Continental Shelf Research 165 (2018) 26–36

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Continental Shelf Research
journal homepage: www.elsevier.com/locate/csr

Intensiﬁcation of water temperature increase inside the bottom cold waterby horizontal heat transport
Xiaojie Yu, Xinyu Guo

T⁎

Center for Marine Environmental Study, Ehime University, 2-5 Bunkyo-cho, Matsuyama 790-8577, JapanA R T I C LE I N FO

A B S T R A C T

Keywords:
Bottom cold water
Temperature increase range
Horizontal heat transport
Ambient current
Seto Inland Sea
Yellow Sea

Bottom cold water (BCW) is widely reported to occur in many coastal areas in summer. Some BCW masses havean increase in temperature of only 1 °C from early spring to summer (e.g., North Sea, Yellow Sea), while theothers have a 4–10 °C increase (e.g., Irish Sea, Seto Inland Sea). A model of heat transport with vertical diﬀusion
alone gave good approximation of the temperature increase in the North Sea type BCW masses, while additional
heat input from other processes was required to simulate the large temperature increases in Irish Sea type BCWs.
BCWs in the Yellow Sea and the Seto Inland Sea are then taken as examples to compare heat transport into thetwo types of BCWs through three-dimensional numerical modeling. The small warming range of the BCW in the
Yellow Sea results mainly from downward heat input by vertical diﬀusion. In contrast, the large temperature
range of warming in the BCW in the Seto Inland Sea is a result of both advection of heat from the surrounding
water and vertical diﬀusion. We therefore infer that advection of heat into the BCW is a necessary condition forthe high temperature increase range in Irish Sea type BCWs. Moreover, advection of heat into one BCW in the
Seto Inland Sea intensiﬁes from April to July, which is induced by gradually intensiﬁed bottom currents. This
example supports the importance of heat transport by advection for BCWs where the temporal change in advection of heat is capable of altering the temperature increase rate inside the BCW.

1. Introduction
The presence of bottom cold water (BCW) during summer has been
well described in many shelf seas and bays such as the North Sea(James, 1989; Warrach, 1998; Luyten et al., 2003), Yellow Sea (Guan,
1963; Yuan and Li, 1993; Xia et al., 2006), Irish Sea (Horsburgh andHill, 2003; Holt and Proctor, 2003), and Seto Inland Sea (Guo et al.,
2004; Yu et al., 2016). In these coastal regions, the water temperature
increase ranges inside the BCW mass diﬀer from spring to summer. For
example, in the North Sea, water temperature inside the BCW increases
from 7 °C in April to 8 °C in August (Warrach, 1998). In contrast, thewater temperature in the BCW in the Irish Sea shows a large increase
from 7.5 °C in April to 11.5 °C in August (Holt and Proctor, 2003).
Therefore, from the viewpoint of temperature increase range in bottom
water masses, the BCWs in the North Sea and Irish Sea show diﬀerent
features: one increases little while the other increases several degrees.
In northwestern Paciﬁc coastal regions, we can also ﬁnd BCWs with
diﬀerent water temperature increase ranges. The Yellow Sea (Fig. 1) is asemi-enclosed shelf sea connected to the northwestern Paciﬁc throughthe East China Sea. The tidal current is strong near the coast but weakin the central deep region. In summer, a BCW forms in the central deep⁎

Corresponding author.
E-mail address: guoxinyu@sci.ehime-u.ac.jp (X. Guo).

https://doi.org/10.1016/j.csr.2018.06.006
Received 7 June 2017; Received in revised form 2 June 2018; Accepted 11 June 2018
Available online 13 June 20180278-4343/ © 2018 Elsevier Ltd. All rights reserved.

basin through weak tidal currents and strong stratiﬁcation (Guan, 1963;
Yuan and Li, 1993; Xia et al., 2006), and the water temperature inside
the BCW increases only ~1 °C from spring to summer (Xia et al., 2006).
Some recent studies have suggested that the BCW in the Yellow Sea has
a southward movement in summer (Zhang et al., 2008; Moon et al.,2009; Wang et al., 2014), and tidal forcing is the dominant factor
driving this ﬂow along the western slope while southerly winds andstrong surface solar radiation are secondary factors in summer.
The Seto Inland Sea (Fig. 2), a semi-enclosed sea in western Japan,
is connected to the Paciﬁc Ocean by the Bungo Channel and Kii Channel
and is also impacted by tidal waves entering through these channels(Yanagi and Higuchi, 1981). It consists of many straits and wide basins(called ‘nada’ in Japanese), and the tidal current is strong in the straits
but weak in the wide basins. The presence of BCW mass with diﬀerent
horizontal and vertical scales in summer has been conﬁrmed in several
wide basins, including the Iyo-nada (Takeoka et al., 1993; Chang et al.,2009; Yu et al., 2016), Suo-nada (Chang et al., 2009), Hiuchi-nada(Takeoka et al., 1991; Guo et al., 2004; Chang et al., 2009), andHarima-nada (Chang et al., 2009). The temperature increase range inthese BCW masses from spring to summer may reach 7–10 °C. Aroundthe BCW, there exists a cyclonic circulation induced by the horizontal

