Observed finite depth wave growth limit in the Wadden Sea

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limit in the Wadden Sea

SBW Wadden Sea

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A. J. van der Westhuysen and J. P. de Waal

Report July 2008

Observed finite depth wave

growth limit in the Wadden Sea

SBW Wadden Sea

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Title Observed finite depth wave growth limit in the Wadden Sea

Abstract

The spectral wind wave model SWAN (Booij et al. 1999) plays a key role in the estimation of the Hydraulic Boundary Conditions (HBC) for the primary sea defences of the Netherlands. Since some uncertainty remains with respect to the reliability of the wind wave model 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 devise a strategy for the improvement of the model. This activity is carried out in parallel with a measurement campaign that is being undertaken in the Dutch Wadden Sea to provide observational data for the calibration and validation of SWAN (‘SBW-Veldmetingen’). The present study aims to compile a reliable set of observations (waves, water depth and wind) from three westerly storms recently observed in shallow regions in the Dutch Wadden Sea (Royal Haskoning 2007), and from three field experiments in shallow lakes, with which to calibrate SWAN for finite depth wave growth in the Wadden Sea. Firstly, the reliability of the observations taken during the mentioned westerly storms in the Wadden Sea interior was assessed, and improved in terms of the interpretation of the wave buoy observations (which were taken in small water depth, namely 1.5-2.0 m) and the modelling of water levels. Whereas Royal Haskoning (2007) reports maximum Hm0/d ratios in excess of 0.6 for the Wadden Sea (0.55 if a plotting error is removed), the present study has shown maximum Hm0/d ratios to rather be in the order of 0.43. It is recommended to reduce the uncertainty of this result further by verifying finite depth wave buoy observations with alternative instrumentation, such as pressure sensors or capacitance probes, and by measuring water depths at the wave buoy locations. Secondly, this data set was compared with the above-mentioned data sets from shallow lakes representing depth-limited wave growth, from which a reasonable agreement was found. In this regard, the empirical relationships for the growth limit proposed by Young and Babanin (2006) appear to be applicable for Lake George and Lake Sloten, but not for the overall data set. Thirdly, a selection of 30 calibration cases of depth-limited wave growth for SWAN has been made from the data sets of the four geographical areas considered. It is recommended to investigate the performance of SWAN for these field cases by hindcasting, and to subsequently apply them in the calibration and validation of the model.

References RWS Waterdienst overeenkomst WD-4968/4500121262

Raamovereenkomst WD-4924 betreffende ‘Specialistische adviezen van de Stichting Deltares t.b.v. het Ministerie van Verkeer en Waterstaat’

Ver Author Date Remarks Review Approved by

1.0 A.J. vd Westhuysen J. P. de Waal

May 2008 Draft J. Groeneweg

June 2008 Final A.V. Babanin W.M.K. Tilmans

July 2008 Final, with small changes

A.R. v Dongeren

M.R.A. v Gent

Project number H5107.35

Keywords SBW Waddenzee, Amelander Zeegat, field measurements, finite depth wave growth limit, SWAN

Number of pages 44 plus figures

Classification None

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List of Tables

2.1 Details of buoys positioned in the Amelander Zeegat during the 2006-2007 storm season.

2.2 Depth-limited conditions selected by Royal Haskoning (2007), and data availability of buoys, indicated by crosses for the various buoys.

3.1 Column description of the overall data set. 3.2 Selection criteria for Amelander Zeegat 3.3 Selection criteria for Lake IJssel

3.4 Selection criteria for Lake Sloten 3.5 Selection criteria for Lake George

3.6 Input settings for the bottom friction source term in SWAN computations 4.1 Selected calibration cases from the Amelander Zeegat data sets

4.2 Selected calibration cases for Lake Sloten 4.3 Selected calibration cases for Lake IJssel

4.4 Selected calibration cases from the Lake George data set of Young and Babanin (2006).

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List of Figures

1.1 Location of three field case sites in the Netherlands considered

1.2 Bathymetry of the Amelander Zeegat in the Wadden Sea, the Netherlands with location of wind, wave and water level observation stations

2.1 Amelander Zeegat storms of January and March 2007. Observed wind speed (10 min average) at Hoorn, Lauwersoog and Huibertgat

2.2 Amelander Zeegat storms of January and March 2007. Observed wind direction (10 min average) at Hoorn, Lauwersoog and Huibertgat

2.3 Amelander Zeegat storms of January and March 2007. Observed water levels at stations Harlingen and Nes

2.4 Amelander Zeegat storms of January and March 2007. Time series of Hm0 (0.03 0.5 Hz) at four buoys, with rejected records indicated

2.5 Amelander Zeegat storms of January and March 2007. Time series of Tm02 (0.03 0.5 Hz) at four buoys, with rejected records indicated

2.6 Amelander Zeegat storms of January and March 2007. Observed wave spectra at AZB41 for thirteen depth limited storm instants

2.10 Amelander Zeegat storms of January and March 2007. Time series of Hm0 (0.03 0.88 Hz) at three buoys, rejected records indicated

2.11 Amelander Zeegat storms of January and March 2007. Time series of T 1,0 (0.03 0.88 Hz) at three buoys, rejected records indicated

2.12 Amelander Zeegat storm of 11 12 January 2007. Computed versus observed water levels at stations Harlingen and Nes

2.13 Amelander Zeegat storm of 18 19 January 2007. Computed versus observed water levels at stations Harlingen and Nes

2.14 Amelander Zeegat storm of 18 19 March 2007. Computed versus observed water levels at stations Harlingen and Nes

2.15 Grids used in Delft3D hydrodynamic simulations. Grids for CSM (top) and Wadden Sea model domains (bottom)

2.16 Amelander Zeegat storm of 11 12 January 2007. Computed water levels at various instants durning the storm

2.17 Amelander Zeegat storm of 18 19 January 2007. Computed water levels at various instants durning the storm

2.18 Amelander Zeegat storm of 18 19 March 2007. Computed water levels at various instants durning the storm

2.19 Amelander Zeegat storm of 11 12 January 2007. Corrected total water depths at the AZB buoys

2.20 Amelander Zeegat storm of 18 19 January 2007. Corrected total water depths at the AZB buoys

2.21 Amelander Zeegat storm of 18 19 March 2007. Corrected total water depths at the AZB buoys

2.22 Amelander Zeegat storms of January and March 2007. Time series of Hm0/d ratio (0.03 0.88 Hz) for buoys AZB51, AZB61 and AZB62

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2.23 Amelander Zeegat storms of January and March 2007. Scatter plots of Hm0/d versus gd/U102, with selected validation cases in red

3.1 Bathymetry of Lake Sloten, The Netherlands, with location of (wind and wave) observation station SL29

3.2 Bathymetry of Lake IJssel, The Netherlands, with location of wind and wave observation stations

3.3 Bathymetry of Lake George, Australia with location experimental site 3.4 Datasets of Lake IJssel and Lake Sloten. Relative wave height versus U10

scaled depth

3.5 Dataset of Amelander Zeegat. Relative wave height versus U10 scaled depth 3.6 Dataset of Lake George. Relative wave height versus U10 scaled depth 3.7 Dataset of Lake Sloten and Lake George. Relative wave height versus U10

scaled depth

3.8 Overall dataset. Relative wave height versus U10 scaled depth

3.9 Lake George, Lake Sloten and Eq. (3.9) (solid line) from Young and Babanin (2006). Nondimensional energy versus U10 scaled depth

3.10 Overall dataset and Eq (3.9) by Young and Babanin (2006). Nondimensional energy versus U10 scaled depth

3.11 Lake George, Lake Sloten and Eq. (3.10) (solid line) from Young and Babanin (2006). Nondimensional wave number versus U10 scaled depth

