04.tsunami modeling (ver.2)

8/6/2019 04.Tsunami Modeling (Ver.2)

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Chapter IV

TSUNAMI MODELING

4.1. Introduction

The tsunami modeling or simulation plays a key role in the issuance of a tsunamiwarning. According to the design of the Indonesian TEWS, the tsunami warning willconsist of information on (a) the possibility of tsunami occurrence, and (b) the

predicted tsunami heights and their arrival times at certain coastal areas. The tsunamimodeling for certain tsunami source could give estimation of tsunami heights andtheir arrival times at several locations along the coastal area. The tsunami modelingwill be done for every expected or assumed tsunami sources in the region. Since

most of tsunamis in the region were generated by earthquake, the tsunami sourcesthat will be used in the tsunami modeling are the tsunamigenic earthquakes. All of the results from the tsunami modeling will be stored in a database.

Basically tsunami modeling can be utilized in a tsunami early warning system in twoways: Real-time monitoring of the tsunami evolution and prediction of coastal effects;

in which real-time tsunami warnings are the mission of tsunami warning centers. Support the evacuation plans and community preparedness by means of

inundation (run-up) calculations of historic or hypothetical events.

4.2. Tsunamigenic Earthquakes

The occurrence of the 26 December 2004 Aceh tsunami and recently the 17 July2006 Java tsunami has confirmed that the Indonesian region is one of the mosttsunami prone regions in the world. According to the historical tsunami records, atotal of 163 tsunamis caused by earthquake occurred in the region for a period fromyear 1801 to 2006. Figure 4.1 shows some of tsunamis that occurred in theIndonesian region since 1600. The figure shown that most of tsunami sources in theIndonesian region are located along the seismic active zones. The earthquakes thatgenerated tsunamis in the Indonesian region are located along the Sunda subductionzone, the Sunda back-arc thrusting zone, the Banda subduction zone, the MoluccaSea collision zone, the Caroline of Pacific subduction zone, and the Philippinesubduction zone.

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Figure 4.1. Tsunami occurrence in the Indonesian region

Tsunami could be generated by three main sources i.e. earthquake, volcanic eruption,and landslide that occurred in the sea. In the Indonesian region, the three sources

could generate large tsunami such as the 2004 Aceh tsunami that generated byearthquake (more than 200,000 people killed), the 1883 Krakatau tsunami thatcaused by volcanic eruption (about 36,000 people killed), and the 1979 Lomblentsunami that caused by landslide (about 550 people killed). According to thehistorical data most of tsunamis that occurred in the Indonesian region weregenerated by earthquake. The historical tsunami data compilation done by Latief etal. (2000) pointed out that about 90 percent of tsunamis in the Indonesian regionwere generated by earthquake.

The earthquake that generates tsunami known as tsunamigenic earthquake usually has special characteristics. The tsunamigenic earthquakes have characteristicsas (a) the epicenter is located in the sea, (b) the earthquake focal depth less than 60km so that could be classified as shallow earthquake, (c) the earthquake magnitude(Ms) greater than 6.0, and (d) the earthquake focal mechanism are dip-slip type of thrusting or normal faulting. The tsunamigenic earthquakes characteristics sometimeslightly different from region to region. For example, Puspito and Gunawan (2005)have shown the characteristics difference between tsunamigenic earthquakes in theSumatra region and the ones in Pacific region as follow.

In the Sumatra region, the tsunamigenic earthquake magnitude Ms varies from 5.6 to9.0. Figure 4.2 shows the tsunamigenic earthquake magnitude distribution, where the

black blocks indicates the Sumatra region data and the striped blocks indicate thePacific region data. The figure shows that about 84 % of tsunamis in the Sumatra

region were generated by earthquakes with magnitude Ms > 6.0, where about 32 %

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were generated by moderate earthquakes (Ms = 6.1 ~ 7.0), about 30 % weregenerated by large earthquakes (Ms = 7.1 ~ 8.0), and about 22 % were generated bygreat earthquakes (Ms > 8.0). This suggests that most of the tsunamis in the Sumatraregion were generated by moderate to great earthquakes. This characteristic is almost

the same as suggested by Iida (1958) that showed, based on the Japanese tsunamidata, that a tsunami could be generated by earthquake with magnitude Ms > 6.0. Thefigures are also comparable to tsunami data for the Pacific region that show thatabout 91% of the tsunamis were generated by earthquakes with magnitude Ms > 6.0.

