Analysis SWAN hindcasts Wadden Sea, Oosterschelde and Slotermeer

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A2085

Prepared for:

Deltares

Analysis of SWAN hindcasts

SBW Waddenzee

Wadden Sea, Oosterschelde

And Slotermeer

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Executive’s summary

General

In compliance with the Dutch Flood Defences Act (‘Wet op de Waterkering, 1995’), the primary coastal structures must be monitored every five years (2001, 2006, 2011, etc.) for the required level of protection. This assessment is based on the Hydraulic Boundary Conditions (HBC) and the Safety Assessment Regulation (VTV: Voorschrift op Toetsen op Veiligheid). These HBC are derived every five years and approved by the Minister of Transport, Public Works and Water Management. The spectral wind wave model SWAN (Booij et al. 1999) plays a key role in the estimation of these HBC. Since some uncertainty remains about the reliability of SWAN for application to the geographically complex area of the Wadden Sea, a number of activities have been initiated under the project ‘SBW-Waddenzee’ to improve the model.

Problem statement and study aim

Recent hindcast studies with SWAN for the Amelander Zeegat (WL & Alkyon, 2007; Royal Haskoning, 2007) and the outer delta of the Oosterschelde estuary (Svasek, 2007) revealed three points of unsatisfactory accuracy in the model. These are (a) the underprediction of low-frequency wave energy in the tidal inlet of the Amelander Zeegat and the Oosterschelde Estuary, (b) inaccurate model results in the presence of ambient current in the Amelander tidal inlet and (c) underprediction of wave height and period measures in the depth-limited conditions in the Wadden Sea interior. In the present study, these three problem areas were analysed in order to improve the performance of SWAN on these points. For each of these, the following was determined: the accuracy of SWAN predictions by comparison with measurements; the characteristics of the situations with the largest prediction errors; and the importance of various source terms in determining the predicted wave conditions.

Underprediciton of low-frequency wave energy

Results of hindcast studies with the SWAN wave model in the Amelander Zeegat and the Oosterschelde estuary were analyzed to detect the cause of under-prediction of low-frequency wave energy. For the Oosterschelde six events from December 2001 and December 2003 were used. For the Amelander Zeegat six events from winter storms in February 2004 and January 2005 were used. In this analysis the normalized source term magnitudes in the frequency range 0.03-0.2 Hz were computed to detect the processes affecting the low frequencies most. In addition, an investigation was performed to determine the effect of refraction and other physical processes modelled in SWAN on the low frequency wave energy. The analysis was performed by making plots of the variation of low frequency wave energy, the ratio of two spectral periods to track the position of low-frequency wave energy, transect plots and wave spectra. The physical processes included in the analysis of the low-frequency energy include the magnitude of refraction speed c_θ (which was decreased by 10%), replacing the JONSWAP bottom friction term with the Madsen friction term, deactivating the triads, using the Komen third-generation physics and replacing the DIA with the exact WRT method. The latter type of analysis was only performed on the 1d-transect taken from the ebb-tidal delta in the Amelander Zeegat.

The results for the first type of situation showed that triad interactions and quadruplet interactions have a relatively small effect on the prediction of the low frequency energy. They also showed that replacing the default formulation for dissipation by bottom friction by the formulation due to Madsen et al. (1988) lead to deterioration in the accuracy of the predictions of low frequency energy but demonstrating that bottom friction is important. Similarly, replacing the formulation for dissipation by whitecapping

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due to Van der Westhuysen (2007) by that due to Komen et al. (1984) leads to a deterioration in the results but demonstrates the importance of whitecapping. However, possibly the most interesting result was obtained by looking at the development of the low frequency energy over a section passing from a shallow bank into a channel. There is a significant and sudden drop in the low frequency energy. It therefore seems likely that this sudden drop is related to propagation effects. It is expected that channel refraction plays an important role here, although reducing the magnitude of this term in the equations only has a small effect on the prediction of low frequency energy at the measurement buoys. The explanation may be that the channel refraction is so strong that by the time the buoys are reached the energy is removed from the channel anyway. In nature, the effects of linear refraction may be counteracted by diffraction or non-linear effects.

Model errors in ambient current

An error trend analysis was performed to determine the conditions leading to prediction errors in the presence of currents, and a modified source term for whitecapping in opposing currents was tested. This analysis was based on the 31 storms considered in the study by Royal Haskoning (2007). These investigations show the clearest error trend with the in-line current, showing an over-prediction of wave height in opposing current. No clear error trend can be found with non-dimensional wave number, water depth or wave height to depth ratio. Similarly there is no clear link between the prediction error and the wind speed, water level or buoy position.

The wave height is slightly over-predicted in the tidal inlet of the Amelander Zeegat. These over-predictions are more severe when the wave steepness is higher. For the waves further into the Wadden Sea the waves are over-predicted in opposing currents and under-predicted in following currents. There may be a relationship between the sensitivity to the current direction and the sensitivity to the wave steepness.

The adapted whitecapping formulation of WL (2007) lead to deterioration in the predictions particularly in opposing currents, showing that whitecapping has an important influence on the predictions.

Depth-limited wave growth

The source terms playing a role in depth-limited situations were determined and a sensitivity study was performed to determine the effect of different source terms in the action balance on the predicted wave heights in depth-limited situations.

Test computations were carried out for the tidal flats in the Wadden Sea and for the Slotermeer. Storm events that were nearly stationary and where high wave height to water depth ratios were selected investigation. These showed that the predicted wave height to depth ratio is generally 10% lower than the measured wave height to depth ratios, even when errors in the prediction of the water level are accounted for.

Estimates of the source term magnitudes show that the deep water source terms (wind input, whitecapping, quadruplets) are significantly larger than the shallow water source terms (breaking, bottom friction and triads). However, this does not necessarily mean that the shallow water terms are unimportant because the deep water source terms tend to be in balance.

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As found for the situation with currents, there is a strong correlation between the prediction error and the wave steepness. However, for depth-limited wave growth, the wave height is over-predicted in situations with low steepness and underestimated for situations with high steepness. The correlations between the prediction error and non-dimensional wave number, non-non-dimensional depth and Ursell number are all low. The wave height is slightly more underestimated in shallow conditions.

Using whitecapping due to Komen et al. (1984) gives even lower predictions of the wave height to depth ratio, again demonstrating the importance of the way whitecapping is represented. Similarly, describing dissipation by bottom friction according to Madsen et al. (1988) leads to a significant deterioration in the results, illustrating the importance of bottom friction. Using a different value (0.8 instead of 0.73) for the critical wave height to depth ratio, gamma, in the Battjes and Janssen (1978) surf breaking term reduces the predicted error, indicating the importance of this source term in depth-limited situations. However, it can not be concluded that this value is better in general without carrying out a thorough calibration in a wide range of types of situation.

The bi-modal measured spectra in the Slotermeer suggest that triad interactions are relevant for depth limited cases. The secondary measured peak at twice the peak frequency is not reproduced by SWAN.

