Run-up processes of the 2011 Tohoku tsunami into the city of Kamaishi, Japan, were simulated numerically using 2-D shallow water
equations with a new treatment of building footprints. The model imposes an internal hydraulic condition of permeable and impermeable
walls at the building footprint outline on unstructured triangular meshes. Digital data of the building footprint approximated by
polygons were overlaid on a 1.0

Comparison of computation results with field data suggests that the case with a small amount of wall permeability gives better
agreement than the case with impermeable condition. Spatial mapping of an indicator for run-up flow intensity (

Recent urbanization of low-lying coastal areas has increased the potential for property damage, human injury, and death caused by tsunamis. Visual data obtained during the tsunami run-up have revealed that arrays of structures in urban areas induced large wave deformation and swift currents on streets, and that the currents washed objects such as garbage, cars, and debris from damaged structures, causing even more damage than the tsunami run-up over uniform ground. Prediction of swift currents in urban areas by numerical flow simulation is expected to be important for evacuation programs and for city layout planning measures to mitigate tsunami damage.

Tsunami simulation models for forecasting wave propagation and deformation from the seismic center to the coast have been developed and improved for decades. These models for high-speed calculations in a wide water body are often based on a set of shallow water equations on a structured rectangular grid system (Imamura et al., 1995). Models with a rectangular grid system were extended to calculate the tsunami run-up on land by formulating the wavefront propagation on a dry bed (Titov and Synolakis, 1995, 1998; Synolakis et al., 2008). However, the tsunami run-up simulation described above requires more precise flow modeling by introduction of the hydraulic effects of building arrangement.

Conditions of inner boundaries:

Building array treatments in urban flood inundation models are classifiable into four types (Schubert et al., 2008, 2012): building-resistance models (BR), in which large surface roughness is assigned to cells that fall within a building footprint (Liang et al., 2007) or developed parcels (Gallegos et al., 2009; Gallien et al., 2011); building-block models (BB), in which spatially distributed ground elevation data are raised to rooftop height (Brown et al., 2007; Hunter et al., 2008; Schubert et al., 2008); building-hole models (BH), in which building footprints are excluded from the flow calculation area with a free-slip wall boundary condition (Aronica et al., 1998, 2005; Schubert et al., 2008); and building-porosity models (BP), in which the impact of buildings in a street block is expressed approximately by porosity and a drag coefficient in a street block (Guinot, 2012; Sanders et al., 2008; Soares-Frazão et al., 2008).

The BR model is commonly adopted for tsunami run-up simulations (Gayer et al., 2010; Kaiser, 2011; Suppasri et al., 2011; Bricker et al., 2015), although the model developers did not predict the velocity field. Komatsu et al. (2010), Conde et al. (2013), and Imai et al. (2013) respectively applied the BB model for the tsunami flooding in the city of Banda Aceh in Indonesia caused by the 2004 Indian Ocean earthquake off the Indian coast of Sumatra island, for the flooding in two cities of Portugal during the 1755 Lisbon tsunami, and for the extreme inundation in Kochi city in Japan during the historical tsunami run-up in 1707. Liu et al. (2002) applied the BH model to tsunami run-up flow caused by the 1896 Sanriku earthquake tsunami. Akoh et al. (2014) proposed a permeable wall model equivalent to the BH model when the permeability constant was zero and applied the model to the tsunami flooding in Kamaishi city in Japan during the 2011 earthquake off the Pacific coast of Tohoku (2011 Tohoku tsunami hereinafter). For the BP model, no report of the relevant literature has described a tsunami run-up simulation, probably because it is not easy to identify the values of porosity and building drag coefficient for the respective street blocks.

