Probability of Tsunami Inundation in Taiwan

Guan-Yu Chen*, Chin-Chu Liu, Department of Oceanography, National Sun

Yat-sen University, Taiwan Jing-Hua, Lin

International Wave Dynamics Research Center (IWDRC), Tainan Hydraulics

Laboratory, Tainan, Taiwan

Previous studies (Geist et al. 2009, in The Sea, Volume 15: Tsunamis)

!  Probabilistic Tsunami Hazard Analysis (PTHA) provides estimates of the likelihood that tsunami flooding at a particular location will exceed a given level within a certain period of time.

!  An extension of Probabilistic Seismic Hazard Analysis (PSHA)

!  magnitude of earthquake" height of tsunami

The threshold tsunami height varies from place to place. If the city is protected by a seawall, 3 m or higher tsunami may do no harm to the resident.

Problem of PTHA (I): Tsunami size/height is not the only factor for hazard assessment

!  The area damaged by earthquake is smaller and the size/magnitude is homogeneous !  The size/magnitude is the most important

parameter

!  The distribution of tsunami size/magnitude varies significantly due to local bathymetry/ topography !  the size/height is not a good parameter for a

vulnerable city

Tsunami size/height is not the only factor for hazard assessment

Both PTHA and PSHA have hazard distribution functions against the size of earthquake/tsunami

Similar to G-R relation of earthquake

Problem of PTHA (II): the specific pdf for tsunami height has not been validated Many historical records are required for empirical analysis of tsunami runup height

!  Previous studies used coarser simulation and calculate the probability at a specific location based on a single tsunami height

!  As a by-product of inundation map generation, the present study uses very fine grid simulation

!  Detailed bathymetry and topography are included

3rd reason to modify PTHA

!  Previous studies provide probability for a given exposure time, not for a specific incidence

!  In the present study, tsunami hazards are assessed as a whole city/town because of the finer grid

!  The results can be used in the Probabilistic Forecast of tsunami hazard that can to reduce the chance of false alarm

4th reason to modify PTHA

Nowadays, Probabilistic Forecast is more and more popular

Probabilistic Forecast of Tsunami Inundation (PFTI) !  PFTI is the conditional inundation

probability once an earthquake is detected at some specific location with a specific magnitude

!  PFTI can be directly applied to a specific tsunami incidence.

Probabilistic Forecast of Tsunami Inundation (PFTI): conditional inundation probability in the existence of an earthquake of magnitude at the i-th sub-fault

ijnPFTIN

≡

1j jM M M +≤ ≤

Inundation Probability with Seawalls

Seawall Height

# Black: Shoreline # Red: 50 m from Shoreline # Aqua: Inundated area # Yellow: Limit of

Inundation>50 cm

# Of the 8 grid points of the coastline, the inundation limit of three points is more than 50m inland

#  Inundation Probability # =3/8=0.375。

Sea

Land

Inundated area

1

2

3

! Inundation Probability without Seawalls

(6.75-7.25) (7.25-7.75) (7.75-8.25)0 0 9.26%

0 0 9.38%

Linyuan Township 0 0 51.92%

Sinyuan Township 0 0 40.00%

Donggang Township 0 0 11.43%

Linbian Township 0 0 84.62%

Jiadong Township 0 5.00% 100.00%

Fangliao Township 0 0 69.05%

CijinSiaogang

Moment magnitude scale(Mw)

N1

Position

For a specific sub-fault, the Probabilistic Forecast of Tsunami Inundation (PFTI) can be obtained by simulating a few scenarios

Trenches around the Pacific Ocean is divided into 141 zones— too many scenarios to simulate

1-13

42-48

23-30 31-41

49-58

14-22

59-70 71-80

81-107

108-139

140-141

Tsunami Source Parameters used in computing PFTI (Tonga trench and Kermadec trench)