3.12 Overall dataset and Eq (3.10) by Young and Babanin (2006). Nondimensional wave number versus U10 scaled depth

3.13 Overall dataset. Relative wave height versus U* scaled depth

3.14 Overall dataset small depth (0.0 < d (m) < 2.0). Relative wave height versus

U* scaled depth

3.15 Overall dataset large depth (3.0 < d (m) < 6.0). Relative wave height versus

U* scaled depth

3.16 Scalability of SWAN results using Collins friction. Relative wave height versus

U* scaled depth

3.17 Scalability of SWAN results using Madsen et al friction. Relative wave height versus U* scaled depth

3.18 Sensitivity of SWAN results for friction and breaking. Relative wave height versus U* scaled depth

4.1 Amelander Zeegat storms of January and March 2007. Spectra of selected calibration cases (based on Royal Haskoning (2007))

4.2 Lake Sloten, The Netherlands. Spectra (at SL29) of selected calibration cases (based on Bottema (2007))

4.3 Lake IJssel, The Netherlands. Spectra (at FL2/FL2n) of selected calibration cases (based on Bottema (2007))

4.4 Lake George, Australia. Spectra of selected calibration cases (based on Young and Babanin (2006))

4.5 Position of selected cases (x) in datasets. Relative wave height versus U10 scaled depth

4.6 Position of selected cases (x) in datasets; line from Eq. (3.9). Nondimensional Energy versus U10 scaled depth

4.7 Position of selected cases (x) in datasets; line from Eq. (3.10). Nondimensional wave number versus U10 scaled depth

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List of Symbols

Symbol Unit Description

Cfw - Friction coefficient for Collins (1972) expression

d m Water depth

d‘ m Corrected water depth (for Amelander Zeegat cases)

E m2 Total variance

E(f) m2/Hz Variance density

cm Surface elevation (heave signal)

fp Hz Peak frequency

g m2/s Gravitational acceleration

BJ

-Breaker parameter for surf breaking

H m Wave height (of an individual wave)

Hm0 m Significant wave height (obtained from spectrum)

H1/3 m Significant wave height (obtained from time series)

KN m Bottom roughness length scale in Madsen et al. (1988)

kp rad/m Peak wave number

NAP m Dutch national levelling datum

R oN Mean wave direction

r - Correlation coefficient

Tp s Peak wave period

Tm-1,0 s Mean wave period (=(m-1/m0))

Tm02 s Mean wave period (=(m0/m2)1/2)

T1/3 s Mean of the longest third of all periods in time series

U10 m/s Wind speed (at 10 m elevation)

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

Because of this problem of a ‘knowledge vacuum’ with respect to the assessment of the safety of flood defenses, the overall SBW (‘Strength and Loading of Water Defenses’ (SBW: Sterkte en Belasting Waterkeringen)) project has the following general objective: ‘To fill the most important knowlegde vacuums in order to achieve a better estimate of the safety against flooding of the primary flood defenses.’

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 (Figures 1.1 and 1.2). 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.’

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

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1.2 Problem statement of the present project

The SBW-Waddenzee project is carried out in parallel with a measurement campaign that is being undertaken in the Dutch Wadden Sea to provide observational data for the calibration and validation of SWAN (‘SBW Veldmetingen’). For the 2006-2007 storm season, the activities of the latter project included the deployment and operation of 12 wave buoys in the Amelander Zeegat and on the shallow banks towards the mainland of Friesland (Figure 1.2, bottom panel). Sensitivity studies undertaken during the 2007 year of the SBW-Waddenzee project (Alkyon 2007a,b; WL 2007) have revealed that wave conditions in the Wadden Sea interior are predominantly locally generated by wind, and are strongly determined by the limited water depths in this region. This implied that in order to produce reliable wave field estimates along the Frisian and Groningen coastlines, the focus of the validation effort of SWAN had to be shifted to the Wadden Sea interior.

In this regard, a hindcast study of the Amelander Zeegat and the Dutch Wadden Sea by Royal Haskoning (2007) suggests that SWAN strongly underestimates the observed significant wave heights and mean periods over the tidal flats in front of the Frisian coast. This would imply that in these regions SWAN underestimates the finite depth wave growth limit, such as described by, for example, Bretschneider (1973), Young and Verhagen (1996a,b) and recently Young and Babanin (2006). Since the underestimation of these parameters would constitute in a non-conservative estimate for the design of the primary sea defenses along the coastlines of Friesland and Groningen, it is essential that the performance of SWAN be corrected on this point.

1.3 Potential error sources in observations and model

In attempting to correct the apparent unsatisfactory performance of SWAN over shallow horizontal bottoms such as found over the tidal flats in the Wadden Sea, attention should be paid both to the accuracy of the observations of the Amelander Zeegat campaign (including those serving as model input) and to the description of physics in the model. In the present study, the former of these two aspects is addressed, namely the reliability of the observations taken over the tidal flats in the Wadden Sea, in order to provide a sound basis for model validation. The model physics is considered in a separate study by Alkyon (2008a) within the project SBW Waddenzee.

Concerning these observations, a specific point of concern is the ratio of significant wave height over depth (an indication of the finite depth wave growth limit) that was obtained in the Amelander Zeegat campaign during the 2006-2007 storm season. In this data set, Royal Haskoning (2007) found dimensionless ratios of observed significant wave height over water depth (Hm0/d, where d is the water depth) to have

values of up to 0.551. Due to the apparent similarity in the physical conditions, it is hypothesised that these values can be compared to those obtained over nearly flat bottoms in shallow lakes. In extensive measurement campaigns in Lake Sloten and Lake George, under comparable wind conditions as those in the Wadden Sea data set, observed Hm0/d ratios of up to 0.44-0.45 were found (De Waal 2002; Bottema 2007;

Young and Babanin 2006). In this regard, Babanin et al. (2001) found in Lake George

1. Although Royal Haskoning (2007) reports an even higher maximum ratio of Hm0/d = 0.6, this latter value

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that an individual wave can instantaneously reach a ratio of higher than H/d = 0.44 (with

H the individual wave height), but then breaks so that H/d is reduced to below this level.

These values are much lower than those reported over the tidal flats in the Amelander Zeegat campaign by Royal Haskoning (2007), and therefore suggest a lower finite depth growth limit.

In this regard, the observations taken in the Amelander Zeegat are not ideal in two respects. Firstly, doubts exist over the suitability of wave buoys for the measurement of waves in very shallow water, such as found at the buoy locations AZB41, ABZ51, AZB61 and AZB62 (see Figure 1.2, lower panel) during low tide (Alkyon 2008b). Secondly, during the 2006-2007 storm season, water depths were not measured at the buoy locations in the Wadden Sea. In order to complete the data set of environmental conditions, Royal Haskoning (2007) used water depths computed by Rijkswaterstaat, using the hydrodynamic model WAQUA, in their hindcasts. However, as will be discussed in Section 2.3, the model setup used in these computations (the ‘Wadden West’ model setup) included neither the effect of wind in the model interior nor the influence of waves in the hydrodynamic calculations. Especially the effect of wind is essential in order to compute reliable water levels. Although it is possible to include wind input in WAQUA, it was omitted in this case. This was unbeknownst to Royal Haskoning (2007). The effect of waves is not modelled in WAQUA, but their influence on the water levels is generally small by comparison. Therefore, because of the omission of the wind input, the computed water levels of the WAQUA Wadden West model setup have to be considered with caution.