Conclusion

In summary, the following source terms and effects were found to play an important role in one or more types of situation:

• Whitecapping including the way it is influenced by currents. It also influences the low frequency energy;

• Bottom friction in complex coastal areas (low-frequency wave energy) and depth-limited wave growth;

• Wave breaking in situations with depth-limited wave growth;

• Triad interactions in some situations with depth-limited wave growth;

• Wave refraction and other (non-linear) propagation effects in coastal situations with banks and channels, particularly for the low frequency energy.

Main recommendations

The results of the analysis of the under-prediction of low-frequency wave energy lead to the following recommendations:

• Analyse in more detail the propagation effects in the ebb-tidal deltas, such as the Oosterschelde estuary or the Amelander Zeegat. Attention must be given to the effect of uncertainties in the bathymetry, the influence of currents, non-linear propagation effects and the role of diffraction. The conditions selected for this study can be used as a starting point.

• The method to analyse the direct effect of each source term on integral wave parameters should be applied to other Amelander Zeegat cases to determine which processes are responsible for changes in the spectral shape at frequencies lower than 0.15 Hz.

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The results of the computations and analysis of the effect of currents lead to the following recommendations:

• The hindcast of Royal Haskoning (2007) should be redone using accurate current and water level fields to verify the findings on the role of currents on wave propagation in tidal inlets. In general, hindcast studies in areas with spatially varying currents and water levels need to be carried out with accurate current and water level fields, especially in areas where shallow water wave phenomena are hindcast.

• To further investigate the energy dissipation in currents. In particular, the WBJ whitecapping formulation should be further developed to allow the growth of waves on currents. However, these investigations should not be limited to this particular model concept.

Based on the results and conclusions of the analysis of finite-depth depth-limited wave conditions, it is recommended to:

• Investigate the modelling of steepness-related and depth-induced wave breaking in finite-depth situations.

• The modelling of triads in finite-depth situations should be improved such that it is able to reproduce the second harmonic peak.

• The hindcast of Royal Haskoning (2007) should be redone using accurate current and water level fields to verify the findings on finite-depth situations in the Wadden Sea.

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List of tables

2.1 Summary of main characteristics of the 6 hindcast events for the Oosterschelde. 2.2 Summary of main characteristics of the 6 hindcast events for the Amelander

Zeegat of the WL& Alkyon hindcast.

2.3 Location of wave measurement buoys in the Amelander Zeegat.

2.4 Wind and water level conditions for 31 selected hindcast moments of the Royal Haskoning hindcast (2007).

2.5 Name, date and time (h CET) of Slotermeer wave model calibration case, with the local water depth, the measured SL-29 wind and observed integral wave

parameters.

2.6 Summary of types of model computations for the different study phases.

3.1 Summary of combinations of non-linear source term settings.

4.1 Statistical parameters of integral wave parameters for the SWAN computations in the Amelander Zeegat. SWAN computations without versus SWAN computations with corrected water levels

4.2 Summary of run codes for SWAN computations to investigate current effects. 4.3 Statistical parameters of integral wave parameters for the SWAN computation in

the Amelander Zeegat based on the buoys in the tidal channel. Observations versus SWAN computations with uncorrected water levels.

4.4 Statistical parameters of integral wave parameters for the SWAN computation in the Amelander Zeegat based on the buoys in the tidal channel. Observations versus SWAN computations with uncorrected water levels and modified WBJ whitecapping dissipation.

5.1 Summary of SWAN model settings for the sensitivity analysis. 5.2 Summary of SWAN model settings for addition simulations

5.3 Summary of observed and computed significant wave height Hm0 and spectral

period Tm-1,0 for station SL29 in the Slotermeer for SWAN runs with various model

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List of figures

2.1 Computational grids and location of wave buoys used in the Oosterschelde hindcast by Svasek.

2.2 Computational grids and location of wave buoys used in the hindcast of the Amelander Zeegat by WL & Alkyon.

3.1 Geographical variation of integral wave parameters in the Oosterschelde estuary for the storm of 26 December 2001, 9:00 hours.

3.4 Normalized source term magnitudes in the Oosterschelde estuary for the storm of 26 December 2001, 9:00 hours. Computed for the frequency range 0.03 – 0.2Hz. 3.5 Normalized source term magnitudes in the Oosterschelde estuary for the storm of

26 December 2001, 12:00 hours. Computed for the frequency range 0.03 – 0.2Hz. 3.6 Normalized source term magnitudes in the Oosterschelde estuary for the storm of

23 December 2003, 2:30 hours. Computed for the frequency range 0.03 – 0.2Hz. 3.7 Variation of normalized low-frequency significant wave height, normalized

spectral periods and normalized source term magnitudes in the Oosterschelde transect for the storm of 26 December 2001, 9:00 hours. Computed for the frequency range 0.03 – 0.2Hz.

3.8 Variation of normalized low-frequency significant wave height, normalized spectral periods and normalized source term magnitudes in the Oosterschelde transect for the storm of 26 December 2001, 12:00 hours. Computed for the frequency range 0.03 – 0.2Hz.

3.9 Variation of normalized low-frequency significant wave height, normalized spectral periods and normalized source term magnitudes in the Oosterschelde transect for the storm of 23 December 2003, 2:30 hours. Computed for the frequency range 0.03 – 0.2Hz.

3.10 Geographical variation of integral wave parameters in the Amelander Zeegat for the storm of 22 Jan. 2005, 10:00 hours.

3.13 Normalized source term magnitudes in the Amelander Zeegat for the storm of 2 Jan. 2005, 10:00 hours. Computed for the frequency range 0.03 – 0.2Hz.

3.16 Variation of normalized wave heights, spectral periods and normalized source term magnitudes in the Amelander Zeegat transect for the storm of 2 Jan. 2005, 10:00 hours. Frequency range: 0.03-0.20 Hz.

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3.19 Spatial variation of low frequency wave energy and ratio of spectral periods in the Oosterschelde for the storm of 26 Dec. 2001, 9:00 hours. Relative differences wrt effect of reduced refraction. Frequency range 0.03-0.15 Hz.

3.22 Comparison of computed and measured spectra at the buoy locations in the Oosterschelde for the storm of 26 Dec. 2001, 9:00 hours. Sensitivity wrt effect of reduced refraction.

3.25 Spatial variation low frequency wave energy and ratio of spectral periods in the Amelander Zeegat for the storm of 2 Jan. 2005, 10:00 hours. Relative differences wrt effect of reduced refraction.

3.28 Comparison of computed and measured spectra at the buoy locations in the Amelander Zeegat for the storm of 2 Jan. 2005, 10:00 hours. Sensitivity wrt effect of reduced refraction.

3.31 Spatial variation of low frequency wave energy and ratio of spectral periods in the Oosterschelde for the storm of 26 Dec. 2001, 9:00 hours. Relative differences wrt effect of Madsen bottom friction. Frequency range 0.03-0.15 Hz.