16

5

27

21

9

18

43

9

22

29

20

10

1

0

5

10

15

20

25

30

35

5. 6 - 6.0 6. 1 - 6. 5 6. 6 - 7. 0 7. 1 - 7.5 7. 6 - 8.0 8.1 - 8.5 8.6

Earthquake Magnitude (Ms)

P e r c e n

t a g e

( % )

Figure 4.2. The tsunamigenic earthquake magnitude distribution

In the Sumatra region, the depth of tsunamigenic earthquakes varies from 10 to 130km. Figure 4.3 shows the tsunamigenic earthquake depth distribution, where the

black blocks indicates the Sumatra region data and the striped blocks indicate thePacific region data. The figure shows that about 86% of the tsunamis in the Sumatraregion were generated by earthquakes that have focal depth less than 100 km, whereabout 26% have focal depth = 0 ~ 20 km, about 20% have focal depth = 21 ~ 40 km,

about 7% have focal depth = 41 ~ 60 km, about 27% have focal depth = 61 ~ 80 km,and about 6% have focal depth = 81 ~ 100 km. This suggests that most of thetsunamis in the Sumatra region were generated by shallow earthquakes. Thischaracteristic is almost the same as suggested by Iida (1958) based on the Japanesetsunami data and also comparable with the tsunami data for Pacific region. Thefigure shows that about 97% of tsunamis in the Pacific region were generated byearthquakes with depth less than 100 km.

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26

20

7

27

6

24

44

19

8

2

0

5

10

15

20

25

30

35

40

45

50

0 - 20 21 - 40 41 - 60 61 - 80 81 - 100

Earthquake Depth (km)

P e r c e n

t a g e

( % )

Figure 4.3. The tsunamigenic earthquake depth distribution

Iida (1958) has proposed an empirical relationship between the tsunamigenic

earthquake magnitude (Ms) and the tsunami magnitude (m). Based on the Japanesetsunami data he proposed an empirical relationship m = 2.61 Ms 18.44. Figure 4.4shows the tsunami intensity (I) on Soloview-Imamura scale and the tsunamigenicearthquake magnitude (Ms) data for the Sumatra region. Although the datadistribution is very scattered (especially the 2005 Nias tsunami is not in line with theothers), the empirical relationship between the tsunami intensity (I) and theearthquake magnitude (Ms) for the Sumatra region can be written as I = 0.80 Ms 4.18. In comparison the empirical relationship for the Pacific region can be written asI = 1.22 Ms 8.89. If the 2005 Nias tsunami data is not included, the empiricalrelationship for the Sumatra region (shown as a dashed line in Figure 4.4) can bewritten as I = 1.15 Ms 6.19 and its trend is parallel to the trend for the Pacificregion data. The comparison between the three empirical relationships indicates thatthe tsunamigenic earthquakes in the Sumatra region tend to generate larger tsunamithan the ones in the Pacific region. However, it should be noted that the data of earthquake magnitude Ms for great earthquakes (M > 8.0) might be underestimated

because of its saturation.

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I = - 8.89 (Pacific)

I = 0.80 Ms - 4.18 (Sumatra)

-1,5

-1

-0,5

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

6 6,5 7 7,5 8 8,5 9 9,5

Earthquake Magnitude (Ms)

T s u n a m

i I n

t e n s i

t y ( I )

1.22 Ms

2005

Figure 4.4. The tsunami intensity and earthquake magnitude

Most of the tsunami sources the tsunamigenic earthquakes in the Indonesianregion are located not far from the coastal areas (see Figure 4.1). Most of thedistances between tsunami sources and the nearest coastal areas are less than 200kilometers. Therefore, most of the tsunamis in the Indonesian region could beconsidered as local tsunamis. The travel times of tsunami wave from the source tothe nearest coastal areas are usually less than 30 minutes. In some places the traveltimes even less than 10 minutes such as in the case of the 1996 Biak tsunami and the2004 Aceh tsunami. Therefore, the tsunami warning in the Indonesian region should

be issued in very short time.

Many of the tsunamis that occurred in the Indonesian region have caused greatdamages in the affected coastal areas. The tsunamis have also caused thousands of

people killed and billions of Indonesian rupiah losses. Most of the destructivetsunamis in the Indonesian region were caused by earthquakes; few of them werecaused by volcanic eruptions and landslides that occurred in the sea. The destructive

tsunamis that caused by tsunamigenic earthquakes, among others are the 1815 Balitsunami that killed about 10,250 people, the 1861 West Sumatra tsunami that killedabout 725 people, the 1968 Central Sulawesi tsunami that killed about 390 people,the 1977 Sumba tsunami that killed about 190 people, the 1992 Flores tsunami thatkilled about 2,100 people, the 1994 Banyuwangi tsunami that killed about 230

people, the 1996 Biak tsunami that killed about 190 people and the 2004 Acehtsunami that killed more than 200,000 people. Example of destructive tsunami thatgenerated by volcanic eruption is the 1883 Krakatau tsunami that killed more than36,000 people. While the example of destructive tsunami that caused by landslide isthe 1979 Lomblen tsunami killed about 550 people. Table 4.1 below shows some of major tsunamis that occurred in the Indonesian region.

