DEVELOPMENT OF VIDEO IMAGE ANALYSIS METHODS FOR ESTIMATING BATHYMETRY AND THE DIRECTIONAL WAVE SPECTRUM IN SHALLOW WATER AREAS

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Kyushu University Institutional Repository

DEVELOPMENT OF VIDEO IMAGE ANALYSIS METHODS FOR ESTIMATING BATHYMETRY AND THE DIRECTIONAL WAVE SPECTRUM IN SHALLOW WATER AREAS

Zikra, Muhamado

Department of Marine Systems Engineering, Graduate School of Engineering, Kyushu University

https://doi.org/10.15017/25191

出版情報：Kyushu University, 2012, 博士（工学）, 課程博士 バージョン：

権利関係：

DEVELOPMENT OF VIDEO IMAGE ANALYSIS METHODS FOR ESTIMATING BATHYMETRY

AND THE DIRECTIONAL WAVE SPECTRUM IN SHALLOW WATER AREAS

Muhammad Zikra

DEVELOPMENT OF VIDEO IMAGE ANALYSIS METHODS FOR ESTIMATING BATHYMETRY

AND THE DIRECTIONAL WAVE SPECTRUM IN SHALLOW WATER AREAS

A Dissertation Submitted

In Partial Fulfillment of the Requirements For the Degree of

Doctor of Engineering

By

Muhammad ZIKRA

to the

DEPARTMENT OF MARITIME ENGINEERING GRADUATE SCHOOL OF ENGINEERING

KYUSHU UNIVERSITY Fukuoka, Japan

August, 2012

DEPARTMENT OF MARITIME ENGINEERING GRADUATE SCHOOL OF ENGINEERING

KYUSHU UNIVERSITY Fukuoka, Japan

CERTIFICATE

The undersigned hereby certify that they have read and recommend to the Graduate School of Engineering for the acceptance of this dissertation entitle

“Development of Video Image Analysis Methods for Estimating Bathymetry and the Directional Wave Spectrum in Shallow Water Areas” by Muhammad Zikra in partial fulfillment of the requirements for the degree of Doctor of Engineering.

Dated: August, 2012

Thesis Supervisor:

______________________________________

Prof. Noriaki Hashimoto, Dr. Eng.

Examining Committee:

______________________________________

Associate Prof. Akinori Yoshida, Dr. Eng.

_______________________________________

Associate Prof. Yasuhiro Mitani, Dr. Eng.

i

Abstract

Since the first development of the video image measurement and analysis method in 1980 by Coastal Imaging Lab, Oregon State University, USA, similar methods have been developed and applied as a very convenient measurement tool for monitoring near-shore zones. Although the methods have been applied at some specific coastal areas, the methods have not been used for practical applications yet since the applicability and accuracy of the methods are still unclear. Therefore, it is of great importance to evaluate them with other field measurement data so as to be applied for practical purposes.

The objectives of this dissertation are to examine the applicability and accuracy of video image analysis methods through the following specific aims. The first aim is to examine the wave number inversion method for estimating shallow water bathymetry.

The second aim is to develop a new method for estimating directional wave spectra from video image data based on the Bayesian directional wave spectrum estimation method (BDM), which was originally developed by Hashimoto (1987) for in-situ measurement using wave gauges.

This dissertation consists of seven chapters. Chapter 1 gives the background information, problem identification, and the motivation and objectives of this research.

The framework of the thesis structure is also presented.

Chapter 2 presents a historical review of the development of video image measurement and analysis methods. It also describes the specification of video camera, the feature of video image, and the video image processing. The image processing involves inverse transformation method from image coordinates to real coordinates system.

Chapter 3 presents the estimation method of shallow water bathymetry using time series data of pixel brightness at an array along a cross-shore and long-shore transections in the rectified image sequences. The estimation method of shallow water bathymetry consists of the wave number inversion method, which is based on cross- spectral correlation technique (Plant et al., 2007) and the bathymetry inversion method, which is based on the wave dispersion equation. The analyzed results by the wave number inversion method showed that the method has the capability to derive wave numbers for estimating shallow water bathymetry with small root-mean-square errors especially in the area between shoreline and breaker zone.

Chapter 4 discusses the spectral analysis method applicable to the time series data of pixel brightness on video images for estimating sea surface elevation. Although the time series of pixel brightness on video images depend on not only wave slope but also other phenomena such as sea ripples, wave breaking, and sun glitter, etc., the

analyzed results showed that the wave spectra estimated from video images are in good agreement with those estimated from in-situ measurements of water surface elevation. The positions of peak frequency in both wave spectra are very close to each other

Chapter 5 describes the development of a new method for estimating directional wave spectra from video images in shallow water areas based on the BDM. The method is not only accurate but also robust in estimating directional spectra since it satisfies the two requirements, i.e., the minimization of errors and the smoothness of the energy distribution with respect to direction. A star and a polygon array designs from the pixels brightness of video images are examined to improve the accuracy of directional spectral estimation. The proposed method showed that it can estimate directional spectra successfully from pixels brightness on video images in shallow water areas. Comparative study showed that the BDM provides more suitable results than the Maximum Likelihood Method (MLM) although the MLM is the most common method in the directional spectrum analysis. The energy distribution of the directional spectra estimated by the BDM showed more peaked and concentrated energy distribution at frequency and direction.

Chapter 6 compares the directional wave spectra estimated by the proposed method with the numerically simulated ones with a third generation wave model, SWAN. The SWAN can simulate directional spectra in near-shore areas with high accuracy by taking accounts of the effects of refraction, bottom friction, nonlinear interaction, wave breaking and currents. The comparative study showed that there are good agreements between directional spectra estimated by the proposed method and the ones with the SWAN, showing almost similar energy concentration in frequency and direction of the directional wave spectra

Finally, Chapter 7 presents the conclusions from the previous chapters. The major conclusion is that the examined and proposed methods for estimating bathymetry and directional wave spectra from video images are accurate enough for practical applications.

iii

Acknowledgements

I would like to acknowledge the people that support me over the past years when I was running my study and presenting their outcomes. The first thanks goes to Professor Noriaki Hashimoto, for providing me the opportunity to continue my study with his expertise in wave fields, especially on directional wave spectra. Thank you for continuous support, guidance and assistances throughout of my research and letting me take my sweet time in Japan. Thank you to my committee members, Associate Professor Akinori Yoshida and Associate Professor Yasuhiro Mitani for their focused and thoughtful examination on my research with their valued inputs to and critiques.

