DOCTORAL DISSERTATION

Investigating tidal evolution and tide–river runoff
interactions in a two-inlet lagoon and multi-channel
estuary㸦 ࡘࡢධཱྀࢆᣢࡘࣛࢢ࣮ࣥ࡜࣐ࣝࢳࢳࣕࢿࣝἙཱྀ࡟࠾
ࡅࡿ₻ộ㐍໬࠾ࡼࡧ₻ộ࡜Ἑᕝὶฟࡢ┦஫స⏝࡟㛵ࡍࡿㄪᰝ◊✲㸧

July 2022

Department of Civil and Environmental Engineering
Graduate School of Engineering
Hiroshima University

KHADAMI, FARUQAcknowledgement

The members of my supervisory committee deserve the best accolades and my deepest
thanks for their expertise, encouragement, and support. First, I would like to thank mysupervisor, Prof. Kawanishi, for his excellent guidance, support, and patience during my
doctoral studies at Hiroshima University.
I would like to express my sincere appreciation to Nakashita sensei for his help in thelaboratory and to Dr. Mohamad Basel Al Sawaf for his excellent guidance, invaluable support,
and critical science. I also thank all the laboratory members, Gillang, Xiao, Torigoe, and Hiep,for their help.
In the opportunity, I would thank the Japanese Government (MEXT) scholarshipprogram for supporting my doctoral program at Hiroshima University.
Thanks to all my friends who supported me during my time at Hiroshima. PPIHiroshima (Indonesian Student Association in Hiroshima) that introduce me to the Indonesiancommunity in Hiroshima. I also thank member group chats WA Les Bahasa for the nice talkand discussion. Many thanks to Mika for the support, understanding, and patience.
Last but not least, Special thanks to my parents, Ibuk Catur Wirononingsih and Bapak
Imron Rosyadi, who prayed a lot for me; they deserve great respect. I also thank my sisters,
Mbak Novi and Dek Tia, for their support and love.

1

Tables of Contents

Acknowledgement ..................................................................................................................... 1
Tables of Contents ..................................................................................................................... 2
List of Symbols .......................................................................................................................... 6
List of Abbreviations ................................................................................................................. 7
List of Figures ............................................................................................................................ 8
List of Tables ........................................................................................................................... 12
Abstract .................................................................................................................................... 13
Chapter 1:

Introduction ........................................................................................................ 16

1.1.

Study Overview ......................................................................................................... 16

1.2.

Literature Review ...................................................................................................... 17

1.2.1.

Tidal dynamics in lagoons ................................................................................. 18

1.2.2.

Tides in Channel network .................................................................................. 19

1.3.

Research Motivation and Objectives......................................................................... 20

1.4.

Novelties of Thesis .................................................................................................... 22

1.5.

Site Location and Research Methods ........................................................................ 23

1.5.1.

Site Location ...................................................................................................... 23

1.5.2.

Data and Methods .............................................................................................. 25

1.6.

Research Outline ....................................................................................................... 27

Chapter 2:

Tidal asymmetry in two-inlet lagoon: a case study on Segara Anakan Lagoon,

Central Java, Indonesia ............................................................................................................ 29
2.1. Introduction ................................................................................................................... 29
2.2. Data and Methods ......................................................................................................... 31
2.2.1. Data ........................................................................................................................ 31
2.2.2. Numerical Modelling ............................................................................................. 322

2.2.3. Model Validation ................................................................................................... 35
2.2.4. Asymmetry Quantification..................................................................................... 35
2.3. Results ........................................................................................................................... 36
2.3.1. Model Validation ................................................................................................... 36
2.3.2. Tidal Level and Discharge ..................................................................................... 38
2.3.3. Tidal Asymmetry ................................................................................................... 40
2.4. Discussion ..................................................................................................................... 42
2.5. Conclusions ................................................................................................................... 44
Chapter 3:

Spatiotemporal response of currents and mixing to the interactions between tides

and river runoff in a multi-channel estuary.............................................................................. 46
3.1. Introduction ................................................................................................................... 46
3.2. Study Area .................................................................................................................... 48
3.3. Materials and Methods .................................................................................................. 50
3.3.1. Data ........................................................................................................................ 50
3.3.2. Methods.................................................................................................................. 51
3.4. Results ........................................................................................................................... 53
3.4.1. General circulation of Ota River Floodway ........................................................... 53
3.4.2. Mixing .................................................................................................................... 60
3.4.3 Wavelet Analysis .................................................................................................... 62
3.5. Discussion ..................................................................................................................... 67
3.5.1. Interpretation of mixing ......................................................................................... 67
3.5.2. Interpretation of the wavelet analyses.................................................................... 68
3.5.3. Convergence Zone in the Ota River Floodway...................................................... 69
3.6. Conclusions ................................................................................................................... 71
Chapter 4:

Propagation of tidal waves in tidal-dominated multi-channel estuary............... 74

4.1. Introduction ................................................................................................................... 743

4.2. Study Area .................................................................................................................... 77
4.3. Materials and Methods .................................................................................................. 78
4.3.1. Data ........................................................................................................................ 78
4.3.2. Tidal Analysis ........................................................................................................ 80
4.3.3. Decomposition of Subtidal Friction ....................................................................... 82
4.4.

Results ....................................................................................................................... 83

4.4.1. Subtidal Variations................................................................................................. 83
4.4.2. Tidal Oscillation..................................................................................................... 85
4.4.3. Tidal Distortion and Tidal Asymmetry .................................................................. 89
4.5.

Discussion ................................................................................................................. 92

4.6.

Conclusions ............................................................................................................... 96

Chapter 5:

Sensitivity of Junction Width to Tidal Nonlinearity on Small and Shallow Tidal

Junction98

5.1. Introduction ................................................................................................................... 98
5.2. Methods......................................................................................................................... 99
5.2.1. Observation Location and Data ............................................................................. 99
5.2.2. Tidal Asymmetry Analysis .................................................................................. 101
5.2.3. Numerical Experiments ....................................................................................... 102
5.3. Results ......................................................................................................................... 103
5.3.1. Water Level Nonlinearity .................................................................................... 103
5.3.2. Sensitivity Analysis ............................................................................................. 105
5.4. Discussion ................................................................................................................... 106
5.5. Conclusions ................................................................................................................. 108
Chapter 6:

Conclusions and future works.......................................................................... 110

6.1. Main conclusions ........................................................................................................ 110
6.2. Future works ............................................................................................................... 113
4

References .............................................................................................................................. 115

5

List of Symbols

Symbolsܿ

celerity of tidal wave݃gravitational acceleration݄water depthߛskewnessܳwater dischargeߟelevation of …

ܴ݅௅Richardson numberߩdensity of …

‫ݎܨ‬௙ Freshwater Froude Number‫ܯ‬

Mixing tidal efficiency‫ܥ‬஽ 

drag coefficient்ܷ amplitude of the tidal velocityܰbuoyancy frequency

ܵ଴ reference salinityܷcurrent velocityܹchannel width‫ܥ‬

Chézy coefficient6List of Abbreviations

Abbreviations
TDA

tidal duration asymmetry

PCA

peak current asymmetry

SWA

slack water asymmetry

PLW

Pelawangan West

PLE

Pelawangan East

TMD

Tidal Model Driver

NSE

Nash-Sutchliffe Efficiency

SAL

Segara Anakan Lagoon

ETM

estuarine turbidity maximum

ADCP

acoustic Doppler current profiler

FATfluvial acoustic tomography

CWT

continuous wavelet transform

XWT

cross wavelet transform

WTC

coherence wavelet transform

ODC

Ota diversion channel

HWLhigh water level

FFT

fast Fourier transform

HA

harmonic analysis

7

List of Figures

Figure 1.1 Segara Anakan Lagoon; The location of the Segara Anakan Lagoon is shown by theyellow mark in the inset map. .................................................................................................. 24
Figure 1.2 Ota River estuary; The location of the Ota River estuary is shown by the yellow
mark in the inset map. .............................................................................................................. 25
Figure 2.1 Bathymetry of the Segara Anakan Lagoon (SAL); Black dots are the tide gauge
stations, and the yellow lines are cross-sections for calculating the discharge. The red dashedline is transecting for spatial change analysis. The grey and green areas show land andmangrove areas, respectively. The computational domain is enclosed by the solid black line.
Solid red lines denote open boundaries. .................................................................................. 30
Figure 2.2 Tidal elevation during dry and wet seasons in Sleko (a, c) and Klaces (b, d). The
black lines denote the simulation results, and the red lines denote the observation data. ....... 37
Figure 2.3 Comparisons of the discharge from the model (black line) and observation data (reddots) on the dry season in Pelawangan West (a, b, c) and Klaces (d), while on the wet season
in Pelawangan West (e, f, g, h) and water exchange station (i, j, k). ....................................... 38
Figure 2.4 Twenty-four hours of the elevation (a, b) and discharge (c, d) during spring condition(a, c) and neap condition (b, d). The black solid line, red dot line, and blue dashed line aremodel results for Sleko, Klaces, and Motean stations, respectively. The spring/neap condition
was on 23 July 2005/31 July 2005. .......................................................................................... 39
Figure 2.5 Depth average velocity vector fields and water elevation (color shading) in the
Segara Anakan Lagoon on spring condition at (a) ebb tide and (b) flood tide. Red lines denotecross-section transects for calculating water volume discharge. ............................................. 40
Figure 2.6 (a) Tidal range, (b) tidal wave celerity (solid line) and bed shear stress (dashed line),and (c) Tidal Duration Asymmetry (TDA) along the red dashed line transect in Figure 2.1. . 44
Figure 3.1. Observation sites and bathymetry along the Ota River Floodway, Hiroshima City,
Japan (a). Transversal locations of the ADCPs in St. A (b), St. B (c), St. C (d). .................... 49
8

Figure 3.2. Time plots of (a) wind magnitude, (b) wind direction, (c) discharge at Yaguchi andGion stations, (d) depth-averaged velocity at St. A, St. B, and St. C, (e) salinity at St. A at thewater surface and bottom, (f) subtidal velocity, (g) temperature, and (h) density in St. A at thewater surface and bottom, and vertical profile along channel currents velocity at (i) St. A, (j)St. B, and (k) St. C. The Yaguchi Station is located around 14.6 km from the river mouth. The
wind direction is shown with north as 0ι, east as 90ι, south as 180ι, and west as 270ι. ........ 54
Figure 3.3. Temporal variation of the (a, e) surface-bottom salinity difference profile at St. A
and (b-d, f-h) velocity profiles at (b, f) St. A, (c, g) St. B and (d, h) St. C during (a-d) springand (e-h) neap conditions. Positive values indicate flood and landward currents conditions. 58
Figure 3.4. Temporal variation of (a, d) the surface-bottom salinity difference profile at St. A
and (b, c, e, f) velocity profiles at (b, e) St. A and (c, f) St. B during (a-c) low and (d-f) highdischarge conditions. Positive values indicate flood and landward currents conditions. ........ 60
Figure 3.5. Time plot of the (a) bulk Richardson number ሺ୐ ሻ and (b) Freshwater Froude
Number ( ୤ ) — Mixing tidal efficiency () .......................................................................... 61
Figure 3.6. Continuous Wavelet Transform (CWT) of depth-averaged velocity at (a) St. B and(b) St. C, (c) surface–bottom density difference, (d) river discharge. ..................................... 63
Figure 3.7. Cross wavelet transform (XWT) between currents in St. B with (a) surface–bottom
density difference and (c) river discharge. Coherence wavelet transform (WTC) between
currents in St. B with (b) surface–bottom density difference and (d) river discharge. ............ 65
Figure 3.8. Cross wavelet transform (XWT) between currents in St. C with (a) surface-bottom
density difference and (c) river discharge. Coherence wavelet transform (WTC) between
currents in St. C with (b) surface–bottom density difference and (d) river discharge. ............ 66
Figure 3.9. Estuarine parameter space, based on the freshwater Froude number ( ୤ ሻ and
Mixing tidal efficiency (). The solid red line is the condition for vertical mixing. The
estuarine classification and example estuary are adapted from Geyer and MacCready (2014).................................................................................................................................................. 68
Figure 3.10. (a) Distribution of Spring/neap peak current asymmetry vs subtidal flow. Alongchannel turbidity in (b) flood and (c) ebb conditions. ............................................................. 71
9

Figure 4.1. Observation stations and bathymetry of Ota River estuary network..................... 76
Figure 4.2. Time plot of water elevation data at (a) Kusatsu Station, (b) Gion Station, (c)Nagawaku Station, (d) Yaguchi Station, (e) Station A, (f) Station B, (g) Station C, and (h)Misasa Station .......................................................................................................................... 79
Figure 4.3. Time plot of tidal range (a, b) and subtidal elevation (c, d) of the water elevation
stations in straight (a, c) and branching (b, d) channel. The straight channel includes Gion andNagawaku Stations. The branching channels includes St. A, St. B, St. C and Misasa. Kusatsu
Station located at river mouth. ................................................................................................. 85
Figure 4.4. FFT power spectra of water elevation data in (a) straight channel, and (b) branching
channel ..................................................................................................................................... 86
Figure 4.5. (a) total amplitude of semidiurnal (D2), diurnal (D1) and quarter diurnal (D4) tidal
species, (b) Ratio of total amplitude quarter diurnal tidal species and semi diurnal tidal species,and (c) tidal duration skewness in straight and branching channel as a function of the distancefrom the river mouth. ............................................................................................................... 89
Figure 4.6. Temporal variation of (a) D2 amplitude, (b) D4 amplitude, (c) ratio of D4 and D2,(d) time duration skewness at Kusatsu, Gion. Nagawaku, St. A, B and C and Misasa stations.
.................................................................................................................................................. 92
Figure 4.7. (a) Channel width and (b) channel depth a a function of the distance from rivermouth ....................................................................................................................................... 94
Figure 5.1. Ota River channel network. ................................................................................. 100
Figure 5.2. Water elevation observation in Sts. A, B, and C (a) during the observations, (b)during neap tide, (c) during spring tide. ................................................................................. 101
Figure 5.3. a) Downstream part of the model domain, including the upstream channel and thebranch that connects to the sea. b) The grid surroundings of the tidal junction. ................... 103
Figure 5.4. Amplitude of (a, c) M2 and (b, d) M4 from the (a, b) observation data and (c, d)idealized model. ..................................................................................................................... 104
10

Figure 5.5. Amplitude of (a, c) M2 and (b, d) M4 from at (a, b) left branch and (c, d) apex ofjunction. ................................................................................................................................. 105
Figure 5.6. (left) Variation of M2 and M4 amplitude to the width of upstream channel. (right)
Variation ratio of M4 and M2 to the width of upstream channel. ......................................... 107

11

List of Tables

Table 2.1 Computation of Tidal Duration Asymmetry (TDA), Peak Duration Asymmetry(PDA), Slack Water Asymmetry (SWA), using a 25 hours window in spring and neap and 14
days. ......................................................................................................................................... 41
Table 3.1. ADCP settings and deployment .............................................................................. 50
Table 4.1. ADCP settings and deployment .............................................................................. 79
Table 4.2. Harmonic analysis of the water elevation data in Kusatsu, Gion, Nagawaku, St. A,
St. B, St. C and Misasa ............................................................................................................ 88
Table 4.3. Correlation value subtidal water level in St. A, B and C with subtidal friction in termof subtidal flow (Fr), tidal-subtidal interaction (Frt), tidal asymmetry (Ft)............................. 95
Table 5.1. Parameter setting of idealized junction model ...................................................... 102

12

Abstract
Understanding hydrodynamics induced by an interaction between tide and river flow isessential to continuously improve the management of delta and estuarine systems. The
investigation of the interaction between tides and river flow could also enhance ourunderstanding of the alteration process of the environment in tidal rivers. This research
investigates the spatiotemporal tidal dynamics in various setting topography, aiming tounderstand the evolution of tidal waves in single-channel, multi-channel and multi-inlet
lagoons. The work was divided into two main projects that worked in two site locations: theSegara Anakan Lagoon and the Ota River Estuary.
The first work aims to investigate the tidal dynamics in Segara Anakan Lagoon, which
can be the main factor that leads to sedimentation patterns. The Segara Anakan Lagoon (SAL)
is a two-inlet lagoon with a high sedimentation rate in the western part. The two-dimensionalhydrodynamic model was used to investigate the tidal dynamics. Spatial computation of tidal
duration asymmetry, peak discharge asymmetry, and slack water asymmetry are used to
identify the tidal dynamics characteristics of the SAL. The model results show that tidal wave
propagates to the lagoon from both inlets and amasses in the central part of the lagoon. Analysisof the tidal asymmetry shows that the tidal duration and slack water asymmetry are ebb
dominance in both inlets, while the peak discharge is ebb dominance in the western lagoon andflood dominance in the eastern lagoon. However, the tidal duration, peak discharge, and slack
water asymmetry show flood dominance in amassing areas. The convergence of tidal waves in
the central part of the lagoon results in abrupt changes in the tidal range and near-zero discharge
in the amassing area. Moreover, the tidal asymmetry pattern might have implications for the
sedimentation pattern in SAL.

13

The second work aims to investigate the tidal evolution in a multi-channel estuary, inthis case, the Ota River Estuary. The Ota River estuary has a straight channel, the Ota diversion
channel (ODC), and a branching channel. This study examines tidal distortion, tidal
asymmetry, and subtidal water elevation variations in two topographical settings, straight andbranching channels, under low-flow conditions. The ratio of the amplitudes of the quarterdiurnal and semidiurnal tidal species shows that the tidal distortions in the straight andbranching channels are similar. The skewness of the tidal duration shows a tendency to be
flood-dominant in both topographical settings. However, the increase in tidal asymmetry on
the branching channel is steeper than that on the straight channel. In addition, changes inbathymetry and channel width also contribute to the steep increase in tidal asymmetry inbranching channels. Moreover, the variation in the subtidal water elevation analysed using thedecomposition of the subtidal friction term shows that the variation is more influenced by theinteraction of the tides and tidal asymmetry in the junction area. In contrast, the variation ismore affected by the subtidal flow in the straight channel. Moreover, the interaction betweentides and river runoff in the straight ODC shows that the mixing was controlled by neap–spring
tidal oscillation; high discharges significantly influence mixing during the neap tide.
Furthermore, the results of the wavelet transform indicates that during the spring, tidal straining
increases and induces intense mixing, while during the neap, river discharge has a moresignificant influence on circulation. The interactions between tides and river runoff influence
the appearance of a convergence zone and estuarine turbidity maxima that are locatedapproximately 4.8 km from the river mouth.
The tidal evolution mechanism in a branching channel is examined using a barotropichydrodynamic model in an idealized junction domain, inspired by the Ota River Estuary
junction. Even though the model was simplified, it successfully reproduced the increase in
nonlinearity at the junction apex. A sensitivity analysis of tidal nonlinearity to the width of the14

upstream channel at the junction was performed by varying the upstream channel width fromthe same width as the branch channel width to three times the branch channel width. The
relationship between the upstream channel width at the diversion point and tidal nonlinearity
was not linear, whereas tidal nonlinearity was maximized when the width was twice the branchchannel width. The convergence of the tides in the narrow junction induces an increase of M4
tidal constituent that raises the tidal nonlinearity, while in the case of a wider channel, which
the wide of the upstream channel is more than twice of the branches channel, the river runoff
dampens the M2 and M4 tidal constituents that lead to decrease tidal nonlinearity.

