Post on 23-Jan-2016
description
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
)(
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