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1D Long-term Modelling of Longshore Sediment Transport U.Bethers (1), J.Sennikovs (1), K.-P. Holz (2) (1) Laboratory for Mathematical Modeling of Environmental and Technological Processes, University of Latvia (2) Institute of Information Technology in Civil and Hydraulic Engineering, Brandenburg University of Technology

1D Long-term Modelling of Longshore Sediment Transport

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1D Long-term Modelling of Longshore Sediment Transport. U.Bethers (1), J.Sennikovs (1), K.-P. Holz (2) (1)Laboratory for Mathematical Modeling of Environmental and Technological Processes, University of Latvia (2) Institute of Information Technology in Civil and Hydraulic Engineering, - PowerPoint PPT Presentation

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Page 1: 1D Long-term Modelling of Longshore Sediment Transport

1D Long-term Modelling of Longshore Sediment

Transport

U.Bethers (1), J.Sennikovs (1), K.-P. Holz (2)

(1) Laboratory for Mathematical Modeling of Environmental and Technological Processes, University of Latvia

(2) Institute of Information Technology in Civil and Hydraulic Engineering,

Brandenburg University of Technology

Page 2: 1D Long-term Modelling of Longshore Sediment Transport

Area of study

The eastern coast of the Bay is island Hiddensee, the southern coast is formed by islands Darss, Zingst and Bock. The system of inland water basins and interconnecting channels (Bodden area) is separated from the sea by these narrow and prolonged islands. The system of channels also forms a waterway from the Gellen Bay to the Bay of Greifswald.

The Gellen Bay is a shallow water area in the south-western part of the Baltic Sea.

Page 3: 1D Long-term Modelling of Longshore Sediment Transport

Overall scheme of modelling

Page 4: 1D Long-term Modelling of Longshore Sediment Transport

Classification of flow patternsMorphodynamical scenario

Classification of flow patterns yielded from the steady state calculations by a 2D model.

Multi-level modelling include

• 2D shallow water wave-current-sediment transport models describe characteristic processes’ patterns (steady-state) or short-term processes’ development (transient) in open water body

• Integral (0D) models describe mass balance of enclosed inner water bodies

• 3D HD model would be needed for channel entrance zone

• 1D littoral drift model is suitable for long-term assessment of sediment transport rates

Page 5: 1D Long-term Modelling of Longshore Sediment Transport

One-dimensional model

1D wave vector and longshore current

Wave field: ky(x)=const, k(x) calculated from dispersion equation yields kx(x) and wave group celerity. Wave energy calculated from ECgx=const and breaking criteria

Bottom roughness: calculated from waves

Hydrodynamics: momentum conservation yields equations for elevation and longshore velocity

01

dx

dSWWC

dx

dgh xx

xw

01

2

dx

dSWWC

C

VgV

dx

dVh

dx

d xyyw

s

yyy

Bed level: assumed constant ),()()(* xhxVxcxq ys

Load transport: littoral drift calculated assuming saturation concentration c* in suspension

T x

s txdxqdtQ0 0

max

,

Page 6: 1D Long-term Modelling of Longshore Sediment Transport

8000 8050 8100 8150 8200 8250 8300 8350 8400

Depth,[m],depthDepth avg. water velocity,[m/s]Load flux density,[m^2]

-4.5

-4-3

.5-3

-2.5

-2-1

.5-1

-0.5

00.

51

1.5

[m],d

epth

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0[m

/s]

-0.0

0055

-0.0

0045

-0.0

0035

-0.0

0025

-0.0

0015

0[m

^2]

8000 8050 8100 8150 8200 8250 8300 8350 8400

Depth,[m],depthWave direction,[Degrees]Sign. wave height,[m]

-4.5

-4-3

.5-3

-2.5

-2-1

.5-1

-0.5

00.

51

1.5

[m],d

epth

00.

10.

20.

30.

40.

50.

60.

70.

80.

91

[m]

02

46

810

1214

1618

2022

[Deg

rees

]

Examples of 1D model behaviour

Momental cross-shore distributions

Page 7: 1D Long-term Modelling of Longshore Sediment Transport

7600 7700 7800 7900 8000 8100 8200 8300 8400

-6-5

-4-3

-2-1

01

2[m

],dep

th-5

E-6

-4E-

6-3

E-6

-2E-

6-1

E-6

01E

-62E

-63E

-64E

-65E

-6[m

^2/s

]-0

.014

-0.0

12-0

.01

-0.0

08-0

.004

-0.0

020

0.00

20.

004

0.00

60.

008

0.01

0.01

20.

014

[mio

.m^2

/s]

Examples of 1D model behaviour

Time-averaged (1993 to 1997) cross-shore distributions

Page 8: 1D Long-term Modelling of Longshore Sediment Transport

01/06/1993 01/06/1994 01/06/1995 01/06/1996 01/06/1997

-150

000

-100

000

-500

000

5000

010

0000

1500

00[m

^3]

Examples of 1D model behaviour

Cumulative (1993 to 1997) integral long-shore transport

Page 9: 1D Long-term Modelling of Longshore Sediment Transport

Meteorological (forcing) data

Windrose for ArkonaMeteorological datasets

• wind measurement data for stations Arkona and Barth - observations of wind velocity and direction for the time period 1973-1997 with time resolution 1 hour.

• wave height and period are predicted from wind speed, duration and fetch.

Fetch for a particular point in the area of interest.

Direction Hs

N 3.06NE 3.25SW 1.04W 2.89NW 2.32

Significant wave height for a particular point in the area of interest for wind speed 20 m/s

Page 10: 1D Long-term Modelling of Longshore Sediment Transport

Description of models

Selected profiles for 1D longshore load transport calculations.

• Local rapid changes of the coastline orientation have not be accounted for.

• The profiles for calculation are taken at an average distance of 3 km between them

• Rate of deposition/erosion between the two profiles are calculated as a divergence of the load flux

Page 11: 1D Long-term Modelling of Longshore Sediment Transport

Calculations by a 1D longshore model

Calculations were performed for the time period 01.01.1973 to 01.07.1997

Cumulative load transport (million m3) along Hiddensee

Calculated annual mean load transport, thousands m3.

Page 12: 1D Long-term Modelling of Longshore Sediment Transport

Calculations by a 2D depth averaged model

Calculated annual mean load transport, thousands m3

Distribution of sediment concentration.Load transport rate, thousands m3 per year.NW-wind 10 m/s Hs=2.0m

Steady state calculations were performed for a variety of storm conditions.

Annual load transport values were obtained from calculated steady state values taking into account storm event probability.

Page 13: 1D Long-term Modelling of Longshore Sediment Transport

Conclusions

• Selection of appropriate meteorological forcing is of the most importance as any model is extremely sensitive to it.

• Ranking of time periods according to their morphodynamical impact should be performed using calculated transport rates instead of meteorological data.

• Mean load transport rates calculated by 1D longshore and 2D depth averaged models are close to each other.

• Transport rates calculated by a present model and HR Wallingford software COSMOS are in reasonable agreement

• 2D calculations for a typical meteorological situations allow classification of flow and load transport patterns.

• 2D model should be used for short-term (e.g. duration of storm) simulations involving rapid morphodynamical changes both in time and in space.

• 1D model is better suitable for long-term simulations, hind- and forecasts due to its simplicity.

• Models of every level have their own areas of application and they should not be treated as alternatives.

• In the case of absence of good data for the verification plausibility of separate models increases if the results obtained by models of different levels agree.