Continental Shelf Research 165 (2018) 26–36

X. Yu, X. Guo

gradient of water temperatures across the bottom front of the BCW(Chang et al., 2009; Yu et al., 2016).
Formation of the BCW is generally associated with weak tidal
mixing that is not capable of transporting suﬃcient heat from thesurface layer to the bottom layer (He et al., 1959). Therefore, the BCW
is usually observed in isolated areas with weak tidal currents and deep
water where the Simpson-Hunter parameter (log10(H/U3), Simpson andHunter, 1974) is large, while the surrounding water is relatively warm
due to strong tidal mixing that transports heat vertically in the entire
water column. However, as we will discuss later, considering only the
combination of tidal mixing and water depth, i.e., the Simpson-Hunterparameter, is not suﬃcient to explain the large increase in water temperature inside the BCW of the Seto Inland Sea. To understand thediﬀerence in the water temperature increase range inside the BCW, wetake BCWs in the Yellow Sea and the Seto Inland Sea as examples for
examining the processes that control heat transport into BCW using
numerical modeling. Along with these processes, not only verticalmixing but also water exchange of the BCW with surrounding water isclariﬁed. Such cross-front water exchange has the potential to impact
nutrient supply and biological activities (Komorita et al., 2016).
In the next section, we brieﬂy describe the conﬁgurations of numerical models used for the Yellow Sea and the Seto Inland Sea, as wellas the observation data in the Seto Inland Sea. Section 3 reports themodel results for the Yellow Sea and in situ data analysis and model
results for the Seto Inland Sea. Section 4 provides interpretation of thediﬀerences between BCWs with small and large temperature increases
through a comparison of heat transport between the Yellow Sea and theSeto Inland Sea. Section 5 provides a summary of this study.
2. Observation data and model description
2.1. Yellow Sea
Fig. 1. Bathymetric map showing depth (m) of the Yellow Sea and surrounding
water masses and the model domain.

To examine BCW and heat transport into the BCW in the Yellow Sea,
we adapt a numerical model based on the Princeton Ocean Model(POM, Blumberg and Mellor, 1987; Mellor, 2003). A bathymetric mapof the model domain is shown in Fig. 1. The model with a nesting
method was set to have a high horizontal resolution (1/18 degrees) for
the Yellow Sea and East China Sea and 21 sigma levels in the verticaldirection (Guo et al., 2003). Wang et al. (2008) improved the model by
including freshwater inputs from the sea surface and rivers and byadding tidal forcing (M2, S2, K1, and O1 tides) along the lateralboundary. We used the same monthly forcing conditions (heat ﬂux, salt
ﬂux, and wind stresses at sea surface; river discharge at river mouths;
water temperature, salinity, sub-tidal velocity and elevation at the open
boundaries) as Wang et al. (2008) to simulate the stationary seasonalvariation in the Yellow Sea and East China Sea. The model was run for 4
years starting from January. We saved the ﬁnal year model results at 1h intervals and applied a tide ﬁlter given by Hanawa and Mitsudera(1985) to remove tidal signals.
2.2. Seto Inland Sea
The prefectural ﬁshery research centers around the Seto Inland Sea
have been carrying out monthly hydrographic observations at 344 hydrographic stations (Fig. 2a) since 1971, providing data on watertemperature and salinity at depths of 0, 10, 20, 30, 50, 75, and 100 mfrom 1971 to 2000. There are four BCW masses in the Seto Inland Sea,
one each in the Iyo-nada, Suo-nada, Hiuchi-nada, and Harima-nada(Fig. 4 in Yu et al., 2016). We previously used this data to examine
fortnightly variations in the bottom thermal front associated with the
BCW in Iyo-nada (Yu et al., 2016). In this study, we chose a station at
the center of one BCW in the Seto Inland Sea and ﬁt all water temperature data collected within the BCW over the past 30 years to a
curve to examine seasonal variation. By repeating this procedure for all
four BCW masses in the Seto Inland Sea (four large red dots in Fig. 2a),Fig. 2. (a) Monthly sampling stations (black dots) in the Seto Inland Sea.
Sampling was conducted at stations 1–7 in Iyo-nada. (b) Bathymetric map
showing depth (m) of the Seto Inland Sea and model domain. The open
boundaries are the south sides of the Bungo Channel (south boundary) and theKii Channel (dashed line). The red dots along the coastline denote the mouths ofrivers. The red line extending from A to B is the Iyo-nada section. The large red
dots in (a) and large black dots in (b) indicate the positions of observed andmodeled BCW masses, respectively, in the Iyo-nada, Suo-nada, Hiuchi-nada,and Harima-nada.
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we determined the temperature increase range in the BCW masses fromspring to summer.
To examine the heat transport into the BCW masses, we used anumerical model developed for the Seto Inland Sea (Chang et al., 2009).
This model is also based on the POM and the bathymetry of the Seto
Inland Sea is shown in Fig. 2b. The resolution of the model is ~1 km in
the horizontal direction and 21 sigma layers in the vertical direction.
This model is driven by monthly heat ﬂux, salt ﬂux, and wind stresses at
sea surface; monthly river discharges; and monthly water temperature,salinity, sub-tidal velocity and elevation at open boundary (Changet al., 2009). Four tidal constituents, M2, S2, K1, and O1, which have
harmonic constants derived from a tide model for larger domains (Guoet al., 2013), are added linearly to the sub-tidal velocity and elevation
at the open boundary.
The model calculation was set to start in January and continued fora period of 3 years. Model results were saved hourly, and the impact oftides was removed by the same tide ﬁlter used for the Yellow Sea(Hanawa and Mitsudera, 1985). The detided current is termed residual
current in this study. The analysis on heat transport into the BCW isbased on model results in the third year when the model results nearlycoincided with those in the second year.

