Influence of cross-shore sediment movement on long-term shoreline change simulation

by H. Kang, H. TanakaDept. of Civil Eng. Tohoku Univ. Japan

Numerical simulation of shoreline change by one-line

model

• Introduction

• Study area

•Measured data

• Empirical Orthogonal Function

• One-line model

• Comparison of calibration K

(sediment transport coefficient)

• Summary

Outline of this presentation Measured data

including both influence of LST and CST

Shoreline evolution ： caused by LST

caused by CST

EOF method

* Longshore Sediment Transport, Cross-shore Sediment Transport

Comparison of calibration K

Calibration of sediment transport coefficient

Data1

Data2

Data3

I. Introduction

* Longshore Sediment Transport, Cross-shore Sediment Transport

Objective of this presentation • To calibrate K (Sediment transport coefficient) 　 in one-line model. • To compare K based on measured data and separated data by EOF method.

Erosion is continually progressing on Sendai Coast sediment is interrupted by coastal structure sediment supply from river is rapidly reduced sediment is keep moving northward

The complex topography change is separated into topography change due to LST and CST by EOF method in order that characteristic of topography change can be more clarified and easily understood.

Survey has been being carried out twice a month since 1996 to examine topography change. It is difficult to analyzes a complicated evolution of shoreline using measured data, because it is containing both influence of LST and CST.

Length : about 12km Bounded by Sendai Port and Natori River mouth

II. Study area

the jetties

the breakwater

Breakwaters

ESE&SE

• Incident wave direction : ESE and SE Longshore sediment transport move northward Breakwater and Nanakita River interrupt longshore sediment transport Accumulation occur St.11, St.10, and St. 4

0

200

400

600

800

1000 0

1020

3040506070

8090

100110120130140150

160170

180

S.L.

Frequency of incoming wave direction

œ

œ œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

123

45

Natori River

Teizan Canal

Nanakita River

Sendai Bay

N

0 1km

Sendai Port

JAPAN

SENDAI

6

7

89

1011

12

13

14

œ

œ œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

123

45

Natori River

Teizan Canal

Nanakita River

Sendai Bay

N

0 1km

Sendai Port

JAPAN

SENDAI

6

7

89

1011

12

13

14

Breakwaters

Nanakita River

the jetties at the Natori River mouth

the breakwater at Sendai Port

St.13

•Station 13 : Shoreline has gradually retreated. And beach slope is steep.

1997 1998 1999 2000 2001 2002 2003 2004Time i yearj

0

50

100

150 Station 13

III. Measured data

œ

œ œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

123

45

Natori River

Teizan Canal

Nanakita River

Sendai Bay

N

0 1km

Sendai Port

JAPAN

SENDAI

6

7

89

1011

12

13

14

Breakwaters

Nanakita River

the jetties at the Natori River mouth

the breakwater at Sendai Port

St.8

III. Measured data

1998 2000 2002 2004time "series," point

150

200

250

Cro

ss-s

hore

Dis

tanc

e

(m

)

Station 8•Station 8 : Due to gentle slope, fluctuation is big. And shoreline is stable.

1997 1998 1999 2000 2001 2002 2003 2004

œ

œ œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

123

45

Natori River

Teizan Canal

Nanakita River

Sendai Bay

N

0 1km

Sendai Port

JAPAN

SENDAI

6

7

89

1011

12

13

14

Length : about 12km Bounded by solid boundaries (Sendai Port & Natori River mouth)

Breakwaters

Nanakita River

the jetties at the Natori River mouth

the breakwater at Sendai Port

St.4

III. Measured data

0

50

100

150 Station 4

T.P.-0.5m T.P.+0.0m T.P.+0.5m T.P.+1.0m•Station 4 : Fluctuation of shoreline is widely varied because of Nanakita River. And shoreline has advanced.

1997 1998 1999 2000 2001 2002 2003 2004

E.O.F IV. Empirical Orthogonal Function

xn

nnn xetCtxy

1

)()(),(

• It assume that shoreline position combines temporal function with spatial function.

