Identification of wave modelling improvements: Survey of possible improvements in the modelling of physical processes for more accurate hydraulic boundary conditions : project 'SBW-Randvoorwaarden'

(1)

Identification of wave modelling

improvements

Survey of possible improvements in the modelling of physical processes for more accurate Hydraulic Boundary Conditions

Project ‘SBW-Randvoorwaarden’

Joint Venture

WL| Delft Hydraulics - Alkyon Hydraulic Consultancy & Research

March 2004

DG Rijkswaterstaat

Rijksinstituut voor Kust en Zee, RIKZ

(2)

CLIENT: DG Rijkswaterstaat

Rijksinstituut voor Kust en Zee, RIKZ

TITLE: Identification of wave modelling improvements;

Survey of possible improvements in the modelling of physical processes for more accurate HBC: Phase 1

ABSTRACT:

To examine the safety of sea defences Hydraulic Boundary Conditions (HBC) need to be determined. These HBC consist of wave conditions and water levels. One of the essential steps is the translation of offshore wave conditions to wave conditions near sea defences by applying a numerical wave model (e.g. SWAN).

Earlier computations for the determination of the HBC have led to significantly higher wave loads for the Dutch coast than the wave loads that are now officially used for design and evaluation of sea defences. Furthermore, the accuracy of the obtained computational results is doubtful. Recent computations for the Westerschelde and for the coastal area near Petten confirmed this conclusion.

Plans have been launched for a large-scale measuring campaign under supervision of RIKZ to contribute to the improvement of wave modelling that will be used to determine the HBC. The measuring campaign will focus on physical processes that are relevant for the HBC and which cannot be investigated in laboratory or desk studies. Since the campaign will be expensive the choices to be made have to be founded carefully. A first step in that direction is taken in qualitative studies of WL | Delft Hydraulics (2002) and Hoekstra and Hoitink (2002). In the present study a more quantitative analysis has been carried out to investigate which new information should be gathered in order to improve the wave modelling to obtain more accurate predictions of the HBC. This includes an analysis on which wave and water level data have to be collected in the Westerschelde-estuary, tidal inlets of the Wadden Sea, or in the coastal area in front of the Petten Sea-defense.

In this report the results of the first phase are presented. The aim of phase 1 is to investigate the relative importance of the physical processes concerning their effect on the HBC. In phase 2 some indications will be given at which locations information on these processes could be gathered.

The performed analysis resulted in conclusions that bottom friction, wind input and the bathymetry are the most important elements of which the information and modelling should be improved. For triads, quadruplets and white-capping the effect on the HBC is clearly less significant, but due to the rather inaccurate modelling of these processes, they require serious attention. Despite the fact that refraction and surf breaking seem to be important for the estimates of the HBC, there is relatively few space left for improvement of modelling of these processes and thus for improving the accuracy of the HBC.

REFERENCES: Proposal no. MCI03367/H4301/JG/jvs, d.d. 6 August 2003 Contract no.RKZ-1338, d.d. 1 September 2003

VER. ORIGINATOR DATE REMARKS REVIEW APPROVED BY

1 J. Groeneweg et al. December 2003 Draft M.R.A. van Gent W.M.K. Tilmans

2 J. Groeneweg, G. Ph. March 2004 Final M.R.A. van Gent W.M.K. Tilmans

van Vledder, A.R. van Dongeren, D. Hurdle

PROJECT IDENTIFICATION: H4301 / A1183

KEYWORDS: field measurements, wave modelling, tidal inlets, estuaries

NUMBER OF PAGES

CONFIDENTIAL: YES, until (date) NO

(3)

List of Symbols

Symbol Units Meaning

a - Charnock constant

C10 - drag coefficient

Cds2 - scale parameter in white-capping formulation

Cnl - scale parameter inDIAformulation

d m depth D m stone diameter E m2/Hz variance density f Hz frequency fp Hz peak frequency g m/s2 gravitational acceleration

G coupling coefficient inDIAformulation

H m wave height of regular wave

Hm0 m significant wave height

Hrms m root-mean-square wave height

Hs m significant wave height

hsvp m storm surge level

k rad/m wave number vector

m0 m2 0thorder spectral moment (or total wave energy)

mn m2Hzn nthorder spectral moment of surface elevation

n m2/Hz2 action density

P arbitrary wave parameter

R - depth scaling factor in shallow-waterDIA Smag m2/s magnitude of source term

δSnl m

2

/s contribution to transfer rate inDIAformulation

T s wave period of regular wave

Tm01 s wave period based on zeroth (m0) and first order moment (m1)

Tm-1,0 s wave period based on zeroth (m0) and first negative moment (m-1)

Tp s wave peak period

Tpb s block peak period

u* m/s friction velocity

U10 m/s wind speed 10 m above sea surface

Ur m/s Ursell number

UU m/s upwind wind speed

Ux m/s wind speed at fetch length x

z0 m sea roughness length

z0U m upwind roughness length

zkr m height of dike (relative toNAP)

zopl m level to which waves reach (relative to storm surge level)

α deg slope of structure

α - scale parameter in Jonswap spectrum

γ - peak enhancement factor in Jonswap spectrum

δ m thickness of atmospheric boundary layer

(6)

Symbol Units Meaning

κ - spectral narrowness

λ - control parameter for interaction configurationsDIAformulation

θ deg wave direction

σ deg directional spreading

ω rad/s radian frequency

(7)

List of Tables

In text:

2.1 Summary ofSWANparameters used in the sensitivity analysis for the Waddenzee

2.2 Maximum changes in significant wave height and mean wave period along the dikes of the Waddenzee

2.3 Wave conditions at several locations in the flume of Beji-Battjes (1993), to laboratory and prototype scale. Note that Tm-1,0 is not obtained directly from the

spectra, but from the value for Tm01

2.4 Measured wave conditions at location at Petten foreshore

2.5 Wave boundary conditions measured at stationsEUR, YM6,ELD andSON. (1:4000 conditions)

2.6 Estimates of maximum possible changes in wave conditions, required block size, overtopping discharges and required crest elevation

In Appendix A:

(8)

List of Figures

In text:

2.1 Bathymetry of laboratory experiment of Beji and Battjes (1993) 2.2 Model set-up in physical model tests (foreshore)

2.3 Measured incident wave energy spectra for test 2.64 2.4 Amplification factor of nonlinear transfer rate

2.5 Comparison of nonlinear transfer rate computed with an exact method (solid line) and with theDIA(solid line with crosses) for a deep waterJONSWAPspectrum with fp=0.1 Hz,α=0.0175,γ=3.3 and a cos2(θ)-directional spreading.

2.6 Nonlinear transfer rates for a deep water JONSWAP spectrum with fp=0.1 Hz,

α=0.0175,γ=3.3 and a cos2(θ)-directional spreading. Results for deep water, a depth of 10 m and the scaled nonlinear transfer rate.

2.7 Relative water depth change, compared to relative wave height change

2.8 Relative water depth change, compared to relative change in block peak period 2.9 Relative change in zoplcompared to the relative change in wave height

2.10 Relative change in zoplcompared to the relative change in peak period

In Appendix Figures:

F2.1 SWANcomputational grids for the Waddenzee

F2.2 Spatial variation of the significant wave height Hs in the Waddenzee for an extreme condition

F2.3 Spatial variation of the mean wave period Tm-1,0 in the Waddenzee for an extreme

condition

F2.4 Spatial variation of relative difference of the significant wave height Hm0 with

reduced wind input for grid W1 in the Waddenzee

reduced white-capping dissipation for grid W1 in the Waddenzee

reduced surf breaking for grid W1 in the Waddenzee

reduced bottom friction for grid W1 in the Waddenzee

reduced triad interactions for grid W1 in the Waddenzee

reduced quadruplet interactions for grid W1 in the Waddenzee

refraction switched off for grid W1 in the Waddenzee

F2.11 Spatial variation of relative difference of the mean wave period Tm-1,0with reduced

wind input for grid W1 in the Waddenzee

(9)

surf breaking for grid W1 in the Waddenzee

bottom friction for grid W1 in the Waddenzee

triad interactions for grid W1 in the Waddenzee

quadruplet interactions for grid W1 in the Waddenzee

F2.17 Spatial variation of relative difference of the mean wave period Tm-1,0with refraction

switched off for grid W1 in the Waddenzee

F2.18 Spatial variation of the source term magnitude for wind input for grid W1 in the Waddenzee for an extreme condition.

F2.19 Spatial variation of the source term magnitude for white-capping dissipation for grid W1 in the Waddenzee for an extreme condition.

F2.20 Spatial variation of the source term magnitude for bottom friction for grid W1 in the Waddenzee for an extreme condition.

F2.21 Spatial variation of the source term magnitude for surf breaking for grid W1 in the Waddenzee for an extreme condition.

F2.22 Spatial variation of the source term magnitude for triads for grid W1 in the Waddenzee for an extreme condition.

F2.23 Spatial variation of the source term magnitude for quadruplets for grid W1 in the Waddenzee for an extreme condition.

F2.24 Spatial variation of the source term magnitude for wind input for grid W1 in the Waddenzee for a moderate condition.

F2.25 Spatial variation of the source term magnitude for white-capping for grid W1 in the Waddenzee for a moderate condition.

F2.26 Spatial variation of the source term magnitude for bottom friction for grid W1 in the Waddenzee for a moderate condition.

F2.27 Spatial variation of the source term magnitude for surf breaking for grid W1 in the Waddenzee for condition.

F2.28 Spatial variation of the source term magnitude for triads for grid W1 in the Waddenzee for a moderate condition.

F2.29 Spatial variation of the source term magnitude for quadruplets for grid W1 in the Waddenzee for a moderate condition.

F2.30 Spatial variation of relative change in significant wave height Hm0in the Waddenzee

due to current effects.

F2.31 Spatial variation of relative change in mean wave period Tm-1,0 in the Waddenzee

due to current effects.

F2.32 Energy spectra for waves propagating over a submerged bar in laboratory experiments of Beji and Battjes (1993)

F2.33 Spatial variation of significant wave height and mean wave period for waves propagating over a submerged bar in laboratory experiments of Beji and Battjes (1993).

F2.34 Spatial variation of depth and integral wave parameters along the Petten transect for a moderate condition for various computational methods for the quadruplets.

(10)

F2.35 Spatial variation of depth and integral wave parameters along the Petten transect for an extreme condition for various computational methods for the quadruplets.

F2.36 Wave spectrum and corresponding source terms for the quadruplets at location x=20 km along the Petten transect for a moderate condition.

F2.37 Wave spectrum and corresponding source terms for the quadruplets at location x=20 km along the Petten transect for an extreme condition.

F2.38 Spatial variation of depth and integral wave parameters along the Petten transect for a moderate condition, for differentDIAsource term magnitudes.

F2.39 Spatial variation of depth and integral wave parameters along the Petten transect for an extreme condition for differentDIAsource term magnitudes

F2.40 Spatial variation of wind speed and integral wave parameters after a land-sea transition for a wind speed of 20 m/s and deep water.

F2.41 Spatial variation of wind speed and integral wave parameters after a land-sea transition for a wind speed of 20 m/s and a water depth of 10 m.

F2.42 Spatial variation of wind speed and integral wave parameters after a land-sea transition for a wind speed of 40 m/s and deep water.

F2.43 Spatial variation of wind speed and integral wave parameters after a land-sea transition for a wind speed of 40 m/s and a water depth of 10 m.

In Appendix A:

FA.1 Amelander Zeegat: bed elevation relative toMSLwith observation points and cross-sections

FA.2 Case 1: time series for four stations indicated in the figure FA.3 Case 1: time series for three stations indicated in the figure

FA.4 Case 1: instantaneous surface elevation along the cross-section parallel (top) and perpendicular (bottom) to the channel axis

FA.5 Case 1: instantaneous water level

FA.17 Case 4: instantaneous water level FA.18 Case 4: instantaneous water level

(11)

FA.20 Significant wave height distribution (SWAN simulation Amelandse Zeegat) in tidal basin

FA.21 Computed wave profiles at seven stations of Case 3 for the swell propagating into Amelander Zeegat (non-hydrostatic case)

(12)

1 Introduction

1.1 Background of the study

To examine the safety of sea defences Hydraulic Boundary Conditions (HBC) need to be

determined. These HBC consist of wave conditions and water levels. They need to be provided by the National Institute for Coastal and Marine Management (RIKZ). The general systematic approach consists of applying basic statistical information of relevant parameters at offshore locations, performing a large amount of computations to translate offshore wave conditions to wave conditions near the sea defences with a numerical wave model (e.g.

SWAN) and combining these computational data within the probabilistic modelHYDRA-Kfor

determining the normative load parameters near the toe of the sea defences.

Computations for the determination of theHBChave already been carried out in 1999 using the wave model (SWAN version 30.62). The results of these computations have led to significantly higher wave loads for the Dutch coast (DWW, 2002) than the wave loads that are now officially used for design and safety assessment of the coastal structures (Rijkswaterstaat, 2001). Furthermore, the accuracy of the obtained computational results is doubtful. Recent computations for the coastal area near Petten (WL/Alkyon, 2003) and the Westerschelde (Gautier, 2003) for which more recent versions ofSWAN have been applied, have not led to more accurate results.

In particular, measures for the wave period are systematically under-estimated (up to 20%, see e.g. WL/Alkyon, 2003) and are not directly applicable for design and evaluation of coastal defences. Several studies (e.g. Gautier, 2003, Rogers et al., 2003) have indicated that

SWAN strongly under-estimates the amount of low-frequency energy in a tidal inlet or estuary in the case of a multi-peaked wave energy spectrum. It is unclear yet how far low-frequency energy (swell) can penetrate into an estuary or tidal inlet. In this study the penetration of low-frequency energy has been addressed. Furthermore, the approximate formulation of three-wave interactions (triads) leads to an over-estimation of high-frequency energy in shallow areas.

In order to determine more accurate estimates of wave conditions, in particular wave period measures, a correction method is being developed as a short term solution. This is not acceptable for the long term. To determine more reliable values for theHBCthe wave model

to be applied and possibly the way the model is driven need to be improved. For that purpose wave measurements in field or laboratory are extremely valuable.

Very recently plans have been launched for a large-scale measuring campaign under supervision ofRIKZto contribute to the improvement of the wave model that will be used to determine the HBC. The measuring campaign will focus on physical processes that are

(13)

campaign will be expensive the choices to be made have to be founded carefully. A first step in that direction is taken in qualitative studies ofWL| Delft Hydraulics (2002) and Hoekstra and Hoitink (2002). In the present study a more quantitative analysis has been carried out to investigate which new information should be gathered in order to improve the parts of the wave model that are essential to improve predictions of the HBC. Since the operational measuring sites at the Petten sea defence and in the estuary of the Westerschelde only gather information that is representative for these areas, performing new field measurements in the Waddenzee could lead to additional insight into physical processes typically occurring in the tidal inlets and shallow areas of the Waddenzee. Nevertheless, there are processes of which the description in the available wave models need to be improved that can be measured frequently and accurately near Petten and in the Westerschelde. Therefore, the areas near the Petten sea defence and in the Westerschelde are included in this study as well. Besides improving the physical knowledge additional field measurements in an area as the Waddenzee will increase the amount of data to be applied for calibration, validation and verification material for this area.

WL| Delft Hydraulics and Alkyon Hydraulic Consultancy & Research carried out this study as a joint venture. WL | Delft Hydraulics acted as leading partner. D. Hordijk and F. den Heijer were involved on behalf of RIKZ. The study described in this report was performed by G.Ph. van Vledder, D.P. Hurdle and C.E.J. Jacobs of Alkyon and J. Groeneweg, M.R.A. van Gent, A.R. van Dongeren, N. Doorn and A. Luijendijk of

WL| Delft Hydraulics. Quality Assurance was carried out by M.R.A. van Gent.

1.2 Objective

The aim of the study is formulated by RIKZ as: “Determine by means of a quantitative analysis which field data should be gathered from measurements in estuaries, tidal inlets or in a coastal strip in front of the closed Dutch coast, in order to improve those aspects of wave modelling that are of importance to the Hydraulic Boundary Conditions (HBC). Measurement locations where the underlying physical processes are active under less extreme conditions should be indicated as well. Furthermore, the added value of laboratory measurements should be determined.”

In this report the results of the first phase are presented. The aim of phase 1 is to investigate the relative importance of the physical processes concerning their effect on the HBC. Also some indications will be given at which locations information on these processes could be gathered. Furthermore, a plan of action for the second phase is drawn up.

1.3 Approach of the study

Problems in transforming wave conditions from offshore locations to shallow water can roughly be summarized as follows:

• Deficiencies in modelling of ‘short waves’ (wind waves and swell with a frequency

(14)

• Lack of information and modelling tools for ‘long waves’ (f < 0.03 Hz).

• Lack of sufficient validation data from measurements, especially in the Waddenzee.

Among other modelsSWANhas been used for the translation of offshore wave conditions to short wave conditions near coastal defences in shallow water. In order to obtain suitable computational results, the wave model itself has to be improved, and improvements to the application of the model are required. The effects of long waves cannot be taken into account in spectral wave models such asSWAN and their contribution to theHBCshould be taken into account separately.

In the present study the deficiencies in wave modelling will not be solved. As already mentioned in the previous section the objective is to determine which laboratory and field measurements should be carried out in order to improve those physical processes that are relevant for theHBC. In order to fulfil this aim the following steps can be distinguished:

1. Make an inventory of weak points in the modelling of wind generated waves.

2. Make an inventory and prioritize the physical processes and model input that are relevant for theHBCunder design conditions and are modelled relatively inaccurately. 3. Determine locations where field measurements should be carried out that will add

significantly to the improvement of the modelling of the prioritized processes and model input. Additionally, the possible contribution of existing and new laboratory measurements should be evaluated.

4. Based on the analysis determine the information (including specifications and required accuracy) to be gathered in field experiments.

An additional step should be added in order to verify whether the identified request for data will indeed lead to the model improvements in so far as relevant for the HBC. For that purpose additional model simulations using the identified data should be carried out. The latter is not part of the present study, in contrast to the four steps mentioned above. The four steps are divided over Phase 1 (step 1 and 2) and Phase 2 (step 3 and 4).

In Phase 1 of the present study the deficiencies of the wave model have been listed as far as this is of any relevance to theHBC. The result is a list of physical processes and model input (wind, current, bathymetry, water level, offshore wave conditions) that may be the origin of the deficiencies. The next step is to prioritize the processes and model input to the importance for the HBC, by using literature, expert opinions and some indicative computations. The quantities that have to be measured, as well as the required accuracy, for improving the prioritized processes and model input are described as well.

To gain insight into the prioritized physical processes an overview has been given of the most suitable numerical models and methods that describe these processes. Examples are:

• Applying SWAN with strict convergence criteria and high (spatial and spectral)

(15)

• Applying the surfbeat module in Delft3D (Reniers et al., 2000) to analyse the

penetration of swell in estuaries and tidal inlets.

• Applying the Boussinesq-type wave model Triton (Borsboom et al., 2000, 2001) to

quantify the effect of non-linear interactions on the wave conditions.

• Using satellite images or X-band ship radar observations of wave crests to visualise

diffraction and refraction patterns.

• Using alternative parameterisations for e.g. white-capping and quadruplets inSWANthat have not yet been implemented in the standard version 40.31.

In Phase 2 different models and methods will be used to gain a quantitative insight into the physical processes that are relevant for the HBC. Both extreme conditions (1/4000 or 1/10000 years) and more frequent storm conditions (1/2 years) will be considered. The computations for the extreme conditions are required to determine which processes are important for theHBCand under which circumstances. The computations for the conditions that occur on average once every two years are necessary to investigate whether the prioritized processes can be measured frequently enough within a period of ten years and at which location they can be measured best. The computations will lead to so-called ‘patch diagrams’ for the Westerschelde estuary, the tidal inlet of the Waddenzee, and the area around the Petten measuring site. The patch diagrams indicate the relative importance of physical processes with respect to wave conditions or wave loads, and can be used to determine the locations to set up measuring sites to collect data that are used to improve the modelling of the prioritized physical processes. The patch diagrams can also be used to specify dedicated laboratory experiment to measure effects of certain physical processes.

The results of the wave measurements will be used in a repeating cycle of wave model improvements. Elements of this cycle are the execution of hindcast studies, analysis of the wave model results, formulation of model improvements and verification studies. In addition, theoretical developments should be included in this cycle as well.

1.4 Restriction of the study

In this report only the results of the first phase of the study have been described. The individual physical processes are identified that need to be improved to give more reliable estimates for the HBC. The possible influences of a combination of several physical processes is not part of this first phase. Nevertheless, the processes are ordered to the relative effect on the wave load at the sea defences based on the analysis of individual processes. To gain insight into the possible influence of these processes, their effects on hydraulic and structural performance of sea defences are studied by using simplified expressions.

1.5 Outline

In Chapter 2 an overview has been given of physical processes and model input that are of important for theHBC. This is based on a brief literature study, expert judgements and some principal computations. Which models and methods should be used to describe these

(16)

processes and model input as accurate as possible are listed in Chapter 3. Finally, conclusions have been drawn in Chapter 4.

(17)

2 Importance of physical processes

A large number of processes affect the wave motion in estuaries, tidal inlets and other coastal geometries. For each single process the impact on the wave conditions near coastal structures is different. Ideally a list of processes can be determined prioritized to their effect on the HBC. Since we are interested in improving wave modelling in coastal areas, only those processes will be considered of which the modelling need be improved. The following steps have been undertaken to come to the prioritized list of processes and model input:

1. In Section 2.1 an inventory has been made of the deficiencies in modelling coastal areas with the presently used wave models based on results of recently performed hindcast studies.

2. An inventory of the physical processes and model input that are relevant for the HBC

have been determined in Section 2.2. Based on expert judgements a first sorting of these processes has been given.

3. By applying SWAN a sensitivity analysis has been performed in Section 2.3 to gain insight in the effect of the major processes that are modelled in SWAN on the wave conditions near coastal structures.

4. In Section 2.4 additional analysis has been carried out to determine the effect of other processes (e.g. wave-current interaction) or sub-effects of major processes (e.g. wind sheltering behind islands) on the wave conditions near coastal structures.

5. To prioritize the analyzed processes and model input with respect to their effect on the

HBCthe changes in wave conditions near the structures are translated to changes in the wave load as a measure for the change inHBC(Section 2.5).

6. The list of prioritized processes has been rearranged by incorporating the estimated accuracy of the modelling of the processes in Section 2.6. Processes which can be strongly improved have received a larger weight than the relatively accurately modelled processes.

7. An inventory of the data to be collected for model improvement purposes with respect to the prioritized processes and model input has been determined in Section 2.7.

The steps mentioned above finalize Phase 1 of the study. In Phase 2 possible locations in front of the Dutch coast, in the Waddenzee and the Westerschelde will be determined where the required data could be obtained. The potential measuring sites will be compared with alternatives if these exist. In this respect laboratory measurements and already existing field campaigns (e.g. in front of the sea defence of Petten) will be considered.

(18)

2.1 Inventory of deficiencies in wave models

2.1.1 Type of wave models

For obtaining the HBC from numerical model simulations, there are several options. The choice is between spectral wave models, time-domain models, or a combination of both. The choice depends on the required accuracy of the wave conditions near the dikes, the available budget and time for obtaining these conditions, the available data, etc. Also possible developments in the future have to be taken into account. Not only the applied hardware (PC, workstations, network) will improve, but also the models themselves. New insight into physics will result in improved parameterisations and more reliable wave predictions. Furthermore, the numerical models may speed up significantly by improving newly developed numerical techniques.

Nowadays it is common practise to use spectral wave models, such asSWAN, to predict the wave field in coastal areas in front of the closed Dutch coast, in the entire Waddenzee, and in the entire Westerschelde estuary. Spectral wave models can rather accurately predict the wave motion inside the tidal basin or outside the surf zone. However, in very shallow regions, such as tidal flats and surf zones, the accuracy decreases.

Spectral models describe the wave motion in a statistical way. The wave parameters such as significant wave height and wave period are averaged measures, which are used for to assess the safety of sea defences.

Alternatively, time-domain wave prediction models can be used. Nowadays, Boussinesq-type wave models are appropriate to determine the wave conditions in the rather shallow tidal basin of the Waddenzee. In the future (say within 10 years from now) non-hydrostatic flow models may also form an alternative. A disadvantage is that time-domain models require significantly more computational time compared to spectral wave models for computing the wave motion in the same domain. Therefore, time domain models are restricted to smaller domains. On the other hand, if the focus is on the wave conditions near the sea defences, it is not necessary to consider the entire Waddenzee or Westerschelde. If proper ‘offshore’ boundary conditions (which are not necessarily deep water conditions) are available, time domain models can be used to determine theHBC. The offshore boundary for the time-domain model is located inside the larger domain of interest. The boundary conditions can be obtained from measurements or from a spectral wave model describing the wave motion in somewhat deeper water.

The pros and cons of spectral and time domain models are often complementary and can be combined. Time domain models provide accurate wave predictions in the region near the sea defences, whereas the wave field in the rest of the tidal basin can be obtained with a spectral model. Consequently, by coupling the two types of models accurate results can be obtained.

(19)

In this study we focus on the numerical modelling of theHBCby applying third generation discrete spectral wave models. If certain physical processes are not modelled by this kind of model, we revert to time-domain models.

One of the first third-generation wave models is the spectral wave model WAM (WAMDI

group, 1988). The WAM model was primarily developed for deep water application, although some shallow water effects were included. For typical shallow water applications the WAM model required extensive enhancements due time steps limitations. Important enhancements were realised within the PROMISE project (Monbaliu et al., 1999). They achieved a considerably reduction in the computational time needed (decoupling the integration time steps for propagation and source term integration), they also included additional shallow-water physics (bottom friction, depth-induced wave breaking, but not three-wave interactions) and improved numerical stability and accuracy (limiter, propagation scheme). A different development to overcome the limitations of the WAM

model was followed by Booij et al. (1999) resulting in theSWANmodel. In the last couple of years the typical shallow water wave model SWAN has improved significantly and may be seen as state-of-the-art for shallow water applications. The major differences betweenSWAN

and WAM is the implicit treatment of the propagation terms in the transport equation in

SWAN, resulting in an unconditionally stable but not necessarily accurate propagation scheme. Furthermore, triad wave interactions were included in theSWANmodel. These non-linear wave-wave interactions typically occur in very shallow water. However, the performance of the implemented LTA approach (Eldeberky, 1996) for modelling triads in

SWAN, is poor (see e.g. WL | Delft Hydraulics, 1998, and WL/Alkyon, 2002). We return to triads later in this section. Since the area of interest is mainly in shallow water,SWANis the only spectral model that is considered in this study.

2.1.2 Hindcast studies

Recently a number of hindcast studies have clearly showed deficiencies in wave modelling. In this subsection use will be made of hindcast studies and measurements used in these hindcast studies with regard to the coastal waters in The Netherlands and other relevant locations in other parts of the world. The result of the brief literature study will be an inventory of shortcomings in the spectral wave model SWAN. Here we consider the following hindcast studies and mention briefly the main conclusions in terms of results and model deficiencies:

• Verification study of Kaiser et al. (2000) and Kaiser and Niemeyer (2001) in which

SWAN has been applied in the Norderneyer Seegat, which is part of the Waddenzee in Germany. Conclusions drawn in these studies are valid for those to be drawn for the Dutch part of the Waddenzee.

• Reliability study ofSWANandRAND2001 (database ofSWANcomputations for extreme

conditions) in Westerschelde by Gautier (2003).

• Reliability study of SWAN and RAND2001 in front of the Petten sea defence by

(20)

• Analysis ofSWANcomputations for three regional-scale applications inUSby Rogers et al. (2003).

• Analysis ofSWANcomputations for the Slotermeer by De Waal (2001).

Verification study Waddenzee

Kaiser et al. (2000) verified SWAN(version 40.01) against the data of a storm surge from February 1999 with a water level of about 3.4m above mean sea level. In their situation the wind velocity was 19m/s coming from 290°. A number of conclusions given by Kaiser et al. (2000) have been listed below:

• The overall performance ofSWANis good with a very good reproduction of significant wave heights and a slight underprediction of the mean periods.

• Intense wave breaking on the shoals leads to complex multi-peak spectra, which are not

reproduced correctly and lead to a mismatch of the peak periods.

• The wave climate at the lee side of the island of Norderney cannot be reproduced by

SWAN. This is probably due to steep gradients in the bottom topography, the presence of hard structures of a ferry terminal and the lack of diffraction in the model. Furthermore, the wave energy in the low-frequency range is under-estimated significantly. Apparently, long waves are not diffracted around the head of the island.

• The high-frequency tail of the spectra is reproduced correctly, indicating that the local

wind input performs well.

• For the landward located model area there is a mismatch in the directions of 10-40°.

In the same study also a numerical wave model was set up to deliver wave spectra in front of a structure. A design water level (mean sea level +5.0m), and design wind velocity of 30m/s coming from 315° were considered. Two important observations were reported, which are also relevant for the Dutch part of the Waddenzee:

• At the ebb-tidal delta and the island shoreface there is a depth-controlled upper limit for

design wave parameters. For the same water level design wave parameters (wave height, period and direction) do not change if the offshore wave conditions exceed a certain threshold.

• For the investigated design water level, further erosion of the ebb delta shoals will not

lead to a further increase of wave energy on the island shore face.

Hindcast study Westerschelde

The hindcast studies of Gautier (2003) andWL/Alkyon (2003) had the same purpose. Both the reliability of the RAND2001 dataset, which contains SWAN computations (applying version 40.11) for a great number of wave conditions, wind directions and water levels for the Dutch coast, and the reliability of SWAN have been investigated. Furthermore, the simulation approach has been studied. Instead of using model input of the SWAN

computations in RAND2001 (constant water level, no current, parameterised offshore boundary conditions) the simulation method has been optimised. The existing bottom

(21)

topography was extended with the most recent bed information that was available along rays, non-uniform water level fields and current fields obtained from computations were incorporated, and the measured offshore spectra (after some smoothing) were imposed.

Gautier (2003) considered 3 storms (May, 28, 2000; December, 28, 2001; October, 27, 2002). From each of these storms five instants were chosen at whichSWANcomputations in the Westerschelde were carried out. Here we summarise the main conclusions drawn by Gautier (2003):

• In general the wave period is underestimated bySWAN with one second. Possibly the

penetration of long wave energy is not computed correctly bySWAN. Moreover, due to inaccurate modelling of triad wave interactions too much wave energy is shifted towards higher frequencies when waves are propagating over shoals.

• During ebb tide results improve significantly when the ebb current is taken into account.

Incorporation of the current during flood tide does not improve the computational results. More research on the effect of currents on the wave motion is required.

• Near steep slopes a small shift in horizontal direction may induce a strong change in

significant wave height. Not only accurate bottom profiles are required, but also the co-ordinates and depth at the measurement locations should be known with sufficient accuracy.

• The predictive ability ofSWANdepends among others on the model input. Water level

and current fields have been computed with WAQUA. For this application the accuracy of theWAQUAfields is not fully known. Probably the model has not been calibrated for storm situations.

Hindcast study Petten sea defence

WL/Alkyon (2003) presented and analysed results ofSWANcomputations (version 40.11 and research version 40.16) in the area in front of the Petten sea defence (in stationary mode) for 21 moments during 4 storms (January 1/2, 1995; January 10, 1995; February 23, 2002; October 26/27, 2002). Based on an analysis of the computational results and a comparison with measurements the following conclusions can be formulated:

• At the shallowest locations both the significant wave height and the spectral wave

period Tm-1,0 are significantly underpredicted. Comparison of one-dimensional

computations with flume experiments in WL | Delft Hydraulics (2000-a) not only showed that triads wave interactions are modelled inaccurately in SWAN, but the effect of triad wave interactions is exaggerated bySWANas well, leading to under-predictions

of wave periods because, among other deficiencies, only the transfer to higher harmonics is modelled.

• The optimised hindcasting approach generally leads to improved results in comparison

with the standard approach. The inclusion of current effects and the use of a more recent bottom topography improves the results significantly.

• Estimates for the spectral wave period Tm-1,0 have improved considerably by applying

(22)

have not been improved. The latter results can be attributed to a poor description of the wind field near Petten and to poor model behaviour for the high-frequency range.

• Especially in shallow areas accurate knowledge of the bed location is important to

obtain reliable information from a hindcast study.

Analysis of regional-scale models in

US

Motivated by generally poor agreement between model results and measurements of lower frequency energy (0.05Hz-0.19Hz), Rogers et al. (2003) analysed three regional-scale applications. Two separate models have been presented for improving predictions of low-frequency energy. Both models act on the white-capping source term, which is generally used as a tunable closure mechanism and therefore widely believed to be the least accurate of the three primary source terms that are active at all depth: wind, quadruplets and white-capping. Comparison of computations with measurements conducted during the Sandy Duck ’97 field experiment made Rogers et al. (2000, 2003) believe that the poor predictions of the spectral shape, reflected in low mean wave period estimates, are due to the model’s white-capping formulation. Strong improved model results were obtained by disallowing breaking of swell. The impact of the second modification, i.e. changing the weighting of the relative wave number by changing two tunable parameters in the white-capping formulation, yielded no conclusive results to improveSWANfundamentally.

Analysis of computations for Slotermeer

SWAN contains a limiter, which was introduced as a numerical tool to stabilise the computations. In order to avoid severe changes in the solution from one iteration to the next, the solution is allowed to change only a fraction of the analytic Phillips spectrum. For some time the general belief was that the limiter acted as a true source term and had a significant effect on the (converged) solution. SWAN computations for the Slotermeer by De Waal (2001) showed that in an equilibrium situation 10% of the wind input was not balanced by the sum of the dissipative source terms. Recently, Van der Westhuyzen (2003, private communications) presentedSWANresults for the same case of the Slotermeer, which proved that the limiter worked properly and the 10% gap was not filled by the limiter but by the quadruplets. Integrated over all discrete frequencies and directions the source term did not vanish. Apparently the presently used implementation of the DIA formulation for the quadruplets is not conservative. This not only holds for theDIAbut also for more accurate descriptions of the quadruplets. The key problem that there is always a transfer to higher frequencies. In combination with a finite frequency range, this automatically leads to a leak of energy (Pushkarev and Zakharov, 2001, unpublished note). Moreover, despite the fact that most of the features are reproduced, such as the shift of energy to the frequencies below the peak frequency, theDIAhas some deficiencies, which hamper the further development of third-generation wave prediction models, such as WAM, SWAN and WAVEWATCH. Van Vledder et al. (2000) recognised the following deficiencies:

• The agreement between the nonlinear transfer rates as computed with an exact method

(23)

• Compared to both measurements and exact computations, the predicted spectral width is

too large.

• The transfer to higher frequencies is over-predicted, causing irregularities in the total

source term, especially at higher frequencies.

• The present implementation of the DIA in SWAN uses a crude depth scaling for finite

depth.

Hashimoto et al. (2002) demonstrated that the accuracy of the DIA may be improved by taking into account more quadruplet wave number configurations. They proposed a so-called MultipleDIA(MDIA) with up to 6 wave number configurations, which is implemented in the latestSWANversion (version 40.31). At present no systematic comparisons have been made between the effects of different quadruplet formulations on the evolution of the wave field for a wide range of circumstances.

2.2 Inventory of physical processes and model input

2.2.1 Wave processes in Dutch coastal waters

In determining theHBC, offshore wave conditions have to be transformed to shallow water conditions near the sea defences. A number of processes are responsible for the changes in wave height, wave period, spectral shape, propagation direction, directional spreading, etc. E.g. in the Waddenzee the wave conditions near the sea defences depend on the incoming wave field through the tidal inlets, the wave processes in the Waddenzee, and the propagation of the waves towards the dikes. Three trajectories can be distinguished to characterise wave propagation and related processes in the Waddenzee:

• From the tidal inlet around the heads of the Wadden Islands towards the sea defence of

these islands.

• From the tidal inlet through tidal channels towards the dikes of the main land. • From the tidal inlet over tidal flats towards the dikes of the main land.

By following the waves along these trajectories a number of physical processes are encountered:

• Local wave growth where wind input, white-capping and quadruplets act together. • Propagation of swell into the tidal basin.

• The effect of currents on the wave motion in tidal channels.

• Non-linear wave-wave interactions in shallow areas (triad wave interactions). • Dissipation of wave energy due to bottom friction in shallow areas.

• Diffraction of waves around the heads of the Wadden islands. • Reflection on dikes.

(24)

Near the Petten sea defence processes such as refraction and shoaling are more profound than in the Waddenzee. Besides triads, quadruplets play an important role in the Waddenzee as a non-linear wave-wave interaction mechanism because of local wind growth behind the islands. Strong dissipation due to depth-induced breaking is responsible for the generation of long-wave energy. Diffraction and penetration of swell are not important in the Petten area. In the Westerschelde estuary strong ebb and flood currents in the channel affect the wave form.

Besides the physical processes mentioned, knowledge of the following quantities that serve as model input is required. The following aspects play a role:

• Computational results are sensitive to the accuracy of the bed profile, especially in

shallow areas.

• Strong variations in wind velocities exist at land-sea transitions. Spatial sheltering

behind the islands (Waddenzee, Westerschelde) affects the generation of wind waves.

• The offshore wave conditions are often obtained from buoy measurements and should

be accurately imposed as boundary conditions (possibly after some postprocessing).

• In order to model wave-current interaction properly, the flow information should at least

be correctly and sufficiently accurately represented.

• The bed profiles are measured with respect to a certain reference level (NAP in The Netherlands). Since the total water depth is required, the water level must be known as well. These can be obtained from numerical models or measurements.

2.2.2 Inventory of physical processes and model input

In the previous sections a first survey was given to identify the major processes and model input in the Dutch coastal waters.

Physical processes

Based on the work of Battjes (1994), the results from a number of hindcast studies (see Section 2.1.3) and the fundamental studies ofWL| Delft Hydraulics (1998), Alkyon (1999a),

WL | Delft Hydraulics (2000-b) and WL/Alkyon (2002), the physical processes mentioned below are identified to be of importance to theHBC. Their relative importance, with respect to other processes, has been studied in the Sections 2.3-2.4.

1. Wave growth due to extreme wind conditions

For the generation of short-wave energy wind is responsible. The presently available models for wind input in wave prediction models have been developed for weak and intermediate wind velocities. The models have not been validated for extreme wind conditions. Ris et al. (2001) were among the first to study the effects of extreme wind velocities. Several additional questions still remain unanswered:

(25)

• What is the effect of the spatially non-uniform extreme wind velocities on the evolution

of the wave field? In Alkyon (1999a) this problem is addressed for moderate wind speeds and various kinds of instable atmospheric conditions.

• The effect of swell on the growth of wind waves is not fully understood. The amount of

available measurements and validated theoretical models is not sufficient to draw unambiguous conclusions.

• Wave growth in shallow water behaves differently from deep water wave growth,

because wave steepness affects the surface roughness.

• The range of applicability of the present parameterisations for wind input is unknown.

This holds especially for wind forcing in extreme conditions. There are also indications that the drag coefficient reaches some kind of saturation level.

• The reliability of alternative parameterisations for wind input, which include a quadratic

scaling with wind speed, is unknown (Donelan, 1999).

2. White-capping

In WL/Alkyon (2002) a number of deficiencies of the present white-capping formulation in

SWAN have been reported. A critical aspect in the present formulation is the use of a mean wave steepness that is used to scale the dissipation rate. Problems with this formulation are likely to occur in the case of multi-peaked wave energy spectra. These kind of spectra often occur in the Dutch coastal regions and should therefore be improved. In the latter study alternatives for the presently inSWANimplemented formulation of Komen et al. (1984) have been given. The Cumulative Steepness Method is one of them and has been implemented in the latest version ofSWAN (Van Vledder and Hurdle, 2002). Furthermore, the suggestions given by Rogers (2003, see Section 2.1.3 of present study) deserve attention.

3. Wave-current interaction

The importance of wave-current interaction is twofold. Firstly, currents affect the wave propagation and secondly, waves may drive a current or cause significant changes to an ambient current by means of radiation stresses. Here we will focus on the effect of current on the wave field. Apart from refraction effects, Alkyon (2001a) emphasised the importance of wave focussing. They observed variations in wave height and wave period along the dikes due to spatial and temporal variations of the flow field.

In SWAN linear wave theory is applied to model refraction by a current. The flow field is assumed to be uniform over depth. This assumption has been verified insufficiently. In the Waddenzee and the Westerschelde the flow can be strongly three-dimensional, of which the effect on wave propagation is not fully understood. A specific example of wave-current interaction is wave blocking. Since the exact physical mechanisms are not fully understood (a first step was made by Suastika et al., 2000), modelling of wave blocking in spectral models can be improved significantly.

For a relatively strong opposing current wave components can be trapped in a narrow strip. Due to current refraction the wave components cannot escape and a so-called wave tunnel is

(26)

created. Consequently the wave components can propagate relatively far into a tidal basin or estuary. Wave-tunneling can be important for the penetration of swell waves in the Waddenzee and the Westerschelde.

4. Depth-induced breaking

Especially on submerged shoals in the Waddenzee and the Westerschelde and on offshore bars in the shallow coastal area, depth-induced wave-breaking is responsible for significant wave energy dissipation. The present wave models predict the wave energy dissipation due to depth-induced wave breaking rather accurately. Nevertheless, improvements can be obtained, e.g. by including the local wave steepness in the expression for the maximum wave height (see Vink, 2001).

5. Three-wave interactions (triads)

Non-linear three-wave interactions, so-called triads, occur in shallow water. They cause a re-distribution of the wave energy over frequencies and directions. Consequently, the mean wave periods change. The Lumped Triad Approximation (LTA) is often used, but is only applicable in limited number of situations. TheLTAapproach cannot transfer wave energy to lower frequencies. Since the approach is co-linear, directional effects are also not taken into account. The hindcast study for the Petten sea defence learnt that the underestimation of the wave periods in the shallow areas is probably due to the LTA approach. Neglecting the modelling of triads by means of LTA often leads to better predictions of the wave period measures. InWL/Alkyon (2002) a Boussinesq-type model has been applied to show where triads are important and what their effect is on the wave conditions.

6. Four-wave interactions (quadruplets)

Non-linear four-wave interactions, also known as quadruplets, occur both in deep and shallow water. In deep water they transfer wave energy from the spectral peak to lower frequencies and have a stabilising effect on the spectral shape (see e.g. Young and Van Vledder, 1993). In shallow water the quadruplet source term has a different shape and is also stronger than in deep water (see Van Vledder and Bottema, 2002). For wave climates characterised by broad spectra, e.g. swell and wind waves, and for strongly varying wind fields, the quadruplets transfer energy between wave components of different frequencies and directions. Presently, the quadruplets are modelled byDIA approach. In Section 2.1.2 deficiencies of this approach have been listed. In fact, improvements in other source terms are difficult to realise as long as theDIAis part of the wave model. In fact, deficiencies in theDIAare compensated by calibration of other source terms. This conclusion holds also in more general form, replacement of any source term by something better initially leads to worsened model performance, and recalibration is needed to improve model performance, hopefully to a better level than before replacement of a source term.

(27)

7. Refraction

Refraction of waves occurs in areas with variable depth and current velocity. The presently available linear spectral wave models predict refraction reasonably accurately. For SWAN

this has been verified with tests contained in theSWANtestbed. For complex field situations refraction has been verified insufficiently. First of all, it is unclear which spatial resolution is required with respect to uncertainties in the bottom profile. Secondly, non-linear effects will make the refraction velocity dependent on the wave amplitude. Increase of the spatial resolution will generally lead to better predictions of the wave propagation. Thirdly, uncertainties in the current field will affect the reproduction of the refraction effects on wave propagation. Currents in the Waddenzee and in the Westerschelde may have a strong three-dimensional character. The dependency of current refraction on the horizontal and vertical distribution of the current velocity is not fully understood. The assumption of a vertically uniform current field, e.g. made in SWAN, might be too crude for accurately modelling wave refraction on the sheared currents in the Waddenzee and the Westerschelde.

8. Penetration of swell waves

In severe storms swell waves are generated. Depending on the location of the storm these swell waves may have periods of 20-30s and can penetrate into the tidal basin of the Waddenzee and the estuary of the Westerschelde. In combination with local wind sea, multi-peaked spectra arise. Especially the effect of multi-multi-peaked spectra on wave growth by wind and dissipation by white-capping is still unclear. How far and how often swell waves penetrate into the Waddenzee and the Westerschelde is unknown at the moment.

9. Diffraction of swell waves

The omission of diffraction in SWAN is considered to be significant for the prediction of wave conditions at the lee side of an island (see e.g. Kaiser et al., 2000). This mainly concerns the long swell waves (wave periods longer than 15s). Also in channels diffraction patterns may be observed due to refraction waves propagate out of the channels. Consequently, along the channel edges wave energy will accumulate. The resulting lateral gradients in wave energy will give rise to diffraction effects.

Possibly less important physical processes

Several other processes exist that occur in the coastal areas, but these are thought to be of minor importance to theHBC. Here these processes are mentioned and described briefly. For

some of these processes quantitative information about the relative importance of these effects will be analysed.

1. Bottom friction

Locally bottom friction has only a minor contribution to the total amount of dissipation, see Section 2.2.9. Because bottom friction acts over long distances, the dissipative effects over

(28)

the entire range can be significant, especially for swell waves. Moreover, bottom friction strongly depends on currents. Several models for bottom friction have been proposed, but a superior model that is applicable for all situations does not exist. Padilla-Hernández and Monbaliu (2001) studied four bottom friction formulations and correctly state that formulations for dissipation by bottom friction which explicitly take into account physical parameters for bottom friction, should be preferred in wave modelling in shallow water. These parameters offer the possibility to adapt the changing in roughness under different wave or wave-current conditions.

2. Reflection

In general reflection of waves against structures such as dikes and guide walls is not taken into account. The effect of reflection strongly depends on the water level. E.g. near the Petten sea defence the measurements might be affected by reflections at the shallowest location MP6, which is very close to the dike and in between two groins. Whereas short waves mostly dissipate on the slopes of sea defences, long waves are mostly reflected. The reflected long waves will probably affect the propagation of the short waves towards the coast line. This effect is mostly local and non-negligible near coastal structures.

3. Bragg scattering

Bragg-scattering is the reflection of waves against irregularities in the bed profile and causes an exchange of wave energy between different wave components. This process leads to an increase of the directional spreading. For details of this process we refer to Ardhuin and Herbers (2002). For the present context, it is important to note that Bragg scattering will occur mainly in the southern part of the North Sea. Effects of Bragg scattering are assumed to be included in the imposed boundary conditions at the offshore boundaries of the models to be used.