15

Chapter 1: Introduction
1.1. Study Overview
Estuaries are a transition zone of the river environment and marine environment. In
recent decades, the estuary has been facing anthropogenic pressure that led to a change in thehydrodynamics and sediment dynamics pattern. These changes potentially cause reforms in theecological function of the estuary’s ecosystem. The critical issues in estuarine zone
management are to protect estuaries' ecological function while still giving economic benefits.
Hence, understanding the mechanism that drives the hydrodynamics and sediment dynamics
changes is essential to solving those issues.
In estuary, of the interaction between the tides and river runoff causes a complexhydrodynamics and water circulation in estuaries. The tides and high salinity water from theseas converges with the fresh water river runoff. The density difference between the fresh waterand saline water induces density currents that increase the complexity of the hydrodynamics inthe estuary. Moreover, the hydrodynamics and the tidal dynamics in estuary is affected by the
topographical setting of the estuary. Thus, understanding interactions between tides and river
runoff is important because it has implications in estuary management quality.
Topography settings of the estuary affects interactions between the tides and river run
off in estuary significantly. In a single channel estuary, the tides–river runoff interaction is
influenced by the width and depth of the channel. In multi-channel estuaries, the interactions
are more complex because the interaction is also influenced by the convergence of the tides
that coming from two inlets or mores. Therefore, on the lagoon estuaries, the interactions are
influenced by the bottom topography during the propagation of tidal waves. A steep changesof bottom topography could induce an abrupt change of the water level and increase of tidal
asymmetry. In single-channel, multi-channel, and lagoon estuaries, the tides–rivers runoff
interactions induce the nonstationary features in tidal elevations and currents profile.
16

Explaining the nonstationary features and distinguishing the mechanism are difficult. Thus, itremains a challenge to examine the nonstationary of tide–river runoff interaction, particularlyin the various topography settings.
Likewise, studying the tides–river runoff characteristics is necessary to further
understanding about the dynamics of the estuary and improve the management of estuary. The
nonstationary interactions between tides and river runoff exhibit nonstationary on spatial andtemporal all physical feature in estuaries, such as the water elevation, currents, salinity andtemperature. Accordingly, characterisation the role of tides and river runoff on the local
circulation that affects the physical features is crucial. Thus, in this study, interactions betweentides and river runoff are investigated on various setting of topography. Moreover, thenonstationary behavior that was influenced by the interactions are examined. In addition, thesurvey sites are located in the Ota River network that represents multi-channel estuaries andthe Segara Anakan Lagoon that represents lagoon estuaries
1.2.Literature Review
Large estuaries, such as Yangtze and Mahakam Estuaries, are often studied due to theirhigh river flow and sediment rates [1, 2]. Moreover, those rivers influence the social economicsof the people that live around the rivers. The river discharge plays a significant role in tidal
evolution at estuaries by delaying the wave celerity and reducing the amplitude. Furthermore,
the river discharge affected the nonlinearity behaviour of tidal waves by dissipating energy toa higher frequency and increasing the tidal asymmetry [3]. The river flow transports thesediment seaward while the tides transport the sediment landward. The river and tidal flow
convergence could induce the ETM [4]. In the water column stratification, the high river flow
could block the salinity intrusion, and their interaction with tides plays a role in the mixing
variation [1].

17

In recent centuries, estuaries got massive anthropogenic stress. The estuaries got thehuman intervention by deepening, dam development, canalization of the rivers, andaccommodating larger ships [5]. The large estuaries have been influenced by the development
long before the small estuaries, accordingly, the studies about the mechanism of thehydrodynamics parameter changes and the influence of development to the ecology have gotten
much attention [5–7]. In recent decades, small estuaries bears the human intervention
accommodate social-economic changes. Hence, the research on dynamics in small estuaries
has increased in recent years. Studies of tidal regime shifting have been conducted in single
channel estuaries or convergence estuaries [8–11]. Mechanism of tidal evolution in difference
shape estuaries, such as multi-channel estuaries and lagoon estuaries are not yet wellunderstood. Therefore, studies on tidal evolution and tidal dynamics particularly in various
forms of estuaries are necessarily to conduct.

1.2.1. Tidal dynamics in lagoons
Tidal dynamics in tidal lagoons are strongly affected by the geomorphological settings.
Geomorphological changes, either natural or anthropogenic influences, can change the tidal
wave properties [12–14]. Moreover, the alteration of tidal wave properties induces shiftinghydrodynamics and sediment distribution patterns in the estuaries [14]. However, the alterationof tidal wave properties is different in every tidal lagoon depending on the tidal forcing, river
runoff, and geometry of the lagoon. Hence, conducting local detail studies of the estuaries isvital to understanding the lagoon's local process.
In multi-inlet lagoon, the tide propagates to the interior of the lagoon from more than
one inlet. The meeting of tidal waves from more than one inlet into the lagoon interior leads to
a complex hydrodynamics system. During the propagation to in lagoon interior, the tidal wave
experiences tidal deformation that changes the tidal regime. For example, in Terminos lagoon,18

Mexico, The tidal regime in inlets is mixed diurnal, while in the interior lagoon, the regime isdiurnal [15]. Moreover, the convergence of tidal waves could induce a standing wave andeddies current inside the lagoon [16]. Due to the complex hydrodynamics system, quantifying
the critical variable that controls the process is difficult. Moreover, because of those specifictopography settings, studies about the dynamics of multi-inlet lagoons are limited. Hence,
studying tidal dynamics in Segara Anakan Lagoon could give additional knowledge about the
dynamics in multi-inlet lagoons. Furthermore, the Sagara Anakan Lagoon is a mangrove fringe;
therefore, the study could improve the understanding of tidal dynamics in the mangrove area.
1.2.2. Tides in Channel network
When tidal waves propagate from the sea to estuaries, the tidal wave experiences tidal
evolution by dissipating the tidal energy, damping/amplification amplitudes, and shifting thetidal phase. The geometry and bottom topography resolving the bed shear stress influence theevolution of tidal waves [11]. Moreover, river runoff interacts with the tidal wave by increasing
the nonlinearity of the behaviour of the tidal waves [11]. High variability affecting the tidal
evolution leads to difficulty in determining the key control variable. Some researches applied
analytical models to solve the critical variable controlling the tidal evolution in a convergent
channels [10, 11]. Several studies used field observation and numerical models to examine thekey variable controlling the tidal evolution. In recent years, the study of channel networks has
focused on tidal dynamics in distributaries channels. Interaction between tides and river runoff
studies in distributary channels using numerical models shows that the branches' length anddepth affect tidal range [17]. Wagner et. al. (2019) [2] suggested that tidal convergence of tidal
waves from the branches strongly affects the tidal wave properties. In addition, the tide
convergence location depends on the distributaries channel's topography settings.
Most of the research in the distributaries channel reviewed above was analysed using
numerical models. Numerical models could provide the dynamics of the multi-channel
19estuaries spatially and temporally. However, there are limitations to using the numerical model.
The numerical model does not efficiently study the small estuaries with narrow and shallow
channels. Besides, the dynamics in shallow estuaries are more complex because the channels
are extremely shallow during the low water, and the hydrodynamics pattern changes [18]. The
processes are difficult to capture in numerical models. Therefore, broad field observation of
the physical properties of the estuaries, including salinity, temperature, water lever, andcurrents, are needed to develop a comprehensive understanding of the dynamics in small
channel networks estuaries.

1.3. Research Motivation and Objectives
The tidal evolution and estuarine circulation in various topographical settings have beenstudied in previous studies. However, most of the studies had been conducted in well-known
large estuaries with hundreds of kilometres tidal compartments and a discharge in excess of1000 m3/s such as Yangtze and Mahakam River. Limited studies consider small estuaries withlimited discharge, whereas small estuaries are most common. For an example, more than 80%of the estuaries in UK have surface areas of less than 50 km2 and are classified as small estuaries[19]. Hence, understanding tidal dynamics and estuarine circulation in small estuary is crucial.
In recent decades, human intervention in the small estuaries increased due to socialeconomic development [8]. Research in estuaries enlarges not limited to large estuaries but also
to small estuaries. Research in small estuaries increased in recent years. Several studies havebeen carried out to investigate the detail mechanism of the tidal evolution in small estuaries.
However, the detail researches are limited to tidal evolution mechanism in single-channel
estuaries [9–11]. Research on tidal dynamics in multi-channel estuaries and lagoons with multiinlets is still limited. Hence, investigating the mechanism of the tidal evolution in various
topography settings of estuaries is needed.
20

In this research, two small estuaries that have different setting topography are selected
to conduct the field studies. The locations are the Segara Anakan Lagoon that is a coastallagoon with two inlets and Ota River Estuary that is a multi-channel estuary. In a coastallagoon, variation of bottom topography has a significant role in tidal transformation [20, 21].
Moreover, in a two-inlet lagoon, the convergence of the tides in the inner lagoon could induce
the standing wave [16] and the residual currents could induce eddies current [22]. The Segara
Anakan Lagoon have unique topography because it is a mangrove fringed with two inlets andit is the river mouth of Citandui River (one of biggest river in Java island, Indonesia). Hence,
the Segara Anakan Lagoon is an ideal research area to study the tidal dynamics in the lagoon
due to the uniqueness of geographical setting. Furthermore, the Ota river estuary is an ideal
location to study interactions between tide and river discharge in small estuary with multichannel and limited discharge. The main channel of the Ota River estuary is the Ota diversion
channel that is a 9 km straight channel. The discharge of the Ota diversion channel is controlled
by the Gion Gate. The channel is suitable for researching the interactions between tides andriver runoff in tidal dominated and limited discharge estuary. Moreover, the Ota River isbranching in the delta. Thus, the river is suitable for studying multi-channel estuary.
Hence understanding the temporal and spatial tidal evolution in various geographic
setting is important to achieve clear understanding the role of tides, river runoff, and the settingof topography for the tidal evolution. Moreover, this understanding can improve themanagement of estuarine system.
From those point of view, the main objectives of this study are:z

To characterize and demonstrate the effects of various topographical settings, including
single channel, multi-channel and multi-inlet lagoon to tidal evolution.

21

z

To understand the response of the estuarine circulation in tidal dominated estuaries causedby the interactions between river runoff and tide, and determine the variables that control
the estuarine circulation.

1.4. Novelties of Thesis
The findings of this thesis are to clarify the deformation of the tidal wave in small
estuaries with multi-tidal inlets, which most studies in estuaries are conducted in well-known
large estuaries. Previous studies in multi-inlet estuaries could not simultaneously present data
in a straight and branching channel during the same periods. Their studies focus on tidal wave
dynamics, either only on a straight channel or branching channel. Data during the same periodsin the straight and branching channel could exhibit the difference in tidal wave deformation in
the straight and branching channel. Moreover, previous studies cannot continuously measure
the current velocity in the upstream and downstream of the branching channel during the same
periods. The lack of continuous data is probably because of (1) the limited number of ADCP
that can be used for the observation, and (2) they used the currents velocity data as the reference
for the numerical model validation.
The condition motivated the author to study multi-inlets lagoons and multi-channel
estuaries. The original work of the studies is we found that the convergence of the tides fromthe inlets plays a role in the tidal deformation in both lagoon and multi-channel estuaries.
Moreover, we continuously observed currents velocity using three ADCPs in upstream anddownstream of the branches channel during the same periods to fill the gap in the previous
studies.

221.5. Site Location and Research Methods
1.5.1. Site Location
This study was conducted in two site locations: the Segara Anakan Lagoon, Indonesia,
and the Ota River Estuary, Japan. The Segara Anakan Lagoon is an estuarine lagoon with two
tidal inlets, while the Ota River Estuary is a multi-channel estuary. Both of the estuaries are
tidal-dominated. These locations are chosen to represent the various topographical setting,which the study focuses on the tidal dynamics in the various setting of topography.
The Segara Anakan Lagoon is a mangrove-fringed shallow coastal lagoon with two
tidal inlets located in Indonesia (Figure 1.1). The tide propagates inside of the lagoon throughthe eastern and western inlets. The tidal regime is mixed and predominantly semi-diurnal,
ranging from 0.8 m during neap tide to 1.9 m during spring tide[23]. The lagoon is the rivermouth of the Citanduy river; the river discharge is estimated 78 m3/s during the dry season and
208 m3/s during the rainy season [24]. Moreover, smaller rivers are emptying into the lagoon
with two orders lower magnitude. The seasonal variation of Citanduy river discharge strongly
affects the salinity and maximum turbidity in the western part of the lagoon [23]. During hightide, the central part is dynamically affected by the water exchange between the eastern andwestern parts. Moreover, the hydrodynamics of the eastern part of the lagoon is strongly
affected by tidal exchange from the eastern tidal inlet from the Indian Ocean [24].

23Figure 1.1 Segara Anakan Lagoon; The location of the Segara Anakan Lagoon is shown by theyellow mark in the inset map.
Ota River estuary is a multi-channel estuary located in Hiroshima city, Japan. It consistsof two main branches, the Ota diversion channel and the Misasa channel. The Misasa branches
into Tenma and Kyu Ota, and then the Kyu Ota channel branches into Kyu Ota and Motoyasu,
as shown in Figure 1.2. The tidal compartment in this estuary reaches 13 km from the rivermouth. The tidal regime of the estuary is semidiurnal, with the range up to 2 m during neap
tide and 3.5 m during spring tide. The hydrological regime shows the discharge maximum
during summer with around 70-100 m3/s and minimum during winter with 20-50 m3/s [25].
The mean bathymetry of the estuary is approximately 3 m. However, the depth of the rivermouth is up to 10 m due to the utilization of the river mouth as a port.

24

Figure 1.2 Ota River estuary; The location of the Ota River estuary is shown by the yellow
mark in the inset map.
1.5.2. Data and Methods
Field observation campaigns and numerical model are utilized to conduct this research.
Two field campaigns were carried out during 22 Dec 2007–16 Jan 2008 and 13-28 July 2021
in the Ota river estuary to explore the tidal evolution and estuarine circulation. During the
campaigns, the currents, salinities, and temperatures were collected. The two-dimensional
depth average model from Delft 3D is utilized to examine the tidal propagation and evolution
inside the Segara Anakan Lagoon. Moreover, the model is applied in a synthetical branching
channel domain to explain the tidal evolution mechanism in Ota River Estuary.
Chapter 2 examines tidal dynamics in the Segara Anakan Lagoon with two tidal inlets.
In this chapter, a two-dimensional depth average hydrodynamic model from Delft 3D is25

utilized. The model is forced by river discharge from the Citanduy River and other small rivers
and tides in the open boundary. The simulation is run during the dry season to minimalize theeffects of the river discharge. The model is validated using data observation from Holterman
et. Al. (2009). Furthermore, the tidal range, tidal wave celerity, bed shear stress, and tidal
asymmetry are calculated to discuss the mechanism of tidal evolution inside the lagoon.
Chapter 3 presents the interactions between the tides and river discharge and the effectsof the mixing and the currents spatial and temporally. The mixing is evaluated using several
methods to analyze the intensity and dominance of the driving variable that induces the mixing.
Richardson number and Freshwater Froude Number are applied to examine the dominant
driving variables in the mixing process, while the mixing tidal efficiency is used to investigate
the mixing intensity. Moreover, continuous wavelet transform analysis is applied to analyze
the dominant frequency and its variation over time. The cross-wavelet transform and coherence
wavelet transform examine the dependency of circulation on stratification and river discharge.
Chapter 4 is an extension of Chapter 3 that examines the interactions between tides andriver runoff in a straight channel. Chapter 4 examines the tidal evolution in a straight andbranching channel. In this chapter, the tidal elevation data in the straight and branching channel
were utilized to discuss the effect of the topographical setting, particularly a junction, on the
tidal evolution in the estuary. Harmonic analysis and the variation of tidal asymmetry areapplied to discuss the tidal oscillation before and after propagating to the estuary. Moreover,the subtidal elevation on the junction is discussed using the decomposition of subtidal friction
from ADCP data.
Numerical model is used in Chapter 5 to examine the effect of the changing of channel
width into the tidal nonlinearity. As an extension of Chapter 4, Chapter 5 focuses on the
behavior of the tidal oscillation on varying upstream channel width. In the investigation, 5scenario were simulated by varying the width of upstream channel of the junction. The width26

is variated from the same width as the branch channel width to three times the branch channel
width.
1.6. Research Outline
The study's main objective is to characterize and understand the tidal evolution indifferent topographical settings. The evolution of tides are examined in a multi-inlet lagoon
estuary and multi-channel estuary. The physical mechanism involved in the tidal dynamics inthose locations is elaborated in the four following chapters. The last chapter presents the study'ssummaries and suggestions for further research.
In chapter 2, we used a two-dimensional hydrodynamic model to investigate the tidal
dynamics in the Segara Anakan Lagoon (SAL). The main purpose of this chapter is to clarify
the dynamics of tidal propagation inside the lagoon by calculating the tidal duration
asymmetry, peak discharge asymmetry, and slack water asymmetry. This chapter has been
reproduced with minor changes from Khadami, Faruq, Kiyosi Kawanisi, and Ayi Tarya. 2020.
“Tidal Asymmetry in Two-Inlet Lagoon: A Case Study on Segara Anakan Lagoon, Central
Java, Indonesia.” Journal of Japan Society of Civil Engineers, Ser. B1 (HydraulicEngineering) 76 (2): I_1411-I_1416. https://doi.org/10.2208/jscejhe.76.2_i_1411.
In chapter 3, Observational data are used to investigate the response of currents andmixing to the interactions between tides and river runoff in a single straight channel. The main
purpose is to examine the interactions between tides and currents, as well as river runoff andcurrents, in a small-sized estuary with a low discharge range. This chapter is reproduced withminor changes from Khadami, Faruq, Kiyosi Kawanisi, Mohamad Basel Al Sawaf, Gillang
Noor Nugrahaning Gusti, and Cong Xiao. 2022. “Spatiotemporal Response of Currents andMixing to the Interaction of Tides and River Runoff in a Mesotidal Estuary.” Ocean Science
Journal, no. 0123456789. https://doi.org/10.1007/s12601-022-00056-0.

27

In chapter 4, Data observation in the junction is used to examine the evolution of thetidal wave propagation in a tidal-dominated multi-channel estuary. This section discusses tidal
distortion, tidal asymmetry, and subtidal water elevation variations in two topographicalsettings, straight and branching channels, under limited discharge conditions. This chapter isreproduced with minor changes from Khadami, Faruq, Kiyosi Kawanisi, Mohamad Basel Al
Sawaf, Gillang Noor Nugrahaning Gusti, and Cong Xiao. “Propagation of tidal waves in tidal
dominated and multi-channel estuary” submitted in Continental Shelf Research
In chapter 5, the barotropic hydrodynamic model is applied in an idealized junction
domain, inspired by the Ota River Estuary junction, to estimate the nonlinearity in the junction
quantitatively. A sensitivity analysis of tidal nonlinearity to the width of the upstream channel
at the junction is performed by varying the upstream channel width from the same width as thebranch channel width to three times the branch channel width. This chapter has been
reproduced with minor changes from Khadami, Faruq, Kiyosi Kawanisi, Mohamad Basel Al
Sawaf, and Gillang Noor Nugrahaning Gusti. “Sensitivity of Junction Width to Tidal
Nonlinearity on Small and Shallow Tidal Junction” submitted in Indonesian Journal of Scienceand Technology
Finally in Chapter 6 presents the summaries of the study and future work related to thisstudy.

.