The apparent lack of agreement between the observations taken in the Amelander Zeegat during 2006-2007, as considered by Royal Haskoning (2007), and the mentioned data sets on shallow lakes may therefore be caused by errors in the wave measurements and by inaccuracies in the computed water depth. Furthermore, in the light of the literature (e.g. Young and Verhagen (1996a,b) and Young and Babanin (2006)), in which the growth limit is expressed in terms of dimensionless parameters featuring also the wind speed such as Eg2/U104, kpU102/g and gd/U102, the difference between these data sets may also be due to possible limitations in using the Hm0/d ratio

for expressing a universal finite depth growth limit. Finally, these discrepancies may also be due to fundamental differences between the wave physics found in shallow lakes and the Wadden Sea interior.

In the present study, the above-mentioned issues regarding the accuracy of the Amelander Zeeland wave and water levels are investigated in order to obtain a reliable data set with which to evaluate the performance of SWAN with respect to the finite depth wave growth limit. In addition, the Amelander Zeegat data set is compared to the above-mentioned data sets recorded in shallow lakes, in order to test the similarity of the physical conditions in the Wadden Sea interior to those in these published datasets. From this comparison, it will be possible to review currently-used empirical relations for depth-limited wave growth.

1.4 Study aim

The aim of the present study is to compile a reliable set of observations (waves, water depth and wind) from the storm events considered by Royal Haskoning (2007) and the mentioned data sets recorded in shallow lakes with which to calibrate the SWAN model for the finite depth wave growth limit perceived to exist in the Wadden Sea interior.

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the storm season of 2006-2007 is to be determined, and where possible improved. Secondly, the agreement of this data set with published data sets representing the finite depth wave growth limit in shallow lakes is to be established. Thirdly, the Amelander Zeegat observations are combined with this existing body of observations for wave growth in shallow lakes, to create a combined data set for the calibration of SWAN. For this combined data set, empirical wave growth relations will be verified, and where possible improved.

1.5 Approach

The first step in compiling a data set of Wadden Sea field cases for the calibration of SWAN for finite depth wave growth is to evaluate the wave observations taken by the buoys AZB41, ABZ51, AZB61 and AZB62 in the Wadden Sea interior during the 2006-2007 storm season. Following on the concerns raised by Alkyon (2008b) on the quality of buoy measurements in shallow water, it was investigated whether the buoys AZB41/51/61/62 have produced reliable wave spectra during the periods of low tides during the storm events considered. To this purpose, a meeting was held with Dutch wave measurement experts, in which the quality of the data obtained from these shallow water buoys was discussed. Based on the insights obtained from this expert meeting, the observations at the buoys AZB41/51/61/62 were re-analysed in order to assess their reliability. The observations were screened with respect to the (computed) water depth at the time of recording, by considering the wave shapes in the time series of water level displacement, and by inspecting the corresponding wave spectra. From the results of this analysis, a selection of reliable wave observations was compiled from the Amelander Zeegat storms hindcast by Royal Haskoning (2007), to be considered in the remainder of this study.

Since water depths were not observed at the wave buoy locations in the Amelander Zeegat during the 2006-2007 storm season, this information must be obtained from modelled water levels and bed levels from bathymetrical studies. As discussed above, Royal Haskoning (2007) used water levels modelled with WAQUA in order to compile these dimensionless ratios. As set out above, these did not include wind forcing in the model interior nor the radiation stresses by waves. Moreover, the bathymetry used in the WAQUA simulations did not make use of the most recent bed level observations at the time of the storm season, which could be an additional source of error in the water level computations. In order to correct these omissions, the water levels were recomputed using the Delft3D model, which included tidal, wind and wave forcing. This model was calibrated to water level data recorded at the stations Terschelling Noordzee and Nes (Figure 1.2). For this model, a new bathymetry was compiled, based on the same depth soundings used in the wave hindcast study of Royal Haskoning (2007). Using this calibrated flow model, the water levels at the buoy locations AZB41/51/61/62 were obtained. Furthermore, the bed levels under the wave buoys were reviewed, and replaced by observations made at buoy deployment. These new bed levels, together the re-modelled water levels, yielded revised estimations of the total water depth d. The verified Amelander Zeegat data set (combinations of Hm0 and d) was subsequently

compared with recently-published observations of the finite depth wave growth limit in shallow lakes (Young and Babanin 2007; Bottema 2007). The location of Lake IJssel and the much smaller Lake Sloten considered by Bottema (2007) are presented in Figure 1.1. An important consideration in this comparison was the selection of the most effective dimensionless parameters with which to consolidate the various data sets. The application of a number of parameters, including Hm0/d, Eg2/U104, kpU102/g and gd/U102, suggested previously by Young and Verhagen (1996a,b), De Waal (2002) and Young

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and Babanin (2006), were investigated (with E the total variance density and kp the

peak wavenumber). For this purpose, observed wind data, obtained at the stations Hoorn, Lauwersoog and Huidertgat (Figure 1.2) were used. From this compiled data set of finite depth wave observations, a number of field cases for the calibration and validation of SWAN were selected. The basis for this data set is the cases compiled by Bottema (2007), to which the cases from the 2006-2007 Amelander Zeegat campaign (insofar as its reliability can be insured) and the Lake George campaign of 1997-1998 (Young and Babanin 2006) were added.

1.6 Project team

This study was conducted by André van der Westhuysen and Hans de Waal, with assistance by Bas Les (Rijkswaterstaat Waterdienst). The internal quality control of this report was carried out by Jacco Groeneweg. The external review of this report was conducted by Alexander Babanin (Swinburne University of Technology, Australia). 1.7 Report structure

This report is structured as follows: In Section 2, the reliability of the observations taken in the Wadden Sea interior during the 2006-2007 storm season is determined, and improved in terms of the interpretation of wave observations and the modelling of water levels. In Section 3, this improved data set is compared with previously-published data sets representing depth-limited wave growth in shallow lakes. In Section 4, a selection of calibration cases for SWAN is made from this combined data set of depth-limited wave growth field cases. Sections 5 and 6 close this report with respectively conclusions and recommendations.

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2 Amelander Zeegat data set for 2006-2007 storm

season

This section presents the validation of the observational data set recorded in the Wadden Sea interior during the 2006-2007 storm season. Firstly, Section 2.1 presents a brief description of the storm events considered. Subsequently, Section 2.2 describes the validation of the wave buoy observations taken during these events. Section 2.3 presents the verification of the water levels and subsequently the total water depths at the selected buoy locations. Finally, Section 2.4 presents the resulting validated data set for the Amelander Zeegat in terms of dimensionless parameters.

2.1 Selection of storm events

During the 2006-2007 storm season, at which time wave buoys were deployed over the shoals between the Amelander Zeegat and the Frisian coast, one severe NW storm (1 November 2006) and three major westerly storm events occurred. Unfortunately, the NW event was not recorded. Therefore, the three westerly storm events, which all feature wind speeds of up to 20 m/s, were considered in the hindcast study of Royal Haskoning (2007), and is also the subject of the present investigation. A brief description of each of these events, denoted as Storms 1 to 3, is given below.

2.1.1 Storm of 11-12 January 2007

The first storm event considered here occurred on 11-12 January 2007, for which the following storm report was issued (SVSD, 2007a): A complicated low pressure field located over the North of Canada propagated southeastwards via Greenland and Iceland. South of this depression, a storm developed above the northern part of the North Sea. On 11 January, a southwesterly storm of 9 Bft reached the Dutch coastline. After the passage of the (cold) frontal zone of the depression, the wind direction changed instantly to west and reduced in force to 8 Bft. During the course of the evening of the 11th, the wind turned to the WNW and increased again in strength to 9 Bft. On the 12th, the wind turned towards the SW and reduced in force to 6 Bft.

