PROPOSAL OF NEW PROCEDURES FOR IMPROVEDTSUNAMI FORECAST BY APPLYING COASTAL AND
OFFSHORE TSUNAMI HEIGHT RATIO
Weniza
MEE09197

Supervisor: Yutaka HAYASHI
Yushiro FUJIIABSTRACT
Regression analysis was performed using observed tsunami height at offshore and coastal tidal station
pairs, which were within 20 km each other, for the 2010 Chile earthquake tsunami. We used 26 setsinitial and 33 sets maximum tsunami height data obtained from the Real-Time Kinematic Global
Positioning System (RTK-GPS) buoys, wave stations and coastal tidal stations throughout Japan. We
obtained the formulas for initial and maximum tsunami height as1

 h 4H c ,init  1.005H o ,init  o  and hc 

1 h 4H c , max  1.180 H o , max  o  ,
 hc 

where Ho,init and Ho,max are the initial and maximum tsunami height observed at an offshore station,
Hc,init and Hc,max are the initial and maximum tsunami height observed at a coastal tidal station, ho andhc are the water depth at an offshore and coastal tidal station from the mean sea level. In the previous
study, similar proportional parameters have been derived. Tsunami simulation of the 1896 Sanriku
earthquake tsunami was performed as a case study of application of these equations to real time
tsunami forecast and tsunami database. Then, we conclude that the former formula is reliable andvaluable enough to be applied in real time tsunami forecast using detected initial tsunami wave at
offshore RTK-GPS buoy, because of the potentially increased leading time to issue tsunami warning.
In addition, preparing maximum tsunami height data by applying the latter formula and using synthetic
tsunami waveforms at forecast points or RTK-GPS buoys should improve the accuracy of tsunami
database.
Keywords: Tsunami height ratio, Offshore and coastal points, Green’s law, Real time forecast,
Tsunami database.

1. INTRODUCTION
Japan Meteorological Agency (JMA) as a national government has responsibility to issue tsunami
forecast including warnings and advisories immediately after occurrence of an earthquake.
Information about tsunami caused by a near-field earthquake is based on a tsunami scenario databaseand seismic observation. The database includes estimations of maximum tsunami heights and arrival
times at coastal points for each scenario. To estimate tsunami height at coastal areas, firstly, JMA
applies numerical tsunami simulation to calculate tsunami height at forecast points at which water
depths are about 50 m; and then tsunami heights at forecast points are converted into tsunami height atcoastal points by applying Green’s law under assumption that water depth at coastal point is 1 m. If
actually utilized offshore observation data and measured water depth values were used instead, the

Meteorological Climatological and Geophysical Agency (BMKG), Jakarta, Indonesia.
Meteorological Research Institute (MRI), JMA, Tsukuba, JapanInternational Institute of Seismology and Earthquake Engineering (IISEE), BRI, Tsukuba Japan

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method would have been more accurate. The purpose of this study is to improve relationship anddevelop a new procedure on tsunami forecasting using tsunami simulation. A case study of the 1896
Sanriku earthquake will be introduced.

2. DATA
We collected the 2010 Chile earthquake tsunami
waveforms observed at tidal stations along the Pacific
Coast of Japan operated by JMA or Ministry of Land,
Infrastructure and Transport (MLIT). Among these stations,pairs which consist of offshore (RTK-GPS buoys or wave
stations) and coastal tidal stations are selected. In this study,
the pairs are selected according to the criterion that the
distance between both composing stations of a pair must bewithin 20 km (Figure 1). Water depth at offshore arereferred to Nationwide Ocean Wave information network
for Ports and HArbourS (NOWPHAS) station catalogueand Hayashi (2010). Water depths at coastal tidal stations
are obtained by reading sea charts and getting averagewater depth within 100 m from the coastal tidal station.