Fig. 4. Time series of vertical diﬀusivity coeﬃcient (log10 (Kh) m2 s−1) in thethermocline and the vertical temperature gradient (°C m−1) above the BCW in
the Yellow Sea over one year.

3. Results

Liu et al., 2009).
In the vertical proﬁle, stratiﬁcation in the South Yellow Sea wasstrong in summer, with surface water temperature higher than 25 °C
and a bottom water temperature lower than 6 °C (Fig. 3c). The thermocline with strongest stratiﬁcation was at a depth of 15 m, below
which the BCW deﬁned as isothermal lines of 6–7 °C stretches to the sea
bottom with a thickness of about 50 m. The BCW forms a bottom front
with surrounding water at around 124.0°E and 125.4°E (Fig. 3c).
The time series of the vertical diﬀusivity coeﬃcient above the BCWat the thermocline (~15 m depth) showed a decreasing trend fromwinter to spring, remained small (~10−5 m2 s−1) in summer due tostrong stratiﬁcation and then increased to the next winter due to sea
surface heat loss and strong winds (Fig. 4a). The background diﬀusivity
coeﬃcient in the model is 10−5 m2 s−1. The vertical temperature
gradient above the BCW at ~15 m depth was nearly 0 from winter tospring, gradually increased to ~1.2 °C m−1 in summer, and then decreased to 0 in the next winter (Fig. 4b).

3.1. Yellow Sea
There are two BCW masses in the Yellow Sea—one in the northernpart and the other in the southern part. In this study, we mainly focus
on the BCW mass in the South Yellow Sea. Seasonal variation of modeled BCW temperature (black line, Fig. 3a) in the South Yellow Sea
showed little increase (~1 °C) from spring to summer, while the surface
temperature increase was large (> 20 °C, red line, Fig. 3a). Here, wedeﬁne spring, summer, autumn and winter in three-month intervals
from March to May, June to August, September to November, andDecember to February, respectively. In summer, the BCW in the South
Yellow Sea is centered around 124.5°E, 36.0°N and covers a wide areaof approximately 300 km × 300 km. The BCW temperature was only
about 6–7 °C, even at the end of July (color, Fig. 3b), which is much
lower than the coastal water temperature (~30 °C). The bottom residual
current around the BCW is generally weak (arrows, Fig. 3b). The general features of the BCWs in the Yellow Sea reproduced by the model
are consistent with the observations (He et al., 1959; Xia et al., 2006;

Fig. 3. (a) Model results of seasonal variation in surface
and bottom temperatures (°C) at the BCW in the South
Yellow Sea at the black dot in (b), (b) horizontal distribution of water temperature (°C, color) and residual
current (m s−1, arrows) in the bottom layer on day 211(31 July), and (c) vertical distribution of temperature (°C)
at the section (shown by black line in (b)) on day 211.

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Fig. 5. Observation data (red points), ﬁt curve (black solid lines) of seasonal variation in BCW temperature (°C) and the temperature (T) increase rate (°C/day, blue
dashed lines) of the BCW at the points corresponding to red dots in Fig. 2a in (a) Iyo-nada, (b) Suo-nada, (c) Hiuchi-nada, and (d) Harima-nada.

increase is large from April to August in the nadas (8–10 °C), although
the patterns do not exactly match those of the observation data (Fig. 5).
Moreover, the temperature increase rate (blue dashed lines, Fig. 7) fromspring to summer shows a diﬀerent pattern in the Iyo-nada (accelerating increase from April to July) (Fig. 7a) compared to those in the
Suo-nada (Fig. 7b), Hiuchi-nada (Fig. 7c), and Harima-nada (Fig. 7d)(remaining almost uniform throughout the season).
In the Iyo-nada, the vertical and temporal variation of model results
for water temperature (black lines, Fig. 8), salinity (color, Fig. 8), anddensity (white lines, Fig. 8) show patterns similar to observations(Fig. 6). Moreover, the diﬀerence in density between the strait and thesurface layer of the nada increased from 0.4 kg m−3 in April to
1.8 kg m−3 in July. The bottom fronts between the BCW and the surrounding warm water are located about 20–30 km and 50–60 km awayfrom the strait, respectively, and the BCW covers an area with a widthof about 40 km and a thickness of 30–40 m on the sea bottom that isdeﬁned by the position of isothermal lines arising from the bottom front
at 20–30 km.
The vertical diﬀusivity coeﬃcient in the thermocline (at ~10 m
depth) above the BCW in Iyo-nada (Fig. 9a) showed obvious seasonalvariation as it was large (10−1 m2 s−1) in winter, decreased sharply
from spring to summer (2 × 10−5 m2 s−1), and increased again fromautumn. The background diﬀusivity coeﬃcient in the model of the Seto
Inland Sea was 2 × 10−5 m2 s−1. A larger background diﬀusivity
coeﬃcient was used for the Seto Inland Sea than for the Yellow Sea
because stratiﬁcation is weaker in the Seto Inland Sea than in the
Yellow Sea. The vertical temperature gradient (~10 m depth) above theBCW (Fig. 9b) began to appear in spring, reached a maximum(~0.3 °C m−1) in July, and then decreased again to autumn.

