Modelling of sedimentation in dredged channels by currents and
waves using wind statistics
Markus Witting1, Peter Mewis2, Ulrich Zanke3
An approach is presented to make mid-term forecasts of siltation volumes in navigation channels
using wind statistics. A set of coupled models is applied for 12 wind directions and 5 classes of wind
speed on high resolution grids. Each situation is weighted with its probability of occurrence using local
wind statistics for several time spans. For each time span measured volumes of channel sections are
compared with computed volumes.
The domain of investigation is a shallow lagoon connected to the non-tidal coast of the Baltic Sea. The
hydrodynamic situation is therefore strongly influenced by the local wind situation. The navigation
channel is partly exposed to the Baltic Sea, partly sheltered in a shallow lagoon connected by an inlet.
Thus the mechanisms of sedimentation along the channel are different, dominated by the local wave
field in the lagoon and by long shore currents, inlet currents and the local wave field on the Baltic Sea.
A set of coupled models is applied to this situation. The set consists of an atmospheric model giving
the spatial wind distribution, a spectral wave model (SWAN), and a 2D-current and morphodynamic
model. The model results show that sedimentation along the channel is a cause of certain wind
situations. It is shown that sedimentation/erosion volumes in the sections of the channel can be
satisfactorily described as a linear superposition of sedimentation/erosion patterns for particular wind
situations using wind statistics. The importance of the spatial wind field given by the atmospheric
model is discussed in this context.
Introduction
Enormous dredging efforts have to be made to maintain navigability in the channel from the
Baltic Sea towards the town Stralsund. Yearly dredging volumes differ extremely along the
channel and depend on the hydraulic impacts during the actual period. It is of great interest
to the authorities to estimate the dredging effort, and to analyze the conditions under which
material is accumulated.
The southwesterly Baltic Sea is almost non-tidal. In the shallow parts of the study area wind
induced currents and wind setup are statistically dominant on the flow situation. Other
impacts e.g. seiches statistically play a minor role.
Excluding all other impacts, merely taking into account wind as the dominant forcing factor,
sedimentation/erosion volumes for 13 sections of the channel (see Fig.1) are calculated,
running the model set for 12 wind directions and 6 wind speeds. Superposition of these
volumes according to a wind statistic yields promising results, establishing a practical method
for the estimation of dredging volumes.
Computational Models
A set of computational models is used to simulate the morphological changes, which come
up during one hour at each wind situation. The model set is composed of 4 coupling submodels: a wave model, a flow model, a sediment transport model and a bed evolution
model. Except the wave model SWAN (RIS , 1997), the others are combined for the current
research (BARTHEL, ZANKE, 1998). The current model (MEWIS, HOLZ, 1993) is solving the
shallow water equations on a FEM grid. Values for the bottom orbital motion, radiation stress
gradients and other wave parameter are interpolated from the FD wave model to the FEM
current model; values for water levels and current velocities vice versa. The morphological
model (ZANKE, 1993/1995) runs on the same FEM grid with a dynamic pick-up formulation
for suspended sediment (VAN RIJN, 1994) based on combined wave and current bottom
shear stresses. Graded sediment transport and mixed transport (sand and cohesive
sediment) can be considered, in the presented application only non-cohesive graded
transport is modeled, because of the grain size distribution in the study area.
Study Area
The study area is situated at the non-tidal coast of the southwestern Baltic sea. It consists of
the Bock inlet and the lagoon behind. This site is subject of the current research project
MORWIN, which investigates the large scale transport processes in an area of 50 x 50 km
including Rügen island and Darss-Zingst peninsula. The navigation channel stretches from
the open Baltic sea along Hiddensee island through the Bock inlet into a lagoon. The lagoon
consists of several shallow flats which are partly dry at mean water level. Great parts of the
navigation channel are surrounded by the flats. Therefore local wind seas have a strong
influence on sediment transport. In order to analyse the behaviour of the channel, it is
divided into 13 sections. Section 1 is located at the narrowest part of Bock inlet, Section 13 is
in the inner lagoon (see fig. 1).