Figure 1. Locations of station pairs which consist of an offshore and a coastal tidal station. Blue dots,
red triangles, and black circles indicate tidal station, RTK-GPS buoys and wave stations, respectively.
3. THEORY AND METHODOLOGY
3.1. Relationship between Offshore and Coastal Tsunami by the 2010 Chile Earthquake
3.1.1. Initial and Maximum Tsunami HeightRaw data of sea-level height in time-series arecontaminated with short period variationaccompanied by wind waves as well as
long-period variation such as tidal components.
To eliminate noise and extract tsunami
component, band-pass filter of 2-209 min isapplied to tsunami waveform data (Figure 2).
Also we used the calculated tsunami travel times
as references in order to avoid misreading of
initial tsunami wave.
In this study, regression analysis was
performed to calculate proportional parameters(αinit, αmax) in

Figure 2. Examples of band-pass filteredwaveforms for a station pair at Hachinohe(coastal tidal station) and Hachinohe(RTK-GPS Buoy). Sea-level anomalies at
red and blue lines were defined as initialtsunami heights and maximum tsunami
heights, respectively.

1 h 4H c , init  αinit H o ,init  o  hc 

(1) and,1

 h 4H c , max  αmax H o , max  o  hc 

2(2),

where αinit, αmax are ratios of initial and maximum tsunami height affected by reflected wave from coast
at offshore station.
3.2. Tsunami Simulation for Case of the 1896 Sanriku Earthquake
TUNAMI-N2 (Tohuku University’s Numerical Analysis Modelfor Investigation of Near-field tsunami No.2) code developed by
the Disaster Control Research Center (DCRC), Tohoku
University, Japan was used for tsunami simulation for the casestudy of the 1896 Sanriku earthquake tsunami. TUNAMI-N2 isbased on a tsunami numerical simulation with the staggered
leap-frog scheme which is applied to a shallow water theory inshallow and deep sea to investigate near-field tsunami.
The fault parameters are presented by Tanioka andSatake (1996). Bathymetry data are prepared by using theGeneral Bathymetry Chart of the Oceans (GEBCO) one arc
minute grid data. Bathymetry grid intervals were of
Δx=1521.2311 m and Δy=1848.7197 m, maximum bathymetry
depth (hmax) was 8,135.68 m in the computation area. We set thetime step of computation as 3 sec which is less than the CourantFriedrics Lewy (CFL) condition. The dimension of computation
area is 480 grid points for longitude and also for latitude. In thebathymetry grid for tsunami simulation, we set 12 coastal
stations and 32 offshore stations which consist of 7 RTK-GPS
buoy stations, 22 JMA forecast points and 3 wave stations(Figure 3).

Figure 3. Locations of offshore
and coastal stations. Red, blue,
green and yellow triangles
indicate RTK-GPS buoy, JMA
forecast points, wave stations
and tidal stations, respectively.

4. RESULTS
4.1. Relationship between Initial and Maximum Tsunami Height
We read initial and maximum tsunami height of the 2010 Chile earthquake tsunami from eachwaveform. Then, we obtained the ratio of the initial and the maximum tsunami height observed atcoastal tidal stations toward offshore stations (Figure 4). The linear initial and maximum tsunami
height relationship has been derived as follow,
1 h 4H c ,init  1.005 H o ,init  o  (3), hc 

1 h 4H c , max  1.180 H o , max  o  hc 

(4).

The standard deviation of the log-scaled residual error of the proportional constant is 0.156 and 0.161.
When the standard deviation of the log-scaled residual error is considered, the accuracy of forecasting
the initial and maximum tsunami height is 70% to 143% and 69% to 145% of the corrected tsunami
height calculated by Equations (3) and (4) with offshore observation data (Ho,init or Ho,max),
respectively.
4.2. Comparison of Initial and Maximum Tsunami Height
The initial and maximum tsunami heights observed at coastal stations, and calculated heights werecompared by applying Equations (3), (4) and conventional equations (Hayashi 2010) to the data
recorded at RTK-GPS buoys and wave stations. The calculation shows that at some stations tsunami
height are overestimated or underestimated of about 0.1 m; especially maximum tsunami height at
Kuji coastal station was underestimated as much as 0.7 m. The underestimations at coastal tidal

