Spatial and temporal variability insalinity and tidal flow in a shallow tidal
channel㸦ὸ䛔ឤ₻Ỉ㊰䛻䛚䛡䜛ሷศ䛸₻ὶ䛾✵㛫ⓗ䛚䜘䜃᫬㛫ⓗኚືᛶ㸧

April 2022
Hiroshima University
Nguyen Thi HiepACKNOWLEDGEMENT
I would like to express my sincerest gratitude to my supervisor, Prof. Kiyoshi Kawanishi,
who has always supported me throughout my research. He has instructed me how to solve
academic research, as well as, interact and develop in international environmental education.
I would also like to gratefully acknowledge my co-supervisors, Prof. Yoshihisa Kawahara,
Prof. Tatsuhiko Uchida, for their kind instructions and supports during my research program.
I am particularly grateful to Asst. Prof. Mohamad Basel Al Sawaf, Dr. Cong Xiao, mylabmates, and the other students at the Coastal Engineering Laboratory of Hiroshima University
for assisting with the field observations.
I must also thank the Vietnamese Government Scholarship Student for the funding support
during my PhD’s course. Besides, I would like to express my gratitude to Hiroshima University
and National University of Civil Engineering (Vietnam) for giving me the chance to study inJapan.
Finally, I give special thanks to my children, my family members who are living in Vietnam
for their love, support, and encouragement.
Hiroshima, April 2022
Nguyen Thi HiepCONTENT
Abstract
CHAPTER 1

INTRODUCTION ....................................................................................... 1

1.1 Introduction .................................................................................................................... 1
1.1.1 The vital role of transverse salinity dynamic ........................................................ 1
1.1.2 The longitudinal distributions of salinity and tidal flow ....................................... 2
1.2 Objectives and challenges .............................................................................................. 4
1.2.1 Challenges ............................................................................................................. 4
1.2.2 Objectives .............................................................................................................. 5
1.3 Outline of the thesis ....................................................................................................... 5
CHAPTER 2
DENSITYVERTICAL AND LATERAL DISTRIBUTIONS OF SALINITY AND
6

2.1 Introduction .................................................................................................................... 6
2.2 Study area....................................................................................................................... 7
2.2.1 Ōta diversion channel ............................................................................................ 7
2.2.2 Study area .............................................................................................................. 8
2.3 Instrumentations........................................................................................................... 10
2.3.1 Compact CTD (Conductivity, Temperature, Depth) sensor ............................... 10
2.3.1.1 Depth sensor of CTD ........................................................................... 11
2.3.1.2 Water temperature sensor of CTD ....................................................... 122.3.1.3 Electric conductivity sensor of CTD ................................................... 122.3.2 Fluvial Acoustic Tomography (FAT) system ..................................................... 122.3.3 Hydrographic survey remote controlled boat RC-S3 .......................................... 13
2.4 Methodology ................................................................................................................ 14
2.4.1 Salinity and density data set collection ............................................................... 14
2.4.2 Fluvial Acoustic Tomography (FAT) system ..................................................... 17
2.4.2.1 Estimating sound speed using FATS ................................................... 17
2.4.2.2 Estimating depth- average salinity using FATS .................................. 17
2.4.3 Freshwater discharge data ................................................................................... 17
2.4.4 Cross-correlations................................................................................................ 18
2.5 Results .......................................................................................................................... 192.5.1 Salinity distributions in the cross section ............................................................ 19
2.5.1.1 Spring tide (the first campaign) ........................................................... 19
2.5.1.2 Neap tide (the second campaign) ......................................................... 24
2.5.2 Density distributions in the cross section ............................................................ 29
2.5.2.1 Tidally periodic density distributions .................................................. 29
2.5.2.2 Lateral density gradient distributions .................................................. 30
2.5.2.3 Vertical density gradient distributions ................................................. 32
2.6 Discussion .................................................................................................................... 38
2.6.1 The effect of freshwater discharge on stratification ............................................ 38
2.6.2 The effect of bathymetry on salinity stratification .............................................. 39
2.6.3 The effect of the water temperature .................................................................... 40
2.6.4 The time delays of the salinity ............................................................................ 42
2.6.5 The effect of the tidal straining and tidal time scale ........................................... 45
2.6.5.1 The effect of the tidal straining............................................................ 46
2.6.5.2 Contribution from the tidal time scale ................................................. 48
2.7 Conclusions .................................................................................................................. 48
CHAPTER 3
FLOW

LONGITUDINAL DISTRIBUTIONS OF SALINITY AND TIDAL
51

3.1 Introduction .................................................................................................................. 51
3.2 Study site ...................................................................................................................... 52
3.3 Instrumentation ............................................................................................................ 54
3.3.1 Fluvial Acoustic Tomography (FAT) system ..................................................... 54
3.3.2 Acoustic Doppler Current Profiler (ADCP) ........................................................ 55
3.3.3 CT (Conductivity, Temperature) sensor .............................................................. 56
3.3.4 Other instruments ................................................................................................ 57
3.4 Methodology ................................................................................................................ 57
3.4.1 The Fluvial Acoustic Tomography (FAT) system .............................................. 57
3.4.1.1 Estimating tidal current and water discharge using FATS .................. 57
3.4.1.2 Estimating depth- average salinity using FATS .................................. 58
3.4.2 Estimating the residual current velocity and residual water discharge ............... 58
3.4.3 Determination of flow direction using FATS...................................................... 59

3.4.3.1 Estimating the flow direction .............................................................. 59
3.4.3.2 Estimating the relative errors ............................................................... 59
3.4.4 Estimating the total error components of measurements of water discharge using
FATs 60
3.4.5 Longitudinal distributions of salinity, salinity gradient, and dispersion
coefficient ............................................................................................................ 61
3.4.6 Measurements of temperature, depth, and bathymetry ....................................... 61
3.4.7 Confirming the FATS feasibility to measure the section-average salinity ......... 61
3.5 Results .......................................................................................................................... 62
3.5.1 Temporal variations in water level along the channel ......................................... 62
3.5.2 Temporal variations in tidal velocity distribution along the channel .................. 63
3.5.2.1 Tidal velocity ....................................................................................... 63
3.5.3 Flow direction variations ..................................................................................... 64
3.5.3.1 The angle between two transmission lines .......................................... 64
3.5.3.2 The variations in area cross the channel at the three transmission lines
65
3.5.3.3 Flow direction variations deduced from FATS ................................... 66
3.5.3.4 The relative errors ................................................................................ 66
3.5.4 Estimating water discharge along the channel .................................................... 67
3.5.4.1 Estimating water discharge and residual water discharge ................... 67
3.5.5 Residual current and residual water discharge .................................................... 67
3.5.6 Temporal variations in salinity ............................................................................ 68
3.5.6.1 Cross-sectional average salinity deduced from FATS......................... 68
3.5.6.2 Longitudinal salinity distribution ........................................................ 69
3.6 Discussions .................................................................................................................. 70
3.6.1 Tidal asymmetry .................................................................................................. 71
3.6.2 Confirming the FAT ability to measure water discharge .................................... 73
3.6.3 Error structure for the river discharge measurement ........................................... 74
3.6.4 The practicability of using the FATs to measure the depth average salinity ...... 74
3.6.5 Longitudinal dispersion coefficient ..................................................................... 76
3.6.6 Time delays of the phases of salinity variation ................................................... 773.6.6.1 The effect of velocity on the travel time .............................................. 79
3.6.6.2 The delays of the phases of salinity variation ...................................... 80
3.7 Conclusions .................................................................................................................. 83
CHAPTER 4

CONCLUSIONS AND RECOMMENDATIONS .................................. 85

4.1 Summary ...................................................................................................................... 85
4.2 Conclusions .................................................................................................................. 86
4.2.1 Investigation of vertical and lateral distributions of salinity and density............ 86
4.2.2 The longitudinal distributions of salinity and tidal flow ..................................... 86
4.3 Novelties and new findings .......................................................................................... 87
4.4 Recommendations ........................................................................................................ 88
Appendix
References
List of Figures
List of Tables
Notations and Abbreviations

ABSTRACT
Estuaries are often the transport connection between rivers and the ocean as well as the source ofseveral factors that impact on human life such as food, water consumption, economic, and so on. The
results of the interaction between freshwater and saltwater will create a unique environment of each
estuary, which affects significantly several estuarine species. Salinity that is the salt amount dissolvedin water body and water current caused by the tides from the ocean always change within the time andspace. Understanding the mechanisms that control the salinity and tidal flow has an important role inestuarine management.
This work focuses on indicating the spatial and temporal variability in salinity and tidal flow inthe Ōta diversion channel which is one branch of the Ōta river system in Hiroshima city, Japan. With
the longest distance, large tidal flats, and freshwater run-off is limited by the gates, the Ōta diversion
channel becomes the most important branch of the Ōta river system in controlling flood, transportation,
economic development, etc. Besides, with the tidal range of 0.5 m to 4 m, the bottom of the Ōtadiversion channel is completely submerged at high water and partly dries out at low water, whichindicates that the Ōta diversion channel is a shallow tidal estuary.
The present study also aims to examine the performance of the proposed scheme using the FAT
system, which is a zigzag configuration in a rectangular tomographic domain of 700 m ൈ 170 m, in
terms of providing sufficiently accurate and cost-effective method to estimate riverine characteristics.
Three field observations were conducted during both neap and spring tides in a river segment withthe length of 850 m at the central part of the Ōta diversion channel (about 4.5 km from the estuary) tocollect the data set of salinity, water temperature, water density, and tidal current. Analyzing these data
set results in the spatial and temporal variation of salinity and tidal flow, then the estuarine dynamics
will be displayed.
By using the quantity and the depth of stratification layers as well as the surface-to-bottom salinity
difference deduced from the transverse and vertical distributions of salinity, the stratification/destratification degree is evaluated in a shallow, narrow, and tidal estuary. In detail, it was found that, inthe lateral and vertical dimensions, density driven is the main mechanism that controls the stratificationin the Ōta diversion channel. Stratification occurs during spring-ebb tides and early of neap-flood tides
because of the effect combination of tidal straining, tidal asymmetry and freshwater inflow fromupstream, while the lateral distribution of salinity appears during spring-flood tide and the late of neapflood tides due to the lateral density gradient.
In the longitudinal dimension, it was found that both tidal flow and salinity patterns reveal acompletely tide-dominated influence. The tidal flow is asymmetry, mostly due to the interaction of theO1 – K1 – M2 tidal constituents; and the topographic effects. The longitudinal dispersion coefficient wasfound to increase toward the mouth of the river, and the tide-driven mechanism might be the dominantmechanism in the dispersion process in the study site.
The salinity in the Ōta diversion channel does not response to the water level fluctuations
immediately. It was found that there are delays in time between the salinity and water level variations,with the salinity response time lags ranged from approximately 12 minutes to 1.5 hours, corresponding
to a phase lag range of 13q–47q. The time lags increase seaward along the channel, and decrease
corresponding with the increase of the upstream freshwater release.
Finally, the present research shows that with the lower needed instrument number, the new zigzag
configuration of FATs can be an accurate and cost-effective measurement method for monitoring
estuarine physics.

1. Introduction

CHAPTER 1

1.1

1

INTRODUCTION

Introduction

Generally, estuary is partially enclosed coastal area where the tide spreads along channels
and mixes with fresh run-off water from one or more rivers flowing into them. Thus, estuaries
are characterized by both river environments and maritime environments. Also, estuaries are
subjects both to fluvial influences such as freshwater and sediment and ocean influences suchas tides and saline water.
Estuaries constitute a significant object of several physical processes that vary in time andspatially, including freshwater input, salinity intrusion, and tidal movement. The salinity
intrusion, tides propagating, and the interaction of tide and/or wave with fresh run-off water
will affect all estuarine activities, including domestic, industrial, agriculture, and aquaculture.
Thus, understanding the distribution of salinity and tidal flow along the river as well as rivercross-sectional is necessary for water resource management.
1.1.1 The vital role of transverse salinity dynamic
Recently, several types of research on the salinity dynamics and its contributing factors havebeen done to provide the overall comprehension of the estuarine dynamics. The previous
researchers have tried to understand how the freshwater, saline water, and/or tide exchange
creates a complex environment. Those previous studies conducted in a various kinds ofestuaries, such as a tideless shallow coastal lagoon (Schumann et al., 2006), a deep and narrow1. Introduction2

dredged channel (Conroy et al., 2020). Besides, most published studies on salinity dynamics
were implemented using numerical models for deep and wide estuaries (Wang et al., 1992,
Lerczak & Geyer, 2004, Martyr-Koller et al., 2017). There are fewer studies focused on tidal
shallow and narrow estuaries where the interaction between freshwater, saltwater, and tide
often occurs very fast. Furthermore, salinity dynamics, mixing mechanisms, and salinity
transport downstream in estuaries are convoluted and primarily depend on estuarine
characteristics and three-dimension process i.e. estuarine circulation. In a three-dimension
structure, the motions in transverse and vertical directions in estuaries are usually smaller thanthe horizontal motion, but these motions have an essential role in the estuarine dynamics(Lerczak & Geyer, 2004, Hunkins K., 1981). However, the dynamics of lateral salinity inestuaries have not known full well. Thus, a research on salinity dynamic in lateral direction ina tidal shallow estuary is a necessary task in order to understand the estuarine dynamics fully.
1.1.2 The longitudinal distributions of salinity and tidal flow
The ability to accurately estimate the salinity intrusion and mixing in estuaries is critical tocoastal engineering and our understanding of estuarine dynamics. Saltwater intrusion isregulated primarily by the tide and river runoff (Laenen & Smith, 1983) and influenced byfactors including topography, wind stress, vertical mixing, tidal range, and freshwater flow
(Prandle, 2006, Chen et al., 2019, Li et al., 2012). However, the real-time monitoring of riverdischarge is necessary to analyze the estuary functioning at an adequate level of precision andto obtain accurate measurements of temporal variations in the freshwater inflow regime overspans of time ranging from several minutes to multiple years (Garel & D’Alimonte, 2017).
Continuous and long-term readings of freshwater inputs to estuaries are acquired using
stage–discharge rating curves established empirically at upstream gauging stations (K.
Kawanisi et al., 2016, Maghrebi et al., 2016). In estuaries influenced by salinity intrusion,
estimating the cross-sectional average velocity and discharge from spatial estimation (using
limited velocity measurements) is problematic due to the possible distortions in conventional,i.e., log or power law, profiles (Garel & D’Alimonte, 2017).
Most methods of estimating the horizontal distribution of salinity and velocity may beclassified as either direct or indirect. For direct methods, information about salinity and velocity
is typically collected during field observations using various instruments deployed at several
locations within the target site at different time periods (Geawhari et al., 2014, McManus, 2005,
Dyer et al., 1992). For indirect methods, one-dimension (1D), two-dimension (2D), or three-1. Introduction

3

dimension (3D) models are used to simulate the interactions among factors such as riverdischarge, tidal variation, bathymetry, and wind effect that significantly influence salinity
intrusion and mixing mechanisms (Li et al., 2012, Vaz et al., 2005).
However, the current methods of estimating the horizontal distribution of salinity andvelocity in estuaries are affected by four limiting factors. First, there are uncertainties
associated with freshwater supplementation from sources such as tributaries, localized rainfall,and human activities. Moreover, freshwater loss due to diversion and other causes may
significantly reduce the accuracy of discharge and salinity measurement estimates which are
not typically addressed in related work. Second, the representation of the spatiotemporal
evolution of salinity fields in an estuary is inadequate because of the gaps in time and space in
the instrumentcs data. Using spatial interpolation from sparse data points to obtain the spatial
distribution of salinity and temperature generally results in a low quality of estimation. Third,for numerical and analytical models, insufficient observational data limits the interpretation ofsensitivity tests. Thus, a significant challenge is how to apply a suitable theory appropriately
to fill the gaps between the model and observations. Fourth, the large number of instrumentsthat must be deployed over a study site to obtain sufficiently accurate field data, and analysis
results adds significantly to the overall cost of the system. For example, (Vaz et al., 2005) used
ten instruments to collect the water temperature and salinity from an 11 km long study site.
Thus, a cost-effective measurement method that is able to provide accurate and beneficial
information on estuarine physics is needed.
The fluvial acoustic tomography (FAT) system, developed at Hiroshima University in 2008,
is a highly versatile hydro-acoustic system for investigating hydrological and hydraulicprocesses. In prior research, the FAT system was used to estimate continuous long-term river
flow and streamflow direction (K. Kawanisi et al., 2018, Bahreinimotlagh et al., 2016) to map
the horizontal velocity of the current field in a depthless river (Xiao et al., 2021, Razaz et al.,2015), and to measure minimal flow rates in extremely shallow streams (Al Sawaf et al., 2020).
Based on the above, FAT is a valid system for measuring river discharge and exploring various
advanced applications in the water resources domain. An aim of this study is to examine theperformance of the proposed scheme using the FAT system in terms of providing sufficiently
accurate estimates of river discharge in tidal estuaries. The significance of this work is its
exploration of the results of examining the cross-sectional average stream velocity in bothlandward and seaward directions.