3.34 Comparison of computed and measured spectra at the buoy locations in the Oosterschelde for the storm of 26 Dec. 2001, 9:00 hours. Sensitivity wrt effect of Madsen bottom friction.

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3.37 Spatial variation low frequency wave energy and ratio of spectral periods in the Amelander Zeegat for the storm of 2 Jan. 2005, 10:00 hours. Relative differences wrt effect of Madsen bottom friction.

3.40 Comparison of computed and measured spectra at the buoy locations in the Amelander Zeegat for the storm of 2 Jan. 2005, 10:00 hours. Sensitivity wrt effect of Madsen bottom friction.

3.43 Spatial variation of low frequency wave energy and ratio of spectral periods in the Oosterschelde for the storm of 26 Dec. 2001, 9:00 hours. Relative differences wrt effect of Komen 3G physics. Frequency range 0.03-0.15 Hz.

3.44 Spatial variation of low frequency wave energy and ratio of spectral periods in the Oosterschelde for the storm of 26 Dec. 2001, 12:00 hours. Relative differences wrt effect of KOmen 3G physics. Frequency range 0.03-0.15 Hz.

3.45 Spatial variation of low frequency wave energy and ratio of spectral periods in the Oosterschelde for the storm of 23 Dec. 2003, 2:30 hours. Relative differences wrt effect of Komen 3G physics. Frequency range 0.03-0.15 Hz.

3.46 Comparison of computed and measured spectra at the buoy locations in the Oosterschelde for the storm of 26 Dec. 2001, 9:00 hours. Sensitivity wrt effect of Komen 3G physics.

3.49 Spatial variation low frequency wave energy and ratio of spectral periods in the Amelander Zeegat for the storm of 2 Jan. 2005, 10:00 hours. Relative differences wrt effect of Komen 3G physics.

3.52 Comparison of computed and measured spectra at the buoy locations in the Amelander Zeegat for the storm of 2 Jan. 2005, 10:00 hours. Sensitivity wrt effect of Komen 3G physics.

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3.55 Spatial variation of low frequency wave energy and ratio of spectral periods in the Oosterschelde for the storm of 26 Dec. 2001, 9:00 hours. Relative differences wrt effect of deactivating triads. Frequency range 0.03-0.15 Hz.

3.58 Comparison of computed and measured spectra at the buoy locations in the Oosterschelde for the storm of 26 Dec. 2001, 9:00 hours. Sensitivity wrt effect of deactivating triads.

3.61 Spatial variation low frequency wave energy and ratio of spectral periods in the Amelander Zeegat for the storm of 2 Jan. 2005, 10:00 hours. Relative differences wrt effect of deactivating triads.

3.64 Comparison of computed and measured spectra at the buoy locations in the Amelander Zeegat for the storm of 2 Jan. 2005, 10:00 hours. Sensitivity wrt effect of deactivating triads.

3.67 Location and depth variation of 1D-transect in the Amelander Zeegat.

3.68 Comparison of integral wave parameters along 1D-transect in the Amelander Zeegat. Peak period 8s. Reference settings: DIA and triads off. Comparison with WRT with WAM scaling and triads off.

3.69 Comparison of integral wave parameters along 1D-transect in the Amelander Zeegat. Peak period 8s. Reference settings: DIA and triads on. Comparison with WRT with WAM scaling and triads on.

3.70 Comparison of integral wave parameters along 1D-transect in the Amelander Zeegat. Peak period 8s. Reference settings: DIA and triads off. Comparison with WRT with full shallow water scaling and triads off.

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3.71 Comparison of integral wave parameters along 1D-transect in the Amelander Zeegat,. Peak period 8s. Reference settings: DIA and triads on. Comparison with WRT with full shallow water scaling and triads on.

3.72 Comparison of frequency spectra at 9 locations along the 1D-transect in the Amelander Zeegat. Peak period 8s. Reference: DIA and triads off. Comparison with WRT with WAM scaling and triads off.

3.73 Comparison of frequency spectra at 9 locations along the 1D-transect in the Amelander Zeegat. Peak period 8s. Reference: DIA and triads on. Comparison with WRT with WAM scaling and triads on.

3.74 Comparison of frequency spectra at 9 locations along the 1D-transect in the Amelander Zeegat. Peak period 8s. Reference: DIA and triads off. Comparison with WRT with full shallow water scaling and triads off.

3.76 Comparison of integral wave parameters along 1D-transect in the Amelander Zeegat. Peak period 12s. Reference settings: DIA and triads off. Comparison with WRT with WAM scaling and triads off.

3.77 Comparison of integral wave parameters along 1D-transect in the Amelander Zeegat. Peak period 12s. Reference settings: DIA and triads on. Comparison with WRT with WAM scaling and triads on.

3.78 Comparison of integral wave parameters along 1D-transect in the Amelander Zeegat. Peak period 12s. Reference settings: DIA and triads off. Comparison with WRT with full shallow water scaling and triads off.

3.79 Comparison of integral wave parameters along 1D-transect in the Amelander Zeegat,. Peak period 12s. Reference settings: DIA and triads on. Comparison with WRT with full shallow water scaling and triads on.

3.80 Comparison of frequency spectra at 9 locations along the 1D-transect in the Amelander Zeegat. Peak period 12s. Reference: DIA and triads off. Comparison with WRT with WAM scaling and triads off.

3.82 Comparison of frequency spectra at 9 locations along the 1D-transect in the Amelander Zeegat. Peak period 12s. Reference: DIA and triads off. Comparison with WRT with full shallow water scaling and triads off.

3.84 Spatial variation of low frequency wave energy and ratio of spectral periods in the Oosterschelde for the storm of 26 Dec. 2001, 9:00 hours. Relative differences wrt effect of deactivating currents. Frequency range 0.03-0.15 Hz.

3.87 Comparison of computed and measured spectra at the buoy locations in the Oosterschelde for the storm of 26 Dec. 2001, 9:00 hours. Sensitivity wrt effect of deactivating currents.

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3.90 Variation of depth and integral wave parameters along Oosterschelde transect and change in wave height and period due to source terms. Storm of 26 Dec. 2001, 9:00 hours. Frequency range 0.03-0.1 Hz.

3.93 Variation of computed frequency spectra along Oosterschelde transect and comparison with observed spectrum at station OS4. Storm of 26 Dec. 2001, 9:00 hours.

4.1 Comparison of integral wave parameters in the Amelander Zeegat. Observations versus SWAN RHK hindcast. Selection criterion: buoys in the Wadden Sea.

4.2 Comparison of integral wave parameters in the Amelander Zeegat. Observations versus SWAN with corrected water levels. Selection criterion: buoys in the Wadden Sea.

4.3 Comparison of integral wave parameters in the Amelander Zeegat. Observations versus SWAN RHK hindcast. Selection criterion: buoys on tidal flats in the Wadden Sea (AZB41, AZB51, AZB61 and AZB62).

