Study of an empirical model
to evaluate tsunami inundation area
Satoshi Shimizu1, Masatsugu Wakaura2
1Risk Management Dept., OYORMS Corporation, Japan, satoshi.shimizu@oyorms.co.jp
2Risk Management Dept., OYORMS Corporation, Japan, masatsugu.wakaura@oyorms.co.jp

Introduction
Many lives became victims of tsunami in Tohoku Earthquake. Although damaged areas due totsunami had been anticipated before the earthquake, they are based on numerical simulations
seeking tsunami height, inundated areas and inundation depth in case of specific scenario
earthquake occurring. While these numerical simulations are elaborate study, it requires large
amount of efforts to model geography and structures along coastlines, and sequential
calculations in general. Also, it is not easy to apply constructed model configuration to various
other scenario.
This study is motivated to put tsunami phenomena to a simple empirical model as a heuristic
for future disaster reduction. The model is a regression model to predict inundation areas withthree explanatory variables, tsunami height at coastline, distance from coast line and groundlevel of an objective point. Data are collected by Tohoku Earthquake Joint Survey Group1).
The model is validated by comparing predicted inundation areas to actual inundated area in
Tohoku Earthquake and simulation results of Nankai-trough earthquake model by Cabinet
Office, Government of Japan published in summer 2012.

Model
1. Regression Model

Residual error (m)-20 -1001020

Given tsunami surge is losing its energy due to frictions and air resistance with beingtransformed to potential energy, the model can be expressed by the function in (1) wherepotential energy and loss energy are assumed to be a function of ground level and distance fromcoastline, respectively. In inundation areas, lower bound of z – h is zero.
(1)
z = H + αh + βL
where, z ：run-up height (m)H ：tsunami height at coastline (m)h ：ground level (m)L ：distance from coastline (m)α,β ：regression coefficient

2. Data

Run-up height, z, and distance from coastline, L,
are collected data, ranked A or B in data confidence,by Tohoku Earthquake Joint Survey Group ranging
from coastal area of Rokkasyo Village, Aomori02000 4000 6000 8000
Prefecture to Shirako Town, Chiba Prefecture.
Distance from coastline (m)Ground level, h, is set to be equal to z by assuming
Fig.1 Distance from coastline
ground level is equal to run-up height.
and residuals
By assuming inundation height at measuring points
located within 50m from coastline approximately equal to tsunami height at coastline, Tsunami
heights along coastline are set continuously by linear-interpolation of those data.

3. Regression Analysis
Regression analysis yields following model in (2)(2)
z = H + 0.2359h － 0.001604L
Residual standard deviation is estimated by 5.39m, which is extremely large at points nearcoastline. However, it becomes smaller with increasing distance from coastline. (See Fig.1)

Observed
Observed Area
Area
Predicted
Predicted Area
Area
Observed
Observed Area
Area
Predicted
Predicted Area
Area(a) Sendai Plain(b) Rikuzentakata City, Ofunato City

Fig.2 Comparison inundation area of predicted area with observed area

2. Nankai-trough earthquake modelby Cabinet Office, Government of Japan (2012)
Table.2 shows comparison of inundation areas by the model with those of the government study
by the Cabinet Office in 2012 for coastal areas in Shizuoka, Aichi, Mie, Wakayama, Tokushima
and Kochi. There are 11 cases of inundation area in Government study, among which Case 1 ischosen. Also, the condition that bank revetment is broken 3 minutes after earthquake, is selected
for comparison.
Table.2 Comparison the inundation area of the empirical modelwith the simulation model by the Cabinet Office in 2012 (unit : km2)
※ The government study byCabinet Office (2012)

Shizuoka Pref.
Atami City
Ito City
Higashi-Izu Town
Kawadu Town
Shimoda City
Minami-Izu Town
Matsuzaki Town
Nishi-Izu Town
Izu City
Numadu City
Fuji City
Shimizu-ku, Shizuoka City
Suruga-ku, Shizuoka City

Yaidu City
Yoshida Town
Makinohara City
Omaezaki City
Kakegawa City
Fukuroi City
Iwata City
Minami-ku, Hamamatsu City
Higashi-ku, Hamamatsu City

