Dynamics of the Ems Estuary

Transcription

1 Dynamics of the Ems Estuary Physics of coastal systems Jerker Menninga Utrecht University Institute for Marine and Atmospheric research Utrecht Lecturer: Prof. dr. H.E. de Swart

2 Abstract During the last decades anthropogenic influence affected the Ems estuary to a great extent. It was observed that the tidal amplitude was amplified at the landward boundary, that the location of the sediment trapping was shifted land inward and in addition that the suspended sediment concentration strongly increased. Only little is known about the origin of this change in sediment dynamics and in the recent years a lot of research is done. This report covers two different models which both aims to find answers to this question. Chernetskey et al. (2010) use a tidal approach and they try to explain the change of the sediment distribution with help of tidal dynamics. In contrast Talke et al. (2009) neglect the effects of the tides and use a subtidal model. Both models concludes that the asymmetric change of the suspended sediment concentration (SSC) is caused by a SSC Current feedback of the system. However Talke et al. (2009) conclude that changes in the eddy viscosity, stress parameter and depth enhance the asymmetry, while Chernetskey et al. (2010) conclude that the asymmetry is caused by changes in the interaction between the M 2 tide and the externally forces M 4 tide. 1

3 Content 1 Introduction Interest of investigation Regional setting Hydrodynamics Chernetsky et al. (2010) Model Results Talke et al.(2009) Sediment Dynamics General model Talke et al.(2009) Solutions Results Chernetsky et al. (2010) Results Conclusions References

4 1 Introduction 1.1 Interest of investigation In the recent history the Ems estuary is subjected to intensive investigation. This is because in the last 25 years both flow as well as sediment dynamics has changed. For instance, the tidal range towards the landward barrier has increased and has become even larger than the tidal range at the entrance. Furthermore the suspended sediment concentration (SSC) has increased as well as the location of the sediment trapping, the so called estuarine turbidity maximum (ETM), which is shifted landward. The mechanics that play a role in the sediment trapping and the change of the sediment dynamics is not yet well understood, but it is suggested that the intensive deepening during the last decades is one of the most important factors. Deepening of the navigational route is necessary, because three harbors and a shipyard for cruise ships are located at the borders of the estuary (figure. 1) (Talke, 2009). In 2009 Talke et al. published a research where they explained the shift of the ETM with an extended version of a subtidal model, formulated by Hansen and Rattray (1965). With this model a number of mechanisms of sediment trapping were identified. However others suggested that changes in tidal behavior influence the sediment distribution (Chernetsky, 2010). Since the tidal range has changed for the Ems estuary it is interesting to investigate this hypothesis. This was done in 2010 by a research of Chernetskey et al. (2010) The aim of this report is to gain insight in which mechanism changed the tidal dynamics of the Ems estuary during the last decades and which mechanisms may be held responsible for the change of location of the sediment trapping. In order to so both researches of Talke et al. (2009) and Chernetskey et al. (2010) will be covered. The second section presents an overview of the hydrodynamics and especially the tidal dynamics. The third section covers the sediment dynamics. Chapter two first discusses the subtidal approach and after that the effect of the tides will be investigated. fig. 1: Change of the bathymetry of the Ems estuary between 1980 (blue line) and 2005 (red line) (Chernetsky et al.2010). 3

5 1.2 Regional setting The Ems estuary is located in the North of the Netherlands on the border with Germany. It reaches from the barrier island Borkum to the tidal weir at Hebrum (figure 1) and is partially well mixed. At the marine side, to the West of Emden, the water depth averages between 10 and 20 meters. To the East of Emden, where the estuary gets significantly narrower, a water depth of about 7 meters is maintained. The river Ems is discharging fresh water with a yearly average of 100 m 3 /s and is responsible for 90% of the fresh water input. Tidal flats cover about 50% of the estuary and 80% of the Dollard subbasin. The dynamics of the system are forced by a semidiurnal tide, freshwater flow from the river Ems and the wind. (Talke, 2009) fig. 2: Overview of the Ems estuary (Chernetsky et al. 2010). 4