Temporal eigenfunction

Spatialeigenfunction

)()( 11 xetC )()( 22 xetC )()( 33 xetC

)()( xetC nn

Sho

reli

ne

posi

tion

(Mea

sure

d da

ta)

tn

tjtit

txij yy

nnaA

1

1

Correlation matrix A

xn

xnn xetxytC

1

)(,)(,nnn eAe

1/2

EOF method separated data of a complex topography change on the coast into parts of data that have the same characteristic of topography change on the coast as simple data.

･・・・ (1)

The 2nd E.O.F. component can express topography change caused by longshore sediment transport.

• 2nd E.O.F. component 2/2

* Longshore Sediment Transport

• A sign changes before and after breakwaters and Nanakita River It can express that accumulation occur at right hand side of breakwaters and Nanakita River due to LST is obstructed by breakwaters and Nanakita River.

yma /94.12 btatC 22 )(

rate of change of the second temporal eigenfunction

1997 1998 1999 2000 2001 2002 2003 2004 Time (yearj

-40

-20

0

20

40

C2(

t) (

m) -1.94(m/year)

Regression Line T.P. +0.0m

ii. 2nd temporal eigenfunction)(22 xea has a similar shape with the

rate of long-term shoreline change.

-1.5

0

1.5

a2e

2 (m

/yea

r)

-3

0

3

a(m

/yea

r)

The rate of long-term shoreline change (measured data)

The rate of change of the 2nd component

-10000 -5000 0 X(m)

-2000

-1000

0

1000

Y(m

)

œœ œœ œ œ

œ

Yuriage Port

œSendai Port

œœœ œ œ

œ

123 4 5 67 8 9 10

11 12 13 14

-1

-0.5

0

0.5

1

e2(

x)

T.P. -0.5m T.P. +0.0m T.P. +0.5m T.P. +1.0m

i. 2nd spatial eigenfunction

V. One-line model

i. Governing equation

･・・・ (2)01

qx

Q

Dt

ys

xsy

tQ

txqr

txqo

Distance of alongshore

Distance of offshore

txx

QQ

)(

sy : Shoreline position of on-offshorex : Shoreline position of alongshoreQ : The Longshore Sediment Transport RateD : The closure depth

One-line(shoreline) model, beach evolution is represented by the shoreline change, is a numerical prediction model based on the sediment continuity equation and an equation for the longshore sediment transport rate.

1-line model

Definition sketch for shoreline change calculation

q : Cross-shore sediment transport rate

Boundary conditions Breakwater at Sendai port • LST is perfectly intercepted by t

he breakwaters at Sandai Port and Yuriage Port.

• Discharged sediment rate from Nanakita River is ignored.

River mouth of Natori River

Closure depth Tohoku Regional Bureau Ministry of Land, Infrastructure and transport,

Miyagi Prefecture Public Works Department ,2000

Discharged sediment rate from Natori River

bsbsbgEcKQ cossin)(

ii. Long shore sediment transport rate

)8

1( 2gHE : 　 wave energy

gc : wave group speed

bs : angle of breaking waves to the local shoreline K : sediment transport coefficient

・・ (3)

b 　 ： wave breaking condition(CERC equation)

* Longshore Sediment Transport

mD 8

yearmQR /000,10 3

01xQ

Rx QQ 2

1x

2x

-10000 -5000 0 x ( m )

-2000

-1000

0

1000

y(m

)

œœ œœ œ œœ

Yuriage Port

œ

Sendai Port

œ

Breakwaters

œœ œ

œœ

123 4 5 6 7 8 9 10 11 12 13 14

)(500,11 mL 1x 2x

• Boundary Conditions and assumption

Bathymetry data In 1980 from Geographical Survey Institute

Initial shoreline position Aerial photo on Nov. 1996

Wave conditions T0 : 8.55(s), H0 : 0.75(m), α : 121.86°

Wave transformation

Wave ray method

Wave breaking (Goda, 1973 )

Sediment transport coefficient (K)

from 0.01 to 0.09

• Conditions for calculation

• Calculated shoreline after 6 years.