4.4 Comparison of integral wave parameters in the Amelander Zeegat. Observations versus SWAN with corrected water levels. Selection criterion: buoys on tidal flats in the Wadden Sea (AZB41, AZB51, AZB61 and AZB62)

4.5 Comparison of integral wave parameters in the Amelander Zeegat. Observations versus SWAN RHK hindcast. Selection criterion: buoys in tidal channel (AZB31, AZB32, AZB42 and AZB52).

4.6 Comparison of integral wave parameters in the Amelander Zeegat. Observations versus SWAN with deactivated currents. Selection criterion: buoys in tidal channel (AZB31, AZB32, AZB42 and AZB52).

4.7 Comparison of integral wave parameters in the Amelander Zeegat. Observations versus SWAN RHK hindcast. Selection criterion: following currents and buoys in tidal channel (AZB31, AZB32, AZB42 and AZB52).

4.8 Comparison of integral wave parameters in the Amelander Zeegat. Observations versus SWAN RHK hindcast. Selection criterion: opposing currents and buoys in tidal channel (AZB31, AZB32, AZB42 and AZB52).

4.9 Relative error of computed integral wave parameters in the Amelander Zeegat as a function of wave steepness s=Hm0/L. Observations versus RHK hindcast with

uncorrected water levels.

4.10 Relative error of computed integral wave parameters in the Amelander Zeegat as a function of dimensionless water depth kd. Observations versus RHK hindcast with uncorrected water levels.

4.11 Relative error of computed integral wave parameters in the Amelander Zeegat as a function of dimensionless water depth δ=gd/U10

2

. Observations versus RHK hindcast with uncorrected water levels.

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4.12 Relative error of computed integral wave parameters in the Amelander Zeegat as a function of wave height over depth ratio Hm0/d. Observations versus RHK

hindcast with uncorrected water levels.

4.13 Relative error of computed integral wave parameters in the Amelander Zeegat as a function of in-line current speed. Observations versus RHK hindcast with

uncorrected water levels.

4.14 Relative error of computed integral wave parameters in the Amelander Zeegat as a function of wind speed U₁₀. Observations versus RHK hindcast with uncorrected water levels.

4.15 Relative error of computed integral wave parameters in the Amelander Zeegat as a function of water level at station Nes. Observations versus RHK hindcast with uncorrected water levels.

4.16 Relative error of computed integral wave parameters in the Amelander Zeegat as a function of buoy number. Observations versus RHK hindcast with uncorrected water levels.

4.17 Comparison of integral wave parameters in the Amelander Zeegat. RHK SWAN hindcast versus SWAN hindcast with WBJ whitecapping. Uncorrected water levels and buoys in tidal channel (AZB31, AZB32, AZB42 and AZB52).

4.18 Comparison of integral wave parameters in the Amelander Zeegat. Observations versus SWAN hindcast with WBJ whitecapping. Uncorrected water levels and buoys in tidal channel (AZB31, AZB32, AZB42 and AZB52).

4.19 Comparison of integral wave parameters in the Amelander Zeegat. Observations versus SWAN hindcast with WBJ whitecapping. Following currents, uncorrected water levels and buoys in tidal channel (AZB31, AZB32, AZB42 and AZB52). 4.20 Comparison of integral wave parameters in the Amelander Zeegat. Observations

versus SWAN hindcast with WBJ whitecapping. Opposing currents, uncorrected water levels and buoys in tidal channel (AZB31, AZB32, AZB42 and AZB52). 4.21 Relative error of integral wave parameters in the Amelander Zeegat as a function

of the in-line current speed. Observations versus SWAN hindcast with uncorrected water levels. Buoys in tidal channel (AZB31, AZB32, AZB42 and AZB52).

5.1 Observed Hm0/d ratios at the buoys AZB41, AZB51, AZB61 and AZB62 for all storm moments of the Royal Haskoning hindcast.

5.2 Spatial variation of significant wave height Hm0, spectral period Tm-1,0, mean wave

direction Dir and wave height to depth ratio Hm0/d in the Amelander Zeegat for

the storm of 11 January 2007, 22:00 hours. Location of output transect indicated with a black line.

the storm of 18 January 2007, 17:20 hours. Location of output transect indicated with a black line.

the storm of 18 March 2007, 15:40 hours. Location of output transect indicated with a black line.

5.5 Spatial variation of normalized source term magnitudes in the Amelander Zeegat for the storm of 11 January 2007, 22:00 hours. Location of output transect

indicated with a black line.

5.6 Spatial variation of normalized source term magnitudes in the Amelander Zeegat for the storm of 18 January 2007, 17:20 hours. Location of output transect

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5.7 Spatial variation of normalized source term magnitudes in the Amelander Zeegat for the storm of 18 March 2007, 15:40 hours. Location of output transect indicated with a black line.

5.8 Spatial variation of wave parameters, wave height over depth ratio and normalized source term magnitudes along the transect in Wadden Sea for the storm of 11 January 2007, 22:00 hours.

5.9 Spatial variation of wave parameters, wave height over depth ratio and normalized source term magnitudes along the transect in Wadden Sea for the storm of 18 January 2007, 17:20 hours.

5.10 Spatial variation of wave parameters, wave height over depth ratio and normalized source term magnitudes along the transect in Wadden Sea for the storm of 18 March 2007, 15:40 hours.

5.11 Variation of integral wave parameters in the Slotermeer for the storm of 26 Febr. 2002, 14:00 hours. Location of station SL29 (black/yellow circle) and upwind output transect indicated (black line).

5.12 Variation of integral wave parameters in the Slotermeer for the storm of 27 Oct. 2002, 15:00 hours. Location of station SL29 (black/yellow circle) and upwind output transect indicated (black line).

5.13 Variation of integral wave parameters in the Slotermeer for the storm of 18 Jan. 2007, 19:00 hours. Location of station SL29 (black/yellow circle) and upwind output transect indicated (black line).

5.14 Spatial variation of normalized source term magnitudes in the Slotermeer for the storm of 26 Feb. 2002, 14:00 hours. Location of station SL29 (black/yellow circle) and upwind output transect indicated (black line).

5.15 Spatial variation of normalized source term magnitudes in the Slotermeer for the storm of 27 Oct. 2002, 15:00 hours. Location of station SL29 (black/yellow circle) and upwind output transect indicated (black line).

5.16 Spatial variation of normalized source term magnitudes in the Slotermeer for the storm of 18 Jan. 2007, 19:00 hours. Location of station SL29 (black/yellow circle) and upwind output transect indicated (black line).

5.17 Variation of significant wave height Hm0, spectral period Tm-1,0, normalized source

term magnitudes and changes in wave height and wave period in the Slotermeer for the storm of 26 Feb. 2002, 14:00 hours.

term magnitudes and changes in wave height and wave period in the Slotermeer for the storm of 27 Oct. 2002, 15:00 hours.

term magnitudes and changes in wave height and wave period in the Slotermeer for the storm of 18 Jan. 2007, 15:00 hours.