I would also like to thank Dr. Masaru Yamashiro for the valuable comments and discussions on my study and especially for helping me to understand daily live in Japan which made my stay easier to get through. Thank you for your guidance, help and assistances throughout of my research. Other people that I want to mention here contributed to the work by inspiring feedback or technical support, many thanks to Mr.

Masaki Yokota, Mr. Mitsuyoshi Kodama and Mr. Kojiro Suzuki (PARI) and others whom I unintentionally forget.

I am very grateful to Coastal and Ocean Engineering Laboratory member for warm welcome and fantastic research environments during my doctoral study. I thank all Bachelor and Master Students, who indirectly inspired me to start and to complete my study at Coastal and Ocean Engineering Laboratory.

I acknowledge DIKTI and Kyushu University research fund for making this research financially possible. As staff members of the Ocean Engineering Department, Sepuluh Nopember Institute of Technology (ITS), Indonesia, I would like to appreciate their continuous supports.

Finally, thank to my parents for their encouragement and my wife (Rosita) for a great support and continuous inspiration during my doctoral study. I also would pay tribute to our kids, Jundullah and Mazaya, who had to deal with a father who was often come home late or absent because travelling.

Muhammad ZIKRA Fukuoka, July 2012

Table of Contents

Abstract... i

Acknowledgements ... iii

List of Symbols... vii

List of Tables ... viii

List of Figures... ix

Chapter 1 ... 1

Introduction ... 1

1.1 Background... 1

1.2 Problem Identification ... 2

1.3 Aim of the Study ... 3

1.4 Outlines of the Study ... 4

Chapter 2 ... 5

Video camera system ... 5

2.1 Introduction ... 5

2.2 Camera Instrument for Hasaki beach ... 6

2.3 Standard Image ... 8

2.4 Image Processing... 10

Chapter 3 ... 13

Analysis of wave number using video images to study shallow water bathymetry ... 13

Abstract... 13

3.1 Introduction ... 14

3.2 Study Area ... 15

3.3 Basic Theory... 17

3.3.1 Near-shore Zone Description ... 17

3.3.2 Linear Wave Theory... 17

3.3.3 Inversion of Wave Number ... 20

3.3.4 Inversion of Bathymetry... 22

3.4 Results ... 23

v

3.4.1 Timestack Image ... 23

3.4.2 Wavenumber results ... 25

3.4.3 Bathymetry results... 27

3.5 Conclusions ... 30

Chapter 4 ... 31

Spectral analysis of pixel brightness on video images for wave analysis at Hasaki beach ... 31

Abstract... 31

4.1 Introduction ... 32

4.2 Basic Theory... 33

4.2.1 Spectral Analysis ... 33

4.2.2 Transfer Function ... 36

4.3 Data Analysis... 37

4.4 Rectification Image Analysis ... 40

4.5 Results ... 41

4.5.1 Spectral Analysis ... 41

4.5.2 Wave Spectra... 46

4.6 Conclusions ... 52

Chapter 5 ... 53

Analysis of the directional wave spectrum in shallow water waves using video images ... 53

5.1 Introduction ... 54

5.2 Basic Theory... 55

5.2.1 Directional Wave Spectrum Estimation ... 55

5.2.2 Extended Maximum Likelihood Method (EMLM)... 56

5.2.3 Bayesian Directional Method (BDM) ... 57

5.2.4 Numerical Computation of BDM ... 60

5.3 Results and Discussions ... 61

5.3.1 Directional wave spectrum ... 61

5.3.2 Evolution of directional spreading ... 65

5.4 Conclusions ... 69

Chapter 6 ... 71

Comparison of directional wave spectra derived from video images data with SWAN wave model ... 71

Abstract... 71

6.1 Introduction ... 72

6.2 Model description of SWAN... 73

6.3 Model Details ... 74

6.4 Results of SWAN computations... 78

6.5 Conclusions ... 84

Chapter 7 ... 85

CONCLUSIONS... 85 References

Appendixes

vii

List of Symbols

Roman symbols

a : smoothing weight

c : wave celerity

cov : covariance

f : focal length

f : frequency

g : gravitational acceleration

h : water depth

k : wavenumber

n : step-size

s : spreading parameter

t : time

u : horizontal image coordinate

u : horizontal velocity

u : hyperparameter

v : vertical image coordinate

v : vertical velocity

x : horizontal cross-shore field coordinate y : horizontal longs-shore field coordinate z : vertical field coordinate

z : water level

E : wave energy

E(X) : expected value of X

G : directional spreading

Hn : transfer function

Hrms : root mean square wave height

Hs : significant wave height

I : pixel intensity profile

J : Jacobian

L : wavelength

R : correlation coefficient

S : spectrum

T : wave period

Tp : wave peak period

Greek symbols

γ : correlatoin coefficient

δ : horizontal field of view

η : surface elevation

θ : angle of wave incidence

µ _{: mean}

π : pi = 3.1416

σ : standard deviation

τ : camera tilt

∆ : difference

ϕ : camera azimuth

ω : angular frequency

Φ : cross spectral

ε ^{: error}

List of Tables

Tabel 3. 1 Coherence and RMS Errors Wave numbers ...26

Table 4. 1 Snapshot images data collected on calm condition...39

Table 4. 2 Snapshot images data collected on moderate conditions ...39

Table 5. 1 Mean direction and spreading index outside and inside breaking wave ...67

Table 6. 1 Nested grid were used in WAM model ...75

Table 6. 2 Boundary conditions for SWAN computations ...78

Table 6. 3 In-situ data along HORS pier ...79

ix

List of Figures

Figure 2.1 Location of Argus station over the world...5

Figure 2.2 Example of video co-ordinate system at Miyazaki, Japan...6

Figure 2.3 Location of the Hasaki site...7

Figure 2.4 Research building at HORS; (b) Hasaki beach around HORS pier and (c) HORS pier. ...7

Figure 2.6 Snapshot image ...9

Figure 2.7 Time exposure image ...9

Figure 2.8 Panaramic image ...10

Figure 2.9 Relation between image coordinates (u, v) and real world coordinates (x, y, z) ...10

