Appendix C - Marine and coasts - Marine and coasts

Advisian Portsea Front Beach Wave Modelling and Monitoring Investigation

301015-03540-Report-Rev 0 160115.docm

Appendix C

Wave Transformation

Advisian Appendix C Wave Transformation Page ii

301015-03540-Appendix C - Wave Transformation - Rev 0 160115.docm

Table of Contents

1 Introduction 1

2 Spectral Wave Model 2

2.1 Flexible Mesh 2

2.2 Boundary conditions 5

2.3 Numerical Parameters 6

2.4 Refraction of swell wave energy 8

2.5 Distribution of Wave Energy along Portsea Front Beach 11

2.6 Sensitivity to Numerical Parameters 13

2.7 Wave-current interaction 15

2.7.1 Current fields 15

2.7.2 Effect of currents on wave refraction 20

2.7.3 Effect of Wave-Current Interaction on Wave Heights at Portsea 23

2.8 Simulated Data at Validation Points 27

2.8.1 Rip Outer Bank Centre Line (ROBCL) 29

2.8.2 Rip Bank Centre Line (RBCL) 30

2.8.3 Nepean Bank Centre Line (NBCL) 31

2.8.4 Popes Eye Bank (PEB) 32

2.8.5 Nicholson Knoll (NK) 33

2.8.6 Portsea Front Beach 34

2.9 Comparison with Measured Data 35

2.9.1 Port Phillip Heads 35

2.9.2 Port Phillip Bay and Portsea Front Beach 36

2.9.3 Comment on Measured Wave Height Coefficients at Portsea 38

3 Boussinesq Wave Model 41

3.1 Grid and Bathymetry 41

3.2 Sponge 42

3.3 Wave conditions 43

Advisian Appendix C Wave Transformation Page iii


3.4 Numerical Parameters 44

3.5 Results and Discussion 45

3.5.1 Refraction of swell wave energy from The Entrance 45

3.5.2 Distribution of wave energy along Portsea Front Beach 50

3.5.3 Comparison with Measured Data 52

4 Spectral Analysis of Wave Refraction 54

5 Simulated Nearshore Wave Climate 64

5.1 Method 64

5.2 Results 64

6 Summary and Conclusions 76

6.1 Spectral Wave Model 76

6.2 Boussinesq Wave Model 76

6.3 Spectral Analysis of Wave Refraction 77

6.4 Wave Climate 77

7 References 78

List of Figures

Figure 2-1: MIKE-21 flexible mesh of Port Phillip Bay

Figure 2-2: Triangulated Irregular Network (TIN) of sea floor levels within Port Phillip Bay, based on

linear interpolation of 2012 LADS survey and navigation chart data obtained from chart

AUS00143. The TIN elevations are interpolated to node positions shown in Figure 2-1.

Figure 2-3: Flexible mesh (upper panel) and bathymetry (lower panel) in the region of Portsea.

Figure 2-4: Propagation of swell wave energy into Port Phillip Bay, for incident Mean Wave Direction

(MWD) of 210°, Peak wave period (Tp) of 10 seconds, and offshore wave height of 1.0m. Wave

heights are presented as a ratio of the wave height applied at the model boundary.




Advisian Appendix C Wave Transformation Page iv












(MWD) of 210°, Peak wave period (Tp) of 20 seconds, and offshore wave height of 1.0m.

Wave heights are presented as a ratio of the wave height applied at the model boundary.

Figure 2-10: Variation of wave height coefficients along Portsea Front Beach between Police Point and

Point King.

Figure 2-11: Variation of simulated wave height coefficient with offshore wave period, offshore wave

height and incident wave direction at Port Phillip Heads.

Figure 2-12: Sensitivity analysis of simulated wave height to: Directional spreading factor, n (upper

panel); Directional resolution (middle panel); Bed friction (lower panel).

Figure 2-13: Depth-averaged current magnitude and direction (upper panel) and surface elevation (lower

panel) for spring tide, peak flood conditions.

Figure 2-14: Depth-averaged current magnitude and direction (upper panel) and surface elevation

(lower panel) for spring tide, peak ebb conditions.

Figure 2-15: Depth-averaged current magnitude and direction (upper panel) and surface elevation (lower

panel) for neap tide, peak flood conditions.

Figure 2-16: Depth-averaged current magnitude and direction (upper panel) and surface elevation

(lower panel) for neap tide, peak ebb conditions.

Figure 2-17: Propagation of swell wave energy into Port Phillip Bay during slack-water. MWD = 210°, Tp

= 12.0s, Hm0offshore = 1.0m. Wave heights are presented as a ratio of the wave height applied at

the model boundary.

Figure 2-18: Propagation of swell wave energy into Port Phillip Bay during peak flood tidal currents,

spring tide. MWD = 210°, Tp = 12.0s, Hm0offshore = 1.0m. Wave heights are presented as a

ratio of the wave height applied at the model boundary.

Figure 2-19: Propagation of swell wave energy into Port Phillip Bay during peak ebb tidal currents,

spring tide. MWD = 210°, Tp = 12.0s, Hm0offshore = 1.0m. Wave heights are presented as a

ratio of the wave height applied at the model boundary.

Figure 2-20: Propagation of swell wave energy into Port Phillip Bay during peak flood tidal currents,

neap tide. MWD = 210°, Tp = 12.0s, Hm0offshore = 1.0m. Wave heights are presented as a ratio

of the wave height applied at the model boundary.

Advisian Appendix C Wave Transformation Page v


Figure 2-21: Propagation of swell wave energy into Port Phillip Bay during peak ebb tidal currents, neap

tide. MWD = 210°, Tp = 12.0s, Hm0offshore = 1.0m. Wave heights are presented as a ratio of the

wave height applied at the model boundary.

Figure 2-22: Distribution of wave height coefficients along Portsea Front Beach, between Police Point

and Point King. Peak spring flood tide, using current fields shown in Figure 2-13.

Figure 2-23 Distribution of wave height coefficients along Portsea Front Beach, between Police Point and

Point King. Peak spring ebb tide, using current fields shown in Figure 2-14.

Figure 2-24: Effect of spring tidal currents on wave height coefficients of different offshore wave heights

and peak wave periods, for the most energetic section of Portsea Front Beach. Upper panel:

Peak flood spring tide. Lower panel: Peak ebb spring tide. Results obtained using current

fields given in Figure 2-13 and Figure 2-14.

Figure 2-25: Locations of spectral wave model validation points. Location of Port of Melbourne

Corporation wave buoy (used to derive bundary conditions for the wave model) also shown.

Figure 2-26: Simulated wave height coefficients at ROBCL for various combinations of offshore wave

height and wave period. Results are shown for slack-water, peak flood tidal flow at spring and

neap tide, and peak ebb tidal flow at spring and neap tide.

Figure 2-27: Simulated wave height coefficients at RBCL for various combinations of offshore wave



Figure 2-28: Simulated wave height coefficients at NBCL for various combinations of offshore wave



Figure 2-29: Simulated wave height coefficients at PEB for various combinations of offshore wave height

and wave period. Results are shown for slack-water, peak flood tidal flow at spring and neap

tide, and peak ebb tidal flow at spring and neap tide.

Figure 2-30: Simulated wave height coefficients at NK for various combinations of offshore wave height

and wave period. Results are shown for slack-water, peak flood tidal flow at spring and neap

tide, and peak ebb tidal flow at spring and neap tide.

Figure 2-31: Simulated wave height coefficients at PSFB for various combinations of offshore wave



Figure 2-32: Locations of available wave data at Portsea.

Figure 2-33: Distribution of Significant Wave Height Ratios versus Pt Nepean Significant Wave Height

and Peak Period � Flood Tide Conditions. From Water Technology (2010).

Figure 2-34: Wave height coefficients at Portsea obtained by least-squares best fit for AWAC

deployment 1.

Figure 2-35: Instantaneous wave height coefficient with tidal current at Portsea, AWAC deployment 1. X

axis is flood-positive.

Figure 3-1: MIKE-21 BW Bathymetry. To show detail in nearshore, colour scale is truncated at -

20 m AHD. Maximum depth through the entrance to Port Phillip Bay is -75 m AHD.

Advisian Appendix C Wave Transformation Page vi


Figure 3-2: Location of Sponge Layer coefficients used in MIKE-21 BW model to absorb wave energy

incident at the coast and exiting from the model domain. White contours show -30, -20, -15, -

10 and -5 m AHD isobaths.

Figure 3-3: Refraction of swell wave energy within Port Phillip Bay, for incident Mean Wave Direction

(MWD) of 195°and peak wave period (Tp) of 12 seconds. Upper panel: Wave coefficients,

shown as a ratio of the wave height incident to the Boussinesq model boundary, calculated

from statistical analysis of the wave field at each model grid cell over a 30 minute period.

Lower Panel: Instantaneous surface elevation at end of simulation.





Lower Panel: Instantaneous surface elevation at end of simulation.





Lower Panel: Example instantaneous surface elevation.

Figure 3-6: Distribution of swell wave energy within the vicinity of Portsea and Sorrento Channel, for

incident Mean Wave Direction (MWD) of 195°and peak wave period (Tp) of 12 seconds. Wave

coefficients are shown as a ratio of the wave height incident to the Boussinesq model

boundary, calculated from statistical analysis of the wave field at each model grid cell over a

30 minute period.





35 minute period.





45 minute period.

Figure 3-9 Variation of simulated wave height coefficients along Portsea Front Beach at -5m AHD

isobath, between Police Point and Point King, obtained with the Boussinesq model.

Figure 4-1: Wave gauge locations in Boussinesq model for spectral analysis.

Figure 4-2: 1-D frequency spectra for wave for simulated wave gauge locations.

Figure 4-3: Directional frequency spectra for wave gauges A and B.

Figure 4-4: Directional frequency spectra for wave gauges C, D and E.

Figure 4-5: Directional frequency spectra for wave gauges F, G and H.

Figure 4-6: Directional frequency spectra for wave gauges I, J and K.

Advisian Appendix C Wave Transformation Page vii


Figure 4-7: Directional frequency spectra for wave gauges L, M and N.

Figure 4-8: Directional frequency spectra for wave gauges O, P and Q.

Figure 4-9: Directional frequency spectra for wave gauges R, S and T.

Figure 4-10: Directional frequency spectra for wave gauges U, V and W.

Figure 5-1: Locations of inshore wave climates.

List of Tables

Table 2-1: Wave height, period and direction combinations imposed at offshore boundary of wave model.

Table 2-2: Commonly used values of directional spreading index, n, in spectral wave modelling and the

equivalent directional standard deviation from the mean wave direction. Summarised from

DHI (2011).

Table 2-3: Reported wave height coefficients within the shipping lane centre line at entrance to Port

Phillip Heads. Adapted from Carndo (2010b).

Table 2-4: Simulated wave height coefficients within the shipping lane centre line at entrance to Port

Phillip Heads, calculated by weighted contribution of simulated wave condition to offshore

wave record.

Table 2-5: Reported wave height coefficients within the shipping lane centre line at entrance to Port

Phillip Heads. Adapted from Carndo (2010b).

Table 2-6: Simulated wave height coefficients within Port Phillip Bay.

Table 3-1: Key spectral parameters used in generating wave time series at model boundary.

Table 3-2: Commonly used values of directional spreading index, n, in spectral wave modelling and the

equivalent directional standard deviation from the mean wave direction. Summarised from

DHI (2011).

Table 3-3: Summary of key numerical parameters used in MIKE-21 BW simulations

Table 3-4: Measured and simulated wave height coefficients at instrument locations within Port Phillip

Bay.

Table 3-5: Measured and simulated wave height coefficients at Advisian AWAC deployment locations at

Portsea Front Beach in 2014.

Table 5-1: Wave climate statistics for inshore location L1. Energy-weighted mean wave direction =

350.75°N.


353.15°N.


350.38°N.

Advisian Appendix C Wave Transformation Page viii



347.86°N.


347.05°N.


347.80°N.


347.86°N.


343.00°N.


339.15°N.


332.93°N.


331.90°N.


337.95°N.


349.75°N.


338.95°N.


340.26°N.


346.93°N.


343.79°N.


343.94°N.


347.80°N.


344.12°N.


344.91°N.


342.29°N.

Advisian Appendix C Wave Transformation Page ix



355.18°N.


344.14°N.


351.47°N.


348.15°N.


346.55°N.


344.42°N.


348.06°N.

Department of Environment, Land, Water & Planning, Victoria

Appendix C

Wave Transformation

Advisian Appendix C Wave Transformation Page 1


1 Introduction

Wave conditions at Portsea Front Beach control the beach process of alongshore and cross-shore

transport of littoral drift, which may cause foreshore recession. Changes to the nearshore wave

conditions may induce changes to these beach processes. Increases in wave height may impact the

rates of littoral drift transport, specifically the rate of cross-shore transport directed offshore,

whereas changes to incident wave angle may affect both the rate of littoral drift transport

alongshore and, in the longer term, the beach alignment.

In this report the nearshore wave conditions as relevant to the coastal processes affecting Portsea

Front Beach have been defined using both spectral and Boussinesq wave transformation

modelling.


Appendix C

Wave Transformation



2 Spectral Wave Model

The spectral wave model used for these simulations was the proprietary program MIKE21 SW,

which is developed by Danish Hydraulic Institute (DHI). It is a new generation spectral wind-

wave model based on unstructured meshes. The model simulates the growth, decay and

transformation of wind-generated waves and swell in offshore and coastal areas. MIKE 21 SW

includes the following physical phenomena: Wave growth by action of wind, Non-linear wave-

wave interaction, Dissipation due to white-capping, Dissipation due to bottom friction,

Dissipation due to depth-induced wave breaking, Refraction and shoaling due to depth variations,

Wave-current interaction, Effect of time-varying water depth, flooding and drying

2.1 Flexible Mesh

A flexible mesh was constructed for Port Phillip Bay that was designed to optimize computational

requirements by providing spatially detailed simulation results in regions of interest and areas of

complex sea floor topography (where high resolution is required). The mesh was designed with

the following target element lengths:

§ 2,000 m offshore of Port Phillip Heads

§ 1,750 m within the deep-water central basin area of Port Phillip Bay, in the region of Fawkner

Beacon

§ 1,000 m along the eastern region of Port Phillip Bay, in the region of Frankston

§ 700 m within north-west Port Phillip Bay, in the region of Geelong

§ 700 m within north Port Phillip Bay, in the region of Williamstown

§ 250 m within the Great Sands area (locally finer within the immediate vicinity of shallow

banks)

§ 125 m at the within region of Port Phillip Heads and Queenscliff This area comprises the

entrance of Port Phillip Bay

§ 100 m within the general vicinity of Portsea.

Figure 2-1 shows the resultant triangular mesh for Port Phillip Bay and the offshore area.

Bathymetric data has been interpolated linearly to the flexible mesh using the following datasets

in order of priority. For the Great Sands region, the 2012 LADS survey data was used to construct

a Triangulated Irregular Network (TIN). Regions not covered by the LADS survey were

interpolated from navigation chart data, converted to m AHD. Figure 2-2 shows the resultant TIN

for Port Phillip Bay. The spatial detail of the flexible mesh around Portsea is shown in Figure 2-3.

The ultimate choice in mesh design was a compromise between computational burden and the

ability to capture the spatial detail of sea floor features. For practical purposes, the maximum

spatial resolution of the flexible mesh is governed, therefore, by the inability of swell waves to

interact with bathymetric features of a scale significantly smaller than the swell wavelength. For

swell waves of 10 second period in 5 m water depth, this corresponds to a minimum practical

element length of about 70 m.


Appendix C

Wave Transformation



Figure 2-1: MIKE-21 flexible mesh of Port Phillip Bay


Appendix C

Wave Transformation



Figure 2-2: Triangulated Irregular Network (TIN) of sea floor levels within Port Phillip Bay, based on linear interpolation of 2012 LADS survey and navigation chart data obtained from chart AUS00143. The TIN elevations are interpolated to node positions shown in Figure 2-1.


Appendix C

Wave Transformation



Figure 2-3: Flexible mesh (upper panel) and bathymetry (lower panel) in the region of Portsea.

2.2 Boundary conditions

Forty eight (48) combinations of swell wave height, period and direction were simulated that,

together, comprise the envelope of the swell wave climate incident at Port Philip Heads. These

data were derived from analysis of measured wave buoy data at the entrance to Port Phillip

Heads. The wave buoys are operated by Port of Melbourne Corporation, and have been in (more

or less) continual operation since at least 1996. The combinations of swell wave height, period and

direction were analyzed on the basis of data measured between 2003 and 2012.


Appendix C

Wave Transformation



Table 2-1: Wave height, period and direction combinations imposed at offshore boundary of wave model.

Hm0 combinations Tp combinations MWD combinations TOTAL

1.0, 2.0, 4.0, 6.0m 10.0, 12.0, 14.0, 16.0, 18.0, 20.0s 195.0°, 210.0° 4 x 6 x 2 = 48

2.3 Numerical Parameters

Simulations were undertaken using the fully spectral solution of Komen et al. (1994), assuming

quasi-stationary conditions. That is, it was assumed that the time evolution of the wave spectrum

within Port Philip Bay was negligible and, therefore, wave conditions at any point within the

model were considered an instantaneous function of the wave climate incident at Port Phillip

Heads.

The frequency spectrum was discretized using 25 frequency bins, logarithmically spaced between

35.0 and 3.2 seconds. The directional resolution was 10 degrees (36 directional bins), chosen

through sensitivity analysis as a compromise between accuracy, simulation time and memory

requirements (see Section 2.6). As the sea floor topography within the Great Sands region domain

is highly variable with large spatial gradients, a high-order (3rd order) geographical space

discretization was used.

Diffraction was neglected in the phase-averaged simulations, due to the general inability of phase-

averaged swell models to simulate the process of diffraction. While diffraction of wave energy is

intrinsically included within the Boussinesq wave simulations, the amount of diffracted wave

energy reaching Portsea is expected to be small given the distance of Portsea from Port Phillip

Heads relative to the incident swell wave length.

The directionality of the wave spectrum was imposed assuming a cosn(!=!main) distribution, where

n is the directional spreading index and was assigned a value of 20 in this study, which is typical

of swell waves (Table 2-2).