The top panels of Figures 2.1 and 2.2 present the observed wind speed and direction (10 minute averages) at three locations in the vicinity of the Wadden Sea, namely Hoorn, Lauwersoog and Huibertgat (see Figure 1.2 for their location). Following Royal Haskoning (2007), Figures 2.1 and 2.2 include spatially averaged time series of wind speed and direction, computed on the basis of:

Valaverage = 0.5*ValHoorn + 0.25*ValLauwersoog + 0.25*ValHuibertgat (2.1) It is noted that unlike the approach of Royal Haskoning (2007), no additional averaging in time has been applied to these signals. Since no wind information was measured at the buoy locations, this spatially averaged time series of U10 will be used throughout the present study. The vertical lines in these figures indicate storm instants for which the wave conditions were depth-limited, selected for hindcasting by Royal Haskoning (2007) and which will also be considered here (see Section 2.2). During this storm event, the maximum surge level reached at Harlingen was +2.1 m NAP and +2.5 m NAP at Delfzijl. Figure 2.3 shows the observed total water levels (tide plus surge) at Harlingen and Nes, which both reached values of just over +3 m NAP.

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2.1.2 Storm of 18-19 January 2007

For the second storm event considered, occurring on 18-19 January, the following storm report was issued (SVSD 2007b): A complex, large-scale depression was generated over the Northern Atlantic. This low pressure area followed a track over the British Isles via Denmark to the Baltic Region, with a heavy storm developing on its southern part. During the morning of January 18th, the passage of this depression caused a severe southwesterly storm with wind forces up to 10 Bft over the southern North Sea and along the Dutch coast. At the peak of the storm, wind gusts reached hurricane magnitudes of 12 Bft. During the afternoon of the 18th, the wind turned to west over the North Sea and in the evening the wind direction changed to northwest. During the whole day wind forces over the North Sea varied around 10 Bft. After the passage of the so-called back-bent occlusion, the wind speed dropped rapidly.

The middle panels of Figures 2.1 and 2.2 respectively show the measured wind speed and direction at Hoorn, Lauwersoog and Huibertgat during 18-19 January. According to the SVSD, this westerly event caused a storm surge of up to 1.7 m along the closed Holland coast and 2.2 m at Harlingen in the Wadden Sea. Despite the high wind speeds, total water levels did not reach extreme levels. In the Wadden Sea, the reduction in wind speed took place just before a new high tide period, so that the water levels did not reach extreme values. Figure 2.3 presents the observed water levels at the stations Harlingen and Nes, which reached maximum values of +3.3 m NAP and +2.9 m NAP respectively.

2.1.3 Storm of 18-19 March 2007

SVSD (2007c) issued the following storm report for this third event: On 17 March, a depression propagated from Iceland to the south of Norway. Over the northern part of the North Sea, the pressure dropped to 955 hPa. During the afternoon of March 18th, a storm developed over the Northern part of the North Sea with northwesterly winds of up to 10 Bft. In the southern North Sea and in front of the Dutch coast, the wind direction was westerly and wind forces reached 8 Bft. During the night of 18 on 19 March, the wind speed dropped down and the direction changed towards north.

The lower panels of Figures 2.1 and 2.2 show the observed wind speed and direction at at Hoorn, Lauwersoog and Huibertgat during 18-19 March. The maximum wind speed was around 20 m/s, with a consistent westerly direction. With the wind conditions being favourable for surge in the Wadden Sea, the storm surge was particularly significant during this event, with a maximum value of 2.1 m reported at Delfzijl. Since it was springtide at the time, high total water levels were reached, with values of up to +3.78 m NAP at Delfzijl. The lower panel of Figure 2.3 presents the total water levels at Harlingen and Nes, where values around +3.20 m NAP were reached.

2.2 Verification of wave buoy observations

During the 2006-2007 storm season, 12 buoys were deployed in the region of the Amelander Zeegat (Figure 1.2). Four of these buoys, namely AZB41, AZB51, AZB61 and AZB62, were deployed over shoals with bed levels of between -0.8 and -1.0 m NAP (Table 2.1). As a result, these four buoy locations are well-suited to investigate the occurrence of depth-limited wave growth in the Amelander Zeegat. From the three storm periods presented in Section 2.1, strongly depth-limited growth conditions can be

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(e.g. during low tide). However, since the observation stations AZB41, AZB51, AZB61 and AZB62 were fitted with wave buoys (the directional Waverider MkIII and omni-directional SG models, see Table 2.1), there are physical limitations to the conditions that could be registered. The most apparent of these are the limited frequency range of buoys and the limitations due to finite water depths, including ultimately the dry falling of the buoys. Therefore, in this section, the reliability of the wave observations at these four buoy locations is investigated.

Table 2.1: Details of buoys positioned in the Amelander Zeegat during the 2006-2007 storm season. Directional Waverider MkIII denoted by ‘DWR’ and omni-directional Waverider SG by ‘WR’. Bed levels obtained from soundings at time of deployment.

2.2.1 Validation by Royal Haskoning (2007)

Royal Haskoning (2007) performed a series of validation and consistency checks on the wave observations by the AZB buoys during the presented three storms periods. From this validated data set, periods were identified during the three storm events over which the data was free from obvious observational errors. In addition, a final selection of 13 instants of strongly depth-limited wave growth conditions was made. Royal Haskoning applied the following validation criteria:

a) An automated validation of the raw signals was carried out by the RMI system and the WAVES2006 software suite, both operated by Rijkswaterstaat. In this computerised analysis of the recorded instrument signal, abnormal instrument behaviour or irrational recordings are corrected or removed. The data set is checked for staggers, spikes, solitary values, data gaps and dummy values. If more than 90% of the available data is approved by WAVES2006, wave parameters (e.g. Hm0 and Tm02) are computed. If less than this percentage is approved, no parameters are available. However, Royal Haskoning (2007) considers this procedure not to be sufficiently robust to remove all unreliable data points. Nr Network Code Since Buoy Type Diameter [cm] X-Coord [m RD] Y-Coord [m RD] Bed level [m NAP] 1 AZB11 27/11/06 DWR 90 160997 616011 -18.25 2 AZB21 27/11/06 DWR 90 167302 610610 -9.7 3 AZB31 27/11/06 DWR 90 167750 607205 -3.0 4 AZB41 28/11/06 DWR 90 168792 600498 -1.0 5 AZB51 28/11/06 WR 70 168003 596498 -1.0 6 AZB61 28/11/06 WR 70 167501 592499 -0.8 7 AZB12 27/11/06 DWR 90 173008 617306 -21.6 8 AZB22 27/11/06 WR 90 170990 612006 -4.2 9 AZB32 23/01/07 DWR 90 169480 607108 -10.6 10 AZB42 23/11/06 DWR 90 171367 604176 -18.1 11 AZB52 23/11/06 DWR 90 175494 600768 -13.0 12 AZB62 23/11/06 WR 70 180498 598627 -1.0

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b) An additional consistency check by Royal Haskoning (2007) between records to eliminate any unexpected observed values: (i) visualising all wave parameters, (ii) visualising the relation of H1/3, T1/3 and wave steepness between the eastern and western branches of the buoy deployment and from offshore to the Wadden Sea (see Figure 1.2), (iii) validating the standard deviation of Hm0 and Tm02, (iv) validating the consistency of wave parameters in the western and eastern branches of the buoy deployment, (v) accumulating the number of errors found per location and time record.

c) To exclude very small wind waves, which were probably inaccurately measured by the buoys, only storm conditions with wave parameters Hm0 and Tm02 falling within predefined ranges were retained. For the buoy AZB41, only values within the ranges 0.25 m < Hm0 < 4 m and 2.2 s < Tm02 < 6 s were retained. For the buoys AZB51, AZB61 and AZB62, acceptance ranges of 0.25 m < Hm0 < 3 m and 2.2 s < Tm02 < 5 s were applied.

d) Records where unrealistically high values of the mean period T1/3 (>6 s) were found in combination with low wave heights H1/3 (< 20 cm) were eliminated from the data set. It is considered that these unrealistically high values of the mean period result from the falling dry of the shallow water wave buoys AZB41, AZB51, AZB61 and AZB62 at receding tide.

e) From this resultant data set, Royal Haskoning (2007) selected 13 conditions for studying depth-limited wave growth. In order to investigate the maximum effect of the depth limitation, hindcast moments were chosen for which the wind speed is high and both the wind speed and direction were fairly uniform in time.

