). Different
estimates of the earthquake source parameters have significant influence on
the wave heights and inundation depths because seismic events of Mw8.0 and Mw9.0, for instance, correspond to very different
tsunami hazard scenarios in terms of size and earthquake slip. It is
important to point out that recent new developments for rapid and reliable
estimation of earthquake magnitude will definitely contribute to the
reduction of uncertainties associated with estimated magnitudes in the early
phase of tsunami disasters (Kanamori and Rivera, 2008; Melgar et al., 2015).
From viewpoints of tsunami early warning and tsunami risk management,
uncertainty of hazard and risk predictions based on macroscopic earthquake
parameters (i.e., magnitude and hypocenter) have important implications. For a
Mw9.0-class mega-thrust subduction event, the fault plane of the
earthquake rupture extends to distances over several hundred kilometers
(Murotani et al., 2013). Moreover, spatial distribution of earthquake slip
varies significantly and these rupture characteristics, which are not
captured by the earthquake magnitude and location, have major influence on
tsunami waves and inundation in coastal cities and towns (Goda et al., 2014,
2015; Fukutani et al., 2015; Mueller et al., 2015). This often leads to
significant uncertainty in predicted consequences due to tsunamis (Goda and
Song, 2016). In addition, with increasing earthquake magnitude, both
amplitude and spatial extent of tsunamis increase rapidly. Hence, warnings
should be issued in recognition of accuracy of the earthquake parameters and
inherent uncertainty of the tsunami risk predictions. Nonetheless, this is
not straightforward because the tsunami damage and loss generation processes
are highly nonlinear and variable.
This study investigates the effects due to underestimation of the earthquake
source parameters in the context of tsunami early warning and tsunami risk
assessment. The 2011 Tohoku earthquake is focused on as a case study to
illustrate the significance of the problems from a retrospective perspective.
In the case study, a building portfolio consisting of about 86 000 buildings
in Miyagi Prefecture is considered. The problem is set up as follows. A
tsunami event of Mw9.0 in the offshore areas of the Tohoku region
is adopted as reference. The magnitude of this event may be underestimated
significantly during the early stage of the disaster (as was the case for the
2011 tsunami). The underestimated scenarios are represented by a set of
earthquake scenarios with lower moment magnitudes than the reference
scenario. For each assumed scenario, stochastic source models are generated
by taking into account the uncertainty of tsunami source characteristics. Using
the multiple sets of tsunami source models corresponding to different moment
magnitudes, probabilistic tsunami loss estimation is carried out. By
analyzing the estimated tsunami loss for coastal cities and towns in Miyagi
Prefecture, potential biases due to underestimation of earthquake magnitude
can be quantified. These results provide useful insights regarding the
importance of deriving accurate seismic information and can be compared with
the effects due to uncertain source characteristics (e.g., geometry and
spatial slip distribution) for given moment magnitudes, which is unavoidable
in making risk predictions based on macroscopic earthquake parameters only.
For this purpose, a new probabilistic tsunami loss model for large Mw8.0+ earthquakes in the Tohoku region of Japan is developed. For a given
scenario magnitude, the loss model generates a tsunami loss curve for a
building portfolio by considering uncertainties in earthquake source
parameters (e.g., geometry, mean slip, and spatial slip distribution). In
particular, a stochastic source modeling method (Mai and Beroza, 2002; Goda
et al., 2014) is incorporated, and nonlinear shallow water equations with
run-up are evaluated for each source model, enabling accurate inundation
simulation. To extend the analyses to different earthquake scenarios, scaling
relationships for the source parameters (Mai and Beroza, 2002; Murotani et
al., 2013; Thingbaijam and Mai, 2016) are employed to generate stochastic
source models that correspond to different moment magnitudes. Subsequently,
Monte Carlo tsunami simulation is carried out, and inundation results at
building locations are integrated with tsunami fragility curves and damage
cost models that are applicable to the buildings of interest (Goda and Song,
2016). The novelty of the current tsunami loss model, with respect to other
developments (e.g., Wiebe and Cox, 2014; Goda and Song, 2016), is that
generation of uncertain tsunami scenarios is not specific for (inverted)
source models and can be applied to a range of scenarios in terms of
earthquake magnitude. This is one step closer to the so-called probabilistic
tsunami hazard analysis (PTHA; Geist and Parsons, 2006; Horspool et al.,
2014), where multiple rupture scenarios are accounted for together with their
occurrence probabilities. It is noteworthy that assignment of occurrence
probability to extremely large earthquakes involves large uncertainty and may
be unreliable (Kagan and Jackson, 2013). For this reason, occurrence
probabilities for the large earthquakes are not considered in this study. It
is noted that typical PTHA studies do not perform full inundation simulations
and tsunami hazard parameters estimated at off-shore locations are
extrapolated into land areas. Therefore, the extension of the current PTHA
methodology to tsunami risk and loss estimation is limited by the fact that
the accurate inundation simulation at local city/town levels is not performed
and it is not possible to evaluate the tsunami damage and loss to individual
buildings. The developed tsunami loss model in this study overcomes these
limitations.
Probabilistic tsunami hazard and risk analysis.