Fig. 1: Southwesterly Baltic Sea, whole study area, the inlet situation with the
sections of the navigation channel
Measurements of current velocity at Bock inlet and the lagoon indicate, that the flow situation
is statistically dominated by the local wind field. At Bock inlet inflow and outflow conditions
depend on the wind direction. Inflow conditions, which carry sediment into the lagoon area,
establish during onshore wind directions from WSW clockwise to NNE. Other wind directions
yield an outflow at Bock inlet. Seiches of different periods of the Baltic sea cause water level
changes within the study area. They add a further contribution to the hydraulic impact
especially concerning Bock inlet; they are neglected in this study. The tidal range is
approximately 15 cm which can be recognized only during very calm conditions.
Set Up of Computation
Sixty wind situations, each a combination of a wind speed and a wind direction are modeled
with a coupled model set. Wind rose is divided into 12 wind direction with intervals of 30
degrees and wind speed is divided into 5 speed classes, ranging from 4 to 8 Beaufort. For
each wind situation the morphological changes within one hour are calculated.
Spatial wind fields are imposed as the driving force for the wave and current model. A
steady-state current field for each wind situation is modeled with the coupled wave - current
model, taking into account current refraction, wave induced currents and water level
variations. Morphological calculations start using an equilibrium suspended sediment
concentration for the actual flow condition. Each of the 12 x 5 model runs starts with the
same bathymetry and grain size distribution, which are both taken from measurements.
Model-nesting is applied calculating the wave field of the onshore wind situations. First the
wave model runs on a curvilinear grid on the area of the Baltic Sea which exhibits finer grid
resolution up to 10 m in the near shore area, so that wave decay in the surf zone is modeled.
Then the lagoon part of the study area is calculated on a 50 x 50 m rectangular grid.
Fig. 2 Grid points of the FD-grids for the wave model. a) curvilinear on the Baltic sea,
b) rectangular in the lagoon area
The mesh of the FEM current and morphological model consist of approx. 30000 nodes,
exhibiting resolutions up to 20 m in the domain of interest around the navigation channel and
inside the surf zones of the two coastal stretches of Hiddensee island and Bock island. By
this means the effect of intense sediment loads from the surf zones towards the Bock inlet
during onshore wind situations is accounted for.
Wave Boundary Conditions and Wind Field
Boundary conditions for the open boundary of the Baltic Sea are taken from a statistical
analysis of wave records. The wave-rider buoy is situated near the boundary. Values for
Hs,Tp and mean wave direction are linearly varied along the boundary according to a
statistical analysis from a large scale wave model for the North Sea and the Baltic Sea. For
each of the onshore wind events the boundary conditions are imposed at the wave model
boundary, using a JONSWAP spectrum with 12 spectral intervals and 72 directional spins.
The wind field, driving the current and wave model is taken from a wind atlas (HINNEBURG
et al.). The wind atlas submits a complete set of simulated discrete wind situations for the
undermost atmospheric layer. These stationary wind situations are characterized and
ordered by the direction and speed of the geostrophic wind. To each wind situation belongs a
field of local wind velocities at a height of 10 m above ground, which are distributed
equidistantly (1 km) on a horizontal grid.
Results for the wind situations
Examining the mean sedimentation/erosion rates for the sections, one can see a strong
influence for each section on the wind direction. The following diagrams Fig. 3-5 show the
calculated sedimentation/erosion rates [m/h] for a wind speed of 7 Beaufort. Positive values
indicate total sedimentation, negative values a total erosion for the section during a particular
wind direction.