1. Introduction

4

However, most published studies on salinity intrusion, stratification, estuarine circulation,and salinity flux that employed FAT were implemented using a traditional scheme that included
an oblique transmission line and several FAT units. A new FAT deployment pattern is proposed
to investigate the longitudinal distribution of salinity and tidal flow in a tidal shallow channel.
That method is expected to expand and improve the unique ability of FATS in monitoring
estuarine physics. Thus, a research that can apply the new FAT schemes in a real estuary isnecessary.
1.2

Objectives and challenges

1.2.1 Challenges
Firstly, the Ōta River system, located in Hiroshima city, Japan has a vital role in its
transportation and ecosystem, with a coastal ecosystem for many tidal species. Changing
salinity is one of the most important factors affecting the productivity aquaculture andagriculture. The Ōta River system consists six branches, in which the Ōta diversion channel isthe longest and largest one (see Fig. 2.1). With the largest width and the extensive tidal flats,the Ōta diversion channel has the important role in the transportation and flood control.
Furthermore, the gates located in the upstream area limited the freshwater flow, which creates
the low freshwater status, and influences the salinity intrusion in the Ōta diversion channel,
resulting in large change of water depth and salinity. Thus, the salinity variation in the Ōtadiversion channel is the one of the important factors that influence the Ōta River system
activities such as domestic, ecosystem, industrial. To understand the salinity dynamics in theŌta diversion channel is a crucial task. That is why the Ōta diversion channel is chosen to be
the observation site.
To clarify the salinity dynamic process in the Ōta diversion channel, the following importantquestions need to be answered: 1) How is the stratification formed? 2) How and why do thestratification layer depths (see Chapter 2, Section 2.5.1) change? and 3) What are the main
controls on stratification in the Ōta diversion channel?
Secondly, a cost-effective measurement method able to provide accurate and beneficial
information on estuarine physics is needed. A new method is proposed (see Chapter 1, Section
1.1.2) in order to solve those challenges. There are two important questions related to that
proposal method needed to be answer: (1) Can an alternative configuration of FAT acoustic
stations improve flow direction measurement capabilities and cover a wider measurement area

1. Introduction

5

at a relatively lower cost? (2) What is the accuracy of the proposed FAT deployment and what
are the associated challenges/difficulties?
1.2.2 Objectives
In view of these challenges mentioned above, the objectives of this study are:x

To examine how the saline water mixes and exchanges with freshwater through adynamic process in the Ōta diversion channel, which is the tidal shallow and essential
channel in the Ōta River system in Hiroshima city, Japan;x

To apply the new FAT deployment to investigating the longitudinal distribution ofsalinity and tidal flow in a tidal shallow channel;x

To examine the performance of the proposed scheme using the FAT system in terms ofproviding sufficiently accurate estimates of river discharge in the mesoscale estuary:
the Ōta diversion channel, in Hiroshima, Japan as a case study;

1.3

Outline of the thesis

The thesis is divided into four parts, including introduction (see Chapter 1); the transverse
and vertical distribution of salinity (see Chapter 2) and longitudinal distribution of salinity andtidal flow (see Chapter 3) of the Ōta diversion channel; the summary conclusions andrecommendations (see Chapter 4).
Chapter 1 shows the general introduction, the information of the study site, challenges andobjectives of the study. It also presents a brief introduction of estuaries, tides propagating,salinity intrusion and the interaction between freshwater and saline water.
Chapter 2 presents a method to clarify the salinity dynamics in a shallow and narrow estuary,
based on the stratification layer. Chapter 2 investigates the vertical and lateral distribution of
the salinity. Chapter 3 shows the longitudinal distributions of tidal flow and cross-sectional
average salinity. Chapter 4 shows the recommendations and conclusions of the study. The
recommendation section presents the further research based on the limitation of the present
study. The conclusions summarize and reflect on the research, it also shows what new
knowledge the present study has contributed.

2. Vertical and Lateral Distributions of Salinity and Density

CHAPTER 2

VERTICALAND

LATERAL

6

DISTRIBUTIONSOFSALINITY AND DENSITY

2.1

Introduction

The motions of transverse and vertical directions in estuaries are usually smaller than thehorizontal motion, but these motions have an essential role in the estuarine dynamic (Fischer,
1976, 1972). Several studies have increased attention on longitudinal structures of salinity
and flow, and the limitation of that approach was also noted by Fischer (1972, 1976). To
fully understand the dynamic process of an estuary, the complete three-dimensionaldescription of the estuary need to be presented. Thus, the understanding requirement of thetransverse and vertical structures of salinity and density is crucial. The degree of salinity anddensity stratification in single cross sections has important role in vertical mixing mechanism.
To clarify how does a shallow and narrow estuary develop and break the stratification will
give a better understanding of the estuarine dynamics.
The Ōta Diversion channel is the largest branch in the Ōta River system, which is themost crucial river in Hiroshima city, and has a vital role in its transportation and ecosystem(Gotoh et al., 2013). Flow rate and salinity intrusion (K. Kawanisi et al., 2015, Soltaniasl etal., 2013), salt flux variability, and water circulation (Soltaniasl et al., 2013), were
investigated to examine the estuarine dynamic in the Ōta River estuary. Soltaniasl (2013)used the gradient Richardson number and the stratification parameter that is a dimensionlessvariable to evaluate the stratification variation in the Ōta River estuary around a high tide

2. Vertical and Lateral Distributions of Salinity and Density

7

during the period of four hours. Their research contributed an important finding to thestratification mechanism understanding in the Ōta River estuary during the later period of
the spring tide. The results show the tidal mixing contributes to decreasing the stratification
over the whole cross-section. However, in order to fully understand the stratification process,and thus the lateral salinity dynamics, investigations of salinity distribution in the crosssections during a tidal cycle are needed.
The present research investigates vertical and lateral salinity variations over a tidal cycle
in both spring tide and neap tide. This research aims are to examine how the saline water
mixes and exchanges with freshwater through a dynamic process in the Ōta diversion
channel, which is the tidal shallow and essential channel in the Ōta River system in
Hiroshima city, Japan. This study is expected to answer the important questions, including
1) How does the stratification form? 2) How and why do the stratification layer depths (seeChapter 2, Section 2.5.1) change? and 3) What are the main control factors on stratificationin this area? By discussing these questions, the transverse salinity dynamics in the Ōtadiversion channel will be clarified.
2.2

Study area

2.2.1

Ōta diversion channel

The Ōta River diversion channel in Hiroshima City, western Japan, is the monitoring siteused in this study. The diversion channel is a tidally dominated channel with floodgateslocated around 9 km upstream from the mouth that restricts the freshwater runoff fromfurther upstream. The bathymetry of the Ōta diversion channel shows a typical shallow
estuary that is presented in several previous studies (Robins & Davies, 2009): whole bottom
is submerged at high water and part of bottom dries out at low water. The estuary has
irregular bathymetry with extensive tidal flats and significant variations in the crosssectional profiles (Gotoh et al., 2013). The mixed tides in this estuary include diurnal andprimary semidiurnal components, and the tidal range at the river mouth ranges from 1.2 m
at the neap tide to about 4 m at the extreme spring tide. The Ōta River has vital environmental
characteristics, with an ecosystem for many tidal species, a large portion of which are oysters
in the downstream area.
The freshwater runoff is controlled by the Gion sluice gates (see Fig. 2.1) located 4.5 km
upstream from the observation site. During the observation period, the Gion sluice gates2. Vertical and Lateral Distributions of Salinity and Density

8

were operated under normal conditions, with only one of the three gates partially open anda cross-sectional stream area of 32 m ൈ 0.3 m for the spilling flow (Kawanisi et al., 2010).

Figure 2.1 The detail of the study site
Figure 2.2 shows the bathymetry distribution of the Ōta diversion channel, based on thedata set of a remote controlled boat campaign in 2019 (see Chapter 2, Section 2.3.3). The
bathymetry of the Ōta diversion channel shows the complicated distribution. The shape ofthe river bed varies slightly at the middle section, and fluctuates significantly near the rivermouth and the meandering location.
2.2.2

Study area

Figures. 2.1 and 2.3 illustrate the location of the study site and the detail of the observationarea, respectively. It is located around 4.3 km upstream from the river mouth. The researchcs
experiments were conducted in the river segment between two bridges (Asahi Bridge andShinkoi Bridge); the distance between the two bridges is approximately 850 m.

2. Vertical and Lateral Distributions of Salinity and Density

9

Figure 2.2 The bathymetry distribution of the Ōta diversion channel (Gusti & Kawanisi,
2020)

Figure 2.3 The detail of the study site
The bathymetry distribution of the observation area is presented in Figure 2.4. It can beseen that, the left riverbank side is deeper than the right riverbank side on the middle of thechannel segment, and the right bank side is deeper than the left bank side at the areas near to
the two bridges (Shinkoi Bridge and Asahi Bridge), resulting in a meandering in theobservation site.

2. Vertical and Lateral Distributions of Salinity and Density

10

Figure 2.4 The bathymetry distribution of the observation site
2.3

Instrumentations

2.3.1

Compact CTD (Conductivity, Temperature, Depth) sensor

Compact-CTD is a small & light-weight temperature/salinity/depth logger. The compact
titanium pressure case, carrying 60 mm in diameter, 462 mm in overall length & light weightof 1.0 kg. In water provides optionally the chlorophyll/turbidity sensor and this instrument
is appropriate to multi-parameter water-quality measurement. The system is comprising ofsonde unit with sensors, interface unit and communication cable, and is designed so as toproceed the measured data and do various setups through PC. This Compact-CTD newly
features a time-trigger function in addition to a depth-trigger provided on our conventional
memory CTD.

2. Vertical and Lateral Distributions of Salinity and Density

11

Figure 2.5 Compact CTD (Conductivity, Temperature, Depth) sensor (Source: JFE
advantech Co., Ltd)
Table 2.1 Compact-CTD specifications (Source: JFE advantech Co., Ltd)
Sensor

Type

Range

Resolution

AccuracyTime
constant

Depth

Semiconductor

0 – 600 m

0.01 m

0.3 % FS

0.03 sec.

Pressure sensor
Temperature

Thermistor-5 – 40 qC

0.001 qC

r0.02qC

0.15 sec.

Salinity

UNESCO

0 –40

0.001

r0.03

0.15 sec.

(Conductivity)

Formula0 – 600.001 mS/cm

r0.05

Inductive cell

mS/cm

mS/cm

2.3.1.1 Depth sensor of CTD
This is a type of absolute pressure detection and also affected by fluctuation of
atmospheric pressure. Moreover, the zero-point is loosing off a little bit due to environmental
temperature variation. For those, this sensor provides an automatic zero-point function andexecutes an automatic compensation in order to clear the error factors caused by the changeof atmospheric pressure and temperature variation. Pressure portion of depth sensor is2. Vertical and Lateral Distributions of Salinity and Density

12

protected by white polyacetar resin cap with small holes. When the holes, therefore, arechoked, the pressure transmission is affected, so it is recommended to clean here regularly.
2.3.1.2 Water temperature sensor of CTD
High-reliable & fast-responding thermistor sensor is used and this sensor is unified withelectric conductivity sensor to let the response time match each other. This mechanism is to
avoid the salinity spike generated when the data are analyzed. Since this sensor is very muchstable, there might not be much affection for temperature measurement even if the dirt andbio-fouling are occurred, but clean up the sensors regularly as the response speed becomesslow due to heavy dirt. Pay your special attention to the damage of the sensor since it is verythin.
2.3.1.3 Electric conductivity sensor of CTD
The conductive rate adjacent to the sensor is measured based on the electromagnetic
inductive method. Hence, in case something is existed beside the sensor, it affects much tothe measurement. Moreover, the accuracy becomes inferior for the dirt fouling, so it isrecommended to clean up the sensor by brush, etc. regularly, especially the inner of ceramic
tube of the inductive cell.
2.3.2

Fluvial Acoustic Tomography (FAT) system

The FAT is an advanced hydro-acoustic instrument designed by Hiroshima Universitythat uses submerged acoustics to observe various hydrological properties of rivers at levels
ranging from 0.28 m to 10 m in depth. FAT emits omnidirectional acoustic signals at
different central frequencies (mainly between 7–53 kHz). The FAT system contains GPS
receivers that help synchronize both FAT units to guarantee the high-precision transmissionof pulses. The periodicity of acoustic pulses was 30 secs, synchronized with a GPS clock.
FAT uses the time-of-travel tomography method and can be used for the long-term
measurement of the velocity and salinity in both freshwater and tidal rivers (Kawanisi et al.
2011; Kawanisi et al. 2010).

2. Vertical and Lateral Distributions of Salinity and Density

13

Figure 2.6 The scheme and principle operation of the FAT system ((K. Kawanisi et al.,2010))
2.3.3

Hydrographic survey remote controlled boat RC-S3

The hydrographic survey remote controlled boat RC-S3 was developed by Coden Co.,Ltd to collect depth data; the depth range is 0.5 – 80 m. The boat is equipped with GPS andecho-sounder, it allows transfer obtained data together with GPS data real-time to the PC
receiver (hereinafter base station). The surveying points of 225 and/or measuring lines of
128 can be pre-set.
Table 2.2 Remote controlled boat RC-S3 specifications (Source: CODEN Co.,Ltd)
1. Boat
Length1.200 mm

Width

350 mmHeight

250 mm (excluding antenna)

Weight13 Kg (16 Kg with batteries)

2. Echo SounderFrequency

200 KHz

Depth range

0.5 m – 80 m

2. Vertical and Lateral Distributions of Salinity and Density
Resolution

14

0.01 m

3. GPS
Positioning accuracy

SBAS (< 0.5 m)

Positioning resolution

1/10000 sec (about 0.03 m)

In the present research, authors used this boat to collect the bed altitude of the Ōtadiversion channel (see Figs. 2.2 and 2.4).
2.4

Methodology

2.4.1

Salinity and density data set collection

The information of salinity was collected from two cross-channel transects in the middle
Ōta diversion channel using two CTD campaigns.
The first campaign was conducted from 14:00 to 17:00 on September 5th, 2018, during
neap tide. This work was done simultaneously along two bridges, Asahi Bridge and Shinkoi
Bridge. The distance between the two bridges was approximately 850 m (see Fig. 2.7). In
this campaign, the vertical salinity distributions were measured at five points every thirty
minutes along the 150 m length of Shinkoi Bridge and the 200 m length of Asahi Bridge,
respectively (see Fig. 2.7).

2. Vertical and Lateral Distributions of Salinity and Density

15

Figure 2.7 a) The observation site for the first campaign; b) and c) the transverse lines ofCompact CTD measurement, yellow symbols indicate the locations of the data collected
points (P1–P5)
The second campaign was operated on October 2nd, 2020, from 8:00 to 23:30, during
spring tide at Shinkoi Bridge, in which Compact CTD ran at six points along the 150 m
length of the bridge every thirty minutes (see Fig. 2.8). Besides, two FAT units were
deployed on the left and right sides of the river near Shinkoi Bridge with a transmission
length of 160 m for four days, from October 1st 2020 to October 5th 2020. The purpose ofusing FATS here is to collect the data to estimate the section-average salinity. The
combination of the cross-sectional average salinity deduced from FAT data and verticalstructure of salinity by the CTD will bring the clearly understanding of transverse salinity
dynamics in Ōta diversion channel.
The purpose of the data collection by iterating the channel intersects is to acquire the
distribution of salinity, temperature and density in the cross section. The first campaign was
conducted at two parallel transects separated by 850 m in three hours while the second

2. Vertical and Lateral Distributions of Salinity and Density

16

campaign was conducted at one transect in 16 hours during one tidal cycle. Thus, the data
were ensured good quality to determine the transverse and vertical structures.

Figure 2.8 The observation site for the second campaign; yellow symbols indicate thelocations of the data collected points (P1–P6) by Compact CTD, red triangles indicate thelocations of FATS.

Figure 2.9 Seven stages of the second campaign
The more extended campaign was divided into seven stages (see Fig. 2.9) for further
clarification, they are the end of the flood of the first tide, early in the ebb of the first tide,
middle of the ebb, the end of the ebb, early to middle of the flood, the end of the flood of thesecond tide, and early in the ebb of the second tide. The stage classification is based primarilyon the pattern of the salinity distribution in the cross section. During the observation period,
the times that show the similar pattern of salinity distribution in the cross section will begrouped into the same stage. For the present research, the quantity and the depth ofstratification layers, and the surface-to-bottom salinity difference were used to evaluate thestratification/de-stratification degree.

2. Vertical and Lateral Distributions of Salinity and Density
2.4.2

17

Fluvial Acoustic Tomography (FAT) system

2.4.2.1 Estimating sound speed using FATS
FAT uses the time-of-travel tomography method. The speed of sound (c) is evaluatedbased on respective travel times, (tup) and (tdown), at the upstream and downstream stations,as follows:‫ͳ ܮ‬ͳܿ ൌ  ሺ൅ሻʹ ‫ݐ‬௨௣ ‫ݐ‬ௗ௢௪௡(2.1)

2.4.2.2 Estimating depth- average salinity using FATS
As described by Medwin (1975), the speed of sound in water is generally a function ofsalinity, water temperature, and depth:ܵ ൌ ͵ͷ ൅  ሺܿȂ ͳͶͶͻǤʹȂ ͶǤ͸ܶ(2.2)

൅ ͲǤͲͷͷܶ ଶ Ȃ ͲǤͲͲͲʹͻܶ ଷ Ȃ ͲǤͲͳ͸‫ܦ‬ሻȀሺͳǤ͵ͶȂ ͲǤͲͳܶሻ
where T is water temperature (°C), c is speed of sound (m/s), and D is depth (m). The valid
parameter ranges in Equation 2.2 are as follows: 0 ≤ T ≤ 35 °C, 0 ≤ D ≤ 1000 m, and 0 ≤ S≤ 45. This relationship helps estimate the cross-sectional average salinity using the speed ofsound in water computed by the FAT system.
2.4.3

Freshwater discharge data

The present study also discusses the effects of freshwater discharge on salinity anddensity distribution. Thus, the information of freshwater flow was also presented in thischapter. There is a Yaguchi Gauging Station that is located at approximately 14 km upstream
from the river mouth (see Fig. 2.1).
From the previous studies (Kawanisi et al., 2010), during normal conditions, thefreshwater rate at Ōta Diversion channel counts approximately 10 y20  of the total riverdischarge of the Ōta River.
The Yaguchi Gauging Station is not tidally modulated, as a result, the freshwater
discharge in October 2020 can be deduced by using the rating curves as below:
QY1 = 102.44 (H+0.05)2; H d 0.92 m
and

(2.3)

2. Vertical and Lateral Distributions of Salinity and Density

18

QY2 = 84.65 (H+0.22)2; H ! 0.92 m(2.4)

where QY1, QY2 (m3/s) are discharges and H is water level (T.P. m). T.P is the average waterlevel in Tokyo Bay.
Figure 2.10 shows the freshwater discharge recorded at Yaguchi Gauging Station as theresults of using rating curve method.

