WAVE MODELLING IN A TIDAL INLET: PERFORMANCE OF SWAN IN THE WADDEN SEA Jacco Groeneweg1, André van der Westhuysen 1, Gerbrant van Vledder2, Sjaak Jacobse3, Joost Lansen3, Ap van Dongeren1 The performance of the spectral wave model SWAN for application in a tidal inlet system has been assessed through hindcasts of storm events. Over the last five years wave measurements have been carried out in the tidal inlet of Ameland, which is part of the Dutch Wadden Sea. Measurements during three severe storms in 2007 have been used here to assess SWAN’s performance in the Wadden Sea. Averaged over all conditions and locations SWAN performs well for these storm conditions but three aspects require further attention. Firstly, focusing on the main channel, SWAN overpredicts the significant wave height in opposing currents, whereas the agreement with measurements for following currents is good. Secondly, over the ebb-tidal delta the wave energy at the primary peak of the spectrum is underpredicted, most likely due to the application of only linear refraction as a propagation mechanism. Thirdly, over the tidal flats the computed ratio of integral wave height over water depth shows an apparent upper limit, because the wave growth over finite depth is hampered by the present formulation of depth-induced wave breaking. The hindcasts and additional analysis and sensitivity studies have identified the physical aspects that are responsible for the inaccurate wave predictions, and have led to the definition of specific future research for model improvement. These improvements will probably lead to a SWAN model that determines reliable wave conditions in the Wadden Sea and related complex areas.
INTRODUCTION
A significant part of the Netherlands lies below sea level and is protected from flooding by dunes and dikes. The safety of these primary sea defences must be assessed every five years for a (pre)defined level of protection. The assessment is based on the Hydraulic Boundary Conditions (HBC) and the Safety Assessment Regulation. The HBC are derived anew every five years. The spectral wind wave model SWAN (Booij et al. 1999) plays a key role in the determination of these HBC, because it is used to transform statistically determined wave conditions from offshore measurement stations to the nearshore locations. However, this procedure can presently only be applied for sea defences along the west coast of the Netherlands, including the uninterrupted Holland coast and the Scheldt estuaries in the southern part of the Netherlands.
1
Deltares | Delft Hydraulics, PO Box 177, 2600 MH Delft, The Netherlands;
[email protected] 2 Alkyon Hydraulic Consultancy & Research, PO Box 248, 8300 AE Emmeloord, The Netherlands 3 Royal Haskoning, PO Box 8520, 3009 AM Rotterdam, The Netherlands;
1
2 At present, there are uncertainties regarding the quality of the wave field predictions by SWAN in the northern part of the Netherlands. There, the Dutch Wadden Sea is a tidal inlet system, which is partly sheltered from the North Sea by barrier islands (Fig. 1). In this complex area many physical processes, such as nonlinear wave-wave interaction, wave breaking, local wave generation, and wave-current interaction, occur, resulting in strong variations in the wave field. In contrast to the performance of SWAN in well-exposed coastal areas, there is currently insufficient confidence in SWAN, to produce reliable wave conditions along the sea defenses in the Wadden Sea. This lack of confidence in the performance of SWAN in tidal inlet systems as the Wadden Sea has two reasons. Firstly, in a hindcast of two storms, Kaiser and Niemeyer (2001) showed that SWAN seems to underestimate the penetration of low-frequency storm waves from the North Sea into the tidal inlet of Norderney in the German Wadden Sea. This inlet is comparable to those in the Dutch part of the Wadden Sea. Secondly, up until recently no relevant wave data were available to validate and improve the SWAN model for the Dutch Wadden Sea region. Therefore, in 2002 an extensive measurement campaign was set up in the tidal inlet of Ameland (for an extensive overview of this campaign, see Zijderveld, 2008). The wave measurement network consists of a series of wave buoys. By means of analysis of measurements and results of hindcast studies, the original setup was fine-tuned over the past five years. Presently, twelve buoys are located in the tidal inlet of Ameland, forming two transects from the North Sea, over the ebb tidal delta, through the tidal gorge towards the mainland. The eastern transect follows the main channel (buoys AZB12 – AZB62), the western transect crosses the tidal flats (buoys AZB11 - AZB61), see Fig. 1. In the figure, the wind stations (in particular HBG, TSW and LWO) and the water level gauge at NES are shown as well.
transect AZB11-AZB61
transect AZB12-AZB62
S
H BG
LW O
TSW
waves wind water level
Figure 1. Bathymetry of Dutch Wadden Sea, with the network of wind stations and wave buoys, including the buoys in the tidal inlet of Ameland.