zone name longitude latitude depth(m) strike dip slip

1

湯加海溝&

克瑪迪克海溝

-174.54 -15.32 15000 -84 43.88649 90

2 -176.51 -17.24 15000 -74.2543 38.72711 90

3 -176.64 -18.92 15000 -51.0241 37.08086 90

4 -177.26 -20.88 15000 -77.9875 28.44976 90

5 -177.64 -23.04 15000 77.62623 28.81268 90

6 -177.72 -24.8 15000 54.95969 32.08721 90

7 -177 -27 15000 42.22768 35.43684 90

8 -177.43 -29.14 15000 36.77013 28.5233 90

9 -178.14 -30.84 15000 34.02716 31.6 90

10 -178.67 -32.93 15000 36.27189 27.72589 90

11 -179.15 -34.78 15000 33.4214 29.09804 90

12 -179.55 -36.87 15000 22.1959 35.27778 90

Max tsunami wave height at Hua-Lien city

 zone name longitude la.tude Mw7.0 Mw7.5 Mw8.0 Mw8.5 Mw9.0

1

湯加海溝&

克瑪迪克海溝

-174.54 -15.32 0.0018 0.0072 0.0206 0.0636 0.2374 2 -176.51 -17.24 0.0012 0.0059 0.0229 0.0644 0.1874 3 -176.64 -18.92 0.0018 0.0059 0.0169 0.0481 0.1411 4 -177.26 -20.88 0.0013 0.0047 0.0207 0.0380 0.1063 5 -177.64 -23.04 0.0012 0.0043 0.0170 0.0439 0.1472 6 -177.72 -24.8 0.0013 0.0053 0.0172 0.0407 0.1256 7 -177 -27 0.0018 0.0059 0.0187 0.0603 0.1918 8 -177.43 -29.14 0.0012 0.0032 0.0126 0.0616 0.2581 9 -178.14 -30.84 0.0019 0.0060 0.0204 0.0651 0.2414 10 -178.67 -32.93 0.0015 0.0064 0.0162 0.0554 0.1893 11 -179.15 -34.78 0.0014 0.0040 0.0107 0.0259 0.0794 12 -179.55 -36.87 0.0011 0.0024 0.0049 0.0150 0.0405

Take Taidong City (台東市) for example, the tsunami from Mariana Trench, Phillipine Islands and Ryukyu Island Arc is highest

0

1

2

3

4

5

6

7

8

1 4 7 10

13

16

19

22

25

28

31

34

37

40

43

46

49

52

55

58

61

64

67

70

73

76

79

82

85

88

91

94

97

100

103

106

109

112

115

118

121

124

127

130

133

136

139

Mariana 馬尼亞納

菲律賓 Phillipine

琉球Ryukyu

The highest tsunami wave height in Hua-Lien and Taidong generated by earthquakes of Mw=9 at each source zone

The highest tsunami wave height and tsunami arrival time in Daren and Changbin generated by earthquakes of Mw=9 at each source zone

The highest tsunami wave height and tsunami arrival time in Chengong generated by earthquakes of Mw=8.5 an Mw=9 at each source zone

For each vulnerable city, the inundation map is obtained by simulating a bell-shaped wave incident normally to the shore

bell-shaped wave of 2 m height

Hua-Lien

Taidong

! Anping

Incident Wave Form

0.5m 1m 2m

! Anping 3m 4m

6m 10m

Anping

Wave Height 0.5m

Wave Height 1m

Wave Height 2m

Wave Height 3m

Wave Height 4m Wave Height

6m

Wave Height 10m

Red: Coastal point where inundation depth>50 cm at 50 m from Shoreline

Location Anping Wave Height (m)

# of Coastal Grid Points

# of Inundation Grid Points

Inundation Probability

0.5

1725

447 25.91%

1 1104 64.00%

2 1477 85.62%

3 1574 91.25%

4 1644 95.30%

6 1714 99.36%

10 1721 99.77%

Inundation Probability for various incident wave height

北門

七股

將軍、七股

將軍、北門

彌陀、梓官

彌陀、永安、茄萣

安南、安平、南區

安南

旗津、小港

左楠、旗鼓

PFTI of Hua-Lien City for Tsunami Generated in Mariana Trench

 zone name longitude la.tude Mw7.0 Mw7.5 Mw8.0 Mw8.5 Mw9.0

19 馬里亞納海溝

146.28 17.08 0.00% 0.00% 0.00% 0.00% 0.91% 20 146.35 14.93 0.00% 0.00% 0.00% 0.00% 1.15% 21 144.07 12.86 0.00% 0.00% 0.00% 0.15% 1.73% 22 142.27 11.35 0.00% 0.00% 0.00% 0.22% 36.47% 23 139.85 8.92 0.00% 0.00% 0.00% 0.04% 8.62% 24 139.53 7.2 0.00% 0.00% 0.00% 0.03% 7.22%

PFTI for incident tsunami of various wave heights in northern Taiwan

PFTI for incident tsunami of various wave heights in eastern Taiwan

The PFTI is the conditional probability once a tsunami occurs

!  To analyze the tsunami hazard in a certain exposure time, we need the chance of tsunamigenic earthquake

!  In SCSTW3, earthquake probability is used

Previous Study: Use Poisson process to find earthquake probability ! Poisson process is usually used to explain the distribution of

earthquakes (Anagnos and Kiureghian, 1988)

1/j jTλ = Mean annual rate of excedance.