200

400

600 initial. Nov.96 K=0.01

0.02 0.04

0.06 0.08

œœ œœ œ œ

œ

Yuriage Port

œ

Sendai Portœœ

œœœ

œ

123 4 5 67 8 9 10

11 12 1314

1998 2000 2002 2004Time (year)

200

250

300

Cro

ss-s

hore

dis

tanc

e (m

)

St.13

100

150St.10

300

350

400St. 4

Data 2: measured data surveyed twice a month as short-term period of survey ( + )

1998 2000 2002 2004Time (year)

200

250

300

Cro

ss-s

hore

dis

tanc

e (m

)

St.13

100

150St.10

300

350

400St. 4

Data 1: separated data that shoreline change caused by longshore sediment transport, C2e2 (— )

Data 3: measured data surveyed once a year as normal period of survey (◎)

1998 2000 2002 2004Time (year)

200

250

300

Cro

ss-s

hore

dis

tanc

e (m

)

St.13

100

150St.10

300

350

400St. 4

Data setCalibration of K (sediment transport coefficient) is carried out using three data set to examine influence of cross-shore sediment transport.

5000 10000X(m)

200

400

600C

ross

-sho

re d

irec

tion

(m

) K= 0.02 K= 0.03 K= 0.04

separated data Jul.2000 surveyed data Jul.2000

initial SL Nov.96

5000 10000X(m)

200

400

600

Cro

ss-s

hore

dir

ection

(m

) K= 0.02 K= 0.03 K= 0.04

separated data Jul.2001 surveyed data Jul.2001

initial SL Nov.96

5000 10000X(m)

200

400

600C

ross

-sho

re d

irec

tion

(m

) K= 0.02 K= 0.03 K= 0.04

separated data Jul.2002 surveyed data Jul.2002

initial SL Nov.96

5000 10000X(m)

200

400

600

Cro

ss-s

hore

dir

ection

(m

) K= 0.02 K= 0.03 K= 0.04

separated data Jul.2003 surveyed data Jul.2003

initial SL Nov.96

1998 2000 2002 2004Time (year)

200

220

240

260

Cro

ss-s

hore

dis

tanc

e (m

)

K=0.02

K=0.04K=0.06

St.13300

320

340

360

K=0.02

K=0.04

K=0.06St. 4

St.4

St.13

Calculated shoreline position by one-line model

• Error is calculated in three case to decide value of K.Case 1 : To calculate error between obtained shoreline position by 1-line model and data1 Case 2 : To calculate error between obtained shoreline position by 1-line model and data2 Case 3 : To calculate error between obtained shoreline position by 1-line model and data3

VI. Comparison of calibration K

ycal : shoreline position calculated by 1-line modelydata1 : shoreline position based on separated dataydata2 : shoreline position based on measured data ydata3 : shoreline position based on measured data once a yearT: the number of survey times from Nov. 1996 to Aug. 2003N: the number of station, from 1 to 13

NT

yyE

T

Tdatacal

N

Ncase

1

23,2,1

13,2,1

)(

• K is calibrated based on three data set in order to examine influence of cross-shore sediment movement on calibration of K.

• Error calculate between calculated shoreline position and measured data

･・・・ (4)

•Relationship between error and K

data3 is including shoreline change due to cross-shore sediment transport.

0.03

•Optimum value of K is 0.03 in case 3.

•Optimum value of K is 0.02 in case 1 and case 2.

0.02

data2 is surveyed in shore-term period of survey but data 2 is including shoreline change due to cross-shore sediment transport.

•The error is bigger in case 2 than that in case 1.

VII.Summary

Case1 : using separated data, the error is smaller in whole area than that of the other cases. Because separated data is shoreline evolution cased by longshore sediment transport.

Case2 : the optimum value of K is same value as that obtained by separated data because survey is carried out in a relative short-term period. However, the error is bigger than that based on separated data because data2 include influence of shoreline change due to cross-shore sediment transport.