6 2 Hydrodynamics This section describes the hydrodynamic models used in the papers of Chernetsky et al (2010) and Talke et al. (2009). There is a fundamental difference between the two approaches, since Chernetsky et al. (2010) take the effects of tides into account, while Talke et al. use a subtidal flow. 2.1 Chernetsky et al. (2010) Model In their research Chernetsky et al. use the width averaged shallow water equations. First they assume that the width B(x) of the estuary is exponentially converging and can be written as,. (1) Here B 0 is the width at the estuary entrance (at x = 0) and L b the converging length. Next the water depth is determined by the difference between the bed at z = -H(x) and the water surface at z = δ(x). The undisturbed water level is set at z = 0. Now the width averaged shallow water equations in the longitudinal direction can be determined. The momentum equation reads The first three terms on the left hand side represent the advective velocity in the longitudinal direction, the fourth and fifth terms are the barotropic pressure (related to variations of the free surface) and the baroclinic pressure (related to variations of the density) gradients. The last term is the friction component and is related to the vertical eddy viscosity coefficient A v, which represent small none defined mixing and dispersion processes (de Swart, 2010). The eddy viscosity is parameterized as where H 0 represents the water depth at the entrance. Furthermore the continuity equation is a balance between variations of the longitudinal and vertical velocities and the width averaged longitudinal velocity. (2) (3) In general the density is denoted by contributions due to the salinity, suspended sediment concentration and temperature. For simplicity Chernetsky et al. chose to neglect the contribution of the suspended sediment concentration. For the Ems estuary this is questionable, since the estuary is characterized by high sediment concentrations. Furthermore the salinity is assumed to be vertically well mixed, which is also accompanied by Talke et al. (2009). The along channel density distribution is modeled ass 5

7 . (4) Here β converts salt into density and the term denote a tidal average of the salinity. As mentioned earlier the water motion is forced by the tide. The tide consists of a semi diurnal (M 2 ) and its first overtide (M 4 ) constituent. The elevation of the surface due to tidal forcing is modeled as (5) In order to solve the equations Chernetsky et al. use the no stress and the kinamitic conditions at the free surface. and. (6a) At the bottom the bed is assumed to be impermeable, in other words; no vertical flow is possible through the bed. Also partial slip condition is assumed near the bed. (6b) 6

8 2.1.2 Results Parameter input Table 1 gives an overview of the used parameters and how they changed after deepening has taken place. All the parameters are the result of field measurements, except the vertical eddy viscosity coefficient A v and the stress parameter s. These values are obtained by calibrating the model to the observed data. From the table it can be seen that the vertical eddy viscosity has decreased from m 2 s -1 in 1980 to m 2 s -1 in 2005 and the stress parameter has decreased from ms -1 in 1980 to ms -1. Furthermore the amplitudes of the externally forced semi diurnal tide M 2 and its first over tide M 4 decreased over the years from 1.43 meter to 1.35 meter and 0.25 meter to 0.19 meter, respectively. Table 1: Parameter input. (Chernetsky et al. 2010) Water Motion; tidal amplitude The discussion of the water motion starts with the tidal amplitude. Figure 3 present the model solution for the amplitude and the phase difference between the horizontal and vertical amplitude of the semidiurnal tide. From figure 3a a clear amplification of the amplitude near the weir at Hebrum is visible. The amplitude of the tide increases from approximately 1.03 meter in 1980 to 1.52 meter in The vertical amplitude at the entrance on the other hand decreases from 1.43 meter to 1.35 meter. Furthermore from figure 3b it can be seen that the phase difference between horizontal and vertical tidal amplitude tend to 90 o at the weir for both 1980 and This indicates that at the weir the tidal wave is characterized by a standing wave (de Swart, 2010). Comparison with the 2005 solution shows that the phase difference through the whole estuary is shifted towards 90 o, so in 2005 the tidal wave has become more resonant through the whole estuary. 7

