i  

DIRECTIONAL CHARACTERISTICS OF WAVES OFF HONNAVAR

Dissertation submitted to

COCHIN UNIVERSITY OF SCIENCE AND TECHNOLOGY

In partial fulfillment of the requirements for the award of the degree of

Master of Technology

In

Ocean Technology

 

By

K A ABHINAV

(Reg. No. 56080002)

 

Under the Guidance of

Dr. V Sanilkumar

Scientist

Ocean Engineering Division

National Institute of Oceanography

Dona Paula, Goa 403 004

ii  

Declaration

   

I hereby declare that the dissertation entitled ‘Directional Characteristics of Waves off Honnavar’ is an authentic record of work done by me on the basis of available literature and data, and to the best of my ability under the guidance of Dr. V Sanilkumar, Scientist, Ocean Engineering Division, National Institute of Oceanography, Goa and no part thereof has been presented before for the award of any other Degree or Diploma in any University.

K A Abhinav

Countersigned

Dr. V Sanilkumar

Scientist

Ocean Engineering Division

National Institute of Oceanography

Goa

Dona Paula, Goa

30 March 2010

 

iii  

CERTIFICATE

This is to certify that the dissertation entitled ‘Directional Characteristics of Waves off Honnavar’ is an authentic record carried out by Mr. K A Abhinav, at the National Institute of Oceanography, Goa, under my supervision in the partial fulfillment of the requirements for the award of the degree of Master of Technology in Ocean Technology of Cochin University of Science and Technology and no part thereof has been presented before for the award of any other Degree or Diploma in any University.

Dr. V Sanilkumar

Scientist

Ocean Engineering Division

National Institute of Oceanography

Dona Paula, Goa

Dona Paula, Goa

30 March 2010

iv  

Acknowledgements

 

  I express my sincere gratitude to Dr. S.R Shetye, Director, National Institute of

Oceanography, Goa, for providing me with an opportunity to pursue my dissertation in

the prestigious organization. I am grateful to Dr. V Sanilkumar, Scientist, Ocean

Engineering Division, for his guidance, sans which this dissertation could not have seen

the light of day. I sincerely acknowledge the help rendered by Dr. V.K Banakar and Mr.

V.K Kumar of HRD, NIO, during my stay at the institute.

I would like to thank Dr. A N Balchand, Head, Department of Physical

Oceanography, Cochin University of Science and Technology, for his constant support

and encouragement. I extent my gratitude to Dr. R Sajeev, Shri. P.K Saji, Dr Benny N

Peter and other staff members of Department of Physical Oceanography, CUSAT.

Many thanks to Dr. P A Brodtkorb, of the WAFO Group, Lund University,

Sweden, for being patient with my doubts. Also, I am deeply indebted to my classmates

and seniors for their suggestions, which proved to be of much help with my dissertation.

K A Abhinav

30 March 2010

 

 

 

 

 

 

 

 

v  

Abstract

 

  Wave directional information has tremendous application potential in the domain

of ocean engineering. These vary from the design and operational safety of marine

structures and ships, to coastal and environmental management, including pollution

control. The information required, ranges from the predominant wave direction to

spectral peak period and directional spread.

The thesis is directed towards the determination and analysis of the directional

wave characteristics off Honnavar, a port town in Uttara Kannada district of Karnataka,

South India. The concept of the ocean wave spectra has been explained. A wave

spectrum depicts the distribution of wave energy with frequency. This has been followed

up with a brief discussion of the various theoretical spectra developed over the years.

The data was obtained using a directional Waverider buoy, deployed at a depth

of 9m, off Honnavar coast. The specifications of the buoy used for the study, its

composition, and working, mooring and spectral computations have been described.

A review of the available literature regarding wave spectral partitioning and swell-

wind sea identification has been performed. According to Portilla et.al. (2009), the

former is a mechanism to detect different wave systems, looking at the morphological

features of the spectral signal alone, whereas the latter labels wind sea or swell as a

supplementary designation, considering both environmental and physical

characteristics.

A one-dimensional spectral partitioning algorithm has been developed adhering

to the suggestions of Portilla et.al and has been checked for robustness. Also, the

performance of three swell identification methods has been compared.

From the study, it has been concluded that the algorithm proposed by Portilla

et.al (2009) for the separation of wind seas and swells works out consistently when

compared to the steepness method and Wang and Hwang’s (2001) method, in the case

vi  

of nearshore waters. The nature of the components of the wave spectra, has been

identified and compared, during the monsoon, pre-monsoon and post-monsoon months

of June, April and November.

A toolbox in MATLAB, WAFO (Wave Analysis for Fatigue and Oceanography),

developed by the Lund University, Sweden, has been used for deriving the directional

wave spectra and the spreading functions from the raw data of the Waverider buoy. The

various methods offered by WAFO for computing directional wave spectra from time

series data have also been compared. The Iterative Maximum Likelihood Method

(IMLM) is found to perform better than the Extended Maximum Entropy Method (EMEM)

and the Maximum Likelihood Method (MLM).

vii  

Contents

Page No.

Declaration ii

Certificate iii

Acknowledgements iv

Abstract v

List of Figures ix

List of symbols x

Chapter 1 Introduction 1

1.1 General 2

1.2 Waves 2

1.3 Importance of Wave Directional Analysis 3

1.4 Objectives of the Study 3

1.5 Study Area 4

1.6 Data Collection 6

1.7 Organization of the Thesis 7

Chapter 2 Literature Review 8

2.1 General 9

2.2 Typical Wave Spectra 9

2.3 Theoretical Wave Spectra 13

2.3.1 The Pierson-Moskowitz spectrum 13

2.3.2 The Bretschneider Spectrum 14

2.3.3 The Ochi Spectrum 14

2.3.4 The JONSWAP Spectrum 15

2.3.5 The Donelan et al Spectrum 15

2.3.6 The Scott Spectrum 16

viii  

2.4 Directional Wave Spectra 16

2.4.1 Computation of Directional Wave Spectra 16

2.4.2 WAFO: Analysis of Wave Spectra 19

2.4.2.1 The Origins of WAFO 19

2.4.2.2 WAFO 2.1.1 19

2.5 Spectral Partitioning 20

2.5.1 Basic Concepts 20

2.5.2 Significance 21

2.5.3 Timeline of Spectral Partitioning 22

2.5.4 Proposed 1D Partition Algorithm 23

2.6 Wind sea-swell Separation Schemes in Nearshore Waters 24

2.6.1 General 24

2.6.2 Characteristics of Wind sea and Swell Spectra 24

2.6.3 Data 26

2.6.4 Methods 26

Chapter 3 Results and Discussions 30

3.1 Spectral Partitioning 31

3.2 Wave Characteristics 32

3.3 Separation of Swell and wind sea 32

3.4 Directional Wave Spectra 41

Chapter 4 Conclusions 46

Chapter 5 References and Bibliography 48

ix  

List of Figures

No. Description Pg. No.

1. Location of wave measurement 5

2. Mooring Layout for the Directional Waverider 7

3. Sample spectrum shapes 10

4. Single-peaked wave spectra at Honnavar 12

5. Two peaked wave spectra at Honnavar 12

6. Multi peaked wave spectra at Honnavar 13

7. Partitioning of Waverider buoy spectrum obtained at 2125 hrs, 08-05-08 31

8. Separation frequency estimated from different methods 34

9. Variation of sea peak frequency and peak frequency with wind speed 35

10. Time series of separation frequency during April, June and November 2008 36

11. Representative wave spectral plots 38

12. Variation of sea and swell height during April, June and November 2008 39

13. Correlation between wind sea and swell and between wind sea and wind speed 40

14. 1-D spectra, directional spreading and directional spectra at 1930 hrs 01-06-08 43

15. 1-D spectra, directional spreading and directional spectra at 2330 hrs 09-06-08 44

16. 1-D spectra, directional spreading and directional spectrum at 1930 hrs 01-06-08 45

 

 

 

 

 

 

x  

List of Symbols

ai, bi - Fourier coefficients

Cp - phase speed

fm - peak frequency of steepness function

fp - peak frequency

fPM - peak frequency of the PM spectrum

fs - separation frequency

g - acceleration due to gravity

Hs - significant wave height

L - wavelength

m, n - centered Fourier coefficients

m0 - zeroth moment

S(f) - spectral density

Tm02 - average wave period

U10 - wind speed at 10m

α - Phillips constant

γ - peak enhancement factor

ωc - limiting angular frequency

σ - spectral width factor

θ - wave direction

ωm - peak angular frequency

1  

1. Introduction

2  

1. Introduction

1.1 General

Offshore and coastal infrastructures are fast developing, due to the increase in

marine traffic and commerce over the recent years. Directional wave studies have

become an integral element in the design of any marine structure, be it a wharf, or a

pipeline. The longevity and robustness of the structure depends on deciding the

orientation that would shelter it from the impact of the wave forces. The directional wave

spectrum concept, though of recent origin, has garnered much vitality in the design

practices. Reliable directional data helps in the cost optimization for marine structures.