5.20 Relative error of wave height over depth ratio H_m0/d in the Amelander Zeegat as a function of dimensionless parameters. Observations versus SWAN hindcast with corrected water levels. Buoys on shallow tidal flats (AZB41, AZB51, AZB61 and AZB62).

5.21 Comparison of observed and computed integral wave parameters in the

Amelander Zeegat based on SWAN computations with corrected water levels and various model settings. Buoys on tidal flats (AZB41, AZB51, AZB61 and AZB62). 5.22 Relative error of wave height over depth ratio Hm0/d in the Amelander Zeegat as

a function of dimensionless parameters. Observations versus SWAN computations with corrected water levels and gamma=0.8. Buoys on shallow tidal flats (AZB41, AZB51, AZB61 and AZB62).

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5.23 Comparison of integral wave parameters in the Wadden Sea. OBSS (Averaged measured spectra) versus CUR (SWAN: corrected water levels) and observed Hm0/d

ratio as a function of various dimensionless parameters.

5.24 Comparison of integral wave parameters in the Wadden Sea. OBSS (Averaged measured spectra) versus GA8 (SWAN: Gamma=0.8) and observed Hm0/d ratio as a

function of various dimensionless parameters.

5.25 Comparison of computed and measured frequency spectra in the Slotermeer at SL29 for the storm of 27 Oct. 2002, 15:00 hours. Default settings and effect of various model settings.

5.26 Comparison of computed and measured frequency spectra in the Slotermeer at station SL29 for the storm of 27 Oct. 2002, 15:00 hours. SWAN computations using default settings and various model settings.

5.27 Comparison of integral wave parameters for fetch-limited wave growth along the 1D-transect in the Slotermeer. SWAN with DIA method versus SWAN with WRT method for computing the non-linear four-wave interactions.

5.28 Comparison of computed frequency spectra along the 1D-transect in the Slotermeer. SWAN with DIA method versus SWAN with WRT method for computing the non-linear four-wave interactions.

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1 Introduction

1.1 SBW project background and problem statement

In compliance with the Dutch Flood Defences Act ("Wet op de Waterkering, 1995"), the primary coastal structures must be monitored every five years (2001, 2006, 2011, etc.) for the required level of protection. This assessment is based on the Hydraulic Boundary Conditions (HBC) and the Safety Assessment Regulation (VTV: Voorschrift op Toetsen op Veiligheid). These HBC are derived every five years and approved by the Minister of Transport, Public Works and Water Management.

The HBC are used to subject the sea defences to a stepwise assessment ranging from "simple" to "advanced" tests. During these assessments so-called "knowledge vacuums" are encountered. The result may be that the assessment cannot be completed and sections of the sea defence are labelled "geen oordeel" (no judgement; safety level unknown), which is an undesirable situation. Another possibility may be that sea defences are erroneously pass or fail the assessment.

Because of this problem of a "knowledge vacuum" (kennisleemte) with respect to the assessment of the safety of flood defences, the overall SBW ("Strength and Loading of Water Defences (SBW: Sterkte en Belasting Waterkeringen)) project has the following general objective:

"To fill the most important knowledge vacuums in order to achieve a better estimate of the safety against flooding of the primary flood defences."

As part of this larger project, the subproject SBW-Waddenzee was started in 2006. The starting point is the observation that there is uncertainty concerning the quality of the HBC which are an important input into the assessment, in particular those for the Wadden Sea. This is because they were obtained from an inconsistent set of

measurements and design values (WL, 2002), while for the rest of the Dutch coast (the closed Holland Coast and the Zeeland Delta) they have been determined with a probabilistic method, in which offshore wave statistics are transformed to nearshore locations, For the latter the wave model SWAN (Booij et al. 1999) has been applied. There is insufficient confidence in the wave model SWAN (initially mainly regarding the swell penetration) to use it to obtain reliable boundary conditions in the Wadden Sea at present. In addition to initially recognized problems with respect to swell penetration, the subproject sets out to determine the general suitability of SWAN in the Wadden Sea and to specify the improvements required to produce reliable HBC in the Wadden Sea.

The objective of the SBW-Waddenzee project is therefore to

"Verify and where possible improve the quality of the models and methods so that in 2011 and beyond better HBC can be calculated."

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The path toward meeting this objective is laid out in a Plan of Action which describes a step by step approach of performing hindcasts of storm events in the Wadden Sea and other relevant areas, analysis of the results, and sensitivity and uncertainty analyses. Despite recent and ongoing measurement campaigns in the Dutch part of the Wadden Sea, the storm events are scarce, and information about the performance of the wave model in relevant areas is highly valued.

1.2 Problem statement

In the context of the SBW Wadden Sea project, recent hindcast studies in the Amelander Zeegat (WL & Alkyon, 2007; Royal Haskoning, 2007) and the outer delta of the

Oosterschelde estuary (Svasek, 2007) revealed three points of unsatisfactory accuracy in SWAN. Firstly, it was found that inshore of the ebb tidal delta, SWAN strongly

underestimates low-frequency spectral components. The underestimation of these components may have important consequences for the penetration of wave energy into the tidal inlets between the barriers islands of the Wadden Sea, and for wave conditions along their coastlines. Secondly, the hindcast study of Royal Haskoning (2007) showed that, in the tidal inlet of the Amelander Zeegat, SWAN both overestimates significant wave height and period measures during (wave opposing) ebb current conditions, and also underestimates these parameters in (wave following) flood conditions. Thirdly, the hindcast study by Royal Haskoning (2007) showed that SWAN strongly underestimates significant wave heights and mean periods over the tidal flats in front of the Frisian coast. This is a point of specific concern, since sensitivity studies undertaken during in 2007 (Alkyon 2007a,b; WL & Alkyon, 2007) revealed that wave conditions in the Wadden Sea interior are locally generated by wind, and are strongly determined by depth-limited wave growth in this region. Since the underestimation of wave height and mean periods here would result in a non-conservative estimate for the design of the primary sea defences, it is essential that the performance of SWAN be corrected on this point.

Observations by Bottema (2007) in the Slotermeer, suggest that SWAN under-estimates the predicted significant wave height in depth-limited situations. This under-prediction may have the same cause as the under-estimation of wave heights in the Wadden Sea. It is therefore of interest to include the Slotermeer data in the present analysis. It is noted that additional information on depth-limited wave conditions can also be obtained from the detailed measurements in Lake George, Australia, (e.g, Young and Babanin, 2007). To limit the scope of this study, only results of hindcasts performed in the Dutch waters were analyzed, notwithstanding the fact that the data from Lake George could add useful insights. The link with the Lake George data was made in Deltares (2008).