Tsunami source region off the Tohoku coast of Japan.
The paper is organized as follows. First, the methodology for probabilistic
tsunami loss estimation is explained. Subsequently, a numerical example is
set up for large subduction earthquakes (Mw8.0 to Mw9.0) off the
Tohoku coast. The results of the tsunami loss estimation for the building
portfolio in Miyagi Prefecture are obtained and are compared for different
cases. In particular, the effects of different scenario magnitudes and
uncertain source characteristics on tsunami loss are investigated from the
viewpoints of tsunami early warning. Finally, conclusions are drawn for the
use of advanced tsunami loss estimation tools in tsunami risk management.
Probabilistic tsunami loss estimation for multiple scenario
magnitudes
This section presents a computational framework for probabilistic tsunami
loss estimation that is applicable to a range of scenario magnitudes. The
method is the generalized version of the stochastic tsunami loss model (Goda
and Song, 2016). It consists of five components: (i) earthquake scenario
generation, (ii) stochastic source modeling, (iii) tsunami inundation
modeling, (iv) building exposure data, and (v) tsunami damage assessment and
loss estimation. A computational flow of the tsunami loss model is
illustrated in Fig. 1. Succinct descriptions of the model components are
given below. The descriptions are based on the Tohoku region of Japan.
Earthquake scenario and scaling laws for source parameters
A seismic source region for possible large earthquakes is defined. The source
region needs to be sufficiently large such that a Mw9.0-class
event, which is regarded as an upper limit in this study, can be
accommodated. For the Tohoku region, a fault plane with 650 km in length and
250 km in width is considered (Fig. 2). The fault plane has a constant
strike of 193 degrees and variable dip angles, gradually steepening from 8 to
16∘ along the down-dip direction. The geometry and location of the
fault plane are determined based on the source model for the 2011 Tohoku
earthquake, developed by Satake et al. (2013), and are consistent with other
source models for the Tohoku event (Goda et al., 2014). The fault plane is
discretized with sub-faults having a size of 10 km by 10 km. Later,
sub-faults of non-zero slips are determined based on sampled fault length and
width of a seismic event for an assumed value of Mw, and slip
values of these sub-faults are synthesized using stochastic synthesis methods
(Sect. 2.2).
The shaded areas in Fig. 2 are sub-faults having the top-edge depth shallower
than 20 km. The source inversion models considered by Goda et al. (2014)
indicate that large slips tend to occur within the gently-dipping shallow
segments along the Japan Trench. This empirical knowledge can be used as a
constraint in selecting suitable synthesized slip distributions. Moreover,
Fig. 2 shows the estimated hypocenter locations by three institutions, i.e.,
JMA, US Geological Survey (NEIC), and Harvard Seismology Group. The
hypocenter locations are variable and are apart from each other by more than
50 km, showing variability of the hypocenter location for a very large
earthquake. In the context of early warning, the observed hypocenter
locations can also be used to determine the acceptance of candidate slip
models in stochastic source simulation. It is noteworthy that the hypocenter
location does not exactly correspond to the so-called asperity areas with the
largest slip but is located within areas of moderate slip near the
asperities (Mai et al., 2005). Therefore, the hypocenter position, which is
uncertain, gives only a loose constraint of areas with large deformation
which cause major tsunami waves.
Empirical scaling laws describe relationships between seismological
parameters (e.g., fault geometry and slip statistics) and earthquake size
parameters, such as Mw and seismic moment Mo (note:
log10Mo=1.5Mw+9.1; Mo in Nm). Many
equations are available in the literature for different earthquake types
(e.g., Wells and Coppersmith, 1994). To synthesize earthquake source models
that have realistic features, a set of scaling laws and empirical models for
the key source parameters is implemented. To account for the uncertainty of
these parameters, probabilistic information of the adopted scaling laws and
empirical models, which is summarized in Table 1, is taken into consideration
in the simulation.
More specifically, three types of source parameters are considered in this
study. The first type is related to fault geometry: the fault rupture area
S (= L × W) and aspect ratio L / W, in which L
and W are the fault length and width, respectively. The scaling
relationship for S, developed by Murotani et al. (2013), is adopted, while
the aspect ratio is treated as a uniform random variable between 1.5 and 3.0
(i.e., L > W), according to typical fault plane
configurations of the inverted source models of the 2011 Tohoku earthquake
(Goda et al., 2014).
Summary of empirical scaling laws and probabilistic information of
fault geometry and stochastic source parameters adopted in this study.
N(0,1) represents the standard normal random variable, whereas U(a,b)
represents the uniform random variable with lower and upper limits of a and
b, respectively.