In this way, earthquake probability always <1 even if there are more than one incidence

1( ), 1 j j dTe jP e λ λ+ −= −

The probability for j-th magnitude range 1j jM M M +≤ ≤

,ie jP

Moment scale magnitude (j)

Probability (in 30 years)

i=1(lat. 21~22.5) i=2(lat. 19.5~21)

i=3(lat.18.2~19.5)

(5.75-6.25) 99.96% 99.98% 99.98%

(6.25-6.75) 93.37% 89.59% 93.24%

(6.75-7.25) 61.47% 45.61% 56.52%

(7.25-7.75) 28.48% 15.12% 22.71%

(7.75-8.25) 11.12% 4.32% 7.66%

Expected earthquake number is used instead of earthquake probability

!  Tsunami inundation probability can be used to calculate the benefit/cost ratio of a structure or tsunami insurance designed to protect an area from tsunami hazard

!  If there are two incidences expected, the benefit of the structure/insurance premium is twice as much as of the same structure that protects people from one incidence

i i ij j jETIP TEN PFTI=

The PFTI is the conditional probability once a tsunami occurs

!  Earthquake-induced Tsunami Inundation Probability (ETIP) for subfault i and magnitude

is the number of tsunamigenic earthquake times PFTI

i i ij j jETIP TEN PFTI=

1j jM M M +≤ ≤

! Nj is the number of earthquakes that occur in some period of time T with magnitude !  a and b are regression constants.

jM≥

log( )j jN a bM= −

Tsunamigenic Earthquake Number (TEN): G-R relation (Gutenberg and Richter,1944)

0

0.5

1

1.5

2

2.5

3

4 4.5 5 5.5 6 6.5 7 7.5 8

Mw(Moment magnitude scale)

log(

N)

log(N) = - 0.9082Mw + 6.3393 in lat. 21-22.5

log(N) = -1.1398Mw + 7.6559 in lat. 19.5-21

log(N)= - 1.0195Mw + 7.0043 in lat. 18.2-19.5

!  NEIC includes earthquake data in mb, Mw , Ms and ML

Magnitude in Incidence

number

mb 15527 Mw 1242 ML 371 UK 337 Ms 247

Total 17724

Regression formula from Ms to Mw (Scordilis 2006)

! Nj is obtained based on the regression of 35 years NEIC data base !  Nj is used to obtain the expected number in 50 and 100 years Assume the seismic movement is uniform in time

log( )j jN a bM= −

(Poisson process)

jM

hT: Expected number of earthquake ≧

in a time extension

G-R relation

,

j

h h j

NTT N

=

,h jN

G-R relations for a source zone

Mw 6.5 7 7.5 8 8.5 9

50 yr 4.0552 1.1116 0.3047 0.0835 0.0228 0.0062

100 yr 8.1099 2.2231 0.6094 0.1670 0.0457 0.0125

,

j

h h j

NTT N

=

1, 1 1( / ) ( / )10 ja b Mh j h j hN T T N T T +−

+ += =

( )1, 10 10j ja b M a b Me j

h

TNT

+− −= −

, ( / ) ( / )10 ja b Mh j h j hN T T N T T −= =

jM

hT: Expected number of earthquake ≧

in a time extension ,h jN

hT: Expected number of earthquake

in a time extension ,e jN 1j jM M M +≤ ≤

Expected Earthquake Number ,e jN

Expected Earthquake Number in the next 100 years

zone name longitude latitude Mw7.0 Mw7.5 Mw8.0 Mw8.5 Mw9.0

1

湯加海溝&

克瑪迪克海溝

-174.54 -15.32 1.5718 0.4566 0.1326 0.0385 0.0112 2 -176.51 -17.24 0.4767 0.1233 0.0319 0.0082 0.0021 3 -176.64 -18.92 0.1642 0.0415 0.0105 0.0027 0.0007 4 -177.26 -20.88 0.4073 0.1115 0.0306 0.0084 0.0023 5 -177.64 -23.04 0.2261 0.0609 0.0164 0.0044 0.0012 6 -177.72 -24.8 0.1990 0.0605 0.0184 0.0056 0.0017 7 -177 -27 0.1360 0.0349 0.0089 0.0023 0.0006 8 -177.43 -29.14 1.7651 0.6374 0.2301 0.0831 0.0300 9 -178.14 -30.84 0.7932 0.2232 0.0628 0.0177 0.0050 10 -178.67 -32.93 0.3216 0.0781 0.0190 0.0046 0.0011 11 -179.15 -34.78 0.0402 0.0098 0.0024 0.0006 0.0001 12 -179.55 -36.87 0.0281 0.0082 0.0024 0.0007 0.0002

Tsunamigenic Earthquake Number (TEN)

( )1, 10 10j ja b M a b Me j

h

TNT

+− −= −

Expected Earthquake Number ,e jN

ocshP conditional probability for earthquakes to be both oceanic origin and shallow, following Liu et al. (2007).