9 Chernetskey et al. (2010) investigate the tidal amplification by adopting two different scenarios. The model input (table 1) shows that the main difference between 1980 and 2005 is the change in water depth, the change of the vertical eddy viscosity and the change of the stress parameter. For the first scenario they fix the eddy viscosity and the stress parameter to the 1980 values and they use the 2005 bathymetry. The second scenario is the opposite; the eddy viscosity and the stress parameter are set to 2005 conditions and for the depth they use 1980 values. The result for the semidiurnal M 2 tide is represented in figure 3 as the solid (2005 bathymetry and 1980 A v and s) and dashed ( 2005 A v and s and 1980 bathymetry) black line. Figure 3a shows that the amplitude is amplified when only deepening is taken into account, however the amplitude is amplified even stronger when the eddy viscosity and the stress parameter are reduced. Figure 3b shows that deepening of the system increases the phase difference between the vertical and horizontal amplitude, hence the system becomes closer to resonance. Reduction of the eddy viscosity and the stress parameter has the same contribution to the relative phase shift. From this Chernetsky et al.(2010) concluded that both deepening and the reduction of the eddy viscosity and the stress parameter contribute to the amplification of the M 2 tide. fig. 3: a) Modeled change of the tidal M 2 amplitude as function of the estuary length due to the deepened scenario and the reduction scenario. b) Modeled change of the relative phase of the M 2 tide as function of the estuary length of the deepened scenario. The same procedure is carried out for the first overtide M 4 (figure. 4). First it is recognized that also the M 4 tide is amplified from 1980 to Figure 4a shows the amplitude of the vertical tide. The figure shows that the reduction of A v and s contributes stronger to the increase of the vertical amplitude than the scenario where only deepening is taken into account. Figure 4b shows that also for the M 4 tide the system becomes closer to resonance. In contrast to the vertical M 4 amplitude, both scenarios contribute to the relative phase shift. 8

10 fig. 4: a) Modeled change of the tidal M 4 amplitude as function of the estuary length due to the deepened scenario and the reduction scenario. b) Modeled change of the relative phase of the M 4 tide as function of the estuary length of the deepened scenario. From the sensitivity test can be concluded that, the deepening, the reduction of the eddy viscosity and the reduction of the stress parameter contribute to the amplification of both the M 2 as the M 4 tide. However, the amplitude of the M 4 tide is mainly amplified by the reduction of A v and s. This result is reasonable, since in general tidal waves lose energy due to friction at the bottom and internally by small internal eddy s. When the channel is deepened the tidal wave is less affected by the bottom and the wave loses its energy slower, hence the amplitude is less damped (de Swart, 2010). Secondly the stress parameter and the eddy viscosity are reduced. It is believed that this results from dredging of the channel. By dredging sediments are loosened and more sediment gets suspended. This results in a smooth and thin layer of suspended sediment above the bed, which decreases the bottom roughness. The increase in resonance of the system and the associated standing character of the tidal wave, should result in a decrease of the tidal return flow. This result is also gained from the model and is shown in figure 5. fig. 5: Change of the tidal return flow between 1980 (left) and 2005 (right) 9

11 2.2 Talke et al. (2009) In their research Talke et al. (2009) developed a model based on the gravitational model of Hansen and Rattray (1965). The model that is used assumes subtidal flow. This means that the model is tidally averaged and it is assumed that the salinity (s) is well mixed in the vertical and that the viscosity A v is constant. Another important assumption is morphodynamic equilibrium. This means that it is assumed that there is no net import or export of sediments. In other words, the model assumes a tank of available sediment and it calculates how the sediment is distributed over the area. Furthermore gravitational circulation is generated by a balance between the baroclinic and barotropic pressure gradients. So the total pressure gradient has to be equal to zero. The resulting balance is derived from the momentum balance and hydrostatic balance, which respectively can be written as (de Swart, 2010) (7) The total pressure gradient can be written as So the total pressure is written as the sum of the atmospheric pressure gradient, the barotropic pressure gradient and the baroclinic pressure gradient (de Swart, 2010). Talke et al. (2009) neglected the Coriolis force in equation (7) and the circulation due to the atmospheric pressure gradient in equation (9). This result in the following balance (8) (9), - (10) Furthermore the horizontal along channel velocity is written as. (11) So the total width averaged along channel flow through a cross section of width b and depth H is equal to the freshwater flow. The density is described as a function of the salinity and suspended sediment concentration. This is in contrast to the previous model, where the density was only a function of salinity Again β is a quantity that converts the salinity into density and γ is the relative density of the suspended sediment to the water in order to convert the suspended sediment concentration to density. 10 (12)