Figures 2.4 and 2.5 present the time series of significant wave height Hm0 and mean period Tm02 at the stations AZB41/51/61/62 as they are produced by the RMI and WAVES2006 automated signal processing systems (validation step (a) above). These parameters have been computed over the frequency range of 0.03-0.5 Hz, which is the standard range employed by Rijkswaterstaat (RIKZ 2000). Comparison with Figure 2.3 shows that the significant wave height and mean period at these shallow water stations are strongly modulated by the water level (tide plus surge). Maximum values of these parameters are found at the respective peaks of the three storms, where both the wind speed and the total water levels are at a maximum.

Figures 2.4 and 2.5 show a number of suspicious records in the observed time series, as have been identified by Royal Haskoning (2007). Particularly at low tide, values of

Hm0 and Tm02, integrated over the range 0.03-0.5 Hz, regularly fall below 0.25 m and 2.2 s respectively, which are considered to have been inaccurately measured by the buoys (validation step (c) above). In addition, at these low tide instants, the values of the mean period often increase sharply when the buoy in question is on the verge of falling dry. The grey shaded areas in these figures indicate the storm periods during which Royal Haskoning (2007) has labelled the data produced by one or more of the wave buoys as suspicious, based on the criteria (a) to (d) above. In addition, the 13 storm instants selected by Royal Haskoning for their hindcasting study are indicated by vertical lines. These instants are also presented in Table 2.2.

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Table 2.2: Depth-limited conditions selected by Royal Haskoning (2007), and data availability of buoys, indicated by crosses for the various buoys.

2.2.2 Expert group meeting

From the observed wave data presented above, it can be concluded that Royal Haskoning (2007) succeeded compiling a shallow water data set for the Amelander Zeegat that is free of obvious observational errors with regard to signal processing and physically expected values. However, for the purpose of compiling a validation data set for this region, some questions with regard to the quality of buoy observations in very shallow water remain. In this regard, two issues are of particular concern: Firstly, it is necessary to establish the minimum water depth at which the Waverider buoys deployed at AZB41/51/61/62 still produce reliable data. Secondly, it is required to establish the frequency range over which the wave spectra produced by Waverider buoys can be considered reliable. This is a concern, since the depth-limited wave fields in the Wadden Sea have energy at high frequencies (fp 0.3 Hz), which need to be registered properly by the Waverider buoys. An indication of the valid frequency ranges for these wave buoys is given in the Datawell Waverider Reference Manual (Datawell, 2005), namely 0.033-0.625 Hz for the Directional Waverider MkIII buoy (station AZB41) and 0.042-1.0 Hz for the Waverider SG model (stations AZB51/62/62). However, no direct mention of the effect of finite depth on the measurement accuracy and these stated ranges is given.

In order to resolve these issues, and specifically how they impact on the Hm0/d ratios computed for the Wadden Sea, a discussion session was held with a number of wave measurement experts with experience with Waverider buoys and their application to Dutch waters. Attending this expert meeting were the following people:

M. Andernach (Rijkswaterstaat, Data-ICT-Dienst) H. Joosten (Datawell B.V.)

A.T.M.M. Kieftenburg (Deltares)

B. Les (Svasek Hydraulics)

Buoy locations Date AZB41 (DWR) AZB51 (WR) AZB61 (WR) AZB62 (WR) 1/11/2007 13:00 x x x x 1/11/2007 14:00 x x 1/11/2007 22:00 x x x x 1/11/2007 22:40 x x x x 1/18/2007 12:20 x x x x 1/18/2007 14:00 x x x x 1/18/2007 17:20 x x x x 1/18/2007 20:40 x x x x 3/18/2007 10:00 x x x x 3/18/2007 14:40 x x x x 3/18/2007 15:40 x x x x 3/18/2007 17:00 x x x x 3/18/2007 19:20 x x x x

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H. Noteboom (Datawell B.V.)

H.C. Peters (Rijkswaterstaat, Data-ICT-Dienst) G.Ph. van Vledder (Alkyon)

The minutes of this meeting (Deltares 2008a) have been included in Appendix A for reference. In the present section, a summary of the most relevant remarks and conclusions are given. The first discussion topic posed to the group was what the minimum depth and the maximum spectral frequency were at which Waverider buoys can measure the wave spectrum accurately, and whether these limits are likely to have been exceeded over the shallow banks in the Wadden Sea. In this regard, the attendees were asked to discuss the frequency ranges stated in the Waverider Reference Manual (Datawell 2005), given above. As a second discussion topic, the time series of the heave signal for the AZB61 buoy, a collection of time series statistics (indicating a significant asymmetry in the signal) and the wave spectra were presented for the storm instants 18/03/2007 at 14:40 and 15:40. The attendees were asked to give their impression of the quality of these records.

Concerning the question of the minimum depth at which Waverider buoys produce reliable data, the following key points came to light. In the late 1960s to early 1970s, extensive testing of the performance of Waverider buoys in shallow water was carried out. In these tests, wave buoys and pressure sensors were co-located and their measurements compared. These tests showed that Waverider buoys (models essentially similar to those presently being deployed in the Wadden Sea) are able to accurately record the wave signal for small depths (1.5-2.0 m). Unfortunately, however, all reports describing these validation tests have been lost.

Concerning the question of the frequency range over which Waverider buoys produce reliable data, the following points came to light. Nominally, spectral densities are obtained over the entire frequency range as given in Tables 5.4.3 and 5.4.4 of Datawell (2005), namely 0.033-0.625 Hz for the directional Waverider MkIII buoy and 0.042-1.0 Hz for the omni-directional Waverider SG model. However, a test performed in 15 m water depth by Datawell (2006) shows that for a 70 cm Waverider SG buoy the cut-off frequency due to geometric attenuation (where wave lengths become shorter than the buoy diameter) is 0.88 Hz, which is lower than the upper limit stated in Table 5.4.3 of Datawell (2005). In addition, for this buoy, the immersion resonance frequency (where the buoy resonates on the wave motion) is found for the interval of 0.80-0.87 Hz. Hence, in the frequency range 0.75-0.88 Hz the observed spectral density is overestimated. However, fortunately, the Rijkswaterstaat AZB buoys are fitted with anti-spin triangles, which damp this buoy resonance to a degree.

Figures C.1 to C.13 (Appendix C) present 5-minute extracts of the heave signal (t) at the buoys AZB41/51/61/62 at the 13 depth-limited storm instants selected by Royal Haskoning (2007), see Table 2.2. Also presented in these figures are the third moment statistics of skewness Sk and asymmetry As, given by:

3 2 3/ 2

( )

k

t

S

t

and 3 2 3/ 2

( )

k

t

A

t

, (2.2)

computed from a 20-minute sample of the heave time series. The operator denotes the Hilbert transform. We associate high values of the skewness Sk with a

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As gives the asymmetry with respect to the vertical axis, with negative values signifying forward-leaning waves and positive values backward-leaning waves.

