Morphological modelling of bar dynamics with Delft3D

Morphological modelling of bar dynamics with Delft3D The quest for optimal parameter settings

Dr.Ir. Alessio Giardino Dr.Ir. Christophe Brière Dr.Ir. Jebbe van der Werf

1202345-000

© Deltares, 2011

7 February 2011, final

Contents 1 Introduction 1.1 Background 1.2 Objective 1.3 Method 1.4 Outline of the report

3 3 3 3 4

2 Description free model parameters 2.1 Introduction 2.2 Wave model 2.2.1 Roller dissipation coefficient rol 2.2.2 Wave breaking index w 2.2.3 Breaker delay F_lam 2.2.4 Bottom friction fw 2.2.5 Roller slope rol 2.3 Flow model 2.3.1 Coefficients in roughness predictor of Van Rijn et al. (2004) 2.3.2 Boundary layer streaming scaling factor fw,fac 2.3.3 Horizontal and vertical background viscosity 2.4 Sediment transport model 2.4.1 Bed slope parameters 2.4.2 Sediment diffusivity 2.4.3 Scaling of sediment transport rates 2.5 Overview free model parameters

5 5 5 5 5 6 7 7 8 8 8 9 9 9 10 11 12

3 Comparison profile model – area model 3.1 Introduction 3.2 Parameter setting 3.3 Model grid 3.4 Boundary conditions 3.4.1 Tidal motion 3.4.2 Wave forcing 3.5 Results 3.5.1 Mild wave conditions 3.5.2 Stormy wave conditions 3.6 Discussions

15 15 15 18 19 19 19 19 20 26 31

4 The calibration procedure 4.1 Purpose of the calibration tool 4.2 Processes and uncertain parameters in Delft3D-Mor 4.3 Requirements for automated calibration 4.3.1 Selection of measures of calibration quality 4.3.2 Calibration technique 4.3.3 The DUD method 4.4 Conclusions

37 37 38 38 38 39 40 42

5 Sensitivity tests and TWIN experiments 5.1 Model set-up

43 43

Morphological modelling of bar dynamics with Delft3D

i


5.2 5.3

5.1.1 Computational grid 5.1.2 Boundary conditions 5.1.3 Computation procedure and other model settings Model sensitivity Testing DUD model (twin experiments) 5.3.1 Introduction 5.3.2 Scenarios 5.3.3 Results 5.3.4 Discussions

43 43 44 44 49 49 50 51 56

6 Model calibration with field data 6.1 Introduction 6.2 Site description 6.3 Measurements 6.4 Model set-up and parameter settings 6.5 Calibration results 6.6 Discussion and conclusions

59 59 59 59 61 61 67

7 Conclusions 7.1 Free model parameters 7.2 Profile model versus area model 7.3 Calibration procedure 7.4 Twin experiments 7.5 Model calibration using field data

69 69 69 69 70 70

8 Recommendations

71

9 References DUD description

73 A-1

Appendices A Appendix

A-1

Preprocessessing tools:

A-1

DUD routines:

A-1

Input files for DUD:

A-1

Output files from DUD:

A-1

Running DUD:

A-1

ii



1 Introduction 1.1

Background The Dutch coast is yearly subjected to a combination of beach and shoreface nourishments. Numerical modelling, accompanied by detailed field measurements, is commonly used to design shoreface nourishments and to assess their development and efficiency. However, the modelling of shoreface nourishments and of the breaker bars to which nourishments are attached is one of the most complex tasks for modellers. This is due to a concurrency of different factors. First of all, the physical processes involved are very complex, especially in the cross-shore direction and their correct balance is crucial in order to determine the direction of transport, and the migration of nourishments and bars (Van Duin et al. 2004). To represent these complex processes, formulations have been developed including a high number of calibration coefficients, often empirical and site dependent (Ruessink et al., 2007). Due to these restrictions, predictions are reliable on a short time scale (weeks). Prediction accuracy decays going towards seasonal time scale, especially moving towards the inner bar (Van Rijn et al., 2003; Ruggiero et al., 2009). Ruessink et al. (2007) implemented an algorithm to estimate the optimum values of the free parameters for the modelling of cross-shore sandbar migration. By means of the Shuffled Complex Evolution algorithm (Duan et al., 1993) they assessed the optimum parameter values for four different data sets, in order to better represent measured bathymetries. The optimization technique was applied to the UNIBEST-TC model. Their results confirmed the impossibility of finding one set of optimum parameters for all four data sets. Bathymetry data are therefore necessary in order to tune the model for a specific site.

1.2

Objective Goal of this work is the setting up of an automatic calibration tool to be used for morphodynamic simulations of bar dynamics and nourishments within Delft3D MOR. The site of Egmond aan Zee (The Netherlands) was chosen for setting up and testing this tool. Main requirements of the calibration procedure are reliable results in a reasonable computational time. This involved the choice of a suitable calibration technique and of a limited number of calibration parameters, which could lead to the best representation of the measured bathymetry. Moreover, the calibration strategy is largely influenced by the choice of target to be reached. Focus of this study was the representation of the bathymetry evolution in the nearshore area between -8 m and -2 m water depth. The results of this project are a first step towards a general calibration guideline for morphological simulations with Delft3D of breaker bar dynamics under different hydrodynamic and wave conditions, and for different locations. This could avoid, in the future, tedious calibration procedures every time a new morphodynamic simulation needs to be executed.

1.3

Method Several steps were undertaken to set up and evaluate the calibration tool. At first, all the free parameters in Delft3D MOR were discussed, focussing on their relative effect on the bar morphodynamics. A second step consisted in the choice of a suitable Delft3D configuration to be used in the calibration tool. For this purpose, hydrodynamic, wave and sediment transport results produced with Delft3D in profile and area mode were intercompared. This assessment showed relatively small differences between results produced adopting the two configurations. Therefore, the profile model was chosen given its higher computational efficiency.


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The next step consisted in the selection of a suitable calibration procedure. Different procedures were evaluated, leading to the final choice of the DUD (Does not Use Derivatives) algorithm of Ralston and Jennrich (1978). Sensitivity tests with the different Delft3D free parameters were performed to reduce the choice of the relevant parameters to be used in the calibration tool. For our applications five parameters were selected: the slope of the wave front in the roller model, the tuning parameter for longitudinal slopes, the scaling factor for current and wave related suspended transport, and the calibration factor for ripples and megaripples in the roughness predictor. The calibration tool was then set-up and tested on a number of artificial experiments (twin experiments) with the aim of converging to a bathymetry developed under known parameter settings, varying the initial values of these parameters. At last, the calibration procedure was applied to a field case at Egmond aan Zee for a 22-day period. A summary of the work methodology and main results can be found in Brière et al. (2010). 1.4

Outline of the report The present report is organized as follows. Chapter 2 gives an overview of all the free parameters in Delft3D MOR. In Chapter 3, Delft3D-MOR results carried out in profile and area mode, for different hydrodynamic and wave conditions, are intercompared. Chapter 4 describes different calibration techniques, with an evaluation of each technique based on suitability to the problem and efficiency. A sensitivity analysis of the parameters described in Chapter 2 is carried out in Chapter 5, leading to a selection of five calibration parameters. Twin experiments were performed based on these five calibration parameters. Based on the considerations from the previous chapters, the calibration algorithm is then applied to the field case of Egmond aan Zee in Chapter 6. Main conclusions of the work are summarized in Chapter 7. Recommendations for further work can be found in Chapter 8.