3.2. Seto Inland Sea
3.2.1. Data analysis
Compilation of the monthly minimum temperatures in the four BCW
masses in the Seto Inland Sea over 30 years of observations showed
clear seasonal variation (black solid lines in Fig. 5, which was obtainedby ﬁtting the discrete data to a polynomial function of degree 3 using
the least squares method in Matlab). The water temperature range fromearly April to August was larger in the four BCW masses in the Seto
Inland Sea (8–10 °C) than in the Yellow Sea (~1 °C). In addition, thetemperature increase rate per day (blue dashed lines, Fig. 5) among thefour BCW masses showed diﬀerences from early April to August: nearly
constant in the Suo-nada (Fig. 5b), Hiuchi-nada (Fig. 5c) and Harimanada (Fig. 5d), but showing an accelerating trend in the Iyo-nada(Fig. 5a), especially in July.
As an example of warming in the BCW from early spring to summer
in the Seto Inland Sea, we show the vertical distribution of temperature,salinity, and density at the section across the BCW in the Iyo-nada(Fig. 6). The temperature of surface water increased from 13 °C in April
to 23 °C in July (black lines, Fig. 6), while that of the BCW (lowest
depth at Sta. 4) increased from 12 °C in April to 18 °C in July; consequently, stratiﬁcation above the BCW increased gradually in the nada.
Taking the example of the Hayasui Strait (Sta. 1), temperature of thewater surrounding the BCW mass was almost uniform throughout theseason from the surface to the bottom and was intermediate to that at
the surface and bottom of the nada (e.g., Sta. 4). Salinity (color, Fig. 6)
showed a decreasing trend over the entire section from April to July.
The diﬀerence in salinity between the surface and bottom layers in thenada (e.g., Sta. 4) increased, while salinity in the Hayasui Strait (Sta. 1)
remained almost uniform over the entire depth. Salinity was always
higher in the strait than in the nada. Water density (white lines, Fig. 6)
decreased from April to July as a result of increasing water temperatureand decreasing salinity. The density diﬀerence between the strait andthe surface layer of the nada increased from 0.2 kg m−3 in April to
1.5 kg m−3 in July.

4. Discussion
4.1. Advection of heat from surrounding warm water to the BCW
The BCW in the Yellow Sea has a small temperature increase (~1 °C)
from spring to summer, while the BCW masses in the Seto Inland Sea
have a large temperature increase of temperature (8–10 °C). Both BCW
masses are related to tidal currents that are too weak to generate vertical mixing of the water column in the summer. The question here iswhether vertical mixing processes alone can explain the two types of

3.2.2. Model results
The modeled water temperature in the BCW masses of the Iyo-nada,
Suo-nada, Hiuchi-nada, and Harima-nada all show an increasing trend
from spring to summer (black solid lines, Fig. 7). The temperature
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Fig. 6. Vertical distribution of water temperature (°C,black lines), salinity (color), and density (kg m−3, whitelines) in Iyo-nada (stations 1–7, Fig. 2a) in (a) April, (b)May, (c) June, and (d) July. Black dots indicate the depthof observation data at each station. Isothermal lines arelabeled with black numbers and isopycnal lines are labeledwith red numbers.

BCWs. To answer this question, we ﬁrst examine the capacity of theheat supplied by vertical diﬀusion into several BCW masses and thenquantitatively calculate the contribution of horizontal and verticalprocesses to the warming of the two types of BCW masses.

BCW gives

∂
∂t

h1

2

1

ΔTv
∂T
(h1 − h2) = K z v |z = h1 .
Δt∂z

4.1.1. Vertical heat transport by diﬀusion into BCWs
With only vertical diﬀusion, the water temperature is governed byfollowing equation,

∂Tv
∂
∂T
(K z v )
=
∂t
∂z
∂z

∫h Tv dz = Kz ∂∂Tzv |z=h − Kz ∂∂Tzv |z=h

2

(2)

(3)

From Eq. (3), we can estimate an approximate temperature increase
ΔTv of the BCW over a time period of Δt using vertical diﬀusivity at the
top of the BCW and the vertical gradient of water temperatures acrossthe top of the BCW.
The vertical gradient of water temperature above the BCW is easily
derived from observation data. However, the value of K z is not easily
determined. For the Yellow Sea, we used the observed K z by Liu et al.
(2009) of ~10−5 m2 s−1 near the thermocline in summer, which is(1)

where Tv is the water temperature associated with vertical diﬀusion,
and K z is the vertical diﬀusivity coeﬃcient. Vertically integrating Eq.
(1) from the sea bottom (h2 ) to the top of the BCW (h1) and assuming noheat supply from the sea bottom as well as unchanged thickness of theFig. 7. Model result of seasonal variation in BCW temperature (°C, black solid lines) and the temperature (T) increase rate (°C/day, blue dashed lines) at the points
shown by black dots in Fig. 2b in (a) Iyo-nada, (b) Suo-nada, (c) Hiuchi-nada, and (d) Harima-nada.
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Fig. 8. Vertical distribution of modeled water temperature (°C, black lines), salinity (color), and density (kg m−3, white lines) along section AB in Iyo-nada in (a)April, (b) May, (c) June, and (d) July. Isothermal lines are labeled with black numbers and isopycnal lines are labeled with white numbers.
Table 1
Parameters and calculated ΔTv and actual temperature increase ΔTreal for selected areas. Values for variables are from Warrach (1998) for the North Sea,
from Xia et al. (2006) and Liu et al. (2009) for the Yellow Sea, from Holt andProctor (2003) and Rippeth et al. (2009) for the Irish Sea, and our numericalmodel for the Iyo-nada of the Seto Inland Sea. The diﬀerence in Δt in these seasis due to the diﬀerent intervals of available water temperature data.
Δt (d)