Table 2-2: Commonly used values of directional spreading index, n, in spectral wave modelling and the equivalent directional standard deviation from the mean wave direction. Summarised from DHI (2011).

Directional spreading

index, n

Directional Standard

Deviation , DSD (°)

4 25.45

8 19.05

12 15.87

20 12.49

40 8.94


Appendix C

Wave Transformation




index, n



100 5.70

Quadruplet-wave interaction was included via the Discrete Interaction Approximation (Komen et

al, 1994). This process controls the downshift of energy to lower frequencies. Wave breaking was

retained at default model values. That is, the dissipation of wave energy is controlled by a

combination of depth-induced wave breaking (�1 = 0.8) and wave �spilling� due to overly-steep

waves (�2 = 1).

Bottom friction was incorporated within the model using the Nikuradse roughness length

(Nikuradse, 1932). For the �model setup� stage, bottom friction was retained at default values of

0.04. Section 2.6 shows the sensitivity of model results to bed friction. This parameter was varied

in the model calibration.

Dissipation due to white-capping was included, assuming coefficient values suggested by Komen

et al. (1994) of Cdis=4.5 and !dis=0.5. Typically, these parameters become significant for adjusting

the dissipation source term at higher frequencies during the propagation of wind waves rather

than swell waves.

For simulations involving wave propagation on an ambient current field (e.g., simulations

corresponding to flood and ebb tide), spatially varying current fields corresponding to peak flood

or ebb tide were used. A wave blocking factor of f=0.1 was used. That is, the wave action density is

set to zero to prevent overestimation of the wave height when currents become too strong.

The numerical solution was converged to steady state using a Newtown-Raphson iteration

method, limited to a maximum of 350 iterations. The criterion for numerical stability was defined

using a tolerance of 1×10-5 (RMS-norm of residual) and 0.01 m (Max-norm of chance in

significant wave height).

The following sections present maps showing the propagation of swell wave energy into Port

Phillip Bay and to Portsea Front Beach:

§ Section 2.4 presents maps of wave height coefficients within the Great Sands region for each

wave period and direction imposed at the model boundary

§ Section 2.5 shows the distribution of wave energy along Portsea Front Beach in the form of

wave height coefficients obtained from each of the simulations

§ Section 2.6 presents a sensitivity analysis of the simulated wave height at Portsea Front Beach

to the direction resolution, assumed directional spreading and bottom friction

§ Section 2.7 presents wave height coefficients simulated using ambient current fields

corresponding to ebb and flood tide at spring and neap tide

§ Section 2.8 presents simulated wave height coefficients obtained at locations corresponding to

wave buoys (shown in Appendix A).

A least-squares fit is used to derive the wave height coefficient at each location for each tidal state

(ebb tide, flood tide, slack-water). The results of this are discussed in Section 2.9.


Appendix C

Wave Transformation



2.4 Refraction of swell wave energy

Figure 2-4 to Figure 2-9 show example maps of swell wave height coefficients within southern

Port Phillip for peak wave periods of 10, 12, 14, 16, 18 and 20 seconds incident from 210°.

The following key processes were identified:

§ Wave energy incident on Nepean Bank is refracted strongly by the very large gradients in sea

floor levels through The Entrance, and focused upon the coast between Point Nepean and

Observatory Point. The severity of wave focusing on this part of the coastline increases with

larger offshore wave periods incident at Port Phillip Heads.

§ Wave energy not refracted back onto Point Nepean is focused eastward past Nicholson Knoll,

towards South Channel. At this point the wave energy appears to be �captured� along the crests

of the banks separating South Channel and Sorrento Channel by total internal wave reflection

off the channels. This process occurs when wave energy incident upon the banks is refracted

away from the deeper channel areas, back toward the sand banks. This phenomenon leads to

the �hole� in incident wave height between Observation Point and Police Point, as the longer,

energy containing wave lengths (larger wave periods) are unable to refract past Sorrento

Channel.

§ Wave energy appears to be focused on to Portsea by the presence of a shallow, linear bank

located approximately 1.5 km north-west of Portsea Pier, combined with a shallow platform

extending seaward immediately offshore of Portsea Front Beach.

Figure 2-4: Propagation of swell wave energy into Port Phillip Bay, for incident Mean Wave Direction (MWD) of 210°, Peak wave period (Tp) of 10 seconds, and offshore wave height of 1.0m. Wave heights are presented as a ratio of the wave height applied at the model boundary.


Appendix C

Wave Transformation






Appendix C

Wave Transformation




2.5 Distribution of Wave Energy along Portsea Front Beach

Figure 2-10 shows the variation in wave height coefficients at 100 m intervals between Police

Point and Point King for all wave conditions simulated. The black line shows the mean wave

height coefficient calculated across all simulations. The point data shows the variation across all

wave directions and periods. Figure 2-11 shows the relationship between wave height coefficient

and offshore wave period and direction for the most energetic region between Portsea Pier and

Point Franklin.

The simulations suggest that the wave height at Portsea Front Beach is governed primarily by

wave period, which would be expected if refraction was the main process governing the

distribution of wave energy within south Port Philip Bay (neglecting wave-current interaction).

For the range of offshore wave directions considered, wave energy at Portsea is relatively

insensitive to wave direction at Port Phillip Heads. The lower wave height coefficients achieved

for larger wave heights applied at the model boundary correspond to increased dissipative losses

via wave breaking through Port Phillip Heads and the shallow sand banks east of Nicholson Knoll.


Appendix C

Wave Transformation



Figure 2-10: Variation of wave height coefficients along Portsea Front Beach between Police Point and Point King.


Appendix C

Wave Transformation



Figure 2-11: Variation of simulated wave height coefficient with offshore wave period, offshore wave height and incident wave direction at Port Phillip Heads.

2.6 Sensitivity to Numerical Parameters

A criticism of past numerical modelling of wave process at Port Phillip Bay is that, in general, a

sensitivity analysis of simulated wave height to numerical parameters within the model was not

undertaken (e.g., Symmonds & McInnes, 2013). Here an analysis has been undertaken of the

sensitivity to wave height at the most energetic point of Portsea Front Beach. The analysis is

undertaken for the key numerical parameters that are varied usually within a spectral wave model

to calibrate results. The analysis was undertaken for:

§ Directional spreading factor, n. Here the value was varied from values that correspond to the

upper value for wind-sea waves, through to directional spreading values correspond to tightly

focussed swell waves. Table 2-2 gives typical directional standard deviations associated with

the spreading parameter values used.


Appendix C

Wave Transformation



§ Directional resolution. Accurate simulation of the wave energy spectrum requires sufficient

representation of the distribution of wave energy about the peak wave direction. Simulations

of locally generated waves, in which the distribution of wave energy is bounded loosely about

the peak wave direction, typically use a directional resolution of 15° (24 directional bins

through a 360° compass). Swell wave energy is more tightly focused and, therefore, requires a

higher directional resolution (more directional bins). Typically, the choice of directional

resolution is a compromise between numerical accuracy and computational burden.

§ Bed friction. The bed friction value used within a numerical simulation is used typically as a

calibration parameter. Higher values of bed friction increases dissipation of wave energy. In

this analysis, the Nikurasde roughness (ks) was varied from 0.01 (low bed friction, typically

encountered in areas of fine bed sediments) to 0.2 (approximately corresponding to areas with

significant bed forms such as large ripples and dunes). A ks of 0.01 corresponds approximately

to a Manning�s n of 0.017, while ks of 0.2 corresponds approximately to a Manning�s n of 0.029.

Although spatial resolution and consideration of wave breaking also may be considered key

parameters, these have not been varied as a sensitivity parameter within the numerical model. For

the range of swell wave heights simulated at Portsea (in the range of Hm0=1 m or less), wave

breaking is not a significant process. The spatial resolution of the model is already close to the

minimum resolvable feature that can be �felt� by the waves and, therefore, is not refined further.

The results show that:

§ Energy is more tightly focused upon Portsea when the directional spread of wave energy is

reduced. This is because less energy is refracted away from the main direction of wave

propagation as it refracts over channels and banks, which increases the effectivess of the

topography to lens propagating wave energy. However, the overall effect is relatively small, for

the given spatial resolution of the simulations.

§ Simulation results are sensitive to the directional resolution with the simulated wave height at

Portsea increasing with the directional resolution. This effect is attributed to numerical

dissipation. Using a directional spreading parameter of 20 (typically used for swell waves), 24

directional bins (15° bin width) are insufficient to capture adequately the shape of the

distribution of wave energy about the peak wave direction. 36 bins (10° bin size) fall within the

directional standard deviation of the wave spectrum (12.49°). For the mesh configuration used,

numerical diffusion reduced the incident wave heights by approximately 10%.

§ Simulation results were most sensitive to bed friction parameters. The total variation in wave

height was about 25%, approaching 40% for the largest waves.

The sensitivity analysis did not alter the pattern of wave refraction for the simulations considered

(no current variation, constant water level of 0 m AHD).


Appendix C

Wave Transformation



Figure 2-12: Sensitivity analysis of simulated wave height to: Directional spreading factor, n (upper panel); Directional resolution (middle panel); Bed friction (lower panel).

2.7 Wave-current interaction

2.7.1 Current fields

Figure 2-13 to Figure 2-16 show simulated current fields and water levels at times of peak spring

flood tide, peak spring ebb tide, peak neap flood tide and peak neap ebb tide. The current fields

are used in the simulation of swell waves to generate wave height coefficients for the general

Portsea area under the influence of peak flow during spring and neap tidal currents. Section 2.7.2

shows the influence of these currents on the most frequently occurring peak spectral wave period

of 12 seconds. Section 2.7.3 discusses the effect of tidal currents on simulated wave height

coefficients along Portsea Front Beach.


Appendix C

Wave Transformation



Figure 2-13: Depth-averaged current magnitude and direction (upper panel) and surface elevation (lower panel) for spring tide, peak flood conditions.


Appendix C

Wave Transformation



Figure 2-14: Depth-averaged current magnitude and direction (upper panel) and surface elevation (lower panel) for spring tide, peak ebb conditions.


Appendix C

Wave Transformation



Figure 2-15: Depth-averaged current magnitude and direction (upper panel) and surface elevation (lower panel) for neap tide, peak flood conditions.


Appendix C

Wave Transformation



Figure 2-16: Depth-averaged current magnitude and direction (upper panel) and surface elevation (lower panel) for neap tide, peak ebb conditions.


Appendix C

Wave Transformation



2.7.2 Effect of currents on wave refraction

Figure 2-17 to Figure 2-21 show example wave height coefficients within southern Port Phillip Bay

during (a) peak flood, spring tide; (b) peak ebb, spring tide; (c) peak flood, neap tide; (d) peak ebb,

neap tide.

The following key processes are shown by the results:

§ Relative to slack-water, wave energy is more focused on Point Nepean and Queenscliff during

flood tide. This is attributed to the entrance channel more effectively refracting wave energy

away from the deepwater area and on to Nepean Bank and Lonsdale Bank, as the effective

wave length increases when waves propagate on a following current. An additional

contribution will occur from flood tidal currents �pushing� wave energy through Port Phillip

Heads.

While the focusing of wave energy on to Lonsdale Bank and Nepean Bank will act to reduce the

total amount of wave energy focused towards South Channel, the increase in effective

wavelength increases the efficacy of the shallow sand banks separating South Channel and

Sorrento Channel to trap wave energy and focused it towards Portsea.

§ Relative to slack-water, less wave energy is refracted towards Point Nepean during ebb tide,

and more wave energy is observed to pass towards South Channel. This is attributed to a

combination of the following processes:

- The presence of an opposing current within south Port Phillip, which acts to increase the

wave height locally through current blocking

- The opposing current through Port Phillip Heads, which shortens the effective wavelength

of the dominant, energy carrying components of the wave spectrum, reducing the efficacy

of the channel running through Port Phillip Heads to refract wave energy away from South

Channel towards Nepean Bank and Lonsdale Bank

- An additional contribution that may be made from current-induced refraction in areas of

high current shear through the entrance of Port Phillip Heads.

For the wave conditions simulated, the wave height is increased locally at Portsea due to

propagation against an opposing current flowing through Sorrento Channel.

The effects of currents on wave height coefficients along Portsea Front Beach are discussed in

more detail and for a greater range of simulation results in Section 2.7.3.


Appendix C

Wave Transformation



Figure 2-17: Propagation of swell wave energy into Port Phillip Bay during slack-water. MWD = 210°, Tp = 12.0s, Hm0offshore = 1.0m. Wave heights are presented as a ratio of the wave height applied at the model boundary.

Figure 2-18: Propagation of swell wave energy into Port Phillip Bay during peak flood tidal currents, spring tide. MWD = 210°, Tp = 12.0s, Hm0offshore = 1.0m. Wave heights are presented as a ratio of the wave height applied at the model boundary.


Appendix C

Wave Transformation



Figure 2-19: Propagation of swell wave energy into Port Phillip Bay during peak ebb tidal currents, spring tide. MWD = 210°, Tp = 12.0s, Hm0offshore = 1.0m. Wave heights are presented as a ratio of the wave height applied at the model boundary.

Figure 2-20: Propagation of swell wave energy into Port Phillip Bay during peak flood tidal currents, neap tide. MWD = 210°, Tp = 12.0s, Hm0offshore = 1.0m. Wave heights are presented as a ratio of the wave height applied at the model boundary.


Appendix C

Wave Transformation



Figure 2-21: Propagation of swell wave energy into Port Phillip Bay during peak ebb tidal currents, neap tide. MWD = 210°, Tp = 12.0s, Hm0offshore = 1.0m. Wave heights are presented as a ratio of the wave height applied at the model boundary.

2.7.3 Effect of Wave-Current Interaction on Wave Heights at Portsea

Figure 2-22 shows the wave height coefficients at 100 m intervals along Portsea Front Beach,

between Police Point and Point King, for peak flood spring tide. Figure 2-23 shows the same for

peak ebb spring tide. The most significant difference between simulation results for flood and ebb

tide is that larger wave heights (represented by simulation results for offshore wave heights of

4.0m and 6.0m) show enhanced dissipation. Conversely, negligible difference is shown between

the simulation results at the smaller offshore wave heights.

The relationship between wave height coefficient at Portsea with offshore wave period, offshore

wave direction and flood or ebb tide, is shown in more detail in Figure 2-24. Salient points are:

§ For a given wave height, the difference between wave height coefficient between flood and ebb

tide decreases with increasing wave period

§ Blocking by ebb-tidal currents is more effective at smaller wave periods

§ There is little difference in wave height coefficients between flood tide and slack-water. Wave

height coefficients are slightly increased at flood tide relative to slack water, for the smallest

wave periods considered in the simulations (Tp!10s)

§ Wave height coefficients are decreased significantly during ebb-tide for the largest offshore

wave heights.

Taken together, the results are interpreted that wave blocking during ebb tide is more effective for

the largest offshore wave heights. The mechanism through which this could occur is most likely to

be via steepness- induced dissipation (�wave spilling�) and enhanced depth-limited breaking over

shallow sand banks by wave heights that are increased by the opposing ebb tidal current.


Appendix C

Wave Transformation



Figure 2-22: Distribution of wave height coefficients along Portsea Front Beach, between Police Point and Point King. Peak spring flood tide, using current fields shown in Figure 2-13.

Ebb-tidal currents are more effective at dissipating larger wave heights via wave spilling through

overly steep waves and enhanced depth-limited wave breaking over the shallow sand banks. An

additional effect is the opposing tide in reducing the effective wavelength of the incident waves,

reducing the ability of the channel running through the entrance of Port Phillip to refract wave

energy towards the adjacent shallow banks. Paradoxically, this may lead to more energy being

directed towards South Channel, although waves propagating against the opposing ebb tidal

current will also act to increase wave heights locally, differentially enhancing wave dissipation for

the higher offshore waves. Strong ebb currents flowing through Sorrento Channel also act to block

incident wave energy from Portsea Front Beach.

This hypothesis is reinforced by analysis of wave height coefficients along Portsea Front Beach at

the -5m AHD isobath. Little difference was observed between simulation results during slack-

water and flood spring tide, while wave height coefficients derived from simulations with higher

waves incident at the offshore boundary were disproportionately reduced. The effect is more

apparent for waves with smaller periods (shorter wavelengths).


Appendix C

Wave Transformation



Figure 2-23 Distribution of wave height coefficients along Portsea Front Beach, between Police Point and Point King. Peak spring ebb tide, using current fields shown in Figure 2-14.


Appendix C

Wave Transformation



Figure 2-24: Effect of spring tidal currents on wave height coefficients of different offshore wave heights and peak wave periods, for the most energetic section of Portsea Front Beach. Upper panel: Peak flood spring tide. Lower panel: Peak ebb spring tide. Results obtained using current fields given in Figure 2-13 and Figure 2-14.


Appendix C

Wave Transformation



2.8 Simulated Data at Validation Points

The following sections show simulated wave height coefficients for various locations within Port

Phillip Bay, for slack-water, peak flood spring tide, peak ebb spring tide, peak flood neap tide and

peak ebb neap tide. The locations of wave data are given inFigure 2-25. Simulation results are

given in order of progression though Port Phillip Heads towards Portsea front beach.

A wave height coefficient is derived for each location and each tidal state (slack-water, peak flood

spring tide, peak ebb spring tide, peak flood neap tide, peak ebb neap tide) by least-squares linear

fit using four methods:

1) Linear fit to all wave height and period combinations simulated

2) linear fit to wave conditions where Hm0!4.0m (approximately 95% of the offshore wave

climate)

3) linear fit to wave conditions where Tp"16s (thus removing contribution from shorter wave

lengths at large wave heights where strong dissipation would be expected due to wave

steepness limitations in regions of strong currents)

4) linear fit to each simulated wave condition.

These are then weighted by contribution to the offshore wave climate and summed to give a single

�representative� value.

Methods (1) to (3) neglect the statistical representation of each simulated wave condition relative

to the wave climate as a whole and, therefore, will tend to be skewed by statistical outliers (larger

waves, large wave height � short wave period combinations). Method (4) provides a single, global

wave height coefficient that is representative of the wave climate as a whole. It is this quantity that

is discussed further in Section 2.9, comparing against data reported in Cardno (2010b).