28

Chapter 2: Tidal asymmetry in two-inlet lagoon: a case study on Segara
Anakan Lagoon, Central Java, Indonesia

2.1. Introduction
Tidal asymmetry is recognized as an important factor that controls residual sedimenttransport in coastal waters and lagoon systems. Tidal asymmetry induces residual currents thattransport sediments. There are three classifications of tidal asymmetry. (1) Tidal duration
asymmetry (TDA) estimates the asymmetry of flood and ebb duration, (2) peak current
asymmetry (PCA) estimates the asymmetry of the peak currents of flood and ebb, and (3) slack
water asymmetry (SWA) computes the asymmetry of high and low water slack duration. The
rising and falling durations are strongly related to the peak currents and the slack water duration[26]. A shorter rising tide will induce stronger flood currents and longer high water slack. Thissystem means flood dominance. In the flood dominance system, seawater inflow to the basin
is greater than the outflow and vice versa on the ebb dominance system. Sedimentation tends
to occur in the flood dominance system, while in the ebb dominance system, erosion tends tooccur.
Tidal asymmetry commonly occurs when the tidal wave propagates into a shallow
water system. The interference of bottom friction in a shallow water system generates
transformations of the tidal wave to be shallow water tide’s components, such as M4 [16]. Theinteraction of principal tides and shallow water tide’s components cause tidal asymmetry [27–29]. Non-tidal aspects such as river discharge can also affect tidal dynamics [29–31]. River
discharge shortens the flood duration and induces the longer ebb duration [28].
Water circulation in a multi-channel lagoon system has more complex hydrodynamics.
Tides can propagate to the lagoon through two open channels or more. Several studies in twoinlet lagoons explain that the tides convergence in a region behaves looks like a standing wave29

[16] and the residual currents in the basin induce eddies [22]. A multi-channel lagoon system
can show a different tidal asymmetry in every inlet because of the morphology and bathymetryof the inlets.
Segara Anakan Lagoon (SAL) is a semi-enclosed, mangrove-fringed estuary with twooutlets located in Cilacap, on the south coast of Central Java, Indonesia (Figure 2.1). The
lagoon is the estuary of the Citanduy River. There are nine rivers flowing into the SAL besides
the Citanduy River. However, the watershed areas of other rivers are not more than 10% of
Citanduy River [24]. The hydrodynamics of the SAL are driven by the interaction of the tides
that propagate from the western and eastern channels, as well as the Citanduy River discharge[12, 24]. Seasonal wind and rain affect the current and salinity distribution in the SAL [23].
Satellite imagery and historical maps recorded high sedimentation occurred in the western partof the SAL but not in the eastern part [32, 33].

Figure 2.1 Bathymetry of the Segara Anakan Lagoon (SAL); Black dots are the tide gauge
stations, and the yellow lines are cross-sections for calculating the discharge. The red dashedline is transecting for spatial change analysis. The grey and green areas show land andmangrove areas, respectively. The computational domain is enclosed by the solid black line.
Solid red lines denote open boundaries.
30

The objective of the present study is to clarify the dynamics of tidal propagation inside
the lagoon. A numerical model is used to represent hydrodynamic circulation in the lagoon,
and the results of the model are utilized as data to compute the tidal asymmetry. The dynamics
of the tides are analyzed using tidal asymmetry computations. The paper presents thefollowings. Section 2.2 explains the numerical model, asymmetry computation formula, andobservation data. Section 2.3 presents the results of the numerical model and the computationsof tidal asymmetry. In section 2.4, we discuss the cause in the spatial changes of the asymmetry
and the implication of the changes.

2.2. Data and Methods
2.2.1. Data
Field observation data from Holtermann et al., (2009)[24] are utilized in this study. We
use bathymetry, discharge, and water elevation data that carried out in the multidisciplinary
German-Indonesian SPICE (Science for the Protection of Indonesian Coastal Marine
Ecosystems) research project as well as additional bathymetry data that measured in 2017 and2018 in the frame of P3MI ITB project. The data on the dry and rainy seasons are used as themodel input as well as to validate the results of the model. The water elevations were measured
in Sleko and Klaces from 9 July to 15 August, 2005 and February 2006 to March 2006. The
discharges were measured in the Pelawangan West (PLW), Citanduy River, Klaces, waterexchange station, and the Pelawangan East (PLE) (Figure 2.1). A more explanation of themeasurement method, quality control, and post-processing of observation data arecomprehensively written in Holtermann et al., (2009)[24].

312.2.2. Numerical Modelling
Delft3D is hydrodynamics model software developed by Deltares that can be applied
for coastal, river and estuaries hydrodynamics simulation. This software has been used formodelling hydrodynamics and sediment transport in various studies [12, 34]. The Delft3D
model could simulate the flow and transport resulting from tidal and atmospheric forcing on
rectilinear and curvilinear coordinates [35]. The model solves the mass conservation andmomentum equation for incompressible fluid under shallow water and hydrostatic assumption.
The Delft3D model uses orthogonal curvilinear coordinates that support two coordinate
systems in the horizontal direction. The coordinates are (1) Cartesian coordinates (ξ, ƞ) and (2)Spherical coordinates (λ, ϕ), in which ξ and λ are longitudes while ƞ and ϕ are latitudes.
Governing equations of Delft3D are presented as follows.
x

Continuity Equation
The depth-averaged continuity equation is derived by the integration of continuity
equation for incompressible fluids (ѭ∙u Ԧ=0) over total depth and applied kinematicboundary conditions at water surface and bed level into consideration.
డ఍
డ௧

൅

ଵ

డሺሺௗା఍ሻ௎ඥீആആ ሻඥீ഍഍ ඥீആആ

డక

൅

ଵ

డሺሺௗା఍ሻ௏ඥீ഍഍ ሻඥீ഍഍ ඥீആആ

డఎൌ ሺ݀ ൅ ߞሻܳ(1.1)

with ܷ and ܸ are the depth averaged velocities
ܷൌ
ܸൌ

఍
଴
ଵ
‫ ݖ݀ݑ ׬‬ൌ ‫ି׬‬ଵ ‫ߪ݀ݑ‬
ௗା఍ ௗ
ଵ

఍

଴

‫ ݖ݀ݒ ׬‬ൌ ‫ି׬‬ଵ ‫ߪ݀ݒ‬
ௗା఍ ௗ

(1.2)
(1.3)

The each variable has meaning as,ߞ: free surface elevation above reference plane (z = 0)‫ݐ‬

: time‫ܩ‬కక: ܴ  ߶, with R = ‫ܩ‬ఎఎ is radius of the Earth݀: the depth below the reference plane
32

The ܳ representing the contributions per unit area due to the discharge or withdrawalof water.
଴(1.4)ܳ ൌ ‫ି׬‬ଵሺ‫ݍ‬௜௡ െ ‫ݍ‬௢௨௧ ሻ݀ߪ ൅ ܲ െ ‫ܧ‬with ‫ݍ‬௜௡ and ‫ݍ‬௢௨௧ are the local sources and sinks of water per unit volume (1/s),
respectively, ܲ represents non-local source term of precipitation and ‫ ܧ‬is non-local sinkterm due to evaporation.
x

Momentum equations in horizontal direction
The momentum equations in ߦ- and ߟ- direction are respectively given by
డ௨
డ௧

െ

ଵ

௨

డ௨

ඥீ഍഍ డక൅௩ଵఘబ ඥீ഍഍

డ௧

൅

௨

డ௩

ඥீ഍഍ డక

൅డ௨ඥீആആ డఎܲక ൅ ‫ܨ‬క ൅ ሺௗା఍ሻమ

డ௩

െ

൅

௩

డ
డఙ

൅

ቀ߭௏

డ௩

ඥீആആ డఎ൅௪ డ௨ௗା఍ డఙ
డ௨
డఙ

െ

௩మ

డඥீആആ

ඥீ഍഍ ඥீആആ

డక

൅

௨௩

డඥீ഍഍

ඥீ഍഍ ඥீആആ

డఎ

(1.5)

ቁ ൅ ‫ܯ‬క௪ డ௩ௗା఍ డఙെെ ݂‫ ݒ‬ൌ௨௩డ ඥீആആ

ඥீ഍഍ ඥீആആ

డక

൅

௨మ

డඥீ഍഍

ඥீ഍഍ ඥீആആ

డఎ

ଵ
ଵ
డ
డ௩
ܲ ൅ ‫ܨ‬ఎ ൅ ሺௗା఍ሻమ ቀ߭௏ ቁ ൅ ‫ܯ‬ఎఘబ ඥீആആ ఎడఙడఙെ ݂‫ ݑ‬ൌ(1.6)

In which,x‫ݑ‬: flow velocity in ߦ- direction‫ݒ‬: flow velocity in ߟ- direction݂: Coriolis parameterߩ଴: reference density of waterܲకǡఎ: gradient hydrostatic pressure in ߦ- and ߟ- direction‫ܨ‬కǡఎ

: turbulent momentum flux in ߦ- and ߟ- directionߪ: scaled vertical coordinate߭௏: vertical viscosity‫ܯ‬కǡఎ

: source or sink of momentum in ߦ- and ߟ- direction

Vertical velocities
Vertical velocity ߱ in the adapting ߪ-coordinate system with taking precipitation andevaporation into consideration can be specified as follows

33

డ఍
డ௧

൅

ଵ

డሺሺௗା఍ሻ௨ඥீആആ ሻඥீ഍഍ ඥீആആ

డక

൅

ଵ

డሺሺௗା఍ሻ௩ඥீ഍഍ ሻඥீ഍഍ ඥீആആడఎడఠ൅ డఙ ൌ ሺ݀ ൅ ߞሻሺ‫ݍ‬௜௡ െ ‫ݍ‬௢௨௧ ሻ
(1.7)

with,

x

‫ݍ‬௜௡

: local source per unit volume‫ݍ‬௢௨௧

: local sink per unit volume

Hydrostatic pressure assumption
Hydrostatic pressure equation is used instead of vertical momentum equation here dueto the assumption of shallow water condition. Thus,
డ௉
డఙ

(1.8)

ൌ െ݃ߩ‫ܪ‬

where,
ܲ: hydrostatic water pressure݃: gravitational accelerationߩ: density of water‫ܪ‬: total water depth

The computational domain of the model is 26.5 km in the west-east direction and 13.3
km in the north-south direction, gridded by a rectangular grid with 67 m horizontal spatial
resolution (Fig. 1). The model is forced by tides through two open channels in the open
boundaries at PLW and PLE (Fig. 1) and river discharge from Citanduy and 8 smaller rivers[24]. In the open boundaries, radiation boundary condition is applied to make boundaries lessreflective [35]. The water level is formed by 8 major tidal constituents, with K1, P1, O1, andQ1 for diurnal constituents and N2, M2, S2, and K2 for the semi-diurnal constituent. The
amplitude and phase of the tidal constituent are obtained from TPXO model using the Tidal
Model Driver (TMD)[36]. Constant river discharge is defined for the Citanduy River and theothers based on Holtermann et al., (2009)[24]. A spatial change of the Manning’s roughness
coefficient (n) is considered, i.e., for the mangrove area and non-mangrove area, n 0.1 and34

n 0.03 are applied, respectively. In this study, we simulated 2 model scenarios: dry season
scenario and wet season scenario. The dry season simulation is run from 15 June, 2005 to 30
August, 2005 while the wet season scenario is run from 1 February, 2006 to 30 March, 2006.
Although we validated both model results, the results of the dry season model are used forfurther analysis.
2.2.3. Model Validation
The model is validated using Nash-Sutchliffe Efficiency (NSE). The NSE formula isshown in equation ( 2.1 )[37].
ܰܵ‫ ܧ‬ൌ ͳ െଶσே௜ୀଵሺ‫ ݏܾ݋ݔ‬െ ‫ ݀݋݉ݔ‬ሻଶσேതതതതതሻ
‫ݏܾ݋‬௜ୀଵሺ‫ ݏܾ݋ݔ‬െ ‫ݔ‬( 2.1 )

where ‫ݔ‬௠௢ௗ is the model result, ‫ݔ‬௢௕௦ is the data observation, ‫ݔ‬തതതതത௢௕௦ is the mean of the data
observation, and N is the number of observed data. The NSE value is classified as excellent for
NSE>0.65, very good for 0.5<NSE<0.65, good for 0.2<NSE<0.5, and poor for NSE<0.2 [37].
2.2.4. Asymmetry Quantification
Tidal asymmetry affects the sortation of residual sediment transport during the tidal
cycle, that is, controlling the morphological change of the basins over the long-term
sedimentation process. Tidal duration asymmetry, peak velocity skew, and slack water
difference are the basic tidal asymmetry indexes that mostly control the net sediment transport.
In this study, we modify the calculation of peak current asymmetry by calculating the peakdischarge asymmetry (PDA) to measure differences in the water flux through the channel. The
asymmetries are calculated as follows [27] :ͳଷσே௜ୀଵሺ‫ݔ‬௜ െ ‫ݔ‬ҧ ሻܰെͳߛሺ‫ݔ‬ሻ ൌ
ଷൗ
ଶ
ͳ
ଶቃ
ሺ‫ݔ‬
െ
‫ݔ‬ҧ
ሻ
ቂܰ െ ͳ σே௜ୀଵ ௜( 2.2 )

35

where ߛ is skewness, ‫ݔ‬௜ is the time series of sample signals, ‫ݔ‬ҧ is the mean value of the samples,and N is the number of time-series data. For the TDA calculation, ‫ ݔ‬denotes the time derivativeof elevation ሺ‫ ݔ‬ൌௗఎௗ௧ሻ, for the calculation of PDA x denotes the discharge ሺ‫ ݔ‬ൌ ܳሻ, and for

SWA x denotes the time derivative of discharge ሺ‫ ݔ‬ൌௗொௗ௧

ሻ. Besides, we compute the asymmetry

using 14 days window and 25 hours window in the spring and neap conditions. A window of
14 days is enforced to capture the asymmetry on a full tidal cycle, while a window of 25 hours
is enforced to capture asymmetry in the neap and spring conditions. The skewness indicators
are based on the previous studies [27, 34]

2.3. Results
2.3.1. Model Validation
The results of the numerical model are validated by comparing with the observation
data (Figure 2.2). The NSE value for tidal elevation at Sleko station from 9 July to 14 August,2005 was 0.87, while on 29 February to 29 March, 2006 was 0.81. Comparison of the tidal
elevation in Klcaces station shows that the NSE value is 0.74 for the 22 July to 11 August,2005 period, and 0.71 for the 17 February to 29 March, 2006 periods, respectively. Thus, thetidal model validation shows acceptable results for further analysis.

36

Figure 2.2 Tidal elevation during dry and wet seasons in Sleko (a, c) and Klaces (b, d). The
black lines denote the simulation results, and the red lines denote the observation data.

A comparison of the discharges resulted from the model and the observation data isshown in Figure 2.3. The NSE between the model and the observation data for PelawanganWest (PLW) and Klaces during dry season periods were 0.85 and 0.24, respectively. During
the wet season periods, the validation of the model is done by comparing the discharge fromthe model with the observation on the Pelawangan West and the water exchange station. The
NSE between the model and the observation at both stations were 0.77 and 0.79, respectively.
The comparison indicates that the results of the model are in good agreement with theobservation data, except at Klaces during the dry season periods. The utilization of different
manning's roughness coefficient for mangrove and non-mangrove areas resulted in good
agreement between the model and observation data. However, NSE value in Klaces is low
because the number of observation data in Klaces is limited. Hence, small variance of37

observation data reduces the NSE value. In spite of that, the discharge in Klaces still shows
acceptable judgment on pattern and range visually.

Figure 2.3 Comparisons of the discharge from the model (black line) and observation data (reddots) on the dry season in Pelawangan West (a, b, c) and Klaces (d), while on the wet season
in Pelawangan West (e, f, g, h) and water exchange station (i, j, k).

2.3.2. Tidal Level and Discharge
The model results show that the tides in the SAL are mix diurnal types. The maximum
tidal range at Sleko is higher than that at Kalces with 1.96 m and 1.82 m, respectively. On thespring tides, the tidal range reaches ~2 m in Klaces and Sleko while in the neap tide condition,
the range is ~1m. The phase of the tides shows an opposite phase during the neap and spring(Figure 2.4a,b). The tides propagate to the inner lagoon from the PLW and PLE, with nosignificant phase difference. However, the tidal levels at Klaces and Sleko station have thephase difference of 20 minutes. The cross-correlation between tides in Motean–Klaces andMotean–Sleko shows that tidal elevation in Motean delays 110 minutes from Klaces and delays
130 minutes from Sleko. These results reveal that tides from PLW propagate eastward while
38

tides from PLE propagate westward and amass around the middle of the lagoon [12]. Figure
2.4c and d show the variations of discharges at Sleko, Klaces, and Motean stations during theneap and spring conditions. Discharges at Sleko and Klaces clearly show the tidal variation
while the discharge at Motean is near zero along the tidal period.

Figure 2.4 Twenty-four hours of the elevation (a, b) and discharge (c, d) during spring condition(a, c) and neap condition (b, d). The black solid line, red dot line, and blue dashed line aremodel results for Sleko, Klaces, and Motean stations, respectively. The spring/neap condition
was on 23 July 2005/31 July 2005.

During the rising periods of tidal elevation, the discharge in Sleko and Klaces flows
into the lagoon, while during the falling tidal periods, the discharge flows out from the lagoon(Figure 2.5). Referring to the tidal behavior in the lagoon, during the rising periods, thedischarge converges to the inner lagoon and fills the lagoon and during the falling tides, thedischarge diverges flowing out of the lagoon. The convergence of the tidal wave in the central
39part of the lagoon results in quasi-standing wave that causes near-zero discharge [16] at the
Motean station.

Figure 2.5 Depth average velocity vector fields and water elevation (color shading) in the
Segara Anakan Lagoon on spring condition at (a) ebb tide and (b) flood tide. Red lines denotecross-section transects for calculating water volume discharge.

2.3.3. Tidal Asymmetry
We calculated the asymmetry of tidal duration, peak discharge, and slack water in 2
windows: 25 hours on the neap and spring to capture the conditions, and 14 days window tocapture the asymmetry on the full tidal cycle. The results of the TDA computation at several
stations in the western and eastern parts of the lagoon are shown in Table 2.1. In the spring
condition, TDA in PLW, Lagoon, PLE, and Sleko shows an ebb dominance, while in the neap40

condition, TDA shows a flood dominance. Despite flood dominance during the neap condition,
the TDA value is close to zero. However, the TDA value at Motean station increases
significantly and shows flood dominance in spring and neap conditions. Computation of TDA
using 14 days window shows the same pattern of TDA in the spring condition.
There are differences in flow direction of the ebb and flood discharges in the westernand eastern parts of the lagoon. The flood discharge in the west is eastward, while the flood
discharge in east parts of the lagoon is westward. Owing to the definition, for PDA and SWA
computation, we multiplied the discharge at the Motean and water exchange station with 1.
Using the transformation, we have the same definition that positive discharge is a flood
discharge.
The PDA computation shows an ebb dominance on the PLW (Table 2.1). However, the
PDA changes spatially to flood dominance in the Motean station. In contrast, the PDA at the
PLE station shows flood dominance and then shifts to ebb dominance in the water exchange
station and then changes dramatically in the Motean to flood dominance. This pattern is shownin all computation windows. A significant change in the asymmetry from the Motean Station
could be caused by the meeting of the tidal wave that propagated from east and west.

Table 2.1 Computation of Tidal Duration Asymmetry (TDA), Peak Duration Asymmetry(PDA), Slack Water Asymmetry (SWA), using a 25 hours window in spring and neap and 14
days.
TDA
Station

PDA

SWA

neap

spring

14
days

neap

spring

14
days

neap

spring

14
days

PLW

0.11

-0.19

-0.09

-0.64

-0.84

-0.77

0.05

-0.08

0

Lagoon

-0.08

-0.18

-0.11

-0.4

-0.45

-0.41

-0.92

0.7

-0.04

Klaces

-0.12

-0.16

0

-0.13

-0.14

-0.05

0.13

-0.04

-0.17

Motean

0.59

0.79

0.78

1.87

1.52

1.73

2.08

3.13

2.95

41

Water exc

0.21

-0.24

-0.19

-0.09

-0.12

-0.09

-0.66

-0.63

-0.67

Sleko

0.04

-0.2

-0.12

0.72

0.45

0.81

-0.16

-0.46

-0.48

PLE

0.04

-0.2

-0.12

0.72

-0.1

0.06

-1.11

-0.99

-1.18

The SWA computation (Table 2.1) shows different results for the eastern and westernparts of the lagoon. Generally, in all computation windows, SWA computations at the westernpart lagoon stations (PLW, Lagoon and Klaces) are near zero. This means that the high andlow slack water durations are nearly the same. While the eastern part of the lagoon, the SWA
value shows ebb dominance. In the Motean station, the SWA value changed to flood
dominance.