Figure 2.10 Temporal variations in freshwater discharge at Yaguchi Gauging Station (blueline), the water level at the observation site (black line), and the studied periods (red line)
for a) the first campaign and b) the second campaign
2.4.4

Cross-correlations

Cross-correlations is the term that denotes the correlations between two time series indifferent space or times, and is used to measure the degree of similarity between them. Oneof the valuable applications of the cross-correlation is to investigate the time delays.
Calculating the cross-correlation will return the maximum of the cross-correlation function(see Eq. 2.5), which points clearly to the time in which these two time series are best matched,and indicating the time delay between them.
The cross-correlation function between two independent time series is defined as follow:ܴ௑ǡ௒ ሺWሻ ൌ‫ ܧ‬ሺܺ௧ାW െ ܺത ሻሺܻ௧ െ ܻതሻඥܸܽ‫ݎ‬ሺܺ௧ାW ሻܸܽ‫ݎ‬ሺܻ௧ ሻ



(2.5)

2. Vertical and Lateral Distributions of Salinity and Density

19

where X,Y are the random variables, t is the time, W is the displacement, also known as lag.
The overbar refers the value of the variable mean. Var means the variance, and E is expectedvalue.
2.5

Results

2.5.1

Salinity distributions in the cross section

Results from two campaigns show the different range of stratification conditions observed
between spring tide and neap tide as well as between ebb and flood tide conditions in theŌta River as shown in Figures. 2.11, 2.12, 2.13 and 2.14. Stratification highly develops
during ebb tide periods while de-stratification occurs during higher flood tides. The
stratification degree is stronger during neap tide than during spring tide.
In the present research, the salinity contours in all mentioned figures are showed with thestep of one psu. Thus, the terms “stratification layers” and “stratification layer depth” areconsidered basing on the one-psu-difference contour of salinity.
2.5.1.1 Spring tide (the first campaign)
A. The ebb stages
The salinity distribution in the cross section of the ebb stages during spring tide, including
early in the ebb of the first tide, early in the ebb of the second tide, the middle of the ebb,
and the end of the ebb are shown in Figures. 2.11, 2.12, 2.13 and 2.14, respectively. Overall,
the figures of ebb stages revealed a complete stratification, with the stratification degreeincreasing sharply from the early to the end of the ebb tide.
The early part of the ebb stages
Figure 2.11 shows there are five significant stratification layers at the beginning of thestage, with corresponding salinity ranges from 26 y 31psu (see Fig. 2.11a). There was a sharp
difference in depth of these stratification layers; the saltiest layer (above 30 psu) had thehighest depth of approximately 2 m, while the total depths of the remaining layers areapproximately 1 m. The number of these significant layers increased, and thus their depths
decreased at the end of the stage, however, the depth of the saltiest layer was always higher
than the total depths of the remaining layers. A similar phenomenon was also found in theearly part of the ebb of the second tide (see Fig. 2.12). This phenomenon suggests that at the2. Vertical and Lateral Distributions of Salinity and Density

20

beginning of ebb tide, the stratification occurred more strongly at the surface than in the
middle and bottom parts of the water column.

Figure 2.11 Salinity distributions in the cross section of the early ebb during spring tide (thefirst tide stage)

Figure 2.12 Salinity distributions in the cross section of the early ebb during spring tide (thesecond tide stage)

The mid ebb and the end of ebb stages
The stratification continues to rise during these stages. The end of the ebb stage presented
the highest number of stratification layers over the observation period (see Figs. 2.14c and2.14d), which suggests that the strongest stratification happened at the end of ebb tide period.
In the middle of the ebb stage, the depth of the saltiest layer (above 29 psu) is still high,2. Vertical and Lateral Distributions of Salinity and Density

21

approximately 1.5 m (see Fig. 2.13a), and dropped down gradually during the first half ofthe ebb tide (see Figs. 2.13b and 2.13c). However, it fell more rapidly during the last half ofthe ebb tide (see Figs. 2.13d, 2.13e and 2.13f).

Figure 2.13 Salinity distributions in the cross section of the middle ebb stage during spring
tide
The last figure of the middle of ebb tide (see Fig. 2.13f) and the first one of the end of
ebb tide (see Fig. 2.14a) also show an equal depth for all significant stratification layers,
approximately 0.2 m. After that, the depth of the layers that were in the middle of the watercolumn increased twofold while the depth of the layers located on the bottom decreased
rapidly (see Figs. 2.14 b, 2.14c, 2.14d, and 2.14e). During the end of the ebb and early stageof flood tide (see Fig. 2.14f), the depths of the significant stratification layers become almost
equal again. The depth variation of the significant stratification layers suggested that thestratification developed gradually from the surface to the bottom of the water column overthe ebb tide period.

2. Vertical and Lateral Distributions of Salinity and Density

22

Figure 2.14 Salinity distributions in the cross section of the end ebb stage during spring tide

B. The flood stages
The plots of the surface-to-bottom salinity of the flood tides during spring tide, including
the end of the first flood tide, the end of the second flood tide, and the early to middle flood
are shown in Figures 2.15, 2.16, and 2.17, respectively. These figures revealed the main
trend of the salinity dynamic during flood tide, which is that the salt wedges moved from theleft side to the right side of the river, resulting in the lateral distribution of salinity. The
salinity distribution in the cross section is not symmetric, as the water was fresher on theright side than on the left side. This might be because of the influence of bathymetry, which
will be discussed in the following parts. The plots of salinity distribution over the crosssectional during flood stages also show a high de-stratification rate, essentially for the earlyflood stage.
The early to middle flood stage
This stage showed a complete lateral salinity distribution. The lateral salinity gradient
was highest at the beginning of the stage (see Fig. 2.17a) close to the previous ebb,
decreasing during mid flood and increasing again during the late flood tide (see Fig. 2.17f).
The difference in advection of the longitudinal salinity gradient during flood tide is claimed
to intensify the force of lateral density gradients, thus increasing the lateral salinity gradient.

2. Vertical and Lateral Distributions of Salinity and Density

23

Figure 2.15 Salinity distributions in the cross section of the end of the first flood tide during
spring tide

Figure 2.16 Salinity distributions in the cross section of the end of the second flood tide
during spring tide

2. Vertical and Lateral Distributions of Salinity and Density

24

Figure 2.17 Salinity distributions in the cross section of the early to mid flood stage during
spring tide

2.5.1.2 Neap tide (the second campaign)
Vertical profiles of salinity at the cross-sectional estimate by CTD
Figures 2.18 and 2.19 show the vertical salinity profiles at five points, P 1 – P5 (see Fig.
2.7b and 2.7c) at the Shinkoi Bridge and Asahi Bridge during the flood neap tide,
respectively. In general, the surface-to-bottom differences of salinity in both upstream anddownstream areas are similar and not too big during the observation period, with value ofapproximately 5 psu. That means the vertical salinity gradients at the observation site aresmall. The surface salinities recorded at the observation site are almost approximately 20
psu, and the bottom salinity values are around 25 psu. The highest salinity is found at the
point P2 that is located on the left side of the river bank.

2. Vertical and Lateral Distributions of Salinity and Density

25

Figure 2.18 Vertical profiles of salinity at the cross-sectional (Shinkoi bridge) estimated by
CTD, P1 (black line), P2 (red line), P3 (blue line), P4 (orange line), P5 (green line)
However, there is a difference between salinity vertical structures recorded at upstream
and downstream sections. At hours 14:30, 15:00 and 15:30, there are significant changing invertical salinity profile at the middle part of the water column near to Shinkoi Bridge (seeFigs. 2. 18a, 2.18b, and 2.18c) while at the same time the significant changing in verticalsalinity profile recoded near to Asahi Bridge is found at the bottom of the water column (seeFigs. 2.19b, 2.19c, and 2.19d).

2. Vertical and Lateral Distributions of Salinity and Density

26

Figure 2.19 Vertical profiles of salinity at the cross-sectional (Ashahi Bridge) estimated by
CTD, P1 (black line), P2 (red line), P3 (blue line), P4 (orange line), P5 (green line)
The vertical salinity profiles measured using CTD of the mid flood during neap tide at
the upriver and the downriver sections are shown in Figures 2.20 and 2.21, respectively. In
general, during neap flood tide, salinity distributions in the cross sections at the downstream
and upstream areas are similar, with stratification developed during the middle of the floodtide, and is weakened during the end of flood tide. There is a slight difference in destratification process close to the end of flood tide between the two locations, with the destratification sharper at the downstream (see Figs. 2.21e and 2.21f) than upstream area (seeFigs. 2.20d and 2.20e).

2. Vertical and Lateral Distributions of Salinity and Density

27

Figure 2.20 Salinity distributions in the cross section at the upstream area (Shinkoi Bridge)
during neap tide
In general, the surface-to-bottom distribution of salinity at the locations along the estuary
at different distances from the river mouth is expected to be different because of several
factors such as the longitudinal salinity gradient and the bathymetry effect. However, it
seems that the distance of 850 m between the two locations in this study is insufficient toreveal the expected difference. A study in vertical salinity distribution at locations along theŌta River estuary with longer distance apart is needed in the future.

2. Vertical and Lateral Distributions of Salinity and Density

28

Figure 2.21 Salinity distributions in the cross section at the downstream area (Asahi Bridge)
during neap tideAlso, the comparison between figures of surface-to-bottom salinity of mid flood during thetwo periods (December 5th 2018 and October 2nd 2020) presents a remarkable difference instratification process between neap and spring conditions, with stratification increasing
significantly more during the neap tide than during spring tide. During spring tide, salinities incross section distribute mostly laterally (see Fig. 2.17), while during neap tide the surface-tobottom salinity difference was 5 y 8 psu (see Figs. 2.20 and 2.21), or 20 y 32 (mean of 25psu). At the middle of the neap flood tide (see Figs. 2.20a, 2.20b, 2.20c and Figs. 2.21 a, 2.21b,
2.21c, 2.21d), the number of significant stratification layers is seven over a water depth of 4 m,
indicating a well stratified water column, then decreases and thus the significant stratification
layer depths increases. On the neap tide, the tidal range of the estuary decreases and the currents
are moving more slowly than at the spring tide. It is because the vertical mixing reduces andinstantaneous mixing energy reaches the minimum value over a spring - neap tidal cycle that
leads to stronger stratification during the neap tide periods than during the spring tide periods.
Stratification between neap and spring conditions are significantly different, which suggeststhat the salinity dynamics of these two tidal periods are different.

2. Vertical and Lateral Distributions of Salinity and Density29

2.5.2 Density distributions in the cross section
2.5.2.1 Tidally periodic density distributions
Tidally periodic stratification is explored as the mechanism of several phenomena inestuaries such as mixing, salinity intrusion (Stacey et al., 2008). The most common reason for
the tidally periodic stratification of density is tidal straining (Simpson et al., 1990). Figures
2.22 and 2.23 show the vertical distribution of density recorded at the Shinkoi Bridge during
the first and second peak of the water level, respectively. The results were estimated from theCTD data set recorded on October 2nd, 2020. It is can be seen that, the density distributions
during spring tide at the observation site have clear tidally periodic characteristic.
In both slack periods, heavier density fluxes move from the left side to the right side of theriver bank at the end of the flood tides. In the early of the ebb tides, when the lateral salinity
intrusion process finished, resulting in vertical density distribution.

Figure 2.22 Density distributions in the cross section at the first high water slack during springtide

2. Vertical and Lateral Distributions of Salinity and Density

30

Figure 2.23 Density distributions in the cross section at the second high water slack during
spring tide
2.5.2.2 Lateral density gradient distributions
Figure 2.17 shows a strong lateral salinity distribution during flood tide. To consider the
relationship between the lateral distributions of salinity and density, the variation of the lateral
density gradient during a flood tide is estimated and plotted in Figure 2.24. The lateral density
gradient (wUy/wy) indicates the density variation in cross section of channel. In this study, lateral
density gradient is estimated from the data set collected in the second CTD campaign, ( Uy) is
the water density collected at the observation points (P1-P6) (see Fig. 2.8), and (y) is the crosssectional distance.
During approximately three hours, from the early to the late of the flood tide, the value ofthe lateral density gradient changed significantly. However, the variation trend of lateral
density gradient is stable. It is evident that in spite of the significant change of density, thelateral density gradient is likely to remain unchanged.

2. Vertical and Lateral Distributions of Salinity and Density

31

Figure 2.24 Lateral density gradient, averaged over a depth from 0 to 2.5m below the surface
at Shinkoi Bridge during a typical flood tide (October 02, 2020), (y) is the lateral distance fromthe left river bank, (B) is the cross-section length of the channel at the observation site.
Normally, the turbulent mixing in the late of the flood tides decreases which maintains thelateral density gradient, and pushes the surface flows to the channel center and leading to lateralsalinity distribution of the water column. For further clarification, Figures 2.25a-2.25e show
the distributions of the lateral density gradient at flood tides. It can be seen that the surface
flows are pushed into the center of the channel, resulting lateral flows (see Fig. 25f) and lateralsalinity distribution as well (see Fig. 2.17). Figures 2.17a and 2.25b respectively present the
distributions in the cross section of salinity and lateral density in the early of flood tide at
Shinkoi Bridge. These figures show clearly the relationship between the lateral distributions ofdensity gradient and salinity as addressed above, with the former is the leading cause of thelater. Nunes & Simpson (1985) and Lacy et al. (2003) also described a similar phenomenon in
their studies, and concluded that the relaxation of the lateral density gradients is a usualmechanism of lateral salinity distribution.

2. Vertical and Lateral Distributions of Salinity and Density

32

Figure 2.25 (a–e) Distributions of lateral density gradient during flood tides at Shinkoi Bridge,“z” is the vertical distance from the water surface, “H” is the water depth, “y” is the lateral
distance from the left river bank, “B” is the cross-section length of the channel at theobservation site, and f) Schematic of lateral circulation.
2.5.2.3 Vertical density gradient distributions
Figures 2.26 and 2.27 present the density distributions in the cross section during a typicalneap flood tide at Shinkoi Bridge and Asahi Bridge, respectively. The results were estimatedfrom the CTD data set recorded on September 5th, 2018 during a period of four hours. In
general, the vertical density variation at both upstream area (Shinkoi Bridge) and downstream
area (Asahi Bridge) have the similar range, from approximately 1012 kg/m 3 to 1016 kg/m3.

2. Vertical and Lateral Distributions of Salinity and Density

33

Figure 2.26 Density distributions in the cross section at upstream area during neap tide
In Figures 2.26a, 2.26b, 2.26c and Figures 2.27a, 2.27b, 2.27c, the degree of the verticaldensity fluctuations in the middle of the neap flood tide at the two sections are nearly similar,
with the vertical density gradient increases in the mid-depth parts. However, close to the endof the flood tides, the vertical density fluctuation at the upstream section (see Fig. 2.26e) isstronger than the downstream section (see Fig. 2.27e) at the same phase. In detail, figure 2.26eshows that the vertical density ranges from 1012 kg/m 3 at the surface to 1016 kg/m3 at thebottom of the water column while figure 2.27e shows the vertical densitycs range of 1015 –1016 kg/m3.

2. Vertical and Lateral Distributions of Salinity and Density

34

Figure 2.27 Density distributions in the cross section at Asahi Bridge during neap tide
Figures 2.28 and 2.29 present the vertical density gradient distributions during neap tide at
Shinkoi Bridge and Asahi Bridge respectively. General, there is a significant difference
between the vertical density variations in the downstream and upstream areas over the riversegment length of 850m, which located around 4.5km from the mouth. At the upstream area
(Shinkoi Bridge), during the middle of flood tide, vertical density gradient is strong in the
middle of the water column at almost positions from the left to the right sides of the riverbank(see Figs 2.28 a, 2.28b, 2.28c), then becomes very weak at the late of flood tide (see Figs. 2.28d,
2.28e). However, at the downstream area (Asahi Bridge), vertical density gradient develops
from the middle to the bottom of the water column at the early of flood tide (see Figs. 2.29a,
2.29b, 2.29c), then becomes weak at the end of flood (see Figs. 2.29d, 2.29e). The onset of thephenomenon that shows vertical density gradient is stronger at the middle of the water column
than that at the surface and the bottom parts can be controlled by the vertical straining due tothe surface-to-bottom difference of transverse velocity. A previous study (Soltaniasl et al.,2013) showed that the surface-to-bottom difference of transverse velocity in the Ōta diversion
channel is significantly which creates a oscillatory flow between the surface to the bottom of2. Vertical and Lateral Distributions of Salinity and Density

35

the water column. This flow may create a straining of the density field in the middle part of thewater column, and enhancing stratification.
Similarly, vertical salinity distributions of this period has the same pattern compare to thevariation of vertical density gradient. At the upstream area (Shinkoi Bridge), a strong
stratification is found in the middle of the water column during the middle of neap-flood tide(see Fig. 2.20). At the downstream area (Asahi Bridge), the stratification strongly develops inthe surface and middle of the water column, then becomes weaker; and the salinity distributionsin the cross section at this area is lateral distribution at the late of the flood tide (see Figs. 2.21).
Thus, the vertical density gradient distributions in the Ōta diversion channel might be an
important factor that controlled the stratification during flood tide.