Figure 2.10 Rectified image (right) from snapshot image (left) ...12

Figure 2.11 Scale distortion result from rectification of snapshot image...12

Figure 3. 1 Study area ...15

Figure 3.2 Wave data record from NOWPHAS for significant wave height (thick lines/black lines) and wave period (thin lines/blue lines). Gray areas indicate storm/typhoons event during wave record at Hasaki beach. A) August, b) September, c) October, d) November and e) December 2006. ...16

Figure 3.3 Typical beach profiles and terminology (Sorensen, 1991) ...17

Figure 3.4 Definition of sinusoidal progressive wave (CEM, 2010) ...18

Figure 3.5 Rectified image from snapshot image on 25/08/2006 at 07.00 around pier area with five cross-shore arrays and twelve long-shore arrays (shown with dots pixel) ...24

Figure 3.6 Timestack images along alongshore array at x = 285 m (left) and x = 185 m (middle). Right figure is for cross-shore timestack at y = 120 m. The speeds of the shoreward progression of waves are calculated by using the slope of the traces of wave crests as shown in images above. Unfortunately, for alongshore timestack at x = 285 m, the trace of wave crest can not be indentify...24

Figure 3.7 Wave number estimates using cross-spectral correlation from snapshot image at 25/08/2006...25

Figure 3.8 (Left figure) Comparison of wave numbers estimated from video images (dot) and wave numbers from linear theory (line). Data represent from frequency 0.09 Hz. Correlation coefficient between wave number estimated and “true” wave number is 0.93. ...26

Figure 3.9 Map of wave numbers estimate and direction ...26

Figure 3.10 Bathymetry inversion result from video images at 25 August 2006 (top) and error prediction (bottom) ...28

Figure 3.11 Comparison between cross section profile in situ survey (dash line) and bathymetry inversion (solid line) from video images collected on August 2006 ...28

Figure 3.12 Time series of depth profile estimated at y = 200 m from September to December 2006 along Hasaki beach using video images...29

Figure 4.1 Overlapped-segmented-averaging procedure in spectral analysis (Percival and Walden, 1993) ...35

Figure 4.2 Snapshot images at Hasaki pier during calm condition ...38

Figure 4. 3 Snapshot images at Hasaki pier during moderate condition ...38

Figure 4.4 Snapshot images at Hasaki pier after a storm event ...38

Figure 4. 5 Rectified images from snapshot images around pier area...40

Figure 4.6 Example of time series on 18/8/06 09.00 at x = 230 m (outside breaking area). Example time series of wave profile from wave gauges with sampling frequency of 0.5 Hz (thick line) and time series of pixel brightness on video images with sampling frequency of 1.0 Hz (thin line) ...41

Figure 4. 7 Auto spectra of signal from video image (thin line) and wave gauge (solid line) on 18 August 2006 at 09.00...43

Figure 4.8 Auto spectra of signal from video image (thin line) and wave gauge (solid line) on 9 October 2006 at 15.00 ...43 Figure 4.9 Estimated squared coherence function on 18 August 2006 at 09.00. Horizontal solid

line indicated the 90% confidence level ...44

Figure 4. 10 Estimated squared coherence function on 9 October 2006 at 15.00. Horizontal solid line indicated the 90% confidence level...44

Figure 4.11 Transfer gain between signal from image and wave gauge on 18 August 2006 at 09.00...45

Figure 4.12 Transfer gain between signal from image and wave gauge on 9 October 2006 at 15.00...45

Figure 4.13 Examples of raw spectrum (top) and smoothed spectrum (bottom) from pixel brightness on video images...47

Figure 4.14 Comparison of wave spectrum from video images and in-situ sensor recorded on 18 August 2006 at 09.00 h...48

Figure 4.15 Time series of wave spectra estimated from video images and in-situ sensor on 18 August 2006...49

Figure 4.16 Time series of single peak frequency, fp from video images and in-situ sensor on 18 August 2006. ...50

Figure 4.17 Time series of wave frequency spectra estimated from video images and in-situ sensor on 9 October 2006 ...51

Figure 4.18 Time series of single peak frequency, fp from video images and in-situ sensor on 9 October 2006 ...52

Figure 5.1 The directional wave spectra estimated by the EMLM and BDM for star array ...63

Figure 5.2 The directional spectra estimated by the EMLM and BDM for polygon array ...64

Figure 5. 3 Comparison of directional spreading at peak frequency for star array ...64

Figure 5.4 Comparison of directional spreading at peak frequency for polygon array ...65

Figure 5. 5 Location of directional wave spectrum (labelled A, B, C, D, E and F) observed along a cross-shore bathymetry profile estimated from video images on August 2006. ...66

Figure 5.6 Directional wave spectrum variation along a cross shore transect on Hasaki beach..68

Figure 6.1 Model domain and bathymetry for SWAN computations ...74

Figure 6.2 WAM computation area...75

Figure 6.3 WAM significant wave height of the Region, Sub 1 and Sub 2 ...76

Figure 6.4 Comparison of significant wave heights between the WAM model and observed data at Kashima Port on August 18, 2006. ...77

Figure 6. 5 Significant wave heights and wave directions computed by SWAN for 18 August 2006...78

Figure 6.6 Significant wave heights comparison for SWAN with data observations ...80

Figure 6.7 Wave spectra obtained using SWAN and data observation at three wave gauge locations, respectively. (a) 370 m, (b) 230 m and (c) 145 m. ...81

Figure 6.8 Directional wave spectrum of swell on 18 August 2006 at 09.00 h from SWAN ...82

Figure 6.9 Directional wave spectra of swell from SWAN model (left) and ...83

Figure 6.10 Normalized frequency spectrum (top) and directional spreading of swell (below) from SWAN model (thin line) and from array of pixel brightness on video images (bold line) ...83

Chapter 1

Introduction

1.1 Background

Near-shore, a region close to the shore, is an area which is characterized by a dynamic interaction between waves, current and underlying bottom bathymetry. Waves are the dominant stirring force for the littoral process in the shoreline area. Mostly, waves are generated by the action of the wind over surface water. The shape, velocity and the motion of the single water wave train are very complex processes and even more complex in real seas. The theory to describe the wave motion is well described by the linear wave theory. When the wave propagates toward the shore into shallow water, during approaching the shore wave shape, its direction, and speed may change due to the effect of shoaling, refraction and diffraction. This is marked by decreases in wave phase speed and transformations in the wave profile from a simple sinusoid to a more peaked, skewed profile. The wave transformation due to diffraction, refraction and reflection is strongly influenced by the directional wave spectra of sea waves, which represents as the wave characteristic. Therefore, the wave spectrum is the most important way of representing and studying the wave field.