2.4. Discussion
The morphological setting of the SAL, which has two open channels, allows the tidal
wave to propagate from the east and west to the inner lagoon. The celerity of wave propagation
along the red dashed line in Figure 2.1 was calculated (Figure 2.6b) using the equation ܿ ൌඥ݄݃, where ܿ is the celerity, ݃ is the gravitational acceleration, and ݄ is water depth. The tidal
celerity is related to the shoaling effect which is lower celerity value affects the increase of
tidal range Moreover, the bed shear stress was computed by the model using equation߬௕ ൌఘబ ௚௎ȁ௎ȁ஼, where ߬௕ is the bed shear stress, ρ0 is reference density of water, ܷ is depth averagevelocity and C is the bottom roughness Chezy coefficient. In contrast, the high value of the bed
shear stress (Figure 2.6b) is related to the damping of the tidal range. The value of celerity andthe bed shear stress is highly correlated with the depth of water column. The lowest value ofcelerity and the increase of bed shear stress in the meeting point (Figure 2.6b) show
concurrently with the drop of tidal range (Figure 2.6a). This mechanism indicates that the42bottom friction effect is more dominant (rising of bed shear stress) than the shoaling effect(lowest value of tidal celerity).
The amassing of a tidal wave significantly changes the tidal asymmetry as well. It canbe seen from Figure 2.6c and Table 2.1. Figure 2.6c shows that the TDA values in PLW and
PLE are close to zero and then decrease gradually to ebb dominance in the inner lagoon.
However, the value increases to flood dominance around the meeting point. In meeting point,
a significant change in the TDA to flood dominance is seen in the Motean station (Table 2.1).
Significant changes in PDA and SWA were seen in Motean station as well. PDA and SWA
showed flood dominance in Motean station, whereas the nearest station from Motean station
showed ebb dominance (Table 2.1).
Peak Discharge Asymmetry (PDA) controls the coarse sediment residual transport andSlack Water Asymmetry (SWA) controls the residual transport of fine sediment [26]. In the
Segara Anakan lagoon, the sediment source is mainly from the Citanduy River [23] which isdeposited in the western area of the lagoon [33]. The Asymmetry pattern might correlate thesedimentation pattern that only happens in the western area. In the western part of the lagoon,
PDA and SWA tend to ebb dominance. The tendency of ebb dominance can be induced byriver discharge [29]. The ebb dominance in the lagoon leads to the transport of sediment fromthe river to the seaward. From the Citanduy river mouth, the sediment is spread in the westernlagoon and transported to the sea. Due to the very low discharge around the amassing area, thesediment from the western area could not be transported to the eastern part of the lagoon. Thismechanism might relate to the sediment dynamics in the Segara Anakan Lagoon. However, a
study that focused on sediment transport and sedimentation should be conducted to get a better
understanding of sediment dynamics in the Segara Anakan Lagoon.

43

Figure 2.6 (a) Tidal range, (b) tidal wave celerity (solid line) and bed shear stress (dashed line),and (c) Tidal Duration Asymmetry (TDA) along the red dashed line transect in Figure 2.1.

2.5. Conclusions
The tidal wave in the Segara Anakan Lagoon is a mixed semi-diurnal tide with around2 m maximum in range. The tidal wave virtually simultaneously propagates to the lagoon
through two open channels from eastern and western inlets. During the rising tide, the tidal
wave converges in the middle of the lagoon and diverges during the falling tides. The amassing
tidal wave from eastern and western inlets in the middle of the lagoon induces an abrupt change
in the tidal range and the tidal asymmetry. TDA and SWA in the eastern and western parts of
the lagoon indicate the ebb dominance but shifts to the flood dominance in the middle of thelagoon. PDA shows that the asymmetry of the western part of the lagoon is the ebb dominance,
while the flood dominance in the eastern part of the lagoon. The differences in the asymmetry
patterns in eastern and western parts of the lagoon and low discharge in the amassing area could

44

be the reason for sedimentation only occurring in the western part of the lagoon, but not in theeastern part.

45

Chapter 3: Spatiotemporal response of currents and mixing to theinteractions between tides and river runoff in a multi-channel estuary
3.1. Introduction
Current circulations in estuaries play a vital role in sediment transportation, suspended
material deposition, saline water intrusion, and the alteration of water quality and estuarine
habitats. The hydrodynamics in estuaries are complex and driven by various forces, includingtides, river discharge [38–40], and geographical settings that modify circulation [2, 17, 26, 41].
Estuarine circulation is determined by its dominant forcing mechanism, which may include i)
tidally dominated, ii) river-dominated, and iii) mixed tidal–river influence [42]. Theinteractions between these forcing mechanisms affect the currents, elevation, salinity, mixing,
and sediment dynamics patterns within estuaries [30, 43–46].
The effects of tides and river discharge on circulation have been studiedcomprehensively by characterizing the circulation response to changes in elevation, current anddischarge profiles, and sedimentation processes [28, 29, 38, 46–48]. The water level response
due to the interactions between river discharge and tides is expressed by the occurrence of
higher frequency tidal components [28, 29]. Furthermore, high river flow enhances friction andincreases tidal damping [49]. The interactions between river runoff and tides in ebb–flood
variation affect mixing, whereas an increase in river runoff may intensify the stratification [40,48]. Stratification and turbulence, as a response to tide and river discharge convergence, tend
to induce the estuarine turbidity maximum (ETM) [50]. In previous researches, several
empirical methods [45, 51] and statistical methods [25, 52] have been applied to examine theeffects of tides and river runoff on circulation. However, most studies that have consideredtide–river discharge interactions with regard to circulation have typically focused on large
estuaries with high discharges, i.e., greater than 1000 m3/s, where tidal oscillations may be up46

to several hundred kilometers. In other words, the majority of previous studies have been
conducted on well-known rivers with a mean discharge in excess of 1000 m3/s and up to ahundred kilometers of tidal penetration, such as the Yangtze and Mahakam.
There are only limited studies that have considered small estuaries with short tidal
penetration distances, despite small estuaries being the most common type of tidal rivers. For
example, more than 80% of the estuaries in the United Kingdom and Wales are small estuaries[53]. In this study, small estuaries are defined as those with surface areas of less than 50 km2[19]. Previous studies on small estuaries have focused on tidal straining, saltwater intrusion,and sediment transport; for example, previous researches have highlighted the role of straining
and mixing limited to the tidal cycle [44, 54]. Other studies have highlighted the dynamics ofthe salt wedge during the tidal cycle [55, 56] or investigated variations in sedimentconcentration in the tidal cycle [25, 57]. However, these studies are generally limited to theeffect of tides on circulation, thus interpretation of the driving variables within small estuaries
has always varied due to local factors. Therefore, a mixing evaluation based on the driving
variables, especially the contribution of tides and river runoff, needs to be conducted to enhance
our understanding of circulation in small estuaries.
The Ota River Floodway is a small, mesotidal estuary with an average depth of 3m inthe western part of Hiroshima City, Japan. Previous studies of the dynamics of the Ota River
Floodway have investigated sediment transport, salinity intrusion, mixing, and turbulence [25,
58–60]. The circulation has been reported to be controlled by flood–ebb and spring–neap tidal
variations and modified by river discharge [25]. During the ebb tide, the near-bed currents were
smaller than those in the flood tide, and consequently, the near-bed turbulence weakened [61].
In the ebb–flood cycle, stratification increased during ebb [61]. In contrast, in the spring–neap
cycle, the stratification weakened during the spring, thereby strengthening tidal mixing [58].
Generally, the aforementioned studies have focused on how tidal oscillations drive circulation.
47

The river runoff modifies the hydrodynamic patterns; where convergence zones appear, theserequire extensive analysis to understand the underlying convergence mechanism [25].
Although a considerable amount of research has been conducted in the Ota River Floodway,the majority of studies have considered the effects of tides and river discharge separately.
Therefore, the dependency and consequences of the interactions between tide and river runoff
on circulation and mixing are imperfectly understood and remain open to study.
In this study, we investigated the interactions between tides and currents, as well as
river runoff and currents, in a small-sized estuary with a low discharge range. To address theidentified research gaps in studies of low discharge and small estuaries, in this work, we
examine the dominance of mixing and currents by applying wavelet analyses to two-week–
one-month records of acoustic Doppler current profilers (ADCPs) at three stations along the
Ota River Floodway. An enhanced understanding of the processes of tidal fluvial interaction isessential for better river management, especially in small and shallow estuaries.
The paper is structured as follows: a description of the study area is presented in Section
3.2. The data and methods are explained in Section 3.3; Sections 3.4 and 3.5 then present theresults and discussion, respectively. Finally, the study’s conclusions are summarized in Section
3.6.

3.2. Study Area
The Ota River Estuary is a multiple-branch delta located in the Hiroshima City, Japan.
The estuary is mainly utilized for transportation and tourism. The downstream area of theestuary is used for the aquaculture of oysters [62].
The Ota River Floodway is the longest straight channel of the Ota River estuary branch(Figure 3.1). Razaz et al. (2015) [63] reported that the maximum velocity values during the ebb
and flood tides were 0.65 m/s and 0.5 m/s, respectively, with tidal wave penetration of up to48

13 km from the river mouth. The tidal regime of the Ota River Floodway has a mixed
semidiurnal tidal cycle, with a range of 2–4 m. The river discharge of the Ota River Floodway
is controlled by the Gion sluice gate, which is located 9 km upstream from the river mouth.
The gate is fully opened whenever the discharge at the Yaguchi Station exceeds 400 m3/s.
Yaguchi Station is located 14.6 km from the river mouth (not shown in Figure 3.1).
Discharge observations using the fluvial acoustic tomography (FAT) system showedthat ~20–50% of freshwater from Yaguchi flows to the Ota River Floodway through the Gion
Gate [64]. The FAT system has demonstrated excellent performance in the Ota River Estuary[65, 66] and mountainous rivers [67–69]. During low discharge, a salt wedge occurs and highlevels of stratification develop during the ebb [59].

Figure 3.1. Observation sites and bathymetry along the Ota River Floodway, Hiroshima City,
Japan (a). Transversal locations of the ADCPs in St. A (b), St. B (c), St. C (d).
49

3.3. Materials and Methods
3.3.1. Data
The data were taken at distances 2.8 km, 4.8 km, and 6 km upstream from the mouth of
the Ota River mouth (Figure 3.1). Current data at stations A, B, and C were obtained using a
ADCP Nortek Aquadopp 2-MHz profiler with three beams. The operation settings anddeployment of the ADCP are summarized in Table 3.1. Two conductivity, and temperature,sensors (CTs) were installed, each one near the water surface and bottom at St. A from
December 22, 2007, to January 16, 2008.
Hourly wind records were obtained from the Japan Meteorological Agency. In addition,
the hourly elevation records at Kusatsu Station and the hourly discharge data from the Yaguchi
Station were gathered from the Water Information System, Ministry of Land, Infrastructure,
Transport, and Tourism (MLIT), Japan. The discharge at Gion Station was calculated from anempirical relationship established between the discharge values at the Gion and Yaguchi
stations; the relation was developed in a previous study [64]. The positions of the windobservations are shown in Figure 3.1

Table 3.1. ADCP settings and deployment

St. A

Bin
size
(m)
0.1

St. B

0.1

0.05

20

St. C

0.1

0.05

20

StationBlank
space (m)Sampling
periods (min)Installation

Observation
periods

0.05

20

Downward
looking

22 Dec 2007 –16
Jan 2008

Upwardlooking
Upwardlooking

22 Dec 2007 –16
Jan 2008
27 Dec 2007 –9
Jan 2008

Notes
Missing
period on 27 Jan 200850

3.3.2. Methods
3.3.2.1. Evaluation of Mixing
The stability and mixing of the water column were examined using the Richardson
number (ܴ݅௅ ), which is a dimensionless value that expresses the ratio of the buoyancy force tothe mechanical force. A high Richardson number indicates that the buoyancy force cansuppress the mechanical force, with mixing taking place when the Richardson number is lessthan 20. The bulk Richardson number [40] was used in this study, which can be estimated as:
ࡾ࢏ࡸ ൌ

ࢍᇲ ࢎ
૛

ࢂ

and ࢍᇱ ൌ ࢍο࣋

( 3.1 )

࣋

where ݃ᇱ and ݃ are the reduced gravityand gravitational acceleration (9.8 m/s2), respectively,οߩ is the density difference between the surface and bottom, ߩ is the depth-averaged densityof the water column, and ܸ is the depth-averaged longitudinal velocity.
Mixing was evaluated based on the dominance of driving factors. River discharge andtidal currents are considered to be the dominant driving variables in the mixing process. The
Freshwater Froude Number (‫ݎܨ‬௙ ) is used to distinguish the effects of freshwater flow on mixing
in the estuary, where a high ‫ݎܨ‬௙ value indicates an intense contribution of river runoff tomixing. The ‫ݎܨ‬௙ is calculated by scaling the maximum velocity owing to river flow to the
maximum speed of propagation gravity wave. The ‫ݎܨ‬௙ is expressed as:ࡲ࢘ࢌ ൌ ሺࢼࢍ࢙
ࢼൌ

࣋
ି૚൰
࣋૙

൬

ࢁࡾ
૚Ȁ૛
࢕ࢉࢋࢇ࢔ ࡴሻ( 3.2 )
( 3.3 )

࢙

where ܷோ is the net velocity due to river flow, which is calculated by applying a 30hour low-pass filter to the current data. ߚis the instantaneous buoyancy frequency as a functionof the depth-averaged density (ߩ) and salinity (‫[ )ݏ‬70], ߩ଴ is the ocean density as a reference
density, ܵ଴ is ocean salinity as a reference salinity, and ‫ ܪ‬is the water depth.
51

Mixing tidal efficiency (‫ )ܯ‬is used to measure the intensity of mixing in a stratified
estuary driven by tidal currents [71]. The effectiveness of tidal mixing is expressed by thefollowing equation:
࡯ ࢁ૛

ࡰ ࢀ
ࡹ૛ ൌ ࣓ࡺࡴ
૛( 3.4 )

where ‫ܥ‬஽ is the drag coefficient (0.0025) [70], ்ܷ is the amplitude of the tidal velocity, ߱isthe tidal frequency, and ܰ is the buoyancy frequency, expressed as:
ࢼࢍࡿ૙

ࡺൌට

( 3.5 )

ࡴ

where ܵ଴ is the reference salinity.
The mixing characteristics of estuaries can be applied to classify estuaries. Based on
the mixing, estuaries are broadly classified as either stratified, partially mixed, or well-mixed[72]. In terms of circulation, stratified estuaries are classified as either fjord, strongly stratified,or salt wedge [73, 74]. Conventional methods to determine the type of estuaries include
measuring the vertical profile of salinity along the estuary over time [56, 75]. However, thesemethods cannot take into account variations in river discharge and tides in terms ofclassification. In this study, the combination of two parameters, ‫ݎܨ‬௙ and ‫ ܯ‬, is applied todetermine the Ota Floodway estuary regime. The mixing condition occurs whenଵȀଷߙ ଵȀଶ ‫ݎܨ‬௙‫ିܯ‬ଶ ൎ ͳ with an ߙ value of 3.4 [71], meaning that mixing occurs when this criticalthreshold value is exceeded. This method has previously been successfully used to map
different estuary classes [71].
3.3.2.2. Wavelet TransformIn this study, the wavelet analyses comprise the continuous wavelet transform (CWT),
cross wavelet transform (XWT), and coherence wavelet transform (WTC) [76]. The CWTapproach is applied to decompose the time series into the time–frequency domain and analyze
the dominant frequency and its variation over time. The CWT is applied to the depth-averaged52

current, stratification, and discharge data. The XWT and WTC methods are used to determine
parameter dependency — we used these approaches to examine the dependency of circulation
on stratification and river discharge. XWT exposes the power of the relationship between twotime series, whereas the WTC reveals the coherence of the datasets. The WTC results can besignificantly coherent, despite having low power on the XWT. The physical relationship shownby XWT and CWT results is uncertain; however, interpretation of the physical association ofthese results is essential to reveal the dependency of circulation on stratification and riverdischarge.

3.4. Results
3.4.1. General circulation of Ota River Floodway
The wind, discharge, depth-averaged velocity, salinity, and mean flow profiles areshown in Figure 3.2. The time series of the wind magnitude shows a diurnal pattern with amagnitude of 2–8 m/s (Figure 3.2a) in a northeast –north direction (Figure 3.2b). The winddirection and magnitude (Figure 3.2a, b) changed significantly to the west between December
28, 2007, and January 1, 2008. However, calculation of the coefficient correlation between thealong-channel wind and non-tidal flow showed that the wind has no considerable effect. On
this basis, we assumed that the wind did not significantly influence circulation, thus, the impactof the wind was ignored in further discussion.

53

Figure 3.2. Time plots of (a) wind magnitude, (b) wind direction, (c) discharge at Yaguchi andGion stations, (d) depth-averaged velocity at St. A, St. B, and St. C, (e) salinity at St. A at thewater surface and bottom, (f) subtidal velocity, (g) temperature, and (h) density in St. A at thewater surface and bottom, and vertical profile along channel currents velocity at (i) St. A, (j)St. B, and (k) St. C. The Yaguchi Station is located around 14.6 km from the river mouth. The
wind direction is shown with north as 0ι, east as 90ι, south as 180ι, and west as 270ι.