Sedimentation rates are greatest near the inlet in Section 1 to 4 (see Fig.1 for location)
showing 330° as dominant direction. Sedimentation rates in Section 2 show highest values
of about 0.025 m/h, decreasing rapidly for Sections 3 and 4 (see Fig. 3). Remarkably section
1 is eroded during that event, showing relative small rates of sedimentation on the other wind
directions. This is mainly caused by the high current velocities in that narrowest part of the
inlet, during strong inflow.
330°
300°
WEST
NORTH
0.03
0.025
0.02
0.015
0.01
0.005
0
-0.005
-0.01
30°
60°
EAST
240°
120°
210°
150°
SOUTH
SEC 1
SEC 2
SEC 3
SEC 4
Fig. 3 Mean Sed./Eros. [m] Sec 1-4, Rose for 7 Beaufort
Sections 5 – 8 inside the lagoon exhibit much lesser rates, but they are like Sections 2 - 4
particularly influenced by above mentioned inflow situations. Sedimentation in Section 6 is
among other things also a consequence of easterly winds, whereas westerly winds lead in
total to erosion.
330°
300°
WEST
NORTH
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
-0.001
30°
60°
EAST
240°
120°
210°
150°
SOUTH
SEC 5
SEC 6
SEC 7
SEC 8
Fig. 4: Mean Sed./Eros. [m] Sec 5-8, Rose for 7 Beaufort
In the inner lagoon from Sections 9 to 12 sensitivity concerning siltation is changing from
WNW-directions in Section 9 to northeasterly directions in Section 11 and 12. Essentially this
is caused by suspended material from the large sand flats north of the channel. The same
holds true for southerly winds. Due to shorter fetch, concentrations of suspended material
are less than those produced by the stirring of the local waves at northeasterly directions
leading generally to minor sedimentation.
NORTH
0.0025
330°
30°
0.002
0.0015
300°
60°
0.001
0.0005
0
WEST
-0.0005
EAST
240°
120°
210°
150°
SOUTH
SEC 9
SEC 10
SEC 11
SEC 12
Fig. 5: Mean Sed./Eros. [m] Sec 9-11, Rose for 7 Beaufort
Analyzing sedimentation/erosion rates e.g. for Section 1 & 2 for all wind situations
remarkable features can be figured out (Fig. 6, Fig. 7). Sedimentation of Section 1 is mainly
induced by north to northeasterly winds. Winds from 300° and 330° have two effects
depending on the wind speed. Higher wind speed result in a greater wind set up and cause
higher current velocities than weaker winds. The limit between eroding and sedimenting
conditions can be set at 6 respectively 7 Beaufort. Westerly winds from 4 – 6 Beaufort have a
crucial consequence on the erosion of Section 1, when later multiplied with the frequency of
these wind situations. Outflow conditions have a considerable effect on sedimentation in this
section. In contrast to Section 1 the neighbor section 2 reacts on inflow situations yielding
high rates of sedimentation on all wind speeds.
0.004
33
0°
30
0°
W
ES
T
24
0°
21
0°
TH
U
15
0°
12
0°
SO
-0.002
EA
ST
60
°
30
°
R
TH
0
N
O
Mean Sedimentation/Erosion [m/h]
0.002
-0.004
BFT 4
BFT 5
BFT 6
BFT 7
BFT 8
-0.006
-0.008
-0.01
Windsituations
Fig. 6: Mean Sed./Eros. Rates [m/h] for Section 1
0.06
0.04
BFT 4
BFT 5
BFT 6
BFT 7
BFT 8
0.03
0.02
0.01
Windsituations
Fig. 7: Mean Sed./Eros. Rates [m/h] for Section 2
33
0°
30
0°
T
W
ES
24
0°
21
0°
TH
U
SO
15
0°
12
0°
EA
ST
60
°
30
°
R
TH
0
N
O
Mean Sedimentation/Erosion [m/h]
0.05
Comparison with measured volumes
Measured volumes of 4 periods of approximately half a year (Fig. 10) are compared with
calculated volumes (Fig. 9) by superposing sedimentation/erosion volumes section wise. The
actual wind statistic is applied for each period (see Fig. 8), which exhibits different
characters. Winter 94 – 95 and spring 98 are dominated by westerly winds, winter 94 – 95
exhibit a broad directional spectrum, whereas spring 98 almost consists of westerly wind
situations. Winter 95 – 96 and spring 97 exhibit high occurrences of northeasterly winds, yet
differ in the occurrence of westerly winds and in the speed of the easterly winds.