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2 2.1

2.2 2.2.1

Description free model parameters Introduction The fate of a model simulation is largely determined by the values of the free model parameters. These parameters reflect the uncertainty on how to model certain physical processes and provide the opportunity to tune models using measured data. This chapter summarises the free model parameters in the Delft3D Roller, Flow and Transport module, which are considered the most uncertain and important given the scope of the study. It discusses how these parameters affect the hydrodynamics and morphodynamics, based on the studies of Walstra et al. (2004), Brière & Walstra (2006), Ruessink et al. (2007), Walstra et al. (2008), and Ruggiero et al. (2009). They report on the simulation of breaker bar dynamics and shoreface nourishments with the modelling systems Unibest-TC and Delft3D. Wave model Roller dissipation coefficient rol The shore wave energy, Ew, is defined as:

1 8

Ew

w

2 gH rms

(2.1)

where w is the water density, g the acceleration due to gravity and Hrms the root-meansquare wave height. The stationary balance equation for the short wave energy Ew is:

x

Ew cg cos

y

Ew cg sin

Dw

Df

(2.2)

where cg is the wave group velocity, the wave angle from shore normal, and Dw and Df the wave energy dissipation due to breaking and bottom friction, respectively. The breaking wave dissipation is computed using the expression Baldock et al. (1998):

Dw

1 4

rol

w gf p exp

2 H max 2 H rms

2 H max

2 H rms

(2.3)

with rol a user-defined constant of order one. rol affects the wave height over the complete cross-shore profile, the higher rol the lower the wave height. It has not been used as calibration parameter in the above-mentioned studies. By default rol = 1.0. 2.2.2

Wave breaking index w In Eq. (2.3) fp is the spectral peak frequency and

H max

0.88 w tanh khref 0.88 k

the maximum wave height. In this expression k is the wave number and index. w is a user-defined parameter.


(2.4)

w

the wave breaking

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It can be set at a constant value, or computed by the expressions of Battjes & Stive (1985) or Ruessink et al. (2003). By default w = 0.55 as derived by Roelvink (1993) for wave propagation models that take into account variations on the time-scale of wave groups. w is an important parameter in the wave height prediction in the surf zone, because it imposes an upper limit on the wave height as a fraction of the local water depth. Walstra et al. (2004) compared the formulation of Ruessink et al. against a number of constant w values. For a low (constant) w value wave breaking increased on the outer bar, which resulted in bar flattening; larger w values gave less flattening of the outer bar. Ruessink et al.’s w expression resulted in a more pronounced outer bar which also migrated further offshore. Interestingly, the inner bar was also more pronounced whereas the constant w values did not have a significant influence on the inner bar. This was also found by Brière & Walstra (2006) and Walstra et al. (2008), except that Brière & Walstra showed that applying Ruessink et al.’s expression resulted in a less pronounced outer bar.

2.2.3

Breaker delay F_lam It has been observed that waves need a distance in the order of a wave length to actually start or stop breaking (Roelvink et al., 1995). In Delft3D this phenomenon can be accounted for in two different ways: (1) replacing the local water depth with a water depth weighted over a certain distance seaward of the point in question (Roelvink et al., 1995) (2) replacing the mean Stokes drift with a Stokes drift weighted over a certain distance seaward of the point in question (Reniers et, 2004). In particular when the user-defined parameter F_lam is negative breaker delay is accounted for according to (1), when F_lam is positive according to (2). For morphological computations (1) is used more frequently then (2). However, it is important to point out that: (1) acts directly on the forcing (wave height) by changing the water depth, and as a consequence on the currents. (2) does not affect wave height but only the currents. More in detail, (1) is implemented in the code by replacing in eq. (2.4) href with a water depth obtained from weighting water depths until F_lam (user-defined parameter) wave lengths seaward of the computational point. For example, F_lam = -2 corresponds to two wave lengths offshore; F_lam = 0 corresponds to no breaker delay. By default F_lam = 0.0. According to Walstra (2000), breaker delay generally improves results in case of swell-type of wave conditions. In case of short waves, it often leads to an overprediction of the wave heights. Walstra et al. (2004) investigated the sensitivity and the effect of breaker delay on the cross-shore beach profile after one year. For the considered period, the effect of breaker delay was surprisingly small. Exclusion of breaker delay did not lead to bar flattening as reported by Roelvink et al. (1995) and Reniers et al. (2004). Possibly one year was not enough to model the complete flattening of the profile or the Van Rijn (2007a,b,c) transport formulations do not require breaker delay. Especially, the roughness predictors that lead to a spatially and temporally varying bed roughness are important for bar dynamics. This was also illustrated in Van Rijn et al. (2003) where a cross-shore varying roughness resulted in a realistic bar behaviour without having to include breaker delay. Sensitivity of the final profiles to variation in the averaging length was limited and F_lam mainly affected the outer bar, while the inner bar and beach profile were not significantly influenced.

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2.2.4

Bottom friction fw The wave energy dissipation due to bottom friction is computed using:

Df

w

fw

3 uorb

(2.5)

where fw is a user-defined bottom friction factor and uorb the orbital velocity based on linear wave theory. Bottom friction is not important for surf zone wave energy dissipation, and has not been used as calibration parameter in the above-mentioned studies. By default fw = 0.0. 2.2.5

Roller slope rol The short wave energy dissipation due to wave breaking is a source term in the stationary balance equation for the wave roller energy Er:

x

2 Er cph cos

y

2 Er cph sin

Dw

Dr

(2.6)

where cph is the wave phase celerity and Dr the roller energy dissipation defined as:

Dr

2

rol

g

Er cph

(2.7)

with rol a user-defined constant of about 0.1. The factor 2 in Eq. (2.7) originates from additional dissipation of roller energy due to a net transfer of water from the wave to the roller (Svenden, 1984, Stive & De Vriend, 1994). By default rol = 0.1. The slope of the wave front, rol, is an important parameter in the roller energy balance. It determines largely the rate of wave energy transferred to the roller and from the roller to the underlying water. Low values of rol cause a delayed response. This parameter only has a small effect on the wave height predictions. However, the wave set-up can be influenced significantly. This parameter can be used to calibrate water levels and currents as it determines the cross-shore distribution of the surface shear stress due to wave breaking. Walstra et al. (2004) and Brière & Walstra (2006) showed that the bar flattened considerably when using values larger than 0.1. Decreasing values for rol resulted in more pronounced inner and outer bars. Although in recent studies there was a lot of attention for breaker delay concepts, it seems that tuning of the roller model using rol has a larger effect. It seems to provide a good handle to calibrate and control the behaviour of breaker bars.


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2.3 2.3.1

Flow model Coefficients in roughness predictor of Van Rijn et al. (2004) The predictor of Van Rijn et al. (2004) (see also Van Rijn, 2007a) contains three contributions to the current-related roughness:

ks,c

2 ks,c,r

2 ks,c,mr

2 ks,c,du

0.5

(2.8)

associated with the presence of ripples, mega-ripples and dunes (only present in rivers). These contributions are scaled through the user-defined coefficients fks,r, fks,mr and fks,du, respectively. The wave-related roughness follows from ks,w = ks,c,r.

Brière & Walstra (2006) tested the roughness predictor of Van Rijn. For low f ks,r and fks,mr values, the outer and inner bars migrated further offshore compared to higher values. On the other hand, increasing fks,r and fks,mr led to a slight flattening and widening of the outer bar. The flattening of the inner bar was much more pronounced when increasing the fks,r and fks,mr values. 2.3.2

Boundary layer streaming scaling factor fw,fac The Longuet-Higgins (1953) streaming is a small current in the wave boundary layer in the direction of wave advance. This process can be important in the outer surf zone where limited wave breaking occurs. In the inner surf zone this effect is insignificant because the offshoredirected flow induced by wave breaking and wave mass transport are dominant. Delft3D includes streaming through an additional shear stress (in the wave propagation direction) having its maximum at the bed decreasing linearly across the wave boundary layer to zero. The streaming in Delft3D can be modified by a user-defined scaling factor fw,fac:

streaming

f w,fac

Df c

f w,fac

0.01

2 w orb

u c

(2.9)

Note: the expression for Df in Eq. (2.9) is identical to the one used in the roller model (Eq. 2.5) if fw = 0.01. By default fw,fac = 1.0. Walstra et al. (2004) and Brière & Walstra (2006) showed that with increasing streaming effects an increased erosion of the lower shoreface occurs. The increased offshore migration of the breaker bars with increased streaming as shown by Walstra et al. is counterintuitive, but probably caused by bed slope effects. Brière & Walstra showed that streaming effects did not strongly influence the development of the upper part and of the outer bar. Ruessink et al. (2007) suggested that near-bed streaming is not very relevant to the simulated onshore bar migration.

