building a quick forecast system for tsunami runup...

Building a quick forecast system for

tsunami runup height

SCSTW6

2013/11/07 Nanyang Technological University, Singapore

Jing-Hua, Lin, Chia-Yan, Cheng, Chin-Chu, Liu, Guan-Yu, Chen

Outline

Tsunami histories in Taiwan

Tsunami Risk of Taiwan

Estimation of Tsunami runup and inundation for arbitrary

waveform

Set up of Run-up database and forecast system

Application in Sri-Lanka, Phuket and Miyagi

Future works

Based on historical records or documents, larger magnitude tsunami

events had occurred in Taiwan, such as Tainan (1721,1782), Kaohsiung

(1781 and 1866), Anping (1921)(southwestern of Taiwan) and Keelung

(1867) (northeastern of Taiwan)

Kaohsiung (1781) and Keelung (1867) tsunami records

(1)1781年(清乾隆46年)5月間(4月24日-6月21日)高雄

(Kaohsiung, May, A.D 1781)

「台灣采訪冊」(p.41)「祥異，地震」的記載。「(乾隆46年)鳳港西里有加藤

港，多生加藤，可作澀，染工賴之，故名云。港有船通郡，往來潮汐無異。

乾隆四十六年四、五月間，時甚晴霽，忽海水暴吼如雷，巨浪排空，水漲數

十丈，近村人居被淹，皆攀援而上至尾，自分必死，不數刻，水暴退，人在

竹上搖曳呼救…………漁者乘筏從竹上過，遠望其家已成巨浸，至水汐時，

茅屋數椽，已無有矣。」

(2)1867年(清同治6年)12月18日基隆 (Keelung, December, A.D 1867)

「淡水廳志」，「（同治六年）冬十一月，地大震。......二十三日，雞籠頭、

金包里沿海，山傾地裂，海水暴漲，屋宇傾壞，溺數百人。」

(Death of hundreds of people)

Tsunami histories in Taiwan

(3)1782/5/22 (Soloviev and Go, 1974)

Chile tsunami (1960) ,Hualien Tsunami (1986) 及 Pingtung-Hengchun

tsunami (2006)

Figure：Keelung tsunami(1867), Tsunami

attacked the coastal of Keelung. Newspaper：Chile tsunami (1960), max.

wave height is 1.9 m and some bridges were

broken by tsunami induced flow.

Seafloor Topography

Manila trench (Southwestern),

Okinawa trough and Ryukyu Trench

(Northeastern) are potential tsunami-

sources (USGS, 2005; Nakamura, 2011).

Potential tsunami sources around Taiwan

Manila trench

Okinawa trough and

Ryukyu Trench

When a sea-earthquake, which magnitude is over than specified limit,

tsunami waves including near/far-field, may be hit Taiwan.

Tonga trench Bougainville trench

Marianas trench

Philippine

trench

Ryukyu trench Izu Bonin trench

Kurile-Japan trench

Manila trench

Peru-Chile trench

Tsunami Risk map

Why to do this topic?

Viewpoints on disaster mitigation：

If there is a enough length-mild slope in the near-shore region,

the run-up and inundation may be occurred due to shoaling effect.

Questions:

(1)How height is the run-up?

(2)How far is the inundation distance?

(3)How fast to estimate the forecasted results?

(4)How is the accuracy of forecasted results?

Estimation of Tsunami run-up and inundation for

arbitrary waveform

Developing a system with high accuracy, real-time, quick to estimate

the run-up height and inundation, can be helpful to disaster

mitigation in the early warning for near/far-field tsunamis.

Maybe using the concept of database can solve

these problems.

AGF (Analytical Green Function)--Carrier et al.(2003)

y

x0

( , )x t

Fully nonlinear shallow-water

equation with a uniform slope

' ' ' '

' '

' ' ' '

' ' '

[ ( )] 0,

0,

x t

t x x

u x

u u u g

[ ( )] 0,

0.

t

t x x

u x

u uu

'u g Lu

' L

'x Lx

' /t L gt

Nondimensional Form

u is the horizontal flow velocity normal to the shoreline is the free surface elevation

is the characteristic length. L

Introduced a distorted coordinate, and

that are defined as

t u ,q x 2

2

( ) ( ) 0,2

( ) 0,2

q

uqu

uu

2( ) 2 0,

10,

2

u

u

4 ( ) 0 Linear second-order partial

differential equation

21

2u is related to the total mechanical energy.

Original nonlinear problem on the canstant slope becomes

as a linear problem over the flat bed in distorted coordinate.

The semi-analytical solution with the convolution form can be

obtained by Fourier-Bessel transform

0 0( , ) 2{ ( ) ( , , ) ( ) ( , , ) },F b G b db P b G b db

( )F b represent the initial waveform condition

( )P b represent the initial flow-velocity condition

b is the spatial variable in the distorted coordinate.

Analytical Green’s Function (AGF)

0 00

( , , ) ( )sin( / 2) ( )G b b J J b d

2 2

2 22 2

10

2

1 4( ) 1( )

16 2

4 16 1( )

4( ) 24( )

for b

b bK for b b

b

b bK for b

bb

2

20( )

1 sin

dK k

k

is the first kind complete

elliptic integral.

It can be numerically integrated by IMSL.

2u

2

2,

8

Analytical horizontal velocity and wave height

Inundation distance and momentum flux (force)

q x 2f qu

It means that the runup height and inundation distance of a point

can be estimated if we have the initial conditions.