1.2 Waves

Water waves may be grouped, on the basis of several criteria. SPM (1984)

suggests classification by period or frequency. Gravity waves, having periods ranging

from 5 to 15 seconds, named after their principal restoring force, are of primary concern

in engineering design practices, as they are associated with a major portion of the total

wave energy.

Gravity waves can be classified into two, wind seas and swells. The former refers

to waves locally generated under the influence of the wind, whereas the latter

represents those travelling from afar, often caused by large scale meteorological

operations such as a storm, and liberated from the effect of winds. Of shorter periods,

the wind seas produce confused sea surfaces (SPM, 1984). They act as forced

vibrations, while swells are free waves, independent on the causative forces.

Wind seas are a result of the wind speed, the stretch over which it blows (fetch),

the width of the fetch, the water depth and the duration of the wind action, working in

tandem. The magnitude of the wind sea varies directly as those of the influencing

parameters. Seas gradually move out of their generating area, gets organized on the

3  

basis of their wavelengths and direction and are called swells when no longer under the

influence of the originating wind forces.

1.3 Importance of the Wave Directional Analysis

The exposure of a beach, harbor or any coastal structure to wave activity is

heavily influenced by the directional wave characteristics at the site under

consideration. Directional information is vital for estimating the sediment transport rates

and the wave loads on marine structures, both fixed and floating. Multidirectional seas

induce forces and extracts responses differing in magnitude from those due to

unidirectional ones. Hindcasting and forecasting of waves and wave diffraction studies

also require information regarding their directional characteristics.

Wave directional properties greatly affect the transformation processes such as

diffraction, reflection and refraction. Directional data regarding swells are being used for

water sports activities, as in the case of surfing. Directional wave spectral estimates find

further applications in ship routing, safety at sea and in validating and constraining

numerical wave forecasting models and remotely sensed observations.

Collins (1981) states that the use of spectral models which neglect the directional

spreading of wave energy, could overestimate up to 20%, the significant wave heights.

This could have serious implications, in the design of coastal structures.

1.4 Objectives of the Study

The study has been carried out using time series wave data collected off

Honnavar with a view to:

a) develop an algorithm for the partitioning of wave spectra into the component

wave systems

b) compare the performance of existing swell-wind sea separation schemes in

nearshore waters.

4  

c) determine the directional properties of component wave systems, during the

monsoon, pre and post monsoon periods.

d) analyze the directional wave spectra at the location for various seasons.

1.5 Study Area

Honnavar is a port town within the Uttara Kannada district of Karnataka. It can be

located on the geographical coordinate system, at 14.28˚ North latitude and 74.44˚ East

longitude. Honnavar is situated on the banks of the river Sharavathi, which forms an

estuary with the Arabian Sea (Figure 1).

The study area falls under the coastal agro climatic zone and is characterized by

the presence of coastal alluvial soil. The region experiences predominant south westerly

winds during the summer monsoon and north easterlies during the winter monsoon. The

year can be classified into four major seasons. The months of January and February

represent the dry season, characteristic of clear and bright climate. During March to

May, hot weather sets in, though thunderstorms are common during the latter. The

monsoon season (June-September) yields around 75% to 90% of the annual rainfall

and is followed by the post monsoon (October-December) (Central Groundwater Board,

Govt. of India, 2008).

Honnavar can be considered as a micro-mesotidal region, as the tide range falls

between 1 and 2.5m. As the orientation of the coast is along north-northwest, winds

approaching from the west during the months of April, May and early June, produces

stress in the southward direction, whereas those coming from the southwest, generates

wind stress northward and are responsible for the surface currents in the respective

direction. During the pre-monsoon, curved, submerged sandbars are observed at the

confluence of the Sharavathi with the Arabian Sea (Hegde et al. 2009).

5  

Fig.1. Location of wave measurement.

6  

1.6 Data Collection

The waves at 9 m water depth off Honnavar were measured using the Datawell

directional waverider buoy. The directional waverider is a spherical, 0.9m diameter buoy

which measures wave height, period and direction. The directional measurement is

based on the translational principle that measures horizontal motions instead of wave

slopes. Hence the measurement is independent of buoy roll motions and its size is

significantly reduced. Sufficient symmetrical horizontal buoy response even for small

motions at low frequencies is ensured by a single point vertical mooring.

Installed within the buoy are, a heave-pitch-roll Hippy-40 sensor, three axis

fluxgate compass, two fixed ‘x’ and ‘y’ accelerometers and a micro-processor.

From the accelerations measured in the x and y directions of the moving ‘buoy

reference frame’, the accelerations along the fixed, horizontal, north and west axis are

calculated. All three accelerations are digitally integrated to get filtered displacements

with a high frequency cut-off at 0.58Hz. Every half hour, Fast Fourier Transforms of 8

series of 256 data points are summed to give 16 degrees of freedom on 1600 seconds

of data.

Transmitting power is saved by compressing the real time data to motion along

the west, north and vertical. Onboard data reduction computes energy density, main

direction, directional spread and the normalized second harmonic of the directional

distribution. The Directional Waverider is fitted with a 5kg ballast chain attached to the

mooring eye (Figure 2). This provides stability only when a small vertical mooring force

is present. A single point vertical mooring with 15 m rubber cord ensures sufficient

symmetrical horizontal buoy response for motions at low frequencies. The low stiffness

of the rubber cord allows the Waverider to follow waves up to 40m. Current velocities up

to 3 m/s can be accommodated (Datawell BV).

7  

Fig.2. Mooring Layout for the Directional Waverider.

1.7 Organization of the Thesis

A general introduction to the nature and scope of the work carried out during the

course of the dissertation, along with a description of the study area and the data

collection, encompasses the current chapter. The theoretical formulations and concepts

on the basis of which the study has been carried out are explained in the second

section. The third chapter comprises the results obtained on the analysis of the data

and their interpretations. In the final chapter the conclusions on the work are presented.

8  

2. Literature Review

9  

2. Literature Review

2.1 General

Winds account for majority of the ocean waves. Planetary forces are responsible

for driving tides, which results in the generation of long period waves of the order of 12

to 24 hours. The other major driving forces are earthquakes. Tsunami, a rare, but

catastrophic phenomenon is the result of major quakes that take place adjacent to the

coast.

As wind begins to blow (between 0.5 to 2 knots) on calm surface small ripples or

capillary waves tend to form. These small waves are on the order of less than 2 cm. As

the wind becomes stronger wave amplitude increases and the waves become longer in

order to satisfy the dispersion relationship. This growth is driven by the Bernoulli effect,

frictional drag, and separation drag on the wave crests.

Winds blowing over long periods of time and larges distances contribute to the

formation of a fully developed sea state. When the phase speed of the wave crest

matches the wind speed non-linear interactions except friction stop and the phase

speed is maximized. The limiting frequency of the waves can be determined by the

equation for phase speed and the dispersion relationship:

/ (2.1a)

/ (2.1b)

where is the phase speed, the wind speed and , the limiting frequency. Decay

in the wind, slowly erodes the waves. Smaller the wavelength, faster is the dissipation.

2.2 Typical Wave Spectra

The single environmental factor exerting maximum influence on the design and

operation of marine structures are waves. Being amongst the most complex and

10  

variable phenomena in nature, it is difficult to obtain a complete understanding of their

behavior.

The potential and kinematic energies of random waves are represented by the

wave spectral density function, or the ‘wave spectrum’. This concept is of much

significance in evaluating the statistical properties of random waves. The wave energy

at any point has got angular distribution, as well as a distribution over a range of

frequencies. The angular or directional distribution of wave energy is termed as

directional spreading.

