remote sensing
ArticleThe Intra-Tidal Characteristics of Tidal Front and Their
Spring–Neap Tidal and Seasonal Variations in Bungo
Channel, Japan
Menghong Dongand Xinyu Guo *Center for Marine Environmental Studies (CMES), Ehime University, Matsuyama 790-8577, Japan;
f870003b@mails.cc.ehime-u.ac.jp* Correspondence: guoxinyu@sci.ehime-u.ac.jp; Tel.: +81-89-927-9824

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Abstract: The intra-tidal variations of a tidal front in Bungo Channel, Japan and their dependence on
the spring–neap tidal cycle and month were analyzed utilizing high-resolution (~2 km) hourly sea
surface temperature (SST) data obtained from a Himawari-8 geostationary satellite from April 2016
to August 2020. A gradient-based front detection method was utilized to define the position andintensity of the front. Similar to previous ship-based studies, SST data were utilized to identify tidal
fronts between a well-mixed strait and its surrounding stratified area. The hourly SST data confirmed
the theoretical intra-tidal movement of the tidal front, which is mainly controlled by tidal current
advection. Notably, the intensity of the front increases during the ebb current phase, which carries
the front toward the stratified area, but decreases during the flood current phase that drives the front
in the opposite direction. Due to a strong dependence on tidal currents, the intra-tidal variations
appear in a fortnight cycle, and the fortnightly variations of the front are dependent on the month inwhich the background stratification and residual current changes occur. Additionally, tidal current
convergence and divergence are posited to cause tidal front intensification and weakening.

Citation: Dong, M.; Guo, X. The
Intra-Tidal Characteristics of Tidal
Front and Their Spring–Neap Tidal

Keywords: sea surface temperature; tidal front; intra-tidal variations; tidal current

and Seasonal Variations in Bungo
Channel, Japan. Remote Sens. 2021, 13,1840. https://doi.org/10.3390/
rs13091840
Academic Editor: Kaoru Ichikawa
Received: 24 March 2021
Accepted: 6 May 2021
Published: 9 May 2021

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Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms andconditions of the Creative Commons
Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

1. Introduction
A front forms where two different water masses converge; there are many types offronts in the shelf sea, which are classified into three types according to where they areformed [1]. Tidal fronts form in the transition area between vertical mixed water andstratified water, caused by tidal stirring and surface heating, respectively, and primarily
occur in summer. Simpson and Hunter [2] first reported the tidal front in the Irish Sea, andmany observational and modeling studies have been performed on the fronts in the Irish,
Celtic, North, and Seto Inland Seas. Earlier studies focused on the formation and seasonalvariations of the fronts and then shifted to front instability and its relationship to biologicalprocesses [3–14]. The Simpson and Hunter [2] parameter, derived from a balance between.
the potential energy increase due to surface heating (at rate Q) and turbulent kinetic energy
dissipation induced by tidal stirring, is an effective method for understanding the location.
of a front. The parameter is Qh/u3 , where h is the water depth and u is the tidal current.
amplitude. Because Q may be regarded as spatially uniform in coastal waters, the tidal
front position depends on the value of h/u3 .
Changes in heating and stirring rates in the movement of the tidal front result in a
new position if a constant value of the above parameter is applied to the front. Simpson
and Bowers [15] determined that the seasonal variations in the position of the tidal fronts
in the Irish and Celtic Seas are minimal, although the heating rates vary significantly insummer. They proposed a feedback effect in which the stratification reduced the tidal
stirring efficiency and utilized this theory to explain the small seasonal variation in the tidal
front position. Utilizing ship-based observational data, Yanagi and Tamaru [5] reported

Remote Sens. 2021, 13, 1840. https://doi.org/10.3390/rs13091840

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Remote Sens. 2021, 13, 1840

2 of 20the seasonal variations of a tidal front in the Bungo Channel (Figure 1) that forms in early
4 of 19
April; its mean position remains unchanged from May to August, although it undergoes awide range of intensity changes.

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Figure(a) Study
location.
Enlargedmap
mapofofthe
thestudy
study area
bathymetry
from
ETOPO1of theofBungo
Figure1. (a)1.Study
areaarea
location.
(b)(b)
Enlargedareashowing
showingthe
thebathymetry
from
ETOPO1the Bungo
Channel
and
Iyo
Nada.
The
black
dot
indicates
thelocation
where
the
tidal
current
was
synthesizedbyharmonic
constants. conChannel and Iyo Nada. The black dot indicates the location where the tidal current was synthesized by harmonicmean
the thesynthesizedtidal current
for 6 hours
maximumebb currentebb(15:0029 April2017)29
to Aprilmaximumflood
stants.Arrows
Arrowsmean
synthesizedtidal current
for 6fromhours
from maximum
current(15:002017)
to maxicurrent(21:00
29
April
2017)
duringone
springtide.
“HyS”
denotes
Hayasui
Strait.
(c)
Tidal
front
locationnear
Hayasui
mum flood current (21:00 29 April 2017) during one spring tide. “HyS” denotes Hayasui Strait. (c) Tidal front location near
Strait.
Contours
indicatemonthly
averageaveragesea surface(SST, ◦ C) in
June,℃)
andincolors
the magnitudeof magHayasui
Strait.
Contours
indicatemonthly
sea temperaturesurface temperature(SST,
June,indicate
and colors
indicate the◦thehorizontal
gradient(
C/km).
(d)
Schematicofthemethodutilizedtodetermine
tidal
front
position.
Colorsindicatethenitude of the horizontal gradient (℃⁄km). (d) Schematic of the method utilized to determine tidal front position. Colors
magnitudeof the SST
are 45sectors,
with a 2◦eachangle.
Theafigure
shows
every
fiveshows
sectorsevery
with dashedindicate
the magnitudeofgradient.
the SST Theregradient.
There
areeach
45 sectors,
with2° angle.
The
figurefive sectors
lines. The
blackThe“X” blacksymbols
indicate
the indicate
position of
theposition
front wherethefront
maximummagnitudeof the SST
gradient alongwith dashedlines.
“X”
symbols
theof thewhere
the maximum
magnitudeof the SST
eachbrokenline
occurs.
gradient along each broken line occurs.