0 0( , ) 2{ ( ) ( , , ) ( ) ( , , ) },F b G b db P b G b db

The form is not easy to use!

The leading wave profile

(red line) and the initial flow

velocity (blue line) in

longitude by the COMCOT

tsunami model.

Second term can be neglected because the initial velocity

condition P(b) is very small.

The displacement of seafloor induced the initial waveform of a

tsunami (Murata et al., 2011)

Energy distribution, wave displacement and inundation of N wave

0( , ) 2 ( ) ( , , )F b G b db

Moving shoreline

Initial waveform condition and Reciprocal Green’s function (RGF)

0( , ) 2 ( ) ( , , )F b G b db

Using the method to calculate run-up height and inundation is

very easy. It doesn’t need the digital grid or topography, just

need a suitable slope.

Sources of initial waveform condition

1. Real-time in-situ data, such as GPS

buoys.

2. Directly tsunami simulation

3. Reciprocal Green’s function (RGF)

Q1: How to get the initial waveform condition?

Obtaining the initial conditions by direct numerical simulation

is time-consuming and is not feasible for tsunami early warning.

Green’s function is the foundational solution of SWE, and it

represents the temporal series.

Shuto (1991) ：Tsunami travelling is the linear process in d > 50m

region.

Green’s function is the

symmetry and inverse

(Loomis, 1979).

The tsunami-wave height

database can be built

beforehand by numerical

model.

Q2:What is the Reciprocal Green’s function (RGF)?

1

( ) ( )N

s

r r s

i

H t GF t H

Reciprocal Green’s Function

It depends on the fault

parameters；unknown

Database built by RGF.

Loading/Input the fault parameters and choose the forecast location,

and then offshore-temporal data can be obtained.

However, this equation needs a spatial waveform along tsunami

travelling direction . In fact, we only get the temporal wave data (time

series) form a nearshore buoy or tidal section.

0( , ) 2 ( ) ( , , )F b G b db

Q3: How to get the spatial waveform from a

known-temporal data?

F(t) F(x) or F(b) transformation

temporal spatial

0

0 0 02( )xd

s m

d gsx sx gddxt

gsx s gd gsx

2 00

1

4

dx st g t gd

s

Then, the equivalent waveform with

the spatial form can be obtained via the

Green’s formula

104

B A

d

sx

Modified method- Equivalent waveform

Q4: What are differences between this

method and COMCOT in estimating the

runup and inundation distance?

Parameters: H=3m、k=6、s=0.02、L=50km

In a constant slope (solitary wave)

Comparison between AGF and common 2-D tsunami

simulation (COMCOT model)

(A): AGF method

(B):COMCOT

In a real topography (North- eastern of Taiwan)

AGF COMCOT

slope Runup (m) Inundation distance (m)

Runup (m) Inundation distance (m)

0.0144 15.48 -1064.1 16.28 -944

0.01509 15.51 -1019.2 10.01 -2910

0.01788 15.5 -856 15.56 -852.57

Q5: How to extend this method for arbitrary

- irregular waveform and build a database?

Q6: How much time to forecast for a point?

Q7: How about is the accuracy to apply in the

real tsunami events?

2004 Indian Tsunami

2011 Tohoku Tsunami (Japan)

Set up of Run-up database using FFT The arbitrary irregular waveform can be decomposed:

0 01 1

0 0 01 1

0 01

( , ) 2 ( ) ( , , ) 2 ( cos( ) cos( )) ( , , )

2( ( , , ) cos( ) ( , , ) sin( ) ( , , ) )

2 ( , , ) cos( ) ( , , )

n n

i i i i

i i

n n

i i i i

i i

n

i i

i

F b G b db A b B b G b db

G b db A b G b db B b G b db

G b db A b G b db

01

0

1 1

sin( ) ( , , )n

i i

i

n n

i ci i si

i i

B b G b db

D A D B D

Fourier coefficients

Run-up database : can be beforehand integrated by numerical method based

on suitable frequency and increment of frequency.

In real cases, after knowing the Fourier coefficients and find the corresponding

component, then total mechanical energy can be quick determined by superposition

. It indicates that complicated numerical integration can be replaced.

Therefore, this process can save a lot of computing time.

1 1

( ) cos( ) cos( )n n

i i i i

i i

F b A b B b

Sample: Phuket (7.9N)

in 2004 Indian tsunami

Run-up and inundation distance

of a point can be estimated

within minutes after database is

built.(In this case, 1.5min)

East Sri-Lanka

Verification of system in real tsunami – 2004 Indian

Tsunami

The ETOPO topography can be taken form NOAA-NGDC

Initial condition obtained by COMCOT model

Comparison between forecasted results and the field measurement

Phuket (Thailand)

2011 Tohoku Tsunami

Available from the Disaster Control Research Center, Tohoku University

Fault parameters with 10 segments

suggested by Sugawara et al.(2013)

1st-layer : 2 min

2nd-layer: 1 min (provided by Prof.

Wu)

Okada model (1985).

Max. wave height = 16m

Simulated time : 18000s (3hr)

Preliminary results in Miyagi city(宮城)

Kim D.C. et al.(2013) Six subfaults and rupture time are

considered in the simulation

Preliminary forecast

Flow chart of present method

Future works Using other fault parameters to compare the forecasted and field

results

Building the runup database and linking the existing database made

by RGF.

Thank your attention

building a quick forecast system for tsunami runup...

Documents