It should be recognized that although a single �representative� wave height coefficient (which

should be thought of as a �best-fit� median value) is useful for gauging the overall performance of

the wave model system, in reality there will be natural variation about this single wave height

coeffficient. The inshore wave height achieved for any particular offshore wave condition will also

have a non-linear dependence on both offshore wave height and peak wave period, especially in

regions of strong currents. This non-linear relationship is visible in the scatter plots shown in

Figure 2-26 to Figure 2-30.


Appendix C

Wave Transformation



Figure 2-25: Locations of spectral wave model validation points. Location of Port of Melbourne Corporation wave buoy (used to derive bundary conditions for the wave model) also shown.


Appendix C

Wave Transformation



2.8.1 Rip Outer Bank Centre Line (ROBCL)

Figure 2-26 compares simulated wave heights for various combinations of wave height and period

applied at the model offshore boundary. The slopes given in the figure represent the wave height

coefficients derived by the methods discussed in Section 2.8.

Figure 2-26: Simulated wave height coefficients at ROBCL for various combinations of offshore wave height and wave period. Results are shown for slack-water, peak flood tidal flow at spring and neap tide, and peak ebb tidal flow at spring and neap tide.


Appendix C

Wave Transformation



2.8.2 Rip Bank Centre Line (RBCL)




Figure 2-27: Simulated wave height coefficients at RBCL for various combinations of offshore wave height and wave period. Results are shown for slack-water, peak flood tidal flow at spring and neap tide, and peak ebb tidal flow at spring and neap tide.


Appendix C

Wave Transformation



2.8.3 Nepean Bank Centre Line (NBCL)




Figure 2-28: Simulated wave height coefficients at NBCL for various combinations of offshore wave height and wave period. Results are shown for slack-water, peak flood tidal flow at spring and neap tide, and peak ebb tidal flow at spring and neap tide.


Appendix C

Wave Transformation



2.8.4 Popes Eye Bank (PEB)




Figure 2-29: Simulated wave height coefficients at PEB for various combinations of offshore wave height and wave period. Results are shown for slack-water, peak flood tidal flow at spring and neap tide, and peak ebb tidal flow at spring and neap tide.


Appendix C

Wave Transformation



2.8.5 Nicholson Knoll (NK)




Figure 2-30: Simulated wave height coefficients at NK for various combinations of offshore wave height and wave period. Results are shown for slack-water, peak flood tidal flow at spring and neap tide, and peak ebb tidal flow at spring and neap tide.


Appendix C

Wave Transformation



2.8.6 Portsea Front Beach



coefficients derived by the methods discussed in Section 2.8. It is noted that the wave height

coefficients for the longer period swells are consistently higher than the average coefficient, which

is expected in such shallow depths as a result of the wave shoaling coefficient.

Figure 2-31: Simulated wave height coefficients at PSFB for various combinations of offshore wave height and wave period. Results are shown for slack-water, peak flood tidal flow at spring and neap tide, and peak ebb tidal flow at spring and neap tide.


Appendix C

Wave Transformation



2.9 Comparison with Measured Data

2.9.1 Port Phillip Heads

Table 2-3 summarizes the results of regression analysis undertaken on AWAC wave

measurements reported in Cardno (2010), for locations within the shipping lane through the

entrance of Port Phillip Heads. �Representative� wave height coefficients are given for two post-

CDP deployments undertaken in 2009. The deployment periods were each of 1 calendar month

duration (approximately).

The R2 values (not shown in this report), which indicate the degree of scatter in the data (and

hence the natural variability about a median value derived from a single fitting relationship)

varied between 0.61 and 0.80 when taken across data over all states of the tide. When analysis

was segregated to times of slack-water, flood tide and ebb tide, the R2 values improved to between

0.71 and 0.95. Values of R2 are bounded by 0 (which indicates no statistical relationship) and 1

(which indicates a perfect statistical relationship). Typically, goodness of fit is described as �good�

for R2 values above ~0.7, and �excellent� for R2 values above ~0.95.

The wave height coefficients in Table 2-3 show the following patterns:

§ The derived wave height coefficient for each location remained approximately consistent

across deployments

§ The wave height coefficient (�all data�, �slack-water�) decreases with distance inside Port Phillip

Bay

§ Wave height coefficients are lower for flood tide than for slack-water and ebb tide

§ Wave height coefficients for ebb tide are greater than slack-water. This is due to the

propagation of wave energy against an opposing current, which acts to decrease the wave

celerity and, therefore, increase the wave height. Rip Bank in particular is known for very

rough seas during times of high wave activity and strong spring tide ebb currents. This pattern

is consistent with the wave height coefficients in Table 2-3, which show amplification of the

incident wave height at Rip Bank.

Table 2-4 shows the fitted wave height coefficients obtained from simulation results in Figure

2-26 to Figure 2-28. Coefficients are segregated to slack-water, peak flood tide (spring and neap),

and peak ebb tide (spring and neap). An average value is calculated for flood and ebb tide, on the

basis of the spring and neap values. The average values are approximately consistent with the

values reported in Table 2-3, on the basis that over a 29-day lunar cycle there will be an equal

number of neap tides and an equal number of spring tides. The values for slack-water, peak flood

tide and peak ebb tide are averaged to give values corresponding to �All Data�. This aggregate

value is considered representative of all wave conditions occurring over a 29-day lunar cycle.


Appendix C

Wave Transformation



Table 2-3: Reported wave height coefficients within the shipping lane centre line at entrance to Port Phillip Heads. Adapted from Carndo (2010b).

Wave height coefficients: Gradient line of best fit

Deployment Entrance

location

All data Slack-water Flood tide Ebb tide

21 RBOCL 0.99 0.93 0.87 1.18

22 RBOCL 0.98 0.92 0.84 1.17

22 RBCL 0.94 0.85 0.74 1.21

23 RBCL 0.96 0.84 0.77 1.24

21 NBCL 0.71 0.70 0.57 0.94

23 NBCL 0.73 0.72 0.59 0.93

Table 2-4: Simulated wave height coefficients within the shipping lane centre line at entrance to Port Phillip Heads, calculated by weighted contribution of simulated wave condition to offshore wave record.


Peak Flood Tide Peak Ebb Tide

Entrance

location

All

Data*

Slack-

water

Spring Neap Average Spring Neap Average

RBOCL 0.98 0.90 0.79 0.85 0.82 1.48 0.97 1.23

RBCL 0.96 0.86 0.74 0.82 0.78 1.49 0.96 1.23

NBCL 0.82 0.76 0.64 0.72 0.68 1.17 0.85 1.01

*Average of slack-water, average flood tide, average ebb tide.

2.9.2 Port Phillip Bay and Portsea Front Beach

Table 2-5 summarizes the results of regression analysis undertaken on wave buoy measurements

provided by PoMC, for Popes Eye Bank and Nicholson Knoll. The locations are given in Figure

2-25. Coefficients have been derived by analysis of the wave record at each location, segregating to

times of slack-water, flood tide and ebb tide. Further details of the analysis are given in Section

2.8. Table 2-6 shows simulated wave heights coefficients at the same locations using MIKE-21 SW.


Appendix C

Wave Transformation



Comparisons of measured and simulated wave height coefficients show the following:

§ Simulations overestimated the wave height coefficients at Popes Eye Bank, particularly during

ebb tide.

§ Simulations underestimated the wave height coefficients at Nicholson Knoll, for all states of

the tide.

§ Simulations underestimated the wave height coefficients at Portsea Front Beach.

Table 2-5: Reported wave height coefficients within the shipping lane centre line at entrance to Port Phillip Heads. Adapted from Carndo (2010b).


Location All data Slack-water Flood tide Ebb tide

PEB 0.12 0.12 0.10 0.13

NK 0.35 0.40 0.36 0.33

PSFB** N/A N/A 0.14 N/A

** Water technology Ltd (2010) report wave height coefficients for flood tide only.

Table 2-6: Simulated wave height coefficients within Port Phillip Bay.


Peak Flood Tide Peak Ebb Tide

Entrance

location

All

Data*

Slack-

water

Spring Neap Average Spring Neap Average

PEB 0.16 0.16 0.10 0.14 0.12 0.21 0.17 0.19

NK 0.23 0.22 0.24 0.22 0.23 0.26 0.23 0.25

PSFB 0.10 0.11 0.10 0.10 0.10 0.10 0.10 0.10

*Average of slack-water, average flood tide, average ebb tide.


Appendix C

Wave Transformation



2.9.3 Comment on Measured Wave Height Coefficients at Portsea

The following sources of measured wave data are available for select locations at Portsea (Figure

2-32):

§ RBR TWR-2050P submersible wave and tide recorder deployment by Water Technology from

10th September to 13th October 2010 (30-day deployment). In approximately 6.5m water depth.

§ AWAC acoustic wave, tide and current meter deployed by Advisian between 22nd July and 23rd

October 2014 (93-day deployment). In 6.0m water depth.

§ AWAC acoustic wave, tide and current meter deployed by Advisian between 23rd October 2014

and 3rd February 2015 (103-day deployment). In 6.0m water depth.

A key property of the wave height coefficients obtained by Water Technology and Advisian is that

there is no observed correlation between calculated wave height coefficient and wave period

(Figure 2-33, Figure 2-34). Although Water Technology only reported wave height coefficients for

flood tide conditions, we have also shown the variation in observed wave height coefficient

between different tidal states (slack water, flood tide, ebb tide, all tidal states).

In the 6.0 and 6.5 m water depth in wave data were obtained, the data showed no variation in the

wave height coefficient across the range of wave periods measured, which varied from 9 s to 18 s

and for which the wave height shoaling coefficient would vary from 1.02 to 1.35; that is, it would

be expected that the wave height coefficient as measured should have reflected such a variation.

This discrepancy is most likely due to the relatively low wave heights observed at Portsea Front

Beach, which probably approach the limits of instrument sensitivity. For practical considerations,

calculations of significant wave height are only accurate to about 0.1m. The tide is the most

significant factor in modulating the wave height at Portsea is the tide (Figure 2-35).

WaterTechnology (2010) report that the observed coefficeints varied by a factor of up to 3 or 4

between flood and ebb tides. Although wave height coefficeints were only reported for flood tide,

when visually averaged across all tidal conditions the average wave height coefficient was closer to

0.10. We find that the average wave height coefficient at a similar area (but slightly shallower

water) is closer to 0.17.

We note that the objective in WaterTechnology (2010) was to estimate design wave conditions to

assist in the design of shore protection works, not necessarily to derive definitive wave height

coefficients at Portsea to validate numerical models. In this regard it is recognised that

WaterTechnology (2013) did not use these field data to validate their spectral wave model

developed to assess the possible impacts of dredging on wave conditions at Portsea Front Beach.

In regions of severe wave refraction such as those that pertain to the region under investigation

herein, it is accepted that spectral wave transformation models are unlikely to be able to provide

accurate estimates of wave height, particularly where median wave height coefficients are of the

order of o.10 - 0.20 and subject to a degree of natural variation about this value. In regions of

severe wave refraction, Boussinesq wave models will provide better estimates, as intimated in

Water Technology (2013). This is the focus of the next section.


Appendix C

Wave Transformation



Figure 2-32: Locations of available wave data at Portsea.

PSFB = WaterTechnology deployment. AWAC-1; AWAC-2 = Advisian deployment.

Figure 2-33: Distribution of Significant Wave Height Ratios versus Pt Nepean Significant Wave Height and Peak Period � Flood Tide Conditions. From Water Technology (2010).


Appendix C

Wave Transformation



Figure 2-34: Wave height coefficients at Portsea obtained by least-squares best fit for AWAC deployment 1.

Coefficients are segregated by tidal state, as defined by measured tidal currents at the AWAC instrument. Coefficients only consider swell waves entering from Port Phillip Heads, which correspond to waves with periods greater than or equal to 10 seconds.

Figure 2-35: Instantaneous wave height coefficient with tidal current at Portsea, AWAC deployment 1. X axis is flood-positive.


Appendix C

Wave Transformation



3 Boussinesq Wave Model

MIKE 21 BW is a state-of-the-art numerical model for the calculation and analysis of gravity and

infragravity waves in coastal areas. It can be used also for detailed modelling of wave-induced

current fields, surf zone dynamics and swash zone oscillations. It is capable of reproducing the

combined effects of all important wave phenomena of interest in port, harbour and coastal

engineering, including shoaling; refraction; diffraction; wave breaking; bottom friction; moving

shorelines; partial reflection and transmission; non-linear wave-wave interaction; frequency and

directional spreading. Phenomena such as wave grouping, surf beats, generation of bound sub-

harmonics and super-harmonics and near-resonant triad interactions, are intrinsically captured

by the Boussinesq equations.

The following sections summarise the steps undertaken in constructing the Boussinesq wave

model. Simulation results are presented in Section 3.5.1 and 3.5.2. Validation of the simulations

against measured data is given in Section 3.5.3.

3.1 Grid and Bathymetry

The bathymetry was interpolated from the 2012 LADS survey dataset (obtained ) at a grid cell

resolution of four metres. The following modifications to the bathymetry were made to satisfy

numerical stability constraints:

§ The maximum slope in the channel area was limited to one vertical to three horizontal (1V:3H).

The cross-sectional footprint of the channel was maintained.

§ A minimum water depth of 4 m was considered within the model. This depth was chosen to

prevent wave breaking processes, which would require impractical spatial and temporal

resolution.

§ A uniform depth was applied across the location of the wave generator line. The uniform depth

selected was the mean value across the location of the wave generation line, and was smoothed

into the ambient bathymetry over a distance of 50 grid cells (200 m).

Figure 3-1 shows the model bathymetry, superimposed on aerial imagery. The location of the

wave generation line and position of wave buoys used to validate the model are shown also.


Appendix C

Wave Transformation



Figure 3-1: MIKE-21 BW Bathymetry. To show detail in nearshore, colour scale is truncated at -20 m AHD. Maximum depth through the entrance to Port Phillip Bay is -75 m AHD.

3.2 Sponge

To avoid spurious wave reflections within the model domain, a numerical �sponge layer' was

applied to absorb incident wave energy at the coast and open-water boundaries. The width of the

sponge layer is required to be at least equivalent to the wavelength of the most energetic portion

of the incident wave frequency spectrum. Figure 3-2 shows the location of the numerical sponge

layer.

Wave generation


Appendix C

Wave Transformation



Figure 3-2: Location of Sponge Layer coefficients used in MIKE-21 BW model to absorb wave energy incident at the coast and exiting from the model domain. White contours show -30, -20, -15, -10 and -5 m AHD isobaths.

3.3 Wave conditions

The simulations were undertaken for Tp = 12 s, Tp = 16 s and Tp=20 s. Approximately 95% of the

incident wave climate occurs between the limits of these wave periods. The most frequently

occurring wave period in the offshore wave record is 12 seconds. Longer wave periods are

associated with larger incident swell wave heights.

A short-crested incident wave field composed of an irregular, directional time series of surface

elevation and depth-averaged flux was applied across the entrance to Port Phillip, seaward of �The

Entrance� canyon. Figure 3-1 shows the location of the wave generation line relative to the MIKE-

21 BW model bathymetry.

The directionality of the incident wave climate spectrum was defined using JONSWAP frequency

spectrum with a mean wave direction of 195°T.N. and a directional spreading parameter, n, with a

value of 20. This value is consistent with the spectral spreading defined within the phase-averaged

spectral wave model (WorleyParsons 2014) and is a value typical of swell waves. Table 2-2

summarizes the wave spectrum parameters used for each simulation. Table 3-4 gives directional

spreading parameters typically used for wind-sea and swell waves. Wave height coefficients were

calculated from the model results using an incident wave height of Hm0 = 0.5 m, which is close to

the �real world� mean annual incident wave height of 1.0 m.


Appendix C

Wave Transformation



Table 3-1: Key spectral parameters used in generating wave time series at model boundary.

Tp

(s)

Tmin

(s)

Hm0

(m)

JONSWAP parameters MWD

(�m) Frequency Direction

12 8 0.5 ! = 3.3; "a = 0.07; "b = 0.09 cosn (#-#m); n=20 195

16 10 0.5 ! = 3.3; "a = 0.07; "b = 0.09 cosn (#-#m); n=20 195

20 10 0.5 ! = 3.3; "a = 0.07; "b = 0.09 cosn (#-#m); n=20 195

Table 3-2: Commonly used values of directional spreading index, n, in spectral wave modelling and the equivalent directional standard deviation from the mean wave direction. Summarised from DHI (2011).


index, n



4 25.45

8 19.05

12 15.87

20 12.49

40 8.94

100 5.70

3.4 Numerical Parameters

Table 3-3 summarizes the key numerical parameters used in the MIKE-21 BW simulations. Deep

Water Terms (DWT) of Masden et al. (1991) and Masden & Sorensen (1992) were used in the

simulations to extend the limit of the Boussinesq assumption in solving the dispersion equation

for irregular wave trains from water depths of h/L0 = 0.22 to water depths of h/L0 = 0.5.

The spatial discretization of the convective terms was solved using a central differencing

numerical stencil. To maintain numerical stability in areas of large numerical gradients, an

additional first-order upwind scheme was employed in areas with steep gradients and near land.

Time discretization of the cross-Boussinesq terms were solved using a time-extrapolation factor of

1. That is, the solutions were time-centered with no truncation of higher-order terms. To maintain


Appendix C

Wave Transformation



numerical stability in the deep water gorge through the entrance of Port Phillip Heads, a depth-

dependent time extrapolation factor of 0.8 was used for water depths greater than 27 meters.

Table 3-3: Summary of key numerical parameters used in MIKE-21 BW simulations

Tp (s) Tmin Tp / Tmin Dt Dx L0Tmin d/L0Tmin LTmin/dx Tmin/Dt Courant

12 8s 1.50 0.05 4 99.84 0.451 24.54 160 0.263

16 10s 1.60 0.05 4 156 0.449 38.34 200 0.328

20 15s 1.33 0.1 6 351 0.199 51.62 150 0.437

3.5 Results and Discussion

The following sections present the results of the MIKE-21 BW simulations. Section 3.5.1 presents

maps showing the propagation of swell wave energy through Port Phillip Heads, interaction with

the deep-water gorge running through �The Entrance�, and subsequent refraction by the sea floor

within the South Channel and Portsea region. Section 3.5.2 shows the distribution of incident

swell wave energy along Portsea Front Beach in more detail. Section 3.5.3 compares wav height

coefficients obtained from the Boussinesq wave model results with those measured at various

locations within southern Port Phillip Bay. A comparison with the phase-averaged spectral wave

model results (WorleyParsons, 2014) is made, thus indicating the general compatibility of both

model systems.