Simpson and James [11] proposed that the movement of the front during a spring–

The SST data were used to identify the position and intensity of a tidal front. In thisneap tidal cycle should correspond to variations in tidal stirring power, i.e., the front isstudy,
the nearmagnitude(𝑇 ) oftheduring
SST gradientwaswhenutilized
to definethelocatedthe stratified
area
spring tide
the tidal
current
is intensity
strong butof the
tidal
front
as
follows:
located near the mixed area during neap tide when the tidal current is weak. However, the
𝑇 =

+

,

(1)

where T is the SST, and x and y are the eastward and northward coordinators, respectively. The tidal front position was determined in a tilted rectangular area in the Bungo

Remote Sens. 2021, 13, 1840

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feedback effect proposed by Simpson and Bowers [15] limits tidal front movement during
the spring–neap tidal cycle. The stratification during neap tide reduces the mixing efficiency
during spring tide; therefore, the stratification is retained, restricting the movement of thefront to the stratified area during spring tide. For the tidal front in the Bungo Channel,
Yanagi and Tamaru [5] noted that the front moves closer to the well-mixed strait during
neap tide than during spring tide, and its intensity increases from neap tide to spring tide.
However, the reported fortnightly variations of the front may contain intra-tidal variations
because the sampling period of the observational data utilized was longer than the tidal
periods. The tidal front modeling study by Sun and Isobe [16] suggested that the intensityof the front varies over a 15-day period, during which the front is destroyed by growing
frontal waves during neap tide and restored during spring tide when strong tidal currents
reconstruct mixed regions.
In addition to variations in tidal currents, wind- and density-driven currents also
affect the tidal front. Wang et al. [14] reported no fortnightly variation in the tidal front
between the well-mixed Irish Sea and the stratified Celtic Sea and that the tidal front was
mainly controlled by wind. Wind-driven advection of well-mixed waters over warmer
stratified water causes convective instability and weakening of the surface front [14]. The
horizontal gradients in the density-driven current can act to promote the development of
the frontogenesis [17]. In addition to the influence of current, the input of fresh water also
affects the formation of the tidal front by strengthening the stratification [18]. Although
there are many studies on the seasonal and fortnightly variations of tidal fronts, intratidal variations have been minimally studied and are poorly understood. It is difficult todetermine how tidal fronts change in a tidal cycle from observational data due to its limited
temporal resolution. The positional change in the tidal front in a tidal period is theoretically
expected; however, it has not been well documented using observational data. Furthermore,
understanding how the tidal front intensity changes with the tidal phase is minimally
understood. Without a full description of the tidal front intra-tidal variations, its temporalchange over a long period cannot be thoroughly understood because the observations were
probably under-sampled if the field had significant intra-tidal variations.
For the tidal front in Bungo Channel, which is one the main channels connecting theSeto Inland Sea and the Pacific Ocean, the water in the northern part of this front was well
mixed vertically due to the strong tidal current whose amplitude is up to 2.5–3.0 m/s near
Hayasui Strait, while the water in the southern part was stratified due to weak tidal current(Figure 1). The water depth in the strait is about 300 m, while that in the middle part ofthe channel is about 100 m (Figure 1b). For the physical aspect of the tidal front, although
the seasonal variations and fortnightly variations have been examined by Yanagi andTamaru [5] using ship-based observational data, the intra-tidal variations are still unclear.
For the chemical and biological aspects around the front, Yanagi et al. [19] reported thatman-made organic chemicals such as polychlorinated biphenyls (PCBs) are concentrated
in the surface water around the front; nutrients are richer in the well-mixed region than in
the surface water of the stratified region; neuston such as marine skaters are accumulated
along the front, and the tidal front plays as a barrier for some oceanic and neritic pontellid
copepods. In addition, there was a water intrusion around the front from the mixed
water to the middle layer of the stratified water, and this intrusion was supposed to be
an important process supplying nutrients from the mixed water to the subsurface of thefrontal region and causing the intense chlorophyll a maximum [6]. The alternation between
homogeneous and vertically stratified water, usually associated with tidal fronts, impacts
on availability of light and nutrients, thus enhancing marine primary productivity [20].
Consequently, the tidal front region tends to be associated with higher trophic organisms
such as jelly fish and fishes. Given this significant role of tidal front on the coastal ecology
and circulation, it is important to quantify and understand the variations of the front fromintra-tidal scales to seasonal scales. In this study, an hourly sea surface temperature (SST)
dataset over five years was utilized to clarify the intra-tidal variations of a tidal front andre-examine its fortnightly and seasonal variations utilizing fully sampled data.

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2. Data and Method
To explore the intra-tidal variations of a tidal front, SST data with a minimum intervalof 1 h are required, while small-scale tidal fronts in coastal areas require high spatial
resolution data. From 7 July 2015, the satellite Himawari-8, a geostationary meteorologicalsatellite and launched by Japan Meteorological Agency (JMA), became operational. Thissatellite is located at 140.7◦ E and observes the Earth for an area from 80◦ E to 160◦ W
and from 60◦ N to 60◦ S. The Advanced Himawari Imager (AHI) is an optical radiometer
onboard the Himawari-8. The AHI has 16 spectral bands from visible to infrared (IR)wavelengths. The IR bands centered at 3.9, 8.6, 10.4, 11.2, and 12.4 µm are usable for sea
surface temperature (SST) retrieval.
The Earth Observation Research Center of the Japan Aerospace Exploration Agency(JAXA) released a skin SST dataset that was used in this study retrieved from 10.4, 11.2,
and 8.6 µm data of the Himawari-8 satellite in nearly real time [21]. Kurihara et al. [22]compared the SST data from the Himawari-8 satellite with data obtained from drifting
and tropical-moored buoys and determined a root-mean-square difference and bias of~0.59 and ~−0.16 K, respectively, which agrees with the mean difference between the skinand bulk temperatures reported by Donlon et al. [23]. The Himawari-8 satellite data havea spatial resolution of 2 km and a temporal interval of 1 h, which allows the tidal front
intra-tidal variations to be examined.
This study utilized SST data from April 2016 to August 2020 downloaded from the
JAXA website [21]. Due to cloud presence, SST data are not always available in the study
area (black box in Figure 1c). By utilizing a standard that the data must cover more than 90%of the target area, 1233, 998, 610, 632, and 1246 data scenes for April to August, respectively,
were selected from the entire dataset covering five years. It must be noted that we did notconsider the difference between daytime and night-time of SST in this study. On one hand,
if we select only the night-time data for analysis, the data scenes for each month will be toofew. On the other hand, as given in Equation (1), we use the gradient of SST to identify the
position and intensity of the tidal front. Because of its large spatial scale, the difference ofdaytime and night-time is expected to have little influence on the gradient of SST aroundthe front.
The SST data were used to identify the position and intensity of a tidal front. In thisstudy, the magnitude (TG ) of the SST gradient was utilized to define the intensity of thetidal front as follows:
s 
 2
∂T 2
∂T
TG =
+
,
(1)
∂x
∂y
where T is the SST, and x and y are the eastward and northward coordinators, respectively.
The tidal front position was determined in a tilted rectangular area in the Bungo Channel,
with an area of approximately 65 × 45 km (black box in Figure 1c), and in this area, thetidal current was the strongest inside the Hayasui Strait. As the strait is exited to the south,
the tidal current gradually weakens, consequently forming stratification; therefore, theHayasui Strait was considered as the reference point, and an arc area with an angle of90◦ was defined from the center at the strait (Figure 1d). This arc area was divided into
45 portions at 2◦ intervals (Figure 1d), obtaining 46 rays from the center to the edge of thearc; therefore, during tidal front formation, 46 points with a maximum TG along each ray(TG f , °C/km) denote the position of the tidal front.
In this study, the distance, D f (unit, km), between the point with maximum TG alongeach ray and the center of the arc area was used to identify the position of the tidal front
and then quantify the movement of the front, and TG f was used to quantify the intensity ofthe tidal front. A snapshot of the SST consisting of 46 pairs of D f and TG f values can beobtained if the spatial coverage of the data is sufficient. However, no data are available atsome rays due to cloud interference. Therefore, the spatially averaged values of D f and
TG f , denoted as (D f ) and (TG f ), respectively, were calculated from the available data andRemote Sens. 2021, 13, 1840

