Multi-level approach to the estimation of the load transport near Ruegen
 

J.Sennikovs1, R.Grzhibovskis2, U.Bethers1, K.-P. Holz3
 

Abstract

Load transport near the northern entrance of the harbour Stralsund causes continuous siltation of the navigational channel. Estimation of typical and critical amounts and locations of deposition is necessary.

Identification of the physical processes is performed. It includes analysis of the meteorological data, bathymetry and the grain size distribution. Mathematical modeling by one and two dimensional models of the load transport improves the knowledge about the physical processes as well as gives reasonable estimates of the load transport rate and volume of deposited sediment.

The analysis of meteorological input data is based on the availability of a dense set of the wind measurements at the particular locations. Performed classification of the seasonal characteristics leads to the determination of the typical and critical years with respect to their influence on the load transport in the area of interest. It allows further extraction of a short (2-week) critical period that is suitable for the real-time calculations by a 2-D model of the coastal hydrodynamics.

Real-time calculations of the longshore load transport along the coastlines in the area of interest have been performed by 1-D model. They allow estimating the annual mean load transport rate. Variability of exposure of coastline with respect to the winds, and differences in the depths of cross-section profiles along the coastline leads to interchanging convergence and divergence zones of the load transport. That determines amount of deposition or sedimentation.

The steady state calculations for the several typical storm events are performed by a coupled 2-D model of the coastal hydrodynamics, load transport and morphodynamics. These calculations together with the probability analysis of the storm occurrence allow estimating the rate of the load transport for the typical year in the whole area. This rate is in good agreement with predictions by 1-D model. The real-time calculation for a 2-week critical period allows determining the critical amount of the sedimentation in the navigational channel.
 

1 Introduction

The Gellen Bay is a quite shallow water area in the southern part of the Baltic Sea, to the West of the Ruegen island, and the Cape Arkona (see Fig. 1.1).
Figure 1.1. Area near island Ruegen.

The eastern coast of the Bay is island Hiddensee, but the southern coast is formed (from West to East) by islands Darss, Zingst and Bock. The rather wide 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 Port of Stralsund is situated in between these two Bays. The sandy coastal regions of the Gellen Bay and the Bodden area are under continuous morphodynamical evolution. Particularly it results in siltation of the main navigation channel in the southeastern edge of the Gellen Bay. The identification of the physical processes responsible for the morphodynamical processes as well as estimation of the development scenarios of the morphodynamics is one of two basic goals of the MORWIN project. This paper is a summary of a part of research performed within MORWIN.

The numerical modelling of morphodynamical processes is not a pure engineering problem resolvable by worldwide-accepted methods. The various approaches are being proposed by different modeler groups mostly depending on the problem under consideration. Thus, morphodynamical modelling still can be regarded as problem-oriented research (see for instance [6]). The difference in approaches includes considered physical processes (both in modelling and forcing of models), particular approximation level for them, dimensionality of the problem formulation, spatial and time scales. The approach described in the present paper involves a closed analysis scheme where careful balancing of the models of different complexity are applied to the Bodden area to yield the inter-comparable results and evaluations. The success of the multi-level modelling is measured by the similar predictions by the different models as well as by the ability to establish cross data flows and evaluations to fill the field data gaps (that is a common problem in morphological studies).

The scheme of modelling is shown on Fig. 1.2.
Figure 1.2. Scheme of modelling.

The overall aim of the study was the identification of key physical processes responsible for morphodynamical processes, inclusion of these processes in mathematical models and quantifying morphodynamic response in real-time hind- and forecasting modes. The iterative scheme of Fig. 1.2 includes

  1. The establishment of the meteorological database and the water levels database, collecting the bathymetric data, and the analysis of these data sets.
  2. The identification of [initial set of] physical the processes for models [mainly from the geometrical considerations].
  3. The preparation of the input data sets for the long-term calculations by 1D longshore (littoral drift) model.
  4. The independent calculation series by the 2D steady state model of the coastal hydrodynamics and 1D littoral drift model.
  5. The classification of the flow patterns and quantifying the littoral drift from the calculations of p.4.
  6. Ranging of time periods according to forcing intensity and/or morphodynamic response and definition of critical/typical time periods.
  7. The real time calculations by 2D hydro- and morphodynamical model for the selected time periods.
  8. The evaluation and reconsideration of the involved physical processes, if necessary; looping to almost any stage of above scheme.