For this study, the permeable wall model based on shallow flow equations proposed by Akoh et al. (2014) was used to investigate tsunami
run-up details for Kamaishi city during the 2011 Tohoku tsunami using more field data than used in the earlier study. Sect. 2
describes the numerical simulation method: basic formulations and building array treatment. Sect. 3 is devoted to an explanation of
numerical modeling for the tsunami flooding in Kamaishi city: explanation of the study site, data sources for modeling, mesh generation,
and calculation conditions. Calculation results are displayed in Sect. 4 along with validation data. In Sect. 5, after presenting
discussion of the influence of the permeability constant on calculation results, the tsunami effects on houses were examined. We
introduce an indicator,

Considering the openings of wooden houses such as doors, windows, or cracks and slits caused by tsunami effects, the shallow water BH model was improved to express the effects of wall permeability by introducing the “assumption of internal hydraulic conditions” on line segments where the walls were located. The seawall overtopping was considered similarly.

Two-dimensional shallow water equations were adopted for numerical simulations: a continuity equation for an incompressible fluid and momentum equations used under the assumption of hydrostatic pressure without horizontal diffusion terms in Cartesian coordinates. The Godunov-type finite volume method (Godunov et al., 1959) was used to solve the hyperbolic differential equations. The spatial domain of integration was covered by a set of unstructured triangular cells, which are not necessarily aligned with the coordinates. Therefore, the topography and building footprints were expressed flexibly. The cell-averaged values for water depth, velocity components, and ground surface elevation were assigned at the centroid of each triangle.

Geometry of coastlines and location of the study site.

By integrating the equation over each triangular cell and by application of Gauss's theorem to the flux integral, a finite-differential
equation for time evolution of variables was obtained. The method of characteristics was applied to the flux terms. Roe's approximate
Riemann solver (Roe, 1981) was adopted, based on the first-order upwind approach. In the finite differentiation of the momentum source
term induced by ground slope, an upwind approach was also adopted to satisfy the

To model wavefront motion, the Eulerian method proposed by Brufau (2002) was adopted to avoid the so-called

Bathymetry and surrounding topography of Kamaishi Bay. Tokyo Peil (T.P.)

Classification of building structures.

Classification of building damage.

Ground subsidence near the coast.

Simplification and redefinition of building footprint polygons.

Area of calculation domain:

Water surface displacement at the GPS wave gauge station.

Estimation of tsunami wave height near the coast:

Time series of water surface displacement near the coast: comparison
between

Data of water surface traces (TTJS Group, 2011): plots show
positions of measurements; numbers show the measured height in T.P.

Comparison between calculated and measured maximum heights. Symbols
are the same as those used for Fig. 12:

Effects of seawalls on a flood flow are expressed by imposing the following internal hydraulic conditions on line segments where the
seawalls are located.

Ordinary BH models exclude building footprints from the calculation area using a free-slip interior boundary condition. In this study,
effects of buildings on a flood flow are expressed by imposing the following internal hydraulic condition on the line segments of
building footprint outlines.

The 2011 earthquake off the Pacific coast of Tohoku, with

Kamaishi city is located at the inner part of the Kamaishi Bay in the southern Sanriku sawtooth coast of Tohoku district, Japan
(Fig. 2). The distance between the bay mouth and the seismic center of the 2011 Tohoku earthquake is only 115

Figure 3 presents the bathymetry and surrounding topography of Kamaishi Bay, where Tokyo Peil (T.P.)

Figure 4 depicts the building distribution in the city center before the earthquake provided by Geospatial Information Authority of
Japan (GSI), where the colors show materials used in the construction of individual buildings. Approximately 2500 small buildings were
clustered close together in a narrow area. More than half of these buildings were mortared wooden houses (shown as red). The old
coastline was at the southern margin of this dense building cluster. The open space between the old coastline and the present coastline
is reclaimed land used as a fishing port, a market, and a loading yard. Most of the steel-frame buildings (shown as yellow) were
workshops and storehouses used for marine industries. Concrete panels covered the side faces of these buildings. The black line along
the coast represents a concrete seawall, the crown elevation of which was T.P.