The wave energy distribution with respect to the frequency alone, disregarding

the wave direction is known as the frequency spectrum, whereas the energy distribution

represented as a function of both frequency and direction is called the directional wave

spectrum (Goda, 2000). Figure 3 shows some of the sample spectrum shapes.

Fig.3. Sample spectrum shapes.

11  

Wave spectra are influenced by the following parameters:

• Sea state, whether the sea is a developing one or a decaying one.

• Fetch limitations, as to whether the area under consideration has some physical

boundary, that prevent the waves from developing fully.

• Strong local currents have a marked effect on the spectrum.

• Seafloor topography: Deep water wave spectra are invalid in shallow waters, and

vice versa.

• Wave refraction also has a significant influence.

• Waves caused by distant storms, or swells, travel large distances and arrive at

an angle different from the wind direction. While measuring waves, the

component that result from swell must be accounted for, separately.

The area under the curve is the zeroth moment m0, which, for a narrow-banded

spectrum, is related to the significant wave height, Hs, as follows:

Hs= 4√m0 (2.2a)

In the case of multi-peaked spectra, it is assumed that a single storm produces a

single-peaked spectrum and any second peak is due to a distant storm that sends

waves to the considered location.

The following half-hour wave spectral plots (Figures 4, 5 and 6) were generated

from the raw data of a Directional Waverider, with the help of Wave Analysis for Fatigue

and Oceanography (WAFO), a wave analysis toolbox developed in MATLAB. All data

were obtained from Honnavar and the corresponding date and time are indicated in

each plot. Spectra have been classified on the basis of the number of peaks formed.

Each peak corresponds to an individual wave system, contributing to the energy of the

spectra.

12  

Fig.4. Single-peaked wave spectra at Honnavar.

Fig.5. Two-peaked spectra observed at Honnavar.

0 0.1 0.2 0.3 0.4 0.5 0.60

0.1

0.2

0.3

0.4

0.5

0.6

Frequency(Hz)

Spe

ctra

l Den

sity

(m

2 /Hz)

fp = 0.069 [Hz]13-03-08 2201 hrs

0 0.1 0.2 0.3 0.4 0.5 0.60

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Frequency(Hz)

Spe

ctra

l Den

sity

(m

2 /H

z)

fp1 = 0.068 [Hz]

fp2 = 0.2 [Hz]16-03-08 0100hrs

13  

Fig.6. Multi-peaked wave spectra observed at Honnavar.

2.3 Theoretical Wave spectra

Some of the theoretical representations of the wave spectra developed over the

years, using data collected by oceanographic platforms and satellites are briefly

discussed:

2.3.1 The Pierson-Moskowitz spectrum

This spectrum (Pierson and Moskowitz, 1964) is representative of the following

conditions: unidirectional seas, North Atlantic Ocean, fully developed local wind

generation with unlimited fetch. It is depicted as:

8.110

. ⁄

where Hs is the significant wave height,

4√

0 0.1 0.2 0.3 0.4 0.5 0.60

0.05

0.1

0.15

0.2

0.25

0.3

Frequency(Hz)

Spe

ctra

l Den

sity

(m

2 /Hz)

fp1 = 0.081 [Hz]

fp2 = 0.24 [Hz]fp3 = 0.29 [Hz]

13-03-08 0901hrs

14  

and ωm is the peak frequency,

0.4√

The most critical of these assumptions is the fully developed sea, as it is possible

to achieve a larger heave response for a platform from a developing sea, even

though the significant wave height may be smaller than that of a fully developed

sea, since the peak frequency is higher and heave motions tend to have higher

natural frequencies. For a rolling ship, the decaying sea might excite a larger roll

motion, since the natural frequency of roll tends to be low.

2.3.2 The Bretschneider Spectrum The limitation of fully developed seas lead to the emergence of a two parameter

spectrum, the Bretschneider spectrum, (Bretschneider, 1963), which later

replaced the Pierson-Moskowitz spectrum as the ITTC standard.

1.254

⁄

where Hs is the significant wave height. The spectrum can be used for sea

states of varying severity, by allowing the user to specify the model frequency

and significant wave height.

2.3.3 The Ochi Spectrum The Ochi Spectrum (Ochi and Hubble, 1976) is a three parameter spectrum that

allows the user to specify the significant wave height, the peak frequency, and

the steepness of the spectrum peak.

14

4 14Γ

4 1

4

λ is the parameter that controls the spectrum steepness. It has a limitation that

it considers only unidirectional seas and unlimited fetch. The Ochi spectrum can

specify the severity of the spectrum (ζ), the state of development (ωm) and isolate

the important frequency range by dictating the spectrum width, thus accounting

for swell from a distant storm.

15  

2.3.4 The JONSWAP Spectrum The JONSWAP spectrum was developed by the Joint North Sea Wave Project

for limited fetch, in 1968 and 1969, along a line extending over 160 km into the

North Sea, from Sylt Island (Hasselmann et. al, 1973) , taking into consideration,

over 2000 spectra, employing a method of least squares. It is important as it

takes into account, the growth of waves over a limited fetch and wave attenuation

in shallow water. It finds extensive applications in the offshore industry.

2 ⁄ /

where S(f) is the spectral energy, α is the Phillips constant with a value of 0.0081,

g is the acceleration due to gravity, f is the wave frequency and fp, the frequency

corresponding to the peak value of the energy spectrum. Also, σ = 0.07, for

values of f<fp and σ=0.09, for all other values of f.

For high waves along the Indian coast, Sanil Kumar and Ashok Kumar (2008)

estimated the JONSWAP parameters as follows:

0.18 . . . ,

8.38 . . . .

Hs, Tp and Tm02 represents the significant wave height, the spectral peak period

and the mean wave period, respectively. Sea state is generally represented in

terms of these parameters.

2.3.5 The Donelan et al Spectrum Donelan et al (1985), on the basis of the assumption that the high-frequency tail

of the spectrum decays proportional to f-4, and supported by vast laboratory and

field data, proposed the following fetch limited spectrum:

2

16  

2.3.6 The Scott Spectrum Scott (1965) spectrum is expressed in terms of Hs, as given below:

0.2140.065 0.26

for 0.26<(ω-ωp)<1.65. For all other values, s(ω) tends to 0, where s(ω) is the

spectral energy at angular wave frequency ‘ω’ and ‘ωp’ is the peak angular wave

frequency.

Sanil Kumar and Ashok Kumar (2008) found out that the measured wave spectra

along the shallow waters of the Indian coast can be represented using the JONSWAP

spectrum. The Scott spectrum, on the other hand, significantly underestimates the

maximum spectral energy of high waves.

2.4 Directional Wave Spectra

The sea state observed at any point comprises waves of different heights and

periods, approaching from various directions. Therefore, directional information forms

an integral part of the complete description of the sea state. The 2D directional wave

spectrum represents the distribution of wave elevation variance as a function of both

wave frequency, ‘f’ and wave direction, ‘θ’. A directional wave spectrum can be

represented as:

, . ,

where, , 1

S(f) being the omnidirectional wave spectrum and D(f, θ) the frequency-dependent

directional distribution.

2.4.1 Computation of Directional Wave Spectra

Wave direction spectrum is computed, taking into consideration, displacements in all the

three mutually perpendicular directions. From the time series of north, west and vertical

(n, w and v), displacements, the three corresponding Fourier series are calculated.

Thus, six Fourier components per frequency f are obtained in the following vector form:

17  

Anf = αnf + iβnf (2.4.1a)

Awf = αwf + iβwf (2.4.1b)

Avf = αvf + iβvf (2.4.1c)

Now, the co (C) and quad (Q) spectra are calculated, both of which are 3x3 matrices.

By definition: Qnn= Qvv=Qww=0

Q represents rotation. A rotation component directed vertically represents eddy currents

that are not part of the physics of waves and hence, Qwn=Qnw=0. Rotation is clearly

evident for waves breaking in the surf zone. According to the right-handed screw law, a

wave rolling eastward will have a rotation component directed to the north and hence

Qvw≠0 and Qwv≠0.