2 Meteorological data analysis

Following meteorological input data sets were considered as a forcing data for models of coastal hydrodynamics:

Figure 2.1. Distribution of measured winds by direction.

Determination of typical and critical situations has been done by classification of the wind events in each of four seasons - Winter (Jan-Mar), Spring (Apr-Jun), Summer (Jul-Sep), and Winter (Oct-Dec). Arkona wind database [1] for the years 1973 to 1997 was used for that purpose.
W/NW/N sector winds are supposed to exert the most of the influence to the sediment transport in the area of interest. Basing on that assumption, characteristic variables for classification of seasons were chosen as follows:

  1. Average wind speed (Wsp) for 90 degrees sector from W to N for the given season and year.
  2. Probability of the storm (P1, wind speed greater than 8 m/s) events for the same sector.
  3. Probability of the storm event (P2) for NW sector alone.
After the sorting of the years according to their ranks one can define that the typical year is a one with the values of characteristic variables are near their average values, while for the critical year these values far exceed average.

Table 2.1. Years by seasons sorted by decreasing rank. (only part of table shown, AV = average value)
Winter (Jan-Mar)
Spring (Apr-Jun)
Summer (Jul-Sep)
Autumn (Oct-Dec)
Year
Wsp
P1
P2
 Year
Wsp
P1
P2
 Year
Wsp
P1
P2
 Year
Wsp
P1
P1
1981
9.73
23.1
8.3
 1995
7.85
16.5
8.2
 1978
8.04
33.6
21.5
 1973
10.27
28.5
16.0
1976
9.60
19.2
9.5
 1977
6.92
19.0
8.1
 1979
7.72
34.9
23.4
 1975
10.24
22.2
13.0
1995
11.64
17.1
7.6
 1973
6.61
15.7
8.6
 1990
7.81
20.6
9.0
 1981
11.24
21.6
10.5
1989
10.87
17.5
6.0
 1975
6.90
14.8
6.6
 1983
7.82
17.8
9.0
 1980
9.90
22.1
9.0
                               
AV 8.42 12.1 4.9 AV 6.61 11.9 4.8 AV 6.97 15.4 7.4 AV 8.94 14.6 6.6
The average wind speed of the winds from W/NW/N sectors is the largest in autumn (8.94 m/s) being only slightly less (8.42 m/s) during the winter and significantly smaller during spring and summer (6.61 and 6.97 m/s, respectively). During the critical seasons it can reach as large values as 11.64 m/s (1995). Probability of events with wind speed larger than 8 m/s (P1) from the W/NW/N sectors is on an average 12.1% during winter and 11.9% during spring, 15.4% during summer, and 14.6% during autumn. These probabilities can enlarge by a factor of 2 during critical seasons (especially summers). The probability of such events for NW sector alone (P2) is smaller, being on average only 5-7%, but reaching 16.0 to 23.5 % during critical seasons.

The models of near-shore hydrodynamics require, besides the wind data, wave data as forcing parameters. At minimum, significant wave height and period are necessary. Three possible ways of obtaining them were considered:

  1. Data can be measured. Measurements were not yet available.
  2. Wave data can be calculated employing some kind of formulae relating wave parameters with the wind parameters, including fetch and duration of the wind.
  3. Numerical wave models of larger scale can be used, giving the characteristics for a wider area.
Following the second possibility, wave parameters were calculated according to the Shore Protection Manual [5]. The water depth had been set to 20 m that corresponds to the average water depth of the Arkona basin. The wind duration has not been taken into account. The fetch for a given point was assumed as the distance between that point and the shoreline in the given direction. Shoreline contours were obtained from the Baltic Sea topographic database [3]. The uncertainty in the measured wind direction and directional spectrum of waves leads to the necessity to use effective fetch length. That length was calculated by averaging the fetch lengths in the 22.5 degrees sector (Fig. 2.2).