The discharge at Gion was indirectly estimated from the discharge data at Yaguchi
Station [64]. During the observation periods, the mean discharge values at Yaguchi and Gion
were approximately 40 m3/s and 13 m3/s, respectively, while the maximum discharge values
54were approximately 132 m3/s and 36 m3/s, respectively. Figure 3.2c shows that the discharge
increased during January 9–16, 2008. During the high discharge period, the surface salinity
was low (Figure 3.2e), the maximum depth-averaged velocity decreased (Figure 3.2d), and thesubtidal velocity tended to flow downstream (Figure 3.2f).
Salinity, temperature, and density clearly show a tidal excursion (Figure 3.2e, g, and h).
Ebb–flood and neap–spring variations in salinity, density, and temperature are demonstrated
from the observation data. During the flood period, the near-bottom salinity and density values
are approximately 32 psu and 1023 kg/m3, respectively, indicating the intrusion of a water massfrom the sea. The temperature data shows that the water is warmer at a deeper level. The highest
salinity, density, and temperature differences occurs during the neap periods.
A tidal excursion was clearly observed in the depth-averaged velocity data (Figure3.2d). The subtidal velocity can be seen in Figure 3.2f, which was calculated using a low-passfilter from the depth-averaged velocity, with a 30-hour cut-off period. In general, the subtidal
velocities at stations A and B are landward during neap conditions, whereas the mean flow atstation C is seaward. The differences in patterns of the daily mean flow at the stations indicatedthat St. A and St. B are more affected by tidal excursions, whereas St. C is more affected byriver runoff. Moreover, because St. C is located on the tidal flat and the exit of curvature,
centrifugal acceleration plays a role in displacing the maximum current towards the exit of thecurvature [77]. In addition, the residual velocity is influenced by bathymetry, with intense
currents located in the shallowest parts of the river cross-section [77]. Vertical profiles of alongchannel currents at St. A, B, and C are shown in Figure 3.2i, j, and k, respectively. Field dataat St. A, B, and C revealed tidal current oscillations, indicating a strong flood-ebb tidal cycle.
The tidal currents at St. A and St. B appear to have similar ranges, while that at St. C has larger
tidal current. In general, these data indicate that the hydrodynamics of the Otagawa Floodway
are dominated by the influence of the tidal cycle.
55

3.4.1.1. Spring–Neap Tidal Variation
To examine the spring–neap variations in circulation, vertical profiles along the channel
currents at St. A, B, and C, and the bottom–surface salinity differences are presented during
spring (December 27–28, 2007) and neap conditions (January 1–2, 2008) (Figure 3.3). The
discharge conditions during these periods were low, i.e., ~20 m3/s in spring and ~30 m3/s inneap, based on observations at the Yaguchi Station (Figure 3.3c). As shown in Figure 3.3a ande, under spring tide conditions, the salinity difference at St. A during flood and ebb was 10–25
psu. The minimum and maximum salinity differences at St. A occur during the first flood andfirst ebb events, respectively. During the neap tide, the salinity difference during the ebb andflood was stable at approximately 27–30 psu. Overall, the tidal forcing controlls thestratification of the water column.
During the spring tide, the current velocities at St. A and St. B (Figure 3.3b, c) show
similar profiles. The upstream velocity during the flood is uniform with depth, whereas during
the ebb, the maximum velocity is near the surface. At St. C (Figure 3.3d), the maximum ebb
and flood current velocities are higher than those observed at St. A and B. The ebb currents at
St. A, B, and C have maximum velocity values near the surface; in contrast, the near-surface
ebb currents at St. C preceded the deeper layer currents. The higher downstream current
velocities and phase differences indicate that the effect of river runoff at St. C is greater thanthat at the other stations. The effect of river runoff could also be identified in terms of theasymmetry of the near-surface maximum downstream currents during ebb conditions at St. C.
The tide dominance at St. A and B is observed during neap conditions. During the neaptide, at St. A and St. B (Figure 3.3e, f, g, and h), the flood duration is longer than the ebb
duration. The flood duration was 7.6–8.3 hours, whereas the duration of the ebb was 5–6.3
hours. In contrast, the effect of river runoff at St. C caused a longer ebb duration than flood
duration, with values of 7–7.6 and 5–5.3 hours, respectively. The observed longer flood
56

durations at St. A and B suggest that even when tidal force during the neap is low, the tidal
straining component is dominant at both St. A and B. Because the locations of St. A and B arenear the river mouth, the tides have a predominant effect on circulation at these sites.
At St. C only, two-layer currents, in which the current in near-surface layer isdownstream and the current in deeper layer is upstream, are observed during flood and hightides for both neap and spring periods, even though discharge is low (Figure 3.3d and h). This
two-layer flow is characteristic of baroclinic circulation in stratified estuaries [78] and usuallyoccurs due to interactions between the river discharge and the horizontal gradient density [45].
However, two-layer flow is only observed at St. C and not at St. A and B; therefore, wehypothesize that the two layers occurs because St. C is located upstream, where the riverinfluence is stronger, and the density at St. C would be lower. As a result, the horizontal density
gradient at St. C would be higher than that at St. A and St. B. Moreover, blocking of water flowat the Gion gate leads to lower tidal current velocities and weaker tidal mixing in the upstream
region of the floodway; the depth-averaged velocity at St. C is lower than velocities at Sts. A
and B as shown in Figure 3.2d.

57

Figure 3.3. Temporal variation of the (a, e) surface-bottom salinity difference profile at St. A
and (b-d, f-h) velocity profiles at (b, f) St. A, (c, g) St. B and (d, h) St. C during (a-d) springand (e-h) neap conditions. Positive values indicate flood and landward currents conditions.

58

3.4.1.2. Influence of Discharge Variation
The effect of discharge variation was examined by comparing the vertical profile oflongitudinal currents during spring tide under low discharge (20 m3/s) and high discharge
conditions (110 m3/s). The longitudinal velocity data were captured on December 25, 2007,
and January 12, 2008. The influence of discharge on the circulation is shown only at St. A andB, as no records were available at St. C during the studied period (Figure 3.4). During the highdischarge condition, the fluctuation in the salinity difference is greater; this parameter
fluctuated from 5 psu during the flood to 30 psu during the ebb. During the low discharge
period, the maximum flood and ebb currents are 0.51 m/s and 0.46 m/s, respectively, whereas,
during the high discharge period, the maximum flood and ebb currents are 0.33 m/s and 0.56
m/s, respectively. Compared with the low discharge condition, under high discharge condition,
the currents in the flood tide are weaker, while the currents in the ebb tide are stronger. The
non-tidal currents (Figure 3.2f) show that the seaward currents strengthen during the highdischarge period, strengthening the ebb currents and damping the flood currents. In addition,
during the high discharge period, there is a phase difference between the flow in the upper anddeeper layers, where the upper phase propagates into a deeper layer.

59

Figure 3.4. Temporal variation of (a, d) the surface-bottom salinity difference profile at St. A
and (b, c, e, f) velocity profiles at (b, e) St. A and (c, f) St. B during (a-c) low and (d-f) highdischarge conditions. Positive values indicate flood and landward currents conditions.

3.4.2. Mixing
The mixing intensity was measured using the bulk Richardson number (Figure 3.5a).
During the neap-spring cycle, the low frequency of the Richardson number increases during
the neap period. High stratification and low tidal velocity during the neap condition are related
to an increase in the Richardson numberሺܴ݅௅ ሻ; therefore, the observed strong fluctuations of60ܴ݅௅ in the spring conditions are mainly caused by the high variability of stratification andcurrent velocity.

Figure 3.5. Time plot of the (a) bulk Richardson number ሺܴ݅௅ ሻ and (b) Freshwater Froude
Number (‫ݎܨ‬௙ ) — Mixing tidal efficiency (‫)ܯ‬

The mixing was evaluated based on the driving forces, which are tidal currents and river
runoff, using the mixing tidal efficiency (‫ )ܯ‬and Freshwater Froude Number (‫ݎܨ‬௙ ). Mixing
analysis was performed only at St. A. Variations in both mixing parameters (Figure 3.5b) are
affected by fluctuations in salinity, which varied with both ebb–flood and neap–spring cycles.
The effect of tidal currents can be seen in the magnitudes of the ‫ ܯ‬value — the tidal velocity
is higher during spring, thus, the magnitudes of ‫ ܯ‬increase during the spring period. The effect61

of discharge can be seen from the low magnitudes of ‫ݎܨ‬௙ . During the high discharge period,
the magnitude of ‫ݎܨ‬௙ increases. During the neap condition, the variation in density is low;hence, the variation in ‫ݎܨ‬௙ is low.
Evaluation of the mixing using the ܴ݅௅ , ‫ݎܨ‬௙ and ‫ ܯ‬values suggests that mixing
variation is affected by fluctuations in the salinity, which vary during ebb–flood and neap–
spring cycles. Horizontal density variations can induce tidal straining, while vertical density
variations can suppress vertical mixing [51, 79]. The daily mixing variation is controlled bydensity fluctuation, which is influenced by tides. Figure 3.5 shows that during flood conditions,the stratification weakens owing to the increasing of the mixing and the current velocity. In theneap and spring cycles, the ‫ݎܨ‬௙ and ‫ ܯ‬values reveal that the role of river discharge in mixing
is more significant during the neap tide. Moreover, during high discharge periods, the effect ofriver flow increased (Figure 3.2f), inducing an increase in the value of ‫ݎܨ‬௙ (Figure 3.5b)— thisincrease in ‫ݎܨ‬௙ indicates that higher river velocities tend to mix the water column and suppress
stratification.

3.4.3 Wavelet Analysis
3.4.3.1. Continuous Wavelet Transform
Wavelet analysis was used to analyze the variability of currents at Sts. B and C, thebottom-surface density difference value at St. A, and river discharge (Figure 3.6). The CWT
results for the current data at Sts. B and C ( Figure 3.6a, b) clearly show a strong semidiurnal
signal during the observation period, except for under the neap condition. Furthermore,strengthening of the diurnal period signal is observed in both CWTs, although the signal is not
significant (Figure 3.6a,b). This strengthening indicates the influence of tidal diurnal
components on tidal currents. In particular, for the CWT of the data from St. B, signals with62

shorter periods (i.e., higher frequencies), such as 0.25 days, showed significant power.
Coincident with increased discharge, the signal is slightly strengthened over periods of 2–4
days.

Figure 3.6. Continuous Wavelet Transform (CWT) of depth-averaged velocity at (a) St. B and(b) St. C, (c) surface–bottom density difference, (d) river discharge.

The CWT of the bottom–surface density difference value at St. A (Figure 3.6c) showsa different pattern from the CWT of the currents. The strongest signal of the CWT density
difference value is in diurnal periods during the observation period, except during the neap
condition. We also note that the power of the CWT weakens significantly during the neap
condition. The strong signal during the diurnal periods demonstrates that tidal straining occurs
63once in one tidal cycle. This differs from the semidiurnal tidal regime in the Otagawa
Floodway, where two flood and ebb events occur per tidal cycle. In addition, the CWT of thedischarge data in Figure 3.6d indicates a strengthening of the signal during January 9–16, 2008,
coinciding with the increase in discharge.

3.4.3.2. XWT and WTC of the St. B Currents
Wavelet transform coherence (WTC) and cross wavelet transform (XWT) are appliedon the currents in St. B, discharge, and vertical density differences to capture the interactionsof currents, discharge, and buoyancy during low–high discharge and neap–spring conditions.
The XWT and WTC between currents and the vertical density difference (Figure 3.7a, b) showthat the power of the XWT is significant in the diurnal and semidiurnal periods in the spring
condition. The WTC results show that the signals are coherent with the diurnal frequency inthe first spring period (December 22–28, 2007), where the phase of the buoyancy signal
influences the current signal. This indicates that buoyancy affects currents by inducing
straining. The WTC during the second spring tide (January 8–16, 2008), which coincides with
the increase in discharge, shows coherence in the semidiurnal and diurnal periods. The
strengthening of the signals indicates an enhancement in tidal straining.
The response of the currents velocity due to fluctuation of the river discharge is
examined using the XWT and WTC between the depth-averaged currents and the discharge, as
shown in Figure 3.7c and d. At St. B, the power of the XWT is significant in terms of thesemidiurnal variation during the observation period, whereas the diurnal frequency issignificant during the high discharge condition (e.g., 11–16 January 2008). The WTC indicatesa significant signal in diurnal variation during the neap tide. Furthermore, during the highdischarge episode, the diurnal variation signal is significant. The coherence of currents andriver discharge on the neap tide suggests a strengthening of influence of the river discharge to64the currents velocity when the tidal force is minimal. Moreover, from 11–16 January 2008,
when the river runoff was high, the effect of discharge is clearly shown in the results of XWTand WTC.

Figure 3.7. Cross wavelet transform (XWT) between currents in St. B with (a) surface–bottom
density difference and (c) river discharge. Coherence wavelet transform (WTC) between
currents in St. B with (b) surface–bottom density difference and (d) river discharge.

3.4.3.3. XWT and WTC of the St. C Currents
Because the duration of current observations at St. C was limited, the data only captured
the neap and spring periods during the low discharge condition. The results of the XWT and
WTC between the current and surface–bottom density differences are shown in Figure 3.8a.
The XWT analysis shows the significant power of the semidiurnal component throughout theobservations and of the diurnal component during the middle to the end of the observation
65

period (December 28, 2007 –January 2, 2008). The CWT shows coherence signals in thesemidiurnal variation from the end of the first spring until the first neap (December 28, 2007 –January 2, 2008); in contrast, during the second period, neap to spring (January 3–10, 2008),
the CWT shows significant coherence in both semidiurnal and diurnal periods. However, thephase of the coherence signal in both periods is completely different, indicating an opposing
relationship between currents and buoyancy.

Figure 3.8. Cross wavelet transform (XWT) between currents in St. C with (a) surface-bottom
density difference and (c) river discharge. Coherence wavelet transform (WTC) between
currents in St. C with (b) surface–bottom density difference and (d) river discharge.

66

The XWT of the depth-averaged currents with discharge (Figure 3.8c) shows
significant diurnal power during the observation period. However, the coherence signal (Figure3.8d) is particularly evident under neap conditions (December 31, 2007 –January 2, 2008). The
coherence suggests that the influence of river runoff significantly influences circulation.
Regardless of the low river discharge condition (approximately 40 m3/s), the effect of river
runoff is noticeable during the neap condition due to the weakening of tidal influence.
3.5. Discussion
3.5.1. Interpretation of mixing
Estuary regime mapping using ‫ݎܨ‬௙ and ‫[ ܯ‬71] was applied to the Ota diversion channel
floodway (Figure 3.9). The solid red line indicates the condition for vertical mixing that divides
the estuary into areas that should always be stratified and areas in which mixing occurs during
the tidal cycle. Figure 3.9 shows that the regime of the Ota River Floodway estuary can beclassified as a salt wedge estuary, even though during spring (low discharge) periods, theestuary was strongly stratified, whereas during spring (high discharge) and neap (lowdischarge) periods, the regime shifted to the salt wedge type. We interpret this range ofclassification to be related to neap–spring tidal variation and river flow variation. Similar
ranges of estuary type classification can also be observed in the Hudson River, ChesapeakeRiver, and Ebro River [71]. Figure 3.9 shows that some points have ‫ ܯ‬values that pass thecondition for vertical mixing. This condition occurs during flood events during the spring(Figure 3.5) indicating that vertical mixing takes place during this period.
Mapping the ‫ݎܨ‬௙ and ‫ ܯ‬values of the estuary is a powerful tool for classifying estuaries
based on variations in river discharge and tidal variation; however, this approach cannot
determine the salt wedge geometry, such as its height and length. In this study, the salt wedge
geometry was not calculated because of insufficient data. Determining the salt wedge geometry
requires the longitudinal vertical salinity profile [56, 75].
67

Figure 3.9. Estuarine parameter space, based on the freshwater Froude number (‫ݎܨ‬௙ ሻ and
Mixing tidal efficiency (‫) ܯ‬. The solid red line is the condition for vertical mixing. The
estuarine classification and example estuary are adapted from Geyer and MacCready (2014)

3.5.2. Interpretation of the wavelet analyses
The CWT of the parameters shows that the currents mainly have 0.5-day periods andthe surface-bottom density difference has 0.5- and 1-day periods, whereas the river discharge
does not show clear periodicity. The 0.5- and 1-day periods captured in the currents and thesurface-bottom density differences show clear tidal influence. However, the CWT of current
data from St. B shows significant power at lower periods (higher frequency), such as 0.25 days.
The appearance of a higher frequency component at St. B could be caused by the convergenceof tidal and river discharges [80].
68The WTC and XWT between currents and density differences show that tides play a
key role in mixing, as the strength of mixing is controlled by the tides. These results
demonstrate the role of the currents to the mixing: the mixing increases due to an increase in
the tidal force during the spring. Furthermore, the tidal force is weak during the neap tide,
prompted a decline in tidal straining. This is exhibited by weakening of the XWT power during
the neap tide (Figure 3.7a and Figure 3.8). The observed phase differences during neap andspring in the WTC (Figure 3.7b and Figure 3.8b) confirm that strong straining occurs during
the spring and weakened during the neap period.
3.5.3. Convergence Zone in the Ota River Floodway
Estuary systems with a stronger flood than the ebb velocity tend to promote thelandward accumulation of suspended material [81]. This accumulation is a result of transportof suspended material and tidal pumping during flood events. River discharge influences theseaward transport of suspended materials. The effects of tidal and river discharge forces will
likely lead to the formation of a convergence zone in an estuarine system; such convergencezones driven by tides and river discharge tend to act as suspended sediment traps [4]. As aresult, estuarine turbidity maxima (ETM) arise in the convergence zone.
In the case of the Otagawa Floodway, a convergence zone is identified around St. A
and St. B [25]. The contrasting characteristics of currents at Sts. A, B and C (Figure 3.2)
confirm the presence of convergence zone occurrence in the middle of the Ota Floodway [4].
The subtidal velocity and tidal asymmetry at Sts. A, B, and C were compared and are presented
in Figure 3.10a. The tidal peak current asymmetry, which shows the skewness between thepeak flood and ebb currents, is used as a measure of asymmetry and is calculated using thestatistical skewness method [81]. During spring, the subtidal velocity at St. A shows a seaward
flow with a weakly flood-dominated asymmetry. Note that neap conditions are not shown
because of the lack of available data during this period. The asymmetry at St. B shows flood69

dominance and a strong landward subtidal flow during the neap and spring. In contrast, at St.
C, the asymmetry is likely to be symmetrical with low subtidal flow during spring but strong
seaward flow during neap conditions.
The asymmetry difference between St. B and St. C in spring conditions suggests that
there is an imbalance of water transport in the middle of the channel of St. B and C, which
could cause sediment trapping (Figure 3.10a). Furthermore, the subtidal currents at St. B and
St. C converged to the middle of St. B and St. C (Figure 3.2f). This flow convergence induce
strong near bottom mixing which enhances sediment resuspension, which results in an ETM inthe convergence zone. The increased flood velocity during the spring tide enhances the bed
shear stress and mixing, leading to a higher SPM concentration [4]. To support this analysis,
we conducted a simple turbidity observation at St. A and St. B. The observations wereconducted during flood and ebb periods in spring conditions on April 17, 2021, and arepresented in Figure 3.10b and c. During both flood and ebb, the turbidity around St. B is higher
than that recorded at St. A. During the flood event, the tidal current is landward and induces
resuspension of sediment at St. B, while during the ebb, the current transports the SPM
seaward. From this work, the patterns of turbidity, asymmetry, and subtidal flow indicate an
ETM and convergence zone around St. B.

70

Figure 3.10. (a) Distribution of Spring/neap peak current asymmetry vs subtidal flow. Alongchannel turbidity in (b) flood and (c) ebb conditions.

3.6. Conclusions
In this study, we investigated the response of the circulation and mixing of the Ota
River Floodway estuary. The results reveal that the currents at three stations, located at 2.8 km,
4.8 km, and 6 km from the mouth of the river, are controlled by ebb–flood and neap–spring71

tidal oscillations. However, when the river runoff is high (i.e., discharge at Yaguchi Station >50 m3/s), the currents can be modified by strengthening the ebb flow and prolonging its
duration. During neap conditions, when the tidal force is weak, the influence of river runoff at
station C (6 km from the river mouth) is clearly shown compared to the other stations that arecloser to the river mouth. Mixing in the Ota River Floodway estuary is driven by tidal control,with this mixing following ebb–flood and neap–spring oscillations. Analysis of the mixing
using the mixing tidal efficiency (‫ )ܯ‬and freshwater Froude number (‫ݎܨ‬௙ ) reveal that the tides
dominantly controlled mixing in the Ota River Floodway estuary, however, the river discharge
contribution could be observed during the neap period. Overall, this study shows that theestuary regime of the Ota River Floodway can be defined as a salt-wedge estuary.
The continuous wavelet transform results show that the currents mainly have 0.5-day
periods, indicating the dominance of astronomical tides as a driving factor. The surface–bottom
density difference revealed periodic 1- and 0.5-day variations. The river discharge does notshow periodicity, however, the signal was strong on January 9–16, 2008, during a period of
increased discharge. The XWT and WTC reveal the relationship between circulation mixing
and river runoff. During spring, the tidal straining increases and induces intense mixing,
whereas during the neap tide, the tidal force is weakened, hence, the role of river runoff incirculation and mixing increases during the neap tide.
An extended analysis of the indication of the existence of a convergence zone using
ADCP data reveals that the convergence zone is estimated to be approximately 4.8 km fromthe river mouth. The presence of the convergence zone is characterized by the occurrence ofan ETM around the same area; however, the location of the convergence zone and the ETM
dynamically change depending on the relative force of the tides and river runoff.