Thus, we have the co and quad spectra as follows:

Co-spectra (2.4.1d)

0 00 0

0 Quad-spectra (2.4.1e)

From these components, important wave parameters such as direction, ellipticity

and directional spread can be computed. The first four Fourier coefficients of the

normalized directional wave distribution G (θ,f) are defined as:

, cos cos 2 sin2

18  

where,

θ0=arctan(b1,a1)

m2 = a2cos 2θ0 + b2sin2θ0

n2 = -a2sin 2θ0 + b2cos2θ0

The m- and n- coefficients are known as the centered Fourier coefficients (Kuik

et al., 1988) or the second harmonic of the directional energy distribution recalculated to

the mean wave direction.

Wave direction

D=θ0=arctan(-Qwv, Qnv)

Directional spread

S=√ (2-2m1)

Wave ellipticity or 1/K, where K is the check factor,

Wave ellipticity is indicative of its shape and its variation with wave frequency, of

the local depth. For wavelengths much smaller than the depth, ellipticity nears one, as

the waves describe circular orbits. On the other hand, if the wavelength nears or

exceeds the depth, the vertical displacements are smaller than the horizontal ones and

ellipticity falls below 1.

19  

2.4.2 WAFO: Analysis of Wave Spectra

WAFO (Wave Analysis for Fatigue and Oceanography) is a toolbox of MATLAB

routines, developed at the Centre for Mathematical Sciences of the Lund University,

Sweden.

2.4.2.1 The Origins of WAFO

Research in mathematical statistics has been carried out in the Lund University,

since the 1970’s, a major breakthrough of which was the Fatigue Analysis Toolbox

(FAT), formulated in 1993. The Wave Analysis Toolbox (WAT, 1995) focused on solving

oceanographic problems, while maintaining the load analysis procedures of FAT.

WAFO derives from both FAT and WAT and is based on the routines written by the

WAFO group headed by Per Andreas Brodtkorb and Par Johannesson of the Lund

University. The first version of WAFO was released in January 2000 and was followed

up with versions 2.1 and 2.1.1 in 2004 and 2005 respectively.

WAFO contains tools for fatigue analysis, sea modeling, statistics and

numerics. The modular structure of WAFO makes it possible to integrate purpose

specific user-defined functions with the toolbox, as and when the need arises. WAFO

2.1.1 has been used to simulate both frequency and directional wave spectra obtained

from Honnavar, during the period of study.

2.4.2.2 WAFO 2.1.1

WAFO 2.1.1 makes use of the raw data from the waverider buoy to compute the

spectra. Raw data is in the form of text files, containing four comma separated integers,

indicating the status, heave, north and west directional displacements, all in

centimeters, sampled at a frequency of 1.28 Hz. Individual records are obtained every

half hour.

The alternatives available for determining the one-sided spectral density in

WAFO 2.1.1 are Welch’s Average Periodogram method, Burg’s method and Maximum

Entropy method. The smoothness of the resultant spectra is a function of the maximum

lag size of the window function used in the transform (The WAFO Group, 2000).

20  

The data-adaptive methods offered by WAFO 2.1.1 for the estimation of

directional wave spectra from time series data are the Maximum Likelihood (MLM), the

Iterative Maximum Likelihood (IMLM), the Maximum Entropy (MEM) and the Extended

Maximum Entropy (EMEM) methods. Compared to a directional Fourier series

expansion, the MLM and MEM provide better directional resolution (Earle et al., 1999).

2.5 Spectral Partitioning

2.5.1 Basic Concepts

Double and multi-peaked wave spectra are often a result of the co-existence of

locally generated wind sea and swells originating from distant storms. Inter-comparison

of such multi-peaked directional wave spectra proves to be a difficult task. Spectral

partitioning involves the splitting of the ocean wave spectra into components

representing the original wave systems. The spectrum is separated into a number of

distinct segments, which relate to the various peaks in it. The basis for this process

derives from the fact that wave systems originating from different uncorrelated

meteorological events can be assumed to be independent.

A partition represents a wave system, corresponding to a certain meteorological

event, such as a swell from a distant storm in the past or a wind sea generated by a

regional wind. Each partition is characterized by three mean parameters: its total

energy, mean direction and mean frequency.

Portilla et.al (2009), defines partitioning as the mechanism to detect wave

systems considering the morphological features of the spectral signals, alone. Partition

algorithms aim at identifying uncorrelated wave systems. The extent to which the

algorithms succeed in replicating the real ocean wave spectra is highly dependent on

the initial assumptions regarding the wave sources. Another factor contributing to the

dependability of an algorithm is the flexibility of the assumed parameters. These

parameters are purpose-specific and often are devoid of any solid mathematical or

physical base.

21  

The earliest partitioning algorithms computed a separation frequency that

distinguished the wind sea portion of the spectrum from the low frequency swell

contributions. The thesis aims at the development of a one-dimensional partitioning

algorithm, on the lines of Portilla et al (2009).

2.5.2 Significance

As sea states consist of local wind-generated waves and swells of distant storms,

the wave energy spectra often show two or more spectral peaks corresponding to

different generation sources. The coexisting of wind sea and swell can significantly

affect the safety of seafarers, offshore structure designs, small boat operations and ship

passages over harbor entrance, and surf forecasting (Earle 1984). The mixed seas also

affect the dynamics of near-surface processes such as air–sea momentum transfer

(Mistuyasu 1991; Dobson et al. 1994; Donelan et al. 1997; Hanson and Phillips 1999).

The ocean wave spectrum gives the distribution of wave energy among different

wave frequencies on the sea surface. Different individual wave systems, originating

from varying meteorological events give rise to the wave spectra. Integral parameters

that suitably represent a spectra composed of a single wave system, are preferred for

the interpretation and archival of voluminous datasets. However the occurrence of

simultaneous, multiple wave systems, render the integral parameters, less meaningful.

The partitioning of wave spectra into component wave systems provides an excellent

tool for data reduction.

Spectral partitioning proves advantageous while comparing datasets, or in

evaluation of model performance, as analysis at the level of wave systems provides

more insight into the processes, when compared to that of mean parameters of the

whole spectra. Further, spectral components can be analyzed in space and time, to

trace the origin of distant wave systems.

Partitioning has a potential application in the determination of wind sea and swell,

in third-generation wave models. As these components are no longer computed

separately, splitting is to be resorted to, for obtaining the necessary information.

22  

2.5.3 Timeline of Spectral Partitioning

Most of the earliest partition algorithms relied on the determination of a

separation frequency, fs for automatic identification of the wind sea and swell

components. Wave components at frequencies higher than fs owe their origin to local

winds, while those at frequencies lower than fs arise due to distant swells. On the

assumption that the separation frequency is linearly related to the spectral peak of a

wind sea, Earle (1984), proposed an empirical relationship between the separation

frequency and the local wind speed U, based on the Pierson-Moskowitz spectrum

(Pierson and Moskowitz, 1964). The relation states that;

(2.5.3a)

where fs is in hertz, U in m/s and β is an empirical constant.

A more desirable approach is to determine a separation frequency between the

wind sea and swell peaks from a given spectrum alone (Vartdal and Barstow 1987).

Wind sea and swell peaks can mix with spectral irregularities, which are the local

maximums in wave spectrum resulting from artifacts of random processes. Identification

of wind sea and swell peaks from the spectral irregularities may not always be very

reliable.

Gerling (1992) presented a two stage procedure for characterizing wave systems

from ocean surface gravity-wave spectral estimates. In the data-intensive first stage,

individual spectra are parameterized in terms of the directions, periods and significant

wave heights of wave systems represented in that spectrum. The latter stage involves

the association of wave systems from the spectra with similar wave systems in the

neighboring spectra.

Using an empirically determined width of the confidence intervals of the spectral

data, Rodriguez and Guedes Soares (1999) developed a procedure to differentiate the

legitimate energy peaks of wind sea and swell from the spectral irregularities caused by

the artifacts of random processes. The methods proposed by Guedes Soares (1984)

and Guedes Soares and Nolasco (1992), for peak identification, require a priori

23  

knowledge of the degree of freedom (DOF) of spectral data and have to examine every

local maximum. Further, this algorithm lacks physical basis of wind wave generation

and can easily result in misidentification of wind sea and swell peaks, especially for

spectra with multiple strong swell peaks.

Based on the proposals of Gerling (1992) and Hasselmann et.al (1994), Hanson

and Phillips (2001), generated the Wave Identification and Tracking System (WITS) that

operated on a series of directional wave spectra, with supporting wind observations.

