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

Influence of cross-shore sediment movement on long-term shoreline change simulation. by H. Kang, H. Tanaka Dept. of Civil Eng. Tohoku Univ. Japan. Data2. Data3. EOF method. Shoreline evolution ： caused by LST caused by CST. Data1. Calibration of sediment transport coefficient.

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

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  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. Data2 Data3 EOF method Shoreline evolution： caused by LST caused by CST Data1 Calibration of sediment transport coefficient Comparison of calibration K Outline of this presentation Measured data including both influence of LST and CST • Introduction • Study area • Measured data • Empirical Orthogonal Function • One-line model • Comparison of calibration K • (sediment transport coefficient) • Summary Numerical simulation of shoreline change by one-line model * Longshore Sediment Transport, Cross-shore Sediment Transport

  3. 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 • 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. • 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. • Introduction • 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. * Longshore Sediment Transport, Cross-shore Sediment Transport

  4. Study area S.L. 0 10 1000 20 30 Frequency of incoming wave direction 800 40 50 600 60 400 70 200 80 0 90 100 110 120 130 140 150 ESE&SE 160 170 180 • 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 the breakwater • Length : about 12km • Bounded by Sendai Port and Natori River mouth Breakwaters the jetties

  5. Measured data • Station 13 : Shoreline has gradually retreated. And beach slope is steep. the breakwater at Sendai Port Nanakita River Breakwaters St.13 the jetties at the Natori River mouth

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

  7. 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 the breakwater at Sendai Port Nanakita River St.4 • Length : about 12km • Bounded by solid boundaries (Sendai Port & Natori River mouth) Breakwaters the jetties at the Natori River mouth

  8. E.O.F • Empirical Orthogonal Function • Correlation matrix A • Spatial eigenfunction • Temporal eigenfunction Shoreline position (Measured data) 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. • It assume that shoreline position combines temporal function with spatial function. ･・・・(1)

  9. 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. 2nd spatial eigenfunction • The rate of long-term shoreline change (measured data) • 2nd temporal eigenfunction • has a similar shape with the rate of long-term shoreline change. • The rate of change of the 2nd component • rate of change of the second temporal eigenfunction 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

  10. 1-line model • One-line model Distance of alongshore Distance of offshore : Shoreline position of alongshore ･・・・(2) 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. Definition sketch for shoreline change calculation • Governing equation : Shoreline position of on-offshore : The Longshore Sediment Transport Rate : The closure depth q : Cross-shore sediment transport rate

  11. Long shore sediment transport rate • Boundary Conditions and assumption :wave energy ・・(3) : wave group speed b　 ： wave breaking condition (CERC equation) : angle of breaking waves to the local shoreline : sediment transport coefficient * Longshore Sediment Transport

  12. Calculated shoreline after 6 years. • Conditions for calculation

  13. Data 2: measured data surveyed twice a month as short-term period of survey ( + ) • 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. • Data 1: separated data that shoreline change caused by longshore sediment transport, C2e2 (— )

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

  15. Comparison of calibration K • K is calibrated based on three data set in order to examine influence of cross-shore sediment movement on calibration of K. • 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 • Error calculate between calculated shoreline position and measured data ･・・・(4) ycal : shoreline position calculated by 1-line model ydata1 : shoreline position based on separated data ydata2 : shoreline position based on measured data ydata3 : 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

  16. 0.02 0.03 • Optimum value of K is 0.02 in case 1 and case 2. • The error is bigger in case 2 than that in case 1. • Optimum value of K is 0.03 in case 3. data2 is surveyed in shore-term period of surveybut data 2 is including shoreline change due to cross-shore sediment transport. data3 is including shoreline change due to cross-shore sediment transport. • Relationship between error and K

  17. 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.

  18. y (m) ESE&SE x (m) • Incident wave direction : ESE and SE • Longshore sediment transport move northward ( from right to left) • Coastal structures interrupt longshore sediment transport Characteristic of shoreline change on study area Nanakita River Advance of Shoreline : St. 10, St. 11 and St. 4

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

  20. and have relationship. considering relation and . (2) C1,Ccal. (m) Verification Regression • Prediction of first temporal eigenfunction continuity of time is low. (mori and tanaka 1998) C1 is predicted in the other term and verified.

  21. T.P. +0.0 (m) 1996-1999.5 C2 (m) • 2nd E.O.F. component 2/2 • 2nd temporal eigenfuncion and Energy flux of longshore direction : Wave direction at breaking point. b : breaking point H : wave height Cg : group celerity : density of seawater : gravitational acceleration (2) * Longshore Sediment Transport

  22. Measured data 2/2 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. 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.

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