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Table 4.1. Some of major tsunamis in the Indonesian region

Year Region Source Death Toll

1815 Bali Island Earthquake 10,2501820 Sumbawa Island Earthquake 400

1833 Bengkulu, Sumatra Earthquake ?

1856 Sangihe, North of Sulawesi Earthquake 100

1861 West Sumatra Earthquake 725

1883 Krakatau, Sunda Strait Volcanic eruption 36,000

1965 Seram, Maluku Earthquake 70

1968 Central Sulawesi Earthquake 390

1969 South Sulawesi Earthquake 60

1977 Sumba Island Earthquake 190

1979 Lomblen, Larantuka Land slide 550

1992 Flores Island Earthquake 2,100

1994 Banyuwangi, East Java Earthquake 230

1996 Biak Island, Papua Earthquake 190

1998 Taliabu, Maluku Earthquake 30

2004 Aceh and North Sumatra Earthquake More than200,000

2006 Java Earthquake More than 500

Based on the historical tsunamis described above, it may be concluded that theIndonesian region is always threaten by tsunami disasters. Therefore, theestablishment of the Indonesian TEWS should be seriously and properly promoted,

planned and implemented.

4.3. Tsunami Modeling

Tsunamis are the oceanic gravity waves generated by various submarine geological processes, such as earthquake, landslide, and underwater volcanic eruption.However, as mentioned earlier, most of the tsunamis are generated by tsunamigenicearthquakes. Tsunamis typically have a very long wavelength compared with thedepth of the ocean basin where they propagate. The evolution of earthquake-generated tsunami has three distinct stages: generation, propagation, and run-up. Areliable numerical model should compute all the three stages, to provide a complete

tsunami modeling capability.

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The tsunami modeling or simulation basically aims to calculate the tsunami heightsand their travel times in space and time. Tsunamis are commonly referred to as longwaves and they are usually modeled mathematically using a depth-averagedapproximation of the Navier-Stokes equations referred to as shallow-water wave

theory. For deep water propagation, the linear long-wave equations are used; whilefor run-up (inundation) model, it uses the non-linear equations. The basic equationsare:

(1)

(2)

(3)

where x and y are horizontal coordinates, t time, h the still water depth, the verticaldisplacement of water surface above still water level,

Integrating equation (1) (3) from sea bottom to sea surface, the following shallowwater theory obtained for discharge flux M and N that are applied in the numericaltsunami modeling are as follows (Imamura et al., 1995)

Continuity equation:

0=++ y N

x M

t

(4)

Momentum equation:

0223

7

22

=+++

+

+ N M M

D

gn x

gD D

MN y D

M xt

M

(5)

0223

7

22

=+++

+

+ N M N

D

gn y

gD D N

y D MN

xt N

(6)

Here x and y are space coordinates in horizontal direction, t is time, u and v water particle velocities in the x- and y-directions, g the gravitational acceleration, x/ andy/ bottom frictions in the x- and y- directions, M and N are discharge in x- and y-direction respectively, is water elevation, D (= h + ) is total depth where h iswater depth, and n is Manning roughness coefficient. The 5 th component in equations(5) and (6) represent the bottom friction where the Mannings roughness coefficient

n is related with the bottom friction coefficient f byg

fDn

2

3/1

= . It is noted that the

bottom friction f becomes rather larger as the total depth is shallower, as long as the

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Mannings roughness n is almost constant. Usually the equations (5) and (6) weresolved linearly by neglecting the 2 nd, 3 rd, and the 5 th components so that the equations(5) and (6) become

0=+ xgDt M (7)

0=+

ygD

t N (8)

In the numerical tsunami modeling done by many Indonesian scientists, the aboveequations are usually solved numerically by applying the leap-frog staggered finitedifferent method (IOC, 1997). The leap-frog scheme used in this study is a centraldifference scheme with the truncation error of the second order. Figure 4.5 showsarrangement of points for computation in the leap-frog method. Suffixes (i, j, k) are

used to express the spatial position (x, y) and the time t.