3
The measured data have been used in extensive hindcasts in the tidal inlet of Ameland (in the Dutch part of the Wadden Sea) and Norderneyer Seegat (in the German part) for a variety of storm conditions. These hindcasts have been carried out to gain insight in the performance of SWAN and in the relevant physical processes in the Wadden Sea under storm conditions (see also Van Vledder at, 2008). A good performance under storm conditions does not necessarily imply that SWAN predicts accurate HBC (because these are calculated for extremely rare events, with yet unknown physics), but at least increases the confidence in the application of SWAN in the HBC process in the Wadden Sea. In this paper the setup of the hindcasts is described, followed by results in the tidal inlet of Ameland for the most severe of the recorded storms. Both the general performance of SWAN is presented and analyzed, as well as some specific aspects. The latter was investigated by considering isolated regions in the tidal inlet system. HINDCAST OF STORM EVENTS Storm events
Since the setup of the measurement campaign in 2003 a number of significant storms passed the Wadden Sea. Wind speeds up to 24 m/s have been measured. The wind directions varied between west and north, which is typical for storms along the Dutch coast during the winter storm season. The storms in 2007 led to particularly high surge levels of over N.A.P. +3 m (Dutch reference level, about equal to MSL). Therefore these 2007 storms, occurring on 11-12 and 18-19 January and 18-19 March, have been considered here. The wind directions in these storms remained in the west to northwestern sector. Fig. 2 presents the hourly-averaged wind speed and direction at location HBG during the two storm days of the three indicated storms (left-hand axis), as well as the water level at the station NES (right-hand axis). The vertical lines indicate the selected hindcast instants. Selection of hindcast instants
A set of 31 instants (Fig. 2) were selected that cover a wide range of conditions, mostly around the peak of the storms. Situations of following and opposing currents, varying in magnitude, have been considered. Various ranges of the water level, both inside the inlet and in the tidal basin close to the mainland, are represented by the selection as well. The wind directions are in the west to northwest sector. The hourly-averaged wind speed varies from mild to strong, reaching a maximum of 23 m/s. It should be noted that for the simulated storm instants, the wind in the Wadden Sea is mainly from westerly
4 directions, rather than from northwesterly to northern directions, which occur more seldomly.
Figure 2. Time series of observed wind speed (in m/s, solid line) and direction (in 10 N, dash-dotted line) at Huibertgat (HBG) on left axis and water level (in m NAP, dashed line) at NES on right axis. Vertical lines indicate selected hindcast instants.
SWAN model setup
Each storm instant was hindcast with a stationary SWAN model (version 40.51AB) run for the three storm periods in January and March 2007 and provides a broad basis for investigating the reliability of SWAN at different storm phases.. The stationary mode was used, since the model is applied as such in the determination of the HBC. The physical model settings use the state-of-the-art formulations and are mostly the default settings of SWAN. For wind-wave generation, the combination of wind input and saturation-based whitecapping proposed by Van der Westhuysen et al. (2007) was applied. Quadruplet nonlinear interactions are modeled using the Discrete Interaction Approximation (DIA) of Hasselmann et al. (1985). The shallow water source terms include triad nonlinear interaction according to Eldeberky (1996), surf breaking according to Battjes and Janssen (1978) and bottom friction according to the JONSWAP formulation (Hasselmann et al. 1973). The computations are performed on two grids. The first is a coarse curvilinear grid, covering a large part of the Wadden Sea, see Fig. 3. The
5 second grid is a detailed curvilinear grid covering the tidal inlet of Ameland and was obtained from refining a section of the larger grid. The typical resolution in the tidal inlet of Ameland is 30-50 m. The outline of the detailed grid is shown in Fig. 3 as well.
Figure 3. Wadden Sea grid (every fourth grid cell is shown) and outline of the detailed grid, covering the tidal inlet of Ameland. The circles indicate the buoy locations, the triangles the locations where boundary conditions are imposed.
Offshore wave boundary conditions for the detailed grid are obtained from the wave buoys AZB11 and AZB12. These buoys provide only boundary conditions along the northern boundary of the detailed grid. The boundary conditions along the eastern and western boundaries of the detailed grid are obtained from nesting in the larger grid. Measured data from the wave buoys SON and ELD are imposed along the offshore boundary of the coarse grid (triangles), indicated in Fig. 3. The frequency range is set to 0.03–1.0 Hz with f =0.1f. The directional space is discretized with 36 bins of 10° over the full directional circle. The stationary simulations are solved iteratively up to 80 iterations, which appeared to be enough for convergence. Bathymetry, hydrodynamics and wind fields
The SWAN computations additionally require input in terms of bathymetry, water level, current and wind fields for all selected hindcast instants. The bed level in the tidal inlet of Ameland is obtained from extensive bathymetry surveys in 2004 and 2007 (see Fig. 4). The bathymetry for the large grid is composed from regular 6-year cyclic surveys.