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utilized to study the dependence of the variations of the front on spring–neap tidal cycles
and month.
To examine the intra-tidal change in the front, it is necessary to know how to identify
the SST data phase in a tidal cycle. In this study, the tidal current, synthesized from theharmonic constants of four major tidal constituents (M2 , S2 , K1 , and O1 ) at the centerof Hayasui Strait (the black dot in Figure 1b) using T_TIDE program [24], was used to
examine the relationship between the tidal current and the movement of the front. The
harmonic constants are referred to in the publication, No. 742 Tidal Harmonic Constants
Tables around Japanese Coast [25].
In order to evaluate the advection of the tidal current, we calculated the distance of avirtual particle that moves with the predicted tidal current velocity. Here, the distance ofthe virtual particle from the strait is called particle coordinator.
k = t −1

L x ( t ) = L x (0) −∑ [u(k)δt],

(2)

k =0

where L x is the particle coordinator (its maximum is tidal excursion) and its positive
direction is southeastward; L x (0) is the distance from the center of the strait when the tidal
current begins to flow southward; u is the tidal current predicted at time t, and its positive
direction is northwestward (Figure 1b); k is the time index; δt is the time interval (δt = 10 min
in this study). During southward ebb current phase, the particle coordinator increases.
3. Results
3.1. Tidal Front Seasonal Variation
Since the formation of tidal front needs buoyancy input that occurs only in warming
season, the monthly mean SST (contours) and the magnitude of the SST gradients (colors)from April to September in the Bungo Channel (Figure 2) were used to study the seasonalvariation of the front. The maximum temperature difference between the mixed andstratified areas was 2.5 ◦ C over a distance of ~10 km in April, indicating the presence ofa tidal front. The monthly averaged position of the tidal front changed little from April
to August and disappeared in September. The intensity of the monthly averaged tidal
front from April to July was approximately 0.25 °C/km and significantly decreased inAugust. The seasonal variation of the tidal front is generally consistent with the reportfrom ship-based observational data [5]. Yanagi and Tamaru [5] reported that the tidal front
in Bungo Channel is formed in early spring and disappears in late September. From May
to August, there is little variation in its average position but a wide range of variation in its
intensity (Figure 8 in Yanagi and Tamaru, [5]).

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Figure2. Monthly(contours)
andthemagnitude
magnitude of(colors)
fromfrom
April April
to Septemberin the in the
Figure 2.
Monthly
meanmean
SST SST(contours)
and
the
ofthe
theSST
SSTgradients
gradients(colors)
to September
Bungo
Channel.
Bungo Channel.

DiurnalVariationofofaaTidal
Tidal Front
SpringTide Tide
and Neap
3.2. 3.2.
DiurnalVariation
Frontduring
DuringSpringand Tide
Neap Tide
To determine the intra-tidal variations in the position and intensity of the tidal front,

To determine the intra-tidal variations in the position and intensity of the tidal front
the tidal front changes in a diurnal cycle must first be determined. Therefore, 24 h of
the tidal
front SST
changes
in a diurnal
cycle
must3)first
determined.
24 h of concontinuous
data during
spring tide
(Figureandbe
neaptide (Figure Therefore,4) were selected.
tinuousdatawereduringspringtidebut(Figure3) andneap
tide (Figure4) wereselected. Both
Both SST
datasetsselectedin Aprilin different
years
becausecontinuous
data during
both tides
not available
the sameyear. years because continuous data during bothdatasets
werewereselectedin Aprilinbut
in different
Duringspring tidein(Figure3), theyear.
tidal front was closest to the strait at 10:00, and its
tides were
not available
the same
intensity was minimal. Then, the tidal front moved southward with the intensity increased
until 16:00, when it was farthest from the strait, and the intensity reached maximum. From
16:00, the tidal front moved northward as the intensity decreased until 22:00, when its
position and intensity were the same as those at 10:00. The maximum movement of thetidal front during the northward flood current or southward ebb current was 15 km within
6 h (star symbol in Figure 3), and the intensity changed by 0.2 °C/km (pink plus symbol in
Figure 5). In order to more quantitatively demonstrate the intra-tidal characteristics of thetidal front, we present Figure A1 in the Appendix A section to show the spatial-temporalvariations in the position (distance from the center point of the strait to the thick gray line
in Figure 3) and intensity (magnitude of the SST gradient on the thick gray line in Figure 3)of the front.

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7 of 19

3. SST gradientmagnitudesof thecontinuoushourly
hourly SST
SST data
07:00
29 April
April to30 April2017(UTC+9)Figure 3.Figure
SST gradientmagnitudesof thecontinuous
datafrom
from
07:00
2906:00
to 06:00
April
30,
2017 (UTC+9)
duringspring
tide.
The
thick
black
lines
indicatetheposition
of
the
tidal
front,
and
the
star,
triangle,andcircledenotethree denote
during spring tide. The thick black lines indicate the position of the tidal front, and the star, triangle, and circle
representative
points.
three representative points.

Figure 3. SST gradient magnitudes of the continuous hourly SST data from 07:00 April 29 to 06:00 April 30, 2017 (UTC+9)
Remote Sens. 2021, 13, 1840
8 of 20during spring tide. The thick black lines indicate the position of the tidal front, and the star, triangle, and circle denote
three representative points.

Figure 4. SST gradient magnitudes of the continuous hourly SST data from 20:00 29 April to 19:00 30 April 2016, during neap
tide. The thick black lines indicate the position of the tidal front, and the star, triangle, and circle denote three representative
points.

During neap tide (Figure 4), the intra-tidal variations of the tidal front were less thanthose during spring tide. The maximum movement of the tidal front (star symbol in Figure 4)
was 8 km over 6 h, and the intensity change was less than 0.1 °C/km (the blue plus symbol in
Figure 5). The spatial-temporal variations in the position (distance from the center point of
the strait to the thick gray line in Figure 4) and intensity (magnitude of the SST gradient on
the thick gray line in Figure 4) of the front are given in Figure A2 in the Appendix A section.
Based on these two datasets, the intra-tidal variations of the tidal front were likely controlled
by semidiurnal tides, and the intra-tidal variations in position and intensity during springtide were twice those during neap tide. Most of the data from April to August over the 5-year
period confirm the dominant role of semidiurnal tides and the difference between spring tideand neap tide in tidal front intra-tidal variations (only April is shown in Figure 6).

Remote Sens. 2021, 13, 1840

symbol in Figure 5). In order to more quantitatively demonstrate the in
istics of the tidal front, we present Figure A1 in the Appendix section
temporal variations in the position (distance from the center point of t
gray line in Figure 3) and intensity (magnitude of the SST gradienton
9 of 20
in Figure 3) of the front.