Knowledge of wave characteristic information due to spatial and temporal variations of the near-shore processes is critically important for scientists and engineers to understand the physical process in this region. Wave measurement and bathymetric data are basic elements for understanding fluid dynamic and the relationship between fluid flow and bathymetry. Increased society demands on the coastal regions in most of the world have attracted significant research interest for scientists and engineers to predict more accurate wave characteristics and bathymetry as an important requirement for near-shore models.

Unfortunately, in-situ environmental measurements in surf zones are difficult to obtain because of difficult environmental conditions or locations that are inaccessible to conventional collection platforms, which make data collections

by in-situ measurement a difficult, expensive and time consuming task. In addition, in situ survey measurements have limitations on spatial and temporal resolutions.

Recently, the development of video camera systems can now provide and improve the additional capability of automated data collection. This technology can provide information of the wave field through time series of images. This image collection using the video camera can be done automatically, regularly and on a long-term basis with large spatial coverage, higher frequency sampling, low cost and easy deployment.

1.2 Problem Identification

The dynamic near-shore system is driven by energy from ocean waves propagating into near-shore domains after generation at sea. The specifications of this incident wave forcing will help to understand the dynamic process in near- shore zones. Therefore, to improve near-shore knowledge, long-term data sets of wave characteristics are required. It was assumed that video images from video cameras can be of great help to collect wave data and bathymetric information because the near-shore is a difficult sampling environment, where breaking waves, strong currents and moving sediment make in situ measurement difficult tasks and challenging.

In the last over twenty years, remote sensing has been a logical choice to provide the necessary observations and it has advanced technology and techniques. Optical imaging, in particular, can provide large spatial coverage while simultaneously achieving fine spatial resolution, high frequency sampling, low cost and easy deployment. Optical signals in near-shore areas are especially rich. The reflected light from wave slope variation, bright intensity from breaking waves, and residual foam are easy to see and to recognize and these signals have been exploited to study near-shore processes.

Since the first development in 1980 by Coastal Imaging Lab, Oregon State University, USA, video image methods have been developed and applied into a very useful tool for monitoring coastal changes in near-shore environmental areas (Aarninkhof and Holman, 1999). These capabilities include the study of sand bar morphology (Lippman and Holman, 1989), foreshore beach slope (Plant and

Holman, 1997), wave runup (Holland and Holman, 1997, Holland et al., 1997), wave phase to estimate bathymetry (Stochdon and Holman, 2000), directional wave spectra (Holman and Chickadel, 2004) etc.

Although the methods have been applied at some specific coastal areas, the methods have not been used for practical purpose yet since the applicability and accuracy of the methods were unclear. Therefore, it is of great importance to evaluate the applicability and accuracy of the video image measurement and analysis methods with another field measurement data for the methods to be applied for practical purposes. The objectives of this dissertation are to examine the applicability and accuracy of the video image analysis methods through the following specific aims. The first aim is to examine the wave number inversion method for estimating shallow water bathymetry. The second aim is to develop a new method for estimating directional wave spectra from video image data based on the Bayesian directional wave spectrum estimation method (BDM), which was developed by Hashimoto (1987) for in-situ measurement using wave gauges.

1.3 Aim of the Study

This dissertation describes a research using video image methods to estimate bathymetry and to derive directional wave spectra in the shallow water area. The specific objectives of the study to achieve this goal are:

1. To examine the wave number inversion method for estimating shallow water bathymetry, and to evaluate the accuracy of the results with field measurements data.

2. To develop a new method for estimating directional wave spectra from pixel brightness on video images using Bayesian Directional Method (BDM) developed by Hashimoto (1987).

3. To compare the directional wave spectra of video images and to verify the validity with the numerical model of SWAN.

1.4 Outlines of the Study

This dissertation contains seven chapters. Chapter 1 gives the background information, problem identification and the objectives of this research work.

Chapter 2 presents the development of video image methods in Japan. Chapter 3 describes an application of video image data to study shallow water bathymetry at Hasaki beach area in Ibaragi prefecture, Japan. Chapter 4 discusses the spectral analysis method applicable to the time series data of pixel brightness on video images for estimating sea surface elevation. Analysis of directional wave spectrum in shallow water using groups of pixel brightness on video images is presented in Chapter 5. Comparisons for directional wave spectra at shallow water areas between the SWAN model and video image method are reported in Chapter 6. Finally, the conclusions from the previous chapters are presented in Chapter 7.

Chapter 2

Video camera system

2.1 Introduction

The video program was first initiated by the Coastal Imaging Lab of Oregon State University (USA) under the guidance of Prof R. Holman, known as Argus system. Since 1992, the Argus system has been improved and developed continuously for the purposes of studying coastal processes in the near-shore. In addition, approximately more than 30 monitoring stations are running worldwide now, including in Japan (Holman and Stanley, 1991).

Figure 2.1 Location of Argus station over the world

Generally, an Argus monitoring station typically consists of five video cameras, spanning a 180⁰ view and full covering about 4 to 6 kilometers of beach area which depends on the elevation and the length of the camera lenses.

Unmanned, automated video stations guarantee the collection of video data at sites of scientific interest. The cameras are mounted on high locations along the coast and connected to a computer on site that has internet connection to communicate with the outside world. Data sampling is usually measured hourly

during the day and continues during rough weather conditions although any schedule can be specified.

At every Argus site, the orientation of the x-axis is shore normal, with the positive x-axis pointing in the seaward direction. The y-axis is directed perpendicular to the x-axis, such that the co-ordinate system thus obtained is positive in a mathematical sense (see Figure 2.2). The latter means that the rotation from the x-axis towards the y-axis indicates the counter-clockwise or positive turning direction. The vertical reference level (z = 0) is generally set to match the mean tidal level or a commonly used (often national) ordinance level (like NAP in the Netherlands). All Argus processing is performed in the GMT time frame.