Naka-ku, Hamamatsu City
Nishi-ku, Hamamatsu City
Kita-ku, Hamamatsu City

Kosai City
Aichi Pref.
Tahara City
Toyohashi City
Toyokawa City
Gamagori City
Hazu Town
Kira Town
Isshiki Town
Hekinan City
Takahama City
Kariya City
Higashiura Town
Handa Town
Taketoyo Town
Mihama Town

simulation※0.50.8
0.7
0.8
5.0
3.5
1.9
2.7
1.3
8.1
3.5
13.7
4.7
14.3
7.3
11.2
9.9
6.1
2.0
17.4
23.9
0.0
3.4
19.1
0.9
8.0
33.2
25.7
2.7
3.3
1.0
7.9
15.3
7.7
1.4
2.9
5.1
5.5
1.5
1.9

empirical
model

ratio

Aichi Pref.
0.8 1.64 Minami-Chita Town
1.5 1.84 Tokoname City
0.9 1.18 Chita City
1.3 1.68 Tokai City
7.8 1.57 Midori-ku, Nagoya City
5.4 1.53 Minato-ku, Nagoya City
3.1 1.62 Minami=ku, Nagoya City
3.1 1.17 Atsuta-ku, Nagoya City
1.4 1.13 Nakagawa-ku, Nagoya City
21.9 2.71 Tobishima Village
15.6 4.50 Yatomi City
17.5 1.28 Mizuho-ku, Nagoya City
12.8 2.70 Nakamura-ku, Nagoya City
21.4 1.49 Kanie Town
8.6 1.18 Mie Pref.
16.7 1.50 Kisosaki Town
19.0 1.92 Kuwana City
26.4 4.33 Kawagoe Town
20.6 10.55 Yokkaichi City
44.9 2.57 Suzuka City
42.9 1.79 Tsu City
1.4 － Matsuzaka City
11.3 3.32 Meiwa City
18.3 0.96 Ise City
0.9 1.01 Toba City
7.2 0.90 Shima City
Minami-Ise Town
44.2 1.33 Taiki Town
27.9 1.09 Kihoku Town
3.9 1.48 Owase City
5.8 1.77 Kumano City
1.7 1.69 Mihama Town
9.1 1.15 Kiho Town
14.6 0.95 Wakayama Pref.
9.6 1.25 Shingu City
2.3 1.67 Nachi-Katsuura Town
1.3 0.46 Taiji Town
3.7 0.73 Kushimoto Town
9.5 1.73 Susami Town
4.0 2.69 Shirahama Town
5.2 2.76 Tanabe City

simulation※

empirical
model

ratio

simulation※

empirical
model

ratio

1.8
1.5
4.6
2.5
1.1
1.7
1.8
1.2
2.2
4.8
19.9

4.0
2.6
9.0
5.92.9
2.0
2.1
1.6
3.6
6.0
19.3

2.28
1.75
1.93
2.33
2.67
1.15
1.14
1.32
1.66
1.25
0.97

16.1
9.1
32.0
18.8
25.8
2.1
1.2
3.3

14.3
4.8
19.1
14.9
28.5
3.4
1.8
5.8

0.89
0.53
0.60
0.79
1.10
1.59
1.51
1.73

1.6
3.4
1.3
1.0
0.8
5.7
0.4
7.5
3.4
26.8
3.5
11.2
3.6
2.4
8.9
6.0
10.5
1.7
10.6
890.0

2.8
5.5
1.8
1.3
2.0
9.3
2.1
10.9
13.3
35.5
5.7
12.2
4.9
3.1
11.1
12.5
11.9
2.710.91182.3

1.72
1.64
1.36
1.27
2.60
1.65
5.61
1.46
3.93
1.32
1.64
1.08
1.38
1.29
1.24
2.06
1.14
1.54
1.03
1.33

Wakayama Pref.

4.6
6.2
0.7
3.0
1.9
28.9
10.7
3.7
14.4
2.6
4.7
1.1
0.6
5.2

6.5
12.9
3.4
7.6
0.4
31.4
6.0
0.6
0.7
11.1
9.6
0.0
0.0
0.0

1.5
3.3
2.1
16.3
7.0
36.8
38.3
13.0
39.4
8.5
22.5
12.5
0.7
10.0
5.9
2.2
2.4
2.3

4.2
7.2
6.2
23.9
14.7
38.1
34.3
14.5
28.0
11.7
28.1
16.6
1.2
11.7
6.8
5.6
6.3
3.3

1.7
6.2
1.0
8.4
2.1
5.3
5.2

4.9
7.7
1.4
10.4
2.9
9.5
6.7

1.41 Minabe Town
2.07 Inami Town
5.09 Gobo City
2.57 Mihama Town
0.23 Hidaka Town
1.09 Yura Town
0.56 Hirokawa Town
0.15 Yuasa Town
0.05 Arita City
4.19 Kainan City
2.06 Wakayama City
0.00 Tokushima Pref.
0.00 Naruto City
0.00 Matsushige Town
Tokushima City
2.86 Komatsujima City
2.22 Anan City
3.02 Minami Town
1.46 Mugi Town
2.10 Kaiyo Town
1.04 Kochi Pref.
0.89 Toyo Town
1.12 Muroto City
0.71 Nahari Town
1.38 Tano Town
1.25 Yasuda Town
1.32 Aki City
1.60 Geisei Village
1.17 Konan City
1.16 Nangoku City
2.53 Kochi City
2.62 Tosa City
1.48 Susaki City
Naka-Tosa Town
2.96 Shimanto Town
1.26 Kuroshio Town
1.36 Shimanto City
1.24 Tosashimizu City
1.33 Otsuki Town
1.79 Sukumo City
1.28
Total

Verification
Predicted inundation areas by the model are compared with inundated areas in Tohoku
Earthquake and simulation results of Nankai-trough earthquake model (M9.0).