12 3 Sediment Dynamics 3.1 General model Before the differences for the sediment dynamics between the tidal and subtidal approach can be discussed, first an expression for the distribution of suspended sediment has to be derived. Talke (2009) and Chernetsky (2010) use similar approaches. The starting point is the concentration equation:. (13) This equation is a balance between the time evolution of the suspended sediment concentration c and the divergence of the sediment flux F. The sediment flux can be decomposed into three parts: the advective flux, the settling flux and the diffusive flux, these are given by (14a) (14b) (14c) Here u represents the horizontal velocity field, w the vertical velocity component, w s the settling velocity and K h and K v are respectively the horizontal and vertical eddy diffusion coefficients (de Swart, 2010). Using equations (14a) to (15c) in equation (13) results in the sediment concentration equation ( ) ( ) ( ) (15) The y-dependence is dropped, since Talke et al. (2009) assumes no variation over the width of the estuary, while Chernetsky et al. (2010) take a width average. Nevertheless both approaches result in the above equation. It is also realized that there is no flow and no sediment flux through the top and bottom boundary, which result in the following conditions:, -, -, (15a) (15b) (15c) From these conditions the vertical sediment distribution can be derived. This is done be vertically integrate the vertical sediment flux, - (16) 11

13 This describes a balance between the deposition of sediment and the stirring due to eddies. The solution for this is (de Swart (2010) (17) Equation (17) is still not completely solved, since the bottom concentration C b is still unknown. To resolve this problem, equation (15) is integrated over depth, and it is realized that there is no flow and no sediment flux through the top and bottom boundary, so the vertical sediment flux vanishes. This result in, - (18) B is a constant of integration and is determined by the difference between erosion (E) and deposition (D), hence B=E-D. However it is assumed that there is no net inflow or outflow of sediment so B has to be zero. In other words, there is no along channel variation of the vertically integrated horizontal flux, hence, - (19) This is called morphodynamic equilibrium (Talke et al. 2009). 12

14 3.2 Talke et al. (2009) Solutions In order to find an expression for the horizontal along channel velocity, the momentum equation (eq.10) is integrated twice with respect to z. The resulting equation depend on the salinity gradient, the bottom turbidity gradient and the surface slope. Finally the equation reads { } (20) So the along channel circulation depends on circulations due to baroclinic, suspended sediment and freshwater contributors. This result is an extension on the known gravitational model, presented by Hansen Rattray (1965), since circulation due to sediment is also taken into account. When the along channel sediment gradient is set to zero, the original model is recovered. Next substituting (20) and the equation for morphodynamic equilibrium (19) into equation (17) results in the solution for the bottom sediment distribution C b *, - + (21) From the described solutions it becomes clear that both the along channel circulation, as well as the sediment distribution vary in a cubic sense with the water depth. This result implies that deepening of the channel has a nonlinear effect on the circulation and the sediment distribution Results To find how the sediment system reacts on changes of the various parameters, a sensitivity study is done. Figure 6 shows the sensitivity test for the river discharge, vertical mixing and water depth respectively. Figure 6a shows that when the river discharge increases, the turbidity maximum shifts downstream. This is because when the river discharge weakens, the near bottom currents (e.g. the salinity driven currents) that have an upstream direction become more important and transports sediment in the upstream direction. In contrast, low discharge values enhance the asymmetry of the sediment distribution. This can be understood by evaluating equation (20). For low discharge values, the depth-depended terms become relatively more important. Since the depth has a cubic relation, asymmetry in the sediment distribution is enhanced. The same pattern can be seen for changing the mixing term (figure. 6b). For large mixing values, the sediment is able to stay longer in suspension. This result in excluding sediment from the system. Also, decreasing of the mixing term result in a relative increase of the asymmetric depth. As expected an opposite trend is shown for depth variations (figure. 6c). Increasing the depth result in stronger asymmetry of the sediment distribution and an upstream shift of the turbidity maximum. 13