Figure 2.2 Example of video co-ordinate system at Miyazaki, Japan

2.2 Camera Instrument for Hasaki beach

This research was achieved with camera video observation from Hasaki beach, Japan. In general, Hasaki beach is known as a straight sandy coast stretching from north to south with length around 17 km long, which is located on 120 km east of Tokyo facing the North Pacific Ocean as shown in Figure 2.3.

Figure 2.3 Location of the Hasaki site

(a) (b)

I

Figure 2.4 Research building at HORS; (b) Hasaki beach around HORS pier and (c) HORS pier.

At Hasaki site, the video camera system was first installed by Port and Airport Research Institute (PARI) on August 16, 2006. The data sets of video images were collected from single camera network Canon VB-C50iR (as shown in Figure 2.5) on 10 m height above ground level to generate images with resolution 640 x 480 pixels (Suzuki and Yanagishima, 2009). In this video camera system, snapshot images were collected at interval s of 1 second every hour using a single camera.

2.3 Standard Image

Two types of images are collected from the digital video camera every hour, which consist of a snapshot and time exposure images. Firstly, the snapshot image serves as simple documentation of the ambient conditions but offers little quantitative information as shown in Figure 2.6. Every daytime hour, snapshot images are collected and averaged over a period of 10 minutes, yielding time- exposure images as shown in Figure 2.7.

These time exposure images provide us with much more information.

These ten minute time exposure of the near-shore wave field average out natural modulations in wave breaking to reveal a smooth pattern of bright image intensities which are a proxy for the underlying, submerged sand bar topography (Lippmann & Holman, 1989 and Van Enckevort & Ruessink, 2001). Time exposure image also ‘remove’ moving objects such as ships, vehicles or people from the camera field of view.

Canon VB-C50iR Resolution: 640 x 480 Pan: +/- 170^o 1-90^o /sec Tilt: -90^o/10^o 1-70^o /sec

Figure 2.5 Canon VB-C50iR

Figure 2.6 Snapshot image

Figure 2.7 Time exposure image

Merged images can be obtained by the rectification of simultaneously collected images from all cameras, giving plan view or panoramic image of near- shore area as shown in Figure 2.8 below.

Figure 2.8 Panaramic image

2.4 Image Processing

Quantification of video image features requires accurate geo-referencing to convert image coordinates (u, v) to the corresponding real world coordinates (x, y, z) as shown in Figure 2.9.

Figure 2.9 Relation between image coordinates (u, v) and real world coordinates (x, y, z)

The relation between image and real world coordinates is defined by means of the camera location (x_c, y_c, z_c), the camera orientation through three camera angles, namely the tilt (τ ), azimuth (φ) and roll (σ ) and the effective focal length f which directly relates to the camera horizontal field of view (δ ^).

The angles τ represent the rotation with respect to the vertical z-axis, the angles φ represent the orientation in the horizontal xy-plane and the angle σ  represent of the focal plane with respect to the horizon (Holland et al., 1997).

The transformation of real world coordinates to image coordinates can be expressed by mean of the co-linearity equations:

1 2 3 4

9 10 11 1

L x L y L z L u L x L y L z

+ + +

= + + + (2.1)

and

5 6 7 8

9 10 11 1

L x L y L z L v L x L y L z

+ + +

= + + + (2.2)

The coefficients L1 to L11 are linear functions of the camera orientation (τ ^,φ^,σ ), camera position (xc, yc, zc) and the effective focal length f. The inverse transformation from image to real world coordinates results in two equations with three unknown parameters (x, y, z). In this transformation, the z-coordinates are assumed to match a certain horizontal reference level such as the tidal water level.

The result of rectification image from snapshot image and spatial resolution of rectified image are shown in Figure 2.10 and Figure 2.11, respectively.

Figure 2.10 Rectified image (right) from snapshot image (left)

Figure 2.11 Scale distortion result from rectification of snapshot image

Chapter 3

Analysis of wave number using video images to study shallow water bathymetry ¹

Abstract

A video camera monitoring system has been installed in Japanese coastal areas by Port and Airport Research Institute for the purpose to study nearshore coastal processes. This video camera system can provide information of the shoreward propagation of waves using the time series of pixel brightness on video image data which were collected at cross-shore or longshore array. From the intensity of the pixel brightness data, we can measure the wave speed or wave number. Then the local water depth is inferred from the wave dispersion equation. In this chapter, the cross-spectral correlation approach has been used to estimate wave numbers from video image data. This approach is based on arrays of pixel brightness analysis that utilizes a non linear inverse method Levenberg-Marquardt to invert the image data into the wave number estimate. The result indicated that the cross- spectral correlation approach have the capability to derive wave number estimates from multiple array of pixel brightness intensities for estimating bathymetry. The method provides reasonable accurate depth estimates near shoreline and breaking areas through bathymetry inversion.

1 An edited and slightly adapted version of this chapter was presented and published at following publications

Zikra, M., Hashimoto, N., Yamashiro, M and Suzuki, K, (2010). Monitoring Nearshore Bathymetry from Remote Sensing of Video Images Using a Non-Linear Inversion Method, Proceedings of International Symposium on Earth Science and Technology, CINEST, pp.107-112.

Zikra, M., Yamashiro, M,, Hashimoto, N and Suzuki, K, (2010). Analysis of Wavenumber Using Video Images to Study Nearshore Bathymetry, Proceedings of International Session in Conference on Coastal Engineering, JSCE, Vol. 1, pp.66-70.

Zikra, M., Yamashiro, M., Hashimoto, N and Suzuki, K, (2010). Bathymetry Inversion Using Video Image in Shallow Water, Annual Journal of Civil Engineering in the Ocean, JSCE, Vol. 26, pp.1161-1166.

3.1 Introduction

Bathymetry information is very important for a variety of coastal engineers to understand the coastal process in near-shore areas. Some near-shore activities like recreation, fishing, navigation, beach nourishment and dredging require the knowledge of bathymetry. Good quality bathymetry information is hence required in order to identify correctly the physical processes that are taking place. However, the combination of traditional in situ survey method and advanced techniques such as global positioning system and modern ship vehicles are time consuming and expensive, especially in shallow coastal water where survey swaths are narrow.

Recently, the development of the video camera systems now can provide and improve the additional capability of automated data collection. This technology can provide information of the shoreward of wave. This automated image collection using the video camera has much greater range of time and spatial scales. Also, this technology is suitable for hazardous coastal areas such as surf zone areas, where the operations of ship vehicles have limitations on the maneuver.