Wave spectrum peaks representing specific wind sea and swell wave systems are

extracted based on topographic minima, with wind sea peaks identified by wave age

criteria, such that wind seas lie within the parabolic boundaries defined by:

1.5 (2.5.3b)

where cp is the phase speed of the wind sea, U10 is the 10 m elevation wind speed and

δ is the angle between the wind and the wind sea.

2.5.4 Proposed 1D Partition Algorithm

A 1-D partition algorithm has been developed in MATLAB. Each local peak

represents the peak of a wave system. The trough between the peaks forms the

partition boundaries. Identification of spurious peaks is an integral fragment of any

partition algorithm. Once these spurious peaks are disregarded, the partitions tend to

get consistent.

The following are treated as spurious:

1. Partitions at the tail of the spectrum, which belongs to the wind sea.

2. Partitions with low total energy, less than 5% of the total energy of the

spectrum.

3. Two peaks which are very close to each other. 0.03 Hz was chosen as the

limiting distance.

24  

4. Partitions that have a lower energy level, when compared to the neighboring

ones, are combined.

On the basis of the above criterion, the algorithm identifies the significant

partitions in the 1-D spectra. The significant wave height and energy of the partitions are

also computed.

2.6 Wind sea-swell Separation Schemes in Nearshore Waters

2.6.1 General

Portilla et al. (2009), defined identification of wind sea and swell as labeling the

wave system with wind sea or swell as a supplementary designation, taking into

account environmental and physical characteristics.

Mixed sea states are characterized by the simultaneous presence of local wind

waves and swells of distant origin, leading to multi-peakedness of the corresponding

wave energy spectrum (Hanson and Phillips, 1999). The separation of the spectrum into

sea and swell contributions is essential for marine operations and design practices.

Further, the mixed sea states have an impact on the dynamics of near surface

processes.

2.6.2 Characteristics of Wind sea and Swell Spectra

Initially, in the generation area, the waves of different periods coexist. However,

with time, the different wave components separate out from each other. Compared to

their shorter period counterparts, the waves of longer periods tend to move fast, and

reach distant sites first. In the wave generation area, energy is transferred from the

shorter period waves to the longer period ones. During their journey through the seas,

waves tend to lose a part of their energy, thanks to interactions within the fluid, and that

with the external air. Friction with the seabed and turbulence created on breaking are

other causes for the dissipation of wave energy. Short period waves tend to lose their

energy more readily, when compared to the long period ones. As a result, swells tend to

have longer periods than the wind sea.

25  

Wind sea waves are characterized by their irregularity, short crests, broad

spectrum and quick response to wind variations. Swell, on the other hand, comprises

regular, long crested waves, whose evolution is rather independent on wind. Under the

effect of varying winds, swell and wind sea often overlap to produce mixed sea states,

represented by a continuous spectrum, from which the separation of the components by

automated procedures is difficult (Portilla et al., 2009).

Even though, the highest waves are associated with the wind sea, swells have

much importance in design considerations for coastal structures. Longer periods of

swell waves affect harbor studies, where sediment mobility, armor stability, overtopping

and harbor resonance are of much importance. Thus, wind sea and swell, when

coexistent, provide alternative extreme wave conditions for design.

Most separation schemes identify a separation frequency (fs) for a given wave

spectrum. The portion of the spectrum lying at frequencies greater than fs is designated

as the wind sea. Swell contributions correspond to wave components at frequencies

lower than fs. Wang and Gilhousen (1998), Wang and Hwang (2001), Gilhousen and

Hervey (2001) and Portilla et al. (2009), recommended different methods for separation

of sea and swell. Kumar et al. (2003) found that along the Indian coast, about 60% of

the wave spectra observed was multi-peaked and they were mainly single peaked when

the significant wave height (Hm0) was more than 2 m.

When multi-peaked spectra are present in the nearshore, the direction of the sea

and swell is required to estimate the longshore currents and sediment transport. Hence

the separation of sea and swell from the measured wave data is of much importance.

The suitability of existing methods for separating sea and swell in nearshore water is

verified based on the wave data collected at 9 m water depth off Honnavar coast in

Karnataka, west coast of India.

26  

2.6.3 Data

Waves in the open ocean at 9 m water depth off Honnavar at a location 14° 18.3’

N; 74° 23.5’ E (Figure 1) were measured using the Datawell directional waverider buoy

(Barstow and Kollstad, 1991) during March 2008 to February 2009. The measurement

location was 3 km from the coast. The oceanographic conditions along the west coast of

India are influenced by the summer monsoon (June-September). The wave

characteristics are also different during summer monsoon, pre and post monsoon

periods (Kumar and Anand, 2004). To represent the pre-monsoon, monsoon and post-

monsoon periods, the wave data collected during April, June and November 2008 is

used in the study.

The wave data were recorded continuously at 1.28 Hz. From the recorded heave

data covering 30 minutes duration, the wave spectrum was obtained through Fast

Fourier Transform (FFT). FFT of 8 series, each consisting of 256 measured vertical

elevations of the buoy data (heave), were added to obtain the spectra. The high

frequency cut off was set at 0.58 Hz. Heave was measured in the range of -20 to 20 m

with a resolution of 1 cm and an accuracy of 3%. The significant wave height (Hmo) and

the mean wave period (Tm02) were obtained from the spectral analysis. Wave length at

the measurement location was estimated using the wave dispersion relationship.

Reanalysis data of zonal and meridional components of wind speed at 10 m height at 6

hourly intervals from NCEP / NCAR (Kalney et al., 1996) obtained for the point (12.5º N;

72.5 º E) was used in the study. These data are provided by the NOAA-CIRES Climate

Diagnostics Center, Boulder, Colorado at http://www.cdc.noaa.gov/.

2.6.4 Methods

Different methods have been proposed to derive the wind sea and swell

components from the wave spectrum. The simplest approach involves designating a

constant separation frequency or period. This approach is particularly reliable in those

areas where wind sea and swell are markedly separated in the frequency domain. The

27  

energy of wind sea waves is contained at higher frequencies between 0.1 and 0.4 Hz

while swell waves have lower frequencies between 0.03 and 0.2 Hz (Portilla et al.

2009).

The spectrum, when split close to the peak frequency (fPM) of the Pierson-Moskowitz

spectrum (Pierson and Moskowitz, 1964), gives an idea about the wave components.

0.13 (2.6.4a)

Separation frequency, fs is given by: fs = 0.8 fPM

The factor 0.8 accounts for the uncertainties in the actual sea state or in the angular

shift between winds and waves (Earl, 1984).

Wang and Gilhousen (1998), for the National Data Buoy Centre (NDBC), USA,

devised a method for separation of sea and swell based on the wave steepness

parameter, which does not require the wind or directional information. It works on the

assumption that wind seas are steeper than swell and that maximum steepness of the

wave spectrum occurs near the peak of wind seas energy.

A wave steepness parameter, ζ is computed at all frequencies:

(2.6.4b)

Hs is the significant wave height and L is the wave length associated with the average

wave period (Tm02) that are computed from the nth moment of the wave spectrum by:

4 , (2.6.4c)

(2.6.4d)

where fu and fl are the upper and lower frequency limits of measured wave spectra. The

separation frequency is given by,

28  

fs = Cfx

fx being the frequency corresponding to the maximum of the steepness function and C

is an empirically determined constant having value of 0.75.

Gilhousen and Hervey (2001) modified the steepness method to limit the

minimum allowable separation frequency on the basis of observed wind speed. The

minimum separation frequency was determined from the peak frequency of the Pierson-

Moskowitz spectrum of a fully developed sea, at the observed wind speed:

. (2.6.4e)

where fsu is the separation frequency and 1.25/U10 is the peak frequency of the Pierson-

Moskowitz spectrum at the observed wind speed adjusted to 10 m (U10). Empirical

constant C has a value of 0.9 (Gilhousen and Hervey, 2001). The higher of fs and fsu is

taken as the separation frequency.

