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). References Barthel, V., Zanke U., A Morphodynamic Model for River and Estuary Management, Coastal Engineering 1998: proceedings of the twenty-sixth international conference. Hinneburg,D., Raabe, A., Tetzlaff,G., Wind-und Seegangsatlas für das Gebiet um Darß und Zingst, 1997, Wissenschaftliche Mitteilungen aus dem Inst. Für Meteorologie der Universtät Leipzig und dem Institut für Troposphärenforschung e.V. 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