Figure 5. Lag correlations between the particle coordinator calculated by the predicted tidal current
Figureusing
5. Lagcorrelations
betweentheparticle coordinator calculated by thevelocity
Equation(2) and (a) front
position (Df , distance between the point denoted by a star, distancethrentvelocity
andpositioninFigures
3 and 4 using
and the Equation
center of the (2)strait),and(a)(b) front
front intensity(TG f ,(𝐷magnitudeof thebetween
SST
gradient
the point3denoteda starin Figures4). Pink
and bluestar in atFiguresand 4byandthecenter3 andof thestrait),andplus(b)symbols
front represent
intensity (𝑇the spring tide (Figure 3) and neap tide (Figure 4) values, respectively. Pink (blue) r2 means the
SST gradient at the point denoted by a star in Figures 3 and 4). Pink and blue
correlation coefficient at spring (neap) tide when the particle coordinator lags behind the tidal front
sent thespringtide(Figurepositionby one(one and
half)
hour. 3) and neap tide (Figure 4) values, respectively. P

the correlation coefficient at spring (neap) tide when the particle coordinator
front position by one (one and half) hour.

Remote Sens. 2021, 13, 1840

Appendix section. Based on these two datasets, the intra-tidal variations of the tidal front
were likely controlled by semidiurnal tides, and the intra-tidal variations in position andintensity during spring tide were twice those during neap tide. Most of the data from
April to August over the 5-year period confirm the dominant role of semidiurnal tides
10 of 20and the difference between spring tide and neap tide in tidal front intra-tidal
variations(only April is shown in Figure 6).

Figure 6. Time series of the front position (D f , distance between the point denoted by a star and the center of the strait
Figure 6.
Time series of the front position (𝐷 , distance between the point denoted by a star and the center of the strait(thick blue line) in Figures 3 and 4), the particle coordinator calculated by the predicted tidal current velocity using Equation(thick blue line) in Figures 3 and 4), the particle coordinator calculated by the predicted tidal current velocity using Equa(2) (black line), and the magnitude of the SST gradient along the line passing through the star in Figures 3 and 4 and thetion (2) (black line), and the magnitude of the SST gradient along the line passing through the star in Figures 3 and 4 andcenter of the strait (color) in April from 2016 (a) to 2020 (e).
the center of the strait (color) in April from 2016 (a) to 2020 (e).

3.3. Tidal Front Intra-Tidal Movement and Tidal Current Advection

3.3. Tidal Front Intra-Tidal Movement and Tidal Current Advection

The intra-tidal movement of the tidal front is highly dependent on the tidal current.
The
intra-tidal
movement
the tidal
fronthighlyonposition
the tidalAs
shownin Figure
7a, the tidalofcurrent
insidethe isstraitleadsdependent
the tidal front
bycurrent
approximately
2–3 7a,h. Duringthe current
flood current,
thethetidal
currents
and
tidal
front
(red positionandAs shown
in Figurethe tidal
insidestrait
leads
the
tidal
front
by
black lines in2–3
Figure7, respectively)
move
northward.
thecurrents
tidal currents
approximately
h. During
the flood
current,
the Astidal
and begintidal flowing
front (red andsouthward (i.e., at the beginning of the ebb current), the front is closest to the strait. During
blacklines in Figure 7, respectively) move northward. As the tidal currents begin flowing
the ebb current, the direction of the tidal current and the movement of the tidal front were
southward(i.e., at the beginning of the ebb current), the front is closest to the strait. During
southward. At the beginning of the flood current, the front is farthest from the strait.

the ebb current, the direction of the tidal current and the movement of the tidal front were
southward. At the beginning of the flood current, the front is farthest from the strait.
In general, the correspondence between the direction of the tidal current and the
movement of the tidal front during neap tide is consistent with that during spring tide
During the neap tide period, the tidal current inside the strait leads the tidal front positionby less than 2–3 h (Figure 7b).

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10 o

Figure 7. Predictedtidal current
at the Hayasuiline),
particlecoordinatorcalculated
calculated by
Figure 7. Predictedtidal current
at the Hayasui
StraitStrait(red (redline),
particlecoordinator
bythe
thetidaltidalcurrent
current velocity
velocity
predicted
byEquation(2)(blueline),
and
the
front
position(D,
distancesfromthecenterpointofthestraitfpredicted by Equation (2) (blue line), and the front position (𝐷 , distances from the center point of the straittoto the tidal
the tidal front of the star, triangle, and circle symbols in Figures 3 and 4) during the (a) spring tide and (b) neap tide
front of thestar, triangle, and circle symbols in Figures 3 and 4) during the (a) spring tide and (b) neap tide periods ofperiods of Figures 3 and 4, respectively. Positive tidal current values indicate northward flow. The black lines with the
Figures 3 and 4, respectively. Positive tidal current values indicate northward flow. The black lines with the circle, triangle,
circle, triangle, and star symbols represent the distance of the front from the center of the strait, D , of the black circle,
and star symbols represent the distance of the front from the center of the strait, 𝐷 , of thef black circle, triangle, star
triangle, star symbols in Figures 3 and 4. The time series length is 48 h, and the shaded periods in (a) and (b) correspondsymbols in
Figures 3 and 4. The time series length is 48 h, and the shaded periods in (a) and (b) correspond to the data
to the data shown in Figures 3 and 4. The pink and cyan dotted lines indicate time of sunrise and sunset, respectively.
shown in Figures 3 and 4. The pink and cyan dotted lines indicate time of sunrise and sunset, respectively.

In general, the correspondence between the direction of the tidal current and the
movementof theduringneap tide
is consistentwiththatcurrents,
during springtide.
To confirm
thetidaltidalfront
front
advection
causedby thetidal
we calculated
During the neap tide period, the tidal current inside the strait leads the tidal front position
particlecoordinator using Equation (2). As shown in Figure 7, the tidal front position gby less than 2–3 h (Figure 7b).
erally follows
the thepositionof advection
the particles;
tidalweexcursion
To confirm
tidal front
causedhowever,by the tidalthecurrents,
calculatedwas
the appro
matelytwicecoordinatorthe movement
range of(2).
theAs
tidal
front.
This difference
causedby the spa
particleusing Equation
shown
in Figure7, the tidalisfront
position
generallyfollows
thepositionoftheparticles;
however,thetidal
excursion
wasapproxivariation in the tidal currents that is strongest inside the strait but weakens with dista
twice the movement range of the tidal front. This difference is caused by the spatial
frommately
the strait.
The tidal current becomes significantly weaker during neap tide, prod
variation in the tidal currents that is strongest inside the strait but weakens with distanceing afromsmallertidal
excursion;
therefore,
the intra-tidal
movement
theproducing
tidal front dur
the strait. The
tidal current
becomes significantly
weakerduring neapof
tide,neapatide(Figure7b) is lessthan thatduring spring
tideof(Figure
smaller
tidal excursion;
therefore,
the intra-tidal
movement
the tidal 7a).
front during neaptide
is less thanspring tide
(Figure7a). a different movement dista
The(Figure
spatial7b)variation
inthattheduringtidal current
also
inducedfor each point along at 46 rays. The tidal front has a form of curve (Figure 3). The moment range changes spatially and is large at the center and becomes smaller as it
proaches either side of the channel. Due to variation in the topography, the tidal curr
is strong in the central portion of the channel but weak along the coast (Figure 5a in G
et al. [26]). The spatial change in the movement range of the front (Figure A1a) is consist