3.5.1 Refraction of swell wave energy from The Entrance

Figure 3-3 shows simulated wave height coefficients and wave crest patterns within Port Phillip

Bay for swell waves incident at Port Phillip Heads from 195° N. with a peak wave period of 12

seconds. Figure 3-4 shows wave height coefficients and wave crest patterns for waves approaching

from 195°N with a peak period of 16 seconds. Figure 3-5 shows wave height coefficients and wave

crest patterns for waves approaching from 195°N with a peak period of 20 seconds.

Simulation results are shown against Google Earth aerial imagery, and are �blanked� in regions

where wave energy is absorbed by the numerical sponge layer. Positions corresponding to wave

buoy data used to validate the wave model are shown. In the wave coefficient maps (upper panels),

isobaths at the -30,-20, -15, -10 and -5m AHD levels also are shown.

The key process highlighted by the Boussinesq model is that wave refraction through the entrance

of Port Phillip is determined by the plan-shape of the deep-water gorge (�The Entrance�) and the

adjacent shallow submarine shelves at Point Nepean and Point Lonsdale. The fine-scale patterns

of refracted wave energy and severity of wave focusing is dependent upon both the peak wave

period (and associated wave frequency spectrum), and the position of incident wave energy

relative to the center line of the shipping channel (delineated by the positions of RBOCL, RBCL

and NBCL).

Wave energy incident to the west of the shipping channel center line is refracted westward and

northward to Queenscliff and Point Lonsdale. Wave energy incident to the east of the shipping


Appendix C

Wave Transformation



channel center line is highly refracted around Point Nepean and strongly focused upon the beach

between �The Bend� and �Observation Point�.

Wave energy incident upon the central 1/3 of The Entrance, roughly corresponding to the location

of the shipping channel, is guided into The Great Sands area via refraction around Nepean Bank.

Once past Port Phillip Heads, wave energy not incident upon Observation Point is either refracted

towards Popes Eye Bank by the northern banks of the gorge, or focused into the South Channel.

Once in this region, wave energy is concentrated along the crests of a series of shallow banks to

the east of Nicholson�s Knoll, and then focused on to Portsea Front Beach by a linear sand ridge

approximately 1.5 km north-west of Portsea Pier. Wave energy propagating across Sorrento

Channel is further focused by the plan-form of a shallow subaqueous shelf directly offshore of

Portsea Front Beach, extending out into Sorrento Channel. Portsea Hole probably acts to further

focus wave energy onto the eastern section of Portsea Front Beach.


Appendix C

Wave Transformation



Figure 3-3: Refraction of swell wave energy within Port Phillip Bay, for incident Mean Wave Direction (MWD) of 195°and peak wave period (Tp) of 12 seconds. Upper panel: Wave coefficients, shown as a ratio of the wave height incident to the Boussinesq model boundary, calculated from statistical analysis of the wave field at each model grid cell over a 30 minute period. Lower Panel: Instantaneous surface elevation at end of simulation.


Appendix C

Wave Transformation



Figure 3-4: Refraction of swell wave energy within Port Phillip Bay, for incident Mean Wave Direction (MWD) of 195°and peak wave period (Tp) of 16 seconds. Upper panel: Wave coefficients, shown as a ratio of the wave height incident to the Boussinesq model boundary, calculated from statistical analysis of the wave field at each model grid cell over a 35 minute period. Lower Panel: Instantaneous surface elevation at end of simulation.


Appendix C

Wave Transformation



Figure 3-5: Refraction of swell wave energy within Port Phillip Bay, for incident Mean Wave Direction (MWD) of 195°and peak wave period (Tp) of 20 seconds. Upper panel: Wave coefficients, shown as a ratio of the wave height incident to the Boussinesq model boundary, calculated from statistical analysis of the wave field at each model grid cell over a 45 minute period. Lower Panel: Example instantaneous surface elevation.


Appendix C

Wave Transformation



3.5.2 Distribution of wave energy along Portsea Front Beach

Figure 3-6 to Figure 3-8 show wave height coefficients within the general vicinity of Portsea Front

Beach for incident peak wave periods of 12, 16 and 20 seconds, respectively. Contours

corresponding to the -30, -20, -15, -10 and -5m AHD isobaths are shown, as is the location of the

wave recorder deployed by Water Technology Ltd. The maps more clearly show the focusing of

wave energy on to the eastern edge of Portsea Front Beach by the configuration of Sorrento and

South Channel, and the shallow banks separating the two.

Figure 3-9 shows the variation in wave height coefficients between Police Point and Point King for

the three MIKE-21 BW simulations. The coefficients are extracted from the model at the -5m AHD

isobath, at the locations given by the black �dots� in Figure 3-6 to Figure 3-8.

Figure 3-6: Distribution of swell wave energy within the vicinity of Portsea and Sorrento Channel, for incident Mean Wave Direction (MWD) of 195°and peak wave period (Tp) of 12 seconds. Wave coefficients are shown as a ratio of the wave height incident to the Boussinesq model boundary, calculated from statistical analysis of the wave field at each model grid cell over a 30 minute period.


Appendix C

Wave Transformation






Appendix C

Wave Transformation



Legend: Blue: Tp = 20s; Green: Tp = 16s; Red: Tp = 12s

Figure 3-9 Variation of simulated wave height coefficients along Portsea Front Beach at -5m AHD isobath, between Police Point and Point King, obtained with the Boussinesq model.

3.5.3 Comparison with Measured Data

Wave height coefficients have been extracted from the model results at the locations of wave buoy

instruments within Port Phillip Bay. A mean coefficient is calculated using a footprint of 11 by 11

grid cells, and compared with measured values and those obtained from MIKE-21 SW simulations.

Table 3-4 shows the results. With the exception of PSFB, measured and MIKE-21 SW coefficients

for all locations are those calculated over all states of the tide. At PSFB the reported wave height

coefficient was calculated for data occurring over the rising tide only (Cardno 2013).

Entrance of Port Phillip Bay

Validation points within Port Phillip Bay entrance comprise wave measurements at RBCL and

NBCL. ROBCL lies a short distance seaward of the model boundary.

Excellent agreement is shown between measured, MIKE-21 SW simulations and MIKE-21 BW

simulations at RBCL. Both MIKE-21 SW and MIKE-21 BW simulations over-estimate the wave

height coefficient at NBCL, with the MIKE-21 SW results being closer to the measured value. The

discrepancy between measured and MIKE-21 BW results at this location are attributed to

schematization of the deep entrance channel required within the Boussinesq wave model.

Portsea region

Validation points within the Portsea region comprise wave measurements at NK and PSFB. Wave

coefficients derived from measured data and MIKE-21 SW simulations for PEB are also shown in

Table 3-4 for context. Excellent agreement between simulated wave height coefficient at PSFB

using MIKE-21 BW and those reported by WaterTechnology Ltd (2010).

Additional validation is shown in Table 3-5 for our AWAC deployments in at Portsea between July

2014 and February 2015. Instrument locations are shown in Figure 2-32.


Appendix C

Wave Transformation



Table 3-4: Measured and simulated wave height coefficients at instrument locations within Port Phillip Bay.

MIKE-21 BW Simulated, slack-water, 0m

AHD

Tp = 12 Tp =16 Tp = 20

Mean

(all periods)

Location Measured

Simulated

(MIKE-21 SW) Mean value

(± Std Dv)

Mean value

(± Std Dv)

Mean

value

(± Std Dv)

ROBCL 0.99 0.98 N/A N/A N/A N/A

RBCL 0.96 0.96 0.91

(±0.01)

0.98

(±0.01)

1.03

(±0.01) 0.97

NBCL 0.73 0.82 1.13

(±0.01)

1.03

(±0.01)

1.01

(±0.01) 1.05

PEB 0.20� 0.16 N/A N/A N/A N/A

NK 0.33 � 0.23 0.24

(±0.01)

0.26

(±0.01)

0.24

(±0.01) 0.25

PSFB 0.14 0.10 0.12

(±0.01)

0.14

(±0.00)

0.15

(±0.00) 0.14

�Obtained from data measured pre-Channel Deepening Project.

Table 3-5: Measured and simulated wave height coefficients at Advisian AWAC deployment locations at Portsea Front Beach in 2014.

Measured Wave Height

Coefficient

MIKE-21 BW Simulated

(slack-water, 0m AHD)

All

Tides Slack Flood Ebb

Tp = 12 Tp =16 Tp = 20 Mean

(all

periods)

Location Mean value

(± Std Dv)

Mean value

(± Std Dv)

Mean value

(± Std Dv)

AWAC-1 0.18 0.17 0.20 0.15 0.15

(±0.01)

0.14

(±0.02)

0.16

(±0.02) 0.15

AWAC-2 0.14 0.15 0.15 0.12 0.14

(±0.01)

0.13

(±0.02)

0.12

(±0.02) 0.13


Appendix C

Wave Transformation



4 Spectral Analysis of Wave Refraction

The efficacy of the bank to the north-west of Portsea in trapping wave energy through refraction is

shown via spectral analysis of Boussinesq wave model results at select locations on and around

the bank (Figure 4-1).

The 1-D frequency spectra (Figure 4-2) show that the relative proportion of energy present at

longer wavelengths (larger wave periods; smaller wave frequencies) increases as swell waves

propagate along the bank. The 2-D directional frequency spectra (Figure 4-3 to Figure 4-10) show

the direction of energy propagation and demonstrate the ability of sections on the bank to refract

and focus wave energy. In particular, the direction of wave energy transformation is shown to

change markedly at locations M and R, where the direction (from) has been turned from an

average of 288° on the bank to 325°. That some of this energy is directed towards Portsea Front

Beach is indicated by the 2-D spectrum at location W showing a direction (from) of 315°, which is

directed towards Portsea Front Beach.

Under these circumstances a simple analysis of the mean wave direction, as plotted usually from

phase-averaged spectral wave model results, would lead to inaccurate conclusions.

Figure 4-1: Wave gauge locations in Boussinesq model for spectral analysis.


Appendix C

Wave Transformation



Figure 4-2: 1-D frequency spectra for wave for simulated wave gauge locations.


Appendix C

Wave Transformation



Figure 4-3: Directional frequency spectra for wave gauges A and B.


Appendix C

Wave Transformation



Figure 4-4: Directional frequency spectra for wave gauges C, D and E.


Appendix C

Wave Transformation



Figure 4-5: Directional frequency spectra for wave gauges F, G and H.


Appendix C

Wave Transformation



Figure 4-6: Directional frequency spectra for wave gauges I, J and K.


Appendix C

Wave Transformation



Figure 4-7: Directional frequency spectra for wave gauges L, M and N.


Appendix C

Wave Transformation



Figure 4-8: Directional frequency spectra for wave gauges O, P and Q.


Appendix C

Wave Transformation



Figure 4-9: Directional frequency spectra for wave gauges R, S and T.


Appendix C

Wave Transformation



Figure 4-10: Directional frequency spectra for wave gauges U, V and W.


Appendix C

Wave Transformation



5 Simulated Nearshore Wave Climate

5.1 Method

A long-term, synthetic inshore wave climate is derived at various locations along Portsea Front

Beach, using wave transfer functions. The steps taken are as follows:

1) The offshore wave climate is grouped monotonically to discrete intervals of Hm0, Tp, MWD and water level that encompass the full range of conditions at the offshore site. This discrete set of reduced conditions then form a lookup table used in step 2:

2) Each combination i of offshore parameters in the lookup table,

is propagated inshore until a steady state is reached. One then obtains for each point k within the model domain of the inshore wave field,

, assuming water elevation to be uniform and equal to the water elevation at point k.

3) Inshore wave parameters, , may then be found for any offshore wave parameter, , through an interpolation scheme based on a weighting function. A wave parameter is

estimated from a linear combination of the N(=24) surrounding points, , extracted from the lookup table and affected by the weights, :

Eq. 5-1

The N surrounding points in the look-up are then the ones satisfying for each coordinate

the relation:

Eq. 5-2

where � = (�Hm0, �Tp, ��m, ��) represents the increments of the lookup table.

The weight of the jth surrounding point is computed following the relation

Eq. 5-3

where the coefficient !j is defined as

Eq. 5-4

Therefore, ultimately the interpolation is a computation of the centroid of the 16 points with

associated weights computed as a product of the differences between increments and the distance

between actual offshore value and the surrounding points within the lookup table.

5.2 Results

The simulated wave climate at each point in Figure 5-1 is provided in Table 5-1 to Table 5-29.

These points are located along the -5 m AHD isobath at 100 m spacing along 2,800 m of coastline


Appendix C

Wave Transformation



from Police Point to Point King. The data and the locations� coordinates are provided separately in

spreadsheet format.

These tables provide occurrences for a range of wave height/wave period combinations in Hm0

wave height increments of 0.25 m with peak wave periods of 12 s, 16 s and 20 s. The wave height

coefficients from the Boussinesq model were used with the nearshore wave directions derived

from the spectral wave model.

These data would be applicable as input for alongshore and cross-shore assessments of potential

littoral drift transport rates.

The wave height estimates are based on reconstructed wave climates at Portsea for the years 2003

to 2012. The wave climates ignore tidal and surge processes, being based on wave height

coefficients that are approximately representative of the average value measured over all tidal

states. Although AWAC wave measurements at Portsea show the largest wave heights are

correlated with storm surge, there is no long-term measured surge data at Portsea to incorporate

in to the long term wave climate.

Figure 5-1: Locations of inshore wave climates.

L1

L8 L15

L20

L25


Appendix C

Wave Transformation



Table 5-1: Wave climate statistics for inshore location L1. Energy-weighted mean wave direction = 350.75°N.




Appendix C

Wave Transformation






4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.05 - 0.15 0.00 0.49 1.24 0.44 1.80 6.64 10.61 6.58 5.47 2.31 1.02 0.43 0.16 0.01 0.02 0.00

0.15 - 0.25 0.00 0.00 1.88 1.93 1.50 4.57 11.11 9.25 6.89 3.69 1.68 0.60 0.21 0.01 0.05 0.00

0.25 - 0.35 0.00 0.00 0.08 1.01 0.69 0.91 2.43 2.90 3.52 2.27 0.94 0.28 0.06 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.00 0.06 0.26 0.20 0.34 0.45 0.66 0.78 0.55 0.14 0.02 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.00 0.04 0.06 0.04 0.06 0.12 0.16 0.17 0.08 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.01 0.02 0.02 0.04 0.03 0.01 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)

Wave Period (Tp) (s)

4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.05 - 0.15 0.00 0.00 0.24 0.08 0.42 1.52 3.84 3.98 3.17 1.67 0.78 0.34 0.12 0.01 0.02 0.00

0.15 - 0.25 0.00 0.00 1.32 0.37 1.29 4.77 7.42 5.10 3.15 1.70 0.86 0.39 0.15 0.01 0.02 0.00

0.25 - 0.35 0.00 0.00 1.64 0.91 1.05 3.62 8.22 6.23 4.97 2.65 1.13 0.34 0.12 0.00 0.03 0.00

0.35 - 0.45 0.00 0.00 0.38 1.30 0.63 1.50 3.48 3.49 2.95 1.78 0.71 0.22 0.04 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.05 0.69 0.43 0.53 1.10 1.07 0.98 0.95 0.51 0.13 0.02 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.13 0.25 0.25 0.35 0.32 0.28 0.38 0.25 0.08 0.01 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.02 0.15 0.10 0.09 0.08 0.08 0.20 0.00 0.05 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.04 0.06 0.02 0.02 0.03 0.07 0.00 0.02 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.01 0.02 0.01 0.01 0.00 0.01 0.00 0.01 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)



Appendix C

Wave Transformation






4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.05 - 0.15 0.00 0.00 1.07 0.26 1.23 4.52 7.41 5.77 3.54 1.78 0.53 0.10 0.03 0.01 0.01 0.00

0.15 - 0.25 0.00 0.00 1.43 0.55 1.05 4.01 7.93 5.70 3.97 2.16 0.90 0.39 0.15 0.00 0.01 0.00

0.25 - 0.35 0.00 0.00 1.08 1.51 0.93 2.60 6.61 6.05 5.01 2.89 0.98 0.43 0.15 0.01 0.04 0.00

0.35 - 0.45 0.00 0.00 0.10 0.99 0.54 0.78 1.97 2.10 2.63 2.00 0.03 0.21 0.08 0.00 0.01 0.00

0.45 - 0.55 0.00 0.00 0.00 0.15 0.31 0.30 0.49 0.54 1.22 0.53 0.02 0.17 0.03 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.01 0.15 0.11 0.10 0.12 0.33 0.36 0.02 0.11 0.02 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.03 0.05 0.02 0.02 0.11 0.14 0.01 0.07 0.01 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.01 0.01 0.00 0.02 0.05 0.00 0.04 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.03 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)


4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.05 - 0.15 0.00 0.00 1.07 0.26 1.23 4.52 7.41 5.77 3.54 1.79 0.58 0.11 0.03 0.01 0.01 0.00

0.15 - 0.25 0.00 0.00 1.90 0.84 1.32 4.86 9.33 6.21 3.73 2.04 0.89 0.44 0.17 0.00 0.02 0.00

0.25 - 0.35 0.00 0.00 0.68 1.66 0.88 2.13 5.84 5.86 4.97 2.90 0.94 0.41 0.14 0.01 0.04 0.00

0.35 - 0.45 0.00 0.00 0.03 0.65 0.51 0.58 1.54 1.91 2.69 2.15 0.03 0.22 0.07 0.00 0.01 0.00

0.45 - 0.55 0.00 0.00 0.00 0.06 0.23 0.17 0.34 0.46 1.38 0.53 0.02 0.16 0.02 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.07 0.08 0.07 0.09 0.37 0.33 0.02 0.09 0.02 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.01 0.02 0.01 0.02 0.12 0.12 0.01 0.07 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.02 0.05 0.00 0.04 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.03 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)


4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.05 - 0.15 0.00 0.00 1.07 0.26 1.23 4.52 7.41 5.77 5.17 1.04 0.11 0.41 0.16 0.01 0.02 0.00