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2.3.3

Horizontal and vertical background viscosity The horizontal viscosity is computed using: h

h,rol

3D

h,back

(2.10)

where the horizontal eddy viscosity, h,rol, associated with lateral mixing is assumed to be related to wave breaking (Battjes, 1975):

Dr

h,rol

1

3

h

w

(2.11)

with a user-defined threshold value set by the keyword Thr. By default Thr = 0.01 m2/s. 3D is the three-dimensional turbulence computed by the turbulence model and h,back a userdefined horizontal background viscosity. According to the Delft3D flow manual, its value depends on the flow and the grid size used in the simulation. For detailed models where much of the details of the flow are resolved by the grid, grid sizes typically tens of metres or less, the value for the horizontal background viscosity (and diffusivity) should be in the range of 1 to 10 m 2/s. It should be realized that when using the roller model, the horizontal viscosity in the surf zone due to the roller is already of the order of 1 m2/s. By default h,back = 0.0 m 2/s. The vertical eddy viscosity is defined according to: v

mol

max

v,back

,

3D

(2.12)

where mol is the (computed) molecular viscosity and v,back a user-defined vertical background viscosity. In case of strongly stratified flow, a background vertical viscosity may be needed to damp out short oscillations generated by e.g. drying and flooding, boundary conditions, wind forcing etc. Without this background viscosity, these short oscillations will only be damped in the bottom layer. The value suggested for the background viscosity depends on the application. The value must be small compared to the vertical viscosity calculated by the turbulence closure model. General experience is that for stratified estuaries and lakes a value of 10-4 to 10-3 m 2/s is suitable. By default v,back = 0.0 m 2/s. 2.4 2.4.1

Sediment transport model Bed slope parameters Bedload is affected by bed level gradients. Two bed slope directions are distinguished: the slope in the initial direction of the transport (referred to as the longitudinal bed slope) and the slope in the direction perpendicular to that (referred to as the transverse bed slope). The longitudinal bed slope results in a change in the sediment transport rate and is computed using the method of Bagnold (1966):


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S b'

s

S b''

(2.13)

''

with S b the bedload vector unaffected by the bed slope and

s

1

bs

cos tan

1

tan zb s

tan

zb s

1

(2.14)

the longitudinal bed slope correction factor with a minimum value of 0. parameter,

the angle of repose (tan

bs

has a constant value of 0.63) and

is a tuning

zb (with a s

maximum value of 0.9*tan ) is the bed slope in the direction of the unadjusted bedload vector. Note: zb is the depth down to the bed from a reference height (positive down), a downward bed slope returns a positive value of

zb . An additional bedload vector is s

subsequently calculated, perpendicular to the main bedload vector. The magnitude of this vector is calculated using a formulation based on the work of Ikeda (1982, 1988) as presented by Van Rijn (1993):

ub,cr zb ub n

' S b,n

bn

Sb'

where

bn

is a tuning parameter, ub,cr the critical near-bed flow velocity, ub the near-bed

velocity vector and

(2.15)

zb the bed slope in the direction normal to the unadjusted bedload n

vector. Walstra et al. (2004) showed that the transverse bed slope gradient mainly removed the “sharp edges” without adversely affecting the profile behaviour. The longitudinal bed slope gradient had a very limited effect when applied within a realistic range (0 to 5). Larger values resulted in a significant unrealistic flattening of the profile. By default bn = 1.5 and bs = 1.0. 2.4.2

Sediment diffusivity The horizontal, Dh, and vertical diffusivity, Dv, are computed similar to the viscosity, except that the horizontal diffusivity does not contain a roller contribution and that the threshold value Thr does not hold. The horizontal and vertical background diffusivity, Dh,back and Dv,back, are user-defined parameters. Walstra et al. (2004) showed that Dh,back can have a large influence on the morphological prediction and that an unrealistically large value (Dh,back = 2 m 2/s) resulted in an increased flattening of the profile.

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2.4.3

Scaling of sediment transport rates The computed sediment transport contains four contributions: 1) current-related bedload S b,c , 2) wave-related bedload S b,w , 3) current-related suspended load Ss,c and 4) wave-related suspended load Ss,w . These contributions can be scaled using fbed, fbed,w, fsus and fsus,w, respectively. Except for the current-related suspended load, the contributions are directly multiplied with these factors. The sink and source terms of the advection-diffusion equation are multiplied by fsus, and by this affecting the current-related suspended load. By default fbed = fbed,w = fsus = fsus,w = 1.0. In the Delft3D version used by Walstra et al. (2004), the current- and wave-related bedload and the wave-related suspended load were added together and multiplied by fbed. They showed that by excluding the onshore transports (fbed = 0.0; the sum of three contributions is generally onshore-directed) resulted in an irregular profile and an enhanced offshore migration of the inner and outer bar. Including these transport components led to a more realistic profile development when applying factors in the range of 0.5 to 1.5. However, when fbed was increased further an enhanced flattening of the profile occurred, caused by bed slope effects. The influence of the bedload was limited when realistic scaling factors were used. They also investigated the influence of fsus,w with which only the wave-related suspended transport was scaled. They showed that a reduction of fsus,w resulted in enhanced offshore bar migration, whereas higher fsus,w values resulted in a reduction of the offshore bar migration. However, a significant smoothing of the profile was observed when increasing fsus,w, caused by the fact that the wave-related suspended load was added to the bedload, which is affected by bed slope gradients. This caused an enhanced smoothing of the profile, which was considered to be unrealistic. In the Delft3D version used by Brière & Walstra (2006) the bed slope gradient still worked on the wave-related suspended load, but this transport contribution was no longer multiplied by fbed. They found a strong effect of the scaling of the current-related suspended load (fsus) and the migration rate of the inner and outer bars, showing that this sediment transport process was dominant in the development of the beach profile. The coefficient changed the final shape, with a significant offshore migration with increasing fsus. High values of fsus (0.6 to 2.0) caused an unrealistic erosion of the upper part of the profile. However, the common practice of setting fsus to 1.0 seemed appropriate to reproduce properly the dynamics of the inner and outer bars. They also showed that the fbed coefficient did not influence the 1-year evolution of the profile, as current-related bedload is not important for bar dynamics compared to the current-related suspended load. They also investigated the effect of fbed,w and fsus,w. Excluding the onshore bedload, resulted in an irregular profile and an enhanced offshore migration of the inner and outer bar. Including the transports, by applying factors in the range of 0.5 to 1.5, led to a more realistic profile development. However, when the bed load factor was increased further, an enhanced flattening of the profile occurred, caused by bed slope effects on the transports. The influence of the bedload was limited when realistic scaling factors were used. Increasing fsus,w resulted in a reduction of the offshore bar migration. However, a significant smoothing of the profile is noticed for the highest fsus,w values, caused by the fact that the wave-related suspended transports are added to the bed load, which is affected by the bed slope gradients. Note: in the Delft3D version used in this study the bed slope only operates on the bedload and no longer on the wave-related suspended load.


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2.5

Overview free model parameters Table 1 presents an overview of the (main) free parameters in the Roller, Flow and Transport module, together with their default value and the values used in the studies of Walstra et al. (2004), Brière & Walstra (2006), Ruessink et al. (2007) (only concerning the Roller module) and Walstra et al. (2008). Table 2.1 Overview of free parameters in the Delft3D Roller, Flow and Transport modules. W04 denotes Walstra et al. (2004), BW06 Brière & Walstra (2006), R07 Ruessink et al. (2007) and W08 Walstra et al. (2008).

Module

Parameter

Keyword

Unit

W04

BW06

R07

W08

Fwee F_lam

Default value 0.0 0.0

Roller

fw F_lam

-

0.0 -2

Alpharol Betarol

1.0 0.1

-

0.0 -1 (?) 1.0 0.1

0.0 -2

rol

w

Gamdis

0.55

-

fks,r

-

1.0

-

0.0 -2 (-3 – 0) 1.0 0.05 (0.03 – 0.2) -1 (0.5-0.8) -

fks,mr

-

0.0

-

-

fks,du fw,fac

FWFac

0.0 1.0

-

Dh,back

Vicouv Vicoww Dicouv

0.0 0.0 0.0

m2/s m2/s m2/s

Dv,back fbed

Dicoww Bed

0.0 1.0

m2/s -

fbed,w

BedW

1.0

-

0.0 (0.0 – 2.0) 0.01 1.0*10-6 0.1 (0.05 – 2.0) 1.0*10-6 1.02 (0.0 – 1.0) -

fsus

Sus

1.0

-

1.0

fsus,w

SusW

1.0

-

bn

AlphaBn

1.5

-

bs

AlphaBs

1.0

-

0.2 (0.0 – 1.0) 50 (0.0 - 80) 1.0 (0.0 – 50)

rol

Flow

h,back v,back

Transport

1.0 0.05 (0.03 – 0.2) -1 (0.5-0.8,01) 1.0 (0.5 – 1.5) 1.0 (0.5 – 1.5) 0.0 0.0 (0.0 – 2.0) 1.0*10-6 1.0*10-6 0.1

-

1.0 0.05 (0.03) 0.7 (-1,0.5) ?