Figures C.1 to C.13 show the individual wave crests, which reveal significant skewness (Sk up to 0.47, see Figure C.7) in the signal and moderate, mostly positive, asymmetry (As up to 0.20, see Figures C.6 and C.11). The latter implies backward-leaning wave crests. Figures 2.6 to 2.9 present the associated frequency spectra for these 13 storm instants, computed over a 20-minute sample. The attendees were asked to give their opinion of the quality of the heave signal and spectrum of the AZB61 buoy at the storm instants 18/03/2007 at 14:40 (Figures C.10 and 2.8) and 15:40 (Figures C.11 and 2.8), which displayed particularly high Hm0/d ratios. All present considered that the wave heave signal, its time series statistics and its associated spectra are in order, without obvious depth-related measurement errors. To this we add that Young and Eldeberky (1998) report negative values of asymmetry (As -0.1) for waves recorded in Lake George, which implies (physically more realistic) forward-leaning waves. It is proposed that the discrepancy between these two results is due to the sampling frequency of the present data set being too low to obtain reliable estimates of the asymmetry As (sampling frequencies of 1.28 Hz and 2.56 Hz for the AZB41 and AZB51/61/62 buoys respectively, versus 8 Hz used by Young and Eldeberky (1998)). This shortcoming does, however, not affect the present analysis negatively.

In addition to the main topics discussed above, some additional points of interest were raised, namely (a) liquefaction of the sea bed, (b) the choice of the mooring system, and (c) the influence of current on the measurement accuracy. The total water depth under the buoy can be affected by the fact that during a storm the mud on the bed of the Wadden Sea can become liquefied. Furthermore, decreasing water depth under the buoy can result in increased flow velocities around the buoy. These increased flow velocities can enhance the liquefaction, resulting in the formation of a pit of typically 1-3 m diameter under the wave buoy, with a depth of a few decimeters. Such phenomena can contribute to a somewhat larger water depth, and hence potentially to somewhat larger wave heights. The choice of the mooring system can affect the accuracy of buoy observations in finite depths. For water depths shallower than 8 m, these mooring layouts are custom-designed together with the client. Since this has been done for the Amelander Zeegat deployment, the mooring system is not a likely source of inaccuracy. Regarding possible negative influence from ambient current, it was stated that the maximum current velocity at which a buoy can still measure accurately depends both on the diameter of the buoy and the water depth. For 70 cm and 90 cm hull diameter buoys the maximum flow velocities at which accurate wave measurements can be obtained are 2 m/s and 3 m/s respectively. However, buoys are relatively more sensitive to current flows in deeper water than in shallower water, hence limiting ambient current as a source of error at the buoy locations under consideration.

2.2.3 Conclusion

Based on the outcome of the wave buoy validation by Royal Haskoning (2007) and particularly the findings of the expert meeting, the following can be concluded: Firstly, there appears to be no (finite depth-related) reason to doubt the wave buoy observations made in water depths greater than 1.5 m. It is noted, however, that it is unfortunate that all documentation of the mentioned finite depth wave buoy validation experiments have been lost. Since the quality of records measured at depths smaller than 1.5 m cannot be guaranteed, no records with total water depths smaller than this

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will be accepted in the validated data set (see Section 2.3.4). Secondly, concerning the valid frequency range of the buoys in the Amelander Zeegat campaign, it appears that the frequency range of 0.03-0.5 Hz is too conservative an estimate for the Waverider SG buoys AZB51/61/62. This is unfortunate, since for these buoys the finite depth conditions result in wave fields with non-negligible energy levels at frequencies higher than 0.5 Hz.

This is illustrated in Figures 2.6 to 2.9, in which the frequency limit of 0.5 Hz is indicated by a solid vertical line. Based on the stated ranges in Datawell (2006), in this study the integral parameters at the 70 cm Waverider SG buoys AZB51/61/62 were integrated over the frequency range 0.03-0.88 Hz (see dashed vertical line at 0.88 Hz in Figures 2.6 to 2.9). In this way, a more realistic estimate of the significant wave height is obtained for these buoys. It is noted that, since small measurement errors are made in these higher-frequency regions (Datawell 2006), a small error will be introduced in the mean period measures. In Figure 2.6 it can be seen that the frequency range of the 90 cm Waverider MkIII buoy at AZB41 does not extend far enough beyond 0.5 Hz to include relevant higher frequency components of the observed spectra. The lack of resolution of high frequency components at AZB41 can also be seen in the time series plots (e.g. Figure C.13). In order to be consistent, the observations taken by the 90 cm Directional Waverider MkIII at AZB41 were therefore not included in the remainder of this study.

Figures 2.10 and 2.11 present the values of Hm0 and Tm-1,0 computed over the extended frequency range (0.03-0.88 Hz). All records rejected on the basis of the validation described above have now been omitted from the plots. We note that henceforth Tm-1,0 is considered as opposed to Tm02, since the former is typically of more interest in Dutch coastal applications than the latter. Comparison between Figures 2.10 and 2.4 shows that particularly the lower values of Hm0 are significantly increased by the extended integration range. For the data analysis presented in Section 3, it is desirable to have the largest possible data set from the Amelander Zeegat observations (without a pre-selection of specific characteristics). For this purpose, all the wave observations in Figures 2.10 and 2.11 that have not been rejected by the above-described validation process (greyed times) will be used. By contrast, for compiling a hindcast data set for validation for the Wadden Sea, a selection of the most depth-limited cases will be used. The 13 depth-limited storm instants proposed by Royal Haskoning (2007) have been indicated in Figures 2.10 and 2.11 with vertical lines. These are discussed in more detail in Section 2.4.

2.3 Verification of computed water levels and bed levels

Having validated the wave observations in the Amelander Zeegat in the previous section, the attention is turned to the quality of the water depth data set obtained over the corresponding time. The total water depth associated with a particular location and time instant is composed of a water level - which in the present case is taken from simulations - and bed levels. The accuracy of these two components is considered below.

2.3.1 Water level errors in the WAQUA ‘Wadden West’ results

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model. Royal Haskoning (2007) does not report any specific verification of these computed water level and current fields2. Figures 2.12 to 2.14 present a comparison between the observed and computed water levels at stations Harlingen and Nes, for the three hindcast periods considered by Royal Haskoning (2007). The vertical lines in these figures again indicate the 13 storm instants of strongly depth-limited wave growth identified by Royal Haskoning (2007). As described in Section 2.1, the observations over the three hindcast periods show the tidal modulation in the water level, and in all three cases a surge of approximately +2 m NAP at Harlingen at the storm peak. Comparison with the results of the WAQUA Wadden West model shows that the astronomical tide is adequately predicted both in terms of phase and amplitude. However, in all three storms, the maximum water levels at Harlingen and Nes are poorly predicted, due to the apparent underestimation of the storm surge. In all three storms, the underestimation appears to be the strongest at Harlingen. The bottom panels in Figures 2.12 to 2.14 present the difference between the observed and computed water levels at Harlingen and Nes for the three storm periods respectively, which can be seen to exceed 0.5 m at the peak of the storms.

Enquiry into the origin of these significant underestimations revealed that wind forcing has not been directly incorporated into the Wadden West model (R. Pliegers 2008, pers. comm.). The water levels in the Wadden Sea are computed using a nested series of models. The greater coastal domain of The Netherlands is modelled with the ‘Kuststrook-grof’ WAQUA model, within which the ‘Kuststrook-fijn’ WAQUA model is nested. In turn, the ‘Kuststrook-fijn model features a nesting of the Wadden West model. The overall Kuststrook-grof model is driven by both astronomical components and wind forcing. In addition, the computed water levels are corrected by means of Kalman filtering, using observations at eight observation stations along the Dutch coast (but none inside the Wadden Sea). These corrected results, which include the effect of wind forcing, provide the boundary conditions on the Kuststrook-fijn and Wadden West models. However, neither the Kuststrook-fijn nor Wadden West models subsequently include wind forcing over the model interior. This model setup explains in large part (as not to claim that model results and data would be perfectly matched if wind forcing had been included) the observed discrepancy with the observations – the storm surge is underestimated due to the absence of wind forcing in the interior of both models. This underprediction is greater at Harlingen than at Nes, since the former is further away from the boundaries of the Wadden West model, where the effect of wind is indirectly included.