Parameter
Equation
Reference
Surface area S (km2)
log10S=-9.873+(2/3)Mo+0.1875N(0,1)
Murotani et al. (2013)
Aspect ratio L / W
L/W=U(1.5,3.0)
Goda et al. (2014)
Average slip Dave (m)
log10Dave=-6.780+(1/3)Mo+0.2148N(0,1)
Murotani et al. (2013)
Maximum slip Dmax (m)
log10Dmax=0.624+0.948×log10(Dave)+0.10N(0,1)
Thingbaijam and Mai (2016)
Hurst number H
H=0.75+0.23N(0,1)
Mai and Beroza (2002)
Correlation length along dip Az (km)
log10Az=-1.79+0.38Mw+0.17N(0,1)
Mai and Beroza (2002)
Correlation length along strike Ax (km)
log10Ax=-2.43+0.49Mw+0.15N(0,1)
Mai and Beroza (2002)
Box–Cox parameter λ
λ=U(0.1,0.3)
Goda et al. (2014)
Scaling relationships and simulated parameters in stochastic scenario
generation: (a) seismic moment – fault area, (b) seismic moment – mean
slip, (c) seismic moment – maximum slip, (d) moment magnitude –
correlation length along strike direction, and (e) moment magnitude –
correlation length along dip direction.
The second type is related to slip statistics: average slip Dave
and maximum slip Dmax (across the fault plane). The scaling
relationships developed by Murotani et al. (2013) and Thingbaijam and
Mai (2016) are considered for Dave and Dmax, respectively.
Because both Dave and Dmax are treated as random variables,
the physical constraint that the maximum slip is sufficiently greater than
the average slip is implemented by requiring
Dmax > 1.5 × Dave. Moreover, in
generating source model parameters probabilistically, the consistency among
seismic moment, rupture area, and average slip is achieved based Mo=μ SDave, in which μ is the rock
rigidity and is taken as 40 GPa in this study. Due to the variability in S
and Dave, (independent) random sampling of S and
Dave may result in a seismic moment that is very different from
the target seismic moment or moment magnitude. To avoid such an inadequate
combination of S and Dave, sampling of these two parameters is
repeated until the calculated seismic moment falls within a certain range; in
this study, the target moment magnitudes minus/plus 0.05 units are considered
for such a range. For instance, when the target moment magnitude is set to
9.0, sampling of S and Dave is continued until the calculated
moment magnitude falls between 8.95 and 9.05.
The third type is related to the spatial slip distribution and characterizes
the heterogeneity of earthquake slip across the fault plane. In this study,
four parameters are considered: Hurst number H, correlation lengths in
down-dip and along-strike directions Az and Ax, and Box–Cox
parameter λ. The Hurst number and correlation lengths define the
spectral characteristics of the slip distribution in wavenumber (see Eq. (1)
in Sect. 2.2). The Hurst number is modeled as a uniform random variable with
respect to moment magnitude, whereas the correlation lengths increase with
moment magnitude (Mai and Beroza, 2002). The Box–Cox parameter is used to
generate slip distributions with heavy right tails, which is a notable common
feature from the inversion models of the 2011 Tohoku earthquake (Goda et al.,
2014). Additional explanations of these parameters are given in Sect. 2.2
where stochastic synthesis of constrained slip distribution is mentioned.
To illustrate the generation of the above-mentioned source parameters,
simulated samples of the fault area, average slip, maximum slip, and
correlation lengths in down-dip and along-strike directions are shown in
Fig. 3 for a range of moment magnitudes (Mw8.0 to Mw9.0). The sample size per moment magnitude is 100. In Fig. 3, the
adopted scaling relationships as well as the source parameters for the 11 inversion models of the 2011 Tohoku earthquake, obtained by Goda et
al. (2014), are also included. The comparisons of the generated source
parameters with the scaling laws indicate that all source parameters, except
for the maximum slip, follow closely the scaling relationships and are
consistent with the parameters obtained for the 2011 Tohoku earthquake. The
simulated maximum slip is generally greater than the empirical relationship
by Thingbaijam and Mai (2016), noting that the maximum slip values from the 11 source models for the 2011 Tohoku earthquake (Goda et al., 2014) are
significantly larger than the Thingbaijam–Mai relationship. Note that the
results shown in Fig. 3c are the final accepted values, which are modified
from originally sampled values of the maximum slip (see the explanations of
constraints discussed in Sect. 2.3). In light of the large differences of the
maximum slip between the Thingbaijam–Mai model and the results for the 2011
Tohoku earthquake, the simulated maximum slip values are considered to be
acceptable.
Stochastic source models
The spectral synthesis of random fields generates earthquake slip
distributions that have desirable spatial characteristics, expressed in terms
of wavenumber spectra in down-dip and along-strike directions (Mai and Beroza
2002). A brief summary of the stochastic method is given below; full details
of the method can be found in Goda et al. (2014) and are not repeated here.
The wavenumber power spectrum can be modeled based on a von Kármán
auto-correlation function:
P(k)∝AxAz(1+k2)H+1,
where k is the wavenumber, k = (Az2kz2+Ax2kx2)0.5. In the von Kármán model, Az and
Ax control the absolute level of the power spectrum in the low
wavenumber range (i.e., k ≪ 1; long wavelength) and
capture the anisotropic spectral features of the slip distribution (when
Az≠Ax). H determines the slope of the power spectral decay in
the high wavenumber range (i.e., short wavelength), and is theoretically
constrained to fall between 0 and 1. As mentioned in the previous section,
the scaling relationships for H, Ax, and Az are available
(Table 1), and can be used in stochastic source simulation. Realizations of
slip distributions with desirable spectral features are generated using a
Fourier integral method (Pardo-Iguzquiza and Chica-Olmo, 1993). For a given
set of H, Ax, and Az, the amplitude spectrum of the target slip
distribution is defined as in Eq. (1), while the phase spectrum is
represented by a random phase matrix. The constructed complex Fourier
coefficients are transformed into the spatial domain via two-dimensional
inverse fast Fourier transform. The generated slip distributions have slip
values that are normally distributed (i.e., symmetrical with respect to mean).