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stations are also found at Hachinohe, Miyako and Onahama. These might be because of local
characteristics of coastal stations. The tsunami height is also affected by the shape of a bay; tsunami
becomes much larger in areas with a V-shaped bay (Earthquake Research Committee 1998)a)b)

Figure 4. Log scaled relationship of (a) initial and (b) maximum tsunami height of offshore and coastal
stations. The horizontal axis indicates corrected initial or maximum tsunami heights. The correctedvalue is defined as the observed offshore initial or maximum tsunami height multiplied by the fourthroot of the ratio of the water depth at offshore and coastal stations. The vertical axis indicates initial or
maximum tsunami heights observed at coastal tidal stations. The thick line indicates the regressionfunction derived by this study. The pair of dotted lines indicates the range of the single standard
deviations.
4.3. Synthetic Tsunami Waveform
After the tsunami simulation, we obtained synthetic waveform for each station pair of offshore andcoastal station. We read the initial and maximum tsunami heights of synthetic waveform at all thestations pairs.

5. DISCUSSION
5.1. Application to Real Time Tsunami Forecast
The Equation (3) derived in this study can be applied to realize real-time forecasting of initial tsunami
heights at nearby coastal area with high accuracy if offshore RTK-GPS buoys or wave stations detect
the initial tsunami heights on the real time-basis. Leading time means time difference between the timeissuing or upgrading tsunami warning and occurrence time of first crest at coastal area. In order toenlarge leading time, it is essential to issue tsunami advisory or tsunami warning before the arrival of
the first crest. Hcoast is tsunami height at the coast by applying the equation. Hth is the threshold value
corresponding to the categories of tsunami warning or tsunami advisory. Threshold values between
tsunami advisory and major tsunami are assumed to be 0.75 m and 2.5 m. By this method the tsunami
warning can be issued when the estimated tsunami height at the coast using the equation becomelarger than the threshold value. This condition is,H 
H offshore (t )   th  βinit 1 h 4βinit  αinit  o  hc 

(5),(6),

where Hoffshore(t) is offshore tsunami height at the time t, βinit is a tsunami height ratio for initial wave.
Example of calculation is shown in Table 1. Here, P is defined as the time when the estimated tsunami

4height at the coast reaches the threshold value (e.g. Hth = 0.75). If tsunami warning is issued at P, theleading time of tsunami warning increase greater than the time in case when it is issued at thedetection of initial crest (Q). According to this case, RTK-GPS buoy has larger leading time than theothers (forecast point or wave station). By using RTK-GPS buoy and applying the Equation (3) in realtime has possibility to upgrade tsunami warning timely and then the accuracy of tsunami warning
could be improved.
Table 1. Example of initial tsunami height application to real time forecast by case study of the 1896
Sanriku earthquake tsunami.
OffshoreNo
Station Name

WD
(m)

Q
(min)

Coastal
H
(m)

P
(min)

Station
Name

WD
(m)

Init.
Time
(min)

H
(m)

Leading
Time
(min)

7
FP
109
142.2 26.2
1.8
24.5 Kamaishi 4.7
31.7
2.4
7.2
10
WS
Kuji
50.0
41.8
2.7
40.0
Kuji
5.4
44.6
3.2
4.6
11
GPS Miyako 200.0 24.4
1.6
22.7
Miyako
7.3
37.3
2.8
14.6
No: Pair number, WD: Water depth, Q: time of initial crest in offshore stations. H: Maximum heightof initial wave, P: time when the estimated tsunami height at the coast reaches the threshold value (e.g.
Hth = 0.75). Init. Time: Time of maximum tsunami height of initial wave. FP: Forecast point, WS:
Wave station, GPS: RTK-GPS buoy,
5.2. Application Proposal of New Procedure to Calculate Maximum Height
We apply a numerical tsunami simulation to calculate the tsunami height at offshore forecast points or
RTK-GPS buoy locations. Then, tsunami amplitudes at the coast are estimated by using Equation (4)with measured water depth values at coastal points as,
1

