1. Influence of cross-shore sediment movement on long-term shoreline change simulation by H. Kang, H. Tanaka Dept. of Civil Eng. Tohoku Univ. Japan

2. 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

3. 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.

4. 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 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 S.L. Frequency of incoming wave direction

5. 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. III.Measured data

6. Breakwaters Nanakita River the jetties at the Natori River mouth the breakwater at Sendai Port St.8 III.Measured data Station 8 : Due to gentle slope, fluctuation is big. And shoreline is stable. 1997 1998 1999 2000 2001 2002 2003 2004

7. 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 Station 4 : Fluctuation of shoreline is widely varied because of Nanakita River. And shoreline has advanced. 1997 1998 1999 2000 2001 2002 2003 2004

8. E.O.F IV. Empirical Orthogonal Function It assume that shoreline position combines temporal function with spatial function. Temporal eigenfunction Spatial eigenfunction Shoreline position (Measured data) Correlation matrix A 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)

9. The 2 nd E.O.F. component can express topography change caused by longshore sediment transport. 2 nd 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. rate of change of the second temporal eigenfunction ii.2 nd temporal eigenfunction has a similar shape with the rate of long-term shoreline change. The rate of long-term shoreline change (measured data) The rate of change of the 2 nd component i. 2 nd spatial eigenfunction

10. V.One-line model i. Governing equation ･・・・ (2) Distance of alongshore Distance of offshore : Shoreline position of on-offshore : Shoreline position of alongshore : The Longshore Sediment Transport Rate : 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

11. Boundary conditions Breakwater at Sendai port LST is perfectly intercepted by the 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 ii.Long shore sediment transport rate : wave energy : wave group speed : angle of breaking waves to the local shoreline : sediment transport coefficient ・・ (3) b ： wave breaking condition (CERC equation) * Longshore Sediment Transport Boundary Conditions and assumption

12. Bathymetry data In 1980 from Geographical Survey Institute Initial shoreline position Aerial photo on Nov. 1996 Wave conditions T 0 : 8.55(s), H 0 : 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.

13. Data 2: measured data surveyed twice a month as short-term period of survey ( + ) Data 1: separated data that shoreline change caused by longshore sediment transport, C 2 e 2 (— ) Data 3: measured data surveyed once a year as normal period of survey ( ◎ ) Data set Calibration of K (sediment transport coefficient) is carried out using three data set to examine influence of cross-shore sediment transport.

15. St.4 St.13 Calculated shoreline position by one-line model

16. 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 y cal : shoreline position calculated by 1-line model y data1 : shoreline position based on separated data y data2 : shoreline position based on measured data y data3 : shoreline position based on measured data once a year T: the number of survey times from Nov. 1996 to Aug. 2003 N: the number of station, from 1 to 13 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)

17. 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.

18. 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.

21. 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

22. ii.1 st EOF component Simultaneous erosion and accretion occur along the coast. The 1 st EOF component can express beach change caused by cross-shore sediment transport. rate of change of the first temporal eigenfunction E.O.F. Erosion Accretion The 1 st temporal eigenfunction The 1 st spatial eigenfunction

23. Regression Verification C 1, C cal. (m) (mori and tanaka 1998) and have relationship. Prediction of first temporal eigenfunction (2) considering relation and. continuity of time is low. C 1 is predicted in the other term and verified.

24. 2 nd E.O.F. component 2/2 1996-1999.5T.P. +0.0 (m) C 2 (m) (2) : Wave direction at breaking point. b : breaking point H : wave height Cg : group celerity : density of seawater : gravitational acceleration i.2 nd temporal eigenfuncion and Energy flux of longshore direction * Longshore Sediment Transport

25. 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. 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