Table 2.2. Fetch length and calculated significant wave heights for a particular point in the area of interest.
Wsp
N
NE
E
SE
S
SW
W
NW
  
 
Hs
F
Hs
F
Hs
F
Hs
F
Hs
F
Hs
F
Hs
F
Hs
F
10 1.61 116 1.75 155 0.81 24 0.56 11 0.46 8 0.52 10 1.50 95 1.17 53
15 2.39 116 2.58 155 1.21 24 0.83 11 0.69 8 0.78 10 2.23 95 1.76 53
20 3.06 116 3.25 155 1.61 24 1.11 11 0.92 8 1.04 10 2.89 95 2.32 53
Figure 2.2. Fetch length for a particular point in the area of interest.

3 Calculations of the long-shore load transport by 1-D model

3.1 Description of the 1-D model of longshore transport

The western coast of Hiddensee, as well as the northern coast of Zingst has an even form. It allows dividing these coastlines into several cells represented by depth profiles normal to the coastline. For each of these profiles the longshore load transport is calculated assuming that the conditions are quasi-uniform for each cell, the current is parallel to the coastline, depth change due to load transport is negligible, there is no wave action when the wind is from the coast.

The wave calculation is based on linear wave theory. The varying water depth is taken into account. The wave energy equation is expanded to account for the wave breaking by means of empirical relationship between the wave height and the depth in the breaking zone. The radiation stresses are calculated in the directions parallel and normal to the profile. The momentum equations are solved for steady state into both directions. The calculated longshore velocity is used for the load transport calculation.

Main assumptions for the load transport model are that the bed load and suspended load can be calculated separately and that the parameterisation for the unidirectional flow can be used for the load transport.

The load flux is calculated without wave influence. The suspended load is considered as depth averaged saturated concentration that is transported by the current. The total load is calculated by summing up the bed and suspended load over the time and length of the defined profile normal to the shoreline.

The calculations for several profiles give an idea about the distribution of the load flux intensity along the coast. The divergence of it gives the value of the deposition/erosion value between the profiles.

The main advantage of the one-dimensional longshore model is that it allows performing fast calculations for a long time period. It requires the depth distribution along the profiles as well as the forcing data, i.e. wind and wave parameters. Depth data were taken from the existing 1.2 million data base on the MorWin server. Each profile was constructed by averaging depth data closer than 50 meters to the geometric line of the profile. It means that local rapid changes of the coastline orientation have not to be accounted for. The profiles for calculation are taken at an average distance of 3 km between them (fig. 3.1). After several numerical experiments the wind events with higher than 3 m/s speed were chosen as significant ones. 
Figure 3.1. Profiles and depth measurement points.

3.2 Results of the calculations

The calculations were performed for the time period 01.01.1973 to 01.07.1997. The cumulative distribution of the load transport along Hiddensee and Zingst is shown on Fig. 3.2 and 3.3, respectively.
Figure 3.2. Cumulative load transport along Hiddensee.

As can be seen (Fig. 3.2) for the last 24 years the load moves to the north in the northern part of Hiddensee, on average. This corresponds to the wind rose for the Cape Arkona (Fig. 2.1). The repetitiveness of SW and WSW winds, as well as their average speed, is quite high. The southern part of Hiddensee is protected from those winds (i.e. fetch for this direction is relatively small). This is the main reason why the load moves to the South along this part of the island. The intensity of the load flux here is up to 6 times lower than in the northern part due to relatively small number of the wind events from NW and NNW. 
Figure 3.3. Cumulative load transport along Zingst.

The load flux along the eastern part of Zingst (see Fig. 3.3) is generally oriented eastwards and has the similar intensity as along the southern part of Hiddensee. Strong NE and NNE winds have small influence in this area because of small fetch. It means that NW and NNW winds are those that determine the longshore load transport near Bock as well as at the Southern part of Hiddensee. Due to exposure, strong NE and NNE winds have approximately the same influence as winds from NW or from NNW at the middle part of Zingst. This is the main reason why the direction of the load transport there strongly depends on separate wind events.