-

?

-

? 0.0

-

0.01 1.0*10-6 0.1

1.0*10-6 1.0 (0.0 – 2.0) 1.0 (0.0 – 2.0) 1.0 (0.0 – 2.0) 0.3 (0.0 – 2.0) 1.5

-

1.0*10-6 1.0

-

1.0

-

1.0

-

1.0

-

1.0

-

1.5 (50) 1.0 (30)

-1

1. Reference to the model of Battjes & Stive (1985) 2. fbed operated on wave-related suspended load as well

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This table shows that most free model parameters have actually been treated as such in these studies, except for the bottom friction factor, roller dissipation coefficient, horizontal background viscosity and the vertical background viscosity and diffusivity. There is agreement across the studies on the settings of the following parameters: • bottom friction factor fw = 0.0 • breaker delay with F_lam = -2 • roller dissipation coefficient rol = 1.0 • boundary layer streaming scaling factor fw,fac = 0.0 • vertical background viscosity v,back = 1.0*10-6 m 2/s • horizontal background diffusivity Dh,back = 0.1 m 2/s • vertical background diffusivity Dv,back = 1.0*10-6 m 2/s • scaling of current-related bedload fbed = 1.0 • scaling of wave-related bedload fbed,w = 1.0 • scaling of current-related suspended load fsus = 1.0 • coefficient longitudinal bed slope effect bs = 1.0 There is no general agreement on values for the roller slope, wave height-to depth ratio, the horizontal background viscosity, scaling of the wave-related suspended load and the coefficient for the transverse bed slope effects. The sensitivity of the predicted breaker bar dynamics will be investigated in Section 5 and 6.


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3 3.1

Comparison profile model – area model Introduction In this section we focus the attention on the intercomparison between morphodynamic simulation results of the bar behaviour, carried out with profile and area models. Walstra et al. (2004) already noticed evident differences between results from hydrodynamics and sediment transport computations obtained with the two models. These discrepancies were mainly attributed to differences in the calculation of the roller input parameters used to calculate the wave height. In both cases, the roller model is used to calculate the wave height. However, in the area model a SWAN calculation is used for deriving the input parameters for the roller (wave direction and boundary conditions). In the profile model, wave direction is derived by applying Snell’s law to the incoming wave, while peak frequency is assumed to be constant inside the domain. We decided to repeat this intercomparison for two main reasons: • The Delft3D code has changed during the last years. Particularly, the Van Rijn 2004 formulation was added to the code (Van Rijn 2007 a, b, c). It is therefore essential to assess whether these differences are still present, despite the changes applied to the code. • The profile model is computationally more efficient than the area model. For the application to the calibration technique described in Chapter 4, where a high number of simulations is required, the use of the profile model is more attractive. However, the use of the profile model in place of the area model is only possible when the differences between the two models are limited. The comparison focuses on the distribution of wave height, currents and transports along the alongshore uniform cross-shore profile.

3.2

Parameter setting Simulations were carried out by means of the Delft3D model (research version, February 2009) In particular the following modules were used: the hydrodynamic module Delft3DFLOW, the wave module Delft3D-WAVE, and the sediment transport module Delft3D-SED. Delft3D-FLOW and Delft3D-SED are now incorporated inside one module named Delft3DMOR (Lesser et al. 2004). A list including the main parameter settings for the three different modules is given in Table 3.1. A detail description of the physical processes related to these parameters can be found in Chapter 2. The Delft3D-FLOW model solves the Navier Stokes equations for an incompressible fluid, under the shallow water and the Boussinesq assumptions. The vertical space was discretized in 12 -layers with a thickness of 2.0%; 3.2%; 5.0%; 7.9%; 12.4%; 19.6%; 19.6%; 12.4%; 7.9%; 5.0%; 3.2%; 1.8%, of the total water depth, starting from the surface towards the bottom. The time step for the hydrodynamic computation was selected equal to 12 s. The superimposed effect of currents and waves on the bed shear stress was taken into account by means of the interaction model of Fredsøe (1984). Turbulence effects were computed by means of the K-epsilon model. Horizontal background eddy viscosity and diffusivity were set equal to 1 m 2/s. A value of 10-6 was used for the vertical background viscosity and diffusivity. Wave heights were computed using the roller model (Reniers et al. 2004), included in the Delft3D-FLOW module. The roller model consists of one balance equation for the short wave energy, and another one for the roller energy. Wave energy dissipation due to wave breaking is regarded as the only dissipative mechanism inside the balance equation for the short wave energy.


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Wave energy dissipation acts as a source term in the balance for the roller energy propagation. Dissipation due to wave breaking was computed according to the formulation of Roelvink (1993), which is an extension of the Battjes and Janssen model (1978). The wave breaking parameter was assumed constant and equal to 0.7. The slope of the wave front on which roller force acts was assumed equal to 0.05. The default value of 1.0 was used for the coefficient, which calibrates the wave dissipation due to breaking. The breaker delay parameterization of Roelvink et al. (1995) was activated in the roller model. Input parameters for the roller model consist of mean wave direction and peak frequency inside the domain. Moreover, the wave energy at the boundary and a value equal to zero for the roller energy have to be prescribed at the open boundary. The mean wave direction used in the roller model of the profile model was obtained by applying Snell’s law inside the domain while the peak period was assumed constant. In the area model the wave input parameters for the roller model were obtained by means of a stationary run of the Delft3D-WAVE module. The Delft3D-WAVE is based on the discrete spectral action balance equation. Wind input was neglected due to the limited spatial extension of the study area. Wave dissipation due to bottom friction was computed according to the JONSWAP model (Hasselmann, 1973), with the default value for the bottom friction coefficient and equal to 0.038 m2 s-3. Depth induced breaking was taken into account by and parameters were means of the Battjes and Janssen model (1978), where the respectively set equal to 1 and 0.8. Whitecapping and non linear wave-wave interactions were neglected. Directional spreading at the boundary was set equal to 10. The coupling time between the Delft3D-FLOW and the Delft3D-WAVE model was set equal to 10 minutes. The sediment transport and morphodynamic computation were carried out by means of the Delft3D-SED module. The update expression of the TRANSPOR2004 formula (Van Rijn, 2007 a,b) was used to calculate the bedload and suspended sediment transport. Bed shear stress calculation was based on the Van Rijn (2007 a) roughness predictor. Sediment was assumed to be sandy with a D50 equal to 200 m, and a sediment density equal to 2650 kg/m 3. The dry bed density was set equal to 1600 kg/m 3. Suspended sediment diameter at the beginning of the computation has a representative diameter equal to the D50. A minimum water depth equal to 0.2 m was assumed for sediment transport calculation. The transversal and longitudinal calibration factors for bed slope effects were respectively set equal to 1.5 and 1.