0.15 - 0.25 0.00 0.00 1.36 0.55 0.98 3.88 8.24 6.31 7.39 1.23 0.06 0.39 0.13 0.04 0.00 0.00

0.25 - 0.35 0.00 0.00 1.15 1.53 0.94 2.70 6.49 5.84 7.31 1.18 0.05 0.32 0.11 0.02 0.00 0.00

0.35 - 0.45 0.00 0.00 0.10 1.00 0.54 0.78 1.83 1.83 3.11 0.70 0.03 0.21 0.04 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.16 0.33 0.30 0.45 0.45 0.89 0.44 0.02 0.11 0.02 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.01 0.15 0.11 0.09 0.09 0.21 0.16 0.01 0.07 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.03 0.05 0.02 0.02 0.05 0.05 0.00 0.04 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.01 0.01 0.00 0.01 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)



Appendix C

Wave Transformation






4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.00 0.02 0.01 0.06 0.21 0.36 0.24 0.17 0.03 0.00 0.01 0.01 0.01 0.00 0.00

0.05 - 0.15 0.00 0.00 2.22 0.70 2.02 7.74 13.98 10.77 10.82 2.26 0.18 0.88 0.31 0.07 0.00 0.00

0.15 - 0.25 0.00 0.00 1.43 2.24 1.37 3.65 8.96 8.01 10.45 1.68 0.07 0.44 0.12 0.01 0.00 0.00

0.25 - 0.35 0.00 0.00 0.02 0.56 0.59 0.60 1.12 1.18 2.40 0.70 0.21 0.00 0.02 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.00 0.01 0.17 0.14 0.10 0.10 0.29 0.13 0.06 0.00 0.01 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.00 0.01 0.03 0.01 0.01 0.02 0.01 0.01 0.00 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)


4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.15 0.15 0.13 0.03 0.01 0.00 0.01 0.01 0.00 0.00

0.05 - 0.15 0.00 0.20 1.56 0.41 2.86 5.63 11.52 9.35 9.66 2.09 1.02 0.04 0.26 0.06 0.00 0.00

0.15 - 0.25 0.00 0.00 2.23 1.60 2.18 4.37 10.50 12.32 6.84 1.72 0.53 0.01 0.12 0.02 0.00 0.00

0.25 - 0.35 0.00 0.00 0.15 1.06 0.77 0.88 1.91 3.19 1.54 0.79 0.22 0.00 0.02 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.00 0.11 0.23 0.20 0.24 0.38 0.24 0.17 0.07 0.00 0.01 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.00 0.04 0.07 0.02 0.03 0.05 0.02 0.01 0.00 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)


4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.05 0.11 0.03 0.02 0.00 0.01 0.01 0.00 0.00

0.05 - 0.15 0.00 0.82 0.59 0.46 2.31 5.34 11.22 6.98 9.32 2.11 1.05 0.04 0.26 0.07 0.00 0.00

0.15 - 0.25 0.00 0.33 2.26 1.17 2.33 4.90 11.96 11.72 7.07 1.71 0.51 0.01 0.11 0.01 0.00 0.00

0.25 - 0.35 0.00 0.00 0.45 1.18 0.91 1.14 2.55 3.68 1.63 0.78 0.21 0.00 0.02 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.00 0.20 0.29 0.32 0.37 0.48 0.27 0.17 0.06 0.00 0.01 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.00 0.10 0.10 0.04 0.04 0.05 0.02 0.01 0.00 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.01 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)



Appendix C

Wave Transformation






4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.06 0.05 0.02 0.02 0.00 0.01 0.01 0.00 0.00

0.05 - 0.15 0.00 0.79 0.45 0.40 2.02 4.75 9.87 10.94 3.53 1.99 1.07 0.04 0.27 0.07 0.00 0.00

0.15 - 0.25 0.00 0.36 2.28 1.22 2.25 5.16 12.48 14.55 4.35 1.76 0.51 0.01 0.11 0.01 0.00 0.00

0.25 - 0.35 0.00 0.00 0.59 1.23 0.98 1.32 3.21 4.69 1.92 0.81 0.20 0.00 0.02 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.01 0.31 0.43 0.33 0.51 0.71 0.39 0.20 0.06 0.00 0.01 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.02 0.15 0.11 0.07 0.10 0.07 0.02 0.01 0.00 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.02 0.04 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)


4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.01 0.00 0.01 0.07 0.13 0.22 0.11 0.05 0.02 0.01 0.00 0.01 0.01 0.00 0.00

0.05 - 0.15 0.00 1.24 0.86 0.64 3.11 6.42 12.92 11.99 3.53 1.95 1.02 0.04 0.26 0.06 0.00 0.00

0.15 - 0.25 0.00 0.50 2.08 1.53 1.98 3.79 10.95 14.49 4.38 1.75 0.53 0.01 0.12 0.02 0.00 0.00

0.25 - 0.35 0.00 0.00 0.22 0.82 0.66 0.65 1.83 3.88 1.90 0.84 0.22 0.00 0.02 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.00 0.06 0.21 0.15 0.20 0.52 0.39 0.23 0.07 0.00 0.01 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.00 0.03 0.04 0.02 0.07 0.07 0.03 0.01 0.00 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)


4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.02 0.01 0.00 0.00 0.01 0.00 0.00

0.05 - 0.15 0.00 1.16 0.75 0.62 2.96 6.11 12.18 11.40 3.38 1.76 0.95 0.04 0.24 0.06 0.00 0.00

0.15 - 0.25 0.00 0.60 2.12 1.43 2.02 4.07 11.43 14.44 4.35 1.80 0.55 0.01 0.13 0.03 0.00 0.00

0.25 - 0.35 0.00 0.00 0.33 0.94 0.71 0.77 2.21 4.47 2.02 0.89 0.24 0.00 0.03 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.00 0.10 0.27 0.15 0.29 0.66 0.46 0.30 0.09 0.00 0.00 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.00 0.06 0.04 0.03 0.09 0.09 0.05 0.02 0.00 0.01 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)



Appendix C

Wave Transformation






4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.02 0.00 0.01 0.08 0.14 0.20 0.05 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00

0.05 - 0.15 0.00 1.28 0.94 0.70 3.17 6.62 12.78 11.19 3.18 1.61 0.84 0.04 0.21 0.04 0.00 0.00

0.15 - 0.25 0.00 0.46 2.05 1.62 1.90 3.64 11.03 14.51 4.38 1.85 0.59 0.02 0.15 0.04 0.00 0.00

0.25 - 0.35 0.00 0.00 0.17 0.75 0.63 0.60 1.89 4.53 2.11 0.92 0.27 0.00 0.03 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.00 0.05 0.23 0.11 0.22 0.69 0.54 0.37 0.12 0.00 0.01 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.00 0.03 0.03 0.02 0.09 0.10 0.07 0.04 0.00 0.01 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)


4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.01 0.00 0.01 0.07 0.11 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.05 - 0.15 0.00 1.18 0.79 0.63 2.96 6.15 11.60 9.93 2.80 1.43 0.77 0.03 0.20 0.05 0.00 0.00

0.15 - 0.25 0.00 0.57 2.12 1.47 2.00 3.97 11.68 14.32 4.21 1.85 0.62 0.02 0.16 0.05 0.00 0.00

0.25 - 0.35 0.00 0.00 0.29 0.90 0.70 0.71 2.46 5.66 2.38 0.97 0.29 0.01 0.04 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.00 0.10 0.26 0.14 0.32 0.99 0.75 0.46 0.12 0.00 0.01 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.00 0.05 0.04 0.03 0.15 0.15 0.10 0.05 0.00 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.02 0.02 0.01 0.01 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)


4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00

0.05 - 0.15 0.00 1.07 0.43 0.52 2.52 8.50 6.53 8.94 2.60 1.42 0.80 0.24 0.00 0.04 0.00 0.00

0.15 - 0.25 0.00 0.92 1.96 1.18 2.20 8.90 8.11 14.13 4.19 1.87 0.61 0.17 0.00 0.04 0.00 0.00

0.25 - 0.35 0.00 0.00 0.61 1.23 0.74 1.97 2.33 6.50 2.51 0.94 0.28 0.04 0.00 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.01 0.27 0.30 0.39 0.37 1.27 0.86 0.43 0.12 0.01 0.00 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.01 0.12 0.06 0.07 0.19 0.18 0.09 0.04 0.01 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.01 0.02 0.01 0.04 0.03 0.01 0.01 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)



Appendix C

Wave Transformation






4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.05 - 0.15 0.00 1.10 0.48 0.50 2.59 8.99 11.33 5.36 3.08 1.21 0.85 0.25 0.01 0.04 0.00 0.00

0.15 - 0.25 0.00 0.93 1.96 1.26 2.19 9.66 14.09 8.23 3.77 1.62 0.55 0.17 0.01 0.03 0.00 0.00

0.25 - 0.35 0.00 0.00 0.55 1.17 0.72 2.01 4.26 3.63 2.15 0.89 0.23 0.04 0.00 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.01 0.24 0.27 0.38 0.65 0.63 0.69 0.39 0.11 0.01 0.00 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.01 0.10 0.07 0.08 0.10 0.13 0.07 0.03 0.01 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01 0.02 0.01 0.01 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)


4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.01 0.00 0.00

0.05 - 0.15 0.00 1.27 0.61 0.61 2.93 10.10 9.41 9.16 3.18 1.66 0.90 0.27 0.01 0.04 0.00 0.00

0.15 - 0.25 0.00 0.76 1.99 1.42 2.01 8.00 14.67 7.57 4.46 1.73 0.57 0.16 0.00 0.03 0.00 0.00

0.25 - 0.35 0.00 0.00 0.37 1.01 0.67 1.47 3.59 2.94 2.21 0.82 0.25 0.03 0.00 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.00 0.15 0.23 0.24 0.49 0.47 0.57 0.32 0.11 0.01 0.00 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.00 0.06 0.04 0.05 0.08 0.10 0.06 0.02 0.01 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.01 0.01 0.00 0.01 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)


4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.01 0.00 0.01 0.07 0.19 0.16 0.10 0.04 0.02 0.01 0.00 0.01 0.01 0.00 0.00

0.05 - 0.15 0.00 1.38 0.73 0.66 3.08 10.88 8.47 11.92 3.48 1.95 1.04 0.17 0.13 0.06 0.00 0.00

0.15 - 0.25 0.00 0.63 2.00 1.55 1.91 7.44 10.42 11.28 4.37 1.75 0.52 0.13 0.00 0.01 0.00 0.00

0.25 - 0.35 0.00 0.00 0.25 0.86 0.59 1.15 2.85 2.46 1.98 0.80 0.22 0.02 0.00 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.00 0.10 0.21 0.18 0.29 0.40 0.42 0.21 0.07 0.01 0.00 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.00 0.04 0.03 0.02 0.07 0.07 0.03 0.01 0.00 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)



Appendix C

Wave Transformation






4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.03 0.00 0.02 0.14 0.42 0.36 0.28 0.09 0.06 0.06 0.02 0.00 0.01 0.00 0.00

0.05 - 0.15 0.00 1.71 1.15 0.90 3.61 13.15 14.43 11.38 4.60 2.51 1.19 0.36 0.01 0.07 0.00 0.00

0.15 - 0.25 0.00 0.29 1.78 1.75 1.59 5.52 11.86 7.16 4.34 1.42 0.45 0.08 0.00 0.00 0.00 0.00

0.25 - 0.35 0.00 0.00 0.05 0.50 0.44 0.68 1.46 1.28 1.31 0.55 0.15 0.01 0.00 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.00 0.01 0.14 0.09 0.11 0.13 0.18 0.07 0.02 0.01 0.00 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)


4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.08 0.02 0.05 0.28 0.87 0.73 0.72 0.21 0.14 0.15 0.00 0.03 0.02 0.00 0.00

0.05 - 0.15 0.00 1.95 1.89 1.25 4.11 15.22 18.71 13.14 5.70 2.94 1.26 0.10 0.28 0.07 0.00 0.00

0.15 - 0.25 0.00 0.00 1.10 1.70 1.21 3.46 8.19 5.79 3.74 1.39 0.38 0.05 0.00 0.00 0.00 0.00

0.25 - 0.35 0.00 0.00 0.00 0.17 0.28 0.29 0.57 0.55 0.65 0.28 0.07 0.01 0.00 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.00 0.00 0.03 0.02 0.02 0.05 0.06 0.01 0.01 0.00 0.00 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)


4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.11 0.03 0.06 0.36 1.13 1.76 0.86 0.45 0.27 0.43 0.02 0.10 0.03 0.00 0.00

0.05 - 0.15 0.00 1.93 2.15 1.41 4.20 15.62 23.93 12.02 6.93 3.15 1.11 0.28 0.03 0.06 0.00 0.00

0.15 - 0.25 0.00 0.00 0.83 1.58 1.09 2.90 5.73 3.71 2.88 1.08 0.29 0.03 0.00 0.00 0.00 0.00

0.25 - 0.35 0.00 0.00 0.00 0.11 0.25 0.21 0.25 0.19 0.25 0.10 0.04 0.01 0.00 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.00 0.00 0.02 0.02 0.01 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)



Appendix C

Wave Transformation






4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.15 0.05 0.09 0.52 1.64 1.89 3.52 1.38 0.91 0.52 0.02 0.14 0.03 0.00 0.00

0.05 - 0.15 0.00 1.88 2.48 1.75 4.33 16.19 13.96 23.79 7.10 2.98 1.07 0.03 0.25 0.06 0.00 0.00

0.15 - 0.25 0.00 0.00 0.48 1.29 0.89 1.92 1.51 3.66 1.76 0.89 0.25 0.00 0.03 0.00 0.00 0.00

0.25 - 0.35 0.00 0.00 0.00 0.03 0.17 0.08 0.06 0.10 0.07 0.04 0.02 0.00 0.00 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)


4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.16 0.05 0.09 0.55 1.12 3.13 5.20 2.10 1.04 0.52 0.02 0.14 0.03 0.00 0.00

0.05 - 0.15 0.00 1.87 2.52 1.81 4.33 8.93 20.89 23.06 6.82 3.07 1.15 0.04 0.26 0.06 0.00 0.00

0.15 - 0.25 0.00 0.00 0.44 1.24 0.87 0.98 2.08 2.74 1.36 0.69 0.18 0.00 0.02 0.00 0.00 0.00

0.25 - 0.35 0.00 0.00 0.00 0.02 0.16 0.08 0.05 0.06 0.04 0.01 0.01 0.00 0.00 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)


4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.50 0.19 0.24 1.38 2.73 6.83 7.27 2.22 1.04 0.52 0.02 0.14 0.03 0.00 0.00

0.05 - 0.15 0.00 1.54 2.91 1.93 3.83 7.77 18.22 22.17 7.16 3.29 1.19 0.04 0.27 0.06 0.00 0.00

0.15 - 0.25 0.00 0.00 0.18 0.72 0.65 0.58 1.08 1.61 0.92 0.48 0.14 0.00 0.01 0.00 0.00 0.00

0.25 - 0.35 0.00 0.00 0.00 0.00 0.04 0.04 0.01 0.02 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)



Appendix C

Wave Transformation





4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.71 0.27 0.33 1.79 3.63 7.66 7.46 2.22 1.06 0.73 0.03 0.19 0.04 0.00 0.00

0.05 - 0.15 0.00 1.33 2.68 2.27 3.51 6.99 17.69 22.46 7.45 3.49 1.07 0.03 0.21 0.05 0.00 0.00

0.15 - 0.25 0.00 0.00 0.06 0.47 0.67 0.48 0.79 1.13 0.64 0.27 0.06 0.00 0.01 0.00 0.00 0.00

0.25 - 0.35 0.00 0.00 0.00 0.00 0.02 0.03 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)


4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5 13.5-14.5 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5

<0.05 0.00 0.91 0.26 0.65 3.02 5.45 9.41 5.31 2.93 1.95 1.16 0.35 0.00 0.09 0.00 0.00

0.05 - 0.15 0.00 1.46 2.93 2.49 5.26 10.91 22.05 11.37 7.24 2.84 0.70 0.13 0.00 0.01 0.00 0.00

0.15 - 0.25 0.00 0.00 0.00 0.13 0.27 0.25 0.21 0.10 0.14 0.03 0.01 0.00 0.00 0.00 0.00 0.00

0.25 - 0.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.35 - 0.45 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.45 - 0.55 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.55 - 0.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.65 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.75 - 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.85 - 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.95 - 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.05 - 1.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.15 - 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

H0

(m)



Appendix C

Wave Transformation



6 Summary and Conclusions

6.1 Spectral Wave Model

A spectral wave model has been constructed to simulate the propagation of swell wave energy

through the entrance of Port Phillip Heads to Portsea Front Beach. The model was based on

bathymetric boundary conditions from the 2012 survey. The simulations were undertaken for

slack-water, flood-tide and ebb-tide.

Maps of wave height coefficients derived from the simulation results suggest that the deep

channel running through Port Phillip Heads is responsible for refracting wave energy around

Point Nepean. Wave energy directed towards South Channel tends to be �captured� via total

internal wave reflection along a system of shallow sand banks separating the deeper water areas of

South Channel and Sorrento Channel. Part of this wave energy is refracted towards Portsea Front

Beach by a shallow, linear sand bank located approximately 1.5 km north-west of Portsea Pier.

Additional focusing on the beach immediately east of Portsea Pier may occur through wave

interaction with Portsea Hole and a shallow submarine bank extending a short distance seaward

into Sorrento Chanel immediately seaward of Portsea Pier.

Wave-current simulations reproduce the phenomena of wave �blocking� by strong ebb currents

and wave �pushing� by strong flood currents flowing through Port Phillip Heads. The simulations

demonstrate the importance of the tidal stage in focusing wave energy along different sections of

the coastline. Spring flood tidal conditions increase the effective wavelength of swell wave energy

propagating through The Entrance and Nepean Bank, increasing the efficacy of the channel in

refracting wave energy around Point Nepean onto the shore between Point Nepean and

Observatory Point. Although wave energy is directed towards South Channel under these

conditions, this mechanism increases the ability of the sand banks to capture wave energy and to

focus it towards Portsea Front Beach.