Some methodologies have been proposed to estimate bathymetry in near- shore areas by establishing the relationship between wave characteristics derived from video image sequences and known water depth. The underlying methodology to extract wave characteristic problem from video images has taken on numbers of different forms. Theseinclude finding wave celerity from the time series of cross-shore pixel brightness intensity using cross-spectral scheme (Stockdon and Holman, 2000) and determining the wave phase speed from the coastal video observation system using cross-correlation analysis technique (Zikra, 2008) as opposed to the cross-spectral technique developed by Stockdon and Holman (2000). Both methodologies above are designed to extract wave speed component at selected frequency from video imagery. However, the wave phase speed estimates near shoreline and at the location where the wave signal changes significantly due to the presence of wave breaking was poorly estimated.

This problem has implication on the bathymetry estimation result derived from video images.

Thus, the objective of this chapter is to determine wave number estimates based on cross-spectral correlation technique that utilizes a non-linear inverse method for estimating bathymetry using video images. For this research, Hasaki beach as one of the beachs in Japan will be used to generate further research in the shallow water area. In the following sections, we will first review about the data conditions in Hasaki beach area. Next, we summarize mathematical formulations of the wave number model and inversion model. Finally, we examine and analyze our application model results and then draw some conclusions.

3.2 Study Area

This research was achieved with a digital video camera from Hasaki beach, Japan. Hasaki beach is located at 120 km east of Tokyo facing the North Pacific Ocean as shown in Figure 3.1. In general, Hasaki beach is known as straight sandy coast stretching from north to south with length around 17 km long.

Since 1986, many coastal studies have been conducted at this location especially around the pier, which is known as HORS (Hasaki Oceanographical Research Station).

Wave data were obtained from NOWPHAS (the National Ocean Wave information network for Port and HarbourS) wave measurement data at Kashima site location (35^o55’37” N and 140^o 44’00” E). The wave gauge is located in 22 m water depth. Wave data records from NOWPHAS are presented in Figure 3.2.

During 2006, the yearly average significant wave height (H1/3) is about 1.06 m with a corresponding wave period (T1/3) of 8.4 seconds. In normal condition, waves approach the coast most often from the East and South East directions. The average of the tidal range is about 1.60 m

Figure 3. 1 Study area

Figure 3.2 Wave data record from NOWPHAS for significant wave height (thick lines/black lines) and wave period (thin lines/blue lines). Gray areas indicate storm/typhoons event during wave record at Hasaki beach. A) August, b) September, c) October, d) November and e) December 2006.

3.3 Basic Theory

3.3.1 Near-shore Zone Description

The area of interest in this subject is that segment of the coast located between the offshore point where shoaling waves begin to move sediment and the onshore limit of active marine processes. This zone is known highly dynamic region, which characterized by a dynamic interaction between waves, current and bottom bathymetry. Coastal profile measured normal to the shoreline over the zone of active coastal processes are of great importance to coastal engineering studies for understanding and quantification of coastal zone processes and the related interaction of coastal structures with these processes. A typical idealized coastal profile is shown in Figure 3.3.

Figure 3.3 Typical beach profiles and terminology (Sorensen, 1991)

3.3.2 Linear Wave Theory

Waves are the dominant stirring force for the littoral process at the shoreline. Mostly, waves are generated by the action of the wind over surface water. The shape, velocity and the motion of water of single water wave train are very complex process and even more complex in realistic sea state. The most elementary wave theory is the linear first-order wave theory (also called small- amplitude or Airy wave theory), and this theory is widely used in coastal engineering and design because it can be applied with ease whilst giving a reasonable approximation of wave characteristics for a wide range of wave parameters.

A simple, sinusoidal progressive wave passing a fixed point in the ocean can be represented by the horizontal spatial coordinates x and time t as shown in Figure 3.4. The following wave parameters are used to describe a simple sinusoidal oscillatory wave:

x – horizontal spatial coordinates t – time

θ – phase, θ=kx−ωt k – wave number, k = 2 / Lπ

ω – angular or radian frequency, ω=2 / Tπ

L– wavelength: horizontal distance between corresponding points on two successive waves

T – wave period: time interval between two successive crests at a given point a – amplitude

H – wave height: vertical distance to its crest from the preceding trough η– elevation of the water surface



d – water depth

Figure 3.4 Definition of sinusoidal progressive wave (CEM, 2010)

Because the wave motion is assumed to be periodic form when

propagating over a horizontal bottom in the x direction, the wave number, k = 2π /L is used to ensure that sinusoidal wave repeat itself over distance L,

wavelength. For periodicity in time, which required that the wave repeat itself

every T seconds is defined as the radial frequency,σ =2 / Tπ , where T denotes as the wave period or the time interval between the passage of two successive wave crests or troughs at a given point. Finally, the phase speed or wave celerity which the speed at which the wave from travels is defined as

c k

=σ (3.1)

As requirement of linear wave theory, the wavelength and period of the wave are related to the water depth by dispersion equation,

2 gktanhkh

ω = (3.2)

Where g is the acceleration of gravity and h is the local water depth. From equation (3.1) and (3.2) the celerity of wave based on linear wave theory is

g tanh

c kh

k σ

= =σ (3.3)

When the wave propagate toward to the shore into shallow water, during approaching the shore the wave shape, direction, and speed may change due to effect of shoaling, refraction and diffraction. The wavelength decreases when the depth decreases, which is consequence of dispersion relation. The wave period is fixed, the wavelength and the wave speed decrease as the wave moves into shallow water. For a long crested wave travelling over irregular bottom depth, the change in wave speed along the wave crest implies that the wave changes direction locally or it refract. The simplest representation of wave refraction is the refraction of wave propagating obliquely over straight and parallel offshore bathymetry. In this case, Snell law is valid which is related with the wave direction and the wave speed in one water depth to that in deep water

sin

sin _o

c co

θ

θ _{= =}

constant (3.4)

Another effect of change in wavelength in shallow water is that the wave height increases. This is a consequence of conservation of energy and the decrease in group velocity in shallow water in concert with decrease in c.