2. Vertical and Lateral Distributions of Salinity and Density

Figure 2.28 Vertical density gradient distributions at Shinkoi Bridge during neap tide36

2. Vertical and Lateral Distributions of Salinity and Density37

2. Vertical and Lateral Distributions of Salinity and Density

38

Figure 2.29 Vertical density gradient distributions at Asahi Bridge during neap tide
2.6

Discussion

The following parts will discuss the contribution of the factors and mechanisms that may
control the stratification process in the Ōta diversion channel.
2.6.1 The effect of freshwater discharge on stratification
Although the water depths at the two peaks of tide are similar (see Fig. 2.10b), the salinity
peak during the first tide is approximately 2 psu higher than during the second tide (see Figs.
2.15c and 2.16c). The lateral salinity gradient in the first tide is also higher than that in thesecond tide. Besides, the number of significant stratification layers during the first tide ranged
from 5–15 (see Fig. 2.11) is higher than that during the second tide of 3–10 (see Fig. 2.12).
This is because, during the second tide, freshwater inflow recorded at Yaguchi Gauging Station

2. Vertical and Lateral Distributions of Salinity and Density

39

almost doubled during the first tide, from approximately 40 m3/s to approximately 70 m3/s (seeFig. 2.10). Comparing the vertical salinity profile between the two stages of the end of flood,the significant influence of the freshwater flow on stratification process is evident. Thus, thesalinity dynamic process in the Ōta River estuary is affected significantly by freshwater input
upstream.
Furthermore, a re-stratification process occurred during late in the flood tide. During thisperiod, tidal currents decelerated leading to a rapid diminishment of turbulent mixing. The
force deduced from the lateral density gradients (see Fig. 2.25) tends to become stronger andovertake the turbulent mixing, enhancing the vertical stratification. The reason for thisphenomenon has been discussed in previous studies with the term “lateral straining” (Scully &Geyer, 2012, Geyer & MacCready, 2014). Thus, the stratification development during floodtides in the Ōta River estuary might be due to of the lateral density.
2.6.2 The effect of bathymetry on salinity stratification
Another reason for the lateral salinity gradient is the effect of significant variation of thebathymetry at the study site. Valle (1997) conducted an observation in one of the largest
estuaries in the United States to describe the influence of the bathymetry on the transversehydrographic structure. Their study stated that the geostrophy of the river bed is one of themain factors that influence to the dynamics in the transverse direction.
The bathymetry of the Ōta diversion channel is complicated and represented by shoals andflood flows (Gotoh et al., 2013). The Ōta diversion channel is the main entrance channel of theŌta River system where the transportation happens regularly. As shown in Figure 2.4, the left
riverbank side is deeper than the right riverbank side on the middle of the channel segment,
and the right side is deeper than the left side at the areas close to the two bridges, resulting inan irregular bathymetry in the observation site. During the flood tide, at the bottom of watercolumn, the water that is saltier and low-moving tends to move toward the deeper area of thechannel while at the surface, river flow tends toward straight. This lateral shear creates aremarkable lateral salinity gradient during the early and middle flood. Previous studies (Ralston
et al., 2010, Fischer, 1972) have reported similar findings and stated that the transverse shear
generates a lateral salinity gradient.
Also, the comparison of the transverse salinity distribution between this stage and otherstages, including the end of ebb and the end of second flood stages, shows that the stratificationand de-stratification respond quickly to tidal changing. In Figure 2.14f, the salinity distribution

2. Vertical and Lateral Distributions of Salinity and Density

40

in the cross section showed a high stratification with the stratification layer depths equal at theend of ebb tide, then changes quickly to the lateral salinity distribution after 30 minutes at theearly stage of flood tide (see Fig. 2.17a). Similarly, the re-stratification happens at the end offlood tide, close to the high water level (see Fig. 2.16a) after the previous lateral distribution
stage (see Fig. 2.17f). To evaluate fully this rapid change, a consideration of the spatial andtemporal variabilities is necessary in future research. In this case, the reason of quick changing
in salinity distributions at the end of ebb and flood tides might be attributed to the shallow
depth of the estuary.
2.6.3 The effect of the water temperature
Generally, the density stratification of a water column is controlled by water temperature
and/or salinity because the water density is a function of the water temperature and salinity(Millero & Poisson, 1981). Table 2.3 shows the typical computed values of sea water density
depending on the variations of temperature and salinity. When salinity ranges from 20-35, andtemperature ranges from 15-30qC, density changes approximately 0.026 for temperature
difference of 1.0qC. However, the density change by the 1-psu change of salinity is around0.075, shows triple the amount of density change as temperature difference. The surface-tobottom temperature differences at the study site are not significant in both CTD campaigns,
under 1.5qC (see Figs. 2.30 and 2.31). This might suggest that salinity dominated the densitychange in Ōta diversion channel, and the effect of temperature variation in vertical direction
on salinity dynamics is not significant compare to other factors that mentioned above.
Table 2.3 The sea water density variations based on the variations of temperature and salinity(Millero & Poisson, 1981)
0

10

20

35

40

0

999.843

1007.950

1016.010

1028.1101032.150

15

999.1021006.780

1014.440

1025.970

1029.83030

999.651

1003.100

1010.530

1021.730

1025.48040

992.220

999.575

1006.910

1017.970

1021.680

Salinity (psu)
Temperature (qC)

2. Vertical and Lateral Distributions of Salinity and Density

41

Figure 2.30 Vertical profiles of temperature at the cross section estimated by CTD of thesecond campaign at Shinkoi Bridge, P1 (black line), P2 (red line), P3 (blue line), P4 (orangeline), P5 (green line) and P6 (gray).

2. Vertical and Lateral Distributions of Salinity and Density

42

Figure 2.31 Vertical profiles of temperature at the cross section estimated by CTD of the firstcampaign at a) Shinkoi Bridge, and b) Asahi Bridge. P1 (black line), P2 (red line), P3 (blue line),
P4 (orange line), P5 (green line).
2.6.4 The time delays of the salinity
Delays in time of salinity maximum are found during slack water periods, with the range isfrom approximately 30 minutes to 1 hour. Figures 2.11a and 2.11b show qualitatively that thefirst high water slack occurred at approximately 9:48 while salinities reached its maximum
value approximately 30 minutes after that. Similarly, during the end ebb stage, the low water2. Vertical and Lateral Distributions of Salinity and Density

43

slack happened between 15:48 and 16:18 (see Figs. 2.14d and 2.14e), while the lowest salinity(salinity at all layers  25 psu) occurred around 16:48 (see Fig. 2.14f). Similarly, the secondhigh water slack occurred at about 21:48 (see Fig. 2.12a). It can be seen that the depth of thelast layer (between 28 psu and 29 psu) is highest at hour 22:18 (see Fig. 2.12b), that means the
maximum of the depth average salinity during this stage happened 30 minutes later, around22:18.
For further clarifications, the FATS data set that collected from the second campaign (seeFig. 2.8) will be analyzed to add more information about time delays of salinity peaks. The
correlation between cross-sectional average salinity estimated by FATS and the water level isshowed in Figure 2.32 and Table 2.4 as follow.

Figure 2.32 The comparison between the cross-sectional average salinity acquired using FATS
(black lines) and water level (red lines) at the study site
Figure 2.32 shows a good correlation between cross-sectional average salinity and waterlevel and delays in the time of the salinity maximum to the peak water level are presented indetail in the Table 2.4.
The time delay between salinity maximum and the peak water level are determined using
the cross-correlation method (see Chapter 2, Section 2.4.4). In this study, cross-correlation isused to measure the time lags between cross-sectional average salinity deduced from FATS
and water level. Calculating the cross-correlation for salinity and water level will return the
maximum of the cross-correlation function that points clearly to the time when these two timeseries are best matched, indicating the time delay between them.

2. Vertical and Lateral Distributions of Salinity and Density

44

Figure 2.33 shows a typical of cross-correlation function between cross-sectional averagesalinity deduced from FATS and the water level. The cross-correlation function is maximum
at the time 61 minutes, meaning the time delay between them is 61 minutes.

Figure 2.33 Cross-correlation of salinity versus the water level in Ōta diversion channel during
the study period
Delays from 38 minutes to 56 minutes are seen for the six salinity peaks. With the tidal
period of the Ōta River is approximately 12.48 hours, the phase shifts are generally of the order
18.27q–26.92q.
Table 2.4 The time delays of the salinity peaks

Peak numberTime lag (minute)

Phase lag (°)

1

38

18.27

2

56

26.92

3

52

25.00

4

55

26.44

2. Vertical and Lateral Distributions of Salinity and Density

45

5

45

21.63

6

50

24.04

Dyer (1973) stated that the density current effects, changes in water depth likely cause thesedelays in time of the salinity peak. In Ōta River estuary, another reason for that phenomenon
is the effects of the freshwater flows from the Yaguchi Gauging station located upstream(Nguyen & Kawanisi, 2021, Kawanisi et al., 2011). Figure 2.34 also shows the relationshipbetween the freshwater discharge recorded at Yaguhi Gauging Station and the delays in timeof salinity peaks. It can be seen that the time lags raise corresponding with the decrease of the
freshwater discharge. It is evident that the freshwater discharge from upstream affects
significantly these time lags. Section 3.6.6 (Chapter 3) addresses in detail this phenomenon.

Figure 2.34 The association between freshwater discharge recorded at Yaguchi Gauging
Station and delays in time of salinity
2.6.5 The effect of the tidal straining and tidal time scale
The field observations of the present research are conducted to collect the data of salinityand density without velocity data. However, some previous studies addressed the contributionof vertical and lateral variations in velocity to the stratification process. Besides, thecharacteristics for velocity in the Ōta diversion channel also are addressed by some previous

2. Vertical and Lateral Distributions of Salinity and Density

46

studies. Thus, this section discusses the role of tidal current in the stratification process in theŌta diversion channel by citing the previous results.
2.6.5.1 The effect of the tidal straining
Tidal straining is the phenomenon that describes the straining effect induced by the vertical
shear of swing tidal currents that act on horizontal density gradients. Another definition of tidal
straining was presented by (Simpson et al., 1990), the interaction of the longitudinal density
gradient in estuaries with the vertical shear in the tidal current leads to a forcing mechanism
termed ‘‘tidal straining’’. There are two main types of tidal straining, horizontal tidal straining
and vertical tidal straining. Horizontal tidal straining is lateral mixing between water masses
which are advected at different speeds, due to lateral gradients in the longitudinal velocity.
Vertical tidal straining is vertical mixing between water masses advected at different speeds
due to vertical gradients in the longitudinal velocity.

Figure 2.35 Schematic of tidal straining: (a) isolines vertical at start of ebb (b) stratificationinduced by shear on the ebb modified by top and bottom mixing (Simpson et al., 1990).
Figure 2.35 shows the mechanism of tidal straining process. The stratification is created byshearing of the faster and lighter layer of the water column over the saltier and slower-moving
water of the next lower layer.
During ebb tides, the surface water that caries freshwater from upstream is often lighter andwill move faster toward the river mouth and overtake the lower layers that are saltier andheavier. This process will continue to happen between two layers that are close, resulting in astable structure and suppressing turbulent mixing. During the flood phase of the tide, thisprocess will be reversed, thus, the stratification will reduce due to the effect of vertical shear.

2. Vertical and Lateral Distributions of Salinity and Density

47

In a previous research that carried out at Ōta diversion channel, Soltaniasl et al. (2013) showedthat during ebb tide the velocity range of the lighter surface water (salinity variation of 2 – 8psu) is +0.1 – +0.3 m/s (“+” denotes downward direction) while the saltier water (salinity
variation of 14 –16 psu) locate on the river bottom and have velocity variation of -0.05 – -0.1
m/s (“-” denotes upward direction) (see Figs. 2.36 and 2.37).

Figure 2.36 Contour plots of salinity at cross-sectional in the Ōta diversion channel estimatedusing CTD during a typical ebb tide (Soltaniasl et al., 2013)

2. Vertical and Lateral Distributions of Salinity and Density

48

Figure 2.37 Contour plots of longitudinal velocity at cross-sectional in the Ōta diversion
channel estimated using ADCP during a typical ebb tide (Soltaniasl et al., 2013)
2.6.5.2 Contribution from the tidal time scale
Nguyen (2021) and Razaz (2013) showed that the Ōta diversion channel is an ebb-dominantestuary, with an asymmetry in ebb-tide and flood-tide velocities: the highest velocities
occurring during the ebb tide. Some previous studies have been conducted on the influence ofthe tidal time scale on the variation of stratification. Jay (1990) stated that the tidal asymmetry
during a spring - neap tidal cycle plays an important role in stratification variability. Simpson(1990) also addressed that this asymmetry creates a vertical shear, and thus a straining; thisphenomenon was described as tidal straining. During ebb tides, the surface current will
accelerate and strain the horizontal salinity gradient, which might increase the stratification.
Furthermore, the combination of strong advection and straining during ebb tides may alsoenhance the stratification process.
2.7

Conclusions

This chapter presents the variations of salinity and density in the vertical and lateral
directions in the Ōta diversion channel. To clarify a transverse dynamic process throughout an
investigation of salinity and density distribution in the cross sections, a field observation in the
Ota diversion channel was conducted. The main novelty of the present research is using the2. Vertical and Lateral Distributions of Salinity and Density

49

number of stratification layers and their depth, as well as the surface-to-bottom salinity
difference to evaluate the stratification/de-stratification degree in a tidal shallow and narrowestuary.
At the middle part of the Ōta diversion channel (approximately 4.5 km from the river mouth),the distributions of salinity, density, and water temperature were measured over a tidal cycle atboth spring and neap tides, using Compact Conductivity-Temperature-Depth sensor as a main
instrument with other instruments, including FATs, CT sensors, remote controlled boat. Two
CTD campaigns to collect salinity data sets were carried out across the river at two bridges(Shinkoi and Asahi bridges), with a longitudinal distance of approximately 850 m between thetwo bridges.
The vertical profiles of salinity, density, and temperature are analyzed over the two periodsof time, the first one is on September 5th 2018 referring a neap tide, and the second one is on
October 2nd 2020 referring a spring tide.
The results of salinity distributions in the cross sections indicate that the density driven
might be the mechanism of the stratification process in the Ōta diversion channel.
In detail, salt wedges moved from the left side to the right side of the riverbank during bothneap flood tide and spring flood tide, resulting in lateral salinity distribution. It is likely due tothe effects of cross-channel bathymetry variation, and the lateral density gradients. The effectof temperature variation on stratification at the study site was weak compare to the above
mentioned factors.
Besides, the stratification developed gradually from the surface to the bottom of the watercolumn over the ebb tide period primarily is caused by the tidal straining, tidal time scale, andfreshwater discharge. The quick response of stratification and de-stratification to tidal changing
seems related to the shallow water condition.
The cross-correlation method is used to estimate the time lags between salinity and waterlevel variations. The results indicate that delays in time of salinity range from approximately
38 minutes to 56 minutes, and the phase shifts range from 18.27q–26.92q. The delays in timeis affected by the freshwater runoff from upstream.
The density distribution at the observation site has clear tidally periodic characteristic. The
saltier water moved from the left side to the right side of the river bank at the end of the flood
spring tides, resulting in lateral density distribution. And density variation shows a vertical
distribution in the early of the ebb spring tide. During the flood tides, vertical density gradientincreases at the middle water column, and lateral density gradient pattern almost remains

2. Vertical and Lateral Distributions of Salinity and Density

50

unchanged. The lateral density gradient might lead to lateral salinity distributions during floodtides. Besides, the vertical density gradient at the downstream area seems smaller than that at
the upstream area, due to the effect of freshwater inflow from the upstream.

3. Longitudinal Distributions of Salinity and Tidal Flow

CHAPTER 3

51

LONGITUDINAL DISTRIBUTIONS OF SALINITY AND

TIDAL FLOW

3.1

Introduction

Section 1.1.2, Chapter 1 mentions the important role of the Ōta diversion channel as wellas the necessity of investigating the longitudinal distributions of salinity and tidal flow using
an accurate and cost-effective method. Several previous studies strongly suggest that FATs isa state-of-the-art technique because of its reliable and accurate feature for the long-term
measurement of river discharge, even in shallow, wide rivers or tidal estuaries with saltwater
intrusions (Soltaniasl et al., 2013, K. Kawanisi et al., 2017, K. Kawanisi et al., 2018).
However, most published studies on salinity intrusion, stratification, estuarine circulation,and salinity flux that employed FATs were implemented using a traditional scheme that
included an oblique transmission line and several FAT units. Thus, the main objective of thisstudy is to apply the new FAT deployment pattern to investigate the longitudinal distributionof salinity and tidal flow in a tidal channel.
The aim of this study is to examine the performance of the proposed scheme using the
FAT system in terms of providing sufficiently accurate estimates of river discharge in tidal
estuaries, a mesoscale estuary, the Ōta diversion channel, in Hiroshima, Japan is used as a casestudy. The main novelty of this work is the use of a new scheme for the tomographic
deployment of the FAT system. Two pairs of four FAT units were installed along a 700 m

3. Longitudinal Distributions of Salinity and Tidal Flow

52

length of estuarine floodway in a zigzag configuration. The significance of this work is its
exploration of the results of examining the current velocity in both landward and seaward
directions.
3.2

Study site
The Ōta River estuary in Hiroshima City, western Japan, is the monitoring site used in thisstudy. A map of the study location is shown in Figure 3.1. The FAT system is deployed about
4.3 km upstream from the estuary. The tomographic scheme is presented in Figure 3.1b, andthe CTD-FAT campaigns for validation during a typical spring tide are shown in Figure 3.1c.
In this study, a series of four FAT units with different transmission lengths are deployed in a
zigzag distribution pattern. The present study focuses on assessing the potential advantages ofthe zigzag pattern rather than a conventional pattern (i.e., measurement at one cross-section) totrace the velocity behavior over the main channel during flood and ebb tides (i.e., landward
and seaward flow directions). As shown in Figure 3.1c, the tomographic zone is extended over
700 m ൈ 170 m. During the observation period, the freshwater runoff is limited by the Gionsluice gates (see Fig. 3.1a) located 4.5 km upstream from the observation site; the crosssectional area of stream was 32 m ൈ 0.3 m for the spilling flow (Kawanisi et al., 2010). The
water level is recorded at Yaguchi Gauging Station located approximately14 km upstream fromthe river mouth (see Fig. 3.1a).