Comparison of wave model results against measured wave data at select locations within the

entrance to Port Phillip Bay and in the general Portsea region found that the model is robust.

Although the model under-predicts wave height coefficients in some areas and over-predicts in

others, the same qualitative changes (i.e., increase or decrease) are observed in wave height

coefficients at a given location for different tidal stages.

6.2 Boussinesq Wave Model

A Boussinesq wave model has been developed for the entrance to Port Phillip Bay and the Portsea

Region. The model is capable of simulating all major non-linear wave processes within the coastal

zone.

The fine resolution in spatial detail of the Boussinesq simulations shows the importance of the

plan-shape of the deep canyon running through Port Phillip Heads in governing wave refraction

into the South Channel region of The Great Sands. Wave energy refracted by the channel edges is

focused towards the South Channel. The presence of shallow, mobile sand banks separating South

Channel and Sorrento Channel causes refraction of wave energy away from channel areas,

�capturing� wave energy and concentrating it through repeated total internal wave reflection.


Appendix C

Wave Transformation



The model results show that some wave energy is focused onto Portsea Front Beach by a shallow

sand bank lying approximately 1.5 km north-west of Portsea Pier. The severity of the wave

focusing causes spatial gradients in swell wave energy for the area a short distance to the east of

Portsea Pier.

Excellent agreement is shown between measured and simulated wave height coefficients using

MIKE-21 BW for a variety of locations within south Port Phillip Bay, the Great Sands region and

for field data obtained for this study directly off Portsea Front Beach and with the distribution of

wave energy as simulated using MIKE-21 SW. This indicates the general robustness of both

models in capturing the relevant coastal processes at Portsea Front Beach.

6.3 Spectral Analysis of Wave Refraction

Spectral analysis of Boussinesq wave model results shows the complex nature of wave refraction

around the crest of the sand banks approximately 1.5 km north-west of Portsea. The crest is

effective at trapping wave energy at various frequencies via wave refraction and internal

reflection. Frequency spectra show that the larger wave periods (smaller wave frequencies) are

trapped and focused more effectively by the bank, leading to amplification of wave energy present

at longer wave lengths (larger wave periods) on the east side of the bank. The data indicate

portions of the bank that induce changes to the direction of wave energy transformation towards

Portsea Front Beach.

6.4 Wave Climate

Wave climate tables have been prepared for the Portsea Front Beach foreshore extending from

Police Point to Point King at 100 m centers along the -5 m AHD isobaths.


Appendix C

Wave Transformation



7 References

Cardo (1998). Port Phillip Heads � Offshore wave climate. Report RM105/J5099, 56p. Report

prepared for Victorian Channels Authority.

Cardno (2010)a. AWAC current measurements. Comparison before and after dredging.

RM2243/LJ5518, 17p. Prepared for Port of Melbourne Corporation.

Cardno (2010)b. AWAC wave measurements. Comparison before and after dredging.

RM2247/LJ5518, 17p. Prepared for Port of Melbourne Corporation.

Cardno (2011)a. The Great Sands and adjacent coasts and beaches. Report RM2289_LJ5518, 137p.

Report prepared for Port of Melbourne Authority.

Cardno (2011)b. Sediment Transport Modelling. Great Sands, Port Philip. Report

RM2271_LJ5518, 78p. Report prepared for Port of Melbourne Authority.

DHI (2011). MIKE21 SW Spectral Wave Module. Scientific Documentation.

Komen, G.J., Cavaleri, L., Doneland, M., Hasselmann, K., Hasselmann, S. and Janssen, P.A.E.M.

(1994). Dynamics and modelling of ocean waves. Cambridge University Press, UK, 560pp.

Madsen, P A, Murray, R & Sørensen, O R (1991), "A new form of the Boussinesq equations with

improved linear dispersion characteristics, (Part 1)." Coastal Eng., 15, 371-388.

Madsen, P A & Sørensen, O R (1992), "A new form of the Boussinesq equations with improved

linear dispersion characteristics. Part 2: A slowly-varying Bathymetry". Coastal Eng.., 18, 183-204.

Nikuradse, J. (1932). �Laws of flow in rough pipes.� NACA Tech. Mem.1292.

Symmonds, G. and McInnes, K. (2013). Review of OEM Assessment of Potential Causes of Beach

Erosion at Portsea, CSIRO, Australia. 19p.

Water Technology Ltd (2010). Estimation of design wave heights and water levels at Portsea

Front Beach. Report

Water Technology Ltd (2013). Review of wave transformation processes through Port Phillip

heads. Report 2668-01R02v04.

Young, I.R. (1999): Wind generated ocean waves. In: Elsevier Ocean Engineering Book Series,

Volume 2. Eds, R. Bhuttacharyya and M.E. McCormick. Elsevier.


301015-03540-Report-Rev 0 160115.docm

Appendix D

Sediment Transport

Advisian Appendix D Sediment Transport Document Number 301015-03540

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301015-03540-Appendix D - Sediment Transport - Rev 0 160115.docm

Table of Contents

1 Introduction 1

2 Morphological Observations on Quarantine Bank 2

2.1 Introduction 2

2.2 Observations Encompassing 2007 to 2010 2

2.3 Observations Encompassing 2010 to 2012 5

2.4 Summary 5

3 Sediment Transport on the Banks 7

3.1 Introduction 7

3.2 Impact of Wave Action on Sediment Transport 7

3.3 Numerical Modelling System 8

3.3.1 Introduction 8

3.3.2 Sediment Transport Model 8

3.4 Calibration of Sediment Transport Model against Field Data 9

3.4.1 Methodology 9

3.4.2 Validation 9

3.4.3 Results 10

4 Littoral Drift Transport 13

4.1 Introduction 13

4.2 Morphology Study 13

4.2.1 Measured Changes in Beach Alignment 13

4.2.2 Sediment Budget 13

4.3 Transport Parameters for Modelling 16

4.3.1 Grain Size 16

4.3.2 Beach Profiles 16

4.3.3 Nearshore Wave Climate 18

4.4 Simulations 18


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4.4.1 Model Configuration 18

4.4.2 Summary of Key Parameters 18

4.4.3 Calculation Method 19

4.4.4 Distribution of Littoral Drift Transport Potential 19

4.4.5 Potential Sediment Transport Rates of Portsea Front Beach 23

4.5 Model Calibration 24

4.5.1 Calibrated Annual Rates of Littoral Drift Transport 24

5 Conclusions 26

6 References 27

List of Figures

Figure 1 Comparison of sediment transport vectors and the difference between LADS surveys 2007 and

2010. Modified from Cardno (2011).

Figure 2 Selected “beach profiles” (from Cardno 2011).

Figure 3 LADS 2010 and 2012 surveys on the offshore sand banks (data courtesy Port of Melbourne

Corporation). A: Bathymetry in 2010. B: Bathymetry in 2012. C: Change in bathymetry between 2010

and 2012. Depth contours correspond to 2012. D: Cross-sections through the sand wave fields.

Figure 4 Calibration of the sediment transport model for the offshore sand bank

Figure 5 Verification of the sediment transport model for the offshore sand bank

Figure 6 Error assessment for the calibration (left panel) and verification (right panel) of the offshore

sediment transport model

Figure 7 Calculated gross sediment transport rates on Quarantine Bank resolved in the cardinal

directions

Figure 8 Net sediment transport vectors on Quarantine Bank

Figure 9 Net sediment transport rates on Quarantine Bank

Figure 10 Changes in foreshore alignment at Portsea Front Beach 2005 to 2015 (Courtesy Google earth)

Figure 11 Changes in beach width at the western end of the Weeroona Bay embayment 21/11/2005 to

10/2/2015 (courtesy Google earth)

Figure 12 Sediment Budget for Weeroona Bay

Figure 13 Locations of beach profiles used in littoral drift modelling. Profiles are named L2 to L11 from

west to east and correspond to the locations where wave climates were extracted at the -5m AHD isobath.


Page iv


Figure 14 Example of 2DV model grid for beach profile simulations at L09. Vertical resolution of the

model is shown.

Figure 15 Cross-shore distribution of littoral drift potential on profile L02








Figure 23 Salient rates of littoral drift transport identified for calibration

List of Tables

Table 1 Summary of Relevant Exerpts from Cardno (2011)

Table 2 Key to Legend in Figure 2

Table 3 Profile Orientations as Interpreted by the Wave Refraction Model

Table 4 Summary of Parameters describing Sediment Properties, Coastline Definition and Wave

Conditions for Littoral Drift Transport Computations.

Table 5 Sediment Transport Potential at Beach Profiles


Appendix D

Sediment Transport

Advisian Appendix D Sediment Transport Client Reference: 301015-03540

Page 1


1 Introduction

The report details the results of sediment transport modelling undertaken at Portsea Front Beach.

The study is split in to two aspects:

1) The dynamics of the sand shoal system adjacent to Portsea offshore in the Bay

2) The transport of littoral drift along the beach fronting Portsea, between Police Point and

Point Franklin.

The original focus of this project, as proposed by DEPI, was to understand the sediment dynamics

of the beach system fronting Portsea (and immediately adjacent areas), in terms of the directions

of net transport, the distribution of sediment transport in the cross-shore dimension of the beach

and the relative influence of cross-shore and long-shore sediment transport during a ‘normal’ year

and during storm events.

Detailed wave modelling of wave refraction through Port Phillip Heads showed that the

configuration of the banks had a major influence of the amount of wave energy reaching Port

Phillip Bay. Swell wave energy refracting through the entrance to Port Phillip Bay is focussed

towards the sand banks lining the south edge of South Channel by the shape of the underlying

channel system. Wave energy incident upon the banks is then trapped by total internal reflection

along the crests. This mechanism enables a proportion of swell wave energy incident through Port

Phillip Heads to penetrate some considerable distance into and eastward within the southern

region of Port Phillip Bay.

The geometry of the sand shoal system and associated mobile sand waves at Nicholson Knoll and

Quarantine Bank are of sufficient dimension to interact with incident swell. The shape of the bank

causes wave energy to ‘peel’ off the shoal system adjacent to Portsea and be focussed onto the

coastline at the exact location where beach erosion is known to be most severe. That is, at the

location of the geotextile sand bag wall fronting Portsea Hotel.

As Nicholson Knoll is known to be an area of very active sediment transport (due to strong tidal

currents), this implies that any change over time to the geometry and dimensions of the bank

crest and associated bed forms, will be likely to change the magnitude of wave energy arriving at

Portsea Front Beach.

Therefore, the focus of this coastal processes investigation changed to include an understanding

the sediment dynamics and morphodynamic behaviour of the bank and sand shoal system. A field

campaign was designed and implemented to measure sediment transport at the crest of the sand

bank to calibrate sediment transport modelling there also.

In the following, Section 2 summarises available data on sediment properties and

morphodynamic observations on Quarantine Bank, Section 3 details the validation of the

numerical sediment transport model and presents an understanding of sediment transport

processes on Quarantine Bank and Section 4 documents the modelling of littoral drift transport

on Portsea Front Beach.


Appendix D

Sediment Transport


Page 2


2 Morphological Observations on Quarantine Bank

2.1 Introduction

Two periods of survey data are available to assess the behaviour of the Quarantine Bank sand

shoal system adjacent to Portsea. The first period spans multiple bathymetric surveys undertaken

between 2007 and 2010. Table 1 summarises the dates of the survey data. Analysis of this data

was undertaken in Cardno (2011) and is summarised in the following. The second period spans

changes observed between successive LADS surveys occurring in 2010 and 2012. This data has

been analysed for the present study.

2.2 Observations Encompassing 2007 to 2010

Figure 1 shows the difference between the 2007 and 2010 surveys. Vectors corresponding to the

net (residual) transport simulated in Cardno (2011) are shown also. Cardno (2011) did not specify

the magnitude of gross or nett transport rates estimated from their sediment transport model.

Instead a qualitative analysis was undertaken by comparing the directions and relative

magnitudes of net transport vectors with observed changes between successive bathymetric

surveys.

The data within the area of the sand bank and shoal system adjacent to Portsea, highlighted in the

black rectangle, shows that the net transport is ebb-dominant and that large-scale changes in the

bank geometry and bed levels occurred between 2007 and 2010. This is manifest by a net erosion

of ~3 m on the north side of the bank and net accretion of ~3 m on the south side of the bank. The

absolute values of the erosion and accretion vary due to the migration of bed forms, but the

general pattern is clear.

Cardno (2011) presented an analysis of cross-sectional data (“beach profiles”) in the region of

Portsea. The most relevant profiles for this study are described in Table 1 and are shown in Figure

2. The migration of bed features on the bank is shown clearly, but the north-south alignment of

the cross-sections means that they are unsuitable for assessing the dimensions of the sand waves

or the direction and patterns of movement.

Changes to the north side of the bank are visible clearly on “beach profile 23”, which extends

offshore. Cardno (2011) did not comment on this feature as the analysis focussed predominantly

on assessing changes to the beach area of Portsea.

Table 1 Summary of Relevant Exerpts from Cardno (2011)

Beach Profile Location

23 Weeroona Bay, Portsea, east of Portsea Pier, to South Channel

25 Weeroona Bay, Portsea, off The Cutting, to South Channel

27 Quarantine Station to South Channel


Appendix D

Sediment Transport


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Figure 1 Comparison of sediment transport vectors and the difference between LADS surveys 2007 and 2010. Modified from Cardno (2011).

Table 2 Key to Legend in Figure 2

Legend Survey Source and Year

“Pre 1” DSE 2007

“Pre 2” PoMC, late 2007/ early 2008

“Post 1” DSE, late 2008/ early 2009

“Post 2” PoMC, early 2010


Appendix D

Sediment Transport


Page 4


Figure 2 Selected “beach profiles” (from Cardno 2011).


Appendix D

Sediment Transport


Page 5


2.3 Observations Encompassing 2010 to 2012

An analysis of changes to the sand shoal system between 2010 and 2012 is presented in Figure 3.

Changes in bed level between the two surveys are shown in panel ‘C’. Cross sections through the

sand shoals are shown in panel ‘D’, which also infer net bedload transport direction based upon

the asymmetry of the sand wave crests.

The sand waves are up to 5 m high and approximately 200 m long, which is of a similar scale to

the wavelength of the incident swell trapped on the banks. The asymmetry of the sand wave crests

indicates that the net bedload transport is directed westerly in the ebb-tide direction. The

bedforms at the western-most edge of the bank suggests that there may be areas that experience

net transport in the flood-tide direction. This feature is not reproduced by the depth-averaged

hydrodynamic model employed in this study, or the residual transport vectors shown in Figure

2-1, which was the product of a 3-D hydrodynamic model. The flood dominance shown at the

western edges of cross-section A and B may be due to some localised sheltering effects by the bank

crest and is unlikely to be representative of the wider area.

The net bed level changes shown in panel C indicate that the thickness of the mobile sediment

layer over the core of the bank, which itself is a relict geological feature, is some 4 m. In general,

the bed level change is due to migration of large sand waves along the crest of the bank. Large

scale behaviour is indicated also with net erosion on the north side of the bank and net accretion

on the bank crest and to the south and west of the bank.

2.4 Summary

§ The sand shoal system has exhibited large-scale change between 2007 and 2010. The net

erosion was around three metres on the northern side and accretion of around three metres on

the eastern side. The level of detail in the figure from Cardno (2011) precluded a more detailed

analysis but was sufficient to show the general trend.

§ A more detailed analysis of the bed level changes in the sand shoal system between 2010 and

2012 indicated that the thickness of active layer covering the bank is in the order of four to five

meters.

§ There was a large-scale trend of erosion on the northern flank of the bank, adjacent to the

South Channel.

§ There was large scale accretion of the sandbank to the southwest.


Appendix D

Sediment Transport


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Figure 3 LADS 2010 and 2012 surveys on the offshore sand banks (data courtesy Port of Melbourne Corporation). A: Bathymetry in 2010. B: Bathymetry in 2012. C: Change in bathymetry between 2010 and 2012. Depth contours correspond to 2012. D: Cross-sections through the sand wave fields.


Appendix D

Sediment Transport


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3 Sediment Transport on the Banks

3.1 Introduction

The large sand wave features on the offshore sand banks, shown in Figure 3, attest to significant

sand transport rates under tidal flows.

3.2 Impact of Wave Action on Sediment Transport

Sand transport rates on the sand banks may be enhanced by wave action. The relative

contribution from wave stirring has been examined by comparing typical bottom shear stresses

generated by waves and tidal currents.

The bottom shear stress, τb,w, generated by waves is (after van Rijn, 1989):

τb,w = 0.5 ρ fw U2δ

where:

τb,w = instantaneous wave-related bed shear stress

ρ = fluid density

fw = wave-related friction coefficient

Uδ = instantaneous wave-induced flow velocity just outside the boundary layer.

In rough turbulent flow, the friction coefficient fw can be expressed as:

fw = exp[-6 + 5.2(Aδ/ks)-0.19]

where:

Aδ = amplitude of the water particle excursion at the bed

ks = bed roughness as experienced by waves (taken herein as D50).

For a wave height of 0.5 m with period 15 s in a water depth of 10 m, on a sand bed with

D50 = 0.3 mm, the maximum wave shear stress would be 0.3 Pa.

The bed shear stress induced by tidal flow is given by (after van Rijn, 1989):

τb,c = 0.125 ρ fc u2

where:

τb,c = current related bed shear stress

ρ = fluid density

fc = current related friction coefficient

u = depth averaged flow velocity.

In rough turbulent flow the friction factor fc is:

fc = 0.24 log-2(12h/ks)


Appendix D

Sediment Transport


Page 8


where:

h = water depth

ks = the current-related bed roughness.

For a tidal current speed of 1.5 m/s in a water depth of 10 m, on a sand bed with D50 = 0.3 mm,

the maximum current-related bed shear stress would be 2 Pa.

Therefore, in this instance, as the bed shear stress under tidal flows is an order of magnitude

larger than that induced by waves, the bed shear stresses and, hence, rates of sediment transport

on the sandbanks offshore of Portsea Front Beach would be dominated by tidal flows with wave

action providing little enhancement.

This observation was borne out by ‘sensitivity’ simulations during the course of the analysis,

which found no discernible difference in simulated sediment transport rates when considering

wave and current processes against current processes alone.