3.3.3 Inversion of Wave Number

The estimation of wave celerity, c (or, equivalent to wave number, k) is determined by using nonlinear inversion method related to the cross-spectral correlation as proposed by Plant et al., (2007). We assume that time delay information is available from the spatially separated pixels such that

(

) (

)

I x y t =I x y t+ ∆t (3.5)

In 1-Dimension (x-direction), time delay equation can be expressed as described by Bendat and Piersol (1986)

( [ ] )

[ ] ( [ ] ) ^{[ ]}

, ,

cos cos

xj n xj n n

i j n

xi xi

n n

x x k x

t dx dx

c x f

α α

∆ =

∫

∫

where α_n is the direction of the nth wave component, fn is wave frequency and cn is the celerity of the wave component. The wave field can be described in discrete spatial domain, with spacing, ∆_x and then the discrete time delay equation becomes:

( [ ] ) _{[ ]}

, , 1 , ,

M cos n m

i j n m i j m n m

n

t x D x k x

f α

∆ = ∆

∑

where D is design matrix defined on both the sample domain (xi, xj), and xm is the estimation of domain and α_n (wave direction) and c_n (wave celerity) as unknown model parameters.

To utilize the time delay equation with remotely sensed imagery, we first must estimate time lag, ∆_t, associated with the propagation of the visible wave signal. The time lag will differ for all sensor pairs. This requires some sort of a search for ∆_t that corresponds to a maximum in the cross correlation function (r_ij) as described by:

( ) ( ) ( ) ( )

, * , ,

i j i j

r ∆ =t W ∆t I x t I x t+ ∆t (3.8)

In which W is a band-passed filter that is convolved against the cross correlation and the angle brackets indicate an ensemble average over all observation times.

Since it is natural to work with wave processes in the frequency domain, a discrete Fourier transform is applying to the observation to compute the cross-spectra between two sensors pair.

The time delay equation can be described as:

( ) ( ) { }

~ ~

, , , * , , , exp 1 , ,

OBS

i j f i j i j f i j f

C = I x f I x f =γ − Φ (3.9)

where the tildes indicate the Fourier Transform, the asterisk indicates complex conjugate, angle brackets indicate ensemble or band averaging, γ is the coherence, and Ф is the phase shift between two sample locations xi and xj. Since the phase shift between two sensors isΦ_{i j f, ,} =2πf t∆_{i j f, ,} , replace ∆t with the right hand side of (3) and replace Ф in (5) to get a model for cross-spectral correlation equation:

( )

, , , , , ,

1

exp 2 1 cos

M MODEL

i j f i j m m f m f

m

C π x D k α

=

 

=  ∆ − 



∑

where f is wave frequency, ∆_x is spacing between pixels, D is design matrix defined on both sample domain (x_i, x_j), α (wave direction) and k (wave number) as unknown model parameters.

The sample design matrix, D is designed as basis function:

, , ,

' j

i j m i m

i i

D a

=

=

∑

where a_i,m is smoothing weight of Hanning filter

( )

{ }

, ,

(_{i m}) 1 cos 0.5 1 _{i m} a r = − π^ +r ^

1 ,

i m i m x

r = x −x L⁻

(3.12)

where Lx is smoothing lengths scale. Using observation data from timestack images, cross-spectral observation data can be acquired by applying discrete Fourier transform to the observation to compute the cross-spectral between two pixels (sensors pair) (Bendat and Piersol, 1986).

( ) ( )

~ ~

, , , * ,

OBS

i j f i j

C = I x f I x f (3.13)

where the tildes indicate the Fourier transform, the asterisk indicates complex conjugate, angle brackets indicate ensemble or band averaging.

When the wave number is nonlinearly related to the cross-spectral correlation, a non-linear inversion method Levenberg-Marquardt (LM) (Press et al., 1992) is used to minimize the weighted squared difference between successive estimated of the model and the observations:

{

}

, , , , , , , ,

MODEL OBS

i j f i j f i j f i j f

C^τ γ C ^τ C

∆ = − ^(3.14)

where, at each iteration τ, the model-observation mismatch is weighted by the observed coherence, γ_i,j,f. An iterative procedure starts with an initial valuek^o_{f m,} and new estimate of wave number model are obtained using:

1

, , ,

f m f m f m

k^τ+ =k^τ + ∆k^τ (3.15)

where the variation ∆k^τ_{f m,} calculated from

( )

, , ,

T T

f m i j f

k^{τ }R^τ R^τ λ^τI ^{− }R^τ C^τ

∆ =   +   ∆ (3.16)

where λ^τ is the damping parameter, I is the identity matrix and R is sensitivity matrix for the cross-spectral correlation as describe:

( )

, , 1 , , ^MODEL, , i j f i j m i j f

R^τ =γ − D C ^τ ∆x ^(3.17)

The iterative procedure of sequentially calculating ∆k^τ_{f m,} and k^τ_{f m,}⁺¹ from Eq. (3.15) and (3.16) is continued until the convergence criterion ∆k^τ_{f m,} <ε is satisfied, where ε in this model is 10^-6.

3.3.4 Inversion of Bathymetry

The bathymetry inversion method based on timestack method computes water depth by relating wave number parameters k using a suitably accurate dispersion equation. Water depth h is related to local wave number k and frequency f through the dispersion relationship in the linear wave theory (Dean and Dalrymple, 1991)

(

)

where g is gravitational acceleration and h is local water depth.

Given a value for f (sample wave frequencies) and an initial depth, h, this equation can be solved iteratively for wave number. The Levenberg-Marquardt non-linear inverse method (Press et al., 1992) was used again to minimize error between the wave number predicted by Eq. 3.18 and the wave number estimated form images derived from Eq. 3.15.

3.4 Results

3.4.1 Timestack Image

Besides snapshot and time averaged images, data sampling schemes can be designed such to collect the time series of pixel brightness on video images.

Waves and flow characteristics can be derived from this time series, because strong correlation is commonly observed between a time series of pixel brightness intensities and the wave height signal obtained from a wave gauge at the same location as investigated by Lippmann and Holman (1991).

In this image analysis, the procedures consist of image rectification and timestack image analysis in which the main aim is to obtain physical information from images. In Hasaki site, the camera took successive snapshot images around Hasaki pier at the interval of 1 second. To extract pixel brightness time series from successive images, firstly, the image coordinates of pixel (u, v) on the snapshot image need to be converted to the real coordinate system (x, y, z). In this rectification, the relationship between the image coordinate and real coordinate as described by Holland et al., (1991) was used. The result of the rectification image from snapshot image is shown in Figure 3.5.