Figure 4.5. Computation in the leap-frog method

First, the equation of continuity is approximated by a difference equation. With thecentral difference scheme, three terms in equation (4) are given by

[ ]k jik jit t ,1

,1

=

+ (9)

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21

,21

21

,21

1 +

+

+

=

k

ji

k

ji M M

x x M

(10)

=+

+

+2

1

21

,2

1

21

,1

k

ji

k

ji N N y y N (11)

On assuming that values at k and k+1/2 time steps are known, the only unknown(i,j,k+1) is solved by

21

21

,

21

21

,

21

,21

21

,21,

1,

+

+

+

+

+

++

=

k

ji

k

ji

k

ji

k

ji

k ji

k ji N N y

t M M

xt

(12)

Second, the equation of motion is approximated. The linear equation of motion in

the x-direction is given by equation (7). A central difference at the point (i+1/2,j,k)yields the following equation for an unknown M(i+1/2,j,k-1/2)

[ k jik jik ji

k

ji

k

ji xt

gD M M ,,1,

21

21

,21

21

,21

= ++

+

+

+] (13)

where the total water depth D(i+1/2,j,k) is expressed by

[ ]k jik ji ji

k

ji ji

k

jihh D ,,1

,21

,21

,21

,21 2

1 ++== +++++ (14)

The similar manipulation yields the following difference equation for the linear equation of motion in the y-direction given in equation (8)

[ k jik jik ji

k

ji

k

ji yt

gD N N ,1,21

,

21

21

,

21

21

, +

= +

+

+

+] (15)

[ ]k jik ji ji

k

ji ji

k

jihh D ,1,

21

,21

,21

,21

, 21

+=+= +++++ (16)

It is now possible to solve equations (12), (13) and (14) simultaneously and obtainthe solution of linear long waves. A comment is necessary to explain a difference

between the origin equation of linear long waves and equations (13) and (14). Theoriginal equation of linear long waves uses h (still water depth), but equations (13)and (14) use D (total water depth). If h is sufficiently larger than , a linear computation with equations (13) and (14) can yields reliable result. It should be keptin mind that this linear computation may become unstable if h is smaller than . Inorder to ensure the stability of the computation the temporal grid t and spatial gridx should satisfy x/t C, where C is the propagation velocity that is assumedconstant.

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The computation was done by assuming that no wind waves and tides are included.The still water level is given by tides and is assumed constant during thecomputation. This means that no motion is assumed up to time k-1/2. Therefore, theinitial condition in sea is set as

0,0,0 21

21

,

21

,21

1, ===

+

+

k

ji

k

ji

k ji N M

For tsunami simulation in a deep sea including a tsunami source, there are two kindsof initial condition with and without dynamic effects of fault motion (rupturevelocity and rising time). In such dynamic effects can be negligible for tsunamiinitial propagation, the final vertical deformation of the sea bottom caused by thefault is given as the initial water surface. The equation (1) is modified as

t y N

x M

t

=

+

+

(17)

where is the vertical deformation of sea bottom. The boundary condition on land isthe perfect reflection. The velocity component (discharge flux component) normal tothe land boundary is made equal to zero so that

;0=

x M

0=

x N

At present several Indonesian institutions deal with the tsunami modeling studies,among others are Institute of Technology Bandung (ITB) and BPPT. The studies ontsunami modeling by Indonesian scientists actually were just started since the

beginning of 1990s. The initiation of the tsunami modeling studies by Indonesianscientists was triggered by the occurrence of the 1992 Flores tsunami that killedabout 2,100 people in Flores Island. Most of the tsunami modeling studies were donein collaboration with foreign scientists, most of them are Japanese scientists. Thestudies have successfully modeled the 1992 Flores tsunami.

Since the success story of the collaboration in the modeling of the 1992 Florestsunami, the Indonesian scientists are considered to have a relatively good capabilityin tsunami modeling studies. The Indonesian scientists have successfully modeled

several tsunamis that occurred before and after the 1992 Flores tsunami. Amongthem are the 1833 Bengkulu, the 1883 Krakatau, the 1935 North Sumatra, the 1977Sumba, the 1992 Flores, the 1994 East Java, the 1996 Sulawesi, the 1996 Biak, the2000 Banggai, and the 2004 Aceh tsunamis. Figure 4.6 shows location of thetsunamis in the Indonesian region that have been modeled by Indonesian scientists.

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Figure 4.7. Tsunami modeling of the 1833 Bengkulu tsunami

Other examples of tsunami modeling are the 1977 Sumba tsunami modeling and the2004 Aceh tsunami modeling. Figure 4.8 shows the 1977 Sumba tsunami modelingand Figure 4.9 shows the 2004 Aceh tsunami modeling. Figure 4.10 shows thecomputed tsunami wave time-series at Phuket, Thailand due to the 2004 Acehtsunami.