1. The 2011 off the Pacific coast Tohoku Earthquake andTsunami
Table.1 shows comparison of actual inundated area with predicted inundation area bymunicipal administration unit. Fig.2 shows actual and predicted inundated area in Sendai
Plain, Rikuzentakada City and Ofunato City.
Table.1 Comparison with the actual inundation area and predicted areain Tohoku Earthquake.
observed(km2)

Aomori Pref.
Rokkasho Village
Oirase Town
Misawa City
Hachinohe City
Hashikami Town
Iwate Pref.
Hirono Town
Kuji CityNoda Village
Fudai Village
Tanohata Village
Iwaizumi Touwn
Miyako City
Yamada Town
Otsuchi Town
Kamaishi CityOfunato City
Rikuzentakata City
Miyagi Pref.
Kesennuma City
Minami-Sanriku Town

Onagawa Town
Ishinomaki City
Higashi-matsushima City

Matsushima Town
Rifu Town

53
6
9
0.5

predicted(km2)

18
4
20
15
0.5

observed(km2)

ratio

Miyagi Pref.
3.60 Shiogama City
1.33 Shichigahama Town
3.33 Tagajo City
1.67 Miyagino-Ku, Sendai City
1.00 Wakabayashi-Ku, Sendai City
Taihaku-Ku, Sendai City

142
111105478132853372787131615181037337
20.53214550
36
10.5

2.00 Natori City
2.00 Iwanuma City
2.50 Watari Town
3.00 Yamamoto Town
3.00 Fukushima Pref.
7.00 Shinchi Town
2.70 Soma City
1.60 Minami-Soma City
1.75 Namie Town
1.86 Futaba Town
2.00 Okuma Town
1.15 Tomioka City
Naraha Town
1.78 Hirono Town
1.40 Iwaki City
1.67 Shinchi Town
0.68 Soma City
0.97 Minami-Soma City
0.50 Namie Town
1.00 Futaba Town

predicted(km2)65620292272935243662230
3252628231129396321321511293963102835
107555332
102835107

ratio

observed(km2)

Fukushima Pref.
0.50 Okuma Town
2
1.20 Tomioka City
1
1.00 Naraha Town
3
1.10 Hirono Town
2
1.03 Iwaki City15
1.50 Ibaragi Pref.
0.93 Kita-Ibaragi City
30.90 Takahagi City
10.80 Hitachi City
4
0.96 Tokai Village
3
Hitachinaka City
30.91 Oarai Town
2
0.97 Hokota City
20.90 Kashima City3
1.67 Kamisu City3
2.33 Chiba Pref.
2.50 Choshi City
15.00 Asahi City3
1.67 Sosa City
1
1.50 Yokoshiba-Hikari Town
1
2.13 Sammu City
6
0.91 Kujukuri Town
20.5
0.97 Oamishirasato Town
0.90 Shirako Town
1
1.67
2.33
total
668.5

predicted
(km2)

ratio

55
5
3
32

2.50
5.00
1.67
1.50
2.13

5
2
3
4
2
2
2
818

1.67
2.00
0.75
1.33
0.67
1.00
1.00
2.67
6.00

2 2.00
9 3.0011 11.00
5 5.0012 2.00
9 4.505 10.00
8 8.00869.0

1.30(a) Around Kochi City(b) Around Shizuoka CityFig.3 Comparison inundation area of the empirical model with the simulation
model by the Cabinet Office in 2012Conclusion
1. Empirical model to predict Tsunami inundation area is developed by using data of Tohoku
Earthquake Joint Survey Group.
2. In a comparison with actual inundated areas in Tohoku Earthquake, the model generally
replicates inundated area where Tsunami surge linearly from the origin while in particulargeography there are gaps between predicted and actual inundated area.
3. In a comparison with Nankai-trough earthquake model (M9.0) by Cabinet Office, Governmentof Japan, targeting Pacific coastal area from Shizuoka to Kochi, the model predicts larger
inundation areas to a certain extent than those of government study. Nonetheless, the model isstill deemed to generally replicate inundation area except for areas of particular geography asgaps are laid within 0.5 to 2 times of predicted area.
Reference 1) The 2011 Tohoku Earthquake Tsunami Joint Survey Group : http://www.coastal.jp/tsunami2011/