Some of these discrepancies might be attributed to errors in the observations. For example, there are some doubts regarding the reliability of the observations taken over the tidal flats in front of the Frisian coast. However, In a recent study, Deltares (2008) found that the magnitude of measurement errors of wave buoys deployed in shallow water (depths less than 2 m) is acceptable. Another error source is the specification of the boundary conditions driving the SWAN model for a specific storm case. Despite efforts to specify these conditions as well as possible, it is still a non-negligible source of errors on model outcomes. However, the discrepancies with measurements are consistent in various hindcast studies and it is therefore expected that a significant contribution to them can be attributed to errors in the representation of physical processes. Possible causes of erroneous model results include inaccurate propagation of the wave energy in

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current fields or over complex tidal inlet bathymetries, inaccurate transfer of energy from the wind to the waves, incorrect dissipation of energy, or erroneous modelling of nonlinear wave-wave interactions. A careful analysis of the relative contribution of the various model components to model-observation discrepancies is required to direct further efforts in the improvement of SWAN in the Wadden Sea.

As a first step to identify critical aspects of model performance in the coastal zone, various alternative model settings were applied for situations with current and situations where the wave height is depth-limited.. The changes in the settings included both deactivation of currents, bottom friction or triads in SWAN (non- simulataneously), and changes in the representation of physical processes applied, such as the Madsen et al. (1988) bottom friction, the Komen et al. (1984) third-generation physics or quadruplets. In addition, some parameters in the modelling of refraction, surf breaking or quadruplet interactions (as modelled by the DIA) were varied. These sensitivity computations do not amount to a complete systematic sensitivity analysis, but do serve as an exploratory first step to identify critical parts of the SWAN model.

1.3 Objective

The objective of the work is to identify the causes of the recently identified discrepancies between SWAN model results and observations in hindcast studies in the Oosterschelde estuary, the Amelander Zeegat and the Slotermeer. The results of this investigation will be used to develop further activities within the SBW Wadden Sea project.

1.4 Approach

The analysis of the hindcast results in this study were conducted in three parts, each focussing on one of the three aspects of poor model performance. The three study parts are referred to with the numbers 1, 2 and 3, in combination with the letters A, B, C to denote sub-items.

The first part addresses the under-prediction of low-frequency wave energy as found in hindcast studies in the Amelander Zeegat (Royal Haskoning, 2007) and Oosterschelde (Svasek Hydraulics, 2007). The following aspects are considered: the effect of refraction (1A), the magnitude of physical processes (1B), the effect of non-linear wave-wave interactions (1C).

The second part addresses the effect of currents on the computed wave conditions in the Amelander Zeegat. This includes an investigation into the performance of the adapted whitecapping formulation of WL (2007) based on Ris and Holthuijsen (1996) featuring enhanced dissipation in counter-currents (2A) and an error analysis to pinpoint possible causes of prediction errors (2B) of SWAN in the presence of currents.

The third part addresses the under-estimation of wave heights in depth-limited wave situations in the Wadden Sea. In this phase the following aspects were be investigated: the magnitude of physical processes (3A); an error analysis to pinpoint possible causes of prediction errors (3B) and a sensitivity analysis (3C).

1.5 Project team

The work was carried out by Gerbrant van Vledder of Alkyon. The internal quality control was performed by David Hurdle of Alkyon. The external quality control was

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performed by Leo Holthuijsen of Delft University of Technology on behalf of the Client. The project was coordinated with André van der Westhuysen of Deltares.

1.6 Report structure

The structure of the report is as follows. The model set-up of the different hindcast studies is described in Chapter 2. The results of the study parts 1, 2 and 3 investigations are given in the Chapters 3, 4 and 5. Conclusions and recommendations are given in Chapter 6.

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2 Data sets and model set up

2.1 Introduction

The analysis of the sources of under-prediction of low-frequency wave energy, the effects of current dissipation and the under-prediction of wave energy in depth-limited situations is based on four datasets.

The first dataset is taken from six storm events in the outer delta of the Oosterschelde estuary in the south of the Netherlands. These events occurred in December 2001 and December 2003. They were hindcast by Svasek Hydraulics (2007). Of special interest is the under-prediction of the low-frequency wave energy at station OS4 (see Figure 3.23). WAQUA based current and water level fields for the hindcasted storm events were provided by Rijkswaterstaat.

The second dataset is from the Amelander Zeegat, a tidal inlet connecting the Wadden Sea with the North Sea. Various wave buoys are deployed by Rijkswaterstaat in this tidal inlet, generating a large amount of measurement data. WL & Alkyon (2007) performed a hindcast of six events in the February 2004 and January 2005 storms with SWAN. Current and water level fields for the hindcasted storm events were provided by Rijkswaterstaat/RIKZ.

The third dataset is also from the Amelander Zeegat, but from a more recent

measurement season. Thirty-one events from storms in January 2007 and March 2007 were hindcast by Royal Haskoning (2007). This hindcast used the same model set-up as the hindcast of WL& Alkyon (2007). A recent study by Deltares (2008) revealed that the water levels, as predicted by the WAQUA model, are systematically too low (by up to 0.5 m) for most of the storm events. This implied that the conclusions drawn in the hindcast of Royal Haskoning (2007) need to be reconsidered. Despite this shortcoming in input conditions for the SWAN computations, it was deemed useful to use this data-set in two ways. Firstly, the uncorrected water level fields were used to determine the sensitivity od the results to modifications in the source term for wave dissipation in situations with current, but only for the wave buoys located in the relatively deep tidal channels. The results of this analysis are presented in Chapter 4. The benefit of this approach is that the water levels and currents are mutually consistent. Secondly, a first correction to the computed water level fields was made, using observed water levels at the stations Nes and Harlingen. These modified water levels were subsequently used to re-hindcast all 31 cases in the Amelander Zeegat to study the source term balance in shallow water, where the effects of the water correction are most relevant. The results of this hindcast are presented in Chapter 5.

The fourth dataset is from measurements in the Slotermeer (Bottema, 2008). For the present study a number of situations with depth-limited waves were hindcast with the SWAN model.

2.2 Oosterschelde hindcast (Svasek)

For a detailed description of the hindcast for the Oosterschelde, reference is made to Svasek Hydraulics (2007). In the present study the same model set-up as used by Svasek was used. The only modifications are the directory structure and coding of the input and output files.

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The SWAN model set-up includes a set of 4 nested computational grids (K, B, D and F) in the Oosterschelde estuary and a fifth North Sea grid (N) providing frequency dependent mean wave directions for the nested grid (K). Figure 2.1 shows the outline of the

computational grids and the buoy locations. Spatial results of the present analysis are presented for grid K. Spectral information is taken at the location of the buoys from the finest grid in which they are situated.

The coding and main characteristics of the six storm events are given in Table 2.1.