4. Diffraction of short waves

Diffraction of short waves around the heads of the islands. For short waves the typical length scales of diffraction are much shorter than the typical length scale of the heads of the islands. Directional spreading will dominate over diffraction on short-wave scale.

Some processes only have a local effect and are of importance far away from the sea defences under consideration:

5. Wave-induced driving forces

Wave-induced driving forces due to breaking waves near the edges of shoals only have a secondary effect on the current. Incorporation of the ambient current (tidal and/or wind-driven) will probably be sufficiently accurate for the prediction of the wave conditions.

(29)

6. Wave blocking and wave tunnelling

Wave blocking and wave tunnelling are already implicitly modelled within the routines for current refraction inSWAN. The effect on theHBCis probably not significant. For now, the specific aspects of wave tunnelling and wave blocking will not be considered.

Model input

The wave models require input such as bathymetry, wind fields, current fields, water level fields and offshore boundary conditions. The effect of inaccurate model input has also been emphasised in Section 2.1.3. Especially inaccurate bottom profiles gave rise to poor predictions of the wave conditions. Wind, current and water level measurements are obtained at a limited number of locations. Among others, the atmospheric model X-HIRLAM

and the flow modelsWAQUAor Delft3D can be used to determine spatially and temporarily

varying wind fields, current and water level fields respectively.

1. Bathymetry

The wave field is strongly affected by the bathymetry in shallow water, where surf breaking, nonlinear wave-wave interaction and to a lesser extent the bottom friction are dominant. Hindcast studies, such as WL/Alkyon (2003), show that a variation of 0.5m in the bathymetry in the surf zone will change the wave height and wave period, and consequently the wave load, significantly.

2. Land-sea effects on wind field

Land-sea transitions affect the spatial evolution of the wind field due to changes in surface roughness. Furthermore, land and water generally have a different temperature, causing stability effects in the transfer energy from the atmosphere to the wave field. The X-HIRLAM

model is capable to account for these effects. Downscaling techniques are applied taking into account the local roughness.

3. Flow modelling

In general numerical flow models such as WAQUAand Delft3D-Flow can predict currents and water levels reasonably accurately. For complex areas such as the estuary of the Westerschelde and the tidal inlet of the Waddenzee the following questions arise:

• How accurately is the three-dimensional flow structure predicted? Is the vertical

variation in the flow velocity, which is profound especially in channels, correctly determined?

• TheWAQUAmodels for the Dutch coastal area have been calibrated primarily on water

levels in a number of coastal stations and not on current velocities. It is unclear what the effect is of uncertainties in the current velocity on the prediction of the wave field. This will be addressed in Section 3.4.

(30)

• Wave-induced driving forces will affect the flow pattern. Not only in the surf zone

waves are responsible for driving long-shore currents and undertow, but also over shallow shoals the effect of wave-induced radiation stresses may be significant. The latter is insufficiently known.

Summary

The list of physical processes and wave input mentioned in this section give a first impression of the processes that are important to theHBC. Furthermore, the deficiencies of the modelling of these processes have been mentioned. Summarizing, the following physical processes and wave model input will be analyzed quantitatively in the following sections.

1. Depth-induced wave breaking. 2. White-capping.

3. Wind input, including spatially non-uniform wind fields. 4. Three-wave interactions (triads).

5. Four-wave interactions (quadruplets). 6. Refraction.

7. Penetration and diffraction of long waves (swell) into a tidal basin and estuary. 8. Wave-current interaction.

9. Bathymetry.

In the next sections a more quantitative analysis will be carried out by means of some indicative computations. The relevance of the physical processes with respect to the HBC

will be quantified. These computations give a first indication of the methods to be applied in determining the patch diagrams (see Section 3, to be worked out in Phase 2), but cannot lead to definite locations for measurements to be conducted. Therefore, the computations to be carried out in Phase 2 are required.

The importance of the physical processes for theHBChas been determined based on expert judgment, literature review and indicative computations. For a number of possibly representative locations in the Waddenzee, the Westerschelde and in front of the sea defence near Petten, combinations of wave conditions and water level (and wind velocity and direction at deep water) have been chosen which lead to so-called test points. These test points are combinations of wave conditions and water levels which correspond to the standards as used to derive the HBC. For these extreme conditions the effect of a single physical process or model input parameter on the wave conditions near the sea defence under consideration has been determined. Using simple relations the changes in wave conditions are translated into changes in wave load. In this way the effect of the different processes and model input can be compared.

2.3 Sensitivity analysis

SWAN has been used to gain insight in the relative importance of a number of physical processes listed in the previous section. The sensitivity of wave conditions to variations in

(31)

the source terms in SWAN (white-capping, quadruplets, wind input, depth-induced wave breaking, bottom friction and triads) has been studied by determining the effect of a change (10%) in source term on the wave conditions. Refraction due to depth-changes is also modelled in SWAN. The sensitivity of wave conditions to variations in refraction has been studied by completely switching off the effect of refraction. Furthermore, the spatial distribution of the magnitude of the source terms has been determined for a number of extreme wave conditions from which an assessment can be made about the spatial relative importance of various processes.

2.3.1 Sensitivity to source terms variations

TheSWAN model has been applied for the Waddenzee for performing a sensitivity study, in which the ‘elements’ consist of the source terms for wind input, white-capping dissipation, bottom friction, surf breaking, triads and quadruplets. In addition, the effect of switching off refraction was determined. In view of the purpose of this study, an extreme condition is used.

The extreme condition refers to a condition that happens on average once every 4000 years. These are taken from Alkyon (1999b), corresponding to wind class 2 and a wind direction of 285°. Characteristics of this condition are an offshore significant wave height of 9.71 m, a peak period of 16.7 s, an offshore wind speed of 38 m/s, and a wind direction of 285°. The corresponding water level for this condition was set toNAP+5 m (SDU, 2000).

The wave model computations were performed with two nested computational grids: a course grid (N1) with a resolution of 500 m and a finer grid (W1) for the western part of the Waddenzee. The location of these computational grids is shown in Figure F2.1.

The characteristics of the magnitudes of theSWANsource terms used in the sensitivity study

are summarised in Table 2.1. In this table a number of variables are used that refer to the following source terms:

Ufac scale factor for wind input

Cds2 magnitude of white-capping dissipation alpha magnitude of surf breaking

cfjon scale factor of bottom friction trfac magnitude of triad

Cnl4 magnitude of quadruplets

The source terms for depth-induced wave breaking and the quadruplet interactions also contain internal parameters that may affect the evolution of the wave fields. This parameters are the gamma and lambda parameter, respectively. In the calibration study ofSWAN40.20 (Alkyon, 2003) it was shown that these parameters can have a significant effect on the wave heights and wave period measures. Effects of variations of these parameters on the wave conditions are not included in this report.

Identification of wave modelling improvements: Survey of possible improvements in the modelling of physical processes for more accurate hydraulic boundary conditions : project 'SBW-Randvoorwaarden'