2.3.2 Water levels modelled with Delft3D

In order to obtain improved estimates of the water levels at the buoy locations during the three considered storms, a new hindcast was performed of the hydrodynamic conditions in the Wadden Sea using the Delft3D model suite. This hydrodynamic simulation, described in detail in Deltares (2008b), features the influence of the astronomical tide, atmospheric pressure and wind fields, and the influence of waves. The simulations were conducted on three computational grids (see Figure 2.15): the first, large-scale grid is that of the so-called Dutch Continental Shelf Model (CSM) setup, which covers the entire continental shelf, including the North Sea and Britsh Isles. This model domain is forced by pressure and wind fields from the HIRLAM model, with the boundary conditions being provided by astronomical components. Nested inside the CSM domain is a higher resolution model covering the entire Dutch Wadden

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Sea. This model is again forced by the HIRLAM pressure and wind fields, and uses the boundary conditions from the larger-scale CSM model. Waves are computed (using the SWAN model) over a computational grid that is contained inside the higher-resolution hydrodynamic grid. The wave boundary conditions are provided by buoy observations at the offshore boundary (at stations ELD and SON). Over the wave modelling grid, radiation stresses are computed and communicated to the hydrodynamic simulation, in order to include wave-driven currents.

The hydrodynamic model is run in depth-averaged mode. The hydrodynamic time step is set at 10 minutes and 1 minute for the CSM and coastal domains respectively, which fulfil the Courant number criteria for free surface waves. The wind drag coefficient is set using the Charnock relation. The bed roughness for the hydrodynamic simulations was prescribed with a Chézy coefficient, which was space-varying in the CSM model and uniform (66 m1/2/s) in the coastal model domain. The wave simulation was conducted in stationary mode at regular intervals (every 60 minutes) during the hydrodynamic simulation. The SWAN model version 40.51AB was applied, with the setting GEN3 WESTH for the deep-water physics and the default settings for the remainder of the physical processes.

Figures 2.16 to 2.18 present the water level fields in the region of the Amelander Zeegat produced by the hydrodynamic model described above, for the 13 depth-limited instants during the three westerly storms considered here. These figures show the various water levels associated with the investigated storm instants, ranging from low levels (e.g. +0.6 m NAP on 18 January 2007 at 14:00) to quite high levels (e.g. +3.2 m NAP on 18 January 2007 at 20:40). The water levels can be seen to be quite non-uniform in space, with the levels at Harlingen being generally higher than those at Nes for the instants considered (predominantly at rising tide). Validation data for these results are available at the observation stations Harlingen and Nes.

Figures 2.12 to 2.14, considered above, include a comparison between the results of the Delft3D simulations, the WAQUA simulations and the observations. These figures show that the water levels produced by the Delft3D simulation, which feature the influence of both wind and waves, are generally higher than those by the WAQUA Wadden West model used by Royal Haskoning (2007). These differences are visible particularly during the passing of the storm, where storm surge is experienced. As a consequence, the Delft3D results can be seen to generally fit the observations better than those of the WAQUA model. It is noted, however, that the water levels are sometimes overestimated by the Delft3D model, namely during the afternoon of 11 January 2007, and at the peak of the storm on 18 March 2007. Nonetheless, the errors in water level are in general relatively small (at most 0.4 m) at the 13 storm instants considered by Royal Haskoning (2007). It is concluded that the water levels produced by the Delft3D simulations provide a better basis for the compilation of the Amelander Zeegat data set than those of the WAQUA Wadden West model.

2.3.3 Bed levels

A second source of inaccuracy in the water depth applied in the Hm0/d ratio is the bed level. It is well known that the sea bed in the Wadden Sea is morphologically active. During the time of buoy placement, the local bed level under the buoy is measured with an accuracy of 0.1 m (B. Spelt 2008, pers. comm.). At the time of placement in the 2006-2007 season, the bed levels under the AZB51, AZB61 and AZB62 buoys were

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observed bed levels were not used in the hindcast study of Royal Haskoning (2007). Instead, these values were extracted from the bed levels used in the SWAN calculation. These bed levels are obtained by interpolating bed level soundings onto a 2D bathymetrical grid, which is subsequently interpolated onto the computational grid of SWAN. These bed levels can therefore have small inaccuracies with regard to both the sounding date of the depth samples used, and also due to triangulation and interpolation errors. Consequently, the bed levels extracted from the bathymetry file, namely -0.73 m, -0.66 m and -1.02 m NAP respectively at the buoys AZB51, AZB61 and AZB62, differ somewhat from the soundings made at buoy placement. Although apparently small, these differences constitute a relatively large error for small values of the total water depth. As a result, in the Amelander Zeegat data set compiled here, the water depths will be based on the observed bed levels at the time of buoy placement.

2.3.4 Time series of total water depth

In Sections 2.3.2 and 2.3.3 above, the computation of the water levels and the accuracy of the observed bed levels were reviewed, and alterations were made to both. Figures 2.19 to 2.21 present the changes to the total water depth (water level plus bed level) that result from the alteration to these two variables. These figures show both the time series of the original total water depth based on the WAQUA water levels and the bathymetric files used in SWAN (considered by Royal Haskoning (2007)) and that based on the Delft3D water levels and the bed levels observed at buoy placement. Compared to the water level comparison (Figures 2.12–2.14), the comparison of the total water depths show differences during the almost the entire observed time, also when the forcing is mainly astronomical. This is due to the generally lower bed levels used in the recomputed water depths. This, together with the generally higher water levels, results in the recomputed total water depths being almost consistently greater than the original values used by Royal Haskoning (2007).

Figures 2.19 to 2.21 also include the periods, indicated by light grey blocks, over which wave data have been rejected based on the selection criteria of Royal Haskoning (2007) (see Section 2.2.1). In addition, a dash-dot line is included to indicate the minimum total water depth at which wave buoy data is accepted based on the outcome of the wave measurement expert group meeting (Section 2.2.2). It can be seen that times during which the water depth are below 1.5 m are mostly contained within the periods over which wave records have already been rejected using the Royal Haskoning criteria. However, at two instances, namely 11/01/2007 around 12:00 (Figure 2.9) and 18/03/2007 around 06:00 (Figure 2.21), water levels below 1.5 m are found just outside of these greyed regions for the buoys AZB51/62/62. In addition, on 18/01/2007 around 14:00, buoy AZB62 was in a water depth of 1.45 m (Figure 2.20). Over these periods, indicated by darker grey areas, wave records will also be rejected in the following.

2.4 Validated Amelander Zeegat data set

From the validated and recomputed (integration over 0.03-0.88 Hz) time series of significant wave height observations (Figure 2.10) and the newly modelled total water depths (Figures 2.19–2.21), the time series of the Hm0/d ratio for the three westerly storms under consideration can be produced. Figure 2.22 shows this Hm0/d ratio for the buoy locations AZB51, AZB61 and AZB62 for the intervals over which the wave buoy observations have been accepted (see Sections 2.2 and 2.3.4). It is noted that the dark

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grey band on 18/01/2007 around 14:00 indicates the rejection of the records of buoy AZB62 only. It can be seen that the Hm0/d ratio varies between 0.12 and 0.43 for the accepted intervals during these three storms. The highest ratios are found for the buoys AZB51 and AZB61, with those of the AZB62 buoy being generally lower. Also shown in Figure 2.22 are the 13 storm instants (vertical lines) of strong depth limitation selected by Royal Haskoning (2007) for their hindcast study (see Section 2.2.1). These storm instants have been selected on the basis of having a high wind speed and having both the wind speed and direction fairly uniform in time (see Figures 2.1 and 2.2). It can be seen that this selection yields Hm0/d values mostly in the range 0.30-0.40, with a maximum value at 0.41. However, one storm instant, namely 11/1/2007 at 14:00 is not ideally chosen – for this instant, the wave records of the buoys AZB51 and AZB61 are not available. This record, indicated by a dashed vertical line, will therefore not be included in the data set for model calibration (see Section 4).