The cumulative curves (Fig. 3.2, 3.3) also show possible critical periods for the load transport. Every significant wind event can be detected from these curves. For example, the end of 1973 for each of the profiles is a period of very intensive load flux in the direction of Bock. This period was suggested as meteorologically critical (see Chapter 2). Moreover, it can be seen from cumulative curves, that the probability of the extreme events is higher during the winter. Unfortunately, there was no information about time periods when the area of interest was covered by ice. It could have a sufficient influence on the cumulative curves, but the order of load transport would remain the same.

The typical spatial distribution of the load for Hiddensee and Zingst is shown on Fig. 3.4 and 3.5, respectively. 
Figure 3.4. Total spatial load transport distribution along the profile "h4" for years 1973 to 1997.
As we can see from Fig. 3.4 and 3.5, almost all the load transport takes place in the wave-breaking zone, where the depth is less than 3 meters. Usually this is not more than 300 - 400 meters from the coast. The spatial distribution curves have two characteristic features. At first, there is a maximum of the load transport at the breaking point of the high number of small waves. Another, smaller maximum, is found in the breaking zone of relatively higher waves. For the profile at Zingst at this second maximum the load moves westwards, because the high waves arrives from NE, NNE.
Figure 3.5. Total spatial load transport distribution along the profile "v2" for years 1973 to 1997.

Calculated annual mean load transport through the profiles is shown on Fig. 3.6.
Figure 3.6. Calculated annual mean load transport, thousands m3.

Coastal erosion occurs almost everywhere in the region of interest. The accumulation zone for the load fluxes along the eastern part of Zingst and the southern part of Hiddensee is the navigational channel and Bock area.

The one-dimensional model was not used to investigate the longshore load transport along the western part of Zingst. In this area obvious two-dimensional effects occur. According to [4] there is a quite intensive accretion.
 

4 Calculations by 2-D model

4.1 Description of 2-D model

The calculations were performed by the improved coupled hydrodynamic/wave /sediment transport/morphodynamical model [9].

Transport equations for the wave vector and energy are employed for the calculation of wave field. Spectrum of waves has not been accounted for in the present model. Any input information of the wave height (H) is obtained from the given significant wave height (Hs) by means of the relationship: H=Hs/1.4.

The hydrodynamics is calculated by a depth averaged shallow water model. Coupling with the wave model is due to radiation stresses depending on wave parameters. The wave model is based on linear theory. It accounts for the wave refraction and shoaling, and for frictional losses of the wave energy. Empirical dependence of the wave height on the water depth in the breaking zone is employed.

The sediment transport's module accounts for the bed and suspended load transport. The action of waves is taken into account. Bed load change equation takes into account load flux divergence and the down-slope gravitational transport.

Suspended load is calculated by the transport equation for the depth averaged volumetric sediment concentration. Sources and sinks are assumed to be proportional to the difference between the actual sediment concentration and saturation concentration. The vertical turbulent diffusion coefficient is assumed to be constant throughout the water column. That results in the exponential distribution of concentration. Threshold is calculated according to Shields diagram.

Numerical solution of the system of the partial differential equations was performed by the finite element method using triangular elements. Wave parameters, hydrodynamics, sediment transport and morphodynamics are calculated separately at each time step.

Wave energy (height) and direction was prescribed for the open sea boundary. The water-level elevation was set here from the larger scale oceanographic model [7]. Incoming wave parameters were prescribed for the side boundaries, as calculated from the respective 1-D wave model along them. The elevation calculated from the assumption of the geostrophic flow [10] with account for the wave forces was prescribed on all side boundaries. The discharge was set to zero on the coastal boundary.
 

4.2 Steady state calculations. Classification of hydrodynamical patterns. Estimation of annual mean load transport.

The steady state calculations were performed on the finite element mesh (see Fig. 4.1) that has been generated according to depth criteria [8]; namely, the finest mesh is at the smallest depths. The high density of nodes is in the wave breaking zones that are the most important places where the sediment transport occurs.
Figure 4.1. Finite element mesh.

Steady state calculations were performed for the wind and waves coming from W, NW, N, and NE directions. The constant wind speed of 10 m/s and significant wave heights of 1.4 m and 2.0 m were applied. The corresponding wave periods were assumed 5.0 s and 5.8 s, respectively.
Figure 4.2. Wave height distribution. NW-wind.