The height of the first wave of the 2011 Tohoku tsunami was approximately 10

Based on GPS elevation monitoring by GSI, large ground displacement occurred within a short time immediately after the first shock of the earthquake. The movement ceased before the first tsunami wave's arrival at Kamaishi Bay (GSI). Figure 6 shows ground elevation data obtained near the coastline of Kamaishi Bay before and after the earthquake, which indicate approximately uniform subsidence of 1 m.

Therefore, the ground elevation data for the numerical flow simulation were referred from a 1.0

GSI (2011) provided by GSI includes a dataset of structure plane figures before the earthquake. The seawall positions were approximated by line segments using GIS software SIS.

The digital base map also includes building footprint outlines as corner positions of polygon geometry. However, overly fine expression
of irregular building shapes and tight spacing are expected to degrade the computational efficiency. For that reason, building
footprints were simplified: polygon sides shorter than 2.5

The red line in Fig. 8a presents the total area for tsunami run-up simulation. The blue dotted line shows the area of detailed
calculations in which building footprints were quantified. Figure 8b and c portray enlarged images of the two areas. For areas with
detailed calculation, a triangular mesh system was constructed from the position dataset of seawalls and building corners using
software (ANSYS

Manning's roughness coefficients.

For the areas of suburbs and water (outside the blue dotted line), triangular mesh systems were constructed using
ANSYS

The hydraulic conditions at the east open boundary of calculation area were given by the conventional tsunami propagation model in the
ocean (TUNAMI-N2, Imamura, 1996) with rectangular grids. For calculation efficiency, a seven-step, one-way nesting method was adopted
with grid sizes of 3240 to 10

Numerical simulation cases.

Numerical simulations were conducted with time increment

Data of many kinds were collected by academic groups, governments, and municipalities after the earthquake. The results obtained from the numerical simulation described in the previous chapter are presented herein and are compared to those real data.

As described earlier, the breakwater at the bay mouth was considered with damaged configuration measured after the tsunami because of
the uncertainty of its destruction process. In this study, therefore, time series of tsunami wave height near the coast line were
obtained using image analysis of digital photographs taken by residents. Using them, we examined the calculated time series near the
coast line for use in run-up calculations in the city center area. Figure 10a portrays the shooting point and the view angle, shown
respectively by the yellow dot and the blue lines, in an area (shown as red) where some concrete buildings withstood the tsunami. The
water surface elevation at each time was estimated by comparison with the window height, as measured by the authors after the area was
made accessible for tsunami damage investigations. Figure 10b presents an example in which the red numbers denote heights from the
ground of the lower window frames. Blue numbers and black numbers respectively denote the vertical angle differences and the elevation
differences of the lower window frame and the water surface from the upper window frame, as measured from the digital image. Based on
this analysis, the water surface elevation at the moment was estimated as 6.865

Location of video recording:

Images of wavefront passage at crossing.

Calculated wavefront propagation corresponding to the measured values in Fig. 13.

Degree of regression by

The colored dots depicted in Fig. 11a show the respective water surface levels ascertained from the photographic analysis described for
Fig. 10 for four points located near the coast. They are shown with the same symbols in Fig. 11b. The colored solid lines represent the
calculated time series of the water surface level at the location of

The calculated highest water surface level was from T.P. 10.2

An academic joint research group was organized to conduct an extensive survey of the disaster caused by the 2011 Tohoku tsunami (TTJS Group, 2011; Mori et al., 2011). Their survey covered almost the entire Pacific coast damaged by the 2011 Tohoku tsunami, as marked by red in Fig. 2a. For the Kamaishi area, after estimation of the highest water surface level at several points from water surface traces remaining on poles, roofs, building walls, and the ground, they made the dataset available to other research groups via the internet. We present those data on the map displayed in Fig. 12.