Code Date Time U₁₀ (m/s) Wind Dir (°N)

A1 26 Dec. 2001 09:00 16 310 A2 26 Dec. 2001 12:00 13 315 A3 29 Dec. 2001 15:00 9 280 B1 21 Dec. 2003 13:30 18 317 B2 21 Dec. 2003 16:00 17 300 B3 23 Dec. 2003 02:30 9 295

Table 2.1: Summary of main characteristics of the six hindcast events for the Oosterschelde.

To distinguish between the original and additional files created by the various sensitivity runs, an extra block of three letters has been added. This coding is described in Section 2.6.

For the present study the storm events A1, A2 and B3 were selected for further analysis. The first two events were selected because they have wind and offshore wave directions pointing straight into the ebb-tidal delta towards buoy OS4. The third event was

selected because of its high amount of missing low frequency energy at buoy OS4 and because it has a low wind speed. This selection gives a representative set of conditions from this dataset.

2.3 Amelander Zeegat (WL & Alkyon)

The model set-up used by WL & Alkyon uses an overall grid (GridCL) covering the whole Wadden Sea. Nested in this grid is the dedicated curvi-linear grid (AZG3A) around the tidal inlet of Ameland. A special feature of this grid is the finer resolution in the central part of the tidal inlet. Water level and current fields were obtained from the WAQUA model. Figure 2.2 shows the outline of these grids and the location of the wave buoys.

In WL& Alkyon (2007) various combinations of water levels, current and wind fields were used. For the present study the ‘FLU’ type of computations were repeated. The type ‘FLU’ computations consist of stationary SWAN computations using flow and water level fields from the WAQUA model and a constant wind field based on the wind speed and wind direction at an offshore point in the downscaled HIRLAM wind field.

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Code Date Time U10 (m/s) Wind Dir (°N) 20040208_2000 8 Feb. 2004 20:00 13.52 314.0 20040208_2230 8 Feb. 2004 22:30 16.64 325.1 20040209_0130 9 Feb. 2004 01:30 16.26 328.4 20050102_1000 2 Jan. 2005 10:00 19.96 276.8 20050102_1200 2 Jan. 2005 12:00 17.82 277.4 20050102_1700 2 Jan. 2005 17:00 16.28 275.4

Table 2.2: Summary of main characteristics of the six hindcast events for the Amelander Zeegat of the WL & Alkyon (2007) hindcast.

To distinguish between the original and additional files created by the various sensitivity runs, an extra block of three letters was added. This coding is presented in section 2.6.

For the present study the 2005 events were selected for further analysis because they clearly show an under-prediction of the low frequency peak and because information from the ten wave buoys is generally available. The wind directions were generally from the west.

2.4 Amelander Zeegat (Royal Haskoning)

Royal Haskoning (2007) performed a hindcast study with SWAN in the Amelander Zeegat. The grid setup of their hindcast study was the same as used by WL& Alkyon (2007). This consists of a coarse grid covering the whole Wadden Sea (grid GridCL). Nested in this grid is the grid AZG3A, centered around the Amelander Zeegat. Figure 2.3 shows an outline of the grid for the Amelander Zeegat together with the buoy locations deployed in the storm season 2006-2007. The buoy locations, type of buoy and bottom level with respect to NAP are summarized in Table 2.4

Nr. Buoy code

Since Buoy type

Diameter X-coor. Y-coor Bottom level (NAP) 1 AZB11 27/11/06 DWR 90 160,997 616,011 -19.25 2 AZB21 27/11/06 DWR 90 167,302 610,610 -9.70 3 AZB31 27/11/06 DWR 90 167,750 607.205 -3.00 4 AZB41 28/11/06 DWR 90 168,792 600,498 -1.00 5 AZB51 28/11/06 WR 70 168,003 596,498 -1.00 6 AZB61 28/11/06 WR 70 167,501 592,499 -0.80 7 AZB12 27/11/06 DWR 90 173,008 617,306 -21.60 8 AZB22 27/11/06 WR 90 170,990 612,006 -4.20 9 AZB32 23/01/07 DWR 90 169,480 607,108 -10.60 10 AZB42 23/11/06 DWR 90 171,367 604,176 -18.10 11 AZB52 23/11/06 DWR 90 175,494 600,768 -13.00 12 AZB62 23/11/06 WR 70 180,498 598,627 -1.00

Table 2.3: Location of wave measurement buoys (DWR=Directional Waverider; WR=Waverider) in the Amelander Zeegat.

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The SWAN model was applied to 31 conditions. An overview of these conditions as used in the Haskoning hindcast is given in Table 2.3. The wind speed was determined as the weighted average of wind at the hindcast moment and two preceding wind

measurements according to U10,repr = 0.5*U10,T + 0.33*U10,T-1 + 0.17*U10,T-2. to obtain more

representative wind speeds.

Date & Time Wind speed Wind dir Water level (Nes) Water level (W-Terschelling) 1/11/2007 00:00 11.88 237 136 80 1/11/2007 12:00 19.12 224 70 72 1/11/2007 13:00 19.46 228 96 80 1/11/2007 14:00 16.95 273 101 82 1/11/2007 15:00 13.46 257 122 73 1/11/2007 16:00 14.84 265 106 61 1/11/2007 16:40 14.81 264 95 46 1/11/2007 20:40 18.17 268 44 44 1/11/2007 21:20 18.70 271 63 71 1/11/2007 22:00 17.91 275 93 102 1/11/2007 22:40 18.83 279 129 130 1/12/2007 02:00 15.52 283 306 269 1/12/2007 05:00 14.33 281 226 166 1/12/2007 08:00 10.77 271 128 88 1/18/2007 12:20 21.07 233 82 56 1/18/2007 14:00 20.24 263 60 39 1/18/2007 17:20 20.30 267 143 145 1/18/2007 18:00 20.06 268 182 169 1/18/2007 18:40 19.91 269 224 197 1/18/2007 20:40 18.85 274 281 250 1/18/2007 21:20 18.19 274 291 248 1/19/2007 07:40 13.09 271 145 137 1/19/2007 12:00 14.27 272 136 70 3/18/2007 07:40 14.78 274 110 113 3/18/2007 09:20 13.77 275 176 125 3/18/2007 10:00 13.79 279 169 121 3/18/2007 14:40 18.10 266 67 27 3/18/2007 15:40 17.91 271 63 65 3/18/2007 16:00 18.67 270 64 87 3/18/2007 17:00 17.07 268 117 141 3/18/2007 19:20 16.32 268 299 265

Table 2.3: Wind and water level conditions for 31 selected hindcast moments (Taken from Table 4.6 of Royal Haskoning, 2007).