72

This study highlighted the characteristics of mixing and longitudinal currents in shallow
floodway estuaries with limited discharge. Although the estuary is a tidal dominated and has alimited discharge, the role of discharge significantly affects the circulation and mixing,
particularly during neap tide. Moreover, the role of the discharge is significant in inducing theappearance of the ETM, which usually appears in high discharge estuary. The existence of theETM could affect the morphological change that could cause problems in the future. It isnecessary to investigate these issues further. In addition, studies in small and limited discharge
estuaries are still challenging, particularly those with unique geometries, such as multi-channel
estuaries and estuaries with curvature.

73

Chapter 4: Propagation of tidal waves in tidal-dominated multi-channel
estuary
4.1. Introduction
Tides are one of the main drivers of estuarine circulation in addition to river runoff.
Tidal wave dynamics in estuaries are modified by shallow water friction and topographicalsettings [9, 10, 82]. Increasing the damping of water elevation in an estuary is a balance
between channel convergence and friction [9]. Moreover, the same factors are responsible forthe modulation of compound tides and overtide constituents, which induces tidal distortion andasymmetry [10, 82]
The interaction between river runoff and tides influences the tidal wave dynamics byincreasing friction [11, 49]. Friction delays the phase, reduces the amplitude of the principal
tidal constituent, and increases tidal distortion and asymmetry [28, 29, 83]. In the case of highdischarge estuaries such as the Yangtze River, the river plays a significant role in modifying
the water level [84, 85]. Nonstationary and nonlinear tidal behaviours depend on variations in
the river discharge. Tidal nonlinearity increases with increasing river discharge [84, 85].
Additionally, river runoff affects circulation and sediment transport, causing estuarine turbidity
maxima [4, 50]. Although the effect of river discharge on the modulation of tidal evolution is
known, the tidal nonlinearity behaviour of short tidal penetration channels in small estuaries
has received less attention, although estuaries are the most common type of tidal river [53]. In
this study, a small estuary was defined as an estuary with a surface area of less than 50 km2[19].
In tidal-dominated estuaries, where the ratio between river runoff and tidal discharge isless than one, river runoff plays a limited role in modifying the elevation of tidal waves [46,86]. Tidal wave evolution is mainly affected by topographical settings, including changes in74the channel width and bathymetry [82, 86–88]. Shallow water friction in shallow bathymetry
decays the principal tidal component and modulates tidal asymmetry [82]. In an estuary with abifurcation channel, the tidal range decreases significantly at the apex of the bifurcation [17].
This is caused by the amassing of tidal waves from the convergence of the two channels [2,17]. The meeting location of the tides is not exactly at the junction but depends on the length,
width, and depth of the channel [2]. Although some studies have explored the changing tidal
range in bifurcation, the tidal evolution along the estuary and the nonlinear behaviour of thewater level at the junction require further analysis.
The Ota River Estuary is a multi-channel and tidal-dominated estuary located in thecentre of Hiroshima City, Japan. The estuary functions as a tourism area, port, and for oyster
cultivation. Water quality and river monitoring in the Ota River Estuary are important for
supporting these economic activities. The normal discharge in the Ota River estuary upstream(Yaguchi Station) is approximately 20-50 m3/s. The discharge from the upstream flows to twoareas of the Ota River estuary: the Ota diversion channel (ODC), which is a straight channel,
and the branching channel (Figure 4.1). The discharge of the Ota diversion channel (ODC) iscontrolled by watergate in the Gion (Figure 4.1), while the rest of the river runoff flows throughthe branching channel. With the controlled discharge and channel configuration that has
straight and multi-channel, the Ota River estuary is suitable for examining the effect of different
topographical setting on tidal wave dynamics. Moreover, river observation systems owned by
the government installed in the Ota River Estuary can be utilised to support studies in the Ota
River Estuary.

75

Figure 4.1. Observation stations and bathymetry of Ota River estuary network.

Previous studies [2, 17] have shown changes in the tidal range and the tidal nonlinearity
behaviour when the tides converge in the bifurcation channel. However, it remains uncertain,
for instance, what the mechanism of the changing nonlinear behaviour is, and how thecompound tides and overtide constituents are modulated in various channel topographicalsettings. Therefore, in this study, we explored tidal wave dynamics regarding the 2 different
topographical settings: a straight channel and a branching channel. We examined the temporaland spatial nonlinear behaviours of tidal waves in both channels using water elevation datafrom seven stations and current data from three ADCP stations. Bathymetric changes, channel
76

convergence changes, and subtidal friction decomposition were used to elucidate themechanism of the tidal wave nonlinearity modulation.
The remainder of this paper is organised as follows. The study area is described in
Section 4.2. The data and methods are explained in Section 4.3. The results and discussions arepresented in Sections 4.4 and 4.5, respectively. Finally, the conclusions of this study aresummarised in Section 4.6.

4.2. Study Area
The Ota River Estuary is located in Hiroshima Bay, Japan. The Ota River Estuary is
divided into natural multi-branching channels, including the Tenma, Kyu Ota, Motoyasu, andMisasa channels, and one artificial straight channel, the Ota diversion channel (ODC) (Figure4.1). The ODC is the main channel with mean channel depth and width around 2.1 m and 248
m, respectively, while the mean depth and width of the branching channel are 2.0 m and 212
m, respectively. However, the water depth at the mouth of the branching channel is up to 10
m, and Hiroshima harbour is located at the river mouth.
The Gion water gate is formed by rows of sluice gates located 8.8 km from the rivermouth upstream of the ODC (Figure 4.1). The sluice gates control the volume of the river
runoff in the ODC. Under normal conditions, the two gates is closed and one gate is slightly
open. When the discharge at Yaguchi exceeded 400 m3/s, all the sluice gates are opened. The
Gion gates are designed to runoff approximately half of the total water discharge when all thegates are opened.
The Ota River Estuary is a tidal-dominated estuary with a semi-diurnal tidal regime.
The maximum and minimum tidal ranges in the Ota River mouth are 3.6 m and 2.1 m
respectively. The maximum tidal compartment is approximately 13 km upstream of the rivermouth around the Kusatsu Station. The discharge at the Yaguchi gauging station ranged from77

50 to 80 m3, and during summer decreased to 20–30 m3 during winter, respectively [25, 65,89]. The discharge flows 20-50% to the ODC, and the rest flows to the branching channel [58].
A previous study reported that there was an equal discharge flow at the Misasa junction, where
50-63% discharge flowed to the east branch [90] and reached a maximum during spring.
Discharge and tidal range play a role in the tidal distortion and asymmetry at this junction [86].

4.3. Materials and Methods
4.3.1. Data
Current and water elevation data at stations A, B, and C from the ADCP observations wereused to study the propagation of tides in the branching channel. Water elevation data is obtained
from water depth data. Stations A, B, and C were located 3.11 km, 3.12 km, and 5.04 km fromthe river mouth, respectively (Figure 4.1). Observations were conducted from 13-28 July 2021.
Moreover, hourly elevation data from the Water Information System, Ministry of Land,
Infrastructure, Transport, and Tourism (MLIT), Japan, during the same periods at St. Kusatsu,
Gion, Nagawaku, Misasa, and Yaguchi, were acquired to cover the entire estuary area. Stations
were located at 0 km, 8.2 km, 8.9 km, 5.04 km, and 13.7 km, respectively. The baseline of thewater elevation data from the Water Information System is the mean sea level of Tokyo Bay.
The water depths observed by ADCP (Station A, B and C) were transformed into water
elevations using water level at the nearest gauging station. Namely, the transformation was
done by matching the water depths at the high water to the high water level (HWL) of thenearest gauging station under low river runoff because the water surface gradient at HWL in
the estuary is negligible under low river runoff. The water depths at the station A and B weretransformed to the water elevations using HWL at Kusatsu station and the water depth at thestation C was transformed using HWL at Misasa station. The water elevations at these stations78

are shown in Figure 4.2. Water elevation data for Kusatsu are shown as tidal waves before
entering the estuary. The water elevation in Gion and Nagawaku represents a tidal wave
propagating in a straight channel. The water elevations at St. A, B, C, and Misasa represent the
tidal waves after propagation in the branching channel. The water elevation at Yaguchi is the
upstream station that is not affected by tidal waves but is associated with the river runoff
flowing at Yaguchi. Detailed locations of the stations are shown in Figure 4.1, and a descriptionof the ADCP data is presented in Table 4.1.

Figure 4.2. Time plot of water elevation data at (a) Kusatsu Station, (b) Gion Station, (c)Nagawaku Station, (d) Yaguchi Station, (e) Station A, (f) Station B, (g) Station C, and (h)Misasa Station

Table 4.1. ADCP settings and deployment
79

Station Bin size (m) Blank Space (m) Sampling periods (min)Installation

Observation periods

St. A

0.5

0.2

10

Upward Looking

13-28 July 2021

St. B

0.5

0.2

10

Upward Looking

13-28 July 2021

St. C

0.5

0.2

10

Upward Looking

13-28 July 2021

4.3.2. Tidal Analysis
4.3.2.1. Power Spectrum Analysis
Fourier analysis is a method for converting a continuous signal from time to the frequency
domain. The discrete Fourier transform (DFT) is a Fourier analysis for decomposing a timeseries with a certain time step into different amplitudes and frequencies. This method iscommon in earth science, particularly for exposing the variability of time-series data. In thisstudy, the fast Fourier transform (FFT) which is a fast DFT algorithm, was applied todecompose water elevation data. Water elevation data were analysed to determine thedifferences in energy distortion between the straight and branching channels.
4.3.2.2. Tidal Harmonic Analysis
Least-square harmonic analysis (HA) using the T_Tide package [91] was applied to water
elevation data. The method expresses the water level time series as the summation of the meanvalue and cosine function series, as follows:ே( 4.1 )

‫ܪ‬ሺ‫ݐ‬ሻ ൌ ܾ଴ ሺ‫ݐ‬ሻ ൅ ෍ሾ‫ܣ‬௡ ሺ߱௡ ‫ ݐ‬െ Ȱ௡ ሻሿ ൅ ‫ݎ‬ሺ‫ݐ‬ሻ௡ୀଵwhere ‫ܪ‬ሺ‫ݐ‬ሻ is the water elevation time series, ܾ଴ is the mean water level; and ‫ܣ‬, ߱, and Ȱarethe tidal amplitude, frequency, and phase, respectively, of tidal constituents n (n=1,2.. .N) and‫ݎ‬ሺ‫ݐ‬ሻ represents the residual components. The length of the time series determines the output of
the tidal constituents. Water elevation time series with a length of 30 days produced 29 tidal
constituents, while 25 h of data resolved six tidal constituents.
80

The tidal constituents resolved from HA can be used to estimate tidal asymmetry. Tidal
asymmetry is estimated by calculating the phase difference and amplitude ratio of tidal
constituents [28]. However, asymmetry assessment using HA is limited by the interaction ofparticular component e.g. M2-M4, and cannot calculate the net asymmetry resulting from thecomplex interaction of tidal constituents. In this study, we calculated the ratio between the total
amplitude of the quarter-diurnal constituents and semi-diurnal tidal constituents to examine thedistortion of the tidal amplitude along the channel.
4.3.2.3. Statistical Skewness of tidal duration
Tidal duration asymmetry (TDA) was estimated using a statistical approach by calculating
the skewness value [27, 28] computed as follows:ͳଷσே௜ୀଵሺ‫ݔ‬௜ െ ‫ݔ‬ҧ ሻܰെͳߛሺ‫ݔ‬ሻ ൌଷଶͳଶቂ ܰ െ ͳ σே௜ୀଵሺ‫ݔ‬௜ െ ‫ݔ‬ҧ ሻ ቃ( 4.2 )

where ߛ is the skewness, and ‫ݔ‬௜ is the time series data, ‫ݔ‬ҧ is the expected value (mean value),and ܰ is a number that equals the length of the time series. The TDA was computed byassuming x to be the derivation of water elevation ሺ‫ ݔ‬ൌ ݀ߟΤ݀‫ ݐ‬ሻ. ሻ. A positive skewness
indicates flood dominance, where the rising tides are longer than the falling tides, whereas anegative skewness indicates ebb dominance, where the rising tide is shorter than the fallingtide. Guo et al. (2019) [27] showed that the calculation of TDA using the skewness method isequivalent to the calculation of tidal asymmetry using phase difference. Skewness methods canalso be applied to diurnal, semidiurnal, and mixed-tidal regimes. The skewness method can beused to calculate the net asymmetry caused by multiple tidal compounds and subtidal
variations. However, the skewness value is limited to measuring the absolute value ofasymmetry in a relative manner, and lacks a physical background. The physical connection
between skewness and tidal wave distortion must be explained.
81

4.3.3. Decomposition of Subtidal Friction
The friction term in the subtidal momentum balance equation is a nonlinear source of the tidal
dynamics in estuaries. Friction plays a significant role in the damping and amplification of tides[10, 92]. The friction term is expressed as follows:
‫ܹ݃ۃ‬

ܷȁܷȁ
ܹ݃ ଶగ
‫ۄ‬
ൌ
න ܷȁܷȁ݀‫ݐ‬‫ܥ‬ଶʹߨ‫ ܥ‬ଶ ଴( 4.3 )

where ܷ is the current velocity, ܹ is the channel width, ‫ ܥ‬is the Chézy coefficient, and theangular bracket represents the average over the diurnal tidal cycle.
The product ܷȁܷȁ in the friction term is approximated analytically using an oddfunction [93, 94], which adequately explains the interaction of tidal components and evaluates
the compound tides associated with friction [94]. The approximation is expressed as follows :ܹܷ݃௠ ଶ ଶగܹ݃ ଶగ෩ ൅ ܾܷ෩ ଷ ൯݀‫ݐ‬නܷȁܷȁ݀‫ݐ‬ൎන ൫ܷܽʹߨ‫ ܥ‬ଶ ଴ʹߨ‫ ܥ‬ଶ ଴( 4.4 )

෩ is the current velocity nondimensionalised by the maximum velocity ሺܷ௠ ሻ , ܽ ൌwhere ܷͲǤ͵͵ͻͷand ܾ ൌ ͲǤ͸͹ͻͳ[93, 94]. Moreover, the current velocity can be decomposed based on
current velocity decomposition [85, 92]. which is approximated as෩ ൌ ‫ݑ‬෤଴ ൅ ‫ݑ‬෤ଵ ሺ߱ଵ ‫ ݐ‬൅ ߶ଵ ሻ ൅ ‫ݑ‬෤ଶ ሺ߱ଶ ‫ ݐ‬൅ ߶ଶ ሻ
ܷ

( 4.5 )൅ ‫ݑ‬෤ସ ሺ߱ସ ‫ ݐ‬൅ ߶ସ ሻ
where, ‫ݑ‬෤௜ , ߱௜ and ߶௜ are the nondimensional velocity, frequency, and phase of tidal current
constituents, respectively, with the subscripts ݅ ൌ ͲǡͳǡʹǡͶ indicating the subtidal current,
diurnal, semi-diurnal, and quarter-diurnal, respectively.
To resolve subtidal friction, Equation 4.4 was integrated over the diurnal cycle. The
integration resolved the three subtidal friction terms, as follows:82ܹܷ݃௠ ଶ ଶగ෩ ൅ ܾܷ෩ ଷ ൯݀‫ݐ‬න ൫ܷܽʹߨ‫ ܥ‬ଶ ଴ൌܹܷ݃௠ ଶ
൭൫ܽ‫ݑ‬෤‫ݑ‬଴ ൅ ܾ‫ݑ‬෤‫ݑ‬଴ ଷ ൯ʹߨ‫ ܥ‬ଶ൅͵ܾ൫‫ݑ‬෤‫ݑ‬଴ ‫ݑ‬෤‫ݑ‬ଵ ଶ ൅ ‫ݑ‬෤‫ݑ‬଴ ‫ݑ‬෤‫ݑ‬ଶ ଶ ൅ ‫ݑ‬෤‫ݑ‬଴ ‫ݑ‬෤‫ݑ‬ସ ଶ ൯ʹ൅͵ܾ൫‫ݑ‬෤‫ݑ‬ଵ ଶ ‫ݑ‬෤‫ݑ‬ଶ ሺʹ߶ଵ ൅ ߶ଶ ሻ ൅ ‫ݑ‬෤‫ݑ‬ଶ ଶ ‫ݑ‬෤‫ݑ‬ସ ሺʹ߶ଶ ൅ ߶ସ ሻ൯൱Ͷ

( 4.6 )

The first term of the integration product is ‫ܨ‬௥ which reflects the contribution of the subtidal
flow to the friction term; the second term is ‫ܨ‬௥௧ that expresses the friction induced by thesubtidal flow and tidal interaction; and the third term is ‫ܨ‬௧ which indicates the friction term
induced by tidal asymmetry.
4.4.

Results

4.4.1. Subtidal Variations
The water elevation data in Figure 4.2 show that both straight and branching channels
were controlled and dominated by tides, except at the Nagawaku and Yaguchi stations. The
absence of tidal domination at the Yaguchi gauging station revealed that the tidal wave
penetration did not reach the Yaguchi station. Moreover, the water level data from the
Nagawaku station show that river runoff plays a significant role because the tidal wave isblocked by the Gion gates.
The water elevation at Kusastu (channel entrance) represents the water elevation prior
to entering the estuary. The highest and lowest water levels at Kusatsu was 2.21 m and -1.48
m, respectively, and occur during spring tide. The highest water level did not significantly
change after entering the estuary. However, the lowest water level had noticeable changes inGion with -0.65 m, while in Misasa stations was -1.02 m, respectively. The changes in thelowest water level indicate the damping of the tidal wave amplitude.

83

The tidal ranges in the straight and branching channels are shown in Figure 4.3a, b. The
tidal range was calculated by subtracting the maximum and minimum values of water elevation
every 25 h. The tidal range at the Yaguchi station was not calculated because of the absence oftidal effects on water elevation. The tidal range in both the straight and branching channels
showed that the tidal range varied in the neap-spring cycle, where the tidal range increased
during spring. In straight channel, during spring tide, the tidal range decreased from 3.6 m at
Kusatsu to 2.8 m at Gion, then dropped to 1.9 m at Nagawaku. The decreasing tidal range from
Gion to Nagawaku is more significant than from Kusatsu to Gion, even though the distance
Kusatsu –Gion is 8.2 km while Gion –Nagawaku is 0.6 km. The considerable decrease in the
tidal range at Nagawaku indicates the effect of the Gion gate. Similarly, in the branching
channel, the decrease in the tidal range was gradual toward the distance from the river mouth,
except at St. C. During the spring tide, the tidal range at St. C was less than that at Misasa
Station. St. C was dry during the lowest water level in spring. As we did not observe the lowest
water level at St. C, the tidal range at St. C was lower than that at Misasa during spring tide.
The subtidal water elevation was calculated by averaging the water elevation data overa 25-hour window. The subtidal elevation in Kusatsu showed an increasing trend (Figure 4.3c,d). A similar trend was observed for the subtidal elevations at Gion, St. A, St. B, and Misasa.
This increasing trend was caused by seasonal fluctuations in the mean water level of Hiroshima
Bay. In contrast, the subtidal elevation in Nagawaku showed a decreasing trend similar to thatof the water elevation in Yaguchi (Figure 4.2d). The similarity pattern indicates the effect ofriver runoff on the subtidal elevation at Nawagaku Station. Furthermore, the subtidal elevation
at St. C shows a different pattern from the other stations, where it fluctuated around -0.05 –0.05m.

84

Figure 4.3. Time plot of tidal range (a, b) and subtidal elevation (c, d) of the water elevation
stations in straight (a, c) and branching (b, d) channel. The straight channel includes Gion andNagawaku Stations. The branching channels includes St. A, St. B, St. C and Misasa. Kusatsu
Station located at river mouth.