North Sea
Yellow Sea
Irish Sea
Iyo-nada

120
6 Apr–4 Aug
90
Apr–Jul100
1 May–10 Aug
120
1 Apr–31Jul.

h1 − h2 (m)

40
45
60
30

Kz
(m2
s−1)
1.0 ×
10−5
1.0 ×
10−5
6.0 ×
10−5
2.0 ×
10−5

ΔTv (°C)

ΔTreal (°C)

0.35

0.9

1.0

0.60

1.0

1.0

0.2

1.7

4.0

0.30

2.1

7.1

∂Tv
(°C
∂z

m

−1

)

Luyten et al. (2003) compared the temperature in the North Sea reproduced with and without an advection term in a three-dimensionalmodel and showed that there was little diﬀerence in the temperature of
the BCW between two cases, supporting the conclusion that the BCW in
the North Sea is not inﬂuenced by advection. Wei et al. (2010) demonstrated that interannual variation of temperature in the BCW of
Yellow Sea depends primarily on the temperature in the preceding
winter, which also indicates that there is little contribution from advective heat transfer to the BCW.
On the other hand, for BCW masses in the Irish Sea and Iyo-nada of
the Seto Inland Sea, ΔTv is much smaller than ΔTreal (Table 1). For the
Irish Sea, ΔTv (1.7 °C) is lower than ΔTreal (4.0 °C) by 2.3 °C, indicatingthat heat transfer by other processes must contribute to the warming of
the BCW. Horsburgh and Hill (2003) suggested that lateral processes(both diﬀusion and advection) may be as important as vertical processes in the warming of the BCW in the Irish Sea. Through analysis of
the transfer equation for temperature, Holt and Proctor (2003) also
concluded that advection of heat from a weakly stratiﬁed water mass to
the BCW in the Irish Sea is a more important factor than verticalFig. 9. Time series of vertical diﬀusivity coeﬃcient (log10 (Kh) m2 s−1) in thethermocline and the vertical temperature gradient (°C m−1) above the BCW in
the Iyo-nada over one year.

consistent with the model result for K z in our study. Since stratiﬁcationin the North Sea is as strong as that in the Yellow Sea, we also set K z to
10−5 m2 s−1 in the North Sea. In the Irish Sea, the observation gave an
average value of ~6 × 10−5 m2 s−1 near the thermocline (Rippeth
et al., 2009). In Iyo-nada, Seto Inland Sea, we used a value of ~2 ×
10−5 m2 s−1 generated by our numerical model.
The calculated temperature increase ΔTv by Eq. (3) and the observed
temperature increase ΔTreal (Table 1) are consistent for the North Sea
and Yellow Sea, which are around 1 °C, indicating that the temperature
increase in the BCW there is primarily caused by the vertical diﬀusion
process from spring to summer. In practice, many one-dimensionalmodels have been successfully applied to the North Sea (Sharples andTett, 1994; Warrach, 1998) and the temperature increase in the BCW
has been demonstrated to be mainly due to vertical diﬀusion of heat.

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X. Yu, X. Guofrom the surrounding warm water to the BCW by advection. Heat input
by vertical diﬀusion is large (~0.18 °C day−1) in the surface layer andsmall (< 0.01 °C day−1) in the bottom layer (Fig. 10d) due to strong
stratiﬁcation at the depth of 10–20 m (black lines, Fig. 10d). Temperature variation over the entire depth (Fig. 10a) is primarily determined by vertical diﬀusion of heat (Fig. 10d). As the downward heatby vertical diﬀusion through the thermocline is limited, the temperature inside the BCW in the South Yellow Sea increases little from April
to July.
For large temperature increase BCWs, we chose the center of the
BCW mass in the Iyo-nada (black point between A and B, Fig. 2b) toillustrate heat transport into the BCW from early April to the end of July(Fig. 11). The daily increase in water temperature at depths of 20–40 m
was small in April (< 0.05 °C day−1) and gradually increased toward
July (0.20–0.25 °C day−1, Fig. 11a). The daily change in BCW temperature (T increase rate) is mainly controlled by advection and vertical
diﬀusion since the sum of these terms (Fig. 11b) shows a pattern similar
to the daily change in temperature (Fig. 11a). The advection term
(Fig. 11c) is always positive in the upper part of the BCW (30–40 m
depth) and shows an accelerating trend from April (< 0.05 °C day−1) to
July (~0.40 °C day−1) as well as the spring-neap tidal variation. Consequently, advection transfers heat to the area above and to the upper
part of the BCW in the Iyo-nada.
A positive (negative) value of the vertical diﬀusion term indicatesthat heat is transported downward into the grid is larger (smaller) thanthat transported downward out of the grid. The vertical diﬀusion term
(Fig. 11d) at the depth of 20 m is very small, indicating that the
downward transport of heat by vertical diﬀusion is limited around thethermocline. However, vertical diﬀusion is negative (positive) in theupper part (lower part) of the bottom layer, i.e., BCW and also shows anaccelerating trend, indicating that vertical diﬀusion is important to heat
redistribution in the BCW.
Apparently, vertical diﬀusion diﬀuses heat by advection in theupper part of BCW downward to the lower part of the BCW. Therefore,
warming of the entire BCW in the Iyo-nada is under the control of the
combination of advection and vertical diﬀusion. The necessary heatcomes mainly from the surrounding warm water with movement ofwater (advection), and the acceleration of the temperature increase ratein the BCW should be attributed to gradually strengthening advection ofheat in the upper part of the BCW from April to July.
To conﬁrm the prevailing eﬀect of advection on the warming of the
BCW in Iyo-nada, we carried out another numerical experiment by POM
for Tv calculated by Eq. (1) using the same K z as in Eq. (4) fromdiﬀusion of heat. In the Iyo-nada (Table 1), ΔTv is ~2.1 °C while ΔTreal isabout 7.1 °C, indicating that other processes of heat transfer can increase the temperature by about 5.0 °C, a contribution that is more than
twice that by vertical diﬀusion from spring to summer.
Therefore, a one-dimensional equation for vertical diﬀusion is likely
capable of reproducing the behavior of BCWs with small temperature
increases. However, the BCWs with large temperature increases needmore processes to supply heat to the BCW. Apparently, vertical mixing
alone is not suﬃcient to explain the presence of small and large temperature increases in the warming BCWs of shelf seas.
4.1.2. Three-dimensional model analysis of heat transport into the BCWs in
the Yellow Sea and Seto Inland Sea
The presence of BCWs is due to a slower increase in water temperature in the sea bottom relative to that of the surrounding waterfrom spring onward. Factors contributing to the heating of the BCW
include vertical diﬀusion of heat from above and advection of andhorizontal diﬀusion of heat from the surrounding warm water. To
better understand the processes related to diﬀerences between small
and large temperature increases in the warming of BCWs, we take the
Yellow Sea and Iyo-nada in the Seto Inland Sea as examples and calculate the contribution of each process to the change in water temperature. In the three-dimensional model, the temporal change in watertemperature T is controlled by the following equation,∂T= AdvT + VdfT + HdfT∂t(4)