3. Longitudinal Distributions of Salinity and Tidal Flow

53

Figure 3.1 a) The location of the field observation at the Ōta diversion channel; b) thearrangement of the tomographic scheme of the FAT system over the diversion channel. Yellow
and purple symbols indicate the locations of the CT instruments; and c) the Compact CTD(yellow circles) and FAT (red triangles) campaigns for validating section-average salinity using
the FAT system.
The bathymetry distribution of the Ōta diversion channel is presented in Figure 2.2. Figure
3.2 shows the oblique cross-sections between each pair of acoustic stations. The cross-sectional
areas along the transmission lines are estimated from the data set collected using Stream-Pro
ADCP. In general, the riverbed is irregularly shaped and not flat. The river bed altitudes along3. Longitudinal Distributions of Salinity and Tidal Flow54

S1S2 and S3S4 transmission lines have the similar trend that decreases from the left side to theright side of the river while the river bed altitude of the transmission line along S 2S3 shows the
opposite trend, resulting in a meandering along the observation site.

Figure 3.2 Oblique cross-sections along transmission lines between S1S2, S2S3, and S3S4.
Dashed lines denote the Highest Water Level (HWL) and the Lowest Water Level (LWL), andblack dots denote the locations of transducers.
3.3

Instrumentation

3.3.1 Fluvial Acoustic Tomography (FAT) system
Section 2.3.2, Chapter 2 shows the measurement principle as well as the specifications of
FATs. This part will introduce the unique ability of FATs in monitoring the estuarine physics
in detail. During a time period of 12 years (from 2010 – 2021), objects of FATs application
have expanded continuously in both study area as well as FATs scheme.

3. Longitudinal Distributions of Salinity and Tidal Flow

55

FATs can be applied in several kinds of area, including deep, shallow to extreme shallow
rivers; tidal and non-tidal rivers; river conjunction; river bifurcation. The required number ofthe deployed FATs in the field observation also varies diversely, according to the research
purpose. For example, to investigate the depth average velocity along a channel, FATs mostly
is deployed with a pair of transducers at both sides of the river. To investigate the twodimension field of velocity/salinity, a network of FATS is required.
In the present study, FATs are used as the main instrument, in the zigzag configuration.
3.3.2 Acoustic Doppler Current Profiler (ADCP)The Stream-Pro ADCP is an equipment for measuring velocity and discharge in shallow
stream (from 0.15 – 6m in depth), using the sound wavecs Doppler effect. Stream-Pro has four
broadband transducers (see Fig. 3.3). The monostatic system measures the Doppler shift of thesound pulses under the water in different directions. In this study, we attached this equipment
into a moving boat to collect the discharge and river bed shape data along the three transmission
lines of FATs (see Fig. 3.1b).

Figure 3.3 StreamPro Acoustic Doppler Current Profiler (ADCP) (Source: Teledyne Marine)
Table 3.1 Stream Pro specifications (Source: Teledyne Marine)
Max Profiling Range

6m

Max Bottom Tracking Range

7m

Max Depth Detection

7m

Velocity Accuracy (typical)±1.0% of measured velocity, ± 0.2 cm/s

Velocity Range±5 m/s3. Longitudinal Distributions of Salinity and Tidal Flow
Resolution

0.1 cm/sec

Data output rate

1 Hz

Beam Angle

20°

Standard Sensors

Temperature, tilt, compass

Communications

RS-232, Bluetooth

Weight in air

5 Kg

Dimensions

Electronics housing: 15 x 20 x 10 cm

56

Transducer: 3.5 cm diam. x 15cm length
Float: 44 x 70 x 11 cm

3.3.3 CT (Conductivity, Temperature) sensor
INFINITY-CT is an accurate conductivity and temperature meter making use of 7-electrodesensor. This 7-electrode generates an electric current only inside of the conductivity cell,minimizing external influences and improving data quality. Thus, precise salinity
measurements are possible under bio-foul forming conditions. The compact design is suitable
to be deployed/integrated with various sites/platforms. Some of the technical specifications ofCT sensor are presented in Table 3.2.
Table 3.2 CT sensor specifications (Source: JFE advantech Co., Ltd)Model

A7CT2-USB (for shallow water)

Parameter

Temperature

Conductivity

Principle

Thermistor

7-electrodeRange-3–45 qC

0.5 – 70 mS/cm

Resolution

0.001 qC

0.001 mS/cm

Accuracyr0.05 qC (0 – 35qC)

r0.05 mS/cm (28–65 mS/cm)

3. Longitudinal Distributions of Salinity and Tidal Flow

57

3.3.4 Other instruments
This study also uses the data that collected using another instruments, such as water level
logger, Compact CTD (Conductivity, Temperature, Depth) sensor, remote controlled boat.
3.4

Methodology

3.4.1 The Fluvial Acoustic Tomography (FAT) system
The FAT is an advanced hydro-acoustic instrument designed by Hiroshima University thatuses submerged acoustics to observe various hydrological properties of rivers at levels ranging
from 0.3 m – 10 m in depth (Razaz et al., 2015, Al Sawaf et al., 2020). FAT emits
omnidirectional acoustic signals at different frequencies (mainly between 7–53 kHz). The FAT
system contains GPS receiver that helps synchronize FAT units to guarantee the high-precisiontransmission of pulses. The acoustic pulse was transmitted every 30 secs in the experiments.
In this work, four broadband transducers with a central frequency of 30 kHz were used tomeasure the cross-sectional average velocity, discharge, and salinity over the period from
December 28th 2018 to January 16th 2019, and were deployed as shown in Figure 3.1b. The
horizontal distances are shown in Figure 3.1b, with the longest transmission line between S2S3(332 m) and the shortest between S3S4 (249 m).
3.4.1.1 Estimating tidal current and water discharge using FATS
FAT system uses the time-of-travel tomography method. The mean velocity along thetransmission line (u) and mean speed of sound (c) are evaluated based on respective travel
times, (tup) and (tdown), at the upstream and downstream stations, as follows:‫ͳ ܮ‬ͳܿ ൌ  ሺ൅ሻʹ ‫ݐ‬௨௣ ‫ݐ‬ௗ௢௪௡

(3.1)

‫ܮ‬
ͳ
ͳ
‫ ݑ‬ൌ  ቆെቇʹ ‫ݐ‬௨௣ ‫ݐ‬ௗ௢௪௡

(3.2)

and

where L is the horizontal spacing between the upstream and downstream stations. For a given
cross-section, the section-averaged velocity (V) and discharge acquired by FAT (Q) arecalculated using the following equations:3. Longitudinal Distributions of Salinity and Tidal Flowܸ ൌ ‫ݑ‬ൗܿ‫ߠ ݏ݋‬

58
(3.3)
(3.4)

ܳ ൌ ܸ ൈ ‫ܣ‬ሺ‫ܪ‬ሻ ൈ ‫ߠ ݊݅ݏ‬where A (H) is the cross-sectional area along the ray path as a function of the water level (H),and θ is the angle between the ray path and streamline.
3.4.1.2 Estimating depth- average salinity using FATS
As described by Medwin (1975), the speed of sound in water is generally a function ofsalinity, water temperature, and depth:ܿ ൌ ͳͶͶͻǤʹ ൅ ͶǤ͸ܶ െ ͲǤͲͷͷܶ ଶ ൅ ʹǤͻͳͲିସ ܶ ଷ ൅ ሺͳǤ͵Ͷ െ ͲǤͲͳܶሻሺܵ െ ͵ͷሻ ൅ ͲǤͲͳ͸‫ܦ‬(3.5)

The cross-sectional average salinity can be deduced from Equation (3.5) as:ܵ ൌ ͵ͷ ൅  ሺܿȂ ͳͶͶͻǤʹȂ ͶǤ͸ܶ ൅ ͲǤͲͷͷܶ ଶ Ȃ ͲǤͲͲͲʹͻܶ ଷ Ȃ ͲǤͲͳ͸‫ܦ‬ሻȀሺͳǤ͵ͶȂ ͲǤͲͳܶሻ

(3.6)

where T is water temperature (°C), c is speed of sound (m/s), D is depth (m), and S is salinity.
The valid parameter ranges in Equation 3.5 are as follows: 0 ≤ T ≤ 35 °C, 0 ≤ D ≤ 1000 m, and
0 ≤ S ≤ 45. This relationship helps estimating the cross-sectional average salinity using the
speed of sound in water computed by the FAT system.
3.4.2 Estimating the residual current velocity and residual water discharge
In this study, the term “residual current” refers to the current left after removing the tidal
component from the observed current. In general, this residual current might be due to several
factors, such as freshwater inflow from the upstream, wind forcing, the interaction of tidal
motion and bathymetry, etc.
The residual current and residual discharge in the study will be estimated using low-passfilter method. In this case, digital low-pass filter is used to remove the tidal components fromthe current and discharge data. The mixed tides in the Ōta river estuary include diurnal andprimary semidiurnal components, thus, the cutoff period of low-pass filter was set to the tidal
period of 24.5 hours.

3. Longitudinal Distributions of Salinity and Tidal Flow

59

3.4.3 Determination of flow direction using FATS
3.4.3.1 Estimating the flow direction
The accurate calculation of the flow direction angle is critical to obtaining precise results.
Bahreinimotlagh et al. (2016) proposed an equation for calculating the flow direction, using
four transducers to create two crossed acoustic transmission lines. The equation is based on thecontinuity condition: the water discharge of the two related parts should be equal.
Many factors influence the degree of fluctuation in discharge along the channel. However,
it is assumed in this study that the discharge variations are negligible because of the shortdistance of the study site (700 m). Thus, for simplicity, the degree of discharge fluctuation was
not considered in the calculations. Equation 3.7 was used to calculate the temporal variationsin the flow direction obtained from the FAT system data:ߠଵξʹܿ‫ݏ݋‬ሺ‫׎‬ሻඥ‫ܣ‬ଵଶ ‫ݑ‬ଵଶ ൅ ܿ‫ݏ݋‬ሺʹ‫׎‬ሻሺ‫ܣ‬ଵ ‫ݑ‬ଵ െ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻଶ ൅ ͸‫ܣ‬ଵ ‫ܣ‬ଶ ‫ݑ‬ଵ ‫ݑ‬ଶ ൅ ‫ܣ‬ଶଶ ‫ݑ‬ଶଶ ൅)‫ ͳۇ‬ඩ
‫ۊ‬ܿ‫ݏ݋‬ሺʹ‫׎‬ሻሺ‫ܣ‬ଶ ‫ݑ‬ଶ െ ‫ܣ‬ଵ ‫ݑ‬ଵ ሻ ൅ ͵‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶିଵൌ ܿ‫ۈ ݏ݋‬‫ʹۈ‬‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶ
‫ۉ‬

(3.7

‫ی‬

where ‫ ׎‬is the angle between two transmission lines (e.g., S 1S2 and S2S3). The ‫ ׎‬may be
expressed as:‫ ׎‬ൌ ‫ି݊ܽݐ‬ଵ ൬ܺଶ ܻଵ െ ܺଵ ܻଶ൰ܺଵ ܺଶ ൅ ܻଵ ܻଶ(3.8)

where X1, X2, Y1 and Y2 are determined using the coordinates of the acoustic stations.
3.4.3.2 Estimating the relative errors
A formulation of the structure of the relative error was also proposed in this study that
included the following five terms:
ߜߠ ߜߠ‫ߠߜ ׎‬஺భ ߜߠ஺మ ߜߠ௨భ ߜߠ௨మ
ൌ
൅
൅
൅
൅

ߠ
ߠ
ߠ
ߠ
ߠ
ߠ
ఋఏ‫׎‬

The error term ቀ

ఏ

(3.9)

ቁ represents the uncertainty in the angle between two crossed paths andఋఏಲ

has a large impact on the error analysis. The second and third error terms ቀ ఏ భ ǡ

ఋఏಲమ
ఏ

ቁ are

3. Longitudinal Distributions of Salinity and Tidal Flow60
ఋఏೠerrors in the water level measurements. The fourth and last terms ቀ ఏ భ ǡఋఏೠమఏቁ are errors in themean velocity along the transmission lines. The detailed equations of these error components
are shown in Appendix A.
3.4.4 Estimating the total error components of measurements of water discharge using
FATs
An important issue to be addressed in discharge computation is how to quantify the error
structures in the discharge measurements made by the FAT system. Kawanisi et al. (2016)
stated that the error structure of the discharge estimating by the FAT system is induced by thefollowing terms:(i)errors in water depth measurements;(ii)

riverbed uncertainties;(iii)

velocity measurements;(iv)

flow direction estimates.

The error structures induced by the discharge measurements of the FAT systems are
summarized in Equation 3.10 below:
ฬ

ߜܳி஺்
ߜܳு
ߜܳ஺
ߜܳ௨
ߜܳఏ
ฬൌฬ
ฬ൅ฬ
ฬ൅ฬ
ฬ൅ฬ
ฬ
ܳி஺்
ܳ
ܳ
ܳ
ܳ
ߜ‫ܪ‬
ߜܼ௓
ߜ‫ݑ‬
ߜߠ
ฬ൅ฬ ฬ൅ฬ
ฬൌ ฬ ฬ ൅ ฬ‫ܪ‬‫ݑ‬ߠߠ
‫ܪ‬(3.10)

where:
ఋொಹ

ቚ

ఋொಲ

ቚ

ொ

ఋு

ቚ: ቚ ቚ is the error component that relative to the mean water depth;
ு

ொ

ఋ௓ೋ

ቚ: ቚ

ு

ቚ is the error component that relative to the imperfection of the bathymetry

survey and the variations of the bottom shape;
ఋொೠ

ቚ

ொ

ఋொഇ

ቚ

ொ

ఋ௨

ቚ: ቚ ቚ is the error component that relative to the velocity deduced from FATs;
௨

ቚ: ቚ

ఋఏ

ୡ୭ୱఏୱ୧୬ఏ

ቚ is the error component that relative to the angle between the flow

direction and the transmission line.
Finally, the results of the error calculation process were compared with the results of themoving boat Stream – Pro ADCP (Acoustic Doppler Current Profiler), which measured at thesame three transmission lines for 2 days (December 12-14th 2019).

3. Longitudinal Distributions of Salinity and Tidal Flow

61

3.4.5 Longitudinal distributions of salinity, salinity gradient, and dispersion coefficient
The salinity gradient and dispersion coefficient is estimated using the distribution of
longitudinal salinity. The longitudinal dispersion coefficient indicates the capacity of a river
flow to scatter substances in the longitudinal direction. In a normal channel, the advective
transport is proportional to the water velocity and longitudinal concentration gradient. Salinity
transport may be calculated using the following equation:
߲ܵ
߲ܵ
߲ଶܵ
൅‫ݑ‬
ൌ ‫ܦ‬௫ ଶ 
߲‫ݔ‬
߲‫ݐ‬
߲‫ݔ‬

(3.11)

where S is the section-averaged salinity, u is the water velocity, x is the distance upstream fromthe estuary’s mouth, and Dx is the longitudinal dispersion coefficient.
3.4.6 Measurements of temperature, depth, and bathymetry
As mentioned in the previous section, Stream-Pro ADCP (Teledyne RDI; Stream-Pro
Acoustic Doppler Current Profiler) was used to obtain the data on the bathymetry of theriverbed of the monitored cross sections and to determine the flow directions for the measured
flow. In addition, the discharge data generated by the Stream-Pro ADCP was compared to thedischarge estimated by FAT. During the observation period, the moving-boat ADCP
campaigns were regularly carried out.
The temporal variations in water temperature were measured using three CT (conductivity
and temperature) sensors attached to tripods side-by-side to the S1 station at 0.52 m, S3 station
at 0.5 m and S4 station at 0.4 m above the bottom. The temperature data were used to calculate
salinity using Equation 3.6 (see Fig. 3.1).
The temporal variations in water level (H) were recorded using water level loggers deployedside-by-side at each acoustic station (i.e., at S1, S2, S3, and S4). The water level records provided
temporal data on water surface heights, which were used to measure the temporal variations of
the cross-sectional area at each transmission path.
3.4.7 Confirming the FATS feasibility to measure the section-average salinity
CTD campaigns were carried out at two FAT units between the left and right sides of theriver bank concurrently along Shinkoi Bridge during a typical spring tide to confirm thefeasibility of the FAT system for measuring the section-average salinity. The measurements of

3. Longitudinal Distributions of Salinity and Tidal Flow62

salinity distribution in the cross-sectional were taken on October 2nd 2020, from 08:20 to 23:30(see Fig. 3.1c). During these campaigns, two FAT units were deployed on the left and rightsides of the river near Shinkoi Bridge with a transmission length of 160 m. The CTD collected
the vertical salinity distribution at six points along the bridge every thirty minutes.
3.5

Results

3.5.1 Temporal variations in water level along the channel
The temporal variations in the water levels recorded at S1S2, S2S3, and S3S4 are shown in
Figure 3.4. Compared to the average water level in Tokyo Bay (T.P), the water level was
estimated to evaluate the temporal variations of the cross-sectional area for each section. In thepresent study, water level data was collected from the water level loggers that were attachedinto the transducer tripod at each station. The missing data occur at the low water periods during
the spring tide because of the instrument were dried out.

Figure 3.4 Temporal variations of water level during the study period recorded at the observed
cross-sections.