The results of calculations for NW winds are shown on Figs. 4.2-4.4. Calculated wave patterns are shown on Fig. 4.2, velocity and elevation distribution on Fig. 4.3, sediment concentrations and load transport values on Fig. 4.4.
Figure 4.3. Distribution of velocity and elevation. NW-wind.

The values of annual load transport depicted on Fig. 4.4 are calculated for the hypothetical year, for which all the time the prescribed conditions (wave height/direction/period, wind speed) exist. 
Figure 4.4. Distribution of sediment concentration. NW-wind.

All calculated wave field patterns indicated presence of the wave energy focusing zones. Especially distinct they are at the southern part of the Hiddensee Island. They are mainly caused by a shallow area in the middle of the sea domain.

The water-level elevation distribution showed the combined effect of wind and wave set-up, especially large at the Bock during the N/NW winds, causing the Bock to flood. The highest velocities are for the NW winds both along the Zingst and Hiddensee, while the lowest are for W winds at the middle of Zingst, and for NE winds at Hiddensee.

Sediment concentrations for the NW storms are not the highest among the directions considered. The highest longshore velocities cause, however, the highest rates of load transport both along the Zingst (eastwards) and along the Hiddensee (southwards). The largest load transport rate occurs at the eastern part of Bock, nevertheless concentrations and velocities here are even smaller than along the Zingst. The load transport rate becomes smaller eastwards along the Bock, so the sedimentation gradually occurs here. Erosion could take place at the western part of Zingst, where the longshore current starts to develop eastwards. The load transport along the Hiddensee is directed southwards, being with the higher sediment concentration than that along the Zingst and being concentrated in a narrower coastal zone.
The smallest sediment concentrations along Zingst occur for the W-winds. The load transport starts to develop only at the eastern part of Zingst, being maximal at the middle of Bock. Erosion should occur at the eastern part of Bock, where material previously has been deposited by N/NW winds. This material then is carried up to the shoal northwards from Bock and deposited there. The load transport along the Hiddensee had moderate values and was concentrated in the narrow coastal zone. Erosion can occur at the southern part of Hiddensee coast.
The calculated annual load transport rates for the typical wind directions allow to predict the annual mean load transport through the cross sections and deposited/eroded amount of sediment. The possibility of summing of the contributions of storms over the year independently was explicitly assumed during the analysis. The wave height probability study was performed for that purpose. It was assumed that calculation with the Hs=1.4 m is representative for the significant wave heights of 1.2-1.6 m, while calculation with Hs=2.0 m is representative for larger wave heights.

Table 4.1. Repetitiveness of wave events for different directions.
  W NW N NE
Hs 1.2 -1.6 m 2.14% 0.73% 0.42% 0.63%
Hs > 1.6 m 1.04% 0.12% 0.13% 0.2%

The load transport values from the 2-dimensional longshore model were multiplied by a corresponding repetitiveness from the table 4.1. Summation of them lead to the resulting load transport values (Fig. 4.5).
Figure 4.5.Calculated annual mean load transport, thousands m3.

So obtained load transport values vary from 18 to 35 thousand m3 per year eastwards along the eastern part of Zingst and Bock. According to these values, erosion occurs at part of Zingst, being maximal just at the connection between Zingst and Bock. The sedimentation occurs along Bock, being the most distinct at the central part of it (approximately 22000 m3 per year). In the western part of Zingst the load transport is oriented westwards being 17000 m3 per year. The most western profile at Zingst indicates flux of 6000 m3 eastwards. The load flux through this profile, however, is very sensitive to the wave direction changes. Load transport is oriented southwards along Hiddensee in its southern part and northwards along the northern part of the island. One remark about the fluxes along Hiddensee is that due to the protection of the coast there would be no material to erode and to suspend. Such an effect had not been taken into account in this study. If the sediment flux through the Stralsund channel is assumed to be zero, then it can be calculated that annual amount of sediment deposited in and nearly the navigational channel in the SE "corner" of the open sea area is approximately 25000 m3 per year.
 