15 fig. 6:Sensitivity study of a) the freshwater discharge, b) the vertical eddy viscosity and vertical eddy diffusivity and c) the depth. (Talke et al. 2009) 14

16 3.3 Chernetsky et al. (2010) From the previous paragraph it became clear that changing the depth, river discharge and vertical mixing parameters affected the sediment dynamics in for the subtidal approach. The Ems estuary however is a tidal embayment, so it is convenient to study the effect of the tide to the sediment distribution. Chernetsky et al. did this in their research, with help of the same model described in section 3.1. However, since tides are now allowed in the system, equation (19) has to be tidally averaged. First it is realized that the that the velocity and the sediment concentration can be written as the sum of the mean and the perturbation (22) (23) Combining equation (22) and (23) result in (24) Next the boundary conditions state that there is no sediment flux into or out of the domain, so when taking the tidal average of (24) the first term on the right hand side will vanishes. Using this, Chernetsky et al. (2010) found an expression for the tidally averaged morphodynamic equilibrium equation ( ) (25) where δ represents the free water surface and, represents a tidal average. For their analysis, Chernetsky et al. (2010) describe equation (25) in terms of the erosion coefficient a(x), which is the horizontal distribution of the total erodible material. In order to do so two new function are introduced, F which represent the vertically integrated horizontal distribution due to the turbulent eddies and T which represents the vertically integrated horizontal distribution due to horizontal flow transportation (26) ( ( )) (27) Using equation (26) and (27) into equation (25) result in a differential equation for the erosion coefficient The transport parameter T can schematically be represented as the sum of the transport contributors from the residual flow T res, the semi diurnal tide T M2 and its first overtide T M4 and transport due to diffusion T diff : T = T res + T M2 + T M4 + T diff. (28) 15

17 3.2.1 Results From equation (28) the location of the estuary turbidity maximum (ETM) can be determined. Since the available eroded sediment concentration reaches maximum values at the ETM, the erosion coefficient a will also reach its maximum. In addition the gradient of the erosion coefficient will be zero at the ETM. Since a reaches its maximum, the transport parameter should be zero in order to obey morphodynamic equilibrium. So the four contributors of the transport parameters should balance at the ETM. In order to investigate the relative importance of the different transport contributors, Chernetsky et al. plotted the different transport functions for course and fine silt for both 1980 and 2005 (fig. 7). From the figure it can be seen that for fine silt between 1980 and 2005, the ETM was shifted about 20 kilometers land inward. This shift can almost completely be attributed to transport due to the M 2 tide, since this transport function remains constant stream upward, almost until 50 kilometers. This is in contrast with the 1980 situation, where this function reaches its maximum around 10 kilometers and decreases almost linear after that. fig. 7:Dimensionless transport function and its components. a and b show fine silt and c and d coarse silt. (Chernetskey et al. 2010) For course silt the plot gives a different view. In 1980 the ETM was located around 10 kilometers from the entrance. The M 2 contributor was the only agent that transported sediment stream upward and decreases rapidly behind the ETM. In 2005 however two ETM s are visible. The first is located about 15 kilometers from the entrance and the second around 45 kilometers. For the first ETM the M 2 component is the main contributor. In agreement with 16

18 1980 it decreases close to the entrance, however in 2005 it reaches a certain positive constant value at the location of the first ETM. After that it remains constant for several kilometers before it decreases further and becomes an exporting contributor. Another difference between 1980 and 2005 is the shift of the transportation due to the M 4 tide. Until 20 kilometers the M 4 contributor becomes less negative and after that it becomes more positive. As a result the M 4 tide transports sediment stream upward in the second half of the modeled area. Together with the M 2 contribution, this results in the second ETM. From this result Chernetsky et al. concluded that the change of the sediment trapping location is mainly the result of changes in transport due to the M 2 tide, both for fine and coarse silt. To understand which mechanism is responsible for the change of the transportation by the M 2 tide, the T M2 component is decomposed in two main components; the interaction between the M 2 velocity and both the M 4 and the residual velocity. This is denoted by and respectively. The relative importance of the two transportation components to the change of T M2 is shown in figure 8. From the figure it can be seen that both for fine and coarse silt the component shows no significant changes between 1980 and So it can be concluded that this component is not responsible for the change of T M2. The profile for however remains for both fine and coarse silt at higher values in 2005 than it did in Furthermore it follows the profile of T M2 in fig. 8:Components of the dimensionless transport function T M2 (Chernetskey et al. 2010) 17