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Table 3.1 List of the main numerical parameters used in the simulations

Parameter

Thick

Description Delft3D - FLOW

Value

Vertical distribution of numerical grid

2.0; 3.2; 5.0; 7.9;12.4; 19.6; 19.6;12.4;

(%) ( -layers, from surface to bottom)

7.9; 5.0; 3.2; 1.8

Dt

Time step

12 (s)

Dryflc

Minimum depth for drying and flooding

0.2 (m)

Tkemod

Type of turbulence closure model

K-epsilon

Vicouv

Horizontal eddy viscosity (background

1 (m /s)

2

value, is determined by local production of turbulence due to breaking waves) Dicouv

Horizontal eddy diffusivity

Vicoww

Vertical eddy viscosity (background

2

1 (m /s) 1.0

-6

(m /s)

2

-6

2

value, is determined by local production of turbulence due to breaking waves) Dicoww

Vertical eddy diffusivity (background

1.0 (m /s)

value, is determined by local production of turbulence due to breaking waves) 3

Rhow

Water density

1023 (kg/m )

Rhoa

Air density

1.0 (kg/m )

Rouwav

Bottom stress formulation due to

Fredsoe (1984)

3

wave-current action F-lam

Breaker delay parameter (Roelvink et

-2

al. (1995)) in roller model GamDis

-expression (wave height to water

Constant = 0.7

depth ratio) in roller model Betaro

Slope of wave front on which roller

0.05

force acts in roller model Alfa

Calibration coefficient for wave

1

dissipation due to breaking

Delft3D-WAVE (only for area model) -

Model for bottom friction

Jonswap

Bottom friction coefficient

0.038 (m2 s-3)

-

Model for depth induced breaking

Battjes and Janssen (1978)

Calibration coefficient in Battjes and

1

Janssen (1978) formulation Wave height to water depth ratio in

0.8

Battjes and Janssen (1978) formulation ms

Directional spreading


10

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Delft3D-SED Trafrm

Sediment transport formula

Van Rijn (2007)

-

Roughness predictor

Van Rijn (2007)

SedDia

Median grain size

200 ( m)

RhoSol

Sediment density

2650 kg/m3

CDryB

Dry bed density

1600 (kg/m3)

FacDSS

Factor for defining suspended

1.0

sediment diameter FacDss * SedDia SedThr

Minimum depth for sediment

0.2 (m)

calculation Alfabn

Tuning parameter for transverse bed

Alfabs

Tuning parameter for longitudinal bed

1.5

slope 1

slope Sus

Scaling factor for the current related

SusW

Scaling factor for the wave related

1

suspended transport 0.3

suspended transport ks,r

Calibration factor for ripple roughness

ks,mr

Calibration factor for megaripple

1

predictor 1

roughness predictor

3.3

Model grid The area model was implemented on a longshore uniform bathymetry (Figure 3.1). The grid size ranges between 37 m and 20 m in the cross-shore direction, and it is equal to 40 m in the longshore direction. The wave grid size is coarser with a cross-shore and longshore resolution of 50 m. The profile model correspond to one single cross section of the previous grid.

Figure 3.1 Left panel: wave grid (blue) and flow grid (black). In background the bathymetry of the flow grid. Right panel: bathymetry profile of one cross section..

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3.4

Boundary conditions The computational domain for both the profile and the area model is limited by 4 boundaries: three open boundaries (North, West, and South), where the tidal motion is imposed, and one closed boundary (East).

3.4.1

Tidal motion At the Northern and Southern boundary, the tidal motion was ensured by a longshore gradient in the water level (Neumann boundary) (Roelvink and Walstra, 2004). Due to the limited extension of the model in the cross shore direction, a uniform value of the gradient was assumed along the northern and southern boundary. The sea boundary was forced by a harmonic water level representing a progressive wave in the northern direction. One representative tide was selected and imposed at the Northern and Southern boundary. This representative tide can be described as a superimposition of 6 tidal components. The description of the different components used in the area model is given in Table 3.2. The sea boundary conditions in the profile model were computed through linear interpolation of the boundary conditions used in the area model. The selection of the representative tide was done according to the procedure described by Roelvink (1999). Table 3.2 Harmonic components at the three open boundaries of the area model.

Frequency

Southern Boundary (Neumann)

Northern Boundary (Neumann)

Phase ( )

Amplitude (-)

-5

239.4

1.0583 10

-51.0

1.9849 *10

( /h)

Amplitude (-)

28.8

1.0552 * 10

57.6

2.1222 * 10

-6

86.4

2.8119 * 10

-7

0.70422

149.4

0.70460

151.1

0.26068

-140.9

0.25755

-140.0 -28.8

82.2

9.872 *10

-8

222.2

3.4258 * 10

220.0

5.4651 * 10

172.8

4.8295 10

-7

Phase ( )

239.4

-7

7.8292 * 10

Amplitude (m)

-48.553

4.1933 * 10

144.0

Phase ( )

-6

60.4

1.0348 *10

Amplitude (m)

-5

-6

115.2

Phase ( )

Sea boundary (harmonic) South North

-7

62.528

0.04653

-29.5

0.05016

86.489

0.07163

-7.8

0.07102

-6.2

-7

229

0.00691

132.2

0.00904

134.7

-7

228.69

0.01713

129.9

0.01753

133.1

3.4.2

Wave forcing Two categories of wave conditions were simulated: mild wave conditions (Hs = 1 m; Tp = 6 s) and stormy wave conditions (Hs = 3 m; Tp = 10 s). Simulations were carried out with and without including tidal effects, and assuming different angles of wave approach. A list of all the simulation is given in Table 3.3.

3.5

Results Simulations forced by mild wave conditions, with and without tidal effects, are given in Paragraph 3.5.1. Paragraph 3.5.2 summarizes the results for simulations forced by stormy wave conditions, both neglecting and taking tidal effects into consideration. All simulations were carried out without bed updating in order to have a fair comparison between profile and area model, only dependent on the hydrodynamic and wave conditions but not influenced by the water depth.


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Figure 3.2 – show the outcomes of this study. For each combination of wave and tidal condition the following parameters are plotted: cross-shore velocity, longshore velocity, rootmean-square wave height, cross-shore transport and longshore transport. Table 3.3 List of simulations

Simulation num. 1 2 3 4 5 6 7 8 9 10 11 12 3.5.1

Wave condition Mild waves (Hs = 1 m; Tp = 6 s)

Tidal condition No tide

Wave + tide

Stormy waves (Hs = 3 m; Tp = 10 s)

No tide

Wave + tide

Wave direction ( ) 270 290 310 270 290 310 270 290 310 270 290 310

Mild wave conditions Waves only Figure 3.2, Figure 3.3, and Figure 3.4 show the comparison between profile and area model in case of simulation forced by waves only, and neglecting tidal effects. Wave conditions are characterized by a wave height of 1 m and a peak period equal to 6 s. The direction of the incoming waves is respectively equal to 270 , 290 , and 310 (wave angles given according to the nautical convention). The following conclusions can be drawn: • Differences between the two models are very small for all investigated parameters. • Differences in wave height are in particular negligible despite the fact the wave height is derived with a different approach in the profile and area model. Hrms predicted with the area model is about 1 cm lower than the wave height predicted with the profile model. • Differences in longshore velocities and transport can be locally noticed very close to the shore when the wave angle is equal to 270 . However, these differences are meaningless, due to the fact that longshore velocities and transports for this wave angle are not physically founded and therefore almost nil in magnitude..

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Figure 3.2 Comparison between profile model (blue solid line) and area model (blue dashed line) in case of mild wave conditions (Hs = 1 m; Tp = 6 s ) approaching with a wave angle equal to 270º. No tidal effects were taken into account. The black line represents the bottom profile.



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Waves and tide Figure 3.5 - Figure 3.10 show a comparison between profile model and area model in case of simulation where both wave and tidal effects are taken into account. Wave conditions are characterized by a wave height of 1 m and a peak period equal to 6 s. The direction of the incoming waves is respectively equal to 270 , 290 , and 310 . In the comparison, both low and high tide conditions are shown. The following conclusions can be drawn: • Differences between the two models are now clearly visible, in terms of cross-shore and long shore velocity, sediment transport and locally also wave height. • For wave approaching with a 270 angle, the offshore directed velocity is systematic lower in magnitude in the area model with respect to the profile model. This results in higher onshore transport in the area model due to wave skewness effects. This is clearly visible at the two bars during low tide. • Difference are more pronounced at low tide rather than at high tide, due to relative lower water depths. • Differences in wave height offshore of the inner bar are still very small, even when tidal effects are included.

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Figure 3.5 Comparison between profile model (blue solid line) and area model (blue dashed line) in case of mild wave conditions (Hs = 1 m; Tp = 6 s ) approaching with a wave angle equal to 270º. Parameters representative of low tide conditions. The black line gives the bottom profile.

Figure 3.6 Comparison between profile model (blue solid line) and area model (blue dashed line) in case of mild wave conditions (Hs = 1 m; Tp = 6 s ) approaching with a wave angle equal to 270º. Parameters representative of high tide conditions. The black line gives the bottom profile.