where AdvT is sum of the advection terms, VdfT is the vertical diﬀusion
term, HdfT is the horizontal diﬀusion term, and the overbar above eachterm indicates procedure of detiding. Integrating Eq. (4) over 24 h
produces an equation for the daily change in water temperature,

ΔTdaily =

24

24

24

∫0 AdvT dt + ∫0 VdfTdt + ∫0 HdfTdt.

(5)

For small temperature increase BCWs, the center of the BCW mass in
the South Yellow Sea (black point, Fig. 3b) was chosen to illustrate heattransport into the BCW from April to July (Fig. 10). Temperature variation is relatively large (~0.18 °C day−1) in the surface layer but small(< 0.01 °C day−1) in the bottom layer (Fig. 10a). The sum of the advection terms and the vertical diﬀusion term (Fig. 10b) show patterns
similar to temperature variation (Fig. 10a), indicating that horizontal
diﬀusion of heat plays little role. The advection of heat in the lower
layer is very small (Fig. 10c), which means there is little heat supplied

Fig. 10. (a) Daily increase in water temperature (deltT,left hand side of Eq. (5)), (b) sum of advection and vertical
diﬀusion terms on the right hand side of Eq. (5), (c) advection term, and (d) vertical diﬀusion term. For all panels, T increase rate is shown (color with contour intervals
at 0.01 °C day−1 with values shown in black from April toJuly in the BCW (black dot in Fig. 3b) in the South Yellow
Sea. Additionally, temperature contours are shown in (c)and (d) by black lines with red labels (°C).

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X. Yu, X. Guo

Fig. 11. (a) Daily increase in water temperature (deltT,left hand side of Eq. (5)), (b) sum of advection and vertical
diﬀusion terms on the right hand side of Eq. (5), (c) advection term, and (d) vertical diﬀusion term. For all panels, T increase rate is shown (color with contour intervals
at 0.01 °C day−1 with values shown in black from April toJuly in the BCW (black dot in Fig. 2b) in the Iyo-nada.
Additionally, temperature contours are shown in (c) and(d) by black lines with red labels (°C).

temporal temperature change due to vertical diﬀusion divided by that
due to diﬀusion and advection) for the BCW, i.e., the temperaturechange by vertical diﬀusion from April to July divided by that by diffusion and advection, integrated from the sea bottom to a depth of 20 m
(approximately the top of the BCW) in both the Yellow Sea (Fig. 13) andthe Seto Inland Sea (Fig. 14). The center of the BCW in the Yellow Sea ismainly warmed by vertical heat diﬀusion, indicated by a percentage
greater than 90%, while the water around the front, especially in theeastern front, is warmed not only by the vertical diﬀusion with a percentage of about 40%, but also by advection (~60%). In the Seto InlandSea, the percentage controlled by vertical diﬀusion is small in Iyo Nada(~40%), but slightly larger in Suo-nada and Harima-nada (~60%). Thismeans that advection of heat is more important to the BCW temperature
increase in Iyo Nada (~60%) than in Suo-nada and Harima-nada(~40%).
Therefore, both advection and vertical diﬀusion occur in heattransport related to the BCW. The small temperature increase BCWs in

Fig. 12. Time series of bottom water temperature, (°C) in Iyo-nada from April
to July. The black line indicates the temperature, T , calculated by Eq. (4) andthe red line shows the temperature, Tv , calculated by Eq. (1).