To achieve realistic heavy right-tail features of the slip distribution (i.e.,
positive skewness), the synthesized slip distribution is converted via
Box–Cox transformation: y = (xλ-1) / λ (λ≠0), in which y is the transformed slip and x is the original slip
(note: when λ=0, y = log(x)). Subsequently, the transformed
slip distribution is adjusted to achieve the target mean slip
Dave (which is also simulated in stochastic source modeling) and
to avoid very large slip values exceeding the target maximum slip Dmax.
The excessive slip values are resampled from a histogram that is constructed
based on slip values between 0.67Dmax and Dmax (Mai et al.,
2005).
Synthesized earthquake source models: (a) Mw8.0,
(b) Mw8.2, (c) Mw8.4,
(d) Mw8.6, (e) Mw8.8, and
(f) Mw9.0.
Subsequently, the position of the fault plane is determined randomly within
the whole source region (Fig. 2) but ensuring that the fault plane contains
the hypocenter location (to be consistent with the situation for tsunami
early warning). It is noteworthy that the hypocenter location is uncertain
and can vary significantly (Fig. 2). To account for this uncertainty, for
each synthetic source model, a location of the hypocenter is sampled from
four locations; three are based on the JMA, USGS, and Harvard hypocenter
locations (Fig. 2) and the other is the centroid of the three locations. The
weights assigned to the JMA, USGS, and Harvard hypocenter locations are 0.2
each, while the weight assigned to the centroid is 0.4. Further to account
for possible variability of the hypocenter location, deviation from the
sampled location is modeled as a uniform random radius between 0 and 20 km
with isotropic directionality.
Finally, to ensure that the synthesized slip distributions are realistic with
respect to the seismological knowledge of earthquake rupture in the region,
two additional constraints are implemented to determine the final acceptance
of the generated source models. The first constraint requires that the ratio
of the asperity area Sa to the total rupture area S of the
candidate slip distribution falls between 0.15 and 0.25, where Sa
is defined as the total area of sub-faults that have slip values greater than
1.5Dave. This criterion is based on the empirical finding by
Murotani et al. (2013) that for large subduction earthquakes, typically
Sa / S is about 0.20. The second constraint requires that the
simulated earthquake slip is more concentrated in the shallow part of the
fault plane rather than the deep part (Fig. 2), which is in agreement with
the inverted source models for the 2011 Tohoku earthquake (Goda et al.,
2014). Specifically, a candidate slip distribution is accepted if the total
slip in the shallow segments (shaded sub-faults in Fig. 2) has a slip
concentration between 60 and 75 % in terms of total slip across the fault
plane. Multiple slip distributions are simulated until a sufficient number of
acceptable source models are generated. In this study, 100 source models that
meet all the criteria mentioned previously are generated for each of six
moment magnitudes ranging from Mw8.0 to Mw9.0 with 0.2
units step (i.e., in total, 600 source models are generated). Note that the
sample size of 100 is selected based on the authors' previous experience in
tsunami sensitivity analysis (Goda et al., 2014) and practical restrictions
of computational resources.
Figure 4 shows synthesized earthquake source models for six moment
magnitudes. Note that the source models shown in the figure are from the 100
accepted source models only. In the figure, mean and maximum slip values of
the source models are indicated. Inspection of the illustrated six source
models for different earthquake magnitudes indicates that both fault plane
size and slip values increase significantly with moment magnitude. The
location, size, and extent of the asperity areas also change significantly.
Although not shown in Fig. 4, features of the 100 source models for the
same moment magnitude also vary significantly. In particular, the locations
of the asperity areas move around within the fault plane; this variability
can be regarded as due to the inherent uncertainty of earthquake rupture process in the
context of tsunami early warning where only macroscopic earthquake
information is available. In the case study, the effects due to errors in
earthquake magnitudes and the effects of within-scenario variability of
earthquake rupture on estimated tsunami loss will be quantified and compared.
Tsunami inundation modeling
Tsunami modeling is carried out using a well-tested numerical code (Goto et
al., 1997) that is capable of generating off-shore tsunami propagation and
run-up/inundation by evaluating nonlinear shallow water equations using a
leap-frog staggered-grid finite difference scheme. The run-up/inundation
calculation is performed by a moving boundary approach, where a dry or wet
condition of a computational cell is determined based on total water depth in
comparison with its elevation. The computational domains are nested at five
resolutions (i.e., 1350, 450, 150, 50, and 10 m domains). In this study, due
to the computational reasons, the smallest grid size of the nested data is
set to 50 m.
A complete data set of bathymetry/elevation, coastal/riverside structures
(e.g., breakwater and levees), and surface roughness is obtained from the
Miyagi prefectural government. The ocean-floor topography data are based on
the 1:50,000 bathymetric charts and JTOPO30 database developed by Japan
Hydrographic Association and based on the nautical charts developed by Japan
Coastal Guard. The raw data are gridded using triangulated irregular network.