In the following, the contribution of swell waves on rates of sediment transport under tidal flows

on the sandbanks has been neglected.

3.3 Numerical Modelling System

3.3.1 Introduction

A full description of the Delft 3D flow modelling suite is given in Deltares (2014) and the

hydrodynamics undertaken for this project are documented in Appendix B.

3.3.2 Sediment Transport Model

3.3.2.1 Introduction

For the transport of non-cohesive sediment (sand), Van Rijn et al. (2000) sediment transport

algorithms, TRANSPOOR, was used.

The settling velocity of sand sediment fractions is computed following the method of Van Rijn

(1993). For the range of sediment diameters observed on the bed, the formulations used are as

follows:

Where s(l) is the relative density of sediment fraction (l); is the representative diameter of the

sediment fraction, (l); v is the kinematic viscosity coefficient of water [m2/s].

In the case of non-uniform bed material (as is the case at Portsea and the adjacent sand shoal

system), Van Rijn (1993) concluded that, on the basis of measurements, should be in the

range of 60% to 100% of D50 of the bed material.


Appendix D

Sediment Transport


Page 9


For the sediment transport computations, the settling velocities of the seabed sediments, as

measured from the RSA analysis (Appendix A), were used to determine the equivalent fall

diameters using the formulae above for input to the sediment transport algorithms.

3.4 Calibration of Sediment Transport Model against Field Data

3.4.1 Methodology

The van Rijn sediment transport algorithms were calibrated against the field data obtained over

an ebb/flood tidal cycle at one site (ADCP2) and validated against data obtained over another

tidal cycle at a different site (ADCP1).

3.4.2 Validation

The results of the sediment transport model calibration are presented in Figure 4, the verification

data are presented in Figure 5 and error assessments are presented in Figure 6, all of which

present exceptional agreement between the modelling and field data.

Figure 4 Calibration of the sediment transport model for the offshore sand bank

Figure 5 Verification of the sediment transport model for the offshore sand bank


Appendix D

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Figure 6 Error assessment for the calibration (left panel) and verification (right panel) of the offshore sediment transport model

3.4.3 Results

The tidal hydrodynamic and sediment transport models were synthesised to run for a complete

lunar cycle and factored to provide annual sediment transport rates over the Quarantine Bank.

Gross rates of sediment transport in the cardinal directions were up to 5,000 m3/m/a (Figure 7).

Maxima were directly westerly where bed form heights were maxima and water depths minima.

Net sediment transport rate vectors are presented in Figure 8 and net sediment transport rates

are presented in Figure 9. Net transport on the shoals is directed westerly with maxima reaching

5,000 m3/m/a on the crest of the bank.


Appendix D

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Figure 7 Calculated gross sediment transport rates on Quarantine Bank resolved in the cardinal directions

Figure 8 Net sediment transport vectors on Quarantine Bank


Appendix D

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Figure 9 Net sediment transport rates on Quarantine Bank


Appendix D

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4 Littoral Drift Transport

4.1 Introduction

On the assumption that there is no net loss or supply of sediment from the offshore zone to the

beach profile over timescales of a year or longer, the rates of littoral drift transport may be

estimated by considering the variation in the alongshore component of the sediment (littoral

drift) transport rate potentials along with the long-term sediment budget as determined from a

morphology study.

4.2 Morphology Study

4.2.1 Measured Changes in Beach Alignment

Portsea Front Beach has experienced a significant re-alignment over the past 10 years.

Measurements taken from Google earth, shown in Figure 10, have indicated that the beach has

swung anticlockwise with some 30 m of shoreline recession at the western end of the beach near

the Pier and some 14 m of accretion at the eastern end of the beach. The recession at the western

end could have been greater if not for the rock and sandbag revetments constructed since 2012.

At the embayment east of Police Point (the western end of the Weeroona Bay) it appears that,

notwithstanding an increase in wave height coefficients from 2005 to 2012 (Water Technology

2013), there has been doubling in beach width between 2005 and 2015 (Figure 11).

However, these beaches can fluctuate seasonally (Aurecon, 2012) and comparing two snapshot

images may not reflect a long term trend.

4.2.2 Sediment Budget

Estimates of the sediment budget for Portsea Front Beach have been made based on the measured

changes to the beach alignment.

The littoral drift transport modelling indicated that the active beach profile was some 3.5 m high.

The accretion of the western foreshore of Weeroona Bay of 10 m (average) over 9 years gave an

average annual rate of accretion for the 660 m long embayment of 2,500 m3/a. For the 300 m

long segment of Portsea Front Beach that has been eroded, the average annual rate of erosion was

calculated to be 1,800 m3/a. For the eastern 150 m segment of Portsea Front Beach that has

accreted, the average annual rate of accretion was calculated to be 400 m3/a.

A sediment budget for the Weeroona Bay beaches has been derived as presented in Figure 12.


Appendix D

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Page 14


21/11/2005: 120.2 m

21/11/2005: 16.7 m

10/2/2015: 150.4 m

Net Change: 30 m recession

10/2/2015: 30.5 m

Net Change: 14 m accretion

Figure 10 Changes in foreshore alignment at Portsea Front Beach 2005 to 2015 (Courtesy Google earth)


Appendix D

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Page 15


21/11/2005: 12.4m

21/11/2005: 10.4m

10/02/2015: 23.5m

10/02/2015: 20.1m

Figure 11 Changes in beach width at the western end of the Weeroona Bay embayment 21/11/2005 to 10/2/2015 (courtesy Google earth)

Weeroona Bay West Embayment

10/02/2015


Appendix D

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Page 16


Figure 12 Sediment Budget for Weeroona Bay

4.3 Transport Parameters for Modelling

Trends in sediment transport rates and pathways within the littoral zone have been examined

using Delft3D, configured as a beach profile model. The simulations consider sediment transport

landward of the -5 m AHD isobath. The sediment transport estimates were carried out at mean

water level (0m AHD) and neglected tidal variation, which is small. Initially, the parameters

derived from the calibration of the sediment transport model over the sand banks were adopted

but, subsequently, the model was calibrated against shoreline changes gleaned from the

morphology study.

4.3.1 Grain Size

Grain size data for the beach was obtained from field work samples taken from Portsea Front

Beach (Appendix A). The measured fall velocities were converted to an equivalent D50 sediment

diameter using the approach of Van Rijn, as described in Section 3.3.2.1. The grain size parameter

was varied to achieve calibration.

4.3.2 Beach Profiles

Each profile was selected as representative of specific sections of the beach. Cross-sectional

profiles of the shore and dunes were extracted from the 2012 LADS DTM at a native spatial

resolution of two metres in the cross-shore direction. The shore-normal orientation of each beach

profile relative to true north as seen by the model was determined by local wave refraction

modelling, the shore-normal direction being the direction of wave advance at the shore which has

not deviated from the offshore incident wave direction for a wave period 12 s.

Figure 13 shows the locations of each beach profile along Portsea Front Beach. Table 3

summarises the shore-normal angles of the beach profiles and their angles relative to the incident

energy-weighted mean swell wave direction.

2,500 m3/a accretion

400 m3/a accretion 1,800 m3/a

erosion


Appendix D

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Page 17


Figure 13 Locations of beach profiles used in littoral drift modelling. Profiles are named L2 to L11 from west to east and correspond to the locations where wave climates were extracted at the -5m AHD isobath.

Table 3 Profile Orientations as Interpreted by the Wave Refraction Model

Profile Shore normal

(° clockwise TN)

L02 15.0

L03 10.4

L04 8.4

L05 4.8

L06 3.0

L07 6.2

L08 12.2

L09 -1.8

L10 -0.2

L11 12.2


Appendix D

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Page 18


4.3.3 Nearshore Wave Climate

A long-term, synthetic inshore wave climate has been derived at the toe of each beach profile

using wave transfer functions as derived in Appendix C (Wave Transformation).

4.4 Simulations

4.4.1 Model Configuration

An example of the 2DV model grid for beach profile simulations is presented in Figure 14, which

shows the vertical resolution of the model.

Figure 14 Example of 2DV model grid for beach profile simulations at L09. Vertical resolution of the model is shown.

4.4.2 Summary of Key Parameters

The parameters describing sediment properties, coastline definition and wave conditions for

littoral drift transport computations are provided in Table 4-2.

Table 4 Summary of Parameters describing Sediment Properties, Coastline Definition and Wave Conditions for Littoral Drift Transport Computations.

Key Model Parameters

Model Type 2DV (5 vertical layers)

Sediment transport formula TRANSPOOR 2007

Sediment D50 fall diameter 0.34 mm

Geometrical standard deviation 1.54


Appendix D

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Page 19


4.4.3 Calculation Method

Each wave condition of the annual wave climate was run to steady-state conditions over a period

of 40 minutes. The coupling between the wave model and the flow model occurred every 10

minutes. That is to say, the waves were used to impose an initial wave-drive current, with

subsequent couplings used to modify the effects of currents on the shoaling waves, wave set-up

and associated sediment transport. Simulations were run at mean sea level.

The transport fields simulated over all wave conditions, were weighted by their probability of

occurrence and summed to give a single ‘annual average’ sediment transport field. The calculated

potential rates of littoral drift transport were adjusted proportionally so as to match the measured

rates of shoreline change determined from the morphology study.

4.4.4 Distribution of Littoral Drift Transport Potential

The results are summarised in Figure 15 to Figure 22 to show the cross-shore distribution of

littoral drift transport potential along the foreshore. Results were not available for Profile 7 or

Profile 9 due to model instabilities.



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4.4.5 Potential Sediment Transport Rates of Portsea Front Beach

The ‘annual average’ sediment flux in the alongshore direction was integrated across each beach

profile to give the net annual sediment transport potential in cubic metres (Table 5). The rates

given are potential sediment transport rates that serve to describe the wave energy distribution

along the coast but may not be realised in nature. This may be due to availability of sediment

supply from alongshore or cross-shore, the presence of rock under a thin veneer of sand or

armouring from revetments and vegetation such as sea grass or gravel. Nevertheless, it has been

assumed that the alongshore variation in the potential rates of littoral drift transport would be

similar to the alongshore variation in the actual rates, allowing the model to be calibrated against

measured changes. The calibration constant C was determined in the calibration with the data

from the morphology study.

Table 5 Sediment Transport Potential at Beach Profiles

Profile Net Alongshore Transport Potential

(m3/a) +ve Eastward

L02 21,900*C1

L03 21,500*C

L04 18,100*C

L05 35,700*C


Appendix D

Sediment Transport


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Profile Net Alongshore Transport Potential

(m3/a) +ve Eastward

L06 23,800*C

L08 119,600*C

L10 86,900*C

L11 32,100*C

Notes 1. C is a calibration constant

4.5 Model Calibration

4.5.1 Calibrated Annual Rates of Littoral Drift Transport

The potential rates of alongshore littoral drift transport were calibrated with the results of the

morphology study as follows.

The salient rates of littoral drift transport are presented in Figure 15 and comprise:

A – The rate of littoral drift transport entering Weeroona Bay around Police Point

B – The rate of littoral drift transport exiting Weeroona Bay west and entering Portsea Front

Beach

C – The rate of littoral drift transport at the seat of maximum erosion

D – The rate of littoral drift transport exiting the Portsea Front Beach embayment around Point

Franklin.

Figure 23 Salient rates of littoral drift transport identified for calibration


Appendix D

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Based on the data derived in the sediment budget gleaned from the morphology study, the

following equations were derived:

A – B = 2,500 m3/a

C – B = 1,800 m3/a

C – D = 400 m3/a

and from the littoral drift transport modelling (Table 5):

C/B = L8/L6 = 119,600/23,800 = 5.0

Solving these four equations with four unknowns realised the following calibrated rates of littoral

drift transport:

A = 2,050 m3/a

B = 450 m3/a

C = 2,250 m3/a

D = 1,850 m3/a

This result renders the calibration constant C in Table 5 to be C = 53.


Appendix D

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5 Conclusions

The tidal hydrodynamic and sediment transport models have been validated with field data and

synthesised to provide annual sediment transport rates over the Quarantine Bank and calibrated

rates of littoral drift transport for Portsea Front Beach. The modelling was undertaken using

boundary conditions comprising 2012 bathymetry that, most probably, will have changed since

that date.

Gross rates of sediment transport on Quarantine Bank were up to 5,000 m3/m/a with maxima

directed westerly where bed form heights were a maximum of around 5 m and water depths were

a minimum.

2DV simulations of littoral drift transport have been carried out for selected beach profiles

between Police Point and Point Franklin. Littoral drift transport modelling has been calibrated

with a morphology study and has resulted in littoral drift transport directed easterly at average

rates of around 2,000 m3/a bypassing Police Point, 500 m3/a entering Portsea Front Beach from

the western beach of Weeroona Bay, increasing to some 2,300 m3/a at Portsea Pier where

maximum erosion was measured, then reducing to 1,900 m3/a bypassing Point King.


Appendix D

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6 References

Deltares (2014). Delft3D-FLOW Simulation of multi-dimensional hydrodynamic flows and

transport phenomena, including sediments. User Manual Hydro-Morphodynamics Version:

3.15.34158, 28 May 2014.

Hallermeier, R. J. (1981). A Profile Zonation for Seasonal Sand Beaches from Wave Climate.

Coastal Engineering, Vol. 4, 253-277.

Hallermeier, R. J. (1983). Sand Transport Limits in Coastal Structure Design, Proceedings,

Coastal Structures ’83, American Society of Civil Engineers, pp. 703-716.

Kraus, N. C., Larson, M. and Wise, R. A. (1998) Depth of Closure in Beach-fill Design, Coastal

Engineering Technical Note CETN II-40, 3/98, U.S. Army Engineer Waterways Experiment

Station, Vicksburg, MS.

Van Rijn, L. C. (1989). Handbook Sediment Transport by Currents and Waves, Delft Hydraulic

Report H 461.

Van Rijn, L. C. (1993). Principles of Sediment Transport in Rivers, Estuaries and Coastal Seas.

Aqua Publications, The Netherlands.

Rijn, L. C. van, J. A. Roelvink andW. T. Horst, 2000. Approximation formulae for sand transport

by currents and waves and implementation in DELFT-MOR. Tech. Rep. Z3054.40, WL |Delft

Hydraulics, Delft, The Netherlands.

Williams, B.G. (2014). On the medium-term simulation of sediment transport and morphological

evolution in complex coastal areas. Unpublished PhD Thesis, University of Plymouth, UK.


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Appendix E

Glossary

Advisian Appendix E Glossary

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Appendix E

Glossary


Page 1


Glossary

The following meanings are attached to terms that may be used within this report:

Accretion The accumulation of (beach) sediment, deposited by natural fluid flow processes.

Algorithm(s) Formula or combination of formulae used for calculations.

Alongshore Parallel to and near the shoreline; same as longshore.

Astronomical tide The tidal levels and character which would result from gravitational effects, e.g. of the Earth, Sun and Moon, without any atmospheric influences.

Backshore (1) The upper part of the active beach above the normal reach of the tides (high water), but affected by large waves occurring during a high tide.

(2) The accretion or erosion zone, located landward of ordinary high tide, which is wetted normally only by storm tides.

Bank See Shoal

Bar An offshore ridge or mound of sand, gravel, or other unconsolidated material which is submerged (at least at high tide), especially at the mouth of a river or estuary, or lying parallel to and a short distance from, the beach.

Bathymetry The measurement of depths of water in oceans, seas and lakes; also the information derived from such measurements.

Bay A recess or inlet in the shore of a sea or lake between two capes or headlands, not as large as a gulf but larger than a cove. See also bight, embayment.

Beach The zone of unconsolidated material that extends landward from the low water line to the place where there is marked change in material or physiographic form, or to the line of permanent vegetation. The seaward limit of a beach – unless otherwise specified – is the mean low water line. A beach includes foreshore and backshore.

Beach erosion The carrying away of beach materials by wave action, tidal currents, littoral currents or wind.

Beach face The section of the beach normally exposed to the action of wave uprush. The foreshore of the beach.

Beach profile A cross-section taken perpendicular to a given beach contour; the profile may include the face of a dune or sea wall, extend over the backshore, across the foreshore and seaward underwater into the nearshore zone.

Beach width The horizontal dimension of the beach measured normal to the shoreline.


Appendix E

Glossary


Page 2


Beach nourishment

The process of placing sand from elsewhere onto an eroding shoreline to create a new beach or to widen an existing beach. Beach nourishment manages erosion by replacing sand lost and providing new sand to continue to feed the sand losing process.

Bed The bottom of a watercourse, or any body of water.

Berm On a beach: a nearly horizontal plateau on the beach face or backshore, formed by the deposition of beach material by wave action or by means of a mechanical plant as part of a beach recharge scheme.

Boussinesq Boussinesq, J was a French mathematician and physicist who made significant contributions to the theory of hydrodynamics, specifically wave action. Boussinesq-type equations are used in computer models for the simulation of water waves in shallow seas and harbours.

Breaker zone The zone within which waves approaching the coastline commence breaking, typically in water depths of between 5 m and 10 m on the open coast but in shallower waters within bays.

Breaking depth The still-water depth at the point where the wave breaks.

Breakwater Offshore structure aligned parallel to the shore, sometimes shore-connected, that provides protection to the shore from waves.

CD Chart Datum – usually the lowest tide level and a reference level for nautical charts used for navigation.

CDP Channel Deepening Project - The Port Phillip CDP began on 8 February 2008 and was completed on 26 November 2009 with the objective to deepen the shipping channels entering Port Phillip Bay and leading to the Port of Melbourne.

Chart datum The plane or level to which soundings, tidal levels or water depths are referenced, usually low water datum.

Climate change Refers to any long-term trend in changes to mean sea level, wave height, wind speed, etc.

Coastal currents Currents that flow usually parallel to the shore and constituting a relatively uniform drift in the deeper water adjacent to the surf zone. These currents may be tidal, transient, wind-driven or associated with oceanic currents.

Coastal processes

Collective term covering the action of natural forces, such as winds, waves and tides, on the shoreline and the nearshore seabed.

Coastal zone The land-sea-air interface zone around continents and islands extending from the landward edge of a barrier beach or shoreline of coastal bay to the Continental Shelf.

Coastline The line where terrestrial processes give way to marine processes, tidal currents, wind waves, etc.