In this approach, time series of pixel brightness intensities can be sampled along a cross-shore or alongshore array on rectification images. Then timestack images were collected hourly at each point in the array which can be expressed as I (x_i, y_i, t), where x_i, y_i are the spatial coordinate of the image pixel, i^th and t are discrete sampling times. An example of time stack images for cross-shore array at y = 120 m and for alongshore array at x = 185 m and x = 285 m are presented in Figure 3.6.

From the figure 3.6 shows that the dark, slightly curved patterns represent individual waves propagating onshore. The slope of the wave traces can be used to determine the approximate speed of the shoreward progressing waves, before these are dissipated through wave breaking at the shoreline (Aarninkhof, 2003).

From these time series of pixel brightness intensities, the shoreward propagation of waves can be measured to estimate near-shore bathymetry.

Figure 3.5 Rectified image from snapshot image on 25/08/2006 at 07.00 around pier area with five cross-shore arrays and twelve long-shore arrays (shown with dots pixel)

Figure 3.6 Timestack images along alongshore array at x = 285 m (left) and x = 185 m (middle).

Right figure is for cross-shore timestack at y = 120 m. The speeds of the shoreward progression of waves are calculated by using the slope of the traces of wave crests as shown in images above.

Unfortunately, for alongshore timestack at x = 285 m, the trace of wave crest can not be indentify.

3.4.2 Wavenumber results

Using timestack data collected on August 25, 2006, the wave number estimate was computed at a series of wave frequencies ranging from 0.08 Hz to 0.11 Hz. It is expected to find a suitable frequency from those wave frequency resolutions; the optimum wave component will give strong signal for time series analysis of pixel brightness on video images. On this date, the peak wave period based on field measurement was 9.1 seconds; the wave direction was approach from 81 degrees from North direction; and the significant wave height was 1.11 m.

Using the measured bathymetry and the tidal level at the time of the image collection, the wave number estimate was computed for each frequency. The non- linear inversion method of Levenberg-Marquardt was applied to the sample cross- spectral correlation at each frequency over the entire array. Figure 3.7 shows the results of the wave number estimates for each sample frequency. The best of wave number estimates were obtained at frequency 0.09 Hz that showed highest coherence with rms error 0.0342 m^-1 as shown in Table 1. This frequency (f = 0.09 Hz) corresponds with the peak period based on field measurement as shown in Figure 3.8.

Figure 3.7 Wave number estimates using cross-spectral correlation from snapshot image at 25/08/2006

Tabel 3. 1 Coherence and RMS Error Wave number

No Frequency Coherence RMS wave number error

1 0.08 128.745 0.0358

2 0.09 132.153 0.0342

3 0.10 131.161 0.0354

4 0.11 118.333 0.0421

Figure 3.8 (Left figure) Comparison of wave numbers estimated from video images (dot) and wave numbers from linear theory (line). Data represent from frequency 0.09 Hz. Correlation coefficient between wave number estimated and “true” wave number is 0.93.

Figure 3.9 Map of wave numbers estimate and direction

3.4.3 Bathymetry results

The result of the depth inversion method based on timestack data by relating wave number parameters using a suitably accurate dispersion equation is presented in Figure 3.10. The average of bathymetry estimate by inverted all frequencies shows that the Hasaki beach has a sand bar at x = 200-250 m. At near shoreline and wave breaking area, the bathymetry estimate is accurate with small errors.

To evaluate the bathymetry inversion model, the result is compared to the survey measurement data. The evaluation of the bathymetry inversion model was tested using the image data collected on August 2006. Figure 3.11 shows a comparison between measured beach profile and mean estimated profile from video images at y = 200 m. Figure 3.11 also indicates that the region around x = 250 m is associated with the slope break before the shoreface of wave will start to break. Then waves will break again near shoreline around x = 150 m. Estimation of water depth were varied in these regions which shown by positive and negative difference errors in the Figure 3.11. It shows that the performance of bathymetry inversion is the most accurate near shoreline and sand bar, where the differences between estimated and survey water depth is less than 10-30 cm.

Meanwhile, for the seaward direction (x > 270 m) the estimation of bathymetry shows large errors with positive difference error around 1.5-2 m.

Large errors which were found outside the breaking area seem related to poor information on the alongshore timestack image (at x = 285 m) as shown in Figure 3.6 (left image) which causing poor water depth estimate result on the model. This poor information of wave signal on alongshore timestack is likely attributed to the limitation of the camera system where performance of video imaging of waves is degrading with increased distance from the camera and with viewing angle. As the result, the pixel resolution of image rectification will decrease as the consequence of increasing distance of the camera.

Based on the calibration result, the model was used more extensively to monitor long-term observation of bathymetry evolution along Hasaki beach as shown in Figure 3.12. Figure 3.12 shows that the sand bar was eroded and changed due to several typhoons that attacked Hasaki beach during 2006 as shown in Figure 3.2.

Figure 3.10 Bathymetry inversion result from video images at 25 August 2006 (top) and error prediction (bottom)

Figure 3.11 Comparison between cross section profile in situ survey (dash line) and bathymetry inversion (solid line) from video images collected on August 2006

Figure 3.12 Time series of depth profile estimated at y = 200 m from September to December 2006 along Hasaki beach using video images

3.5 Conclusions

An algorithm for video images sequence analysis was presented to monitor bathymetry in shallow water areas using non-linear inversion method to convert pixel brightness values into depth estimates. The method consists of the wave number inversion model, which is based on cross-spectral correlation technique and bathymetry inversion which is based on the wave dispersion equation. The capability of the video image technique was tested using data from Hasaki beach in Japan from August 2006 to December 2006.

The results indicate that cross-spectral correlation approach has the capability to derive wave number estimate from time series of pixel brightness intensity to estimate bathymetry. The model showed relatively small rms errors between 0.0342-0.0421. The correlation coefficient between the estimated wave number and that from linear wave theory is 0.93.

The result of shallow water bathymetry estimates provides reasonably accurate depth estimates near shoreline and breaking areas with rms 0.44. This result indicates that near-shore bathymetry estimates can be derived from video image sequence. Meanwhile, the large errors which found outside breaking area were mainly associated with poor information of wave signal on timestack in outside breaking areas.

By using optical remote sensing of video image, the evolution of near- shore area can be assessed and monitored periodically for long period with very cheap cost compared to the traditional measurement method.