3. Longitudinal Distributions of Salinity and Tidal Flow63

3.5.2 Temporal variations in tidal velocity distribution along the channel
3.5.2.1 Tidal velocity
The time series of the tidal current (denote by black lines) and residual current (denote by
red lines) velocities recorded by the FAT stations are shown in Figure 3.5. The missing periods
resulted from the abovementioned problems during the monitoring program and the drying outof the transducers.

Figure 3.5 Time series for the tidal current velocities (black lines) and the residual mean
velocity (red lines) measured using FAT at the selected stations during the study period.
In general, the comparison between Figures 3.4 and 3.5 shows that the tidal current patternis corresponding to the water level pattern at all three sections.
The observed current velocities at the upstream area (S1S2 section) are smaller than those at
the downstream area (S3S4 section) during the observation period. In the S2S3 and S3S4 sections(see Fig. 3.5b and 3.5c), the velocity fluctuations during neap tides (December 29th 2018 –January 3rd 2019) were smaller than those during spring tides (January 4–9th 2019). The
maximum ebb-tide velocity was roughly 0.45 m/s that found at the downstream areas (S3S4transmission line) and the highest value of flood-tide velocity was estimated as − 0.25 m/s. The

3. Longitudinal Distributions of Salinity and Tidal Flow

64

S3S4 transmission line registered the highest ebb-tide velocity (approximately − 0.45 m/s), andthe lowest velocity (approximately − 0.25 m/s) on 8 January 8th 2019.
3.5.3 Flow direction variations
Equation 3.7 was used to calculate the temporal fluctuations in flow direction using dataobtained from the FAT system. The input data for calculating the flow direction are the angle
between two transmission lines; the cross-sectional areas; and the current velocity of the threetransmission lines.
3.5.3.1 The angle between two transmission lines
The angle between two transmission lines (i.e. S1S2 and S2S3) is calculated using Equation
3.8. The coordinates of the four acoustic stations are presented in the Table 3.3. Figure 3.6
shows the results of the angles of 63.54q and 82.62q between S1S2 - S2S3 and S2S3 - S3S4transmission lines, respectively.
Table 3.3 The coordinates of the acoustic stations
Acoustic station

Latitude (degree)

Longitude(degree)

S1

34°23'44.6672"N

132°25'54.1499"ES2

34°23'39.9654"N

132°25'43.5100"ES3

34°23'29.2019"N

132°25'43.8700"ES4

34°23'27.9484"N

132°25'34.2716"E

3. Longitudinal Distributions of Salinity and Tidal Flow

65

Figure 3.6 The angle between the transmission lines
3.5.3.2 The variations in area cross the channel at the three transmission lines
In this study, the cross-sectional area along the transmission line is estimated from thebathymetry data collected by Stream-Pro ADCP and the water level collected by the water
loggers (see Chapter 4, Section 3.4.5). Figure 3.7 shows the cross-sectional areas variations atthree transmission lines. The S3S4 section has the smallest cross-sectional area while S2S3 has
the biggest cross-sectional area.

Figure 3.7 Temporal variations of cross-sectional area during the study period recorded at thethree observed transmission lines

3. Longitudinal Distributions of Salinity and Tidal Flow

66

3.5.3.3 Flow direction variations deduced from FATS
Figure 3.8 shows the variations of the flow direction at three transmission lines. In general,
the fluctuated ranges of the angle between the flow and transmission lines for all three sections
are approximately 2.2 degrees. Moreover, the variations in the mean flow direction over thethree cross-sections are 17.3–19.4°, 45.4–47.6°, and 35.9–38.2° for S1S2, S2S3 and S3S4 section,
respectively.
The estimation of the averaged angles gained from ADCP for the monitored cross-sections
were ߠ = 18.29° for S1S2, ߠ = 46.33° for S2S3, and ߠ = 37.31° for S3S4. The minor deviations
between the FAT and ADCP estimates further confirm the acceptable efficiency of obtaining
flow direction measurements using FAT.

Figure 3.8 The variation of the flow directions along three sections deduced from FATS
3.5.3.4 The relative errors
ఋఏ

The error analysis results of the angle estimation ቀ ቁ were calculated using Equation 3.9,ఏwith the maximum relative errors shown to be approximately r 6, which was acceptable.

3. Longitudinal Distributions of Salinity and Tidal Flow67

3.5.4 Estimating water discharge along the channel
3.5.4.1 Estimating water discharge and residual water discharge
The angles with tidal current velocities and cross-sectional areas were used to calculate flowrate using Equation 3.4, as shown in Figure 3.9. The variation in water discharge correspondedwith that of the tidal current, with the peak discharge during the ebb tides rising toapproximately 200 m3/s. It is evident that the ebb-tide discharges were twice as high as theflood-tide discharges over the study period.

Figure 3.9 Temporal variations in water discharge (black) and residual flow (red) estimatedusing FAT at the selected stations during the study period
3.5.5 Residual current and residual water discharge
The residual velocities and residual water discharges (plotted in red) of the three crosssections during the study period are presented in Figures 3.5 and 3.9, respectively. These
residuals are relatively complex, as the values reflect the contribution of several elements,
including tidal propagation, direct and indirect wind forces, surface waves, horizontal andvertical density gradients, and upstream freshwater velocity. The interaction between the tidal

3. Longitudinal Distributions of Salinity and Tidal Flow

68

component and any of these components may significantly affect the generation process of theresidual. Therefore, the suitable filtering was used in this study to prevent these non-tidal
components from contributing to the residuals.
In this work, the residual (non-tidal) velocities were derived by filtering O1 that is lunar
diurnal constituent with a tidal cycle period of approximately 25.8 h. However, this frequency
band removes the tidal component and cannot efficiently judge the effects of this component.
As shown in Figure 3.5, the residual current trend is likely to remain unchanged along with thestudy site. The maximum value of 0.06 m/s occurs in December 2018, declining to around 0.03
m/s in January 2019. Similarly, the mean residual discharge variations at all three sections arelargely similar, with the maximum value of 15 m 3/s reaches in the last three days of 2018, anddecreases by half to 7 m3/s by the end of the period.
The freshwater runoff from the upstream of the Ōta River is regulated by an array of gateslocated near Gion Bridge. Under normal conditions only one gate is open. On regular days, theinflow discharge is around 10–20% of the Ōta River flow rate. As shown in Fig. 3.10, themaximum freshwater runoff recorded at Yaguchi Gauging Station is 60 m3/s in late 2018. It
declined to approximately 35 m3/s in January 2019. Thus, the residual current at the study site
is influenced almost by the upstream freshwater flow.

Figure 3.10 Comparison of the freshwater release from the Yaguchi Station (black) and theresidual discharge as estimated using FAT (red).
3.5.6 Temporal variations in salinity
3.5.6.1 Cross-sectional average salinity deduced from FATS
Figure 3.11 shows the variations of cross-sectional average salinity deduced from FATs,
using Equation 3.6. It is clearly seen that, during the observation site, the maximum value of

3. Longitudinal Distributions of Salinity and Tidal Flow69

the depth-average salinity in the upstream area (section S1S2) is lower than that in thedownstream area (section S3S4).

Figure 3.11 The variations of cross-sectional average salinity estimated using FATS at threetransmission lines
3.5.6.2 Longitudinal salinity distribution
The longitudinal distributions of salinity and salinity gradient as deduced using the FAT
system during a typical spring tide and a typical neap tide, respectively, are shown in Figure
3.12.
In general, along the observation site the depth-averaged salinity and the fluctuations in thesalinity gradient followed the opposite trends during both the spring and neap tides, with theformer decreasing upward and the latter increasing upward.
As shown in Figure 3.12, the cross-sectional average salinities show a decline in the
landward direction throughout the observation period, which was likely attributable to theimpact of incoming freshwater.
The differences in cross-sectional average salinity between the downstream and upstream areasof the study site are found to be approximately 0.5–1.6 psu during spring tide andapproximately 0.7–1.3 psu during neap tide. Moreover, the axial salinity during neap tide is3. Longitudinal Distributions of Salinity and Tidal Flow70

approximately 0.5 psu higher than during spring tide, while the salinity gradients along thechannel are lower during spring tide than neap tide. Therefore, at the study site, the variations
in salinity were significantly lower during spring tide, which may be explained by the different
degrees of tidal mixing seen during the two tides, with the larger degree of tidal mixing that
occurs during spring tides weakening the salt intrusion.

Figure 3.12 a) Longitudinal distributions of salinity, and b) salinity gradient deduced using the
FAT system during spring tide and neap tide. “x” is the distance along the river from S4 station,“Lc” is the longitudinal distance from S4 to S1 stations
3.6

Discussions

This work was designed to assess the performance of a promising tomographic system formonitoring the cross-sectional average velocity, discharge and salinity variations with hightemporal resolutions over long time periods. The observation program in this study ran forthree weeks. During the observation, FAT data were occasionally lost because of factors
including transducer cable corruption (due to human error, marine transport, etc.) and battery
shutdown. However, the obtained data were adequate to describe the tidal dynamics at thetarget site.

3. Longitudinal Distributions of Salinity and Tidal Flow71

3.6.1 Tidal asymmetry
Figures 3.4 and 3.5 present the correspondence between the variation trends of water level
and tidal current. For further details, Figures 3.13 and 3.14 present the comparison between
tidal current and water level along the study site during a typical spring and neap tides,
respectively.
During the lowest water slacks, the FATs data and thus, the velocity data are lost because
the transducers are out of water. To recover the missing data during the low water slacks, aninterpolation method is applied. This method was described in detail in (Bain et al., 2019).
Figures 3.13 and 3.14 are plotted after applying the interpolation method.

Figure 3.13 Comparison between tidal current (black lines) and water level (red lines) atthree sections during a typical spring tide.

3. Longitudinal Distributions of Salinity and Tidal Flow72

Figure 3.14 Comparison between tidal current (black lines) and water level (red lines) at three
sections during a typical neap tide.
In Figures 3.5, 3.13 and 3.14, the tidal current during ebb-tides double the flood-tide current,
and the ebb-tide discharges were twice as high as the flood-tide discharges over the study
period (see Fig. 9). The asymmetrical character of the tide indicates that the Ōta River estuary
is ebb-dominant.
Generally, when tidal waves from the ocean spread into a shallow area, the water tides inthat shallow region will surge, which might convince tidal asymmetry (Kang & Jun, 2003,
Boon & Byrne, 1981, Fitzgerald & Nummedal, 1983). Furthermore, Hoitink et al. (2003) andSong et al. (2011) addressed that flow asymmetry is closely associated with astronomical tides.
The previous researchers suggested that the tidal asymmetry phenomenon in mixed tidal
estuaries is usually related to the relationship between the phase of O 1, K1 and M2 tidal
constituents. Hoitink et al. (2003) proposed an equation to indicate the degree of tidal
asymmetry as: T = cos (Iu(O1) + Iu(K1) + Iu(M2)), with Iu(O1), Iu(K1), and Iu(M2) are the phase of
O1, K1 and M2 respectively. Tidal flows will be symmetric, flood dominant or ebb dominant if

T = 0, ! 0, and  0, respectively.
The results of the harmonic analysis for observed tidal within the observation time period
show that Iu(O1) = 191.3q, Iu(K1) = 219.67q, and Iu(M2) = 273.6q, thus T = -0.736, revealing an
ebb dominance. This is suggested that the ebb tidal asymmetry in the Ōta diversion channel
generated by the relation of O1 -K1 -M2 tidal constituents.

3. Longitudinal Distributions of Salinity and Tidal Flow73

3.6.2 Confirming the FAT ability to measure water discharge
To investigate the quality of the obtained data, the discharge acquired using the FAT systemin this study were compared to independent ADCP data acquired from scans of the Asahi
Bridge downstream area (see Fig. 3.15b). The temporal fluctuations in the streamflow
computed using the FAT systems were shown to be the same at all cross-sections based on thecontinuity equation. Thus, the records estimated from the S3S4 section were used for further
comparisons. As shown in Figure 3.15a, the water flow obtained using the FAT system (blackdots) is synchronous with the ADCP estimates (blue points). This provides strong evidence insupport of the ability of the FAT system to accurately capture flow variations. Moreover, theassociation between the respective discharge estimates of FAT and ADCP is illustrated in
Figure 3.15b. Both estimates show a similarity with a very high determination coefficient value(R2 = 0.994), a bias of 4.78 m3/s, and a low RMSE of 10.18 m3/s (13.82 %).

Figure 3.15 Comparison of the discharges acquired using the FAT (black) and ADCP (blue)and (b) The association between the FAT and ADCP estimates.

3. Longitudinal Distributions of Salinity and Tidal Flow74

3.6.3 Error structure for the river discharge measurement
As mentioned in Chapter 3, Section 3.4.4, the deviations in FAT river discharge
measurements may be estimated using Equation 3.10. Water depth and area are the functionsof mean water depth (H). The measurement errors of the water level loggers and the ADCP
moving boat, as obtained from their specification manuals, are ȁߜ‫ ܪ‬ȁ = 0.01 m and ȁߜܼ஻௠ ȁ =0.05 m, respectively. Water depths at the study site range from 1 m to 4 m. Hence, theuncertainty of the cross-sectional area ranges from 0.015 to 0.06, or 1.5 -6.
In addition, the deviations in the velocity term deduced using FAT are ȁߜ‫ݑ‬௠ ȁ = 0.012 m/s,
and the velocity along the three ray paths vary from − 0.18 m/s to 0.4 m/s (Fig. 3.5). Thus, themeasurement errors in the velocity resolution of FAT are 0.03–0.07, or 3-7.
The final term in the present case is attributable to the flow direction fluctuations and isgiven as ቀఋொಐொቁ. In this research, the angle between the streamline and the ray path is estimatedusing Equation 3.6, based on the velocities measured by FAT. Because of the angle between
the ray path and the streamline, the terms of discharge uncertainty are around r 0.045, or 4.5for all three selected stations during the study period. Thus, the maximum probable error isestimated as 17.5%, which is considered acceptable.
3.6.4 The practicability of using the FATs to measure the depth average salinity
The ability of the FAT system to accurately measure the salinity in a tidal estuary andmonitor the salinity intrusion in a tidal floodway was demonstrated previously (Kawanisi et al.,2011, Kawanisi et al., 2015). In previous research, CTD and FAT campaigns were conductedsimultaneously to confirm the feasibility of using the FAT system to measure the sectionaverage salinity.
As shown in Figure 3.16a, the salinity deduced using FAT (black line) and Equation 3.6 issimilar to the CTD estimates (blue points). The association between the salinity estimatesobtained using FAT and Compact CTD, respectively, is illustrated in Figure 3.16b. Bothestimates show a similarity with a very high determination coefficient value (R2 = 0.938), abias of 0.275 psu, and low RMSE of 1.038 psu (4.325%). These observations provide further
evidence that the FAT system is a reliable and accurate technique for the continuous monitoringof variations in salinity. In addition, the FAT dataset collected at three sections along the studysite was used to calculate the section-average salinities, which were subsequently used to
calculate the longitudinal distributions of salinity.

3. Longitudinal Distributions of Salinity and Tidal Flow75

Figure 3.16 (a) Water level variation (red line), and the comparison between the salinity
acquired using FAT (black line) and Compact CTD (blue dots) at Shinkoi Bridge, (b) The

3. Longitudinal Distributions of Salinity and Tidal Flow76

association between the FAT and Compact CTD estimates, and (c) Salinity distributions
obtained using Compact CTD.
3.6.5 Longitudinal dispersion coefficient
The dispersion coefficient is used to quantify the local scattering of salt to adjacent areas.
In this study, only the longitudinal dispersion coefficient was used, as longitudinal scales are
generally larger than either transverse or vertical scales. Savenije (1993) stated that the salt
intrusion process is ruled by three mechanisms, which include riverine–hydraulic dispersion,tide-driven dispersion, and gravitational circulation or density-driven dispersion.
As riverine-hydraulic dispersion is primarily influenced by geometric shapes and is small
compared to tide- and density-driven dispersions, it may be eliminated (Kawanisi et al., 2015).
Other researchers have used other approaches (e.g., the longitudinal salt flux decomposition or
the modelling approach) to verify which mechanisms are dominant in an estuary. In thisresearch, the longitudinal dispersion coefficient deduced from the water velocity and salinity
based on Equation 3.10 is discussed.
As shown in Figure 3.17, the horizontal dispersion generates a relatively small dispersion
coefficient upstream and a significantly increased coefficient downstream. In general, thedispersion coefficient depends primarily on the cross-sectional fluctuations in the velocity andsalinity (see Eq. 3.11). In the Ōta diversion channel, the change of cross-sectional averagevelocity is found to increase toward the mouth of the river (see Fig. 3.5), and the axial salinity
gradient is higher in the upstream section than the downstream section. As a result, thelongitudinal dispersion coefficient increased as the distance to the mouth of the river decreased.

3. Longitudinal Distributions of Salinity and Tidal Flow

77

Figure 3.17 Longitudinal distributions of the dispersion coefficient deduced using the FAT
system during spring tide and neap tide. “x” is the distance along the river from S4 station,“Lc” is the longitudinal distance from S4 to S1 stations
Soltaniasl et al. (2013) decomposed a cross-sectional salt flux into five different components
and grouped these into two categories: landward fluxes and seaward fluxes. Although
Soltaniasl et al. (2013) did not address the salt dispersion attributable to gravitational
circulation due to the lack of related data, in this study, the total salt flux in the Ōta Riverestuary is found to be controlled significantly by the two categories, with the magnitude of theformer category (landward fluxes) measuring half of the later (seaward fluxes). This resultshows a significant effect of the tide on the salt flux in the Ōta diversion channel. Furthermore,
the channel is narrow and shallow, which is a state in which tide-driven shear mechanisms areoften dominant (Savenije, 1993). Thus, the tide-driven mechanism may be the dominantmechanism in the dispersion process in the Ōta diversion channel.
3.6.6

Time delays of the phases of salinity variation

Figures 3.18 and 3.19 show the temporal variations in cross-sectional average salinity
deduced from FATS and water level along the channel during a typical spring tide and neaptide, respectively. It is clearly seen that the phases of salinity variation lag behind the highwater during both spring and neap tides.
To clarify the process and the reason of this phenomenon, the delays in time of the salinity
peaks are calculating using cross-correlation method (see Chapter 2, Section 2.4.4)

3. Longitudinal Distributions of Salinity and Tidal Flow

Figure 3.18 Temporal variations in cross-sectional average salinity (black lines) and waterlevel (red lines) at the study site during a typical spring tide.