Wang and Hwang (2001) related the peak frequency of the steepness function,

fm to wind speed, through regression. The separation frequency was then set at the

frequency where wind speed equals the phase speed and an expression for separation

frequency, disregarding the wind speed, was obtained as:

4.112 . (2.6.4f)

Portilla et al. (2009) proposed a 1D separation algorithm, on the basis of the

assumption that, the energy at the peak frequency of a swell system cannot be higher

than the value of a PM spectrum with the same peak frequency. It calculates the ratio

(γ*) between the peak energy of a wave system and the energy of a PM spectrum at the

same frequency. The energy spectrum is given by:

2 ⁄ / (2.6.4g)

29  

Where, f represents the frequency, α, the Phillips constant, fp, the peak frequency, γ, the

peak enhancement factor and σ, the spectral width factor. In the said algorithm, α is

fixed at its PM value, αPM=0.0081, γ=1 and f= fp. If γ* is above a threshold value of 1, the

system is considered to represent wind sea, else it is taken to be swell.

30  

3. Results and Discussions

31  

3. Results and Discussions

3.1 Spectral Partitioning

The 1-D partition algorithm was used to identify the significant partitions and thus

the constituent wave systems from the waverider spectra. In the following example

(Figure 7) the algorithm has been used to identify three modes in the wave spectra from

Honnavar. The data represents a spectrum, collected at 2125 hours on 08-05-2008.

0 0.2 0.4 0.6

Frequency (Hz)

0

0.2

0.4

0.6

0.8

1

1.2

Spe

ctra

l Den

sity

(m2 /

Hz)

0

60

120

180

240

300

360

Dire

ctio

n (D

eg)

Wave spectraWave directionPartition IPartition II

Fig.7. Partitioning of Waverider buoy spectrum obtained at 2125 hrs, 08-05-08, at Honnavar.

32  

The spectrum is made up of three modes:

1. A first peak near 15s or 0.065 Hz, due to a swell.

2. A second peak close to7s or 0.14 Hz due to wind sea.

3. A third peak near 4s or 0.24 Hz due to local sea.

The first peak signifies a swell, while the other two can be attributed to wind

sea or local sea. Wind sea is generated by a regional or seasonal wind, while local sea

is due to the effect of local winds or squalls.

The results obtained on partitioning are;

1. Hs1=0.53 m; Tp1=15.4 s; Dp1=228°

2. Hs2=0.50 m; Tp2=7.14 s; Dp2=288°

3. Hs3=0.61 m; Tp3=4.17 s; Dp3=301°

where Hs stands for significant wave height, Tp for peak wave period and Dp is the

direction for maximum energy. For significant wave height, the relation

Hs2=Hs1

2+Hs22+Hs3

2, is satisfied.

3.2 Wave Characteristics

Waves were high during June due to the influence of summer monsoon.

Significant wave heights up to 3.6m were recorded. The average Hs was 0.7, 2.1 and

0.6 m and the average Tm02 was 4.7, 6.4 and 5.5 s during April, June and November

respectively (Table 1). 99% of the measured waves satisfied the intermediate water

criteria (SPM, 1984). Long period swells with peak period more than 18.18 s were

present during 6 and 2% of the time during April and November.

3.3 Separation of Swell and wind sea

Figure 8(A) shows the spectra obtained at 0800 hrs on 5 November 2008 and

8(B), that at 0000 hrs on 21 April 2008 along with the separation frequencies

determined by various methods. The Wang and Hwang (2001) and original steepness

(Wang and Gilhousen, 1998) methods identify the separation frequency around 0.13

33  

and 0.12 Hz respectively, thereby overestimating the wind sea contribution (Figure 8A).

Separation frequency obtained based on the modified steepness method was 0.4 Hz

and is not considered for further analysis. The method suggested by Portilla et al.

(2009), when used in combination with partitioning, is able to separate the two systems.

Due to low wind speeds (U10=2.8 m/s), splitting using the PM method also

resulted in a high separation frequency of about 0.36 Hz. During the period of relatively

high wind speed (4 m/s), the PM and modified steepness method estimated the

separation frequency as 0.26 and 0.29 Hz (Figure 8B). Measured data shows that even

when wind speed was less than 4 m/s, sea peak frequency varied from 0.1 to 0.5 Hz

and the peak frequency of the spectrum varied from 0.05 to 0.3 Hz during April and

November (Figure 9A & 9B). Separation frequency as per modified steepness method

for wind speed of 4 m/s is 0.28 Hz and the wind sea and swell separation using this

frequency will underestimate the wind sea.

The PM and modified steepness methods computes fs on the basis of wind

speed and hence during periods of fairly low wind speeds, it estimates high values and

is not used in further analysis. The separation frequency estimated using different

methods for April, June and November 2008 is presented in Figure 10 and it give a

clear idea regarding the performance of different schemes.

During April and November, Wang and Hwang (2001) designate the tail end of

the spectra, as the wind sea, while the original steepness method (Wang and

Gilhousen, 1998) overestimates the swell. Portilla et al. (2009) gives a realistic picture

during all the seasons. During the summer monsoon period (June), the curve of Wang

and Hwang (2001) closely follows that of Wang and Gilhousen (1998) and Portilla et al.

(2009), indicating their suitability for separating sea and swell of high energy spectra.

34  

0 0.2 0.4 0.6

0

0.1

0.2

0.3

0.4

0.5S

pect

ral D

ensi

ty (m

2 /H

z)(A) 05 Nov 2008 0800 hrs

0 0.2 0.4 0.6Frequency (Hz)

0

0.1

0.2

0.3

Spe

ctra

l Den

sity

(m2 /

Hz)

Wave SpectraOriginal Steepness method (1998)Portilla et al.(2009)Wang and Hwang (2001)PM MethodModified Steepness method (2001)

(B) 21 Apr 2008 0000 hrs

Fig.8. Separation frequency estimated from different methods.

35  

0 2 4 6 8 10 12 14Wind Speed (m/s)

0

0.1

0.2

0.3

Pea

k F

requ

ency

(Hz)

0 2 4 6 8 10 12 14Wind Speed (m/s)

0

0.1

0.2

0.3

0.4

0.5

0.6

Sea

Pea

k Fr

eque

ncy

(Hz)

April 2008June 2008November 2008

(A)

(B)

 

Fig.9. Variation of (A) sea peak frequency and (B) peak frequency with wind speed.

36  

91 101 111 121

0.05

0.1

0.15

0.2

0.25

0.3

f s (H

z)Steepness Method (1998)Portilla et.al (2009)Wang and Hwang (2001)

152 162 172 182

0.05

0.1

0.15

0.2

0.25

0.3

f s (H

z)

305 315 325 335

Julian Day

0.05

0.1

0.15

0.2

0.25

0.3

f s (H

z)

(a) April 2008

(b) June 2008

(c) November 2008

 

Fig.10. Time series of separation frequency estimated from different methods during (A) April, (B) June and (C) November 2008.

37  

The method of Portilla et al. (2009) was used to separate the sea and swell from

the wave spectra off Honnavar, during the pre-monsoon (April), monsoon (June) and

post-monsoon (November) periods. Contribution of wind sea is more during pre

monsoon period compared to other seasons (Figure 11A) and monsoon periods have

high energy spectra, compared to the other months (Figure 11B and 11C). The mean

wave direction is different for the swell and the sea and the wind direction matches the

mean direction of the sea (Figures 11D and 11E).

In April, during 54% of the time wind sea overrides the swell contribution (Figure

12A). During June, the spectral energy increases with the onset of summer monsoon

and swells prevails over the seas (Figure 12B). During November, most of the time the

dominance of swells is evident (Figure 12C). The contribution of swell at the

measurement location was 46, 73 and 56% during April, June and November

respectively. During 5, 1 and 8% of the time during April, June and November, the

maximum spectral energy of the sea was more than that of the swell.

The average swell direction was 230, 252 and 230º and the average sea

direction was 293, 251 and 291º during April, June and November respectively (Table

1). During June, the sea and the swell were from the same direction whereas during the

pre-monsoon period the sea was from north-west and the swell was from south-west

(Figures 12D to 12F). Swell was predominant during the summer monsoon period

(Figure 13A). Even though swells were present, good correlation (r=0.7) was found

between the wind sea and the wind speed (U) during June compared to other periods

(Figure 13B).