beginning of April when heating becomes positive. The model result at
the bottom of Iyo-nada shows that Tv increases from 12.2° to 14.5 °C(2.3 °C) by vertical diﬀusion alone (red line, Fig. 12), while the temperature T (black line, Fig. 12) increases from 12.2° to 19.2 °C (7.0 °C)
by the mechanisms captured in Eq. (4), that is, by advection and vertical diﬀusion. Vertical diﬀusion alone can increase the temperature by~2 °C, being roughly consistent with Tv calculated by Eq. (3), which
conﬁrms the rationality of the vertical diﬀusion equation used in
Section 4.1.1. The remaining ~5 °C is increased by the combination ofvertical diﬀusion and advection, conﬁrming again the importance of
advection for warming the BCW in the Iyo-nada from spring to summer.
Comparison of heat transport into the BCW masses in the Yellow Sea
and in the Seto Inland Sea suggests that small temperature increase in
the BCW is mainly due to vertical diﬀusion of heat, while the large
temperature increase BCW is mainly attributable to the combination of
advection of and vertical diﬀusion of heat. Since vertical advection can
only redistribute the heat locally, heat transferred horizontally by advection from surrounding warm water should be the cause for the large
temperature increase inside the BCW in the Seto Inland Sea.
The importance of heat transfer by advection is heavily locationdependent. We show the horizontal distribution of the percentage oftemperature increase controlled by vertical diﬀusion (percentage of

Fig. 13. Horizontal distribution of percentage of temperature increase controlled by vertical diﬀusion (color) for BCW from the sea bottom to 20 m depth
in the Yellow Sea. Black lines indicate the bottom temperature (CI = 1 °C) in
July.
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Fig. 14. Horizontal distribution of percentage of temperature increase controlled by vertical diﬀusion (color) for BCW from the sea bottom to 20 m depth in the Seto
Inland Sea. Black lines indicate the bottom temperature (CI = 1 °C) in July.

111, 140, 168, and 196. Positive advection terms between the BCW and
Hayasui Strait show an increasing trend and also transition toward the
BCW from April to July, and the maximum value always coincides withthe temperature front (black lines, Fig. 15).
The advection term is comprised of horizontal and vertical components. Our analysis shows that the horizontal advection brings heatto the upper part of the BCW, while the vertical advection carries waterat the upper part of BCW upward to upper layer and downward tobottom layer (ﬁgure not shown). This situation is consistent with the
hypothesis proposed by Takeoka (2002). Since the horizontal advectionof heat is always larger than the vertical advection of heat, the advection ultimately results in a positive value in the upper part of BCW.
Moreover, both horizontal and vertical advection terms of heat show
accelerating trends from April to July.
We further decomposed the current and temperature data into
subtidal component and intra-tidal components and calculate the advection term again. The result shows that advection due to currents andwater temperature components with a period shorter than tidal periods
is much smaller than that due to currents and water temperaturecomponents with a period longer than the tidal period. Therefore, thehorizontal advection term of heat is associated with the residual current
and temperature gradient.
Since the temperature gradient around the BCW does not change
markedly through the season (inferred from the black lines in Fig. 15),the variation in the horizontal advection term of heat is mainly attributed to the residual current, which ﬂows against the temperature
gradient direction. From the horizontal distribution of residual current(arrows, Fig. 15) along the 40 m depth, we can see that in April, there isa residual current from the Hayasui Strait to the Iyo-nada, which islimited around the strait. From May to July, the current gradually
moves inward toward the nada. When the current ﬂows against thetemperature gradient direction, it transports warm water from outside
to the inside of BCW, which can explain the coincident positions of the
maximum advection term of heat and the temperature front. Therefore,
this residual current from the Hayasui Strait to the Iyo-nada in theupper part of the BCW brings heat from warm water to the BCW area
and increases the temperature of the BCW through a combination ofvertical diﬀusion and vertical advection inside the BCW. In moving
toward the BCW over time, it induces the acceleration of the temperature increase rate of the BCW in Iyo-nada.
To elucidate the physics of this residual current, we examined thevertical distribution of the residual current along the section AB (arrows, Fig. 16). In April, there is an apparent current from the strait tonada, which is actually the tide-induced residual current that is stronger
in the surface layer than in the bottom layer. From May to July, thecurrent in the surface layer gradually decreases and reverses direction
from nada to strait, while the current in the bottom moves farther to thethe literature (Table 1) are located in open, wide regions, such as in the
North Sea and Yellow Sea, and have large sizes of about 300 km ×
300 km. For these BCW masses, the topography varies smoothly andhorizontal currents in the middle and bottom layers are relatively weak.
Consequently, advection occurs in the boundary of BCWs while vertical
diﬀusion dominates at the center of the BCWs. On the other hand, thelarge temperature increase BCW masses are usually located in narrow
regions, typically having a small size such as about 100 km × 100 km as
in the Irish Sea, and 40 km × 30 km in the Iyo-nada, Seto Inland Sea. In
these areas, the topography changes sharply and the horizontal currents
in the middle and bottom layers are relatively strong, which can bringheat to the BCW from the surrounding warmer water. In these BCWs,
the contribution of advection to warming the BCW diﬀers from eachother. In some regions (e.g., the Irish Sea), advection of heat (2.3 °C)
plays almost the same role as vertical diﬀusion of heat (1.7 °C) to BCW
warming. In other regions (e.g., Iyo-nada), the contribution of advection (5.0 °C) is more than twice that of the vertical diﬀusion (2.1 °C) to
BCW warming (Table 1).
One problem with our estimation of vertical diﬀusion is the use ofmonthly mean forcing in the model calculation. Consideration of shortterm variations (e.g., diurnal variation) in winds can introduce morekinetic energy to the ocean than the monthly mean winds and therefore
enhance vertical mixing in the surface layer (Lee and Liu, 2005;
Cardona and Bracco, 2012). Yu et al. (2017) reported that inclusion ofdiurnal variation in winds into the model can increase the water temperature inside the BCW of Yellow Sea by 0.4 degrees. Our new calculation for the Seto Inland Sea using hourly winds also shows an increase in the water temperature of the BCW in the Iyo-nada by 1 °C.
This process is excluded in both models for the study areas, and while
its inﬂuences on vertical mixing may partly aﬀect the vertical distribution of calculated water temperature, omitting it may not change
our conclusions on the importance of the role of horizontal advection toheat transport into the BCWs in the Seto Inland Sea.
4.2. Model analysis of acceleration of temperature increase rate for the
BCW in the Iyo-nada
The BCW in the Iyo-nada has a large temperature increase fromspring to summer that is attributed to advective heat transfer from thesurrounding warm water. Besides, the temperature increase rate of the
BCW accelerates from April to July, which is likely induced by thegradually intensifying advection of heat into the BCW. To examine thespeciﬁc route of heat transport by advection and its strengthening
process, we show the horizontal distribution of the advection term forwater temperature in Eq. (5) at a depth of 40 m from April to July(color, Fig. 15). To avoid the inﬂuence of spring and neap tides, weselected the days corresponding to spring tide in each month, i.e., days
34