Figure 3.19 Temporal variations in cross-sectional average salinity (black lines) and waterlevel (red lines) at the study site during a typical neap tide.

78

3. Longitudinal Distributions of Salinity and Tidal Flow79

3.6.6.1 The effect of velocity on the travel time
The travel times, tup and tdown, at the upstream and downstream stations were estimated,
respectively, using the following equations:‫ݐ‬௨௣ ൌ‫ܮ‬‫ܮ‬Ǣ‫ݐ‬ௗ௢௪௡ ൌܿ െ ‫ݑ‬ܿ ൅ ‫ݑ‬(3.12)The travel times in the upstream and downstream sections are not equal due to the directionof flow velocities (seaward or landward). Normally, the mean speed of sound (c), and thus
mean salinity, is estimated using the mean travel time, tm = (tup + tdown)/2. However, in cases
where one of the travel times is missing, tup or tdown may be used to calculate the speed of sound,
as the differences between travel times due to water velocity are small compared to the travel
times.
On the S1S2 section, the sound transmitting data along the S1oS2 direction were more often
lost than the data along the S2 o S1 direction. Thus, the travel time data from the S2 station to
the S1 station are used to calculate the salinity along the S1S2 section. Figure 3.20 shows thecomparison between the cross-section average salinity estimated from the travel time tup(denotes by black dots), and from the mean travel time tm (denotes by red dots).

Figure 3.20 The cross-sectional average salinity at S1S2 section estimated from FATs, with themean sound speed is calculated from the travel time tup (black dots), and from the mean travel
time tm (red dots)
Figure 3.21 presents the salinity error induced by the salinity differences (dS) between thesalinity (SS1S2) estimated from the mean travel time (tm) and salinity estimated from the travel3. Longitudinal Distributions of Salinity and Tidal Flow

80

time tup. The salinity differences are small and the salinity error induced by the time differences
between tup and tm is small as well, approximately 5.

Figure 3.21 The salinity error induced by the time differences between the one way travel time
and the mean travel time
3.6.6.2 The delays of the phases of salinity variation
In Figure 3.22, the black dots denote the temporal variations in the cross-sectional averagesalinities that are estimated from the water temperatures, water depth, and the mean of soundspeed collected from FATs at two different cross-sections (S1S2 and S3S4), while red dots
denote the salinities obtained by CT sensors deployed at the S1 and S4 stations, respectively.
Compared to the stable trend of one-point salinities recorded at the S1 and S4 stations using a
CT sensor, the cross-sectional average salinities deduced from the FAT data increases slightly
at midday on December 31st 2018. The reason for these changes might be the change offreshwater discharge recorded at Yaguchi Station on December 31st 2018 (see Fig. 3.10). The
time lags between the salinity maximum and the high water level were examined to clarify theeffects of freshwater on the salinity variation.

3. Longitudinal Distributions of Salinity and Tidal Flow

81

Figure 3.22 Temporal variation of salinity obtained using FAT (black points) at S 1S2 and S3S4transmission lines and CT sensors (red points) at S1 and S4 stations.
For further information, Table 3.4 illustrates the time lags and phase lags between thesalinity and water level which are estimated from cross-correlation function (Fig. 2.2). Overall,
it was evident that the time delay increased toward the mouth of the river, and the time shiftchanges significantly from before December 31st 2018 to after December 31st 2018, which is
discussed as follow.
Table 3.4 Delays in time of salinity peaks.
S1S2 Section
Time Lag(minute)Phase Lag (°)

S2S3 Section
Time Lag(minute)Phase Lag (°)

S3S4 Section
Time Lag(minute)Phase Lag (°)

Before December 31st 2018
14

6.73

17

8.17

28

13.46

21

10.10

27

12.98

37

17.79

15

7.21

24

11.54

31

14.90

12

5.77

24

11.54

36

17.31

16

7.69

26

12.50

40

19.23

After December 31st 2018
22

10.58

31

14.90

87

41.83

32

15.38

26

12.50

94

45.19

3. Longitudinal Distributions of Salinity and Tidal Flow

82

23

11.06

42

20.19

91

43.75

21

10.10

38

18.27

55

26.44

23

11.06

37

17.79

97

46.63

Figure 3.23 A typical cross-correlation function of salinity versus the water level
First of all, the time delay estimated in the downstream area (S 3S4 section) is twice as highas the time delay in the upstream area (S1S2 section) over the study period. Moreover, the delayin the salinity maximum along the channel ranged from 12 min to approximately 1.5 h. All
three sections of the channel significantly show higher time delays after 31st December 2018
than before this date.
In general, the delays found at the time of the salinity peaks are likely attributable to density
current effects and cross-channel processes such as changes in water depth, differences invertical velocities (both values and direction), and secondary flows (Dyer, 1973). In thisresearch, the phase lags noted between the water level and salinity exist primarily because of
the freshwater flows from the upstream. Figure 2.24 clearly shows a significant response
between averaged time lag along the observation area and upstream freshwater discharge.
Generally, the time lag is shorter corresponding with an increase in freshwater rate. In the
middle of the day December 31st 2018, when upstream freshwater decreases fromapproximately 60 m3/s to 20 m3/s, time lag increases twice, from around 40 minutes to 80
minutes. Similarly, during the days after December 31st 2018, time lag decreases fromapproximately 65 minutes to 55 minutes when freshwater discharge increases from 20 m3/s to
35 m3/s. The shorter time lags are corresponding to the increase in freshwater discharge because

3. Longitudinal Distributions of Salinity and Tidal Flow83

when freshwater flow increases, the impact of tidal velocity also increases, which enhances thesalinity intrusion, and resulting in shorter time lag compared to that under the normal conditionof freshwater flow (X. Chen et al., 2000).

Figure 3.24 The association between freshwater discharge recorded at Yaguchi Gauging
Station and delays in time of salinity in the observation site
3.7

Conclusions

This chapter presents longitudinal variation in salinity, tidal flow, and thus, salinity gradient,dispersion coefficient at the Ōta diversion channel. This research was designed to explore theeffectiveness of using a novel and promising method of monitoring the continuous salinity
intrusion and velocity distribution in a tidal channel using new FAT scheme. In detail, four
FAT units were installed near the riverbanks using a new zigzag configuration in a rectangulartomographic domain of 700 m ൈ 170 m.
The longitudinal distribution of intra-tidal changes in the velocity/discharge and salinity inthe middle part of the diversion channel was monitored in this study. Velocity was measured
concurrently using the FAT system and a moving-boat Stream-Pro ADCP. The section-average
speed of sound was measured by placing four acoustic stations installed along the site study
located on the broadest branch of the Ōta River system. The cross-sectional average salinity
could be deduced from the water temperature, and the speed of sound from FAT using
Medwincs formula.

3. Longitudinal Distributions of Salinity and Tidal Flow84

The results indicate that salinity in the Ōta diversion channel does not response to the waterlevel fluctuations immediately. There are delays in time between the salinity and water levelvariations. The salinity response time lags ranged from 12 min to 1.5 h, corresponding to aphase lag range of 13q–47q. The time lag is closely related to the upstream freshwater release,with longer time lag corresponding with lower freshwater rate. Besides, the time lags increaseseaward along the channel.
The differences in the section-average velocities obtained using FAT and ADCP were notsignificant. Moreover, the cross-sectional mean salinity derived using the FAT system was
acceptably similar to the results obtained using the Compact CTD.
The studied section of the river exhibited asymmetric ebb-tide and flood-tide velocities,
with a short-duration ebb phase of the tide and fast ebb currents that created an ebb-dominantphenomenon, which because of interaction of the O1 – K1 – M2 tidal constituents, and the
topographic effects.
The section-average salinity increased seaward, revealing typical estuarine behavior. In
addition, the salinity pattern revealed a completely tide-dominated influence.
The longitudinal dispersion coefficient was found to increase toward the mouth of the river,and the tide-driven mechanism might be the dominant mechanism in the dispersion process inthe Ōta diversion channel.
Finally, this study presents the detailed results of using a novel and promising method ofcontinuous salinity and velocity distribution monitoring along a tidal channel.

4. Conclusions and Recommendations

CHAPTER 4

4.1

85

CONCLUSIONS AND RECOMMENDATIONS

Summary

The present study attempts to monitor the spatial and temporal variability in salinity andtidal flow in a shallow tidal estuary, with the Ōta Diversion channel, in Hiroshima, Japan as acase study. The research addresses the relationship between the distributions of salinity, watertemperature, and water density in lateral and vertical dimensions. Besides, the present researchalso displays the distributions of salinity and tidal flow in longitudinal dimension under thevariational estuarine forces such as freshwater release, tidal motion, and so on.
The three field observations are carried out in a river segment with the length of 850 m at
the central part of the Ōta diversion channel (about 4.5 km from the estuary), they are:(i) Two CTD campaigns in which the Conductivity-Temperature-Sensors (CTDs) are usedwith others instruments to measure the distribution of salinity, density and watertemperature over both spring and neap tidal cycles. The vertical profiles of salinity,
density and temperature are analyzed over two periods. The first observation is related
to the neap tide of September 5, 2018 and the second observation is related to the springtide of October 2, 2020.
(ii) A field observation was conducted with four FAT units installing near the riverbank
using a new zigzag configuration. The purpose of the observation is to collect the dataof tidal flow, water discharge, and salinity along the river segment. The field4. Conclusions and Recommendations

86

observation is conducted during both neap and spring tides with the time period from
December 26, 2018 to January 15, 2019.
With the results displayed in the above chapters, these objectives that are mentioned in the
introduction section have been meet. As a consequence, the conclusions and recommendations
are presented as follow:
4.2

Conclusions

4.2.1 Investigation of vertical and lateral distributions of salinity and density
By using the number and the depth of stratification layers as well as the vertical gradientsof salinity and density deduced from the transverse and vertical distributions of salinity, theprocess of stratification/de-stratification in the Ōta diversion channel is evaluated. In detail, in
the lateral and vertical dimensions, density driven is the main mechanism that controls thestratification in the Ōta diversion channel.
The new findings are that the stratification occurs during spring-ebb tides and early of neapflood tides because of the combination of tidal straining, tidal asymmetry and freshwater inflow
from upstream, while the lateral distribution of salinity appears during spring-flood tide andthe late of neap-flood tides owing to the lateral density gradient. The study results also revealthat salinity dominates the density change in the Ōta diversion channel and the effect oftemperature variation on salinity dynamics is not significant during the observation period.
The density distributions at the observation points have clear tidal cycle characteristics. The
lateral density distributions are found at the end of the flood spring tides, and the verticaldensity distributions appear in the early of the ebb spring tides. During flood tides, the verticaldensity gradient increases in the central water column in the center of the stage. The onset ofthe phenomenon that shows vertical density gradient is stronger at the middle of the watercolumn than that at the surface and the bottom parts can be controlled by the vertical straining
due to the surface-to-bottom difference of transverse velocity. In addition, the turbulent mixing
in the late of the flood tides decreases which maintains the lateral density gradient, and pushes
the surface flows to the channel center and leading to lateral salinity distribution of the watercolumn.
4.2.2 The longitudinal distributions of salinity and tidal flow
Both salinity and tidal flow patterns revealed a completely tide-dominated influence.

4. Conclusions and Recommendations

87

The tidal asymmetry (the ebb-tide velocities higher than flood-tide velocities) shows thatthe Ōta diversion channel is an ebb-dominant estuary. To consider the mechanisms that control
this phenomenon, the relationship between the tidal constituents O1, K1 and M2 is analyzed byusing the harmonic analysis for observed tidal within the observation time period. The resultsof the tidal harmonic analysis show that Iu(O1) = 191.3q, Iu(K1) = 219.67q, and Iu(M2) = 273.6q,
thus T = cos (Iu(O1) + Iu(K1) + Iu(M2)) = -0.736. This parameter suggests that the reasons forthat ebb-dominant tidal phenomenon are the interaction of the O1 – K1 – M2 tidal constituents.
This study investigates salinity and tidal flow distributions along the channel by using new
configuration of FATs. Besides, the flow directions, and thus water discharge are estimated.
The error structure for the river discharge measurement using that new configuration isanalyzed in order to consider its feasibility. Four error components of this error structure are
relative to the mean water depth; the imperfection of the bathymetry survey and the variationsof the bottom shape; the velocity deduced from FATs; and the angle between the flow direction
and the transmission line. The maximum probable value of that error structure is estimated as
17.5%. The small errors in the analyzed results suggest that the new zigzag configuration of
FATs, which needs the lower instrument number, can be a cost-effective measurement method
for monitoring estuarine physics.
The salinity in the Ōta diversion channel does not response to the water level fluctuations
immediately: there are delays in time between the salinity and water level variations. The
salinity response time lags ranged from 12 min to 1.5 h, corresponding to a phase lag range of
13q–47q. The time lags increase seaward along the channel, and decreases corresponding to theincrease of the upstream freshwater flow. The shorter time lags are corresponding to theincrease in freshwater discharge because when freshwater flow increases, the impact of tidal
velocity also increases, which enhances the salinity intrusion, and resulting in shorter time lagcompared to that under the normal condition of freshwater flow.
4.3

Novelties and new findings
9 To find out the lateral circulation driven by the lateral density gradient leading to thelateral salinity gradient during flood tides;
9 To improve the estuarine physics monitoring using the new zigzag configuration of
FATs;

4. Conclusions and Recommendations

88

9 To use a dimensionless parameter (number of stratification layers) and the stratification
layer depth to evaluate the stratification/de-stratification degree in a tidal shallow
estuary.
4.4

Recommendations
9 This study addressed vertical and lateral distributions of salinity along a river segmentwith the length of 850m in the Ōta diversion channel during both neap and spring tides.
The surface to bottom salinity differences at the two locations (upstream anddownstream areas) of the observation site is expected to be different due to several
contributions, i.e. bathymetry effects, longitudinal salinity gradient effects, horizontal
density gradient effects. However, these differences were insignificant may due to theshort distance of the observation site. Thus, a research on vertical distribution of salinity
along the Ōta diversion channel with longer distance apart is recommended in the future.
9 This study focused on the evaluation the transverse salinity dynamics through thestratification layer forming process, and the obtained data reflected good information
about the transverse salinity dynamics. However, it will be interesting to see somequantitative analysis of the turbulent development from the velocity profile
corresponding with salinity profile during a full tidal cycle. Thus, it is recommended tocarry out a study in the future to consider the salinity dynamics base on vertical andlateral distributions of salinity as well as vertical and lateral distributions of velocity.

Appendix

89

APPENDIX
The detailed equation of the relative errors of flow direction estimation:ߜߠ ߜߠ‫ߠߜ ׎‬஺భ ߜߠ஺మ ߜߠ௨భ ߜߠ௨మ
ൌ
൅
൅
൅
൅

