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
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Probability of Tsunami Inundation in Taiwan · Tsunami inundation probability can be used to calculate the benefit/cost ratio of a structure or tsunami insurance designed to protect
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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
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