Remote Sens. 2021, 13, 1840

12 of 20

The spatial variation in the tidal current also induced a different movement distancefor each point along at 46 rays. The tidal front has a form of curve (Figure 3). The movement
range changes spatially and is large at the center and becomes smaller as it approaches
either side of the channel. Due to variation in the topography, the tidal current is strong in
the central portion of the channel but weak along the coast (Figure 5a in Guo et al. [26]).
The spatial change in the movement range of the front (Figure A1a) is consistent withspatial variations in the tidal currents. During neap tide, the tidal current in the central
portion of the channel weakens, and the spatial variation in the tidal current decreases. A
similar movement range of the front was observed at these representative points, which
can be explained by the slight differences between the three black lines in Figure 7b.
During spring/neap tide, the lag-correlation coefficients between the tidal front
movement (black line with star symbols in Figure 7) and the particle coordinator (blueline in Figure 7) are 0.92/0.89 for night-time (19:00–06:00) data and 0.98/0.70 for daytime(07:00–18:00) data. In general, there is a good correspondence between the intra-tidal
movement of the tidal front and the tidal current advection both in night-time anddaytime. However, the tidal front does not move at a specific time. For example, as
shown in Figure 7a, in the first 48 h of spring tide, the front is closest to the strait(approximately 10 km), and between 22:00 and 23:00 on the 28th, the front remained
relatively stationary. The lag-correlation coefficients between the tidal front movement
and particle coordinator in Figure 7 are 0.96 and 0.81 during spring tide and neap tide,
respectively (Figure 5a). Therefore, as the tidal currents weaken, such as during neap
tide and near the end of flood and ebb tides during spring tide, other effects such as
local winds and background residual currents may influence tidal front movement.
3.4. Composite Analysis
The above results about the intra-tidal variations in the position and intensity of thetidal front were from two continuous time series of SST data. However, the SST data are
not always continuous due to the influence of cloud, and discontinuities are inevitable.
Therefore, it is difficult to directly use this SST data to study the fortnightly variationsof the tidal front and whether these variations change with months, which are possibly
because the background residual current changes with months [27] and with spring tideand neap tide [28].
In this study, a composite SST dataset that consisted of data at the same tidal phase
was utilized to overcome the data discontinuity issue. As discussed in Section 3.2, the tidal
front generally moves in a semidiurnal tidal cycle. Therefore, the five tidal phases of the
beginning of the southward ebb current, maximum ebb current, the end of the ebb current(i.e., the beginning of the northward flood current), maximum northward flood current,
and the end of the flood current were selected according to the M2 tide. These phases were
utilized as indexes (numbers 1–5 in Figure 8) for the composite SST dataset preparation.
First, it was necessary to confirm whether the tidal front intra-tidal variations in the SST
composite dataset were consistent with the continuous time series SST dataset described in
Section 3.2. Figure 8 shows the average SST (for the April months of 2016–2020) for thefive phases during spring tide. During the ebb current phase (Indexes 1–3 in Figure 8), thetidal front moved southward, and its intensity increased. At the end of the ebb current
phase (Index 3), the front was located farthest from the strait and exhibited maximum
intensity. During the flood current phase (Indexes 3–5), the tidal front moved northward,
and its intensity decreased. At the end of the flood current phase (Index 5), the front
returned to its original position, and its intensity was the weakest. Compared to springtide, the intra-tidal movement of the front during neap tide was smaller, and the intensity
and intra-tidal change in the front were weaker (Figure 9). These results suggest that the
intra-tidal variations of the tidal front of the composite dataset are consistent with those of
the continuous dataset (Figures 3 and 4). Owing to the averaging performed to prepare
the composite dataset, the composite dataset showed smaller intra-tidal variations in theposition and intensity of the tidal front (Figures 3 and 4).

mote Sens. 2021, 13, x FOR PEER REVIEW
Remote Sens. 2021, 13, 1840

13 of 20

12 o

Figure8. (a) Particle
coordinatorcalculated
tidalcurrent
current velocity
at atHayasui
StraitStrait
using using
Equation(2) for 14(2)days.
Figure 8. (a)Particlecoordinatorcalculated
by bythethetidal
velocity
HayasuiEquationfor 14 days.
Five
phasesdenotedasIndexes
1–5
weredetermined
based
on
the
M
tide
as
follows:
thebeginningofthesouthward
ebb
2
ebb
Five phases denoted as Indexes 1–5 were determined based on the M2 tide as follows: the beginning of the southwardcurrent, maximum ebb current, end of the ebb current (i.e., beginning of the northward flood current), maximum flood
current, maximum ebb current, end of the ebb current (i.e., beginning of the northward flood current), maximum flood
current, and end of the flood current. (b–f) Monthly (for the April months of 2016–2020) average SST (contours) and thecurrent, and end of the flood current. (b)–(f) Monthly (for the April months of 2016–2020) average SST (contours) and themagnitude of the SST gradients (colors) during spring tide corresponding to Indexes 1–5. The thick black lines denote themagnitude of the SST gradients (colors) during spring tide corresponding to Indexes 1–5. The thick black lines denote theposition of the tidal front.
position of the tidal front.

The composite dataset method was utilized to examine the intra-tidal variations of
the tidal front during spring tide and neap tide in different months. Therefore, the dataprocessing procedure utilized to produce Figures 8 and 9 was performed to obtain themonthly averaged positions and intensities of the tidal front for the five tidal phases during
spring tide and neap tide for each month from April to August utilizing data from 2016
to 2020, and then the average positions (D f ) and intensities (TG f ) were obtained from46 points along the tidal front (Figure 10). Generally, the positional intra-tidal variations
identified in Figures 3–9 were the same in all months except August, when the intra-tidal
movement of the tidal front was minimal. The increased intensity at the end of the ebb
current phase during spring tide was observed in all months.

Figure 9. Same as Figure 8 but for the monthly averages during neap tide in April.

Figure 8. (a) Particle coordinator calculated by the tidal current velocity at Hayasui Strait using Equation (2) for 14 days.
Five phases denoted as Indexes 1–5 were determined based on the M2 tide as follows: the beginning of the southward ebb
current, maximum ebb current, end of the ebb current (i.e., beginning of the northward flood current), maximum flood
current, and end of the flood current. (b)–(f) Monthly (for the April months of 2016–2020) average SST (contours) and theRemote Sens.
2021,
13, 1840
of 20
magnitudeof theSST
gradients (colors) during spring tide corresponding to Indexes 1–5. The thick black lines14denotetheposition of the tidal front.

9. Sameas Figure
8 butforthethemonthly
monthly averages
duringneapneap
tide intide
April.
Figure Figure
9. Sameas Figure
8 butforaverages
duringin April.

The intra-tidal movement of the tidal front from the temporally averaged composite dataset

The
compositedatasetmethodto examine
the intra-tidal
variations(Figures8 and 9) were
smallerthan thatwas
fromutilized
the continuous
dataset (Figures
3 and 4). The
intra-tidalof the tidal
front
was
largerduringspring tide months.
than during
neap tide the d
the tidal
frontmovement
during spring
tide
and
neap
tide
in different
Therefore,(Figure7).
However,
after
performing
spatialaveragingonthetemporally
averageddataset,processing procedure utilized to produce Figures 8 and 9 was performed
to obtain
there was no obvious difference for the intra-tidal movement between spring tide and neaptide, especially in April, July, and August (Figure 10). It might be related to the shape of thetidal front that was different at different phases (see the thick black lines in Figures 8 and 9).
With the change in position of tidal front at 46 rays, the spatial averaging process likely reduces
the difference of the intra-tidal movement between spring tide and neap tide. In other words,
the intra-tidal movement of the tidal front has not only fortnight variation but also a strong
spatial variation.
The mean position of the tidal front over a tidal period reverses in the studied months
during spring tide and neap tide. In April and May, the tidal front was farther from thewell-mixed strait during spring tide than during neap tide (pink and blue lines, respectively,
in Figure 10), and this difference was minimal in June. In July, the position of the tidal
front reverses, becoming closer to the well-mixed strait during spring tide than in neap
tide. During spring tide, the tidal front gradually moves closer to the strait from a distance>20 km in April and May to a distance <20 km after June; however, during the neap tide,
the tidal front moves further from the strait from a distance of <20 km in April, May, andJune to a distance >20 km in July and August. Furthermore, the front has a larger intensity
in April (~0.1 ◦ C/km) during the spring tide than during the neap tide; however, thisdifference is minimal (<0.1 ◦ C/km) in the other months.

Remote Sens. 2021, 13, 1840

related to the shape of the tidal front that was different at different phases (see the thblack lines in Figures 8 and 9). With the change in position of tidal front at 46 rays, tspatial averaging process likely reduces the difference of the intra-tidal movement b
15 of of20 the tid
tween spring tide and neap tide. In other words, the intra-tidal movement
front has not only fortnight variation but also a strong spatial variation.

Figure 10. Five points on the pink and blue lines (spring tide and neap tide, respectively) represent the spatially averaged

Figure 10. Five points on the pink and blue lines (spring tide and neap tide, respectively) represent the spatially averaged
position (D f , , top left panel) and intensity (TG f , top right panel) of the temporally averaged tidal front shown as a thickpanel)8b–f
and
intensity(𝑇 , topof thetemporally
averagedtidal position
front shown
position (𝐷black, , toplineleftin Figuresand
9b–f, respectively.
Theright
bar ispanel)
the standard
deviationof the spatiallyaveraged
and the as a thickblack line spatiallyin Figures8(b–f)
and9(b–f),
respectively.
The
bar
is
the
standard
deviationofthespatially
averaged
averaged intensity (left and right, respectively). The other panels correspond to the monthly results of May to position
and the spatiallyaveraged(left and right, respectively). The other panels correspond to the monthly results ofAugust after
the sameintensity
data processing.
May to August after the same data processing.
4. Discussion and Conclusions
In this study, five years of hourly SST data were utilized to examine the intra-tidal
variations of the tidal front located near a strait in the Bungo Channel. An arc-like front
separates the mixed water on the north side near the strait and the stratified water on
the south side in the channel. A gradient-based method was employed to identify the
position and intensity and quantify the intra-tidal variations of the front. The intra-tidal
movement of the tidal front is mainly controlled by tidal current advection, and during
a semidiurnal tidal cycle, the movement of the front corresponds with the ebb and flood
currents. At the beginning of the ebb current, the front is located closest to the strait, and its
intensity is relatively weak (“H” in Figure 11a). With ebb current development, the mixed
water spreads to the stratified water area, causing the front to move southward. DuringRemote Sens. 2021, 13, 1840

Sens. 2021, 13, x FOR PEER REVIEW

16 of 20

15 of 19this process, the water temperature contours become narrow, indicating an increased
front intensity.

Figure 11. (a) Schematic of the intra-tidal variation in position and intensity of the tidal front. The

igure 11. (a) Schematic of the intra-tidal
variation
inlines
positionandthe for
tidal
The
and
red(H)
lines
yellowand reddenotetheintensity
isothermaloflines
thefront.
front attheyellow
end of theflood
and ebb (L)enote the isothermal lines for the front current
at the endof thefloodhave(H) smalland ebb
current
phases,which havesmall andphases,which
and(L)
large
gradients,
respectively.
Schematics
of large
the fortnightly
radients, respectively. Schematics of thefortnightly
theandfrontin (b)April
July.
Bluetheandpink lines
variationsof thevariations
front in (b) of
April(c) July.
Blue
andandpink(c)lines
indicate
isothermallines duringndicate the isothermal lines during neap
tidetide(N)(N)
andspringtide
arrowsshow
showthethedirectionof theneap
andspringtide(S),(S),andandthethe horizontal
horizontal arrows
directionof thebackgroundackground residual currents.
residual currents.

The intensity changes during ebb and flood currents are consistent with the resultsof a previous study on the effect of the horizontal motion of water with a horizontal buoyancy gradient on frontogenesis, which requires the convergence of the velocity component
in the direction of the density gradient [29]. To explain this process, the temporal change
in the temperature gradient across the front is expressed as follows:Remote Sens. 2021, 13, 1840

17 of 20

The intensity changes during ebb and flood currents are consistent with the results ofa previous study on the effect of the horizontal motion of water with a horizontal buoyancy
gradient on frontogenesis, which requires the convergence of the velocity component in
the direction of the density gradient [29]. To explain this process, the temporal change inthe temperature gradient across the front is expressed as follows:


 2

∂2 T
∂T
∂ T
∂u ∂T
∂
u
=− u 2 +
,
=−
∂t∂x
∂x
∂x
∂x ∂x
∂x

(3)
2

where x is the distance from the strait to the channel, u is the southward tidal current, −u ∂∂xT2∂T
is the advection of an existing gradient, and − ∂u∂x ∂x is the intensification or weakeningof the local gradient due to the convergence or divergence of the current in the direction
across the front [30]. Because this study defined the front with a maximum temperature2
gradient, ∂∂xT2 is approximately zero. Additionally, the tidal current gradually weakens
with increasing distance from the center of the strait; therefore, during the southward ebb
current phase, ∂u
Due to the southward increase∂x < 0, indicating that convergence occurs.
 
∂T
∂ ∂T
in water temperature, ∂x > 0, and consequently, ∂t ∂x > 0, indicating the intensity of
the front increases during the ebb current phase. Consequently, the greatest intensity (“L”
in Figure 11a) occurred at the end of the ebb current phase. During the northward flood
current phase, the temperature gradient does not change its sign; however, ∂u∂x becomes ∂ ∂T
positive, indicating that divergence occurs; consequently, ∂t ∂x < 0, and the intensity of
the front decreases.
This explanation of the intra-tidal intensity changes in the tidal front is also applicableto the spring–neap tidal cycle. For example, during spring tide and neap tide in April, theintensity of the front increases by 0.2 and 0.1 ◦ C/km, respectively, at the end of the ebb
current phase. The larger intra-tidal variation of the intensity of the front during springtide compared to that during neap tide is likely attributed to the larger spatial variationsof the tidal current (i.e., a larger convergence and divergence) during spring tide than inneap tide.
The monthly variation in the fortnightly variation of the tidal front depends on the
background residual current. Utilizing a numerical model, Chang et al. [27] demonstrated
that the residual current in the Seto Inland Sea has a two-layer structure in summer. In
this study, although the residual current was weak in April, it exhibited northward andsouthward flow in the surface and bottom layers, respectively (Figure 11b). Due to the weakresidual current, the change in the tidal front position during the spring–neap tidal cycle ismainly controlled by the stirring power produced by the tidal currents. Consequently, themixed water area is larger, and the front is farther from the strait during spring tide thanduring neap tide (“S” and “N”, respectively, in Figure 11b).
From May through August, due to increased stratification and river water input, theresidual current gradually changed to southward in the surface layer and northward in thebottom layer [27]. During this period, particularly after a heavy rain period around theend of June, the two-layer current (Figure 11c) and stratification intensified. The enhanced
stratification in July limits tidal front spread during spring tide, consequently reducing the
movement range of the front between spring tide and neap tide. The background residual
current also has a fortnightly variation that is stronger during neap tide than during springtide [28]; therefore, the tidal front moves farther south during neap tide than during springtide (“N” and “S”, respectively, in Figure 11c) in July.
This study presents a detailed description of the intra-tidal variations of a tidal front
whose position is highly dependent on tidal and background residual currents and, therefore, has strong fortnightly and monthly variations. Additionally, the convergence anddivergence of tidal currents are posited to cause tidal front intensification and weakening,respectively. Additional studies are anticipated on this subject because these phenomena
probably occur globally in most tidal fronts. Because the satellite data utilized in this studyRemote Sens. 2021, 13, 1840

18 of 20

were limited to SST data, future studies utilizing field survey data are needed to clarify
the change in the vertical structure of the tidal front within a tidal cycle and a spring–neaptidal cycle.
Author Contributions: Visualization, writing—original draft preparation, M.D.; conceptualization,
17 of 19
writing—review and editing, funding acquisition, X.G. All authors have read and agreed to the
published version of the manuscript.

Remote Sens. 2021, 13, x FOR PEER REVIEW

Funding: This study was supported by a Grant-in-Aid for Scientific Research (MEXT KAKENHI
Funding:
This study20H01972).
was supported by a Grant-in-Aid for Scientific Research (MEXT KAKENHI
grants: 17H01860,
grants: 17H01860, 20H01972).
Data Availability Statement: The Sea Surface Temperature (SST) data from April 2016 to August
Data
Statement:
The Sea
Surface Temperature(SST) datafrom(https://www.eorc.jaxa.
April 2016 to August
2020Availability
were obtained
from the Japan
Aerospace
Exploration Agency
website2020 were obtained from the Japan Aerospace Exploration Agency website
jp/ptree/index.html, accessed on 24 April 2021).
(https://www.eorc.jaxa.jp/ptree/index.html).
Acknowledgments: The authors thank four reviewers for their helpful comments and Japan Aerospace
Acknowledgments: The authors thank four reviewers for their helpful comments and Japan AeroExploration Agency for providing the SST data. M. Dong thanks the China Scholarship Council
space Exploration Agency for providing the SST data. M. Dong thanks the China Scholarship(CSC) for supporting his stay in Japan.
Council (CSC) for supporting his stay in Japan.
Conflicts of Interest: The authors declare no conflict of interest.
Conflicts of Interest: The authors declare no conflict of interest.

Appendix A. Appendix
Appendix

FigureA1.
A1.Spatial-temporal
Spatial-temporalvariations
variationsofof
the
front
positionfromcenterpoint
Figure(a)(a)
thefront
position(𝐷(D, distancefromthethecenterpoint
f , distanceofofthethestrait
straittotothe
thethickthickgraygrayline
lineininFigure
Figure3)3)andand(b)(b)thethefront
frontintensity
intensity(𝑇(TG, fmagnitude, magnitudeofofthe
theSST
SST
gradient
gradienton
onthe
thethickthickgraygrayline
lineininFigure
Figure3).
3).TheTheordinate
ordinateisisangle
angleforfor4646rays
raysstarting
startingfrom
fromthethestrait
strait(Figure(Figure1d).
1d).

Remote Sens. 2021, 13, 1840
Remote Sens. 2021, 13, x FOR PEER REVIEW

19 of 20
18 of 19

FigureA2.
A2.Spatial-temporal
Spatial-temporalvariations
variationsofof
the
front
positionfromcenterpoint
Figure(a)(a)
thefront
position(𝐷(D, distancefromthethecenterpoint
f , distanceofofthethestrait
straittotothe
thethickthickgraygrayline
lineininFigure
Figure4)4)andand(b)(b)thethefront
frontintensity
intensity(𝑇(TG, fmagnitude, magnitudeofofthe
theSST
SST
gradient
on
the
thick
gray
line
in
Figure4).
Theordinate
is
angle
for
46
rays
startingfromthestraitgradient on the thick gray line in Figure 4). The ordinate is angle for 46 rays starting from the strait(Figure(Figure1d).
1d).

References
References
Yanagi,T.T.Classification
Classificationof
of“siome”,“siome”,streaks
streaks andand fronts.
fronts. J.J.Oceanogr.
Oceanogr. Soc.
Soc. Jpn.
Jpn.1987,
1987,43,
43,149–158,
149–158.doi:10.1007/BF02109215.
[CrossRef]
Yanagi,
Simpson,J.H.;
Hunter,J.R.
Fronts
in
the
Irish
Sea.
Nature1974,
250,
404–406.
[CrossRef]
Simpson, J.H.; Hunter, J.R. Fronts in the Irish Sea. Nature 1974, 250, 404–406, doi:10.1038/250404a0.
James,I.D.
I.D.AAmodel
model
the
annualcycle
temperaturea frontal
regionof theCelticEstuar.
Mar.1977,
Sci. 5,1977,
James,
ofof
theannualcycle
of of
temperaturein ainfrontal
regionof theCelticSea.Sea.
Estuar.
Coast.Coast.
Mar. Sci.
339–5,
339–353.
[CrossRef]
353, doi:10.1016/0302-3524(77)90061-5.
Simpson,J.H.;
J.H.;Pingree,
Pingree,R.D.
R.D.Shallow
ShallowSea
SeaFronts
FrontsProduced
Producedby
byTidalTidalStirring.
Stirring.InInOceanic
OceanicFronts
FrontsininCoastal
CoastalProcesses;
Processes;Bowman,
Bowman,M.J.,
M.J.,
4.4. Simpson,
Esaias,W.E.,
W.E.,Eds.;
Eds.;Springer
Springer:Berlin
Berlin/Heidelberg,
Germany,1977;
pp. 29–42.
ISBN 9783642669873.
Esaias,Heidelberg, 1977;
pp. 29–42,
ISBN
9783642669873.
Yanagi,T.;
T.; Tamaru,
Tamaru, H.
a tidalfront.
Cont.
Shelf
Res.Res.
1990,
10, 615–627.
[CrossRef]
5.5. Yanagi,
H. TemporalTemporalandandspatial
spatialvariations
variationsinina tidalfront.
Cont.
Shelf
1990,
10, 615–627,
doi:10.1016/02786. 4343(90)90041-J.
Takeoka, H.; Matsuda, O.; Yamamoto, T. Processes causing the chlorophyll a maximum in the tidal front in Iyo-nada, japan. J.
Oceanogr.H.;
1993,
49, 57–70.
[CrossRef] T. Processes causing the chlorophyll a maximum in the tidal front in Iyo-nada, japan. J.
6.
Takeoka,Matsuda,O.; Yamamoto,
7. Oceanogr.
Sun, Y.-J.;1993,
Cho, 49,
Y.K.57–70,
Tidal doi:10.1007/BF02234009.
front and its relation to the biological process in coastal water. Ocean Sci. J. 2010, 45, 243–251. [CrossRef]
Brink,
K.H.Cho,
Instabilityof a tidal
front
in the topresenceof realistic
tides andmixing. water.
J. Mar. Ocean
Res. 2013,
227–252.
7.8. Sun,
Y.-J.;
Y.K. Tidal
frontmixing
and its
relation
the biologicalprocess
in coastal
Sci.71,
J. 2010,45, [CrossRef]
243–251,
9. doi:10.1007/s12601-010-0022-3.
Simpson, J.H. The shelf-sea fronts: Implications of their existence and behaviour. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci.
1981, 302,
[CrossRef]
8.
Brink,
K.H.531–546.
Instabilityof a tidal mixing front in the presence of realistic tides and mixing. J. Mar. Res. 2013, 71, 227–252,
10. doi:10.1357/002224013807719473.
Garrett, C.J.R.; Loder, J.W. Dynamical aspects of shallow sea fronts. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci. 1981, 302,
563–581. J.H.
[CrossRef]
9.
Simpson,The shelf-sea fronts: Implications of their existence and behaviour. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys.
11. Sci.
Simpson,J.H.;
James,doi:10.1098/rsta.1981.0181.
I.D. Coastal and Estuarine Fronts. In Baroclinic Processes on Continental Shelves; Mooers, C.N.K., Ed.;
1981, 302,
531–546,
AmericanGeophysicalUnion:
Washington,
USA, 1986;
63–93.
ISBN
9781118664995.
10. Garrett,
C.J.R.;
Loder, J.W.
Dynamical
aspectsDC,
of shallow
sea pp.
fronts.
Philos.
Trans.
R. Soc. Lond. Ser. A Math. Phys. Sci. 1981, 302,
van Aken,
H.M.;
van
Heijst,G.J.F.;
Maas,
L.R.M.
ObservationsofFrontsintheNorth
Sea. J. Mar. Res. 1987, 45, 579–600. [CrossRef]
12. 563–581,
doi:10.1098/rsta.1981.0183.
13.
Yanagi,T.;
Koike,
T.
Seasonal
variation
inthermohaline
and
tidal
fronts,
Seto
InlandJapan. Cont.
Shelf
Res. 1987,
7, 149–160.
11. Simpson, J.H.; James, I.D. Coastal and Estuarine Fronts. In Baroclinic Processes on Sea,
Continental
Shelves;
Mooers,C.N.K.,
Ed.;[CrossRef]
American Geophysical Union, 1986; pp. 63–93, ISBN 9781118664995.
14. vanWang,
D.-P.;
Chen,
D.;Heijst,
Sherwin,
T.J. Maas,
Coupling
betweenmixing andadvection
in aNorthshallowseaJ. front.
Shelf 45,
Res.579–600,
1990, 10,
12.
Aken,
H.M.;
van
G.J.F.;
L.R.M.
Observationsof Fronts
in theSea.
Mar. Cont.
Res. 1987,
123–136.
[CrossRef]
doi:10.1357/002224087788326830.

1.1.
2.2.
3.3.

Remote Sens. 2021, 13, 1840

15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.

26.
27.
28.
29.
30.

20 of 20

Simpson, J.H.; Bowers, D. Models of stratification and frontal movement in shelf seas. Deep Sea Res. Part A Oceanogr. Res. Pap.
1981, 28, 727–738. [CrossRef]
Sun, Y.-J.; Isobe, A. Numerical study of tidal front with varying sharpness in spring and neap tidal cycle. J. Oceanogr. 2006, 62,
801–810. [CrossRef]
Sharples, J.; Simpson, J.H. Periodic frontogenesis in a region of freshwater influence. Estuaries 1993, 16, 74–82. [CrossRef]
Yanagi, T.; Takahashi, S. A tidal front influenced by river discharge. Dyn. Atmos. Ocean. 1988, 12, 191–206. [CrossRef]
Yanagi, T.; Matsuda, O.; Tanabe, S.; Uye, S. Interdisciplinary study on the tidal front in the Bungo Channel, Japan. Phys. Estuaries
Costal Seas 1992, 40, 617–630. [CrossRef]
Pisoni, J.P.; Rivas, A.L.; Piola, A.R. On the variability of tidal fronts on a macrotidal continental shelf, Northern Patagonia,
Argentina. Deep Sea Res. Part II Top. Stud. Oceanogr. 2015, 119, 61–68. [CrossRef]
Japan Aerospace Exploration Agency Himawari Monitor. Available online: https://www.eorc.jaxa.jp/ptree/index.html (accessedon 27 October 2015).
Kurihara, Y.; Murakami, H.; Kachi, M. Sea surface temperature from the new Japanese geostationary meteorological Himawari-8
satellite. Geophys. Res. Lett. 2016, 43, 1234–1240. [CrossRef]
Donlon, C.J.; Martin, M.; Stark, J.; Roberts-Jones, J.; Fiedler, E.; Wimmer, W. The Operational Sea Surface Temperature and Sea Ice
Analysis (OSTIA) system. Remote Sens. Environ. 2012, 116, 140–158. [CrossRef]
Pawlowicz, R.; Beardsley, B.; Lentz, S. Classical tidal harmonic analysis including error estimates in MATLAB using T TIDE.
Comput. Geosci. 2002, 28, 929–937. [CrossRef]
Maritime Safety Agency, Hydrographic and Oceanographic Department. Tidal Harmonic Constants Tables Around Japanese Coast,
2nd ed.; Maritime Safety Agency: Tokyo, Japan, 1992; (in Japanese). Available online: https://www1.kaiho.mlit.go.jp/ (accessedon 24 April 2021).
Guo, X.; Harai, K.; Kandeda, A.; Takeoka, H. Simulation of Tidal Currents and Nonlinear tidal interactions in the seto inland sea,japan. Rep. Res. Inst. Appl. Mech. Kyushu Univ. 2013, 145, 43–52.
Chang, P.-H.; Guo, X.; Takeoka, H. A numerical study of the seasonal circulation in the Seto Inland Sea, Japan. J. Oceanogr. 2009,
65, 721–736. [CrossRef]
Yu, X.; Guo, X.; Takeoka, H. Fortnightly variation in the bottom thermal front and associated circulation in a semienclosed sea. J.
Phys. Oceanogr. 2016, 46, 159–177. [CrossRef]
Simpson, J.E.; Linden, P.F. Frontogenesis in a fluid with horizontal density gradients. J. Fluid Mech. 1989, 202, 1–16. [CrossRef]
O’Donnell, J. Surface fronts in estuaries: A review. Estuaries 1993, 16, 12–39. [CrossRef]