19 With this result the component is decomposed further in advective contribution, free surface contribution, no-stress contribution and the M 4 external forcing. This can schematically be represented as:, respectively. In order to investigate which of these components contributes to the change of and as a consequence to the change of T M2, figure 9 is analysed. From the figure it can be seen that for both fine and coarse silt the external forcing of the M 4 interaction with the M 2 velocity is the main contributor to the change of. Where the other contributors show no significant change between 1980 and 2005, the remains positive longer and as a consequence is responsible for the change of. From this Chernetsky et al.(2010) concluded that the change of the sediment trapping is the main result from changes in the asymmetry of the tides. M fig. 9: Components of the dimensionless transport function T M 18

20 4 Conclusions This report aims to find the processes responsible for the change in tide and sediment dynamics of the Ems estuary. To this end two papers and two different approaches are discussed; the paper of Chernestky et al. (2010), which makes use of a tidal approach and the paper of Talke et al. (2009), which uses a subtidal approach. The biggest similarity between the two is the conclusion that the change in dynamics is because of asymmetry of the basin. However, since the basic assumptions differ in great extent, also different conclusions are drawn. Since tides are not considered in a subtidal approach, the change of the tide dynamics is only explained with help of the paper of Chernetskey et al (2010). To explain the tide dynamics Chernetsky et al (2010) adopted two different scenarios. The first scenario fixes the eddy viscosity and stress parameter to the initial values and uses the 2005 bathymetry. The second scenario is the opposite. From this, it is concluded that both the semidiurnal tide as well as its first overtide are changed due to changes of the stress parameter, eddy viscosity and basin depth. This result is reasonable, since deepening of the channel, result in less influence of the bottom to the tidal wave. So less energy is lost due to friction. Secondly the tidal wave is amplified, because the eddy viscosity and the stress parameter are reduced This can be explained because due to dredging more sediment is in suspension and a thin film of fluid sediment covers the bottom and reduces the stress parameter. Both models are able to explain the change in sediment trapping and both models conclude that asymmetry is the keyword. Talke et el. (2009) use an extended version of a classical subtidal model, first formulated by Hansen and Rattray. The extension also deals with sediment circulation. With this model it is concluded that the change of sediment trapping, result from changes of the freshwater discharge, eddy viscosity and depth. Chernetsky et al. tried to relate the change in sediment trapping by changes in tidal characteristics. They modeled the contributions to sediment transport of both the M 2 and M 4 tides. From this they concluded that the change of sediment trapping was a result of the change of transport contributions of the M 2 tide. After this they subdivided this contribution further to M 2 interactions with the first overtide velocity and the residual velocity. From this it was concluded that the interaction between the M 2 and M 4 velocity infects the location of the sediment trapping. From another subdivision it was concluded that interactions of the externally forced overtide and the semidiurnal tide are responsible of the change in sediment trapping. 19

21 References Chernetskey, A.S., Schuttelaars, H.M., Talke, S.A., 2010, The effect of tidal asymmetry and temporal settling lag on sediment trapping in tidal estuaries, Ocean Dynamics 60: Hansen, D.V., Rattray M. jr., 1965, Gravitational circulation in strait and estuaries. Journal of Marine Research 23: de Swart, H.E., 2010, Physics of Coastal Systems, lecture notes. IMAU, Utrecht University Talke, S.A., de Swart, H.E., Schuttelaars, H.M.,2009, Feedback between residual circulations and sediment distribution in highly turbid estuaries: An analytical model. Continental Shelf Research 29: