Storm hindcasts for Wadden Sea: Hindcasts in inlet systems of Ameland and Norderney and Lunenburg Bay

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Storm hindcasts for Wadden Sea

J. Groeneweg, Gh. van Vledder, N. Doorn, S. Caires and A.J. van der Westhuysen

Report

September 2007

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2.5 Conclusions ... 2–20 3 Analysis of hindcast results for tidal inlet of Norderney ...3–1 3.1 Problem description ...3–1 3.2 Sensitivity analysis...3–2 3.3 Wave conditions for extreme wind and water level ...3–3 3.4 Conclusions ...3–4 4 Analysis of hindcast of events in Lunenburg Bay...4–1 4.1 Introduction ...4–1 4.2 Measurements in Lunenburg Bay ...4–1 4.3 Results of SWAN simulations in Lunenburg Bay...4–2 4.4 Conclusion...4–3 5 Conclusions and recommendations...5–1 6 References ...6–1

Appendices

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List of Tables

2.1 Wind, water level and offshore wave conditions for hindcasted storm instants in Amelander Zeegat

2.2 Numerical characteristics of the SWAN computational grids.

2.3 Measured and computed (with and without triads) wave parameters at 4 buoy locations for 2 January 2005, 12h00

2.4 Minimum and maximum relative variation of computed solution for Hm0 and Tm-1,0 in grid points in radius of 100m around buoy location

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List of Figures

2.1 Computational domains (GridCL and AZG3A) and location of offshore buoys, location of wave buoys in Ameland inlet during 2004 storm and 2005 storm

2.2 Water level at NES and wind speed and direction at Lauwersoog for the storm of 7-9 February 2004

2.3 Water level at NES and wind speed and direction at Lauwersoog for the storm of 1-3 January 2005

2.4 Grid lines of curvi linear grid GridCL and outline of grid AZG3A 2.5 Grid lines of curvi linear grid AZG3A

2.6 Origin of boundary conditions for AZG3A

2.7 Outline of bottom data files used for construction of bathymetry for tidal inlet of Ameland

2.8 Bathymetry on computational grid AZG3A

2.9 Outline of WAQUA grids AZG and WAW

2.10 Spatial variation of current magnitude on AZG grid for 8 Feb 2004, 20:00 hours 2.11 Spatial variation of current magnitude on WAW grid for 8 Feb 2004, 20:00 hours 2.12 Spatial variation of the water level on WAW grid for 8 Feb 2004, 20:00 hours and

dry points

2.13 Spatial variation of the water level on WAW grid for 8 Feb 2004, 20:00 hours after correction of dry points

2.14 Variation of water level and current speed and direction for 8 Feb 2004, 20:00 hours

2.17 Variation of water level and current speed and direction for 2 Jan 2005, 10:00 hours 2.18 Variation of water level and current speed and direction for 2 Jan 2005, 12:00 hours 2.19 Variation of water level and current speed and direction for 2 Jan 2005, 17:00 hours 2.20 HIRLAM wind fields for the northern part of the North Sea for the six considered

storm instants

2.21 Downscaled wind fields for the central part of the Wadden Sea for the six considered storm instants

2.22 Scatter diagram and statistical parameters of measured and computed integral wave parameters at inner buoys (uniform water level and wind field; no current)

2.23 Scatter diagram and statistical parameters of measured and computed integral wave parameters at inner buoys (water level/current from WAQUA; uniform wind field) 2.24 Scatter diagram and statistical parameters of measured and computed integral wave

parameters at inner buoys (water level/current from WAQUA; downscaled wind field)

2.25 Spatial distribution of Hm0, Tm-1,0, Tm02, directional spreading, water level and current for 8 Feb 2004, 22:30 hours (uniform water level and wind field; no current)

2.26 Spatial distribution of Hm0, Tm-1,0, Tm02, directional spreading, water level and current for 8 Feb 2004, 22:30 hours (water level/current from WAQUA; uniform wind field)

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2.29 Comparison of measured and computed energy density spectra and frequency dependent mean direction and spreading for 8 Feb 2004, 22:30 hours

2.30 Comparison of measured and computed energy density spectra and frequency dependent mean direction and spreading for 9 Feb 2004, 01:30 hours

2.31 Comparison of measured and computed energy density spectra and frequency dependent mean direction and spreading for 2 Jan 2005, 10:00 hours

2.34 Sensitivity run: Variation in wave height at the boundary 2.35 Sensitivity run: Negligence of flood current

2.36 Sensitivity run: Negligence of ebb current

2.37 Difference between downscaling based wind fields and uniform wind fields for 6 storm instants

2.38 Sensitivity run: Simulation with downscaled wind field 2.39 Sensitivity run: Increase in water level

2.40 Sensitivity run: Deactivation of triads interaction

2.41 Computed energy density, mean direction and dir. spreading spectra: triads activated and triads deactivated for 2 Jan 2005, 12:00:00

2.42 Water height in tidal inlet of Ameland and 800 m boxes around buoy locations in 2004 and 2005

2.43 Relative energy density spectra in grid points in a circle of 100 m around buoys location AZB21/AZB22 for storm events in 2004/2005

3.1 Depth profile and buoy locations in Norderneyer Seegat

3.2 Spectra for storm of 5 Februari 1999 (3:40hr) and 3 December 1999 (18:30hr) at location RIFFGAT (from WL, 2006)

3.3 Measured and computed wave spectra at RIFFGAT for 5 Feb 1999: uniform wind fields of 19 m/s from 290 ºN, resp. 260 ºN

3.4 Measured spectrum at RIFFGAT and computed wave spectra for February 1999 storm at: RIFFGAT, using regular grid, 200 m south of RIFFGAT, using regular grid , 200 m south of RIFFGAT, using curivilinear grid and 200 m north of RIFFGAT, on regular grid

3.5 Current field from PCA/NN modelling at 5 February 1999, 4:00hr (provided by R. Kaiser, Forschungsstelle Küste, Norderney) for a part of Norderneyer Seegat 3.6 Measured and computed wave spectra for February 1999 storm at RIFFGAT: no

current, current from PCA modelling.

3.7 Distribution of Hm0 for storm and extreme water level 3.8 Distribution of Tm-1,0for storm and extreme water level 3.9 Distribution of Hm0 / d for storm and extreme water level

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4.1 Lunenburg Bay, Nova Scotia, Canada

4.2 Detail map of Lunenburg Bay, including modelling domain

4.3 Spectra measured at Station D, used as boundary values for four time instants 4.4 Observed winds (magnitude and direction) and water levels in Lunenburg Bay 4.5 Simulated and observed wave spectra at three instants and at three locations D, A1

and A2

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1 Introduction

1.1 Reliable wave boundary conditions for the Wadden Sea

In compliance with the Flood Defenses Act (“Wet op de Waterkering, 1996”), the primary coastal structures must be checked every five years (2001, 2006, 2011, etc.) for the required level of protection on the basis of the Hydraulic Boundary Conditions (HBC) and the Safety Testing Regulation (VTV: Voorschrift op Toetsen op Veiligheid). These HBC must be derived anew every five years and established by the Minister of Transport, Public Works and Water Management.

There is a degree of uncertainty concerning the quality of the current HBC, in particular those for the Wadden Sea. This is because they were obtained from an inconsistent set of measurements and design values (WL, 2002). For the rest of the Dutch coast (the closed Holland Coast and the Zeeland Delta) the wave transformation model SWAN (Booij et al., 1999, SWAN homepage http://www.swan.tudelft.nl) was applied.

Presently, there is insufficient confidence in the performance of SWAN in the Wadden Sea. The available data from the Wadden Sea and from elsewhere, has not been studied sufficiently. SWAN needs to be validated, calibrated and if necessary, modified to achieve maximum performance in the Dutch Wadden Sea, using data from that area and from elsewhere.

The “Strength and Loading of Coastal Structures (SBW: Sterkte en Belasting Waterkeringen) project” (SBW, 2005) has the task of improving the quality of the models and methods used to derive the HBC to enable the managers and experts to have sufficient confidence to use these tools for the five-yearly tests. Among other activities this is achieved by performing hindcasts of storm events in the Wadden Sea or comparable tidal inlets. The hindcasts (WL, 2006; Haskoning, 2006) and the additional analyses (Alkyon, 2007a, b) provided insight in the performance of SWAN in the Wadden Sea. The studies resulted in some recommendations that have been investigated in the present study. Based on these recommendations the quality of the hindcast set of storm events in the tidal inlet of Ameland considered in WL (2006) has been improved by changing several aspects of the model set-up (as suggested by the Hydraulic Review Team, see HRT, 2006). By means of sensitivity studies unexplained results in some parts of the tidal inlets of Ameland and Norderney have been analysed.

To evaluate the performance of SWAN under conditions of combined swell and wind sea, the field case of Lunenburg Bay, a coastal embayment on the southern shore of Nova Scotia in Canada, has been considered as well.

1.2 Objective of the study

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hindcasts in Lunenburg Bay have been considered. The present study aims at the unexplained issues rather than fully re-analysing the hindcasted storm events, for which we refer to Alkyon (2007a).

1.3 Contents of the report

The set-up of the hindcast of the events considered in WL (2006) has been adapted for the tidal inlet of Ameland. These adaptations as well as the results and the analysis of some issues thereof are reported in Section 2. A brief sensitivity study has been carried out for the tidal inlet of Norderney, in order to investigate some unexplained differences between measured and computed wave conditions at the lee side of the island Norderney. The results of the sensitivity study have been reported in Section 3. Finally, the analysis of hindcast of events in Lunenburg Bay has been described in Section 4.

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2 Adaptation of hindcast and analysis of results

for tidal inlet of Ameland

2.1 Problem description

In 2003 a ray of wave buoys was deployed in the tidal inlet of Ameland, with which the wave conditions during several storms have been measured. In WL (2006) results of the first hindcast of storms at 8-9 February 2004, 1-3 January 2005 and 8-9 January 2005 have been reported. Several choices for setting up a SWAN model for this hindcast were made. After discussions with the Hydraulic Review Team (see HRT, 2006), other wave experts and performing additional analyses (Alkyon, 2007a) it appeared that some of these choices were open for improvement. In this study the set-up of the model has been adapted and new hindcasts have been performed of several instances in the storms of 8-9 February 2004 and 1-3 January 2005.

As recommended in the studies of WL (2006) and Alkyon (2007a) and by the Hydraulic Review Team (HRT, 2006) further analysis is required of the results of the improved hindcast. This includes the following sensitivities and effects on the simulated wave conditions:

1. Sensitivity to offshore boundary conditions; 2. Effect of currents;

3. Sensitivity to wind speed, wind direction and spatial variation in wind field; 4. Effect of water level on low-frequency waves;

5. Effect of three-wave interactions (triads);

6. Sensitivity to the buoy locations near the edge of a channel;

In Section 2.2 the adaptations of the model set-up for the hindcast of the two storms of February 2004 and early January 2005 have been described. The hindcast results have been reported in Section 2.3, followed in Section 2.4 by an analysis that focuses on the 6 aspects mentioned above. With respect to the first four items use has been made of the sensitivity analysis of WL/Alkyon (2007). Section 2.5 wraps up the conclusions from the analysis.

2.2 Adaptation of previous hindcasts in tidal of Ameland

The hindcasts of the storms in February 2004 and January 2005 have been adapted according to the set-up of the hindcasts performed by Haskoning (2006). In the latter study experiences gained in the study of WL (2006), hindcast procedures reported in Alkyon (2006) and recommendations of the Hydraulic Review Team (HRT, 2006) were taken into account.

Compared to the set up of the hindcast in WL (2006) the major adaptations are summarised below:

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Ameland, and from offshore of the ebb tidal delta to the Frisian coast. The offshore domain boundary has been shifted from 30 km offshore in WL (2006) to the -20 m depth contour in this study;

Offshore boundary conditions: In WL (2006) parametrical JONSWAP spectra were imposed, based on measurements at the offshore locations SON and ELD (see Figure 2.1). These locations are far away from the area of interest. More accurate results are probably obtained when the measured spectra at AZB11 and AZB12 are used;

Wind fields: Spatially varying, computed wind fields based on downscaling techniques have been applied besides uniform wind fields;

Currents: At slack tide currents have been neglected in the computations of WL (2006). In the present study the currents have been included for all tidal stages.

Convergence: The computations have fully converged, which was not true for all computations in WL (2006);

Output: Additional output has been generated for analysis purposes.

For the adaptation of the model set-up the activities described in Sections 2.2.1-2.2.7 have been carried out.

2.2.1 Choice of storm moments

The focus in the study of WL (2006) was on the possible penetration of low-frequency waves in the tidal inlet of Ameland. Therefore high water instants were considered. In Figure 2.2 and 2.3 the measured time series of the water level at NES and wind speed and direction at Lauwersoog for both storms have been given. In WL (2006) three instants for the storm of 1-3 January 2005 were considered (indicated in Figure 2.3 with vertical lines). These were a high water time instant and two instants within the same tidal cycle, one flood situation and one ebb situation. For the storm of 8-9 February 2004 only the high water instant was considered. In the present study two additional instants have been chosen (indicated in Figure 2.2 with vertical lines). In Table 2.1 for all instants the conditions are summarised in terms of wind velocity at the offshore buoy location AZB11 (from KNMI wind model based on a downscaling technique, see Section 2.2.7), water level at NES and offshore wave conditions at AZB11. The wind at AZB11 is presented in Table 2.1, because these values are more representative for the wind in the computational domain than the wind at the land station Lauwersoog.

date time (MET) tidal stage Wind speed (m/s) Wind dir. ( N) Water level (m + NAP) Hm0 (m) Tm-1,0 (s) Wave dir ( N) 08-02-2004 20h00 flood 13.5 314 1.00 4.1 7.4 300 08-02-2004 22h30 slack 16.6 325 2.60 5.3 9.5 319 09-02-2004 01h30 ebb 16.3 328 1.75 4.8 9.7 338 02-01-2005 10h00 flood 20.0 277 1.04 5.1 9.0 310 02-01-2005 12h00 slack 17.8 277 2.07 4.9 9.3 317 02-01-2005 17h00 ebb 16.3 275 1.34 4.6 9.0 326

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2.2.2 Choice of computational grids

Following the recommendations of WL/RIKZ/Alkyon/NRL (2007) a dedicated non-uniform computational grid for the tidal inlet of Ameland was developed. This grid is based on the 'Kuststrook' model for the whole Wadden Sea. The curvilinear grid of the ‘Kuststrook model’ is referred to as GridCL. For the present study a part around the tidal inlet of Ameland was taken and modified to obtain a finer resolution in the mouth of the tidal inlet. This modification was performed in two steps. In the first step the section of the Kuststrook model was refined with a factor 3 in both the x- and y- direction, followed by a shift of grid points in the mouth of the tidal inlet. Following the terminology introduced in WL/RIKZ/Alkyon/NRL (2007) the name of this grid is AZG3A. GridCL is used to determine boundary conditions for the AZG3A grid, south of the barrier islands, see Section 2.2.4. Figure 2.4 shows the outline of the grids GridCL and AZG3A and the location of the offshore wave buoys used in the winter season of 2004-2005. For legibility every fourth grid line is plotted.

The northern boundary of grid AZG3A touches the locations of the buoys AZB11 and AZB12, which provide the offshore wave boundary conditions, see next section. The southern boundary extends to the Frisian coast. The eastern boundary is located near the eastern tip of Ameland, whereas the western boundary is located just west of the island of Terschelling. The AZG3A grid used in this study slightly deviates from the grid AZG3A used in WL/RIKZ/Alkyon/NRL (2007). The main difference is its larger extent in westward direction in order to minimise boundary effects from the western boundary. An overview of the grid lines of grid AZG3A is shown in Figure 2.5. The typical resolution of this grid in the mouth of the tidal inlet and near the buoys is 60 m. Further away from this area, the average cell size gradually increases to values of about 150 m near the mainland, which is too coarse for resolving surf zone processes.

The numerical characteristics of these computational grids are summarized in Table. 2.2. Nx and Ny denote the numbers of grid cells in x- and y-direction.

Name Nx Ny % active points

GridCL 391 161 79

AZG3A 286 412 75

Table 2.2: Numerical characteristics of the SWAN computational grids.

The simulations on the AZG3A grid have typical simulation times in the order of 2.5 hours on a Pentium 3.4 GHz processor with 1 Gbyte internal memory. These simulation times are considerably faster than on the regular 100 m and 20 m grids used in WL (2006). The time required for running on the GridCL grid is in the order of a few hours.

2.2.3 SWAN model settings

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WL (2006). The most significant alteration made in bug fix A with respect to the base version 40.51 is to reduce the proportionality factor of nonlinear triad interaction from TRFAC=0.1 to 0.05, in combination with an increase in the frequency up to which triad interactions are computed. As a consequence the exaggeration of transfer of wave energy to higher frequencies by three-wave interactions is diminished in shallow areas and the wave periods are higher. This is further addressed in Section 2.4.5.

The frequency range was 0.03 Hz – 1.0 Hz with 38 frequencies and 36 directions distributed over the full circle at 10° intervals. Following the recommendations of Alkyon (2007a,b) rather strict convergence criteria were imposed. The following command was applied:

NUM STOPC 0.00 0.01 0.001 99.5 STAT mxitst=80 alfa=0.01

which means that SWAN stops the iteration process if the relative change in the local significant wave height from one iteration to the next is less than 0.01 and the curvature of the iteration curve of Hm0 normalized with Hm0 is less than 0.001:

1 0 0 1 0 ( , ) ( , ) 0.01 ( , ) n n m m n m H i j H i j H i j and 1 2 0 0 0 0 0 ( ) 0.001, 3,4, 2 n n n m m m m n m H H H H n H

These conditions must be satisfied in at least 99.5% of all wet grid points before the iterative process stops.

Following WL (2006) and Haskoning (2006) the following physical settings were applied: GEN3 WESTH

QUAD

TRIAD TRFAC=0.1 BREAKING 1 0.73

FRICTION JONSWAP CFJON=0.067

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Depth-induced wave breaking has been modelled according to Battjes and Janssen (1978) and the JONSWAP formulation for bottom friction (Hasselmann et al., 1973) has been applied.

2.2.4 Determination of wave boundary conditions

Following the procedure applied in Haskoning (2006), the wave boundary conditions for the AZG3A grid are obtained from the wave buoys AZB11 and AZB12. These buoys provide only the boundary conditions along the northern boundary of grid AZG3A and the North Sea part of the western and eastern boundary. The remaining boundary conditions are obtained from the grid GridCL, which consists of a section of the Kuststrook model enveloping the AZG3A grid. Figure 2.6 illustrates the origin of the wave boundary conditions along all boundaries of the AZG3A grid. The eastern and western boundaries receive their information from the overall grid GridCL (red lines), the blue line indicates the area that receives information from wave buoy AZB11, whereas the green line indicates the area receiving information from buoy AZB12. Between the buoys AZB11 and AZB12 information from both buoys is used (purple line). Unfortunately, for three events in 2004 no reliable information from buoy AZB12 was available. For these events, only the data from buoy AZB11 were used. This is only a minor limitation of this study since for this storm period the buoys AZB11 and AZB12 were located close to each other. Time averaging of the measured wave spectra was not applied in this study.

The wave boundary conditions for the AZG3A grid are specified as 2D-wave spectra for all boundary points. As mentioned above these spectra originate from two sources, viz. computed nest output of the grid GridCL and measured spectra obtained from the buoys AZB11 and AZB12.

The representations of measured and computed spectral information differ. The measured spectra are provided as energy density, mean wave direction and directional spreading as a function of frequency. These frequencies are linearly distributed in the interval 0.01 Hz – 0.5 Hz with a resolution of 0.01 Hz. TheSWAN spectra are given as a function of frequency and direction, where the frequencies are geometrically distributed in the interval 0.03 Hz – 1.0 Hz and the directions are steps of 10° distributed over the full circle. The measured spectra have been transformed to 2D spectra in the same format as the computed spectra. The transformation of the measured spectra to 2D spectra is performed in a number of steps to account for the abovementioned differences:

The measured energy density spectra are extended to 1.0 Hz with the same 0.01 Hz resolution using an f--4_{power law. The mean direction and directional spread at these} extra frequencies are taken equal to those at f=0.50 Hz.

The energy densities, mean directions and directional spreadings are interpolated to the frequency domain of theSWAN computations by using an energy conserving method.

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The previous four steps transform the buoy spectra to a 2D-spectrum in SWAN format.

Subsequently, these 2D-spectra are substituted in the data file with all 2D-spectra originally obtained from the GridCL grid along the boundary of the AZG3A grid. Along the northern boundary of the domain west of AZB11 the transformed AZB11 spectra are imposed. East of AZB12 the transformed AZB12 spectra are used. For the area between the buoys AZB11 and AZB12 SWAN interpolates the components of the 2D-spectra (linearly), where the

interpolation factors are proportional to the distance to either buoy. Finally, the data with all 2D-spectra is written to a data file inSWAN format to be used as spectral boundary condition

for the AZG3A grid.

2.2.5 Bathymetry

The bathymetry for the tidal inlet of Ameland and surrounding area was obtained from depth soundings performed by RIKZ in the period 1999 through 2006. These soundings were processed by RIKZ to obtain a digital representation on regular grids with a typical resolution of 20 m.

The depth values for the grid GridCL were provided together with the grid information of the Kuststrook model. For the grid AZG3A the bathymetry was obtained from various sources in order to cover the complete domain of these grids. The following sources were used:

Source 1: Tidal inlet of Ameland from 20042_;

Source 2: Data from a small coastal strip along the ‘kwelder’ of the Frisian coast on a 5

m grid based on laser altimetry measurements in 2004;

Source 3: Data for the complete Wadden Sea from 1999;

Source 4: Tidal inlet of Vlieland from 20042_;

Source 5: Bathymetry of the Kustfijn-V4 model.

The bathymetry on the AZG3A computational grids was generated hierarchically, so that for each grid point the most recent bathymetrical data was used. First, the data from Source 1 was used to cover the area around the tidal inlet of Ameland, whereas the data from Source 2 was used to cover a narrow strip along the Frisian mainland. The data from Source 2 was supplemented with 20 m data from the Source 3, despite the fact that these data were obtained in 1999. Next, data from Source 4 was used to fill further gaps. The remaining missing bottom points were taken from Source 5.

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In this process the kwelder data (Source 2) were gridded in boxes of 20 m to better reflect the size of the grid cells along the Frisian coast. This gridding consisted of computing the average value of all depth values related to grid points that lie in a box with sizes of 20 m around the point of interest. It could be argued that taking the minimum depth in a box would better reflect depth-limited wave conditions. Inspection of the differences between the minimum and average depth values in a cell revealed that in 90% of the grid cells these differences are less than 0.1 m, which is small compared to the depth values used in this study.

Figure 2.7 shows the outline of the areas covered by each data file. The names of the data files that were used to construct the bottom for the computational grids are summarised in Table A.1 in Appendix A. The combined bottom topography on the AZG3A grid is shown in Figure 2.8.

2.2.6 Water level and current fields

Introduction

The observed storm instants were simulated with current and water levels that were computed with the WAQUA Kuststrook and Wadden models. The WAQUA water levels and currents were driven both by astronomical tide and wind. Since there was no coupling between WAQUA and SWAN or with any other wave model, wave-driven set-up and currents were not included explicitly in the WAQUA computations. However, the WAQUA model is calibrated on measured water levels, which include wind- and wave-induced set-up. Consequently, the currents computed by WAQUA implicitly include wave effects, although its actual contribution is still to be determined.

For the purposes of this study a selection of the WAQUA data were provided by RIKZ on two non-overlapping curvi-linear grids covering the Amelander Zeegat. Output fields were written to data files every 30 minutes for a period of a few days around the selected storm events. The information in these files was interpolated to the non-uniform SWAN computational grids. The following sections described the procedure to prepare these fields for the SWAN model.

WAQUA grids

Existing WAQUA model results for the hindcast periods were available on two non-overlapping grids, which were taken from the Kuststrook model. A fine grid provided the currents in an area around the tidal inlet of Ameland and up to the coast of the Frisian mainland. A coarser grid covering a larger part of the Wadden Sea enveloped this fine grid. The outline of these grids is shown in Figure 2.9. In this figure each fourth grid line is shown.

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However, test computations indicated that along the boundary between the two grids the current and water level data at the boundary points in both grids were interpolated in some way between zero and non-zero data values. This is illustrated in the Figures 2.10 and 2.11, which show the spatial variation of the current velocity and water level on the grids AZG and WAW respectively for the situation of 8 February 2004, 20:00 hours. Evidently, these interpolated data values were introduced in the selection procedure applied by RIKZ to generate WAQUA data for selected output areas.

These interpolated data along the boundary of the two grids were removed by ‘cutting’ small strips of data points from each grid before combining them into one set of points for each selected moment of time.

Treatment of dry points

The WAQUA model has a procedure for handling dry points that conflicts with the procedure in SWAN to handle dry points. Some grid points may become dry or wet as the water level changes. In the case a grid point is dry, the u- and v- component of the current velocities are set to zero in the WAQUA computation, and the water level is taken as the land height plus a few centimeters (the actual value depends on the model settings of the WAQUA simulation). Using these water levels as input for a SWAN simulation would cause shallow grid points in a SWAN grid to become wet with a small water depth, whereas they should be treated as dry points. Whenever this happens this will distort the SWAN computation. It is therefore needed to identify these points and to replace the water level in such a point with the water level from the nearest non-dry WAQUA grid point.

In WL (2006) a manual procedure was applied to replace the water levels in dry WAQUA points by extrapolating from the nearest active WAQUA grid point. Such a procedure is time consuming and difficult to reproduce, and it is difficult to account for the spatial variation of the water level along a water-land boundary. To avoid these problems, an automated iterative procedure (coded in MATLAB) was developed to replace the ‘dry’ water levels by the water level in the nearest ‘active’ water level in the WAQUA grid. The first step in this procedure is to identify the dry points in the set of WAQUA grid points on the detailed WAW grid. Such points have zero values for the u- and v-components of the current velocity. This results in blocks and strips of points along the boundaries of the Wadden islands, the Frisian coast and sand banks. An example of such a set of points is shown in Figure 2.12 for the situation of 8 February 2004, 20:00 hours. The dry points are marked with black circles.

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Application of this procedure resulted in some deviating results along the Frisian coast, where water levels were determined that were considerably higher than the overall water level in the Wadden Sea. Close inspection of the results indicated that this area consists of a pool of water that was discharging its contents through a narrow channel. As a consequence these points were treated as active grid points. It could be argued to treat this area as a dry area, which would result in a different (lower) water level for these points. However, it was deemed more conservative with respect to wave conditions at the sea defenses to consider these as wet points.

The current speed was set to zero in all dry points.

Interpolation

The conversion of the WAQUA current and water level data to the SWAN grids was performed on the basis of a triangulation of the set of coordinates resulting from the combined WAQUA grid points. Next, for each point in a SWAN computational grid, a search was carried out to find the enveloping triangle. Finally, bi-linear interpolation in each triangle was applied to obtain the u- and v-components and water level in each computational grid point of the SWAN grid AZG3A. The spatial variation of the current magnitude and direction, and water level for all six hindcast events are shown in the Figures 2.14 - 2.19.

2.2.7 Wind fields

The simulations of the observed storm events were performed with a constant uniform wind speed and direction over the whole computational domain. For the senstitivity runs on the effect of the use of a spatially varying wind field, however, more detailed wind information was required.

These spatially varying wind fields were derived from HIRLAM data on a 11 km grid. These wind fields were provided by RIKZ. A downscaling technique was applied to improve the spatial resolution of these wind fields by including the effect of local surface roughness on wind flow. The downscaling was performed with the KNMI downscaling software version 2.3. The spatial resolution of the down-scaled wind field was 250 m. Detailed information on the principles behind the downscaling can be found in Verkaik (2006) and Verkaik et al. (2006).

Figures 2.20 and 2.21 show the spatial variation of the wind speed and direction of the HIRLAM and downscaled wind fields for the six storm events, respectively. The sheltering effect of the Wadden islands is clearly visible in Figure 2.21, which is obtained after applying the downscaling technique and shows the wind speed at a relatively fine grid. The latter figure shows also some obvious anomalies in the wind speed at the north-western tip of Terschelling and near the western part of Friesland. For the three instants of the February 2004 storm higher wind speeds are obtained locally. These anomalies are probably related to some internal correction in the downscaling procedure. For the present study, however, these anomalies are outside the area of interest and will not be considered.

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single location to validate their method. Since their method is based on well-established physical considerations, it generally provides plausible results. This has been verified e.g. by comparing with results from the model of Tayor and Lee (1984), see WL/Alkyon (2007, Figure 3.22). Nevertheless, the presence of anomalies indicates that the corresponding results of the present study (wave conditions computed using downscaled wind fields) should be considered with care.

To make the model input to SWAN on the uniform and spatially varying wind fields consistent, the speed and direction obtained from the down-scaled HIRLAM wind field at the location of buoy AZB11 was imposed as a uniform wind field (see also Table 2.1). The wind speed and direction at this location are hardly affected by the relatively high surface roughness of the Wadden islands.

2.3 Results from hindcast of storm events

In this section the results of the hindcast have been presented. For the six instants during the two storm events three sets of computations were carried out, with increasing level of detail of the model input of water level, current and wind:

Uniform wind and water level field and no currents (indicated as ‘ccu’);

Uniform wind fields and spatially varying water level and current fields (indicated as ‘flu’);

Spatially varying wind, water level and current fields (indicated as ‘fld’).

The water level and current fields have been determined with WAQUA (see Section 2.2.6). When a constant water level is applied, the value at station NES is used (see Table 2.1). As mentioned in Section 2.2.7 the spatially varying wind fields are determined with the KNMI downscaling software. The values for the uniform wind fields are obtained from the down-scaled wind field at the offshore wave buoy AZB11.

For the comparison with measured wave data, 1D and 2D spectra and integral wave parameters at the buoy locations have been generated as output of the SWAN computations. For further analysis this output was also generated along a number of rays. Furthermore for a number of integral wave parameters block files have been generated, such that the spatial distribution of the wave parameters can be analysed.

For each of the three sets of computations mentioned above, a statistical analysis has been performed, comparing measured and computed integral wave parameters Hm0, Tm01, Tm02, Tm-1,0, mean wave direction and directional spreading. For different classes the bias, standard deviation and correlation coefficient have been determined as well as least squares regression lines y=ax+b and y=cx. The definitions of the statistical parameters are:

x mean value of the measured values;

y

mean of the simulated data values; bias bias =

y x

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Std standard deviation: 1 2 1 1 N i i N i std y x BIAS

r coefficient of linear correlation: 1

1/ 2 1/ 2 2 2 1 1 N i i i N N i i i i

x

x y

y

r

x

y

The relative bias and relative standard deviation are obtained by dividing the bias and standard deviation by the mean value of the measured data.

The following classes have been considered and contain the wave data as mentioned : All buoys: wave data at all buoy locations and for all time instants;

Inner buoys: wave data at all buoy locations excluding the offshore buoys AZB11 and AZB12 and for all time instants;

Single buoys: wave data at a single buoy for all time instants;

Single instants: wave data at all buoy locations excluding the offshore buoys AZB11 and AZB12 for one single time instant.

The statistical parameters for the class ‘Inner buoys’ have been listed in Appendix A. Scatter plots for all parameters for this class have been given in Figures 2.22-2.24. For the ‘ccu’ conditions (uniform wind and water level and no current) the statistical parameters are comparable to those in the previous hindcast of the storms (compare Alkyon, 2007a, Table 4.1 and Figure 4.7). This result is not surprising, since the major change compared to the computations by WL (2006), which have been analysed by Alkyon (2007a), is the application of buoy spectra from AZB11 and AZB12 at the offshore boundary. In Section 2.4.1 it is shown that the offshore conditions hardly affect the results at the inner buoys. For all inner buoys and all events SWAN overestimates the measured significant wave heights with 20%. However, this overestimation is caused entirely due to the relative bias of 40-50% at the buoys AZB4x and AZB5x, the standard deviation being of the same order, i.e. 30-35%. Average over all inner buoys the mean periods are underestimated with 5-10%. The relative bias is largest at the locations in the tidal inlet (AZB2x and AZB3x), being 10-15%. Remarkable are the wide spread in predicted wave direction and the strong underpredictions of the directional spreading. The bias in the latter is 30% on average, with a standard deviation of 20%.

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Further improvements are obtained by imposing a spatially varying wind field, which is more realistic than a uniform wind field (comparing ‘flu’ with ‘fld), but the relative change to current incorporation is minor. The statistical values of the mean wave periods and directional parameters are comparable for the ‘flu’ and ‘fld’ conditions. Only for the wave buoys in the tidal basin (AZB4x and AZB5x) the overprediction of the significant wave height decreases. The bias decreases to 7-10%, whereas the standard deviation is still 30%. The spatial distribution of wave variables Hm0, Tm-1,0, Tm02 (all including the mean wave direction) and directional spreading have been visualised for the three classes of computations. For the sets ‘flu’ and ‘fld’ the current and water level fields have been visualised as well. For the event of 8 February 2004, 22h30 these plots have been given in Figure 2.25-2.27. The wave field on the North Sea side of the barrier islands is characterised by large wave heights and large wave periods, both being strongly reduced on the coasts of the barrier islands and on the ebb tidal delta. Wind sea is generated over the region behind the barrier islands, reaching significant wave heights of up to about 1 m. In WL/Alkyon (2007) spatial plots of the wave height over depth ratio were presented. North of the barrier islands and along the mainland coast the strongly depth-limited conditions have been observed. The more westerly oriented wind directions in the storm of 2 January 2005 resulted in wave fields with similar characteristics as for the NW storm of 8 February 2004. A more detailed comparison is made by comparing the measured and computed 1D spectra at all the buoy locations. In Figures 2.28-2.33 both the measured (if available) and computed energy spectra, as well as mean wave direction and directional spreading as a function of frequency, are given for the three sets of computations for the six instants considered. Especially inside the tidal inlet of Ameland (AZB4x and AZB5x) significant improvements of the SWAN predictions are obtained, when currents are taken into account in the computation (compare ‘ccu’ with ‘flu’). A detailed wind field, obtained by downscaling techniques, leads to a minor improvement of the computational results at the buoy locations (compare ‘flu’ with ’fld’). The effect of incorporating currents in the simulations has been discussed in Section 2.4.2. The difference in effects of uniform wind fields and more detailed, downscaled wind fields is discussed in Section 2.4.4.

2.4 Analysis of hindcast results

The generated computational results described in the previous section have been used to quantify the sensitivity of the offshore boundary conditions (Section 2.4.1), the effect of currents (Section 2.4.2), the sensitivity of wind variations (Section 2.4.3), the effect of water level on low-frequency waves, the effect of triads (Section 2.4.5) and the sensitivity of the buoy locations (Section 2.4.6).

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the first four topics mentioned in Section 2.1, i.e. the sensitivity of the model input in terms of wave boundary conditions, currents, wind and water level to the wave conditions at the buoy locations.

2.4.1 Sensitivity of offshore boundary conditions

The sensitivity study of WL/Alkyon (2007) considered the variation of wave conditions imposed on the offshore model boundary. The sensitivity of wave conditions to variations in the wave height (Hm0 +/- 10%), mean wave period (Tm-1,0 +/- 10%), mean wave direction (+/- 10o) and directional spreading (+/- 10%) imposed at the North Sea boundary were investigated.

In WL/Alkyon (2007) spatial plots of the difference between a particular sensitivity run and the base case (8 February 2004, 22h30) were shown, in terms of wave height, mean period, mean direction and directional spreading. Furthermore, the results of integral parameters along output curve D are presented for all eight sensitivity runs. Curve D runs over the ebb tidal delta, through the main tidal channel and over the salt marches to the mainland shore, and gives insight in the penetration of offshore waves into the Wadden Sea and to the mainland shore. Curve D follows the ray formed by the buoys.

For illustration only the spatial plots showing the effect of increasing the offshore wave height by +10% are presented in Figure 2.34a and 2.34b. Furthermore, the variation of integral wave parameters along curve D is shown in Figure 2.34c and 2.34d, when the offshore significant wave height is changed by -10% respectively +10%. These Figures are identical to Figures 4.7 in WL/Alkyon (2007).

Figures 2.34a and 2.34b show that the effect of an increase in the offshore significant wave height is limited to the region offshore of the ebb tidal delta. Figures 2.34c and 2.34d show that over the ebb tidal delta, the wave height over depth ratio reaches a value of 0.4. Due to the existence of saturated conditions over the ebb tidal delta, both increases and decreases in the significant wave height in the offshore have no effect on the wave field. Regarding variations in mean wave period, Figures 4.8a-d in WL/Alkyon (2007) show that the changes made at the boundary persist somewhat further into the Wadden Sea than was the case with the variation in wave height. Nonetheless, after passing through the tidal inlet, the changes made to the mean wave period at the boundary are overshadowed by the decrease in wave period due to local wind sea growth. Similarly, variations in directional properties at the offshore boundary are overshadowed by the directional properties of the wind sea locally generated in the Wadden Sea.

2.4.2 Effect of currents

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Flood current

In WL/Alkyon (2007) the effect of neglecting a current from the ‘flu’ simulation for one flood condition (8 February 2004) and one ebb condition was investigated. For both conditions the water level is spatially varying. Figures 2.35a shows that the negligence of the flood current field in the simulation leads to increases in significant wave heights and mean periods in the main tidal channel in excess of 10%. Note that Figure 2.35 is similar to Figure 4.15 in WL/Alkyon (2007). Moving towards the shore, the resulting difference in the wave height appears to reduce, whereas the difference in mean period persists to the coast. Figure 2.35b shows that the mean wave direction and directional spreading are also strongly affected by the presence of the current. Figure 2.35c presents the evolution of integral parameters along the output curve D, which is running through the main tidal channel. This figure confirms the strong increase in significant wave height and mean period and the strong change in mean wave direction in the tidal channel due to the negligence of the flood current.

The strong influence of the current on the wave energy and period is also illustrated in Figure 2.35d, where the frequency spectra (in terms of absolute frequency) at regular intervals along Curve D are presented. It is seen that between 10000 m and 15000 m along Curve D, the frequency spectra are strongly affected, presumably due to the combined effect of Doppler shifting and the current-induced refraction of low-frequency waves out of the channel (refer Figure 2.35b). In that same region the buoys AZB4x and AZB5x are located. The effects of the current at these buoy locations is significant. Comparing Figures 2.28a (‘ccu’) and 2.28b (‘flu’) for 8 February 2004, 20h00 and Figures 2.31a (‘ccu’) and 2.31b (‘flu’) for 2 January 2005, 10h00 shows that both the spectral shape and the amount of energy is much better predicted when currents are included in the computation. The directional parameters are also significantly better predicted, due to the effect of current refraction.

Slack tide

Comparison of the computed and measured spectra at buoy locations AZB4x and AZB5x at slack tide (8 February 2004, 22h30 and 2 January 2005, 12h00) shows a significant effect of the current. The current is mostly wind-driven and reaches maxima in the channel of 1 m/s (see Figure 2.26c). A better prediction of the wave propagation direction due to the inclusion of current refraction, leads to better predictions of the wave frequency spectra (compare Figures 2.29a and 2.29b, and Figures 2.32a en 2.32b) when currents are included in the computation at slack tide. Also the directional parameters are much better predicted when a current is included in the computations.

Ebb current

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Figure 2.36c presents the evolution of these quantities along the output curve D through the main tidal channel, showing similar, but opposite effects to the flood current case presented above. Again it is seen that conditions near the coast become saturated (Hm0/depth around 0.4), explaining the insensitivity of the significant wave heights here (vertical dashed line indicates the location at 0 m N.A.P near the Frisian dike). Figure 2.36d presents the progression of frequency spectra (in terms of absolute frequency) along Curve D, showing that at 10 000 m to 15 000 m along this curve the wave period is reduced by the ebb current, presumably due to current-induced refraction of waves towards the channel centre. The same behaviour is observed at locations AZB4x and AZB5x (compare Figures 2.30a (‘ccu’) and 2.30b (‘flu’) for 9 February 2004, 01h30 and Figures 2.33a (‘ccu’) and 2.33b (‘flu’) for 2 January 2005, 17h00). However, comparing with the measured spectra the inclusion of the ebb current leads to a strong overprediction of the total amount of wave energy at these locations. The peak of the computed spectrum was (Doppler) shifted towards the correct frequency for the February 2004 event. However, for January 2005 the measured and computed peak frequencies were equal when the ebb current was neglected (see Figure 2.33a), whereas the measured peak frequencies were overestimated when the current was included (Figure 2.33b).

Overall we conclude that a flood and ebb current have a significant effect on the wave conditions at the buoy locations, especially those in the Wadden Sea. Compared to measurements, inclusion of an ebb current does not always result in better predictions of the wave energy spectra. This might be due to the present implementation of wave-current interaction in SWAN. Note that a wave-opposing current is generally more vertically sheared than a wave-following current. However, in SWAN the effect of the vertical distribution of the horizontal current velocity is not taken into account. Inclusion of this effect may lead to better results for vertically-sheared currents. The vertical shear may be one cause for the observed deficiencies, but other causes may be responsible as well. A study to identify these causes should be carried out.

2.4.3 Sensitivity of wind variations

In the hindcast studies of WL (2006), Royal Haskoning (2006) and WL/Alkyon (2007), a discrepancy was found between simulated and observed wave fields locally generated over short dimensionless fetches. These inaccuracies may affect simulated conditions at the mainland coast. One possible source of this error is that the wind input to the model is inaccurate.

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effect of the wind fields in the tidal inlet for the storm of 2 January 2005. As mentioned in Section 2.2.7 an increased wind speed is obtained at the north-western tip of Terschelling, which is probably related to some internal correction in the downscaling procedure.

Variations in wind speed and direction in the uniform wind fields were shown to have a large impact on the wave conditions (height, period and direction) in the Wadden Sea interior (see Figures 4.18-4.21 in WL/Alkyon, 2007). The use of a spatially varying downscaled wind field results in a reduction of wave height of up to 20% at the lee of the barrier islands for 8 February 2004, 22h30, but this influence dies away in the background wind sea growth before the primary sea defense is reached, see Figure 2.38a and 2.38b. The spatial variation of integral wave parameters along curves E and F, running from the lee side of Ameland respectively Terschelling to the mainland, has been presented in Figures 2.38c and 2.38d. Note that the spatially varying downscaled wind field differs from the uniform wind field also in terms of wind direction. The resulting difference in wave direction alters the wave direction at the sea defense by an equal amount.

The use of a spatially varying wind field only changes the results obtained with a uniform wind field at the locations AZB41 and AZB51. Especially at AZB51 the significant wave height and mean wave period decrease with almost 10% for the storm of 8 February 2004. For the western storm of 2 January 2005 the difference between the downscaled and uniform wind field also stretches into the tidal inlet. The effect on the spectra at AZB31 and AZB32 are negligible (see Figures 2.31-2.33, ‘flu’ vs. ‘fld’).

2.4.4 Effect of water level on low-frequency waves

In the historical storm events penetration of North Sea waves into the Wadden Sea is limited to the inlet. This is clearly illustrated in Figure 2.27 for 8 February 2004, 22h30 (slack tide). At the buoy locations AZB4x and AZB5x low-frequency energy corresponding to the North Sea waves is observed neither in the measurements, nor in the computational results. The water levels are so low that the ebb tidal delta acts as an effective energy filter. To investigate the effect of the water level on low-frequency waves not a historical but a hypothetical 1/4000 year storm was considered in WL/Alkyon (2007). This storm features an offshore wave condition of Hm0 = 9.4 m and Tp = 18.0 s from NW, with a wind of U10 = 34.0 m/s also from NW. The uniform water level used in this simulation is +4.7 m NAP. Currents were not included.

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Figures 2.39c and 2.39d present the integral parameters and frequency spectra along the output curve D. Figure 2.39c shows that along the length of Curve D the wave height to depth ratio remains unaltered (reaching 0.4 at the mainland coast), even though the water depth is increased by a constant 1 m. This indicates that even at this higher water level, conditions at the coast are still saturated. Furthermore, Figure 2.39d shows that in the base case - with a water level of +4.7 m NAP - the low-frequency offshore waves (spectral peak at 0.06 Hz at x = 0 m) do not penetrate much beyond x = 10 000 m, and that this result is not altered much with the 1 m increase in water level. Therefore, it can be concluded that the strong increase in wave height found here is due to the greater depth for the locally-generated, depth-limited wind sea, and not due to the greater penetration of North Sea waves into the Wadden Sea.

2.4.5 Effect of three-wave interactions

In Figures 2.24-2.26 (scatterplots) the wave periods in SWAN are clearly underestimated by approximately 1 s at locations AZB21, AZB31 and AZB32. This observation is made for all of the three situations considered (‘ccu’, ‘flu’ and ‘fld’) and is therefore insensitive to incorporation of currents or spatially varying wind fields. The computed wave energy spectra at those locations are typically double peaked, having a significant amount of energy at the low frequencies, corresponding to the North Sea waves, and a comparable amount of energy at the first harmonic. The shape of the measured spectra is more single peaked. This observation might indicate that SWAN exaggerates the effect of three-wave interactions. Earlier studies in the Westerschelde (Svašek, 2003) and in front of the Dutch coast (WL/Alkyon, 2003) already showed that the present implementation of triads in SWAN, based on the Lumped Triad Approximation (LTA) of Eldeberky (1996), lead to overpredictions of the second harmonic, and therefore underpredictions of the wave periods. The exaggeration of the triad interactions has also been recognized in bugfix A of SWAN’s present version 40.51 (see Section 2.2.3).

Alkyon (2007a) showed for the storm event of 8 February 2004 (22h30) that on the ebb-tidal delta and in the shallow regions of the ebb-tidal inlet surf breaking and triads are dominant over other processes. As expected, deactivating triads led to an increase of the mean wave period measures of more than 10% for Tm-1,0. In the present study the simulation for 2 January 2005, 12h00 (‘flu’), which is at slack tide, is considered. The effect of deactivating triads resulted in a mild increase of the significant wave height over the ebb-tidal delta. The effect on the mean wave period is more significant (see Figure 2.40a). In the surf zone of the beaches north of the barrier islands, over the ebb tidal delta and in the tidal inlet the increase of the wave period is more than 10%. In the same regions also the directional spreading decreases with 5% and even more than 10% in regions with strong breaking (Figure 2.40b). Within the Wadden Sea other processes dominate over triads and its effect becomes less predominant (see Alkyon, 2007a).

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given. Whereas the significant wave height slightly decreases when triads are not included, a significant increase has been obtained for the mean wave periods. Though still underpredicting the wave period, the prediction is significantly better. Application of SWAN 40.51 including bugfix A would have led to wave period predictions between those obtained above (CYT and CNT).

Hm0[m] Tm-1,0 [s] Tm01[s]

M CYT CNT M CYT CNT M CYT CNT

AZB21 - 1.92 1.79 - 6.18 7.64 - 4.95 5.77

AZB22 - 1.91 1.80 - 6.11 7.63 - 4.88 5.72

AZB31 1.88 1.93 1.83 7.43 6.11 6.95 5.71 4.92 5.31

AZB32 1.99 1.85 1.75 7.19 5.87 6.58 5.72 4.76 5.03

Table 2.3 Measured (M) and computed (with triads, CYT and without triads, CNT) wave parameters at 4 buoy locations for 2 January 2005, 12h00.

The predictions for the wave periods might be improved by deactivating the presently implemented form of the triads, but then an essential process is not included within the modelling of waves. On the one hand, the presently implemented LTA formulation does not represent the physics accurately and leads to overprediction of high frequency energy. On the other hand it is well known that three wave interactions play a role in shallow regions, such as the areas around the buoys AZB2x and AZB3x. In order to obtain more accurate predictions, the triad formulation should be improved considerably.

2.4.6 Sensitivity of the buoy locations near the edge of a channel

In the SWAN computations the buoy locations remain unchanged during a storm. In reality wind and currents displace the buoy from its anchor position. The buoy will effectively feel another depth and current at its displaced position. The variation in wave conditions is negligible near depth uniform locations, such as buoys AZB11 and AZB12. The other buoys are located along the main channel in the tidal inlet of Ameland, either close to the ebb-tidal delta (AZB21 and AZB22), along the edge of the channel (AZB31 and AZB32; AZB41 and AZB51 in 2004), in the deepest part of the channel (AZB41 and AZB42 in 2005) or on the tidal flat or shallow part of the channel (AZB51 and AZB52 in 2005). In Figure 2.42 the buoy locations in 2004 (in red) and 2005 (in blue) are given on the bathymetry in the tidal inlet of Ameland. The black boxes denote 800 m square boxes around the buoys, for which the variation of wave energy spectra has been investigated in more detail.

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terms of the SWAN hotfiles. Considering absolute frequency spectra would not have led to different conclusions.

In 2004 the wave buoys where placed around the 10 m + NAP depth contour. Consequently, they were located on the edges of the channel, where the depth gradients are significant. Due to bottom refraction the low-frequency components ( < 0.15 Hz) computed at AZB21 and AZB31 show variations in variance density up to 20% (see Figure 2.43a). The variation at higher frequencies ( > 0.2 Hz) is smaller, except for the ebb situation (third time instant). Due to tunneling effects in the ebb situation all wave components are forced towards the center of the channel. This is clearly illustrated in Figure 2.45 for buoy locations AZB41 and AZB42. The amount of wave energy increases towards the center of the channel. The spatial variation of the current induced spatial variations at the higher frequencies. Towards the deeper part of the channel the current is stronger and the resulting amount of wave energy increases. The changes in energy level are most significant in AZB31, AZB41 and AZB51 and reach values for the relative change up to 40%.

Figure 2.42 shows that the depth variation around the buoy locations for the storms considered in 2005 was smaller than for those of 2004, except for AZB31 and AZB32. Also AZB51 in 2004 and AZB52 in 2005 were positioned at almost the same location. Consequently, depth refraction and the ambient current cause less spatial variation in the wave energy spectra compared to 2004. At the locations where variations are to be expected, these variations are similar is in 2004.

Incidentally, significant variations in energy level are obtained when all grid points in a radius of 100 m are considered. The variations in the resulting integral parameters Hm0 and Tm-1,0 are significantly smaller. For most of the locations and instants in the storm events the variation in Hm0 is less than 3% and in Tm-1,0 less than 2%. For those combinations of location and time for which this is not the case the minimum and maximum relative variation, i.e. grid point versus buoy location, in significant wave height and wave period (obtained at the grid points given in brackets) are listed in Table 2.4. Note that 7 of the 10 combinations are an ebb situation. The other three combinations are in the locations AZB21 and AZB31 for instants in the 2004 storm. The buoys are located on the relatively steep channel edge.

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Hm0 (%) Tm-1,0 (%)

location date Min max min max

AZB21 8-02-2004, 20h00 -2.7 (1) 5.6 (6) -1.5 (1) 3.1 (6) AZB21 8-02-2004, 22h30 -2.6 (1) 5.4 (6) -1.8 (1) 3.5 (6) AZB21 9-02-2004, 01h30 -1.9 (1) 4.1 (6) -1.3 (1) 2.8 (6) AZB21 2-01-2005, 17h00 -3.4 (1) 4.1 (7) -1.8 (1) 2.2 (7) AZB31 8-02-2004, 20h00 -4.1 (6) 2.9 (2) -1.4 (9) 1.1 (1) AZB31 9-02-2004, 01h30 -6.6 (7) 3.7 (6) -4.4 (6) 3.4 (2) AZB41 9-02-2004, 01h30 -8.6 (1) 8.4 (5) -1.0 (1) 1.4 (3) AZB41 2-01-2005, 17h00 -6.0 (2) 4.8 (6) -2.1 (2) 1.1 (6) AZB42 2-01-2005, 17h00 -5.4 (1) 4.4 (6) -1.1 (1) 0.6 (6) AZB51 9-02-2004, 01h30 -6.4 (3) 2.7 (1) -2.7 (3) 0.2 (1)

Table 2.4 Minimum and maximum relative variation of computed solution for Hm0 and Tm-1,0in grid points in radius of 100m around buoy location (in parentheses grid point for which minimum/maximum occurs)

2.5 Conclusions

For the storms of 8-9 February 2004 and 2 January 2005 new hindcasts have been carried out, focussing on the tidal inlet of Ameland. Based on results and experiences from earlier hindcasts of these storms the model set up (grid, convergence criterion) and model input (offshore boundary condition based on local wave buoy measurements, downscaled wind fields, spatially varying water level field) have been adapted. Partly using the results from a sensitivity study (WL/Alkyon, 2007) the following conclusions can be drawn:

For the conditions of uniform wind and water level and no current (‘ccu’) the statistical parameters obtained in the present hindcast are similar to those obtained by Alkyon (2007a), which were based on the computations in the previous hindcast by WL (2006). In general SWAN performs good. The mean wave period is underestimated on the ebb-tidal delta and in the tidal inlet. The significant wave height is overpredicted and the directional spreading is underpredicted in the tidal basin of the Wadden Sea.

Wave conditions in the tidal inlet of Ameland and the tidal basin of the Wadden Sea, south of Ameland and Terschelling are insensitive to variations in wave boundary conditions imposed on the North Sea side of the barrier islands in typical storm conditions and even in a hypothetical 1/4000 year event. This insensitivity is due to the saturated conditions that exist in the surf zone on the ebb tidal delta, in which wave energy is significantly dissipated.

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computational results, whereas an opposing current sometimes led to even worse predictions.