Case3 : using survey data in once a year, the optimum value of K is bigger than that in case 1 and 2. it includes an error due to cross-shore change.

According to these results, shoreline evolution due to cross-shore sediment transport has effect on calibration of K value. Therefore, it is important that raw survey data are separated into a part of data caused by longshore sediment transport and cross-shore sediment transport, when value of K is calibrated in one-line model.

-0.5

0

0.5

Rat

e of

cha

nge

(m/y

ear)

TP-0.5 TP+0.0 TP+0.5 TP+1.0

-10000 -5000 0 X(m)

-2000

-1000

0

1000

Y(m

)

œœ œœ œ œ

œ

Yuriage Port

œ

Sendai Port

œ

Arahama Breakwaterœ

œ œ œœ

-10000 -5000 0 X(m)

-2000

-1000

0

1000

Y(m

) 123 4 5 67 8 9 10

11 12 13 14

x (m)

y (m)

Nanakita River

Characteristic of shoreline change on study area

ESE&SE

• Incident wave direction : ESE and SE Longshore sediment transport move northward ( from right to left) Coastal structures interrupt longshore sediment transport

Advance of Shoreline : St. 10, St. 11 and St. 4

-10000 -5000 0

X(m)

-2000

-1000

0

1000

Y(m

)

œœ œœ œ œ

œ

Yuriage Port

œSendai Port

œœœ œ œ

œ

123 4 5 67 8 9 10

11 12 13 14

0

0.5

1e 1

(x)

T.P.-0.5m T.P.+0.0m T.P.+0.5m T.P.+1.0m

1998 2000 2002 2004 Time (year)

-40

-20

0

20

40

C1(

t) (

m)

Reression Line T.P. +0.0m

ii. 1st EOF component

Simultaneous erosion and accretion occur along the coast.

The 1st EOF component can express beach change caused by cross-shore sediment transport.

yma /94.01

rate of change of the first temporal eigenfunction

btatC 11 )(

E.O.F.

0)()( 11 xetC

Erosion

Accretion

0)()( 11 xetC

The 1st temporal eigenfunction

The 1st spatial eigenfunction

1998 2000 2002T(year)

-50

0

50

100 calculated C1 C1-value

Regression Verification

C1,

Cca

l. (m

)

dtCCC ss )( 0*

(mori and tanaka 1998)

dt

xdys )( and have relationship.sC

• Prediction of first temporal eigenfunction

*sC

-1000 -500 0 500 1000

T.P. +0.0(m)

-40

-20

0

20

40

C1-

valu

e

1996-1999.5

8.220 C

67.0

0

27.0

0

0 )()(tan L

d

L

HCs

2508.0)( *1 sCtC (2)

considering relation and .sCdt

xdC )(1

)(1 tC continuity of time is low.

C1 is predicted in the other term and verified.

• 2nd E.O.F. component 2/2

-100 -50 0 50 Eb-longshore

-20

0

20

C2-

valu

e

1996-1999.5T.P. +0.0 (m)

*E

C2

(

m)

)( * dtEE bl1573.0)( *2 EtC (2)

bbbgbbl CgHE cossin)(8

1 2

: Wave direction at breaking point.b : breaking pointH : wave heightCg : group celerity : density of seawater : gravitational acceleration

b

g

i. 2nd temporal eigenfuncion and Energy flux of longshore direction

* Longshore Sediment Transport

Beach evolution is classified into two types according to direction; one is cross-shore change occurred in short term and the other is longshore change occurred in long-term.

It is difficult to analyzes a complicated evolution of shoreline using measured data, because it is containing both influence of longshore and cross-shore sediment movement.

1998 2000 2002 2004time (year)

0

50

100

150

cros

s-sh

ore

dist

ance

Station 4

T.P.+0.0m • Measured data

If measured data are separated into shoreline change caused by longshore and cross-shore sediment transport, a shoreline behavior will be clearly analyzed and understood.

2/2