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Figure 4.8. Tsunami modeling of the 1977 Sumba tsunami

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Puspito and Gunawan, 2005

Figure 4.9. Tsunami modeling of the 2004 Aceh tsunami

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Figure 4.10. The computed tsunami wave at Phuket

4.4. Database of Tsunami Modeling

Reliable and robust tsunami warnings with minimum false-alarm are the mission of tsunami early warning centers. In order to support that, the creation of a pre-computed tsunami database is considered as an important step. According to designof the Indonesian TEWS, the earthquake parameters will be determined within 3minutes after the earthquake occurrence. When the determined earthquake

parameters meet the characteristic of the tsunamigenic earthquake, the tsunamimodeling will be retrieved from the database to give estimation of tsunami heightsand their arrival time at several locations along the coastal area. Therefore,availability of the database of tsunami modeling is very important in issuance of thetsunami warning. Such database so far is not yet available in Indonesia. Therefore,development of the database of tsunami modeling is very important to support the

establishment of the Indonesian TEWS.The database of tsunami modeling will be developed for the 10 regional centers. Thetsunami modeling will be performed for all of possible hypothetical tsunamis aswell as the historical tsunamis in each regional center. The possible tsunamigenicearthquake sources will be identified based on the tsunamigenic earthquakecharacteristic that occurred in the region. Basic ideas of how to develop the databaseof tsunami modeling are given in Figures 4.11 and 4.12. The ideas could be brieflydescribed in the following.

The first step in the development of the database is the selection of area where thetsunami modeling will be performed. In order to perform the tsunami modeling, the

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modeling area should be divided into several blocks that have same size in the x- andy-directions. Figure 4.11 shows an example of modeling area.

Figure 4.11. The modeling area and magnitudes of hypothetic earthquakes

The selection of block size is much depend on the resolution of the available bathymetry data. If we have high resolution of bathymetry data we could select smallsize of block. Each points in the modeling area could be assumed as epicenters of thehypothetic earthquakes that could generate the tsunamis. However, it will be better if we select only the most possible sources. Information on the seismotectonic of themodeling area the characteristics of the tsunamigenic earthquakes will be veryimportant to identify the most possible tsunami sources. The tsunami modeling will

be performed for all of possible hypothetic earthquakes with several differentmagnitudes. The results of all of the tsunami modeling will be stored in a database asshown in Figure 4.12.

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Figure 4.12. The development of database

The basic ideas of utilization of the database in the Indonesian TEWS is shown inFigure 4.13. When the determined earthquake parameters meet the characteristic of the tsunamigenic earthquake, the determined earthquake parameters will be compareto the available hypothetic earthquakes in the database. The hypothetic earthquakethat close to the determined earthquake parameters will be selected as the tsunamisource. The tsunami modeling will be retrieved from the database to give informationon the tsunami heights and their arrival times along the coastal areas.

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Figure 4.13. The utilization of database in tsunami warning

Figures 4.14 and 4.15 show example of the proposed modeling area and developmentof the database in the Java region.

Figure 4.14. The modeling area and hypothetic earthquakes in Java

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Figure 4.15. The development of database for Java

4.5. Inundation Map

According to recommendation of ICG/IOTWS-II in Hyderabad on December 2005,every country in the Indian Ocean should make tsunami inundation maps for their vulnerability area. The time frame for that is 10 years. In this case, the action plan isto set-up a national working group for making of the inundation map of Indonesiantsunami-prone areas. The group will be composed of competence institutions suchas: BPPT, ITB, LIPI, BAKOSURTANAL, LAPAN, BMG, other local universities,or local governments.

Expected outcome will be (a) Hazard maps showing areas of high potential for

tsunami inundation, (b) Inundation maps (inundation and run-up) for maximumreliable tsunami scenarios of high vulnerability areas, and (c) Decision support for appropriate mitigation option

Serious obstacle for accurate inundation model simulations is the requirement for high-resolution bathymetry and topography data of near-shore areas. The lack of thishigh-resolution data for Indonesian costal area should be fulfilled by the authorityagency/institution. The ideal horizontal resolution of bathymetry and topographydata for run-up simulation is 10-50m grids (or maps scale of 1:1000 1:5000). Suchhigh-resolution data are not easy to obtain. However, it can be done in stages,starting from the most vulnerable area. Until high-resolution data were available, any

existing data with coarser resolution would be utilized.

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4.6. Proposed Action Plans

In the following are the propose plan related to the tsunami modeling for the

development of the Indonesian TEWS Identification of the possible tsunami sources (tsunamigenic earthquakes) in each

regional centers

Development of the database of tsunami modeling for each regional centers Development of inundation maps for selected coastal areas

04.tsunami modeling (ver.2)

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