The land elevation data are based on the 5 m grid digital elevation model (DEM) developed by the
Geospatial Information Authority of Japan. The raw data are obtained from
airborne laser surveys and aerial photographic surveys. These data have
measurement errors of less than 1.0 m horizontally and of 0.3 to 0.7 m
vertically (as standard deviation). The tidal fluctuation is not taken into
account in this study.
The elevation data of the coastal/riverside structures are provided by
municipalities in Miyagi Prefecture. In the coastal/riverside structural
data set, structures having dimensions less than 10 m only are represented,
noting that those having dimensions greater than 10 m are included in the
DEM data. In the tsunami simulation, the coastal/riverside structures are
represented by a vertical wall at one or two sides of the computational
cells. To evaluate the volume of water that overpasses these walls, Homma's
overflowing formulae are employed.
The bottom friction is evaluated using Manning's formula following the Japan
Society of Civil Engineers standard (2002). The Manning coefficients are
assigned to computational cells based on national land use data in Japan:
0.02 m-1/3 s for agricultural land, 0.025 m-1/3 s for
ocean/water, 0.03 m-1/3 s for forest vegetation, 0.04 m-1/3 s
for low-density residential areas, 0.06 m-1/3 s for moderate-density
residential areas, and 0.08 m-1/3 s for high-density residential
areas.
(a) Spatial distribution of buildings in Miyagi Prefecture, and
(b) tsunami fragility curves for wash-away damage state. The map in (a) is shown
in the Japanese plane orthogonal coordinate system.
Differences in earthquake slip result in different boundary conditions for
tsunami propagation and run-up. In tsunami simulation, the initial water
surface elevation is evaluated based on formulae by Okada (1985) and Tanioka
and Satake (1996). The latter equation accounts for the effects of horizontal
seafloor movements in the case of steep seafloor, inducing additional vertical
water dislocation. The fault rupture is assumed to occur instantaneously, and
numerical tsunami calculation is performed for duration of 2 h with an
integration time step of 0.5 s. For each case, the maximum inundation depths
at all in-land computational cells (50 m grids) are obtained by subtracting
the DEM data from the calculated maximum wave heights.
Exposure data and cost information
An extensive tsunami damage database for the 2011 Tohoku earthquake is
available from the Ministry of Land, Infrastructure, and Transportation
(MLIT) of the Japanese Government (MLIT, 2014). In the database, each building
located in the affected areas is classified according to different
attributes, such as geographical location, structural material, story number,
tsunami inundation depth, and sustained damage level. The material types are
categorized into: reinforced concrete (RC), steel, wood, masonry, and
unknown, whereas the number of stories is divided into: 1-story, 2-story, and
3+-story. In this study, all buildings that are located between Soma City
(south) to Minamisanriku City (north) and have information on material and
story number are considered for assessing the tsunami damage and loss. There
are 86 219 buildings in total, consisting of 1446 RC structures, 4866 steel
structures, 72 506 wood structures, and 7401 masonry structures. The spatial
distribution of the building portfolio is shown in Fig. 5a. Note that the map
shown in Fig. 5a is based on the Japanese plane orthogonal coordinate system
(which uses GRS80 as Earth ellipsoid and Gauss–Krüger map projection). The
buildings are concentrated in the Sendai coastal plain.
For tsunami loss estimation, cost information for repairs and reconstruction
is needed. Because the MLIT database does not contain occupancy information
for individual buildings, simplified cost models for replacement that are
based on building cost statistics (i.e., unit costs and footprint areas) are
adopted by classifying buildings into residential houses (wood) and
commercial stores/offices (RC/steel/masonry). It is considered that the unit
costs for houses and stores/offices can be approximated by the lognormal
distribution; the mean and coefficient of variation (CoV) are obtained from
the regional building data statistics maintained by the MLIT. More
specifically, the following cost information is adopted
(USD 1 = JPY 100; note that this conversion rate is an average over
recent years and is adopted for simplicity): mean unit
cost = 1600 USD m-2, CoV = 0.320, and floor
area = 130 m2 for wooden houses; and mean unit
cost = 1500 USD m-2, CoV = 0.318, and floor
area = 540 m2 for stores/offices.
Tsunami damage assessment and loss estimation
Structural vulnerability against tsunami loading can be modeled by empirical
tsunami fragility curves, which relate tsunami intensity measures (IM) to
tsunami damage states (DS) statistically. The MLIT database defines seven
discrete levels to describe the severity of tsunami damage: no damage, minor
damage, moderate damage, major damage, complete damage, collapse, and
wash-away. Using the MLIT tsunami damage database for the 2011 Tohoku
tsunami, Suppasri et al. (2013) developed regional tsunami fragility models
by distinguishing tsunami damage data according to the structural materials
and the number of stories. The refinement for the different material types as
well as for the number of stories is desirable, because the tsunami
capacities for RC, steel, wood, and masonry buildings differ significantly
(Koshimura et al., 2009; Suppasri et al., 2013; Tarbotton et al., 2015).