ߠ
ߠ
ߠ
ߠ
ߠ
ߠ
where:
െͳǤͶͳඥ‫ܣ‬ଶଵ ‫ݑ‬ଵଶ ൅ ͸‫ܣ‬ଵ ‫ܣ‬ଶ ‫ݑ‬ଵ ‫ݑ‬ଶ ൅ ‫ܣ‬ଶଶ ‫ݑ‬ଶଶ ൅ ሺ‫ܣ‬ଵ ‫ݑ‬ଵ െ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻଶ ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿܵ݅݊ሾ‫׎‬ሿ െ ʹሺെ‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻܵ݅݊ሾʹ‫׎‬ሿͳǤͶͳሺ‫ܣ‬ଵ ‫ݑ‬ଵ െ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻଶ‫ݏ݋ܥ‬ሾ‫׎‬ሿܵ݅݊ሾʹ‫׎‬ሿ
െ
ଶ ଶ
ߜߠ‫׎‬
ඥ‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ͸‫ܣ‬ଵ ‫ܣ‬ଶ ‫ݑ‬ଵ ‫ݑ‬ଶ ൅ ‫ܣ‬ଶଶ ‫ݑ‬ଶଶ ൅ ሺ‫ܣ‬ଵ ‫ݑ‬ଵ െ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻଶ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿൌ ͲǤʹͷ
ǡሺ‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻߠߠ͵‫ݑ‬ଵ െ ‫ݑ‬ଵ ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿ ൅ߜߠ஺భൌ ͲǤʹͷ
ߠെ‫ݑ‬ଵ ቀ͵‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶ ൅ ሺെ‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿ ൅ ͳǤͶͳ‫ݏ݋ܥ‬ሾ‫׎‬ሿඥ‫ܣ‬ଶଵ ‫ݑ‬ଵଶ ൅ ͸‫ܣ‬ଵ ‫ܣ‬ଶ ‫ݑ‬ଵ ‫ݑ‬ଶ ൅ ‫ܣ‬ଶଶ ‫ݑ‬ଶଶ ൅ ሺ‫ܣ‬ଵ ‫ݑ‬ଵ െ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻଶ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿቁሺ‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻଶǡߠ‫ݑ‬ଶ ൅ ‫ݑ‬ଶ ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿ ൅ߜߠ஺మൌ ͲǤʹͷߠെߜߠ௨మൌ ͲǤʹͷ
ߠͲǤ͹‫ݏ݋ܥ‬ሾ‫׎‬ሿሺʹ‫ܣ‬ଶଵ ‫ݑ‬ଵ ൅ ͸‫ܣ‬ଵ ‫ܣ‬ଶ ‫ݑ‬ଶ ൅ ʹ‫ܣ‬ଵ ሺ‫ܣ‬ଵ ‫ݑ‬ଵ െ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿሻඥ‫ܣ‬ଶଵ ‫ݑ‬ଵଶ ൅ ͸‫ܣ‬ଵ ‫ܣ‬ଶ ‫ݑ‬ଵ ‫ݑ‬ଶ ൅ ‫ܣ‬ଶଶ ‫ݑ‬ଶଶ ൅ ሺ‫ܣ‬ଵ ‫ݑ‬ଵ െ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻଶ ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿ‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶ‫ܣ‬ଵ ቀ͵‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶ ൅ ሺെ‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿ ൅ ͳǤͶͳ‫ݏ݋ܥ‬ሾ‫׎‬ሿඥ‫ܣ‬ଶଵ ‫ݑ‬ଵଶ ൅ ͸‫ܣ‬ଵ ‫ܣ‬ଶ ‫ݑ‬ଵ ‫ݑ‬ଶ ൅ ‫ܣ‬ଶଶ ‫ݑ‬ଶଶ ൅ ሺ‫ܣ‬ଵ ‫ݑ‬ଵ െ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻଶ ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿቁሺ‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻଶǡߠ‫ܣ‬ଶ ൅ ‫ܣ‬ଶ ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿ ൅െͲǤ͹‫ݏ݋ܥ‬ሾ‫׎‬ሿሺ͸‫ܣ‬ଵ ‫ݑ‬ଵ ‫ݑ‬ଶ ൅ ʹ‫ܣ‬ଶ ‫ݑ‬ଶଶ െ ʹ‫ݑ‬ଶ ሺ‫ܣ‬ଵ ‫ݑ‬ଵ െ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿሻඥ‫ܣ‬ଶଵ ‫ݑ‬ଵଶ ൅ ͸‫ܣ‬ଵ ‫ܣ‬ଶ ‫ݑ‬ଵ ‫ݑ‬ଶ ൅ ‫ܣ‬ଶଶ ‫ݑ‬ଶଶ ൅ ሺ‫ܣ‬ଵ ‫ݑ‬ଵ െ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻଶ ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿ‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶ‫ݑ‬ଶ ቀ͵‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶ ൅ ሺെ‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿ ൅ ͳǤͶͳ‫ݏ݋ܥ‬ሾ‫׎‬ሿඥ‫ܣ‬ଶଵ ‫ݑ‬ଵଶ ൅ ͸‫ܣ‬ଵ ‫ܣ‬ଶ ‫ݑ‬ଵ ‫ݑ‬ଶ ൅ ‫ܣ‬ଶଶ ‫ݑ‬ଶଶ ൅ ሺ‫ܣ‬ଵ ‫ݑ‬ଵ െ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻଶ ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿቁሺ‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻଶǡߠ͵‫ܣ‬ଵ െ ‫ܣ‬ଵ ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿ ൅െߜߠ௨భൌ ͲǤʹͷ
ߠͲǤ͹‫ݏ݋ܥ‬ሾ‫׎‬ሿሺʹ‫ܣ‬ଵ ‫ݑ‬ଵଶ ൅ ͸‫ܣ‬ଶ ‫ݑ‬ଵ ‫ݑ‬ଶ ൅ ʹ‫ݑ‬ଵ ሺ‫ܣ‬ଵ ‫ݑ‬ଵ െ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻଶ ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿሻඥ‫ܣ‬ଶଵ ‫ݑ‬ଵଶ ൅ ͸‫ܣ‬ଵ ‫ܣ‬ଶ ‫ݑ‬ଵ ‫ݑ‬ଶ ൅ ‫ܣ‬ଶଶ ‫ݑ‬ଶଶ ൅ ሺ‫ܣ‬ଵ ‫ݑ‬ଵ െ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻଶ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿ‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶͲǤ͹‫ݏ݋ܥ‬ሾ‫׎‬ሿሺ͸‫ܣ‬ଵ ‫ܣ‬ଶ ‫ݑ‬ଵ ൅ ʹ‫ܣ‬ଶଶ ‫ݑ‬ଶ െ ʹ‫ܣ‬ଶ ሺ‫ܣ‬ଵ ‫ݑ‬ଵ െ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿሻඥ‫ܣ‬ଶଵ ‫ݑ‬ଵଶ ൅ ͸‫ܣ‬ଵ ‫ܣ‬ଶ ‫ݑ‬ଵ ‫ݑ‬ଶ ൅ ‫ܣ‬ଶଶ ‫ݑ‬ଶଶ ൅ ሺ‫ܣ‬ଵ ‫ݑ‬ଵ െ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻଶ ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿ‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶ‫ܣ‬ଶ ቀ͵‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶ ൅ ሺെ‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿ ൅ ͳǤͶͳ‫ݏ݋ܥ‬ሾ‫׎‬ሿඥ‫ܣ‬ଶଵ ‫ݑ‬ଵଶ ൅ ͸‫ܣ‬ଵ ‫ܣ‬ଶ ‫ݑ‬ଵ ‫ݑ‬ଶ ൅ ‫ܣ‬ଶଶ ‫ݑ‬ଶଶ ൅ ሺ‫ܣ‬ଵ ‫ݑ‬ଵ െ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻଶ‫ݏ݋ܥ‬ሾʹ‫׎‬ሿቁሺ‫ܣ‬ଵ ‫ݑ‬ଵ ൅ ‫ܣ‬ଶ ‫ݑ‬ଶ ሻଶߠReferences

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List of Figures and Tables

96

LIST OF FIGURES

Figure 2.1 The detail of the study site ....................................................................................... 8
Figure 2.2 The bathymetry distribution of the Ōta diversion channel (Gusti & Kawanisi,2020) ...................................................................................................................... 9
Figure 2.3 The detail of the study site ....................................................................................... 9
Figure 2.4 The bathymetry distribution of the observation site .............................................. 10
Figure 2.5 Compact CTD (Conductivity, Temperature, Depth) sensor (Source: JFE
advantech Co., Ltd) ............................................................................................. 11
Figure 2.6 The scheme and principle operation of the FAT system ((K. Kawanisi et al.,2010)) .................................................................................................................. 13
Figure 2.7 a) The observation site for the first campaign; b) and c) the transverse linesof Compact CTD measurement, yellow symbols indicate the locations of
the data collected points (P1–P5).......................................................................... 15
Figure 2.8 The observation site for the second campaign; yellow symbols indicate thelocations of the data collected points (P1–P6) by Compact CTD, red
triangles indicate the locations of FATS. ............................................................ 16
Figure 2.9 Seven stages of the second campaign .................................................................... 16
Figure 2.10 Temporal variations in freshwater discharge at Yaguchi Gauging Station(blue line), the water level at the observation site (black line), and thestudied periods (red line) for a) the first campaign and b) the second
campaign.............................................................................................................. 18
Figure 2.11 Salinity distributions in the cross section of the early ebb during spring tide(the first tide stage) .............................................................................................. 20
Figure 2.12 Salinity distributions in the cross section of the early ebb during spring tide(the second tide stage) ......................................................................................... 20
Figure 2.13 Salinity distributions in the cross section of the middle ebb stage during
spring tide ............................................................................................................ 21

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97

Figure 2.14 Salinity distributions in the cross section of the end ebb stage during springtide ....................................................................................................................... 22
Figure 2.15 Salinity distributions in the cross section of the end of the first flood tide
during spring tide ................................................................................................. 23
Figure 2.16 Salinity distributions in the cross section of the end of the second floodtide during spring tide .......................................................................................... 23
Figure 2.17 Salinity distributions in the cross section of the early to mid flood stage
during spring tide ................................................................................................. 24
Figure 2.18 Vertical profiles of salinity at the cross-sectional (Shinkoi bridge)
estimated by CTD, P1 (black line), P2 (red line), P3 (blue line), P4 (orangeline), P5 (green line) ............................................................................................. 25
Figure 2.19 Vertical profiles of salinity at the cross-sectional (Ashahi Bridge)
estimated by CTD, P1 (black line), P2 (red line), P3 (blue line), P4 (orangeline), P5 (green line) ............................................................................................. 26
Figure 2.20 Salinity distributions in the cross section at the upstream area (Shinkoi
Bridge) during neap tide ...................................................................................... 27
Figure 2.21 Salinity distributions in the cross section at the downstream area (Asahi
Bridge) during neap tide ...................................................................................... 28
Figure 2.22 Density distributions in the cross section at the first high water slack during
spring tide ............................................................................................................ 29
Figure 2.23 Density distributions in the cross section at the second high water slack
during spring tide ................................................................................................. 30
Figure 2.24 Lateral density gradient, averaged over a depth from 0 to 2.5m below thesurface at Shinkoi Bridge during a typical flood tide (October 02, 2020),(y) is the lateral distance from the left river bank, (B) is the cross-section
length of the channel at the observation site. ...................................................... 31
Figure 2.25 (a–e) Distributions of lateral density gradient during flood tides at Shinkoi
Bridge, “z” is the vertical distance from the water surface, “H” is the water
depth, “y” is the lateral distance from the left river bank, “B” is the cross-List of Figures and Tables

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section length of the channel at the observation site, and f) Schematic oflateral circulation. ................................................................................................ 32
Figure 2.26 Density distributions in the cross section at upstream area during neap tide............................................................................................................................. 33
Figure 2.27 Density distributions in the cross section at Asahi Bridge during neap tide ....... 34
Figure 2.28 Vertical density gradient distributions at Shinkoi Bridge during neap tide ........ 36
Figure 2.29 Vertical density gradient distributions at Asahi Bridge during neap tide............ 38
Figure 2.30 Vertical profiles of temperature at the cross section estimated by CTD of
the second campaign at Shinkoi Bridge, P1 (black line), P2 (red line), P3(blue line), P4 (orange line), P5 (green line) and P6 (gray). ................................. 41
Figure 2.31 Vertical profiles of temperature at the cross section estimated by CTD of
the first campaign at a) Shinkoi Bridge, and b) Asahi Bridge. P1 (blackline), P2 (red line), P3 (blue line), P4 (orange line), P5 (green line). .................... 42
Figure 2.32 The comparison between the cross-sectional average salinity acquired
using FATS (black lines) and water level (red lines) at the study site ................ 43
Figure 2.33 Cross-correlation of salinity versus the water level in Ōta diversion channel
during the study period ........................................................................................ 44
Figure 2.34

The association between freshwater discharge recorded at Yaguchi
Gauging Station and delays in time of salinity .................................................... 45

Figure 2.35 Schematic of tidal straining: (a) isolines vertical at start of ebb (b)stratification induced by shear on the ebb modified by top and bottom
mixing (Simpson et al., 1990).............................................................................. 46
Figure 2.36 Contour plots of salinity at cross-sectional in the Ōta diversion channel
estimated using CTD during a typical ebb tide (Soltaniasl et al., 2013)............. 47
Figure 2.37 Contour plots of longitudinal velocity at cross-sectional in the Ōtadiversion channel estimated using ADCP during a typical ebb tide
(Soltaniasl et al., 2013) ....................................................................................... 48
Figure 3.1 a) The location of the field observation at the Ōta diversion channel; b) thearrangement of the tomographic scheme of the FAT system over theList of Figures and Tables

99

diversion channel. Yellow and purple symbols indicate the locations of the
CT instruments; and c) the Compact CTD (yellow circles) and FAT (redtriangles) campaigns for validating section-average salinity using the FAT
system. ................................................................................................................. 53
Figure 3.2 Oblique cross-sections along transmission lines between S1S2, S2S3, andS3S4. Dashed lines denote the Highest Water Level (HWL) and the Lowest
Water Level (LWL), and black dots denote the locations of transducers. .......... 54
Figure 3.3 StreamPro Acoustic Doppler Current Profiler (ADCP) (Source: Teledyne
Marine) ................................................................................................................ 55
Figure 3.4 Temporal variations of water level during the study period recorded at theobserved cross-sections. ...................................................................................... 62
Figure 3.5 Time series for the tidal current velocities (black lines) and the residual
mean velocity (red lines) measured using FAT at the selected stations
during the study period. ....................................................................................... 63
Figure 3.6 The angle between the transmission lines ............................................................. 65
Figure 3.7 Temporal variations of cross-sectional area during the study period recordedat the three observed transmission lines .............................................................. 65
Figure 3.8 The variation of the flow directions along three sections deduced from
FATS ................................................................................................................... 66
Figure 3.9 Temporal variations in water discharge (black) and residual flow (red)estimated using FAT at the selected stations during the study period ................ 67
Figure 3.10 Comparison of the freshwater release from the Yaguchi Station (black) andthe residual discharge as estimated using FAT (red). .......................................... 68
Figure 3.11 The variations of cross-sectional average salinity estimated using FATS atthree transmission lines ....................................................................................... 69
Figure 3.12 a) Longitudinal distributions of salinity, and b) salinity gradient deduced
using the FAT system during spring tide and neap tide. “x” is the distancealong the river from S4 station, “Lc” is the longitudinal distance from S4 to
S1 stations ............................................................................................................ 70

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Figure 3.13 Comparison between tidal current (black lines) and water level (red lines)
at three sections during a typical spring tide. ...................................................... 71
Figure 3.14 Comparison between tidal current (black lines) and water level (red lines)
at three sections during a typical neap tide. ......................................................... 72
Figure 3.15 Comparison of the discharges acquired using the FAT (black) and ADCP
(blue) and (b) The association between the FAT and ADCP estimates. ............. 73
Figure 3.16 (a) Water level variation (red line), and the comparison between the salinity
acquired using FAT (black line) and Compact CTD (blue dots) at Shinkoi
Bridge, (b) The association between the FAT and Compact CTD estimates,and (c) Salinity distributions obtained using Compact CTD............................... 75
Figure 3.17 Longitudinal distributions of the dispersion coefficient deduced using the
FAT system during spring tide and neap tide. “x” is the distance along theriver from S4 station, “Lc” is the longitudinal distance from S4 to S1 stations............................................................................................................................. 77
Figure 3.18 Temporal variations in cross-sectional average salinity (black lines) andwater level (red lines) at the study site during a typical spring tide. ................... 78
Figure 3.19 Temporal variations in cross-sectional average salinity (black lines) andwater level (red lines) at the study site during a typical neap tide. ..................... 78
Figure 3.20 The cross-sectional average salinity at S1S2 section estimated from FATs,
with the mean sound speed is calculated from the travel time tup (blackdots), and from the mean travel time tm (red dots) .............................................. 79
Figure 3.21 The salinity error induced by the time differences between the one way
travel time and the mean travel time ................................................................... 80
Figure 3.22 Temporal variation of salinity obtained using FAT (black points) at S 1S2and S3S4 transmission lines and CT sensors (red points) at S 1 and S4
stations. ................................................................................................................ 81
Figure 3.23 A typical cross-correlation function of salinity versus the water level ............... 82
Figure 3.24 The association between freshwater discharge recorded at Yaguchi
Gauging Station and delays in time of salinity in the observation site ............... 83

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101

LIST OF TABLES

Table 2.1 Compact-CTD specifications (Source: JFE advantech Co., Ltd) ........................... 11
Table 2.2 Remote controlled boat RC-S3 specifications (Source: CODEN Co.,Ltd) ............. 13
Table 2.3 The sea water density variations based on the variations of temperature andsalinity (Millero & Poisson, 1981) ...................................................................... 40
Table 2.4 The time delays of the salinity peaks ...................................................................... 44
Table 3.1 Stream Pro specifications (Source: Teledyne Marine)............................................ 55
Table 3.2 CT sensor specifications (Source: JFE advantech Co., Ltd) .................................. 56
Table 3.3 The coordinates of the acoustic stations.................................................................. 64
Table 3.4 Delays in time of salinity peaks. ............................................................................. 81

Notations and Abbreviations
NOTATIONS AND ABBREVIATIONS
SymbolsA

Cross-section area along the ray path (L2)

B

Cross-section length of the channel (L)DxLongitudinal dispersion coefficient (-)

cSound speed (LT-1)

D

Water depth (L)E

Expected value of variance (-)

H

Water level (L)K1

The diurnal tidal constituent

L

The distance between the upstream and downstream stations (L)M2

The principal semidiurnal lunar constituent.

O1

The diurnal tidal constituent

QY1,2

Fresh water discharge (L3T-1)

Q

Water discharge (L3T-1)

R2

Determination coefficient (-)

S

Section-averaged salinity (psu)

S1,2,3,4

Name of the acoustic stations (-)

S1S2Name of the transmission line between S1, S2 stations (-)

S2S3Name of the transmission line between S2, S3 stations (-)

S3S4Name of the transmission line between S3, S4 stations (-)

T

Temperature along the ray path (C)tTime (T)tup

Travel times in the upstream section (T)Tdown

Travel times in the downstream section (T)uMean velocity along the transmission line (LT -1)

102

Notations and Abbreviations
V

Section-averaged velocity (LT-1)

X

Random variable (-)ܺത

Mean of random variable X (-)

X1,2

Coordinates of the acoustic stations

Y

Random variable (-)ܻത

Mean of random variable Y (-)

Y1,2

Coordinates of the acoustic stationsx

Longitudinal distance (L)yLateral distance (L)zVertical distance (L)W

Time lag (T)T

Angle between the ray path and streamline

I

Angle between two transmission lines

Iu(O1)The phase of O1 tidal constituent

Iu(K1)The phase of K1 tidal constituent

Iu(M2)The phase of M2 tidal constituent

103

Notations and Abbreviations
Abbreviations
ADCP

Acoustic Doppler Current Profiler

CTD

Conductivity- Temperature- Depth sensor

CT

Conductivity-Temperature sensor

FATs

Fluvial Acoustic Tomography system

HWL

Highest Water Level

LWL

Lowest Water Level

RMSE

Root Mean Square Error

T.P

The average water level in Tokyo Bay

104