,j e j ocshTEN N P=

!  The statistics of submarine earthquakes is based on NEIC

!  The depth is also available

NEIC Database !  Year：1976-2008 !  Study area：118

。~123

。E、18

。~23

。N。

!  Total earthquake events： 2124. !  Both oceanic origin and shallow：(<15km) ：392

ocshP

392 16.76%2124ocshP = =

19

馬里亞納海溝

146.28 17.08 622 85 13.66%

20 146.35 14.93 1033 176 17.05%

21 144.07 12.86 2107 359 17.06%

22 142.27 11.35 745 186 25.00%

23 139.85 8.92 98 20 20.41%

24 139.53 7.2 59 14 23.33%

ocshP

35 133.4038 33.13188 1433 371 25.86%

36 131.46 31.02878 1235 89 7.20%

37 130.3494 28.92551 1851 172 9.30%

38 128.5244 27.13333 1458 180 12.36%

39 126.6147 25.13265 2675 682 25.51%

,i i i i ij j j e j ocsh jETIP TEN PFTI N P PFTI= =

!  Earthquake-induced Tsunami Inundation Probability (ETIP) for subfault i and magnitude

is the number of tsunamigenic earthquake times PFTI

1j jM M M +≤ ≤

ETIP for a tsunami prone coast

summed over all indices i and j to give a desired probability for all possible sources

,

ij

i j

i i i ij j e j ocsh j

i j i j

ETIP ETIP

TEN PFTI N P PFTI

=

= =

∑∑

∑∑ ∑∑

For the east coast of Taiwan, the trenches around the Pacific Ocean is divided into 141 zones

1-13

42-48

23-30 31-41

49-58

14-22

59-70 71-80

81-107

108-139

140-141

19

馬里亞納海溝

146.28 17.08 622 85 13.66%

20 146.35 14.93 1033 176 17.05%

21 144.07 12.86 2107 359 17.06%

22 142.27 11.35 745 186 25.00%

23 139.85 8.92 98 20 20.41%

24 139.53 7.2 59 14 23.33%

ocshP

35 133.4038 33.13188 1433 371 25.86%

36 131.46 31.02878 1235 89 7.20%

37 130.3494 28.92551 1851 172 9.30%

38 128.5244 27.13333 1458 180 12.36%

39 126.6147 25.13265 2675 682 25.51%

Expected Earthquake Number in the next 100 years

zone name longitude latitude Mw7.0 Mw7.5 Mw8.0 Mw8.5 Mw9.0

1

湯加海溝&

克瑪迪克海溝

-174.54 -15.32 1.5718 0.4566 0.1326 0.0385 0.0112 2 -176.51 -17.24 0.4767 0.1233 0.0319 0.0082 0.0021 3 -176.64 -18.92 0.1642 0.0415 0.0105 0.0027 0.0007 4 -177.26 -20.88 0.4073 0.1115 0.0306 0.0084 0.0023 5 -177.64 -23.04 0.2261 0.0609 0.0164 0.0044 0.0012 6 -177.72 -24.8 0.1990 0.0605 0.0184 0.0056 0.0017 7 -177 -27 0.1360 0.0349 0.0089 0.0023 0.0006 8 -177.43 -29.14 1.7651 0.6374 0.2301 0.0831 0.0300 9 -178.14 -30.84 0.7932 0.2232 0.0628 0.0177 0.0050 10 -178.67 -32.93 0.3216 0.0781 0.0190 0.0046 0.0011 11 -179.15 -34.78 0.0402 0.0098 0.0024 0.0006 0.0001 12 -179.55 -36.87 0.0281 0.0082 0.0024 0.0007 0.0002

PFTI of Hua-Lien City for Tsunami Generated in Mariana Trench

 zone name longitude la.tude Mw7.0 Mw7.5 Mw8.0 Mw8.5 Mw9.0

19 馬里亞納海溝

146.28 17.08 0.00% 0.00% 0.00% 0.00% 0.91% 20 146.35 14.93 0.00% 0.00% 0.00% 0.00% 1.15% 21 144.07 12.86 0.00% 0.00% 0.00% 0.15% 1.73% 22 142.27 11.35 0.00% 0.00% 0.00% 0.22% 36.47% 23 139.85 8.92 0.00% 0.00% 0.00% 0.04% 8.62% 24 139.53 7.2 0.00% 0.00% 0.00% 0.03% 7.22%

ETIP in the next 100 years

City/Town 秀林鄉 新城鄉 Hua-Lien 壽豐鄉 豐濱鄉 長濱鄉

50 yr 0.10% 0.00% 0.16% 0.04% 0.45% 0.32%

100 yr 0.20% 0.00% 0.31% 0.08% 0.89% 0.64%

City/Town 成功鎮 東河鄉 Taidong 太麻里鄉 大武鄉 達仁鄉

50 yr 2.12% 6.21% 4.07% 0.27% 1.91% 2.47%

100 yr 4.25% 12.41% 8.14% 0.55% 3.81% 4.94%

PFTI for incident tsunami of various wave heights in eastern Taiwan

Thank you for your attention

Questions/Comments ?