Figure 5b shows four fragility curves that correspond to the wash-away damage
state for four material types, indicating that wood structures are more
vulnerable in comparison with others.
The exceedance probability of damage state dsi for a given value im
is expressed as
P(DS≥dsiim)=Φ[ln(im)-μlnIMDSi]/σlnIMDSi,
where Φ is the cumulative distribution function of the standard normal
variate, and
μlnIM|DSi and
σlnIM|DSi are the mean and standard
deviation of lnIM|DSi, respectively. For mutually exclusive
damage states that are defined in a discrete manner, the probability of being
in dsi is given by
p(dsiim)=P(DS≥dsiim)-P(DS≥dsi+1im).
Note that dsi+1 is severer than dsi (i.e.,
P(DS ≥ dsi+1|im) < P(DS ≥ dsi|im)).
For each building, probabilities of attaining particular damage states
p(ds|im) can be estimated. By taking into account variability of
source models (for a given scenario magnitude), the cumulative distribution
functions of aggregate tsunami risk metrics, such as the number of buildings
falling into a specific damage state, can be evaluated through Monte Carlo
sampling of damage states for the buildings of interest (Goda and Song, 2016).
Probability distributions of wash-away damage ratios (i.e., percentages
of damaged buildings to all buildings) for different earthquake scenarios by
distinguishing material types: (a) RC, (b) steel, (c) wood, and (d) masonry.
Probability distributions of tsunami loss for different earthquake
scenarios by distinguishing material types: (a) RC, (b) steel, (c) wood, and
(d) masonry.
Finally, by incorporating the cost models for different buildings
(Sect. 2.4), the tsunami damage information can be transformed into tsunami
loss information for individual buildings as well as building portfolios. The
loss ratios in terms of replacement cost of a damaged building for the seven
damage levels (i.e., from no damage to wash-away) can be assigned as: 0.0,
0.05, 0.2, 0.4, 0.6, 1.0, and 1.0 (MLIT, 2014). Using the damage state
probability p(ds) and loss ratio RL(ds), tsunami damage
cost for a given tsunami hazard intensity can be calculated as (for discrete
cases)
L=CR∑i=17pdsi×RLdsi,
where CR is the replacement cost of a building. The tsunami loss
curve can be used for deciding upon various tsunami risk mitigation actions.
In the context of tsunami warning, differences of the loss curves for
different scenario magnitudes are the quantitative estimates of the errors
due to inaccurate source information. Moreover, the tsunami loss curve can be
used to define critical scenarios for tsunami hazard mapping purposes. These
are investigated quantitatively in Sect. 3.
Probability distributions of total tsunami loss for different
earthquake scenarios.
Application to major tsunami events in the Tohoku region of Japan
Focusing on the building portfolio in Miyagi Prefecture, the effects of
underestimation/errors of earthquake magnitude are investigated in the
context of tsunami early warning and tsunami risk assessment. The
investigations are conducted using the probabilistic tsunami loss estimation
tool developed in Sect. 2. In total, six scenario magnitudes from
Mw8.0 to Mw9.0 are considered, and for each magnitude
100 stochastic source models are generated to represent the within-scenario
uncertainty of the earthquake rupture. In Sect. 3.1, two questions are mainly
considered: When the magnitude is in error, what would be
the impact in terms of tsunami loss prediction? And, what is the uncertainty of predicted tsunami loss given a moment magnitude
and hypocenter location? The former question is relevant when the warnings need to be
given shortly after a very large seismic event, whereas the latter is always
present in issuing tsunami early warnings. Comparison of the two cases will
provide emergency officers with valuable insights related to their
challenging tasks in an extreme situation. In Sect. 3.2, the usefulness of
rigorous tsunami risk assessment is discussed in defining critical hazard
scenarios based on potential consequences due to tsunami disasters.
Earthquake source model and inundation height maps that correspond
to a critical tsunami loss scenario. For the inundation height maps (bottom
two figures), results are shown in the Japanese plane orthogonal coordinate
system.
Tsunami loss curves for different earthquake scenarios
The developed loss estimation tools can produce various results of tsunami
risk assessment. Figure 6, for instance, displays probability distributions
of the number of buildings that are in the wash-away damage state for
different scenario magnitudes by distinguishing building material types. The
results are shown in terms of damage ratio (i.e., percentage of damaged
buildings with respect to all buildings for each material type). The results
clearly indicate that for all material types the occurrence of wash-away
damage in the considered building portfolio becomes increasingly more
frequent. It is noteworthy that although appearances of these damage ratio
curves for different material types are similar (i.e., how relative positions
of these curves change with the increase in Mw), the horizontal
axes of Fig. 6 (i.e., damage ratio values) are different for the four material
types. The maximum range of the damage ratio for wood structures is greater
than those for other structures, reflecting the higher vulnerability of these
structures (Fig. 5b; note that spatial distribution of the buildings also has
influence). The observations regarding the changes of the damage ratio curves
with respect to earthquake magnitude (as in Fig. 6) are applicable to
different damage states.