6
Figure 4. Bed level (in m NAP) in tidal inlet of Ameland, including wave buoy locations
For each of the selected time instants a water level and current field is required. The numerical model Delft3D, in which SWAN is embedded, is used to determine the hydrodynamics for the three storms. The resulting water level and current fields at the 31 selected hindcast instants are input for the final SWAN simulations. Uniform wind fields are applied over the entire computational domain. The wind velocity is defined as a weighted average of the measured wind at the three wind stations Huibertgat (HBG), Lauwersoog (LWO) and TerschellingWest (TSW), see Fig. 1. GENERAL PERFORMANCE OF SWAN
All of the hindcasted storm instants reveal a similar pattern in hydrodynamic conditions, wave propagation and wave evolution. The mainly westerly winds induce a surge in the Wadden Sea basin, resulting in a water level increase, superimposed on the astronomical tide. Both in the inlet throat and in the tidal channels, the computed current velocities are high, up to 1.5 m/s. During all of the hindcast instants, waves of up to Hm0 = 6 m have developed over the North Sea, propagating onto the outer ebb delta by refraction on the sloping foreshore north of the series of Wadden islands. Significant depth-induced wave breaking occurs over the outer delta, and waves propagate further into the inlet. Somewhere in the tidal throat of the inlet system of Ameland, mixed seas occur. In the Wadden Sea interior the waves are clearly young, locally generated waves, propagating in the wind direction
7 (SW to NW). Fig. 5 shows the significant wave height on 11 January 2007 at 22:40.
Figure 5. Computed spatial distribution of significant wave height in tidal inlet system of Ameland on 11 January 2007 at 22:40.
The measured and computed wave parameters have been compared for all hindcast instants for all buoy locations. The performance is expressed in both a relative bias and a relative standard deviation. In general, for all buoy locations, both the significant wave height Hm0 and the speactral wave period Tm-1,0 are underpredicted. The relative bias is -12% and -6% respectively, with a relative standard deviation of 16% and 9% respectively. The underprediction of these parameters manifests itself mainly over the ebb-tidal delta and in the shallow areas of the tidal basin. This will be analyzed in more detail in the next section. The performance of SWAN in the tidal channels is good in terms of the bias for both the wave height Hm0 and the wave period Tm-1,0. The scatter in terms of the relative standard deviation, however, is large in the results of the tidal channels.
8
Figure 6. Measured versus computed significant wave height (left) and spectral wave period T m-1,0 (right) for following currents (first row), opposing currents (second row), penetration of low-frequency waves (third row) and depth-limited wave growth (fourth row).
9 PERFORMANCE OF SWAN FOR SPECIFIC ASPECTS
In this section the performance of SWAN is discussed with respect to specific aspects that can be investigated by applying a division of the tidal inlet system into three regions: 1. The penetration of wave energy from the North Sea into the tidal basin was investigated on and over the ebb-tidal delta. Measurements from the buoys AZB21, AZB31 and AZB32 (buoy locations indicated in Fig. 4) have been used. For this purpose AZB22 was not considered for the storms in 2007; 2. In the main channel the effect of an ambient following or opposing current on relatively young waves is studied. For this purpose, the buoys AZB42 and AZB52 have been used. Buoy AZB32 is in the main channel, but in contrast to the former two buoys strongly affected by incoming North Sea waves; 3. On the tidal flats wave growth in finite depth was examined, mainly at buoy locations AZB51, AZB61 and AZB62. Due to its limited frequency range towards higher frequencies, buoy AZB41 was not considered here. In the tidal channel the current magnitudes are significant. Only those instants have been considered for which the difference in mean wave direction and current direction was less than 45 degrees for following currents or more than 135 degrees for opposing currents. In Fig. 6 the scatter plots of measured and computed significant wave height Hm0 and wave period Tm-1,0 are shown for the three aspects mentioned above. The situations with following and opposing currents are separated and presented in the first and second rows respectively. The results with respect to North Sea wave penetration and finite depth wave growth are presented in the third and fourth rows respectively. Above each of the plots, the lines of linear regression y=ax+b and y=cx, as well as the linear correlation coefficient r and the number of values used in the plots (N) are given. Following currents
The overall performance of SWAN under following current conditions is good, see Fig. 6 (upper row). The relative bias in the wave height of all the storm instants and buoys under consideration is only 5%. The relative bias for the mean wave period Tm-1,0 is -3%, but this is mainly due to the underprediction at AZB32. This location is vulnerable to North Sea waves and therefore less relevant for interaction between an ambient current and typically young, locally generated waves in the interior of the Wadden Sea. Opposing currents
The scatter diagrams with respect to opposing currents (second row of Fig. 6) show that the overall comparison of the SWAN results and the measurements is not very good. The overprediction of the significant wave height and mean wave period Tm-1,0 at the buoys AZB42 and AZB52 for the selected storm instants is 13% and 3% respectively in terms of the relative bias.