 

38  

0 0.2 0.4 0.6

0

0.1

0.2

0.3

0.4

Spe

ctra

l Den

sity

(m2 /H

z)

Wave SpectraSeperation Frequency

0 0.2 0.4 0.6

0

60

120

180

240

300

360

Dire

ctio

n (D

eg)

Wave DirectionSeperation FrequencyWind Direction

(A) 19-Apr-08 1825hrs

0 0.2 0.4 0.6

0

4

8

12

Spe

ctra

l Den

sity

(m2 /H

z)

0 0.2 0.4 0.6Frequency (Hz)

0

0.1

0.2

0.3

0.4

Spe

ctra

l Den

sity

(m2 /H

z)

0 0.2 0.4 0.6

0

60

120

180

240

300

360

Dire

ctio

n (D

eg)

0 0.2 0.4 0.6Frequency (Hz)

0

60

120

180

240

300

360

Dire

ctio

n (D

eg)

(C) 19-Nov-08 0851hrs

(B) 19-June-08 0356hrs

(D)

(E)

(F)

Fig.11. Representative wave spectral plots with separation frequency, steepness function and wind and mean wave direction.

39  

91 101 111 121

0

1

2

3

Hs

(m)

152 162 172 182

0

1

2

3

Hs

(m)

305 315 325 335Julian Day

0

1

2

3

Hs

(m)

91 101 111 121

0

60

120

180

240

300

360

Dire

ctio

n (D

eg)

SwellWind SeaWind Direction

152 162 172 182

0

60

120

180

240

300

360D

irect

ion

(Deg

)

305 315 325 335Julian Day

0

60

120

180

240

300

360

Dire

ctio

n (D

eg)

(A)

April 2008

(C) November 2008

(B) June 2008

(D)

(E)

(F)

 

Fig.12. Variation of sea and swell height along with mean wave direction during April, June and

November 2008.

40  

0 0.5 1 1.5 2 2.5Hs Sea (m)

0

1

2

3

4H

s S

wel

l (m

)April 2008June 2008November 2008

0 4 8 12 16Wind Speed (m/s)

0

0.4

0.8

1.2

1.6

2

Hs

Sea

(m)

(A)

(B)

 

Fig.13. Correlation between wind sea and swell (A) and between wind sea and wind speed (B).

41  

Table 1: Range and average values of wave parameters

Parameter April 2008 June 2008 November 2008

Range Average Range Average Range Average

Hs (m) 0.4-1.1 0.7 0.8-3.6 2.1 0.3-1.0 0.6

Tm02 (s) 3.1-7.8 4.7 4.3-8.0 6.4 3.2-9.8 5.5

Hsswell (m) 0.2-0.8 0.4 0.3-3.3 1.8 0.2-0.8 0.4

Hssea (m) 0.2-1.0 0.5 0.3-2.3 1.0 0.1-0.9 0.4

Tm02swell (s) 8.1-18.1 12.4 7.2-17.4 9.5 6.4-15.7 11.5

Tm02sea (s) 2.6-4.7 3.5 2.8-6.4 3.8 2.3-5.6 3.7

Θp (deg) 180-316 234 204-269 252 200-330 235

Θpswell (deg) 180-267 230 208-269 252 194-302 230

Θpsea (deg) 83-316 293 184-297 251 1-354 291

% swell 5-85 46 6-92 73 5-93 56

% sea 15-95 54 8-94 27 7-95 44

Wind

speed(m/s)

0.6-7 3.5 0.5-12.5 6.6 0.05-6.7 2.5

3.4 Directional Wave Spectra

Typical directional wave spectra obtained at the study area have been plotted

along with the corresponding one dimensional spectra and spreading functions, using

the WAFO toolbox in MATLAB. Directional spreading obtained using Maximum

Likelihood Method (MLM), Iterative Maximum Likelihood Method (IMLM) and Maximum

Entropy Method (MEM) have been compared. WAFO is able to identify the wave

systems representing significant energy values.

42  

Figure 14 represents the spectrum obtained at 0900 hrs on 17 March 2008. It

corresponds to a significant wave height of 0.63m. Two wave systems prevail, swells

approaching from the south-west and local wind seas from the west. The directional

spreading function is bimodal in nature, with the peaks corresponding to the direction of

approach of the two significant wave systems.

Figure 15 portrays a swell dominated high energy spectrum, at 2330 hrs on 09

June, 2008. It has a significant wave height of 2.62 m. Swells arrive from a broad

region, spanning the south west to the north west. The contribution of the wind sea is

negligible, which results in a unimodal spreading function, peaking around west

southwest.

The spectrum in figure 16 (1930 hrs, 01 June, 2008) shows a unimodal energy

distribution, with swells approaching from the south west. The spectrum is of low

energy, with a significant wave height of 0.8m.

43  

Fig.14. 1-D spectra, directional spreading and directional spectra at 1930 hrs 01-06-08.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

0.05

0.1

0.15

0.2

0.25

0.3

Frequency [Hz]

S(f)

[m

2 s]

0

0.2

0.4

0.6

0.8

1

1.2

0 315 270 225 180 135 90

Wave directions (deg)

D( θ

)

MLMEMEMIMLM

0

315

270

225

180

Frequency [Hz]

Dire

ctio

n (d

eg)

0 0.05 0.1 0.15 0.2 0.25

44  

Fig.15. 1-D spectra, directional spreading and directional spectra at 2330 hrs 09-06-08.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

1

2

3

4

5

6

7

8

9

Frequency [Hz]

S(f)

[m2 /H

z]

0

0.5

1

1.5

2

2.5

3

0 315 270 225 180 135 90

D( θ

)

Direction (deg)

IMLMMLMEMEM

0

315

270

225

180

Frequency [Hz]

Dire

ctio

n (d

eg)

0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14

45  

Fig.16. 1-D spectra, directional spreading and directional spectrum at 1930 hrs 01-06-08.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Frequency [Hz]

S(f)

[m2 /H

z ]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 315 270 225 180 135 90

D( θ

)

Direction (deg)

IMLMMLMEMEM

0

315

270

225

180

Frequency [Hz]

Dire

ctio

n (d

eg)

0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14

46  

4. Conclusions

47  

4. Conclusions

The spectra used in the study were measured at 9 m, water depth off the

Honnavar coast in the west coast of India, using a directional Waverider buoy. An

algorithm for the separation of wave spectra into the components has been prepared,

on the basis of Portilla et al. (2009).

The method proposed by Portilla et al. (2009) proved to be the most consistent in

intermediate waters, for the separation of wind sea and swell, while those proposed by

Wang and Gilhousen (1998) and Wang and Hwang (2001) underestimated the wind

sea. Wang and Gilhousen (1998) and Wang and Hwang (2001) method estimated the

separation frequency reasonably well during June when the high waves were present.

The modified steepness method (Gilhousen and Hervey, 2001) and PM method

underestimates the wind sea when the wind speed is low.

The estimates of the directional spreading function, made by the Extended

Maximum Entropy Method (EMEM) are found to be bounded by those made by the

Iterative Maximum Likelihood Method (IMLM) and the Maximum Likelihood Method

(MLM). Both MLM and EMEM estimations are found to be broader than the IMLM ones.

The IMLM is found to be more consistent for the spectra under consideration. The

coexistence of wind sea and swell as in March gives bimodal directional distributions.

On the other hand, swell dominated periods have a unimodal spreading function.

48  

5. References and Bibliography

49  

5.1 References

Barstow,S.B., Kollstad, T., 1991. Field trials of the directional waverider. In:

Proceedings of the First International Offshore and Polar Engineering Conference, vol.

III, pp. 55–63.

Central Ground Water Board, Government of India, 2008: Ground Water Information

Booklet, Uttara Kannada District, Karnataka.

Datawell BV: Waverider Reference Manual, Datawell BV, the Netherlands.

Dobson F. W., S. D. Smith, and R. J. Anderson, 1994: Measuring the relationship

between wind stress and sea state in the open ocean in the presence of swell. Atmos.–

Ocean, 32, 237–236

Donelan, M.A., Hamilton, J. and W.H. Hui, 1985. Directional spectra of wind

generated waves. Philosophical Transactions of Royal Society, London A 315, 509–

562.

Donelan M. A., W. M. Drennan, and K. B. Katsaros, 1997: The air–sea momentum

flux in conditions of wind sea and swell. Journal of Physical Oceanography, 27, 2087–2099.

Earl, M.D, and J.M Bishop, 1984: A Practical Guide to Ocean Wave Measurement and

Analysis, ENDECO, INC, Marion, U.S.A.