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Fig. 15. Horizontal distribution of the advection term for water temperature (°C day−1, color), residual current (m s−1, arrows), and water temperature (°C, blacklines) at a depth of 40 m in Iyo-nada in (a) April, (b) May, (c) June, and (d) July.

of the Iyo-nada and the Hayasui Strait increasing from 0.4 kg m−3 inApril to 1.8 kg m−3 in July (Fig. 8) led to the occurrence of gravitational circulation with the surface ﬂow being outward and the bottom
ﬂow inward. According to Wong (1994), the velocity of density-induced
gravitational circulation is positively correlated with the horizontal
density gradient and negatively correlated with the vertical eddy viscosity Az . The vertical eddy viscosity in the Iyo-nada (color, Fig. 16)
decreases from April to July due to stronger stratiﬁcation. Therefore,
with the former increasing and the latter decreasing, the gravitational
circulation intensiﬁes from April to July, which ﬁnally induces thenada. Taking the actual situation of the Seto Inland Sea into account,
we suggest that this current from May to July is a density-induced
gravitational circulation. Since the river discharge gradually increases
in summer, more low salinity water ﬂows from the east side into the
Iyo-nada in the surface layer while saline water from ocean side ﬂows
through the Bungo Channel to the Hayasui Strait in the bottom layer.
Meanwhile, the temperature in the surface of the Iyo-nada is higher
than that in the Hayasui Strait due to strong thermal stratiﬁcation in thenada. As stated in the model results, owing to the coupled eﬀects of thethermal and saline diﬀerences, the density diﬀerence between surfaces

Fig. 16. Vertical distribution of density (kg m−3, black lines), vertical eddy viscosity (log10Az, m2 s−1, color), and the current along section AB (m s−1, arrows) in
Iyo-nada in (a) April, (b) May, (c) June, and (d) July.
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acceleration of temperature increase rate in the BCW of the Iyo-nada.
The accelerating advection of heat by the gradually intensifying
gravitational circulation to the BCW in the bottom layer of the Iyo-nadafrom April to July demonstrates the importance of advection of heat for
the large temperature increase in the BCW. The temporal variation of
advection of heat also induces variation in the temperature increase
rate inside the BCW.

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5. Conclusions
In many coastal regions, BCW is usually found in the areas wheretidal mixing is relatively weak, such that it cannot transport suﬃcientheat from sea surface to the bottom water. The temperature increase of
BCW from spring to summer has been thought to be due to limited
downward heat transport from the thermocline. In some wide regions,such as the North Sea and Yellow Sea, where thermal stratiﬁcation is ina place over a range of hundreds of kilometers, the temperature increase in the BCW is mainly due to vertical diﬀusion of heat through thethermocline and thereby, the temperature increase is small (~1 °C)
from spring to summer. However, in some relatively smaller regions,such as in the Irish Sea and the nadas in the Seto Inland Sea, wherestratiﬁcation above the BCW is strong, advection from surrounding
warm water transports heat to the BCW. Consequently, the temperature
increase of the BCW from spring to summer is relatively large (7–10 °C).
Moreover, the relative contribution of the advection and vertical diffusion to the change in water temperature diﬀers by region. For example, in the Irish Sea, the advection and vertical diﬀusion play comparable roles in the warming of the BCW. In contrast, advection
contributes as twice of vertical diﬀusion to the warming of BCW in Iyonada in the Seto Inland Sea.
Advection of heat changing with time can produce variation in thetemperature increase rate inside the BCW. As demonstrated in the Iyonada, advection of heat is associated with gravitational circulation fromthe Hayasui Strait to the BCW in the bottom layer, which intensiﬁes
with increased river discharge and thermal stratiﬁcation from spring tosummer. This makes the temperature increase rate of the BCW accelerate from April to July.
Acknowledgements
This study was supported by the Japanese Ministry of Agriculture,
Forestry and Fisheries through the research project ‘Development oftechnologies for mitigation and adaptation to climate change inAgriculture, Forestry and Fisheries’ and by grants from the Japanese
Ministry of Education, Culture, Sports, Science and Technology (MEXT)
to national university corporations for Joint Usage/Research Center. X.
Guo is supported by JSPS KAKENHI Grant number JP17H01860. The
data used in this paper are available on request to the corresponding
author.
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