4.4.2. Tidal Oscillation
The FFT method was applied to water elevation data from Kusatsu, Gion, Misasa, andSts. A, B, and C to examine and compare the energy spectra of tidal oscillations in the straightand branching channels. The FFT results are affected by the durations of the observation andsampling periods. Longer observation periods revealed longer-period signals and a smaller
sampling frequency yielded a larger frequency signal. The data at St. A, B, and C were
resampled hourly to obtain the same variability results as the other data before applying themethods. The energy spectral analysis was expected to reveal changes in tidal oscillation fromthe river mouth to the inside of the estuary.
Figure 4.4a shows the change in the water elevation energy spectra from the river mouth
upstream in the straight channel and Figure 4.4b shows the spectra in the branching channel.
The water elevation spectrum at Kusatsu shows that the energy was dominated by 12- and 2485

hour period signals associated with semidiurnal and diurnal tides, respectively. Peak energy isobserved in shorter periods of 8, 6, 5, and 4 h and is attributed to compound tides. In the straightchannel, the decrease in energy in the 12- and 24-hour periods is clearly shown fromdownstream to upstream, whereas the shorter-period signals show increasing peaks. This result
indicates energy transfer from the major tidal components (diurnal and semidiurnal tides) tothe compound tides. In branching channels, an increase in energy in shorter-period signals isshown from downstream to upstream, particularly on 6 and 8-hour period signals, indicatingenergy distortion due to tidal distortion in the branching channel.

Figure 4.4. FFT power spectra of water elevation data in (a) straight channel, and (b)branching channel

Spectral analyses of water elevation data revealed the evolution of tidal oscillations
from downstream to upstream. However, spectral analyses are limited to showing the tidal
oscillation regime, and cannot analyse the exact tidal constituents involved in the oscillation.
Harmonic analyses were applied to the data to examine the evolution of tidal constituents fromdownstream to upstream. The results of harmonic analysis are presented in Table 4.2. The eighttidal constituents are listed in Table 4.2, consisting of two semidiurnal constituents, two semidiurnal constituents, three quarter diurnal constituents, and one subtidal constituent. In general,
tidal oscillations are dominated by semi-diurnal tidal constituents, followed by diurnal andquarter-diurnal tidal constituents. At Kusatsu, M2 is the most dominant tidal constituent,86

followed by K1, S2, O1, M4, MS4, and S4. The tidal constituent amplitudes at the upstream
stations have a similar pattern to that of Kusatsu station, except at St. A, where the MS4
amplitude is higher than the M4 amplitude. The results indicate a different tidal evolution inwhich the M2 constituent interacts with S2, resulting in a compound tide MS4 constituent.
However, the results of the harmonic analysis are consistent with those of the energy spectra
analysis, revealing tidal energy distorted from major tidal constituents (semi-diurnal anddiurnal tides) to compound tides.

870.372

O1

K1

D1

㻌

D4

D2

0.250

MSF

sub

0.016

0.015

0.001

MS4

S4

0.327

S2

M4

1.054

M2

0.075

㻌

㻌

A

㻌

㻌

P

195.540111.250

19.110336.280

274.190230.080

191.89022.720KusatsuA㻌 0.002

0.038

0.049

0.295

0.980

0.280

0.179

P

166.260

208.460

176.340

343.230

277.850223.460

193.100

29.630Gion㻌 0.101

㻌

㻌

㻌

㻌

㻌

㻌

0.013

0.072

0.147

0.212

0.580

0.174

0.102

0.066

A

50.610275.560

206.430331.860

286.660

202.760

160.330

143.850

P

Nagawaku

㻌

㻌

㻌

㻌

0.008

0.026

0.005

0.318

1.035

0.362

0.238

0.146

A

P

236.040

150.950

67.570340.790275.010226.250

187.030

11.980St. A
A

P

45.950㻌 0.002 273.930

0.018 137.060

0.018

0.325 337.380

1.053 274.290

0.368 227.850

0.249 190.330

3.920

St. B

㻌 0.059㻌㻌A

㻌 0.007

0.032

0.029

0.310

1.005

0.333

0.209

㻌 0.011

㻌㻌
P

281.960

204.540

150.500

338.330

276.550

230.130

192.240

310.360

St. C

Table 4.2. Harmonic analysis of the water elevation data in Kusatsu, Gion, Nagawaku, St. A, St. B, St. C and Misasa

㻌

㻌

㻌

㻌

0.004

0.029

0.046

0.305

0.988

0.317

0.203

0.078

A

P

88

50.660200.430

136.490338.750279.590226.900

193.040

36.430Misasa4.4.3. Tidal Distortion and Tidal Asymmetry
4.4.3.1. Spatial variation of Tidal Distortion and Tidal Asymmetry
The amplitude ratio of the quarter-diurnal and semidiurnal tidal species (D4/D2) wasused to estimate the net tidal distortion, without considering the differences in tidal evolution
and tidal constituent interactions at every station. The amplitudes of the semi-diurnal (D2),
diurnal (D1), and quarter-diurnal (D4) tidal species in the straight and branched channels areshown in Figure 4.5a. The amplitude of the tidal species was calculated by summing theamplitudes of the tidal constituents in the same species. The tidal constituents were produced
from harmonic analysis of the water level data during the observation period. This analysis
could diminish the effect of river discharge variation on tidal distortion estimation. Therefore,
the effect of the channel setting on tidal distortion could be evaluated.

Figure 4.5. (a) total amplitude of semidiurnal (D2), diurnal (D1) and quarter diurnal (D4) tidal
species, (b) Ratio of total amplitude quarter diurnal tidal species and semi diurnal tidal species,and (c) tidal duration skewness in straight and branching channel as a function of the distancefrom the river mouth.

The semidiurnal tide dominated the tidal oscillations in both straight and branching
channels, followed by diurnal and quarter-diurnal tidal components (Figure 4.5a). The
amplitudes of all tidal components change gradually from the river mouth upstream, except at
Nagawaku station. The amplitude ratios of the semidiurnal and quarter-diurnal in the channels
shows that the tidal distortion increases gradually in a similar pattern in both the straight and89

branching channels (Figure 4.5b). However, tidal distortion increases at Nagawaku. Rapidchanges in tidal component amplitude and tidal distortion in Nagawaku are influenced by theGion watergate between the Gion and Nagawaku stations, which blocks river runoff fromupstream and tidal flow from the Ota floodway entrance. The gate blocks the tidal propagationof the tidal wave, which causes a significant reduction in D2 and D1 amplitudes at Nagawaku
station.
Tidal asymmetry in semidiurnal tidal regime estuaries is commonly estimated by thephase difference between constituents M2 and M4 [27]. However, tidal asymmetry wasestimated using the skewness of the elevation-time derivative in this study. This method is
considered more suitable because the results of the harmonic analysis show that there arestations where the amplitude of MS4 is much higher than that of M4, which indicates adifference in the tidal compound mechanism. The skewness method can estimate the net tidal
asymmetry caused by all the tidal constituent interactions.
The calculation results of time duration asymmetry (TDA) using the data along theobservation duration are shown in Figure 4.5c. The TDA at the river mouth (Kusatsu Station)
showed flood dominance asymmetry, indicating a longer flood duration. In straight channel,
TDA at Gion and Nagawaku are 0.16 and 0.08, respectively. In the branching channel, TDA
increased with increasing distance from the river mouth. In both cases, the asymmetry increases
gradually with increasing distance from the river mouth, except at Nagawaku, where theasymmetry increases rapidly. However, the increase in TDA in the branching channel is steeper
than that in the straight channel. This indicates that the morphological setting of the branching
channel plays a role in the tidal asymmetry. In the ODC, the Gion gate blocks the propagationof the tidal wave and reflects the tidal wave. The reflected tidal waves could have increased theasymmetry of the Gion stations. Moreover, the rapid increase in asymmetry at Nagawaku could
have been caused by the existence of the Gion gate between the Nagawaku and Gion stations.
90

4.4.3.2. Temporal Variation of Tidal Distortion and Asymmetry
Theoretically, river runoff influences tidal interactions and the formation of compoundtides and overtides [85]. River runoff influences tidal dynamics by enhancing subtidal friction,
which plays a key role in tidal damping [11]. Moreover, when the tide propagates in an estuary,friction diminishes tidal energy and induces energy transfer related to overtides and compoundtide formation [84, 85]. Some studies have observed landward enhancement of the M4
constituent, damping of M2, and an increasing amplitude ratio (D4/D2) from neap to spring[84, 85]. In this study, the tidal response to tidal forcing was evaluated using variations in tidal
distortion and asymmetry. Tidal distortion was calculated using the ratio of daily D4 to D2,
whereas tidal asymmetry was evaluated using daily TDA. According to the tidal distortion
shown in Figure 4.6c, tidal distortion was high at the upstream stations and peaked during thespring tide, whereas during the neap tide, tidal distortion was minimal at all stations. The
variation in tidal distortion is related to the daily variation in the D2 and D4 amplitudes, as
shown in Figure 4.6 a and b, which show higher D2 and D4 values during the spring tides.
However, D2 decreases inside the estuary, whereas D4 increases. The variation in amplitude
D4 at the upstream station (Misasa and Gion Station, St. C) is higher than that at thedownstream station (Kusatsu, St. A, and St. B).
Amplitudes D2 and D4 at Nagawaku station have exceptional patterns, where D2
decreases and D4 increases significantly (Figure 4.6a, b). Amplitudes D2 and D4 were higher
during the spring tide; however, in the first spring period (13 July –18, 2022), the amplitudedecreased. The decrease in amplitudes D2 and D4 in Nagawaku is related to the higher river
runoff during this period, as shown by the water elevation in Yaguchi ( Figure 4.2d). This result
revealed that river runoff significantly affected the tidal dynamics at Nagawaku Station. Gion
watergates cause tidal damping and intensify the role of river runoff in Nagawaku tidal

91

dynamics. Moreover, the tidal elevation in Nagawaku is influenced more by the tide from
Misasa because of the limitation of tidal propagation from the Gion to Nagawaku.

Figure 4.6. Temporal variation of (a) D2 amplitude, (b) D4 amplitude, (c) ratio of D4 and D2,(d) time duration skewness at Kusatsu, Gion. Nagawaku, St. A, B and C and Misasa stations.

The daily variation in tidal asymmetry (Figure 4.6d) shows flood dominance,suggesting a longer flood duration with a neap-spring variation. However, the neap-spring
fluctuation was consistent at all stations except for Nagawaku and Gion. The TDA in Gion andNagawaku tended to ebb dominance during 13 July –18, 2022, coinciding with the increase inriver discharge.
4.5.

Discussion
The interaction of tidal constituents, generation of compound tides, and over-tides canbe modified by river runoff [11, 49, 85, 95]. Daily variations in tidal distortion and asymmetry
captured the effect of river discharge at Nagawaku Station from 13 July to 18, 2022 (Figure
4.6c, d). Furthermore, a slightly different pattern of tidal asymmetry was observed at the Gion
station during this period (Figure 4.6d). The exceptional pattern during this period is related to92

the increase in discharge, as shown by the increase in the water level in Yaguchi (Figure 4.2d).
During these periods at both stations, river runoff modifies the tidal asymmetry from flood
dominance asymmetry to symmetrical/ebb dominance tidal duration. This means that the river
shortens flood duration. The river discharge affected the tidal distortion and asymmetry in
Nagawaku the most because of the existence of the Gion water gate. The water gate, locatedbetween the Gion and Ngawaku stations, blocks the river flow and accumulates river runoff,
amplifying the effect of river runoff around the water gate. River flow enhances the frictionthat leads to energy transfer from the major tidal frequency to compound tides and overtides[85].
Despite river discharge, the nonlinearity of tidal behaviour can be affected bymorphological settings, including channel convergence, bathymetry variation, and junctions[9, 10, 17, 82, 86, 96]. The changes in bathymetry and convergence channel of the Ota River
Estuary are shown in Figure 4.7. The channel width of the straight channel narrows gradually,
while the branching channel narrows rapidly from the first 4 km and then widens gradually.
The straight channel bathymetry shallows gradually from 3 m in the river mouth to 1 m inGion, while the branching channel bathymetry changes rapidly in the first 1 km. The change inthe topographical setting implies a variation in tidal asymmetry which balances convergence,
bathymetry change, and friction, determining tidal damping/amplification [9]. Moreover, theconvergence of tides at a junction between two channels can generate compound tides thatinduce tidal asymmetry that plays a role in the transport of suspended sediments [2, 38, 86].
The implication of the different topographical settings between the straight andbranching channels can be seen in the tidal asymmetry and tidal distortion variation in the Ota
River Estuary network. The spatial variation of the tidal distortion and asymmetry in the Ota
River estuary network shown in Figure 4.5 exhibits the difference in the tidal distortion andasymmetry in the straight and branching channels. The tidal distortions in the straight and93branching channels were not significantly different (Figure 4.5b), whereas the tidal asymmetry
showed a considerable difference; the asymmetry in the branching channel increased rapidly
from the river mouth to the inner estuary (Figure 4.5a). The TDA in Sts. A and B is comparable
than the TDA of water elevation in Gion even though the location of St. A and B is 3.1 km
while Gion station is 8.2 km. The rapid increase in TDA at St. A and B was induced by the
rapid change in bathymetry (Figure 4.7b) and convergence channel (Figure 4.7a). Moreover,the convergence of tidal propagation at junctions at St. C and Misasa induces tidal interactions
that increase tidal asymmetry [2, 86]. The aggregate effect of the morphological setting of thechannel on tidal oscillations was evaluated; however, the effects of each parameter were notexamined in this study. A sensitivity analysis of these parameters can be applied to tidal
oscillations in future studies.

Figure 4.7. (a) Channel width and (b) channel depth a a function of the distance from rivermouth

Friction is a crucial term that play a role in tidal distortion and asymmetry [10, 92].
Current velocity data were used to estimate the contributions of subtidal currents, tidal currents,
and tidal asymmetry to the subtidal friction at St. A, B, and C using Equation 4.5. The equation
decomposes subtidal friction into the contributions of subtidal flow ሺ‫ܨ‬௥ ሻ , tidal-subtidal
interaction ሺ‫ܨ‬௥௧ ሻ and, tidal asymmetryሺ‫ܨ‬௧ ሻ. The correlation of the decomposition results withthe subtidal elevation (Table 4.3) showed a high correlation between the subtidal elevation and94

friction related to the subtidal flow at St. A and B. Moreover, the combination of subtidal
friction with other frictions was also highly correlated (Table 4.3). In contrast, the subtidal
elevation at St. C was highly correlated with the combination of friction related to tidal andtidal asymmetry ሺ‫ܨ‬௧ ൅ ‫ܨ‬௥௧ ሻ with a negative correlation. The negative contribution of the tidal
asymmetry friction term to water elevation indicates that friction results in a higher tidal
asymmetry [92]. The results suggest that subtidal flow modulates the subtidal water level at St.
A and B, where the channel is straight, whereas at St. C, where the junction area is located, thewater level is modulated by the interaction between tides and tidal asymmetry. This finding
again supports the previous argument which said the meeting of tides at the junction induces
tidal interactions that generate tidal asymmetry.
Table 4.3. Correlation value subtidal water level in St. A, B and C with subtidal friction interm of subtidal flow (Fr), tidal-subtidal interaction (Frt), tidal asymmetry (Ft).
Fr

Frt

Ft

Ft+FrtFr+Frt

Fr+Ft

Fr+Frt+Ft

St. A

0.91

0.60

0.40

0.55

0.90

0.90

0.89

St. B

0.65

0.50

-0.38

0.48

0.91

0.91

0.91

St. C

0.25

0.47

-0.30

-0.85

-0.56

-0.43

-0.59

Tidal asymmetry plays an important role in the residual sediment transport [30]. Owing
to the limited river runoff in the Ota River Estuary, tidal current asymmetry induces suspended
sediment transport [25]. This differs from a high-discharge estuary (discharge > 3000 m3), in
which discharges induce tidal asymmetry and play a role in suspended sediment transport [1].
However, in the ODC, the interaction between tides and river runoff results in estuarine
turbidity maxima [89]. The river runoff-tidal interaction and its relationship with sedimenttransport may be related to erosion and deposition in the Ota River estuarine network.

95

4.6.

Conclusions
We explored tidal wave dynamics in the straight and branching channels of the Ota

River estuarine network. The tidal oscillations were evaluated using spectral and harmonic
analyses. The spectral energy shows that there is an energy transfer from the primary tidal
frequency to the compound tide and over-tide frequency when the tidal wave propagates fromthe river mouth upstream. The result of the harmonic analysis supports the result that showsthat the diurnal and semidiurnal tidal species dominate the tidal oscillation, but the amplitudedecreased upstream, while the amplitude of the quarter diurnal tidal species increased.
Moreover, tidal distortion and asymmetry of the straight and branching channels of the Ota
River estuarine network were investigated. The ratio of semidiurnal and quarter-diurnal tidal
amplitudes and the skewness of the tidal duration were used to examine tidal distortion andasymmetry. The tidal distortions of the straight and branching channels are comparable in termsof spatial variation. In contrast, the tidal asymmetry in the branching channel increased rapidly
from the river mouth to the inside of the estuary, compared to the tidal asymmetry in the straightchannel. The rapid increase in tidal asymmetry in the branching channel was related to the
topographical setting of the branching channels, including rapid changes in the bottom
topography, channel width, and junctions.
In both the straight and branching channels, the tidal range decreased from the rivermouth to the interior of the estuary. The mean water levels at all stations, except Nagawaku,
showed an increasing trend with respect to seasonal water levels. The mean water level at thebranching channel was correlated with friction related to tides and tidal asymmetry, whereas
in the straight channel, the mean water level was correlated with friction related to subtidal
flow. Nagawaku Station, located near the water gate, had an exception in the tidal range andmean water level variation. The tidal range decreased and the mean water level showeddecreasing trends. The noticeably different patterns of tidal range and mean water level at the96

Nagawaku station are related to the effect of the water gate, which amplifies the influence ofriver runoff on the water level.
The effect of river runoff was clearly observed at stations around Nagawaku and Gion
stations around the water gate. River runoff affects tidal range, mean water level, tidal
distortion, and tidal symmetry. The water gate blocked river flow and controlled the runoff
volume of the ODC. The accumulation of water in the water gate amplified the effects of river
runoff. River runoff dampens tidal amplitude constituents, leading to a decrease in the tidal
range and water level. Moreover, river runoff shortens flood tide duration.
This study highlights the tidal wave dynamics difference between branching andstraight channels in small and short tidal-dominated estuary. The results showed that different
settings of topography, including channel configuration and bottom topography, played a rolein the tidal evolution of straight and branching channels. However, this study was limited tothe characteristics of the water elevation in both channels. Studies of estuarine dynamics insmall estuaries with multi-channel branches are still challenging, particularly regarding river
runoff-tidal interactions, and their relationship to sediment transport might be related toerosion/deposition.