4.3 Real-time calculations

The real-time calculations were performed for the time period selected as the most critical (11.11.1973 to 21.11.1973).

The calculated distribution of sediment concentration shows maximum concentrations during the highest waves from NW. The SW/W sector storms can influence the sediment concentrations at locations near the Darsser Ort. The W winds influence the concentration at locations northern from the Bock. This is in agreement with the conclusions drawn from the results of the steady state calculations.

The calculated volume of sediment transport through the selected profiles is shown on Fig. 4.6.
Figure 4.6. Calculated load transport, thousands m3, fo tiome period 1973.06.11 to 1973.21.11.

Load transport rates along the Zingst and along the Hiddensee are in the range 18 to 134 thousand m3 during these two weeks. They are larger than those for the typical year calculated. The chosen 2-week period is the most critical in the autumn 1973. If it is assumed that other storms of that autumn contribute just for the typical values of load transport then these calculated values can be considered as values of load transport during the critical season. As it is likely that during the year not more than one critical season can occur, the load transport values for the critical year can be calculated by summing up load transport during the critical season and during the typical year.

The erosion during the selected period should be expected at the middle of the Zingst, while sedimentation at the area northwards from the Bock and at the SE corner of the open sea area, near or in the navigational channel. Volume of deposited sediment here can be estimated as 130000 m3, approximately 5 times more than during the typical year. The calculated morphodynamical changes (Fig. 4.7) during that period show that above-mentioned reasoning is correct.
Figure 4.7. Calculated seabed changes during time period (blue - erosion, orange - deposition).
The intensive morphodynamical processes occur at the Prerow bank, it moves to the Southeast. The depth of it, however, most probably is not correct (too small) in the present mesh. The changes occur at the Darsser Ort, too. The sedimentation tries to lengthen it using material from the Northwest. The erosion occurs at the middle of Zingst; the material taken here is deposited at the eastern part of it. The large area of sedimentation can be seen also between the Bock and the Hiddensee. The inter-switching of erosion and sedimentation is observable at the other parts of the domain. That can be the adaptation of the bed morphology to the forcing. The numerical effects due to the non-uniformity of mesh near the coast, however, also should be considered.
 

5 Conclusions

The main conclusions about the coastal hydrodynamics load transport and morphodynamics near Ruegen, stand as follows

The following features that up to now are not taken into account can be important: References

[1] Long-term measured wind data from DWD. Available on MorWin server.
[2] U. Bethers. Subjective notes on hydro- and morphodynamical processes near
Ruegen. Report of the study at the MorWin project.
[3] T. Seifert, B. Kayser: A high-resolution spherical grid topography of the Baltic Sea. Meereswissenschaftliche Berichte / Marine Science Reports, Institut fuer Ostseeforschung Warnemuende, 1995.
[4] Untersuchungen zur Moeglichkeit der Errichtung eines Hafens in Bereich der Ostseeküste. Gemarkung Prerow. Braunschweig, 1997.
[5] Shore Protection Manual (1984): Coastal Engineering Research Centre, Department of the Army, Vickburg, Mississippi.
[6] H.J. de Vriend. Mathematical Modelling of 3D Coastal morphology. Proceedings of the Short Course on Design and Reliability of Coastal Structures. Venice, 1992.
[7] IOW calculated elevation. Available on MorWin server.
[8] F.Molkenthin, O. Horstmann. Grid Modeling Methods for Coastal Regions.
[9] U.Bethers, J.Sennikovs. Mathematical modelling of longshore load transport  near Latvian harbour Ventspils. Proceedings COSTAL'97.
[10] J.Sennikovs, U.Bethers. Shallow water calculation of circulation in the Gulf of  Riga. FIMR series, in press.
 
 

  1. Scientist, Laboratory for mathematical modelling of environmental and technological processes, University of Latvia, 8 Zellu, Riga LV1002, Latvia.
  2. Graduate student, Laboratory for mathematical modelling of environmental and technological processes, University of Latvia, 8 Zellu, Riga LV1002, Latvia.
  3. Professor, Institute of Information Technology in Civil and Hydraulic Engineering, Brandenburg University of Technology, 17 Karl-Marx-Str., Cottbus D-03044, Germany