H CP  βmax H FP

 h 4βmax  αmax  FP  hCP 

(7),

(8),

where βmax is a coastal and offshore tsunami height ratio for maximum height, αmax is a proportionalparameter defined in Equation (2) (αmax=1.180 in Equation (4)), hFP and hCP are water depths at aforecast point and a coastal point, HFP and HCP are calculated maximum tsunami height at a forecast
point from tsunami simulation and the predicted maximum tsunami height at a coastal point. Table 2
shows the calculation of maximum tsunami height at coastal points by present JMA’s method andproposed method in this study (Equation (8)). To estimate maximum tsunami height at coastal area, byapplying the method in this study, the predicted tsunami heights are close to directly simulated ones atcoastal points.
Table 2. Example of calculation of maximum tsunami height at coastal points by case study of the1896 Sanriku earthquake tsunami.
CoastalOffshore
Sim. EQ JMA
Max.
Max.
No
WD
Hmax Hmax Hmax
WD
Hmax
Station Name
Time
Station Name
Time
(m)
(m)
(m) (m)
(m)
(m)
(min)
(min)
4 GPS Hachinohe 87.0 40.3
1.4
Hachinohe
6.7 57.6
1.9
3.0
4.1
10 WS
Kuji
50.0 41.1
2.7
Kuji
5.4 44.6
3.2
5.7
7.3
22 FP
127
99.0 43.2
0.2
Onahama
10.2 70.7
0.2
0.3
0.5

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No: Pair number, WD: Water depth, Max. Time: Time of maximum tsunami height, Hmax: Maximum
tsunami height, Sim.: Simulated tsunami waveform, EQ: Equation (4), JMA: Green’s law which isadopted by JMA, GPS: RTK-GPS buoy, WS: Wave station, FP: Forecast point.

6. CONCLUSIONS
Regression analysis was performed using observed tsunami height at offshore and coastal tidal station
pairs, which were within 20 km each other, for the 2010 Chile earthquake tsunami. Tsunami
simulation of the 1896 Sanriku earthquake tsunami was performed as a case study of application of thederived equations for real time tsunami forecast and tsunami database. We conclude that Equation (3)derived in this study is reliable and valuable enough to be applied in real time tsunami forecast using
detected initial tsunami wave at offshore RTK-GPS buoy because of the potentially increased leading
time before of issuing tsunami warning. In addition, preparing maximum tsunami height data by
applying Equation (4) and using synthetic tsunami waveform at forecast points or RTK-GPS buoy
should improve the accuracy of tsunami database.

7. ACTION PLAN
The 2010 Chile earthquake tsunami reached the north of Papua, eastern part Indonesia at almost sametime to Japan which is 21 hours after the earthquake with amplitude of about 5 cm. This tsunami gave
lesson to technical operational work in InaTEWS especially to BMKG, to generate advisory bulletin
which is needed by local governments and also about requirement of a new Standard Operational
Procedure (SOP) for distant tsunami (National Report Submitted by Indonesia 2010).
The accuracy of tsunami warning and earthquake bulletin could improve if we utilize
offshore data. Although InaTEWS buoy is located at more offshore area and water depth is deeper
than 1000 m compared with RTK-GPS buoy in Japan, we will apply equation derived in this orprevious studies and also use tsunami simulation after setting forecast points along the Indonesiancoastal area.
ACKNOWLEDGEMENT
I would like to express my sincere gratitude to Dr. Bun’ichiro Shibazaki (Tsunami Course Leader of
IISEE), Prof. Yukihiro Terada, Prof. Hitoyoshi Nishimura (Kochi National College of Technology) for
their valuable discussion and suggestion during my study.

REFERENCES
Earthquake research committee, 1998, Headquarter for Earthquake research promotion, Prime
Minister’s Office, Government of Japan.
GEBCO Bathymetry; http://www.gebco.net/data_and_products/gridded_bathymetry_data/
Hayashi, Y., 2010, Earth Planets Space, 62, 269-275.
National Report Submitted by Indonesia, 2010, Regional Tsunami Watch Provider, ICG/IOTWS-7
Meeting Banda Aceh, Indonesia.
Tanioka, Y., and Satake, K., 1996, Geophys. Res. Lett., 23, 1549-1552

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