This study investigates the issues related to underestimation of the earthquake source parameters in the context of tsunami early warning and tsunami risk assessment. The magnitude of a very large event may be underestimated significantly during the early stage of the disaster, resulting in the issuance of incorrect tsunami warnings. Tsunamigenic events in the Tohoku region of Japan, where the 2011 tsunami occurred, are focused on as a case study to illustrate the significance of the problems. The effects of biases in the estimated earthquake magnitude on tsunami loss are investigated using a rigorous probabilistic tsunami loss calculation tool that can be applied to a range of earthquake magnitudes by accounting for uncertainties of earthquake source parameters (e.g., geometry, mean slip, and spatial slip distribution). The quantitative tsunami loss results provide valuable insights regarding the importance of deriving accurate seismic information as well as the potential biases of the anticipated tsunami consequences. Finally, the usefulness of rigorous tsunami risk assessment is discussed in defining critical hazard scenarios based on the potential consequences due to tsunami disasters.

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

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 (

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

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

For this purpose, a new probabilistic tsunami loss model for large

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 (

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.

A seismic source region for possible large earthquakes is defined. The source
region needs to be sufficiently large such that a

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

More specifically, three types of source parameters are considered in this
study. The first type is related to fault geometry: the fault rupture area

Summary of empirical scaling laws and probabilistic information of
fault geometry and stochastic source parameters adopted in this study.

Scaling relationships and simulated parameters in stochastic scenario
generation:

The second type is related to slip statistics: average slip

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

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 (

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:

Synthesized earthquake source models:

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

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 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

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.

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

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

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 ds

Probability distributions of wash-away damage ratios (i.e., percentages
of damaged buildings to all buildings) for different earthquake scenarios by
distinguishing material types:

Probability distributions of tsunami loss for different earthquake
scenarios by distinguishing material types:

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

Probability distributions of total tsunami loss for different earthquake scenarios.

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

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.

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

Earthquake source models corresponding to critical loss scenarios:

Inundation height maps in Sendai-Soma areas corresponding to
critical loss scenarios:

Inundation height maps in Ishinomaki–Minamisanriku areas
corresponding to critical loss scenarios:

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

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

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

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.,

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

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.

The bathymetry and elevation data for the Tohoku region were provided by the
Miyagi prefectural government. The tsunami damage data for the 2011 Tohoku
earthquake were obtained from the Ministry of Land, Infrastructure, and
Transportation (