97

Chapter 5: Sensitivity of Junction Width to Tidal Nonlinearity on Small andShallow Tidal Junction

5.1. Introduction
Investigations of the tidal wave evolution in tidal river networks have received
increasing attention in the literature. Many studies have been conducted in large estuarine
networks such as the Yangtze [85] and Mahakam Rivers [83], because they have high discharge
and sedimentation rates. In these estuaries, tidal wave dynamics are significantly modulated byriver runoff [85]. River runoff modulates tidal nonlinearity behaviour by increasing tidal
damping and asymmetry [49, 85]
In a tidal dominated estuary, where the ratio of river runoff to tidal discharge is lessthan one, the role of the river runoff inducing the tidal wave nonlinearity is limited.. The
evolution of tidal waves is affected more by shallow water friction with respect to bottom
topography changes [18, 82, 87, 88]. Using analytical approaches, the relation between friction
and convergence channel in tidal dominated estuary was examined by Savenije et al. (2008)[9].
However, this study was limited to a single, straight channel. Small estuarine networks withlimited discharge have achieved poor recognition, and the variation in the topographical setting
is rarely discussed. Studies on tidal wave evolution in small and narrow estuary networks
provide a better understanding of the tidal dynamics.
The water elevation in estuarine networks is more complicated than that in straight tidal
rivers. In an estuarine tidal network, tides propagate from multiple tidal inlets to the estuaries.
Topographical settings, including variations in bathymetry and channel length and width, affectthe tidal propagation [2]. This study focused on the water elevation in shallow and narrow tidal
junctions with limited river runoff. Moreover, in estuarine tidal junctions, the tidal range drops
because of the convergence of tidal propagation at the apex of junction [17]. Understanding the98

variables controlling tidal nonlinearity behaviour is important because tides may become adominant factor that controls sediment transport and nutrient mixing in estuarine networks.
However, this study limits the studies on the sensitivity of water elevation to variations in the
upstream channel width.
The remainder of this paper is organised as follows. Section 5.2 explains the methods,
including the observation data, analysis methods, and numerical model setup. In Section 5.3,
the results of the tidal asymmetry analysis from the observation data and models are presented.
A discussion and conclusion of the results are presented in Sections 5.4 and 5.5.

5.2. Methods
5.2.1. Observation Location and Data
The Ota River Estuary is an estuarine network dominated by tidal forcing and is locatedin Hiroshima city, Japan. The junction is located 5.3 km upstream from the river mouth (Figure5.1) The junction involved the upstream Kyu Ota branch (northern branch), downstream Kyu
Ota (west side branch), and Motoyasu (east side branch). Danial et al. (2019) [90] studied theMisasa junction that is located 1 km upstream from the studied junction, and showed theexistence of tidal discharge asymmetry induced by branch channel geometry variation. At thesame junction, Xiao et al. (2021) [18] showed that limited river runoff plays a role in tidal
asymmetry at the tidal junction.

99

Figure 5.1. Ota River channel network.

The water elevations at three stations at Sts. A, B, and C were observed using a pressure
sensor from aquadop ADCPs during 12–30 July 2021. Sts. A and B were located downstreamof Kyu Ota and Motoyasu branches, respectively. St. C was located at the junction upstream of
the Kyu Ota branch. Observational data are shown in Figure 5.2. During the neap tide, thewater elevations at St. A and St. B have the same amplitude and phase, whereas the water
elevation at St. C has slightly different amplitudes and phases (Figure 5.2b). On the other hand,during spring tide, at the highest high-water level, St. A and St. B water elevations are higher
than St. C (Figure 5.2c); however, at the second high-water level, St. C water elevation is higher
than St. B and St. A. Unfortunately, during the lowest low water level, we could not capture
the water elevation data at St. C and St. A because the station was dry. Visually, this100

observation shows a difference in tidal asymmetry between the straight channels in the Sts. AB and St. C. Tidal asymmetry assessment requires further analysis to quantify asymmetry.
Moreover, this result motivated the modelling examination, which aimed to understand thevariables controlling tidal asymmetry at junctions.

Figure 5.2. Water elevation observation in Sts. A, B, and C (a) during the observations, (b)during neap tide, (c) during spring tide.

5.2.2. Tidal Asymmetry Analysis
Harmonic analysis using the T_Tide package [91] was applied to the water elevation
data to decompose them into tidal constituent amplitudes and phases. The method shows thatthe time series data are composed by summation harmonic signals with a certain frequency,
amplitude, and phase, as follows:ே‫ܪ‬ሺ‫ݐ‬ሻ ൌ ܾ଴ ሺ‫ݐ‬ሻ ൅ ෍ሾ‫ܣ‬௡ ሺ߱௡ ‫ ݐ‬െ Ȱ௡ ሻሿ ൅ ‫ݎ‬ሺ‫ݐ‬ሻ

( 5.1 )

௡ୀଵ101

where the water elevation time series is denoted as ‫ܪ‬ሺ‫ݐ‬ሻ, ܾ଴ is the mean water level, and ‫ܣ‬, ߱,and Ȱ are the tidal amplitude, frequency, and phase, respectively, of tidal constituents n(n=1,2...N), and ‫ݎ‬ሺ‫ݐ‬ሻ represents the residual components.
The outcome of the harmonic analysis is the amplitude and phase, which were utilised
to estimate tidal asymmetry. The tidal asymmetry was calculated from the amplitude ratio of
the tidal constituents [38]. In this study, the ratio amplitudes of M4 and M2 are used to estimate
tidal distortion because the tidal regime in the Ota River Estuary is semi-diurnal [86].
5.2.3. Numerical Experiments
A depth-averaged version of the Delft3D model is used in this study. The depthaveraged model is selected instead of a 3-dimensional model because the 3-dimensional flow
is not important for studying the propagation of tidal waves. Furthermore, this model uses abarotropic mode and neglects density gradient.
Table 5.1. Parameter setting of idealized junction model
SymbolVariable

Value

∆x
∆y
h

along channel grid size
cross channel grid size
still water depth
length of seaward
channelriver discharge
amplitude of M2
amplitude of S2

40-170 m
10 m
5m

width seaward branch

70 mwidth upstream branch

160 m

Chezy coefficient

55 m1/2s-1

L
Q
M2
S2
Width
Branch
Width
Apex
C

10 km
50 m3s-1
0.7 m
0.4 m

An idealised model of the junction is built based on the Ota River Estuary junction. The
model grid is shown in Figure 5.3. The junction was located 10 km from the open-sea boundary,and the total length of the channel is 560 km. The upstream channel is set to be very long toensure that the tides are smoothly damped. The depth and width of the channel are designed
102

based on the average depth and width of the Kyu-Ota junction. The upstream branch width is
160 m, and the width of the downstream branches is 70 m. In this model, tidal forcing is limited
to only the M2 and S2 tidal constituents because the Ota River Estuary is dominated by semidiurnal tides. The parameter settings are listed in Table 5.1. Moreover, a series of simulations
is conducted to analyze the sensitivity of the model to width changes, while the otherparameters are fixed. The width of the upstream channel varies from to 70–208 m. The
sensitivity test aims to explain how the change in the width of the upstream branch affects thenonlinear behaviour of the water elevation in the junction.

Figure 5.3. a) Downstream part of the model domain, including the upstream channel and thebranch that connects to the sea. b) The grid surroundings of the tidal junction.

5.3. Results
5.3.1. Water Level Nonlinearity
Harmonic analysis on 25-hour window water elevation data shows that the amplitudesof M2 and M4 vary in the spring-neap cycle (Figure 5.4Figure 5.4). The highest amplitudes of103

M2 and M4 occur during the spring tide. M2 amplitudes at Sts. A and B are similar, whereas
the M2 amplitude is lower at St. C. In contrast, the M4 amplitude at St. C is higher than thoseat Sts. A and B. Although the amplitudes M2 at Sts. A and B have similar values, the M4
amplitudes at Sts. A and B have slightly different values and peaks. The topographical setting,including the bathymetric profile, channel length, and width, could have affected the different
M4 amplitude profiles at Sts. A and St. B. A significant increase in M4 at St. C indicates thatthe nonlinearity increases at the apex of the junction.

Figure 5.4. Amplitude of (a, c) M2 and (b, d) M4 from the (a, b) observation data and (c, d)idealized model.

The application of harmonic analysis to the water elevation of the idealised junction
model shows a pattern similar to the observations, where the amplitude of M2 at the apex of
the junction is less than the M2 amplitude in the downstream branches, and the M4 amplitude
at the apex of the junction is higher than the M4 amplitude in the branches. However, both theamplitudes of M2 and M4 of the model exhibit lower values than those of the observations.
The difference between the model and the observations can be attributed to the high degree ofsimplification of the model. However, the model reproduces the increase in tidal nonlinearity
from the downstream to the apex of the junction.
1045.3.2. Sensitivity Analysis
A sensitivity analysis by varying the upstream channel width is shown in Figure 5.5.
Only the amplitudes of M2 and M4 at the apex of the junction and left branch are shown
because the amplitudes of M2 and M4 at the right and left branches had the same value. The
results show that the M2 amplitudes at the left branch and apex decrease with an increase in
upstream channel width. In contrast, the M4 amplitude showed an increasing pattern with anincreasing upstream channel width. However, an exception pattern was observed at the 206 m
upstream channel width. The M4 amplitude was 0.07 m during the spring and 0.02 m duringneap, which is less than the amplitude of M4 at 160 m and 112 m channel widths.

Figure 5.5. Amplitude of (a, c) M2 and (b, d) M4 from at (a, b) left branch and (c, d) apex ofjunction.

105

The damping/amplification of water elevation is affected by the changes in friction andthe cross-sectional area of the channel[9]. Sensitivity analysis examined the changes in the
cross-section area to the water elevation damping/amplification by varying the width of the
upstream channel. The results show that the damping of the tidal wave increases with a larger
cross-sectional area: it is clearly observed that the M2 amplitude decreases with an increase in
the upstream channel width. However, this behaviour is not observed for the overtide
constituent; in this case, M4, which increases when the width of the upstream channel is morethan twice that of the downstream channel.

5.4. Discussion
The spring tide, neap tide, and 30 days period time-windows harmonic analysis was applied inwater elevation data. The neap tide window harmonic analysis shows the lowest amplitude
owing the low tidal forcing during neap tide, while the spring tide window harmonic analysis
shows the highest amplitude. The 30 days window harmonic analysis showed shows the meanvalue of the M2 amplitudes (Figure 5.6). Figure 5.6 summarises the sensitivity analysis of thejunction with changes in the upstream channel width. When the channel width increases, theamplitude of M2 gradually decreases. In contrast, the amplitude of M4 increases with the widthof the channel, except for the 220 m width of the upstream channel.

106Figure 5.6. (left) Variation of M2 and M4 amplitude to the width of upstream channel. (right)
Variation ratio of M4 and M2 to the width of upstream channel.

The application of the model at the junction is highly simplified. The Ota River junction
is more complex with variations in geometry and bathymetry. The complexity of the junction
is not considered in this model. Moreover, at the Ota River junction, the branches of thejunction (downstream Kyu Ota and Motoyasu) are connected downstream. However, thesimplified model can capture the nonlinear phenomena that occur at the junction.
The sensitivity of the tidal wave amplitude at the junction is used to analyse the changes
in upstream channel width to tidal nonlinearity at the junction. The ratios of the M4 and M2
amplitudes are used to measure the nonlinearity (Figure 5.6). We found that nonlinearity
increased as the width of the channel increased until the width of the upstream channel was
twice that of the downstream channel. Meanwhile, when the width of the upstream channel
was more than twice that of the downstream channel, nonlinearity decreased significantly(Figure 5.6).
When the tidal converges from the branches to the junction, the meeting of tidal waves
causes increasing tidal nonlinearity [17]. In a wider channel, the change of width from thenarrow channel in the branches to a wider channel in the junction induces decreasing of major
107

tidal constituents' amplitude significantly. However, when the junction becomes wider, the roleof river runoff is more influential. The river runoff dampens the tidal wave amplitude; hence,
the nonlinearity decreases. A decrease in the amplitude ratio in Figure 5.6 indicates an increasein role river runoff to the tidal evolution [97]. Horrevoets et al. (2004) [98] explained that thecritical point where river runoff dominated tidal damping was when the river runoff velocity
was larger than the tidal velocity. River runoff velocity could be a factor that determines the
maximum tidal nonlinearity. However, the study was conducted in a straight channel, andstudies on tidal junctions require further research.
5.5. Conclusions
Water elevation observations were conducted at the Ota River junction during neap andspring tides. We found an increase in tidal nonlinear behaviour from the river mouth to thejunction. The increasing of tidal nonlinearity during the spring tide indicates that tidal
nonlinearity is controlled by tidal amplitude. Based on these results, an idealised model using
a simplified scenario was applied to examine whether the junction geometry induces the tidal
nonlinearity. The model was simulated using constant discharge at the land boundary, M2 andS2 tidal constituents as open-sea boundaries, and uniform depth. The result of the numericalmodel can capture the observed phenomena. The results of the model indicate that the widthchannel changes in the junction play a significant role in increasing the nonlinearity of tidal
elevation.
The upstream channel width variation in the sensitivity analysis showed a splitting
result. The tidal nonlinearity increases for the width of the upstream channel is less than twiceof the downstream channel. Meanwhile, tidal nonlinearity decreases for the width of the
upstream channel is more than twice that of the downstream channel. The increasing tidal
nonlinearity was caused by the convergence of tides in the junction. However, at a wider
108

junction, the river runoff plays a significant role by damping both M2 and M4, which results
in a decrease in tidal nonlinearity. The results suggest that the tidal convergence of the channel
plays a role increasing the tidal nonlinearity in a narrow junction (the width of upstream
channel less than twice of downstream channel), whereas in a wider channel (the width of
upstream channel more than twice of downstream channel), river runoff plays a significant rolein the reduction of the tidal amplitude.
This study limited the investigation of the role of the upstream channel width on water
elevation in junctions using numerical model under simplified condition. The simplified
condition helps us reduce the complexity of tidal nonlinearity dynamics and focuses how theeffect of the channel width on tidal nonlinearity. However, the model is highly simplified byneglecting the depth variation, real channel length variation, and complexity of the
topographical settings. Therefore, a sensitivity analysis that considers these variables should
be conducted in the future to examine those variability to the tidal nonlinearity.

109Chapter 6: Conclusions and future works

6.1. Main conclusions
This research aims to characterize the tidal dynamics and its interactions with the river
runoff in a variate topographical setting. We conducted field observations and numericalexperiments to examine the mechanism of the tidal-river runoff interaction. The fieldobservations were conducted in the Ota river estuary. The numerical experiments were appliedin Segara Anakan Lagoon and a synthetic domain. The synthetic domain was adapted from thejunction in the Ota river estuary.
This study focuses on (1) characterization of tidal dynamics in the lagoon, single
straight channel, and multi-channel estuary (2) Interactions between tide and river runoff andhow the interactions affect the tidal currents and tidal elevation as well as mixing of the watercolumn.
The specific conclusions and contributions of this study can be summarized as follows:
1. The tidal wave simultaneously propagates to the lagoon through two open channels fromeastern and western inlets. During the rising tide, the tidal wave converges in the middle ofthe lagoon and diverges during the falling tides. The amassing tidal wave from eastern andwestern inlets in the middle of the lagoon induces an abrupt change in the tidal range andthe tidal asymmetry.
2. TDA and SWA in the eastern and western parts of the lagoon indicate ebb dominance but
shifting to flood dominance in the interior of the lagoon. The bottom friction delays thetidal wave celerity, leading to a longer flood duration in the interior of the lagoon.
3. In straight and branching channels, there is an energy transfer from the primary tide to thecompound tide and over-tide when the tidal wave propagates from the river mouth upstream,
as shown from the spectral energy and harmonic analysis.
110

4. The spatial variation of tidal distortions (ratio of amplitude: D4/D2) of the straight andbranching channels are comparable. In contrast, the tidal asymmetry in the branching
channel increased rapidly from the river mouth to the inside of the estuary compared to thatin the straight channel. The rapid increase in tidal asymmetry in the branching channel isrelated to the topographical setting of the branching channels, including rapid changes inthe bottom topography, channel width, and junctions.
5. The variation of mean water level is affected by the friction. The variation of mean waterlevel at the branching channel is correlated with the friction related to tides and tidal
asymmetry, whereas in the straight channel, the variation of mean water level is correlatedwith the friction related to subtidal flow
6. The water level station near the water gate has an exception in the tidal range and meanwater level variation. The noticeably different patterns of tidal range and mean water levelat the station are related to the effect of the water gate, which amplifies the influence ofriver runoff on the water level.
7. Sensitivity analysis shows that the width of the upstream channel in the junction plays asignificant role in the variation of the tidal nonlinearity. The tidal nonlinearity increases
when the width of the upstream channel is less than twice that of the downstream channel.
The increasing nonlinearity is caused by the convergence of tides in the junction. In
contrast, the tidal nonlinearity decreases when the width of the upstream channel is morethan twice that of the downstream channel. When the width of the upstream channel isequal to 2 times the branch channel, the cross-sectional area in the upstream is equal to thetotal cross-sectional area in the branches. Therefore, the tidal interaction due toconvergence in the junction is minimal. Hence, the river runoff could play a significant rolein damping both M2 and M4 amplitude, which results in a decrease in tidal nonlinearity.
111

8. Mixing analysis using Freshwater Froude Number (‫ݎܨ‬௙ ) — Mixing tidal efficiency (‫ )ܯ‬is
adequate to reveals that mixing in the ODC is driven by tidal control due to the limited
discharge during the observation (ܳ௬௔௚௨௖௛௜ = ~30 m3/s), with this mixing following ebb–
flood and neap–spring oscillations. The river discharge contribution could be significantly
observed during the neap period, even in limited discharge. The river discharge
contribution could be significantly observed during the neap period. During the spring tide,the contribution of river discharge to the mixing is considerable when the river discharge
increases more than the amplitude of tidal discharge. The contribution of river discharge tothe mixing is significant when the ratio between river discharge in Yaguchi and tidal
discharge amplitude is more than one (QYaguchi> Qtidal).
9. The cross wavelet transforms (XWT) and wavelet transform coherence (WTC) is able toreveal the nonstationary interaction of circulation, mixing, and river runoff, even though
the analysis is applied in short time-series data (less than 30 days).
10. Interactions between tides and river runoff induce the existence of a convergence zone thatis estimated to be approximately 4.8 km upstream from the river mouth based on theobservation of turbidity along the ODC. The presence of the convergence zone ischaracterized by the occurrence of an ETM around the same area; however, the location of
the convergence zone and the ETM dynamically change depending on the relative force ofthe tides and river runoff. The dynamics location of ETM could be determined using
polynomial regression between the observation of the ETM location and the discharge.
However, in this study, the equation could not be proposed because the longitudinalturbidity observation was only conducted once to confirm the existence of the convergencezone..

112

6.2. Future works
The research does not stop. An enormous number of points must be investigated infuture research:
1.

This research has investigated the tidal dynamics in the Segara Anakan lagoon. Studies
exploring tidal mixing, sediment transport, and sedimentation are important to conduct in
the future. Hence, more detailed and longer observations of the discharge, currents,
sediment characteristics, salinity, and temperature spatially and temporally would becomea database for more comprehensive research. The data can facilitate a solid understandingof hydro-sediment dynamics in the Segara Anakan Lagoon.

2.

Study of estuarine circulation and the interaction with the discharge and mixing in a single
straight channel have been explored in Chapter 3, showing the existence of ETM as theresult of the convergence zone. However, the interaction in the multi-channel estuary has
not been explored because the available data cannot be used to study mixing and sediment
dynamics in multi-channel estuary. Observation of the discharge, currents, sedimentcharacteristics, salinity, and temperature upstream and downstream of the junction could
give insight into the interaction of those parameters in the junction. In addition, it isimportant to understand how the tide–river runoff interaction affects the transport of
sediment and sedimentation in the long term.

3.

The ETM location dynamically changes depending on the relative force of the tides andriver runoff. The location could be determined using polynomial regression between theriver discharge and ETM location. In the future, along channel turbidity observations will
be conducted on various river discharges to develop the empirical equation of the ETM
location in the ODC. Moreover, since the ETM formation is on the head of the salt
intrusion, the analytical solution of the advection-diffusion equation for salt transport [99]will be applied as a proxy to predict the location of the ETM. The prediction of the113analytical solution will be validated using the empirical model that was built from theobservation.
4.

Examining the tidal nonlinearity behaviour is conducted by variating the width of the
upstream channel in numerical experiments. However, the experiment is limited on
examining the influence of the upstream channel area to the tidal nonlinearity behaviour.
We focused on how the transformation of tidal wave when the tidal wave converged invarious junction area. In future researches, I will investigate the effect of length and depthof the channel geometry to the tidal nonlinearity.

114

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