Earl, M. D., 1984. Development of algorithms for separation of sea and swell. National

Data Buoy Center Tech. Rep. MEC-87-1, NDBC, 53 pp.

Earle, M.D, Steele, K.E, and D.W.C Wang, 1999: Use of Advanced Directional Wave

Spectra Analysis Methods. Ocean Engineering, 26, 1421-1434.

Guedes Soares, C., 1984: Representation of double-peaked sea wave spectra. Journal

of Ocean Engineering, 11, 185–207.

Guedes Soares, C., and M. C. Nolasco, 1992: Spectral modeling of sea states with

multiple wave systems. Journal of Offshore Mechanics and Arctic Engineering, 114, 278–284.

50  

Gerling, T. W., 1992: Partitioning Sequences and Arrays of Directional Ocean Wave

Spectra into Component Wave Systems. Journal of Atmospheric and Oceanic

Technology, 9, 444–458.

Gilhousen, D.B., and R.Hervey.2001: Improved Estimates of Swell from Moored

Buoys. Fourth International Symposium WAVES 2001.San Francisco, USA.

Goda, Y. 2000: Random Seas and the Design of Maritime Structures, World Scientific

Publishing Co. Ltd.

Hanson, J., L., and O. M. Phillips, 1999. Wind sea growth and dissipation in the open

ocean, Journal of Physical Oceanography, 29, 1633-1648.

Hanson, J.L., and O.M. Phillips, 2001: Automated Analysis of Ocean Surface

Directional Wave Spectra. Journal of Atmospheric and Oceanic Technology, 18, 277-

293.

Hasselmann, K., Barnett, T.P., Bouws, E., Carlson, H., Cartwright, D.E., Enke, K., Ewing, J.A., Gienapp, H., Hasselmann, D.E., Kruseman, P., Meerburg, A., Muller, P., Olbers, D.J., Richter, K., Sell, W., Walden, H., 1973. Measurements of wind-wave

growth and swell decay during the Joint North Sea Wave Project (JONSWAP).

Deutsche Hydrographische Zeitschrift A 12, 95.

Hasselmann, S., K. Hasselmann, and C. Bruning, 1994: Extraction of wave spectra

from SAR image spectra. Dynamics and Modelling of Ocean Waves, G. J. Komen et al.,

Eds.,Cambridge University Press, 391–401.

Hegde, V.S et al. 2009: Low-Scale Foreshore Morphodynamic Processes in the Vicinity

of a Tropical Estuary at Honnavar, Central West Coast of India. Journal of Coastal

Research, 25, 305-314.

Kalnay et al. 1996: The NCEP/NCAR 40-year reanalysis project. Bulletin of the

American Meteorological Society, 77 (3), 437-471, 1996.

Kuik, A.J., Vledder, G. and Holthuijsen, L.H. 1988: A method for the routine analysis

of pitch and roll buoy wave data, Journal of Physical Oceanography, 18, 1020-1034.

51  

Kumar, V. S., Anand, N.M., Kumar, K.A., and S. Mandal, 2003. Multipeakedness and

groupiness of shallow water waves along Indian coast. Journal of Coastal Research,

19, 1052-1065.

Kumar, V.S. and N.M. Anand, 2004. Variations in wave direction estimated using first

and second order Fourier coefficients, Ocean Engineering, 31, 2105–2119.

Mitsuyasu H., 1991: The effect of swell on the growth of wind waves. Oceanography of 

Asian Marginal Seas, K. Takano, Ed., Elsevier, 381–391.

Ochi, M.K., Hubble, E.N., 1976. On Six Parameter Wave Spectra. Proceedings of the

15th Coastal Engineering Conference. ASCE, New York, pp. 321–328.

Pierson, W.J. and L. Moskowitz, 1964. A proposed form for fully developed seas

based on the similarity theory of S.A. Kitaigorodski. Journal of Geophysical Research

69, 5181–5190.

Portilla, J., 2009: Buoy Data Assimilation in Nearshore Wave Modeling. PhD Thesis of

Katholieke Universiteit Leuven, Belgium.

Portilla,J., Ocampo-Torres,F.J., and J. Monbaliu 2008:Spectral Partitioning and

Identification of Wind Sea and Swell. Journal of Atmospheric and Oceanic Technology,

26, 117-122.

Rodrıguez, G., and C. Guedes Soares, 1999: A criterion for the automatic identification

of multimodal sea wave spectra. Applied Ocean Research, 21, 329–333.

Sanil Kumar, V., 1999: Analysis of Directional Spreading of Wave Energy With Special

Reference to Indian Coast, PhD Thesis of Indian Institute of Technology, Bombay,

India.

Sanil Kumar, V. and K Ashok Kumar, 2008: Spectra Characteristics of High Shallow

Water Waves. Ocean Engineering, 35, 900-911.

Scott, J.R., 1965: A sea spectrum for model test and long-term ship prediction. Journal

of Ship Research 9, 145–152.

52  

Shore Protection Manual, 1984. U.S. Army Coastal Engineering Research Center,

Department of the Army, Corps of Engineers, U.S. Govt. Printing Office, Washington,

DC, USA, vol. 1.

The WAFO Group (2000): Wave Analysis for Fatigue and Oceanography - Tutorial.

Mathematical Statistics, Centre for Mathematical Sciences, Lund University.

Vartdal L., and S. F. Barstow, 1987: A separation algorithm for wind sea and swell for

applications to directional Metocean data buoy. Oceanographic Center, SINTEF Group

Tech. Rep. ANODA-30, Trondheim, Norway, 104 pp.

Wang, D.W, and D.B. Gilhousen, 1998: Separation of Sea and Swell from NDBC Buoy

Wave Data, Fifth International Workshop on Wave Hindcasting and Forecasting, ASCE.

Melbourne, FL, Jan. 1998.

Wang, D.W, and P.A Hwang, 2001: An Operational Method for Separating Wind Sea

and Swell from Ocean Wave Spectra. Journal of Atmospheric and Oceanic Technology,

18, 2052-2062.

5.2 Bibliography

Alves, J.H.G.M., and E. Melo, 1999: On the Measurement of Directional Wave Spectra

at the Southern Brazilian Coast, Applied Ocean Research, 21, 295-309.

Baba, M., and N.P. Kurian (eds), 1988: Ocean Waves and Beach Processes of the

South-West Coast of India and Their Prediction, Monograph, Centre for Earth Science

Studies, Trivandrum.

Collins, J. I., et al. 1981: Refraction of Directional Spectra, Proceedings, Directional

Wave Spectra Applications, ASCE, New York, N.Y., pp 251-266.

Cumming, D. 2005: Comparison of Neptune and Datawell Directional Wave Buoy Data

Acquired Fall 2004, Laboratory Memorandum, Institute for Ocean Technology, National

Research Council, Canada.

53  

Earle, M.D., 1996: Nondirectional and Directional Wave Data Analysis Procedures.

Technical Document 96-01, National Data Buoy Center, Mississippi.

Gilat, A. 2004: MATLAB: An Introduction with Applications. John Wiley & Sons, Inc.

Asia.

Hauser, D et al. 2005: Measuring and Analyzing the Directional Spectra of Ocean

Waves. From the European COST Action 714.

Huang, M-C, and Chen J-Y, 1998: Wave Direction Analysis from Data Buoys. Ocean

Engineering, 25, 621-637.

Krogstad, H.E, et al. 1999: Some Recent Developments in Wave Buoy Measurement

Technology. Coastal Engineering, 37, 309-329.

Sanil Kumar,V., Deo,M.C., Anand,N.M, and R. Gowthaman, 1996: Directional Wave

Spectra Off Southeast Coast of Tamil Nadu. International Conference in Ocean

Engineering COE ’96, 254-258.

Tracy, B., Devaliere, E., Hanson, J., Nicolini, T., and H. Tolman, 2007: Wind Sea and

Swell Delineation for Numerical Wave Modeling, 10th International Workshop on Wave

Hindcasting and Forecasting and Coastal Hazard Symposium, Oahu, Hawaii.

Wang, D.W, and P.A Hwang, 2001: Evolution of the Bimodal Directional Distribution of

Ocean Waves. Journal of Physical Oceanography, 31, 1200-1221.

Young, I.R. 1994: On the Measurement of Directional Wave Spectra. Applied Ocean

Research 16, 283-294.