10 The scatter is large as well (relative standard deviation 15% and 6% respectively). In this regard, Ris and Holthuijsen (1996) showed that the pulse-based whitecapping expression of Komen et al. (1984), the default expression in SWAN, does not provide strong enough dissipation of the very steep waves found in opposing current, near-blocking situations. Ris and Holthuijsen (1996) propose enhancing the whitecapping dissipation of these steep waves by the addition of a steepness-based dissipation expression, based on the bore-based breaking model of Battjes and Janssen (1978). This model deficiency identified by Ris and Holthuijsen (1996) was found to also apply to conditions in the Wadden Sea, simulated using the whitecapping formulation of Van der Westhuysen et al. (2007). Accordingly, enhancing the whitecapping dissipation, as proposed by Ris and Holthuijsen (1996), offers an approach to correct the overestimation of wave heights and periods shown in Fig. 6. Penetration of North Sea waves
According to Figure 6 (third row) the significant wave height and mean wave period are underpredicted by almost 10% at the locations on and over the ebb-tidal delta. The relative standard deviation is 15% and 9% respectively. The results at AZB32 are slightly better than at AZB21 and AZB31. This apparently good performance in the scatter results of Hm0 for AZB32 is caused by an overprediction of the high-frequency wave energy, balancing the underprediction of wave energy at the low-frequency part of the spectrum. Taking a closer look at the wave spectra for these locations shows that the high frequency part of the energy spectrum for both AZB21 and AZB31 is reproduced correctly, as well as the mean wave direction and the directional spreading. However, the wave energy of the low frequency waves from the North Sea is strongly underpredicted. This is illustrated in Fig. 7 for 19 January 2007, 18:40 at location AZB21. The wave buoys AZB21 and AZB31 are located over the ebb tidal delta on the tip of the main tidal channel. Wave behavior as presented above has also been observed by Magne et al. (2007) in their numerical experiments of wave propagation over the Scripps Canyon (USA). They concluded that wave tunneling, i.e., a transmission of waves to water depths greater than allowed by Snel’s law, for obliquely incident waves, cannot be represented in the geometrical optics approximation. When applied without diffraction, SWAN predicts that all wave energy is trapped on the tidal flats for large incidence angles relative to the depth contours, while a small fraction of the wave energy is in fact transmitted across the tidal channel. Results of Magne et al. (2007) suggest that inclusion of diffraction effects may improve the SWAN results over the ebb-tidal delta.
11
Figure 7. Measured (dark line) and computed (light-colored line) variance density (left), mean wave direction and directional spreading per frequency component at buoy location AZB21 on 18 January 2007 at 18:40.
Wave growth in finite depth conditions
The Wadden Sea interior is characterized by tidal channels and flats, as well as regions with a nearly horizontal bathymetry. The latter are mostly found close to the mainland. Using the data from the buoys AZB51, AZB61 and AZB62 the performance of SWAN with respect to wave growth in finite depth has been investigated. Fig. 6 (bottom row) shows that both significant wave height and mean wave period are underpredicted. The relative bias is -12% and -10% respectively. Fig. 8 shows that SWAN predicts values for the Hm0/d ratio of not higher than 0.35. Such an apparent upper limit is not present in the measurements, where values of 0.42 have been observed. The latter values are not exceptional and have been observed in lakes with nearly horizontal beds before (see e.g. Young and Babanin, 2006). In Fig. 8 the depth in the computed Hm0/d ratio is taken from the SWAN model. The measured water depth at the deployment of the buoys is applied to determine the measured Hm0/d ratio.
Figure 8. Measured and computed ratio of significant wave height and total water depth at finite depth location AZB51, AZB61 and AZB62.