400
winter 95-96
winter 94-95
spring 98
spring 97
350
Occurence [h]
300
Bft 8
Bft 7
Bft 6
Bft 5
Bft 4
250
200
150
100
50
0
27
0
18
90
0
0
27
0
18
90
0
0
0
27
18
90
0
0
27
0
18
90
0
0
wind directions
Fig. 8: Wind statistics for 4 periods
Data of measured volumes are derived from regular line bearings. Therefore data quality is
relatively poor, having gaps for some sections.
Calculated Volumes
40,000
Sedimentation/Erosion [cbm]
35,000
SEC 1
SEC 2
SEC 3
SEC 4
SEC 5
SEC 6
SEC 7
SEC 8
SEC 9
SEC 10
SEC 11
SEC 12
SEC 13
30,000
25,000
20,000
15,000
10,000
5,000
0
winter 94-95
winter 95-96
spring 98
spring 97
-5,000
Fig. 9: Calculated volumes for 4 periods
Measured Volumes
30000
SEC 1
Sedimentation/Erosion [cbm]
25000
SEC 2
SEC 3
20000
SEC 4
SEC 5
15000
SEC 6
SEC 7
10000
SEC 8
SEC 9
5000
SEC 10
SEC 11
0
winter 94-95
winter 95-96
spring 98
spring 97
-5000
SEC 12
SEC 13
Fig. 10: Measured volumes for 4 periods
Generally the total values of volumes are modeled correctly. The relations between the
sections are good, showing great sedimentation volumes at the inflow influenced sections
and less sedimentation in the inner lagoon. Merely Section 5 and 6 exhibit significantly more
sedimentation in winter 94-95 and winter 95-96 than calculated. Moreover measurements
show that Section 1 is affected less by sedimentation especially during periods with
dominating westerly winds. The contribution of easterly winds to the overall sedimentation of
section 1 during period winter 95 –96 and spring 97 can be retraced on the basis of the
measurements.
Period Spring 98 is generally calmer with a high occurrence of westerly winds leading to a
total erosion in section 1, which is realistically reproduced by the model. Measurements
indicate that also section 2 is affected by erosion. Fluctuations of sedimentation volumes in
Section 3 and 4 during the different periods are the relations between the two sections are
reproduced. The strong effect of northeasterly wind on sedimentation in section 11 and 12
can be verified by the measurements and are reproduced by the model. Winter 95 – 96 ,
which has a strong occurrence of northeasterly winds, show strong sedimentation in these
sections, whereas spring 98 exhibit significantly lesser sedimentation.
The over-estimation of sediment volumes in section 1 as well as the underestimation of
sedimentation in section 5 may possibly be due to the neglection of water level dynamics
caused by seiches of the Baltic Sea. Seiches could cause strong inflow and outflow
conditions affecting sections 1 – 5.
Conclusion
The approach to simplify complex conditions, taking into account solely wind as the dominant
hydraulic force, leads to satisfying results in the area of investigation. The calculated matrix
of sedimentation/erosion rates explain important characteristics of the channels behavior
concerning siltation processes and allows a rough estimation on actual dredging volumes. A
very good accordance is achieved concerning the total volumes in many sections. It would
be desirable, to testify the calculation with more and better measured data.
Acknowledgments
The project MORWIN is sponsored by the BmBF (Bundesministerium für Bildung, und
Forschung) and was established by the KfKI (Kuratorium für Küsteningenieurwesen).
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