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2.5 Slotermeer

Wave measurements are routinely carried out in the Slotermeer. The Slotermeer is small shallow lake located in the province of Friesland. The size of this lake is about 4 km by 2 km. It is has reasonably flat bottom and a water depth of about 1.8 m. Bottema (2007) gives an extensive description of the measurements in the IJsselmeer and in the

Slotermeer. Table 2.4 gives an overview of quasi-stationary situations that were used by Bottema (2007) for SWAN wave model verifications. The integral wave parameters are based on the wave measurements at station SL29. The layout of the Slotermeer and the location of the measurement station are shown in Figure 2.4.

name date Time Depth (wrt NAP)

U₁₀ Dir H_m0 T_p T_m-10 T_m01 T_m02

dd/mm/yy h (CET) m m/s degN m s s s S

SLA 10/2/02 4-5 1.65 11.0 245 0.34 2.27 2.01 1.82 1.73 SLB 12/2/02 13-14 1.69 15.0 253 0.47 2.86 2.53 2.09 1.95 SLC 26/2/02 14-15 1.83 20.8 243 0.70 3.45 2.98 2.61 2.39 SLD 10/10/02 12-13 1.65 10.6 88 0.23 1.67 1.66 1.47 1.42 SLE 27/10/02 15-16 1.67 21.4 252 0.71 3.23 2.96 2.53 2.30 SLF 20/3/04 20-21 1.66 19.4 241 0.66 3.13 2.85 2.48 2.27 SLG 1/11/06 5-6 1.70 17.1 314 0.45 2.52 2.32 2.05 1.90 SLH 18/1/07 12-13 1.66 21.9 234 0.66 3.23 2.92 2.50 2.27 SLI 18/1/07 19-20 1.68 22.6 276 0.67 3.26 2.87 2.43 2.20 Table 2.4: Name, date and time (h CET) of Slotermeer wave model calibration cases, with

the local water depth, the measured SL29-wind and the observed integral wave parameters (integration range: 0.03-1.5 Hz).

For the present study three events were selected for the analysis of depth-limited wave conditions (phase 3). The three conditions with the highest observed significant wave height over depth ratio were selected (SLC: H_m0/d=0.38; SLE H_m0/d=0.43 and SLI,

H_m0/d=0.40). These also coincide with the three conditions with the highest wind speeds.

The wave measurements in the Slotermeer were carried out with a capa-probe mounted on a steel pile with a diameter of 0.4 m. The coordinates of location SL29 are x=172,489 m, y=548,502 m in the Rijksdriehoekstelsel. The local bottom level is NAP –2.12m. Wind measurements were carried out using a cup-anemometer. A detailed description of the setup of the Slotermeer measurements can be found in Bottema (2007).

2.6 Source term magnitudes and low frequency wave

parameters

A key element of the analyses is the inspection of source term magnitudes. The total magnitude of a certain source term is defined as:

(

)

2 0

,

high low f tot _f

M

=

∫ ∫

π

S f

θ

dfd

θ

(0.1)

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For the source terms for triads and quadruplets also the magnitudes of the negative and positive parts are determined according to:

(

)

(

)

{

}

2 1 2 ₀

,

high low f pos _f

M

=

∫ ∫

π

S f

θ

+

S f

θ

df d

θ

(0.2) and

(

)

(

)

{

}

2 1 2 ₀

,

high low f neg _f

M

=

∫ ∫

π

S f

θ

−

S f

θ

df d

θ

(0.3)

The source term magnitudes could not be computed with the present SWAN version (40.51). Therefore, they were recomputed on the basis the HOTFILE output of the SWAN model. Such an output file contains the 2-dimensional spectra of all computational points. Together with information on depth and wind, the corresponding SWAN source terms were recomputed and their magnitudes determined. This was achieved with the program HOTSOURCE developed by Alkyon, yielding the same results as SWAN.

To investigate the evolution of the low-frequency wave energy, three new significant wave height parameters were defined on limited frequency intervals: H₁₀, H₁₅ and H₂₀. These parameters are computed for the frequency ranges (0.0-0.1 Hz), (0.0-0.15 Hz) and (0.0-0.20 Hz), respectively. For instance H10 is computed as:

0.1

10 0

4 ( )

H

=

∫

E f df

(0.4)

In the present project the lower limit of the frequency range is 0.03 Hz, corresponding to the lowest model frequency in the SWAN computations.

2.7 Summary of computations

In this project various types of additional computations were performed to investigate certain aspects of the wind wave evolution in the Oosterschelde, the Amelander Zeegat and Slotermeer. To distinguish between the various sets of computations a unique coding is applied. This coding is used in the naming of all input and output files for this study. Table 2.3 summarizes the different types of additional computations performed for each data set and in each project phase.

The coding for the different datasets is as follows: OS for the Oosterschelde cases, as hindcast by Svasek (2007). AZ for the Amelander Zeegat cases, as hindcast by WL& Alkyon (2007). HK for the Royal Haskoning hindcast of the Amelander Zeegat (2007) and SL for the Slotermeer cases. A special set is the AZ profile used for the computations with the exact nonlinear transfer rate in activity 1C.

In phase 2 a new set of hindcast results for the Royal Haskoning hindcast was made using the corrected water levels, coded as CUR (using currents). These corrected water levels were only used in the analysis of the under-prediction of depth-limited conditions in the Wadden Sea.

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Phase Purpose Code Description Model cases 1A Reduced refraction Effect of currents R90 NOC 90 ctheta Currents deactivated AZ, OS 1B Dissipation KOM MAD

Komen et al. physics Madsen et al. bottom friction

AZ, OS AZ, OS

1C Non-linear interactions NOT XNL

Triads deactivated Comparison DIA & Xnl

AZ, OS AZ-profiles 2A Effect of currents RHK COR NOC Original computations Corrected water levels Currents deactivated

HK

2A Current dissipation WBJU Modified Battjes-Janssen dissipation by Westhuysen

HK

3A Source term magnitude COR Producing HOTFILES HK 3B Error behaviour Statistical analysis HK 3C Sensitivity analysis KOM

MAD XNL

Komen et al. physics Madsen bottom friction Accurate quadruplets

HK, SL HK, SL SL

Analysis SWAN hindcasts Wadden Sea, Oosterschelde and Slotermeer

Deltares

Analysis of SWAN hindcasts

SBW Waddenzee

Wadden Sea, Oosterschelde

And Slotermeer

Executive’s summary

Contents

List of tables

List of figures

1

Introduction

1.1 SBW project background and problem statement

1.2 Problem statement

1.3 Objective

1.4 Approach

1.5 Project team

1.6 Report structure

2

Data sets and model set up

2.1 Introduction

2.2 Oosterschelde hindcast (Svasek)

2.3 Amelander Zeegat (WL & Alkyon)

2.4 Amelander Zeegat (Royal Haskoning)

2.5 Slotermeer

2.6 Source term magnitudes and low frequency wave

parameters

(

)

,

M

=

∫ ∫

S f

θ

dfd

θ

(

)

(

)

{

}

,

,

M

=

∫ ∫

S f

θ

+

S f

θ

df d

θ

(

)

(

)

{

}

,

,

M

=

∫ ∫

S f

θ

−

S f

θ

df d

θ

4

( )

H

=

∫

E f df

2.7 Summary of computations