12 At all instants and at all three locations the computed wave energy spectrum shows less wave growth compared to the measured spectra. The underprediction by SWAN becomes less for higher water depth. It seems as if the wave growth over nearly horizontal regions is hampered in SWAN, leading to underprediction of the significant wave height and mean wave period. By means of a sensitivity analysis several physical parameters and formulation in SWAN were varied. Increasing the parameter in the formulation of Battjes and Janssen (1978) for depth-induced breaking led to an increase of the computed Hm0/d ratio. The computed wave spectra showed more wave growth. This is an indication that the present formulation of depth-induced breaking obstructs the wave growth over horizontal bathymetries too strongly. CONCLUSIONS
The hindcasts of storm events have shown that, in general, SWAN performs well for storm conditions in the tidal inlet of Ameland. Taking into account all selected time instants and all buoy locations the significant wave height Hm0 is underpredicted by 12% and the mean wave period Tm-1,0 by 6%. In the main channel SWAN performs well for following ambient currents. For opposing currents an overprediction of the significant wave of more than 10% is observed. By analyzing the results at locations over the ebb-tidal delta at time instants that North Sea waves penetrate into the tidal inlet system, the lowfrequency part of the energy spectrum is significantly underpredicted. This leads to underpredictions of the significant wave height and the mean wave period of almost 10%. It is believed that not only linear wave refraction should be accounted for, but also diffraction should be taken into account. In the regions with a nearly horizontal bed close to the mainland the SWAN results show an apparent upper limit of the wave height over depth ratio. Depth-induced wave breaking in the SWAN model seems to hamper the wave growth in finite water depth. This leads to underpredictions of the significant wave height and the mean wave period of 10%. The hindcasts and additional analysis and sensitivity studies identified the physical aspects that are responsible for the inaccurate wave predictions, and have led to the definition of specific research for model improvement. These improvements will probably lead to a SWAN model that determines reliable wave conditions in the Wadden Sea. ACKNOWLEDGMENTS
The presented work is part of the SBW (Strength and Loads on Water Defenses) project commissioned by Rijkswaterstaat - Centre for Water Management in The Netherlands.
13 REFERENCES
Battjes, J.A., and J.P.F.M. Janssen. 1978. Energy loss and set-up due to breaking of random waves, Proceedings of 14th International Conference on Coastal Engineering, ASCE, 466-480. Booij, N., R.C. Ris and L.H. Holthuijsen. 1999. A third generation wave model for coastal regions, Part I, Model description and validation. J. Geophys. Res., 104, C4, 7649-7666. Eldeberky, Y. 1996. Nonlinear transformation of wave spectra in the nearshore zone, Ph.D. thesis, Delft University of Technology, Department of Civil Engineering, The Netherlands. Hasselmann, K., T.P. Barnett, E. Bouws, H. Carlson, D.E. Cartwright, K. Enke, J.A. Ewing, H. Gienapp, D.E. Hasselmann, P. Kruseman, A. Meerburg, P. Müller, D.J. Olbers, K. Richter, W. Sell and H. Walden. 1973. Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP), Dtsch. Hydrogr. Z. Suppl., vol. 12, A8. Hasselmann, S., K. Hasselmann, J.H. Allender and T.P. Barnett. 1985. Computations and parameterizations of the nonlinear energy transfer in a gravity wave spectrum. Part II: Parameterizations of the nonlinear transfer for application in wave models, J. Phys. Oceanogr., 15 (11), 1378-1391. Kaiser, R. en H.D. Niemeyer. 2001. Analysis of directional spectra in shallow environment. Proceedings of 4th international symposium WAVES, 944952. Komen, G.J., S. Hasselmann, and K. Hasselmann. 1984. On he existence of a fulldeveloped wind-sea spectrum. J. Phys. Oceanogr., 14, 1271-1285. Magne R., K. A. Belibassakis, T. H. C. Herbers, F. Ardhuin, W. C. O'Reilly, V. Rey. 2007. Evolution of surface gravity waves over a submarine canyon, J. Geophys. Res., 112, C01002, doi:10.1029/2005JC003035. Ris, R.C. and L.H. Holthuijsen. 1996. Spectral modelling of current waveblocking. Proceedings of 25th International Conference on Coastal Engineering, ASCE, 1247-1254. Van Vledder, G.Ph., J. Groeneweg, and A.R. van Dongeren. 2008: Numerical and physical aspects of wave modelling in a tidal inlet. To appear in Proceedings of 31st International Conference on Coastal Engineering. Van der Westhuysen, A. J., M. Zijlema, and J. A. Battjes. 2007. Nonlinear saturation-based whitecapping dissipation in SWAN for deep and shallow water. Coastal Engineering 54, 151-170. Young, I. R. and A.V. Babanin. 2006. The form of the asymptotic depthlimited wind wave frequency spectrum, J. Geophys. Res, Vol. 111, C06031, doi:10.1029/2005JC003398. Zijderveld, A. 2008. Field measurement campaign in the Dutch Wadden Sea. To appear in Proceedings of 31st International Conference on Coastal Engineering, ASCE.