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3.5.2

Stormy wave conditions Waves only Figure 3.11, Figure 3.12, and Figure 3.13 show the comparison between profile and area model in case of simulation forced by only waves, and neglecting tidal effects. Wave conditions are characterized by a wave height of 3 m and a peak period equal to 10 s. The following conclusions can be drawn: • Differences in the cross-shore and longshore transport are now more important than for simulations forced by mild wave conditions. Differences are especially noticeable at the outer bar. • The magnitude of the transport is nearly the same when the wave angle is equal to 290 . However, for a 270 and 310 wave angle both, the offshore and longshore transport, are higher in the area model rather than in the profile model at the outer bar, and offshore directed. • Differences in wave height are negligible.

Figure 3.11 Comparison between profile model (blue solid line) and area model (blue dashed line) in case of stormy wave conditions (Hs = 3 m; Tp = 10 s) approaching with a wave angle equal to 270º. No tidal effects were taken into account. The black line represents the bottom profile.

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Figure 3.12 Comparison between profile model (blue solid line) and area model (blue dashed line) in case of stormy wave conditions (Hs = 3 m; Tp = 10 s ) approaching with a wave angle equal to 290º. No tidal effects were taken into account. The black line represents the bottom profile.

Figure 3.13 Comparison between profile model (blue solid line) and area model (blue dashed line) in case of stormy wave conditions (Hs = 3 m; Tp = 10 s ) approaching with a wave angle equal to 310º. No tidal effects were taken into account. The black line represents the bottom profile.


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Waves and tides Figure 3.14 - Figure 3.19 show a comparison between profile model and area model in case of simulation where both wave and tidal effects are taken into account. Wave conditions are characterized by a wave height of 3 m and a peak period equal to 10 s. The direction of the incoming waves is respectively equal to 270 , 290 , and 310 . In the comparison, both low and high tide conditions are shown. The following conclusions can be drawn: • Similarly to what has been noticed in Figure 3.11, Figure 3.12, and Figure 3.13, differences in sediment transport are clearly visible between simulations run in profile and area mode. For wave approaching with a 290 angle these differences are negligible. However, when the wave angle is equal to 310 , both cross-shore and longshore transport at the outer bar are more important in the area model rather than in the profile model. • Differences in wave height are negligible.

Figure 3.14 Comparison between profile model (blue solid line) and area model (blue dashed line) in case of stormy wave conditions (Hs = 3 m; Tp = 10 s ) approaching with a wave angle equal to 270º. Parameters representative of low tide conditions. The black line gives the bottom profile.

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Figure 3.15 Comparison between profile model (blue solid line) and area model (blue dashed line) in case of stormy wave conditions (Hs = 3 m; Tp = 10 s ) approaching with a wave angle equal to 270º. Parameters representative of high tide conditions. The black line gives the bottom profile.



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3.6

Discussions A number of hydrodynamic and sediment transport simulations were carried out with Delft3D in profile and area mode, under different combinations of wave and tidal conditions, to better understand possible differences between the two models. Despite results being slightly different for different wave conditions, a number of general considerations can be drawn. First of all, very little difference can be noticed for simulations carried out under mild wave condition. The difference increases when simulations are driven by stormy wave conditions. Main discrepancies in terms of sediment transport patterns are observed at the outer bar, up to 20 % for integrated transport over the tidal cycle. In order to identify possible causes of these differences one simulation was carried out under the same conditions used in Figure 3.18 and Figure 3.19 (Hs = 3 m; Tp = 10 s; direction = 310º). However, in the area model currents were not exchanged from Delft3D-FLOW to Delft3D-WAVE. This was done in order to reproduce with the area model the physical processes inside the profile model, which does not account for wave refraction due to currents. The results are shown in Figure 3.20 and Figure 3.21 respectively for low and high tidal conditions. The figures show that the red dashed line (area model without exchange of currents) and the blue solid line (profile model), almost overlap in all plots. This shows that the main mechanism leading to the differences observed between profile and area model is related to the fact that the area model accounts for wave refraction due to currents, neglected in the profile model. These differences are bigger for higher wave heights, when wave driven longshore currents are also stronger and the interaction processes more important.


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Figure 3.20 Comparison between profile model (blue solid line), area model considering the two way coupling between Delft3D-FLOW and Delft3D-WAVE (blue dashed line), and area model neglecting the coupling between Delft3D-FLOW and Delft3D-WAVE (red dashed line). Boundary conditions are representative of a stormy period (Hs = 3 m; Tp = 10 s,

= 310º) at low tide. The black line gives the bottom profile.

Figure 3.21 Comparison between profile model (blue solid line), area model considering the two way coupling between Delft3D-FLOW and Delft3D-WAVE (blue dashed line), and area model neglecting the coupling between Delft3D-FLOW and Delft3D-WAVE (red dashed line). Boundary conditions are representative of a stormy period (Hs = 3 m; Tp = 10 s,

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= 310º) at high tide. The black line gives the bottom profile.



Another possible source of differences between profile and area model results is related to the method used to calculate the wave boundary conditions in the two modules. In particular, the area model accounts for directional spreading at the boundary of Delft3D-WAVE, parameter which is neglected inside the profile model. In order to investigate this effect, one set of simulations was carried out adopting the same wave conditions as in the previous simulation (Hs = 3 m and Tp = 8 s), but using the directional spreading as a calibration parameter inside the area model. Simulations were carried out assuming for the parameter ms, defining the cosine power of the spreading, the values of 4, 20, and 50. These values approximately correspond to spreading of 24.9 , 12.4 , and 8.0 . Results at low and high tide are plotted respectively in Figure 3.22 and Figure 3.23. The Figures show that the directional spreading has a limited effect on the wave height calculation. On the other hand, flow velocities and transport appear to be highly influenced by the value chosen for the directional spreading. In particular at the outer bar, differences in longshore transport up to 30% are observed. This can be explained by the fact that different directional spreading result in different spectral distributions in directional space of the wave energy inside the domain, resulting in different values for the mean wave direction used as input parameter for the roller model. The mean wave directions for different values of spreading are shown in Figure 3.24 and Figure 3.25. The Figures shows that increasing the value of ms (corresponding to a decrease of the angular spreading), waves approach the coast to a higher angle, leading to an increase of the longshore currents. The best agreement between profile model and area model in terms of velocities and transport is obtained for a value of spreading equal to 4 (default value in Delft3D-WAVE).


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Figure 3.22 Comparison between profile model (red line) and area model (blue lines), for different directional spreading: spreading equal to 4 (blue crosses), 20 (dashed line), and 50 (asteriscs). Boundary conditions are representative of a stormy period (Hs = 3 m; Tp = 10 s,

= 310º) at low tide. The black line gives the

bottom profile.

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Figure 3.23 Comparison between profile model (red line) and area model (blue lines), for different directional spreading: spreading equal to 4 (blue crosses), 20 (dashed line), and 50 (asteriscs). Boundary conditions are representative of a stormy period (Hs = 3 m; Tp = 10 s,

= 310º) at high tide. The black line gives the

bottom profile.

Figure 3.24 Mean wave direction for different values of the directional spreading at low tide.

Figure 3.25 Mean wave direction for different values of the directional spreading at high tide.


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4 4.1

The calibration procedure Purpose of the calibration tool Process or physically based models are simplified representations of natural systems, containing equations that express scientifically accepted principles, for instance, continuity and energy and/or momentum conservation for particular (partial) processes and their manifestation on specific scales of interest. However, model predictions are only as reliable as the model assumptions, inputs, and parameter estimates. The presence of parameters in process-based models is a direct consequence of the need to simplify reality or even represent unknown or sub-scale processes as a simple black box term. Essentially, parameters (or actually parameterizations) account for lacking information in the model due to complexity, or non-described spatial and/or temporal variability of the processes considered. In general, model parameters (sometimes referred to as settings in a Delft3D-MOR context) do not represent measurable attributes of the study area and, therefore, their values have to be determined through calibration using input/output relationships. In this study, the purpose of the calibration tool is to determine in an efficient and effective way the optimum parameter setting of the Delf3D-MOR model to compute morphological evolutions in coastal areas with complex bottom topography. This description implies that a piece of software or software environment needs to be developed in which series of model simulations can be made and evaluated for efficient and effective assessment of the effects of variations in Delft3D-MOR parameter settings in a (semi-) automated, quantified, objective and reproducible way. In general, calibrating a computational model comprises of the execution of many model runs with different parameter settings and choosing a set of parameter values that produces the best fit with observational data. Since many automated and semi-automated techniques are available, a choice must be made of the best method. This issue is addressed in paragraph 4.3, according to a.o. the processes and parameters judged uncertain in Delft3D-MOR, the computational time required for one simulation, and the criteria used for the calibration. The calibration tool is effective if the calibration methodology or strategy is such that the evaluation measures (often a combination of quantitative norms and graphical presentations) are sensitive to changes in the Delft3D-MOR parameter settings, both for strongly varying and more smooth error surfaces (i.e. strong or weak response of the Delft3D-MOR solution to parameter variation). In general, interdependence between parameters reduces the effectivity and should be minimized by fixing or limiting the range of one of the parameters. Efficiency implies that a calibration of the Delft3D-MOR model should be possible within reasonable time to allow different combinations of parameter sets to be evaluated. This criterion puts requirements on various aspects of the calibration tool: the calibration method should use only a limited number of model runs; the calibration should only consider a limited number of parameters to be determined; a basic Delft3D-MOR computation should not take too much time. Presently, a typical Delft3D-MOR computation for Egmond-aan-Zee case (with 5 schematized wave conditions) requires an amount of CPU time in the order of 15 minutes and of 15-20 hours, when running the model in a 2DV or 3D mode, respectively.