Earthquake source models corresponding to critical loss scenarios:
(a) 50th loss percentile for Mw8.2, (b) 50th loss percentile for
Mw8.6, (c) 50th loss percentile for Mw9.0, (d) 90th loss percentile
for Mw8.2, (e) 90th loss percentile for Mw8.6, (f) 90th loss
percentile for Mw9.0.
Inundation height maps in Sendai-Soma areas corresponding to
critical loss scenarios: (a) 50th loss percentile for Mw8.2, (b) 50th
loss percentile for Mw8.6, (c) 50th loss percentile for Mw9.0,
(d) 90th loss percentile for Mw8.2, (e) 90th loss percentile for
Mw8.6, (f) 90th loss percentile for Mw9.0. The inundation height
maps are shown in the Japanese plane orthogonal coordinate system.
Inundation height maps in Ishinomaki–Minamisanriku areas
corresponding to critical loss scenarios: (a) 50th loss percentile for
Mw8.2, (b) 50th loss percentile for Mw8.6, (c) 50th loss percentile
for Mw9.0, (d) 90th loss percentile for Mw8.0, (e) 90th loss
percentile for Mw8.6, (f) 90th loss percentile for Mw9.0. The
inundation height maps are shown in the Japanese plane orthogonal coordinate
system.
To evaluate the economic consequences due to tsunami events with different
scenario magnitudes, probability distributions of tsunami loss for the
building portfolio are obtained for different magnitude values and for
different material types. The results are shown in Fig. 7. One notable
difference of the results shown in Figs. 6 and 7 (apart from the
incorporation of damage cost models) is that the tsunami loss curve includes
all buildings with different damage states by weighting their relative impact
based on the tsunami damage cost, whereas only a subset of buildings that
sustain a specific damage state is considered in developing the damage ratio
curve. Hence, the tsunami loss curve is more useful for assessing overall
tsunami impact for the building portfolio. Inspection of Fig. 7 suggests that
for all material types, the tsunami loss curves become more severe with
increasing magnitude, noting that the horizontal axes of Fig. 7 are
logarithmic with base 10. This indicates that the tsunami loss generation is
an exponential process with respect to earthquake magnitude.
To discuss the effects of underestimation/errors of earthquake magnitude on
total tsunami loss, tsunami loss curves for the entire building portfolio are
shown in Fig. 8 by considering different earthquake scenario magnitudes. It
is obvious that the tsunami loss curve shifts towards the right with the increase
in Mw, and its increment per magnitude change is approximately
constant or slightly increasing (to conclude this definitively, more
simulations are necessary). For example, at the median probability level, the
tsunami loss increases by about a factor of 100 from Mw8.0 to
Mw9.0 scenarios. Practically, this means that the
over-/underestimation of earthquake magnitude by certain units in the tsunami
warning might correspond to very different situations in terms of potential
consequences. If there is a possibility that the estimated earthquake
information, which is obtained quickly, is in error or biased, the risk
manager may wish to issue tsunami warnings by taking into account the
uncertainty associated with risk predictions.
On the other hand, the within-scenario variability of the tsunami loss curve
is caused by the uncertainty associated with detailed earthquake slip
characteristics that are not captured by the macroscopic earthquake
information. The results shown in Fig. 8 indicate that this variability is
significant, and the main contributor of the variability is the spatial slip
distribution, especially the location and extent of major asperities with
respect to the building portfolio. For instance, the range between the
minimum and maximum loss scenarios can be as large as a factor of 100 for the
Mw8.0 case, and it tends to decrease gradually as the scenario
magnitude increases. Because the position of the fault rupture plane has more
influence on tsunami loss when the earthquake size is small, the
within-scenario variability of tsunami loss is greater for smaller earthquake
magnitudes. The within-scenario variability of tsunami loss is grossly
comparable with the tsunami loss differences caused by the biases in
earthquake magnitude (depending on the probability levels of that are
referred to in the tsunami loss curves). This highlights the importance of
the earthquake rupture process and slip distribution for accurate tsunami
risk prediction. The results suggest that the further deployment of deep
ocean-bottom sensors near the source areas (e.g., Iinuma et al., 2012) will
not only improve the early detection of tsunami waves but also help constrain
the earthquake rupture process more rapidly.
Critical tsunami loss scenarios and corresponding source and
inundation maps
An integrated understanding of the quantitative tsunami loss results is
useful for defining critical scenarios for tsunami hazard mapping and risk
management purposes, and thus enhances the resilience of coastal communities
against catastrophic tsunami disasters. This section aims at demonstrating
the advantages that can be gained from such rigorous risk assessments.