Figure 2.23 presents the depth limitation in terms of scatter plots between the Hm0/d ratio and the dimensionless depth expressed as gd/U102 (with the wind speed U10 taken as the mean of the observations at Hoorn, Lauwersoog and Huibertgat, see Figure 2.1). To produce these figures, the accepted individual records of the time series of wave height, water depth and wind speed have been plotted at intervals of 20 minutes. Figure 2.23 shows three panels, illustrating the influence that the various validation steps have had on the final version of the data set. Included in these panels is the correlation coefficient r for each version of the data set, Figure 2.23 panel (a) shows the original data set of the three westerly storms, obtained by integrating the observed wave spectra over the range 0.03–0.5 Hz, using the water levels from the WAQUA Wadden West model and the bottom levels from the bathymetric grid used in the SWAN hindcasts by Royal Haskoning (2007). It can be seen that when compiling the data set in this manner, the Hm0/d ratio increases with decreasing dimensionless depth gd/U102 with quite a large scatter (r = -0.71), and reach values exceeding Hm0/d = 0.553. As discussed in Section 1.1, such Hm0/d high values over horisontal bottoms have not been reported yet in the literature, and are in part due to underpredictions in the simulated water levels. Panel (b) shows the Amelander Zeegat data set of accepted records compiled with the newly modelled total water depths (Section 2.3), denoted by d’. It can be seen that with the recomputed – mostly increased - water depths (d’) the highest

Hm0/d ratios do not exceed 0.37. However, the scatter in the data set increases, with the correlation coefficient dropping to r = -0.56.

Finally, panel (c) of Figure 2.23 presents the scatter plot of the Amelander Zeegat data set presented as a time series in Figure 2.22, namely that compiled using the significant wave height integrated over the frequency range 0.03-0.88 (Section 2.2) and the newly modelled total water depths d’. By extending the integration range for the wave heights, the Hm0/d ratios increase, now reaching the maximum values of 0.43 reported for Figure 2.22 above. Although still significant, the scatter in the data set has decreased with respect to those presented in panels (a) and (b) (correlation coefficient r = -0.76). Also shown in panel (c) are the data points (in red) belonging to 12 of the 13 storm instants selected by Royal Haskoning (2007) for hindcasting, as indicated in Figure 2.22. As noted above, these hindcast moments feature Hm0/d ratios mostly in the range 0.30-0.40, making them representative of the higher Hm0/d values in the data set.

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3 Analysis of finite depth growth limit data sets

In Section 2, the data set of the Amelander Zeegat was validated with respect to wave observations and water depths. In this section, this verified data set is compared with, and integrated into, the large body of observations for the wave growth limit in shallow lakes available in the literature. These include the shallow Lake IJssel and Lake Sloten in the Netherlands (Figure 1.1) and Lake George in Australia. The central aspect of this comparison is to determine the most effective set of dimensionless parameters with which to consolidate the data contained in the various observational sets. The relationship between the dimensionless parameters found in the overall data set may be used to compose an empirical relation for the finite depth wave growth limit, which may subsequently be used for the calibration of SWAN. The model settings for SWAN found in such a procedure should be validated using selected field cases from the Amelander Zeegat data set.

This section is structured as follows. Section 3.1 presents the individual data sets used in this comparison and the selection criteria applied. In Section 3.2 the formulas for the derived parameters used in this comparison are presented. Section 3.3 presents the actual data analysis, and Section 3.4 closes with some conclusions.

3.1 Data selection and collection

This section gives an overview of the individual data sets included in the comparison study, namely the Amelander Zeegat, Lake Sloten, Lake IJssel and Lake George, and how they were combined into a composite data set.

3.1.1 Wadden Sea: Amelander Zeegat

The data set of Amelander Zeegat is described in Section 2. Before adding these data to the overall data set, the selection criteria listed in Table 3.1 were applied. The criteria with respect to the wave height and water depth correspond to those presented in Section 2. In addition, cases were selected on the basis of having relatively strong wind speeds.

Criterion Formula Dimension

Realistic wind speed 12 < U10 < 50 m/s Realistic wave height 0.25 < Hm0 < 1.5 m

Minimum water depth d’ > 1.5 m m

Table 3.1. Selection criteria for Amelander Zeegat

3.1.2 Lake IJssel and Lake Sloten

The field cases for Lake IJssel and Lake Sloten in the Netherlands (Figures 1.1, 3.1 and 3.2) are comprehensively described by Bottema (2007). Both lakes are shallow compared to their horizontal dimensions and have a fairly flat, sandy bottom. A characteristic water depth for Lake IJssel is about 4.5 m and for Lake Sloten about 1.7 m.

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The wave and wind data for these lakes have been extensively validated and analysed by Bottema (2007). Section 6.6.1 of Bottema (2007) presents a brief analysis of the finite depth wave growth limit. For this analysis, Bottema selected data from a SW-W wind direction sector recorded at station FL24 in Lake IJssel and station SL29 in Lake Sloten in the period 1999-2007 (see Figures 3.1 and 3.2). In the present analysis, the same data are collected, extended with the data at FL2 for 1997 to 1999. For these SW-W directions, a characteristic fetch length for FL2 is about 20 km and for SL29 about 2.9 km.

All measurement data are supplied on the DVD which is enclosed in Bottema (2007). The data were taken from the directory:

\DVD-RWS-RIZA-report2007020\METINGEN_\data\Tabellen A matlab script was applied to collect the data from the files:

vztabSV19971998defFL2.tbx vztabSV19981999defFL2.tbx vztabSV19992000defFL2.tbx vztabSV20002001defFL2.tbx vztabSV20012002defFL2.tbx vztabSV20022003defFL2.tbx vztabSV20032004defFL2.tbx vztabSV20042005defFL2.tbx vztabSV20052006defFL2.tbx vztabSV20062007vlpFL2.tbx vztabSV19992000defSL29.tbx vztabSV20002001defSL29.tbx vztabSV20012002defSL29.tbx vztabSV20022003defSL29.tbx vztabSV20032004defSL29.tbx vztabSV20042005defSL29.tbx vztabSV20052006defSL29.tbx vztabSV20062007vlpSL29.tbx

Before adding these data to the overall data set, the following selection criteria were applied for Lake IJssel (Table 3.2) and Lake Sloten (Table 3.3), in agreement with the procedure applied by Bottema (2007):

Criterion Formula Dimension

Exclude data from summer months Month nr 5,6,7,8,9

-Relevant wind directions 215 < R < 290 oN

Realistic wind speed 12 < U10 < 30 m/s

Realistic wave height 0.1 < Hm0 < 2.5 m

Realistic wave period Tp < 8.0 s

Observed finite depth wave growth limit in the Wadden Sea

limit in the Wadden Sea

Observed finite depth wave

growth limit in the Wadden Sea

Contents

List of Tables

List of Figures

List of Symbols

1 Introduction

2

Amelander Zeegat data set for 2006-2007 storm

season

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t

S

t

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t

A

t

3

Analysis of finite depth growth limit data sets