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In case a time series for the wave input is used, a typical 2DV Delft3D-MOR computation of 1-month morphological developments (Egmond-aan-Zee case) requires an amount of CPU time in the order of 3 hours. This implies that calibration methods requiring thousands of model runs are currently not feasible. 4.2

4.3 4.3.1

Processes and uncertain parameters in Delft3D-Mor The fate of a model simulation is to a large extent determined by the value of the free parameters. Based on the considerations described in chapter 2, the Delft3D-MOR model will be applied by calibrating different parameters in the roller, wave and sediment transport module. Requirements for automated calibration Selection of measures of calibration quality Regarding morphodynamics, the primary variable solved by Delft3D-MOR is the bed level. Such an integral quantity allows for a quantitative evaluation. During the calibration process, a cost function (i.e. the criterion that must be minimised to find an estimate of uncertain model parameters) will be expressed in terms of the integral quantities , i.e. the bed levels zb , as available from measurements on the one hand, and from Delft3D-MOR model computations on the other hand. In a model calibration, the computed values are compared to observations. The latter are here denoted by ˆ . This comparison of model and observations is often based on the residuals ˆ - . In practice a least squares criterion is used in the calibration process. For the associated cost function, J(-) , this will lead to the following generic formulation:

1 2

J( )

While

N n

w 1 n

ˆ

n

(4.1)

denotes the model prediction, the corresponding measured value is denoted by

n

ˆ . The model predictions n 1

2

n

2

,...,

n

and these

P

1,...,P

are a function of P uncertain model parameters are the estimates of the model parameters. N is the total

number of measurements and is in this case the number of selected grid cells. The coefficient wn is a weight assigned to the n-th measurement. These weights can be different. They allow us to give more weight to the results obtained in the active bar zone v.s. the ones obtained in the swash zone (limit of validity of the shallow water equations). The cost function can be also written in an equivalent form:

J( )

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1 2

N

ˆ

n

2

n

n 1 n

(4.2)



4.3.2

Calibration technique Existing reviews (e.g., Sorooshian and Gupta, 1995; Lewis et al., 2000; Duan, 2003) show a bewildering number of calibration techniques. Despite the large amount of techniques, some sort of classification can be made. At the highest level, calibration techniques can be separated into manual and automated techniques. The present-day practice with Delft3DMOR is manual calibration (e.g. sensitivity analysis). Here we focus on an automated technique, which has the advantage over manual techniques that it can speed up the process of calibration and is more objective. Automated calibration starts with two phases, viz. (1) the selection of the parameters to be included in the calibration procedure and (2) the actual selection of values for these parameters (see chapter 2). The calibration consists then to try to improve these values following specific rules. The following table summarizes the main pros and cons of the optimization techniques that have been discussed in van den Boogaard et al. (2007) as potential suitable calibration techniques for SWAN model. These calibration techniques can be used for Delft3D-MOR model as well. In the table, a first assessment of suitability for Delft3D-MOR is given, according to the arguments discussed in van den Boogaard et al. (2007). Table 4.1 Pros and cons of selected optimisation techniques. The suitability for Delft3D-MOR in column four is indicated on a range from “ -- “ (highly unsuitable) to “ ++ “ (highly suitable).

Technique

Downhill simplex

Pros

- Robustness - Ease - Error surface is used in relative sense only

Powell

- Reasonably efficient

DUD

- Highly efficient; - Often much less than 100 model simulations

Gradient

- Efficient when gradient information is known - Provides first-order approximations of parameter uncertainty

Multistart

- Global search - Ease - Global search - Detailed knowledge of

Gridding

Cons

- Local minimum - Not very efficient - Poor convergence for interdependent parameters - Unconstrained (although easy to fix) - Local minimum - Unconstrained (although easy to fix) - Local minimum - Unconstrained (although easy to fix) - Only for least squares criteria - Requires gradient information (time-consuming or inaccurate) - Local minimum - Inefficient when error surface is not quadratic - Unconstrained - Inefficient, individual starts do not exchange information - Highly inefficient (often many thousands of model simulations)


Suitable for Delft3DMOR 0/+

+

++

--

--

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URS, ARS

Genetic algorithm

SCE

4.3.3

error surface is obtained - Constrained - Global search - Detailed knowledge of error surface is obtained - Good starting point for local search method - Constrained - Global search - Reasonably efficient - Can provide good starting point for local search method - Constrained - Potentially the best method available - Constrained

- Inefficient (hundreds to often thousands of model simulations); ARS is still more efficient than URS, however

-

- Poor convergence once the vicinity of the optimum parameter set has been found

-

- Very computationally demanding

--

The DUD method The DUD (Doesn’t Use Derivatives) technique of Ralston and Jennrich (1978) is a directional minimization method. The main issue in the algorithm is that search directions are repeatedly computed on the basis of a linearization of the model response functions

n

in Equations

(4.1) and (4.2). This linearization is in the form of a so-called secant approximation of the n

, rather than computing a tangent plane as commonly used in gradient descent

techniques. The DUD method operates as follows: the model must be evaluated for P+1 (mutually linearly independent) parameters (2)

(P)

(1)

,

(P+1)

, …, , . As an example, Figure 4.1 shows a sketch on how the DUD method operates. In this case, the method is applied to optimize two model parameters and . Tree simulations are then carried out, with parameters [ 0 , 0 ],[ 0+d , 0 ] and [ 0 , 0+d ]. a search direction is then computed, and a (one dimensional) line minimization procedure is carried out. In Figure 4.1, the search direction results in the determination of a set of parameters [ 1 , 1 ] to be tested. In fact, the first iteration step may require a few more model evaluations to find a new and better estimate. The procedure is therefore repeated (see Figure 4.2) using the P+1 sets, that provide the lowest cost functions, until a minimum is found. still, when no minimum is found, a line search is performed along the segment that provides the lowest cost functions. In this way, the DUD method is a (i) local, (ii) directional, and (iii) iterative minimization method. The number of iterations is model dependent, and will be about P but when P 10. In this way a reasonable estimate for the total number of required model evaluations is expected to be about 5 to 8 times P. Although this has yet to be verified for Delft3D-MOR, this number will not be limiting the practical feasibility of the DUD method.

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costF

( 0+d , 0+ d ) ( 0+d , 0)

( 0, 0)

Figure 4.1 Sketch for operation of the DUD method

costF

costF

Figure 4.2 Repetition of the procedure for evaluation of the minimum

Considering functional and practical requirements, the DUD-minimisation algorithm of Ralston and Jennrich (1978) satisfies all the demands for Delft3D-MOR calibration. In fact,

The technique is optimally designed for least squares minimization criteria, i.e. for cost functions J

of the form: J ( )

1 2

N n

w 1 n

n

ˆ

2

n

Although gradient free (DUD stands for Doesn’t Use Derivatives), the method algorithm, and more importantly its computational efficiency to identify the minimum of the J of Equation (4.1), is comparable to those of quasi-Newton (or, in other words, variable metric) gradient descent techniques.