Figure 9 illustrates a procedure to develop inundation hazard maps that are
based on a critical tsunami loss scenario. The top-left panel of Fig. 9 shows
the tsunami loss curves for the Mw9.0 scenario (same as those
shown in Figs. 7 and 8). Each point of the loss curve
corresponds to a specific source model and inundation results– for example,
the median case in terms of tsunami loss distribution for the entire building
portfolio is focused on (which is indicated by a circle). The tsunami loss is
estimated as USD 3581 million. The earthquake source model that causes the
median tsunami loss is shown in the top-right panel of Fig. 9. The source
model has large concentrations of earthquake slips in the shallow segments of
the fault plane. Furthermore, two maximum tsunami wave height contours for
Soma to Sendai and for Ishinomaki to Minamisanriku that correspond to the
source model shown in the top-right panel are presented in the bottom-left
and bottom-right panels, respectively. It can be observed from the inundation
maps that the tsunami loss is generated in the coastal plain areas (south of
Sendai), low-lying parts of Ishinomaki, and locations along the ria coast in
northern Miyagi Prefecture. The source models and inundation maps that are
identified through the loss calculations are useful because the scenario and
hazard information is directly associated with the tsunami loss percentile
(i.e., median loss for the Mw9.0 scenario). It is noted that the
hazard maps based on critical tsunami loss are different from conventional
tsunami hazard maps that are prepared for coastal cities and towns. The
conventional tsunami hazard maps lack the link with the potential
consequences and, importantly, the assessment of the uncertainty. The
proposed tsunami hazard mapping method, although it requires much significant
calculation, is more transparent and meaningful for communicating the
tsunami risk with stakeholders. Therefore, it can be used as decision-support
systems for tsunami risk reduction.
To further demonstrate how the proposed tsunami hazard mapping method can be
used for various situations, earthquake source models and inundation height
maps in Soma-Sendai and Ishinomaki–Minamisanriku areas are developed by
considering three scenario magnitudes (i.e., Mw8.2, Mw8.6, and Mw9.0) and two loss percentiles (i.e., 50th and 90th
percentiles); the loss curves that are referred to are shown in Fig. 8. The
results are shown in Figs. 10–12. The source models for different
scenarios and loss percentiles (Fig. 10) clearly show that both rupture area
and slip statistics increase significantly with the scenario magnitude and
with the loss percentile. Furthermore, it can be observed that with the
increase in the loss percentile, the location of the asperities tends to be
positioned directly across the areas where the building portfolio is
distributed (i.e., between Soma and Minamisanriku); thus larger tsunami waves
are radiated towards the buildings of interest. The effects of greater
tsunami waves can be appreciated by inspecting the tsunami inundation maps
for the two local areas. In the Soma-Sendai areas (Fig. 11), the maximum
tsunami wave heights near the coastal line and in the inundated areas
increase rapidly with more severe tsunami scenarios. In the Ishinomaki–Minamisanriku areas
(Fig. 12), two features can be seen in different topographical
regions. In the ria coast, the maximum tsunami wave heights become larger but
the spatial extent of the inundation does not change significantly when more
severe tsunami scenarios are considered. On the other hand, in the coastal
plain of Ishinomaki, both maximum tsunami wave heights and inundated areas
increase with more severe tsunami scenarios, similar to the cases for the
Soma-Sendai areas.
Conclusions
Issuing accurate and prompt tsunami warnings is vital for reducing the
potential consequences due to catastrophic tsunami disasters. Recognizing
the unavoidable uncertainty in the estimation of earthquake information that
is used for tsunami early warnings as well as the uncertainty of the
earthquake rupture process (e.g., slip distribution), it is important to
evaluate the effects of such uncertainties on the tsunami risk predictions
quantitatively. For this purpose, a case study focusing on tsunamigenic
events in the Tohoku region of Japan was set up to illustrate the
significance of the problems. The new comprehensive probabilistic tsunami
loss model was developed by implementing various scaling relationships for
the key source parameters and stochastic spectral methods of synthesizing
the spatial earthquake slip distribution. The generated stochastic source
models for different scenario magnitudes were used as input in Monte Carlo
tsunami inundation simulation and subsequent tsunami damage assessments. The
developed tsunami risk assessment tool can produce tsunami loss curves for a
range of scenario magnitudes. Focusing on the building portfolio in Miyagi
Prefecture, the effects of underestimation/errors of earthquake magnitude
were investigated in the context of tsunami early warning and tsunami risk
assessment, and were compared with the within-scenario variability of the
tsunami loss due to the uncertain earthquake rupture process. In addition, a
procedure to define critical hazard scenarios based on potential
consequences of tsunami disasters was suggested to promote more transparency
and effectiveness in communicating tsunami risks.
The main conclusions of this study are as follows.
The tsunami loss generation process is exponential with respect to
earthquake magnitude. Therefore, biases/errors in earthquake source
information (magnitude and hypocenter location) can have major influence on
the potential consequences of the tsunami event in the context of tsunami
early warning and risk prediction.
At the median probability level, for instance, total tsunami loss increases
by about a factor of 100 from Mw8.0 to Mw9.0 scenarios (note that
various loss quantities can be extracted from the calculated loss curves).
Such quantitative information of predicted tsunami risk is useful for risk
managers who decide to issue warnings and evacuation orders.
For a given scenario magnitude, tsunami loss curves vary significantly due
to uncertain earthquake rupture characteristics that are not captured by the
macroscopic earthquake information. The within-scenario variability of
tsunami loss is comparable with the tsunami loss differences caused by the
biases in earthquake magnitude.
The definition of critical tsunami scenarios based on probabilistic tsunami
loss calculations are useful for more effective tsunami hazard mapping and
risk management. The deficiency of current tsunami hazard maps can be
addressed by explicitly taking into account uncertainty associated with
hazard scenarios and their characteristics.