Configuration dredging

A process of shaping the seabed in such a way as to modify the wave transformation process to change wave direction and/or height.


Appendix E

Glossary


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Continental Shelf The underwater landmass that extends seaward from a continent, resulting in an area of relatively shallow water, generally less than 200 m deep, lying between the shoreline and the deep ocean. Much of the Continental Shelf was exposed during the ice ages.

Current Ocean currents can be classified in a number of different ways. Some important types include the following:

- Periodic - due to the effect of the tides; such currents may be rotating rather than having a simple back and forth motion. The currents accompanying tides are known as tidal currents

- Temporary - due to seasonal winds

- Permanent or ocean - constitute a part of the general ocean circulation. The term drift current is often applied to a slow broad movement of the oceanic water

- Nearshore - caused principally by waves breaking along a shore. Also, coastal currents such as California and Davidson currents that run parallel to the coast.

Datum Any position or element in relation to which others are determined, as datum point, datum line, datum plane.

Deep water In regard to waves, where depth is greater than one-half the wave length. Deep-water conditions are said to exist when the surf waves are not affected by conditions on the bottom.

Depth of closure (DoC)

For a given or characteristic time interval, the depth on a beach profile seaward of which there is no significant change in bottom elevation and no significant net sediment transport between the nearshore and the offshore during storms and ensuing calm weather.

Design storm Coastal protection structures will often be designed to withstand wave attack by an extreme design storm. The severity of the storm (i.e., return period) is chosen in view of the acceptable level of risk of damage or failure. A design storm consists of a design wave condition, a design water level and a duration.

Downdrift The direction of predominant movement of littoral drift.

Dredging Excavation or displacement of the bottom or shoreline of a water body. Dredging can be accomplished with mechanical or hydraulic machines. Most is done to maintain channel depths or berths for navigational purposes; other dredging is for shellfish harvesting or for cleanup of polluted sediments. It can be used also to win sand to nourish beaches.

Dunes Accumulations of windblown sand on the backshore, usually in the form of small hills or ridges, stabilised by vegetation or control structures.

Ebb tide A falling tide or that portion of the tidal cycle between high water and the following low water.

Ebb tide (current) The tidal current generated by a falling tide and associated with the waters within an estuary or bay being directed seaward.


Appendix E

Glossary


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Elevation The distance of a point above a specified surface of constant potential; the distance is measured along the direction of gravity between the point and the surface.

Embayed Formed into a bay or bays; as an embayed shore.

Embayment (1) An indentation in a shoreline forming an open bay.

(2) The formation of a bay.

Erosion (1) Wearing away of the land by natural forces. On a beach, the carrying away of beach material by wave action, tidal currents or by deflation.

(2) The wearing away of land by the action of natural forces.

Escarpment A more or less continuous line of cliffs or steep slopes facing in one general direction which are caused by erosion or faulting, also called scarp.

Event An occurrence meeting specified conditions, e.g. damage, a threshold wave height or a threshold water level.

Fetch The length of unobstructed open sea surface across which the wind can generate waves (generating area).

Flood tide A rising tide or that portion of the tidal cycle between low water and the following high water.

Flood tide (current)

The tidal current generated by a rising tide and associated with the flow of waters directed towards an estuary or bay from the ocean.

Foreshore In general terms, the beach between mean higher high water and mean lower low water.

Geology The science which treats of the origin, history and structure of the Earth, as recorded in rocks; together with the forces and processes now operating to modify rocks.

Geomorphology That branch of physical geography which deals with the form of the Earth, the general configuration of its surface, the distribution of the land, water, etc.

High water (HW) Maximum height reached by a rising tide. The height may be solely due to the periodic tidal forces or it may have superimposed upon it the effects of prevailing meteorological conditions. Also called the high tide.

Inshore (1) The region where waves are transformed by their interaction with the sea bed.

(2) In beach terminology, the zone of variable width extending from the low water line through the breaker zone.

Inshore current Any current inside the surf zone.

Intertidal The zone between the high and low water marks.

Isobath A line on a plan that defines points of equal depth.

LADS Laser Airborne Depth Sounder used for bathymetric survey.

Leeward The direction toward which the prevailing wind is blowing; the direction toward which waves are travelling.


Appendix E

Glossary


Page 5


Littoral (1) Of, or pertaining to, a shore, especially a seashore.

(2) Living on, or occurring on, the shore.

Littoral currents A current running parallel to the beach and generally caused by waves striking the shore at an angle.

Littoral drift The mud, sand, or gravel material moved parallel to the shoreline in the nearshore zone by waves and currents.

Longshore Parallel and close to the coastline.

Longshore transport rate

Rate of transport of sedimentary material parallel to the shore. Usually expressed in cubic meters per year.

Low water (LW) The minimum height reached by each falling tide. Also called low tide.

Mean high water (MHW)

The average elevation of all high waters recorded at a particular point or station over a considerable period of time, usually 19 years.

Mean high water springs (MHWS)

The average height of the high water occurring at the time of spring tides.

Mean low water (MLW)

The average height of the low waters over a 19-year period. For shorter periods of observation, corrections are applied to eliminate known variations and reduce the result to the equivalent of a mean 19-year value.

Mean low water springs (MLWS)

The average height of the low waters occurring at the time of the spring tides.

Mean sea level The average height of the surface of the sea for all stages of the tide over a 19-year period, usually determined from hourly height readings (see sea level datums).

Morphology River/estuary/lake/seabed form and its change with time.

Neap tide A tide around the first or third quarters of the moon when there is least difference between high and low waters.

Nearshore In beach terminology an indefinite zone extending seaward from the shoreline well beyond the breaker zone.

Nearshore circulation

The ocean circulation pattern composed of the nearshore currents and the coastal currents.

Nearshore current The current system caused by wave action in and near the breaker zone and which consists of four parts: the shoreward mass transport of water; longshore currents; rip currents; and the longshore movement of the expanding heads of rip currents.

Nourishment See Beach nourishment.

Offshore In beach terminology, the comparatively flat zone of variable width, extending from the shoreface to the edge of the Continental Shelf.

Offshore breakwater

A breakwater built towards the seaward limit of the littoral zone, parallel (or nearly parallel) to the shore.

Offshore currents (1) Currents outside the surf zone.

(2) Any current flowing away from the shore.

Offshore wind A wind blowing seaward from the land in the coastal area.


Appendix E

Glossary


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Onshore wind A wind blowing landward from the sea.

Outflanking erosion behind or around the inner end of a Groyne or bulkhead, usually causing failure of the structure.

Photogrammetry The science of deducing the physical dimensions of objects from measurements on images (usually photographs) of the objects.

Progradation The seaward movement of a coastline when sediment input exceeds the rate of inundation by sea level rise.

Recession A net landward movement of the shoreline over a specified time.

Reflected wave That part of an incident wave that is returned (reflected) seaward when a wave impinges on a beach, seawall or other reflecting surface. Waves may be reflected off deep channels by the process of wave refraction.

Reflection The process by which the energy of the wave is returned seaward or in a partially opposing direction to which it is travelling. Waves may be reflected off deep channels by the process of wave refraction.

Refraction The process by which the direction of a wave moving in shallow water at an angle to the bottom contours is changed. The part of the wave moving shoreward in shallower water travels more slowly than that portion in deeper water, causing the wave to turn or bend to become parallel to the isobaths. Refraction also can cause waves to “reflect” off a deeper channel.

Return period Average period of time between occurrences of a given event.

RSA Rapid Sediment Analysis – settling tube analysis equilibrating the fall velocities of the sands to their grain diameters as carried out at the University of Auckland.

Sand An unconsolidated (geologically) mixture of inorganic soil (that may include disintegrated shells and coral) consisting of small but easily distinguishable grains, usually and mainly quartz, ranging in size from about 0.062 mm to 2.000 mm.

Sand dune A mound formed of sand that extends usually along the shore at the back of a beach.

Sand wave A seabed feature in sand comprising a long undulating form generated by strong currents and reflecting sand transport.

Sea level rise The long-term trend in mean sea level.

Seawall A structure separating land and water areas primarily to prevent erosion and other damage by wave action.

Sediment Loose, fragments of rocks, minerals or organic material which are transported from their source for varying distances and deposited by air, wind, ice and water. Other sediments are precipitated from the overlying water or form chemically, in place. Sediment includes all the unconsolidated materials on the sea floor.

Shoal (1) (noun) A detached relatively shallow area of sand or mud the depths over which may be a danger to surface navigation. Can also be termed a bank.

(2) (verb) As pertaining to waves becoming shallow gradually.


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Glossary


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Shore That strip of ground bordering any body of water which is alternately exposed, or covered by tides and/or waves. A shore of unconsolidated material is usually called a beach.

Shoreface The narrow zone seaward from the low tide shoreline permanently covered by water, over which the beach sands and GRAVELS actively oscillate with changing wave conditions.

Shoreline The intersection of a specified plane of water with the shore.

Shoreline protection structure

A structure on the shore or nearshore, such as a groyne, revetment or seawall, constructed typically of rock, concrete or sandbags, and designed to protect the shore from recession.

Significant wave A statistical term relating to the average of the one-third highest waves of a given wave group and defined by the average of their heights and periods.

Significant wave height

Average height of the highest one-third of the waves for a stated interval of time.

Silt Sediment particles with a grain size between 0.004 mm and 0.062 mm, i.e., coarser than clay particles but finer than sand.

Spectral wave model

A computer program that schematises wind wave spectra in all directions and frequencies and computes their evolution and transformation in coastal regions with shallow water and ambient current.

Spring tide A tide that occurs at or near the time of new or full moon and which rises highest and falls lowest from the mean sea level (MSL).

Storm surge A rise or piling-up of water against shore, produced by strong winds blowing onshore. A storm surge is most severe when it occurs in conjunction with a high tide.

Sub-aerial beach That part of the beach which is uncovered by water (e.g. at low tide sometimes referred to as drying beach).

Surf zone The nearshore zone along which the waves become breakers as they approach the shore.

Survey, hydrographic

A survey that has as its principal purpose the determination of geometric and dynamic characteristics of bodies of water.

Survey, photogrammetric

A survey in which monuments are placed at points that have been determined photogrammetrically.

Survey, topographic

A survey which has, for its major purpose, the determination of the configuration (relief) of the surface of the land and the location of natural and artificial objects thereon.

Swell Waves that have travelled a long distance from their generating area and have been sorted out by travel into long waves of the same approximate period.


Appendix E

Glossary


Page 8


Tide The periodic rising and falling of the water that results from gravitational attraction of the moon and sun acting upon the rotating earth. Although the accompanying horizontal movement of the water resulting from the same cause is also sometimes called the tide, it is preferable to designate the latter as tidal current, reserving the name tide for the vertical movement.

Tidal Current The flow of water induced by the rise and fall of the tide.

Topographic map A map on which elevations are shown by means of contour lines.

Topography The form of the features of the actual surface of the Earth in a particular region considered collectively.

Vector In this context, an arrow on a plan delineating the speed and direction of tidal flow or the transport of sediment as derived from modelling.

Wave (1) An oscillatory movement in a body of water manifested by an alternate rise and fall of the surface.

(2) A disturbance of the surface of a liquid body, as the ocean, in the form of a ridge, swell or hump.

Wave climate The range of wave conditions and their occurrence, as shown by height, period, direction, etc., at a place as measured over periods of years.

Wave direction The direction from which waves are travelling.

Wave generation Growth of wave height and period by wind action.

Wave height coefficient

The ratio between the height of a wave in a nearshore area to its height in deep water

Wave propagation The development of water waves from wind action.

Wave transformation

The process of wave transmission through shallow waters and tidal currents.

Wind current A current created by the action of the wind.


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Appendix F

Project Brief

Advisian Appendix F Project Brief

Page ii

301015-03540-Appendix F - Project Brief - Rev 0 160115.docm

Table of Contents

1 Objective 1

2 Background 2

3 Scope of this Investigation 3

4 Deliverables 5

5 Documents for Review 6

List of Figures

Figure 1 Area for Hydrodynamic and Wave Model

Figure 2 Area for Sediment Transport Investigation - Police Point to Point King


Appendix F

Project Brief


Page 1


1 Objective

The Department of Environment and Primary Industries (“the Department”) is commissioning a

wave monitoring and modelling investigation in southern Port Phillip Bay and Portsea Front

Beach, in consultation with the Portsea community and stakeholders. The Portsea community and

stakeholders have requested the Department to conduct further investigations to understand the

wave generation processes at Portsea Front Beach. Hence, the objective of this investigation is to

utilise detailed numerical models to examine the wave generation processes at Portsea Front

Beach to inform future management options.


Appendix F

Project Brief


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2 Background

The key physical coastal processes influencing Portsea Front Beach are swell waves from Bass

Strait entering Port Phillip, local wind waves generated across Port Phillip, strong tidal currents,

and storm surges. In particular, around 600 metres of Portsea Front Beach and foreshore are

being affected by waves, resulting in an estimated 25 to 30 metres of severe beach and foreshore

erosion near the Portsea Pier.

The Department has responded to the coastal conditions at Portsea Front Beach by managing the

impacts of waves and erosion on the foreshore reserve and assets. Since 2010, the Department

has: underpinned the pier abutment, constructed a 30 metre rock revetment to protect the pier

abutment and pier access road, constructed a 160 metre geotextile sandbag seawall to protect the

foreshore and assets, reinstated walking paths and fencing, and monitored sand movement and

the new structures. Further works planned to foreshore structures include: strengthening the

sandbag seawall toe with large rock, the masonry seawall toe with large rock, and replacing the

concrete retaining wall with a similar retaining wall. Since 2010, the Department has invested an

estimated total of $2.5M to date in coastal management works at Portsea Front Beach.

A sand monitoring program was also undertaken in 2011/2012 to determine the effectiveness of

the works to stabilise the Portsea foreshore by assessing beach and nearshore changes and the

condition of the new sandbag seawall. The relatively short period of the monitoring program

provided insufficient data to determine exactly where the sand is moving from the sandbag wall

area.

Numerous reports concerning coastal erosion at Portsea have been undertaken in recent years by

the Department and are available on the Department’s website.


Appendix F

Project Brief


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3 Scope of this Investigation

This investigation will thoroughly describe the coastal processes (hydrodynamics, wave climate

and sediment transport) in the investigation area. The investigation area includes Port Phillip

Heads, the Great Sands, and the shoreline from Point Nepean to Portsea Front beach (Refer to

Figures 1 and 2.)

It will utilise detailed numerical modelling of physical coastal processes (such as Spectral wave

(SM) and Boussinesq wave (BM) or equivalent models) to investigate, in particular, the wave

climate affecting the Portsea Front Beach area, including but not limited to potential wave

reflection, refraction, diffraction, shoaling, bottom dissipation, and effect of tidal currents on

waves. High resolution bathymetry data of the investigation area will be made available for the

wave model. A series of bathymetric and topographic surveys of the Portsea Front Beach will be

made available for the sediment transport model.

At present there are no existing long term wave data at Portsea Front Beach although it is not

uncommon to have limited data at a local scale on the coast. If further wave information is found

to be available it will be supplied to the successful consultant. In 2010, three months of non-

directional wave data were collected offshore from Portsea Pier and compared with longer wave

records from offshore Point Nepean in Bass Strait. The results of the wave data for 0.5% Annual

Exceedance Probability were significant wave height of 1.45 m, maximum wave height of 2.83 m,

peak wave period of 11 s, at the 6.5m water depth. Hence, it is necessary to collect data through

the deployment of environmental monitoring instruments to calibrate the numerical models and

to understand the wave climate including seasonal patterns in the investigation area. It is

envisaged that up to three environmental monitoring instruments will be deployed during this

investigation to provide data on waves, currents and water levels.

As discussed above, the Department has constructed seawalls to protect the foreshore and assets

at Portsea front beach. This investigation will form an important consideration for the

Department, the community and stakeholders for future coastal management directions at

Portsea Front Beach. This investigation will be subjected to Peer Review.


Appendix F

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Figure 1 Area for Hydrodynamic and Wave Model

Figure 2 Area for Sediment Transport Investigation - Police Point to Point King


Appendix F

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4 Deliverables

1) Review of documents and data on erosion and wave climate at Portsea (listed below).

2) Setup and run detailed coastal processes numerical models (such as Spectral wave (SM) and

Boussinesq wave (BM) or equivalent) for the investigation area, examining and describing

the hydrodynamics, waves, and sediment transport for the investigation area at Southern

Port Phillip and Portsea Front Beach. The wave modelling will investigate potential wave

reflection, refraction, diffraction, shoaling, bottom dissipation, and the effect of tidal currents

on waves.

3) Prepare a program, requirements and locations for the deployment of up to three directional

wave, current and water level monitoring instruments, for the collection of data to calibrate

the numerical models and describe the wave climate. (Note that the Department would

prefer that the lease of monitoring instruments and data collection is managed under a

separate Contract.)

4) Calibrate the models with the data collected, adjustment of model parameters accordingly,

and confirmation that model is accurately representing the physical processes in the

investigation area.

5) Prepare a draft report that presents the findings, data, recommendations and conclusions,

that uses ‘plain English’ for a range of audiences including the community and stakeholders,

the Department Project Working Group and other staff, as well as peers reviewers. The draft

report will need to incorporate a range of comments, feedback and amendments from the

reviewers.

6) Prepare a final report to the satisfaction of the Department Project Working Group.

7) Provide at least four presentations to the Department Project Working Group on the progress

of the investigation.


Appendix F

Project Brief


Page 6


5 Documents for Review

§ Water Technology (2011) Estimation of Design Wave Heights and Water Levels Portsea Front

Beach

§ GHD (2010)Sand Bag Seawall design

§ GHD (2011) Report for Portsea Foreshore remediation Monitoring Report September 2011

(“Sand report”)

§ Bird (2011) Changes on the Coastline of Port Phillip Bay

§ Aurecon (2012) Portsea Beach Prefeasibility Assessment of Erosion Response Options May

2012

§ CSIRO (20130 Review of OEM Assessment of Potential causes of Beach erosion at Portsea

April 2013

§ Water Technology (2013) Review of Wave Transformation Processes Through Port Phillip

Heads. March 2013

Appendix C - Marine and coasts - Marine and coasts

Documents

Transcript of Appendix C - Marine and coasts - Marine and coasts