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For more details and benchmarks where the performance of the DUD-method is compared to other minimization techniques, one is referred to Ralston and Jennrich (1978), who conclude that the DUD method works well on a variety of minimization problems and often outperforms other techniques. 4.4

Conclusions Generic and model independent calibration techniques discussed in paragraph 4.3.2 simply treat the (Delft3D-MOR) model as a mathematical function of the parameters. On request of the calibration technique, the numerical model must produce its response to a variation of the parameters. This response of the numerical model is merely used by the calibration technique to adapt the Delft3D-MOR parameter settings and activate a new model evaluation. The calibration technique does not use, and is neither dependent on, or interested in, any detail about the internal properties of the model and algorithms that are used to produce the output that corresponds to the prescribed parameter settings. As a result, the communication between the calibration technique and the numerical model is relatively simple, and highly independent of the actual calibration techniques. From a practical viewpoint this means that an existing calibration environment (DUD-environment developed by H. van den Boogaard) can be and will be used. For the calibration of a Delft3D-MOR model for Egmond-aan-Zee (or comparable model areas), the computation time for a model evaluation is in the order of 3 hours, when running the model in the 2DV mode with time series of wave input. This suggests that an (automated) calibration session should not exceed an approximate number of 50 evaluations, to limit the computational time. By all means, the model high computation time is then by far the limiting factor in choosing practically feasible and suitable calibration techniques. Among all the techniques considered, the DUD-method of Ralston and Jennrich (1978) is undoubtedly the best candidate for the calibration of Delft3D-MOR. The number of required model evaluations is (roughly estimated) about 5 to 8 times the number of uncertain model parameters. In practice, the number of uncertain model parameters in a Delft3D-MOR calibration will vary from about 4 to 8, which restricts the total number of computation to a value close to 50 (4 - 8 uncertain parameters 5 8). Thus, the Delft3D-MOR model will be employed by allowing adjustments in model output by the parameters in the flow and roller model (e.g. rol, w) and in the sediment transport equations (e.g. fsus, fsusw, bs). It must be mentioned, however, that the DUD-method is optimally designed for least squares criteria and cannot readily be generalised to arbitrary other forms of cost functions. For Delft3D-MOR, this is not really a disadvantage since a quadratic cost function can be chosen as a suitable Goodness of Fit measure. This cost function (i.e. the criterion that must be minimised to find an estimate of uncertain model parameters) will be expressed in terms of integral quantities, i.e. the bed levels, as available from measurements on the one hand, and from Delft3D-MOR model computations on the other hand.

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5

Sensitivity tests and TWIN experiments In this chapter we study the sensitivity of the model to the free model parameters as described in Chapter 2 and test the DUD calibration procedure (see Chapter 4) using socalled TWIN experiments. We do this for the same model set-up, which is described in Section 5.1. The next two sections discuss the model sensitivity and the testing of the DUD model, respectively.

5.1

Model set-up The hydrodynamics, sand transport rates and bed level changes are simulated with a twodimensional vertical (2DV) Delft3D model (Version 3.60.01.7844, July 13 2009). Wave transformation follows from the Roller module and Snell’s law, both part of Delft3D-FLOW. The derived bathymetry and boundary conditions are representative for Egmond and Zee, which is located in the northern part of the 120 km long closed Holland coast that runs from Hoek van Holland in the South to Den Helder in the North. The nearshore morphology can be considered as alongshore uniform and is characterized by two subtidal breaker bars and one intertidal swash bar. In paragraph 5.1.1 - 5.1.3 a brief description of the model set-up is given.

5.1.1

Computational grid The same grid as described in paragraph 3.3 (profile model) was used to carry out the sensitivity tests and twin experiments. The grid covers a cross shore distance equal to 1500 m, including the upper shoreface, surf zone and beach, with a resolution ranging between 37 m and m at the seaward boundary to 20 m in the surfzone.

5.1.2

Boundary conditions The tidal forcing is accounted for by a so-called morphological tide, which consists of a single semi-diurnal tidal cycle (with a duration of 12.5 hrs) representing the average long-term situation. Water levels are imposed at the offshore boundaries and water level gradients at the lateral boundaries (see Paragraph 3.4). The wave climate is represented by four wave conditions ensuring identical yearly gross northward and southward transports by scaling the selected wave conditions (see Van Duin et al., 2004; Walstra et al., 2004). Table 5.1 shows the morphological wave climate, i.e. the significant height (Hs), the peak period (Tp), angle of incidence ( ), duration and the morphological scale factor (Morfac), which is discussed in the next section. Table 5.1 Morphological wave climate

Name d225h d225a d325h d325a

Hs (m) 2.75 1.25 2.75 1.25

Tp (s) 8.3 6.5 9.5 7.5


(oN) 225 225 325 325

Days 5.8 66.6 4.6 47.4

Morfac 11.1 127.8 8.8 91.0

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5.1.3

Computation procedure and other model settings Every flow time step (12 s) the waves, currents, sand transport rates and bed level changes are computed. To reduce computational time, the bed level changes are multiplied with a morphological scale factor (Morfac), so that after one time step, t, we have in fact modelled morphological changes over a period equal to Morfac* t. This is valid since changes in morphology occur on a much longer time scale than changes in hydrodynamics (see Roelvink, 2006). The Morfac values are determined by dividing the duration of each wave condition by the duration of the morphological tide. The wave conditions are run serially. The wave condition d225h start with the initial bathymetry. The resulting bathymetry (after one morphological tide) feeds into the simulation with the wave condition d225a. This is repeated until four model simulations (one for each wave condition) have been carried out. In this way one year of morphological change is simulated. The roughness is predicted using the method of van Rijn (2007a). The imposed bed sediment is uniform with a D10, D50 and D90 of 0.15, 0.20 and 0.30 mm, respectively.

5.2

Model sensitivity In this section we look into the sensitivity of the model to the following free model parameters: the bed slope coefficients bn and bs, roller parameters rol and rol, sand transport multiplication factors fbed, fbed,w, fsus and fsus,w, horizontal background viscosity and diffusivity (Vicouv and Dicouv), roughness factors fks,r and fks,mr and the streaming factor fw,fac. We carry out 200 computations for pairs of free model parameters, which settings follow from sampling using a Latin hypercube sampling strategy within parameter ranges which are considered to be realistic based on morphological modelling practice (see therefore Table 2.1). For each computation we calculate the model skill R in the following way: 2

zmodel ( x) zobs ( x) R 1

x

zobs ( x ) zini ( x )

2

(5.1)

x

where zmodel is the predicted bed level after one year, zobs the observed bed level after one year and zini the initial bed level (Van Rijn et al., 2003). The model skill equals 1 when the model predictions and the observations are in perfect agreement and reduces to 0 when the model error (numerator in the fraction of Eq. 5.1) is equal to the persistence error (denominator in Eq. 5.1; an indication of the morphological change and thus of the persistence of initial bed level). In case the model performs worse than the no-change mode, R becomes negative. The model skill is calculated for bed levels in the range of NAP -2 to -8 m, which is the area on interest. In our case zobs follows from a computation with the settings as presented in Table 5.2.

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Table 5.2 Default setting model computations.

Symbol

Name

Value

F_lam

breaker delay

-2

rol

roller dissipation coefficient

1.0

rol

roller slope

0.05

w

wave breaking index

-1 (Ruessink et al., 2003)

fks,r

scaling factor ripple-related roughness

1.0

fks,mr

scaling factor megaripple-related roughness

1.0

fks,du

scaling factor dune-related roughness

0.0

fw,fac

boundary layer streaming scaling factor

0.0

h,back

horizontal background diffusivity

0.01 m2/s

Dh,back

horizontal background diffusivity

0.1 m2/s

fbed

scaling of current-related bedload

1.0

fbed,w

scaling of wave-related bedload

1.0

fsus

scaling of current-related suspended load

1.0

fsus,w

scaling of wave-related suspended load

0.3

bn

coefficient transverse bed slope effect

1.5

bs

coefficient longitudinal bed slope effect

1.0

Figure 5.1 to Figure 5.6 show the sensitivity of the model skill to (pairs of) the free model parameters. Figure 5.1 shows that the relation between the model skill and roller parameters rol and rol is asymmetric. An increase in these parameters with respect to their default values hardly affects the model skill, whereas a decrease strongly lowers skill. Furthermore, it shows that at low values of rol (

Morphological modelling of bar dynamics with Delft3D

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