Variations in wind speed and direction to a uniform wind field have a large local impact on the wave conditions (height, period and direction) in the Wadden Sea interior (“fld” vs. “flu” cases). The use of a spatially varying downscaled wind field results in a reduction of wave heights of up to 20% at the lee of the barrier islands, but this influence dies away in the background wind sea growth before the primary sea defense is reached.

Wave conditions were found to change significantly due to an increase in water level during an extreme NW storm. The increase in wave height and wave period is in no significant way due to the entering of low-frequency energy from the North Sea, but due to the higher asymptote value of the depth-limited wind sea growth, and the fact that the saturated conditions allow a higher wave height.

During historical storm events surf breaking and triads are dominant over other processes on the ebb-tidal delta and in the shallow regions of the tidal inlet. Deactivating triads leads to an increase of the mean wave period measures of more than 10% for Tm-1,0. Within the Wadden Sea other processes dominate over triads and its effect becomes less predominant. The wave period predictions at the buoy locations on the ebb-tidal delta and in the shallow regions of the tidal inlet strongly improve when triads are deactivated in the computations. However, an important process is then neglected. Therefore, the present triad formulation should be improved.

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3 Analysis of hindcast results for tidal inlet of

Norderney

3.1 Problem description

WL (2006) performed hindcasts of two storm events in the tidal inlet of Norderney with SWAN version 40.51. The model settings were taken identical to those applied by Kaiser and Niemeyer (2001), who used version 40.01.3_{The overall conclusion was that the} performance of SWAN was good. Mismatches between measured and computed wave conditions in the tidal inlet of Norderney were mainly attributed to the quality of the input data, i.e. bathymetry, wind and current fields. However, for the location RIFFGAT, indicated in Figure 3.1 together with the other buoy locations, these differences could not be explained from the results of the performed computations. Figure 3.2 shows the measured and computed energy density and wave direction as a function of frequency at RIFFGAT for the storms of February 5, 1999 at 03h40 (upper panel) and December, 3, 1999 at 18h30 (lower panel). These figures are taken from WL (2006, Figure 2.7d and 2.8f respectively). SWAN predicts the high-frequency part of the spectrum fairly well. For frequencies lower than 0.3 Hz SWAN predicts hardly any wave energy, whereas the measured spectrum contains most energy in the range between 0.2 Hz and 0.3 Hz for the storm in February 1999. This mismatch was also observed by Kaiser and Niemeyer (2001), using SWAN version 40.01.

Note that these differences do not occur for the storm of December 3, 1999, although the storm characteristics are similar, except for the wind speed. In both storms the wind direction was from West-northwest, with a large amount of swell energy offshore, high storm surges and strong wave breaking over the shoals of the ebb-tidal delta. The water level (WL), wind direction and speed ( _w and U10) and the offshore wave conditions at the offshore location SEE (see Figure 3.1) are given in Table 3.1. The wind in the December storm is significantly stronger and the differences in wave direction at the peak frequency, denoted as peak, at location SEE is 30 .

date time WL [m MSL] _{[ N]}w U10 [m/s] Hm0 [m] Tp [s] [ N]peak 5/02/99 03h40 3.4 290 19.0 6.0 14.3 330 3/12/99 18h30 3.2 290 25.7 5.9 13.3 300

Table 3.1 Characteristics of 2 storm events around Norderney.

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As already remarked in WL (2006) the wind speed considered here is higher than that reported in Kaiser and Niemeyer (2001); Instead of being based on measurements at the wind station at Norderney the new value is based on recalculations of the German Weather Service for open sea conditions (Ralf Kaiser, personal communication).

3.2 Sensitivity analysis

In this section the observed mismatch in RIFFGAT for the storm of 5 February 1999 will be investigated by performing a sensitivity analysis. The SWAN settings in the sensitivity computations are similar to those applied in WL (2006). Several aspects have been considered, viz. uncertainty in the wind, offshore boundary condition, bathymetry and currents. In WL (2006) two computational grids were considered: a regular and a curvilinear grid (cf. Figures 2.1 and 2.3 in WL, 2006). Both were considered also in the present sensitivity study.

Wind input

In order to check whether a change in wind direction would improve the comparison between the computational results and measurements at the RIFFGAT location the regular grid hindcast has been recomputed using an uniform wind field with direction 260 ºN (change of 30 degrees southward, see Table 3.1). Figure 3.3 compares the regular grid model results at RIFFGAT considering a uniform wind field with direction 260 ºN with the original results, which are obtained with a wind direction of 290 ºN. Although the increase in fetch at RIFFGAT produces an increase in the peak wave energy, it does not produce the desired shift of the peak frequency towards lower frequencies.

Comparison of the computed results for the December storm and the February storm (Figure 3.2) shows that imposing a 35% stronger wind (25.7 m/s versus 19m/s) leads to a significant increase in energy level at the peak frequency of a factor 2, but only a minor shift towards lower frequencies (Tp = 4s versus Tp = 3.3s).

Offshore boundary conditions

Comparison of the computational results for both storms also indicates that imposing different offshore boundary conditions does neither lead to the desired shift of the energy density towards lower frequencies. The difference in offshore boundary condition considers a shift in wind direction from 330 N to 300 N. In WL (2006) the penetration of North Sea waves was found to be limited to the tidal gorge in between the islands. Therefore the effect of the offshore boundary conditions at RIFFGAT can be neglected for the two considered storm events.

Location of the buoys

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RIFFGAT the peak frequency is smaller and the energy level at 0.2 Hz is significant. These results show the importance of knowing the exact buoy location at the moment being considered in the hindcast of the storm.

Effect of currents

The results presented in WL (2006) were computed without taking currents into account, following the approach of Kaiser and Niemeyer (2001). To study the effect of a current, Kaiser (Forschungsstelle Küste, Norderney) provided a current field obtained from PCA/NN modelling. For details about PCA/NN modelling, see Herman et al. (2006). The hydrodynamic processes in the area in and around the tidal inlet of Norderney are simulated on a curvilinear grid with a resolution of approximately 50 m with a 2DH version of the Delft3D model. The model is driven by the interpolated 1-hourly water level time series from the HIPOCAS dataset (Weiße et al., 2003) applied as open boundary conditions and by wind fields obtained from a wind atlas produced by the German Weather Service (DWD). Wave effects are not included in the flow modelling. As a consequence, wave-driven set-up and the wave-induced part of the currents are not determined.

The current field for 5 February 1999, 04h00 has been applied in the SWAN computations and is shown in Figure 3.5. The current field is driven by the tide, as well as by the wind. This explains the change in current direction in the lee side of the island near RIFFGAT. Note that the obtained current fields were derived from boundary conditions (HIPOCAS-Dataset) which are statistically correct but were not able to reproduce single events with the same performance as measured boundary conditions, especially during storms (Kaiser, personal communications). Since our goal is to investigate the sensitivity of a current, the current prediction does not necessarily have to be 100% accurate.

The current field in Figure 3.5 has been imposed in the SWAN computations. According to Figure 3.6 this results in a significant change in energy density. Both the energy level at the peak, as well as the position of the peak are well predicted. This result is in line with SWAN results in WL (2006) and Alkyon (2007a, b). In these studies it was concluded that at several locations the effect of currents is important.

3.3 Wave conditions for extreme wind and water level

For both storms in 1999 waves from the North Sea mainly dissipated on the ebb tidal delta and hardly penetrated into the tidal basin of the Norderneyer Seegat. At none of the buoy locations inside the tidal basin long wave energy from the North Sea was measured. In WL (2006) spatial distributions of the significant wave height and peak period were obtained from the SWAN computations. From these spatial distributions it was concluded that for the observed water levels (between 3 and 3.5 m, see Table 3.1) the North Sea waves dissipated on the ebb-tidal delta or on the tidal flats just south of the gorge in between the islands after having refracted out of the channel. Whether this conclusion is also valid for an extreme situation is not a priori evident.