Figure 13 shows correlation between the measured and calculated highest water surface levels for four cases with symbols used in
Fig. 12. Lines show perfect agreement (- -

Time series of flow variables at the city center:

Cases with

A local resident recorded a video (YouTube, 2013) of tsunami waves from the point shown as the yellow dot in the direction
indicated by the blue arrow presented in Fig. 14a. After we selected three images in which the tsunami front had just passed the street
through three intersections –

Figure 16 depicts snapshots of the inundation depth for Case-3(a) at the three moments when the calculated tsunami wavefront reached
the three intersections denoted by

The reasonable value of

Mappings of maximum depth and maximum flow velocity during flooding (Case-3(a)):

Figure 17 presents characteristics of data scattering around the regression lines of

Figure 18b and c respectively shows the time series of water depth and flow velocity obtained using the five cases of the Case-(a)
series at two points A and B in the city center, as shown in (a). Although the tsunami wave arrival time and peak values of depth and
velocity depend on the value of

Although the discussion presented above might appear to be unclear and indefinite, the overall permeable constant

Figure 19 presents spatial distributions of the maximum inundation depth and the maximum flow velocity obtained from the Case-3(a) calculation, in which black rectangles represent houses destroyed by tsunami waves. The water depth was greater in the eastern part of the building collapse concentration area because the tsunami approached the city from the east, whereas higher flow velocities were found in western areas because the wavefront hitting at the end of the bay intruded directly into open spaces and the streets.

Considering that the forces on structures are proportional to the momentum flux, an indicator for tsunami run-up flow intensity,

Construction of high embankments along the coast was stated as the primary countermeasure against tsunami run-up in reconstruction guidelines issued by the Japanese Government after the 2011 Tohoku tsunami (Cabinet Office, Government of Japan, 2011). However, such structures obstruct access to the sea, causing great inconvenience to cities with local communities that are mainly reliant on marine product industries. Some reports have suggested that large buildings protected the houses behind them from tsunami impact (e.g., Matsutomi et al., 2012; Takagi et al., 2014).

Therefore, the effects of building arrays along the coast on controlling the flood flow instead of a continuous seawall were tested numerically. White rectangles in Fig. 21 show the trial building plot: two building layers are lined alternately to prevent seawater from flowing straight to the city center, with daily traffic given access through a hook-shaped road system. The building footprint dimensions are presented above the figure.

The color contour in Fig. 21 shows the calculated

The approach presented in this paper demonstrated the possibility of accurate urban flood modeling with an internal hydraulic condition
at building side faces, which allows water leakage into buildings, in the context of tsunami run-up in Kamaishi city caused by the 2011
Tohoku earthquake. When the wall permeable constant is set to zero, the model is equivalent to a BH model. A mesh system for
calculation was generated using software (ANSYS

The permeable wall assumption is both the distinctive point and the weak point of the model because of the difficulty in assigning
a realistic value of permeability to each building. In actuality, the value is expected to vary depending on the building condition and
stage of tsunami impact. Moreover, it is true that some amount of water leakage occurs through openings, slits, and cracks on building
side faces. In this study, five values of the permeability constant

Examination of time series of water depth and flow velocity at the city center revealed that the consequent sensitivity on

The purpose of modeling the tsunami run-up process is not only to predict hydraulic quantities such as inundation water depth but also
to propose effective measures against tsunami disasters based on calculation results. This study adopted an indicator for run-up flow
intensity:

Numerical tests conducted for buildings along the coast demonstrated that two lines of alternately arranged concrete buildings can prevent seawater from flowing straight into the city center while maintaining daily traffic through a hook-shaped road system. Therefore, the present model offers great potential as a tool to support the improvement of city layouts for enhanced safety against tsunami waves.

The digital data of the building footprint are available at

The authors declare that they have no conflict of interest.

We would like to thank the academic joint research group for their extensive survey of the 2011 tsunami disaster and for sharing the valuable data obtained in their survey. We also thank the River Division of the Department of Prefectural Land Development, Iwate Prefecture, for providing topographic data of the Kamaishi area for this study. Finally, we thank Prof. Takashi Nakamura of the Tokyo Institute of Technology for his assistance in compiling the program used for GPGPU (general-purpose computing on graphics processing units) calculation. Edited by: Mauricio Gonzalez Reviewed by: two anonymous referees