water
ArticleLong-Term Trend and Inter-Annual Variation of Ocean Heat
Content in the Bohai, Yellow, and East China Seas
Min Yang 1 , Xinyu Guo 2, * , Junyong Zheng 2,3
1
2
3

4

*

Citation: Yang, M.; Guo, X.; Zheng, J.;
Sun, Q. Long-Term Trend andInter-Annual Variation of Ocean Heatand Qun Sun 4

Graduate School of Science and Engineering, Ehime University, 3 Bunkyo-Cho, Matsuyama 790-8577, Japan
Center for Marine Environmental Studies, Ehime University, 2-5 Bunkyo-Cho, Matsuyama 790-8577, JapanKey Laboratory of Physical Oceanography, Ocean University of China, 238 Songling Road,
Qingdao 266100, China
College of Marine and Environmental Sciences, Tianjin University of Science and Technology,
1038 Dagu Nanlu, Tianjin 300457, China
Correspondence: guoxinyu@sci.ehime-u.ac.jp; Tel.: +81-(089)-927-9824

Abstract: The long-term trend and interannual variation of ocean heat content (OHC) in the Bohai
Sea, Yellow Sea, and East China Sea (BYECS) were examined using 27 years (1993–2019) of daily
reanalysis data from the Japan Coastal Ocean Predictability Experiment 2 (JCOPE2M). The annual
mean OHC was 4.25 × 1021 J, with a linear warming rate of 0.13 W m−2 with a confidence level of 95%.
The spatial distributions for the annual and linear trends of OHC in the BYECS were inhomogeneous,and a considerable quantity of heat was stored on the outer shelf. The warming rate was considerably
elevated in the areas northeast of Taiwan and southwest of Kyushu, showing a rate greater thanthat of the Pacific and global oceans by a factor of 4–5. Heat budget analysis indicated that the
Taiwan Strait (TAS) is the dominant source of heat for the BYECS. The mechanisms of the OHC
interannual variation in the outer and inner shelves varied. On the outer shelf, the OHC interannual
variation was dependent on the Kuroshio onshore intrusion, while on the inner shelf, the OHC
interannual variation was related to the variation in air-sea heat flux. The rapid warming in the outer
shelf corresponded to the increasing trends of heat transport across northeast Taiwan and southwest
Kyushu, which were dominated by the temporal variation of current velocity.

Content in the Bohai, Yellow, andEast China Seas. Water 2022, 14, 2763.
https://doi.org/10.3390/ w14172763

Keywords: Kuroshio intrusion; oceanic heat transport; air-sea heat flux; ocean heat budget; ocean
model; variance analysis

Academic Editors: Ioannis
Panagiotopoulos, Serafeim E. Poulos
and Vasilios Kapsimalis

1. Introduction
Received: 14 July 2022
Accepted: 31 August 2022
Published: 5 September 2022
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Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
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distributed under the terms andconditions of the Creative Commons
Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

As a heat reservoir, the global ocean accumulates excess heat as a result of greenhousegas emissions from anthropogenic activities [1]. The global ocean heat content (OHC)
indicates mean warming at a rate of 0.35 W m−2 from 1955 to 2019. This rate is averaged
over the global oceanic surface, and the mean rate since 1990 has increased to approximately
0.61 W m−2 [1–3]. Despite the rapid warming of the global ocean surface, the OHC warming
rate has never been observed to be spatially uniform. The western boundary current
regions have been reported to have a particularly elevated warming rate [4–6]. Specifically,
marginal seas, which are highly sensitive to climate change, show a much greater warming
rate than open oceans [7,8]. The Sea of Japan, a marginal sea in the northwest Pacific Ocean,for example, was observed to have a mean OHC warming rate that was two times that of
the Pacific Ocean from 1976 to 2007 [5].
The Eastern China Seas, which include the East China Sea (ECS), the Yellow Sea, andthe Bohai Sea, also marginal seas located in the northwest Pacific Ocean are bound by the
200 m isobaths (BYECS, Figure 1). The ECS has also been observed to have a warming
trend during the last century [9,10]. Long-term sea surface temperature (SST) data havebeen widely used to examine the rapid ECS warming [11–13]. The mechanism responsible
for the SST rise in the ECS was examined using both observational and reanalysis data. The

Water 2022, 14, 2763. https://doi.org/10.3390/w14172763

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warming SST has been demonstrated to be controlled by an increase in ocean advection
and local atmospheric forcing [10,13–15].

Figure 1. Annual-mean sea surface current distribution in the Bohai Sea, Yellow Sea, and East China
Sea (BYECS, black arrows). The study region (BYECS) is closed with three lines indicating the Taiwan
Strait (TAS), shelf break section (SBS, 200-m isobath), and Tsushima Strait (TUS). Between each set ofadjacent red dots on the black lines, there are 20 grid points. The grid points are counted from south tonorth. Arrows across these black lines represent heat (volume) transport across the sections measured
in ×1014 W (Sv, ×106 m3 s−1 ). Gray contour lines represent the 100-m isobaths, the Kuroshio enters
the East China Sea from the East Taiwan Channel (ETC).

Compared to SST data, OHC data indicate a larger signal-to-noise ratio and are lessinfluenced by natural variability [16]. OHC is more suitable for investigating the temporalvariation of ocean warming over the water column than SST [1,17]. However, few studies
have focused on OHC on the BYECS shelf [18]. To analyze the OHC budget and thecause for its variation, a combined assessment of the heat transport from both the lateralboundaries and the air-sea heat fluxes were required.
The change of OHC in the BYECS is determined by heat transport through the lateralboundaries and air-sea heat flux [19,20]. As for the lateral boundaries, the BYECS exchanges
heat with the surrounding seas principally through the shelf-break section (SBS, usually
defined by the 200 m isobaths), Taiwan Strait (TAS), and Tsushima Strait (TUS). Alongthe SBS, water exchange between the Kuroshio and shelf was responsible for a substantial
portion of the heat transport. The Kuroshio Current enters the ECS from the East Taiwan
Channel (Figure 1) and intrudes onto the ECS shelf, mainly in the northeast of Taiwan andsouthwest of Kyushu [21,22]. Warm water from the South China Sea is also transported
into the ECS through the TAS, and eventually, the Tsushima warm current envelops thisexternal water and heat from the BYECS to the Sea of Japan through the TUS. The waterexchange between the ECS and the surrounding seas through these three sections has been
discussed [21,23,24], and some studies have evaluated heat transport [25,26]. Using a global
ocean model, Liu et al. [25] reported that the time-averaged heat transport through the TAS,

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TUS, and SBS was 2 × 1014 , 2.1 × 1014 , and 0.5 × 1014 W, respectively. In addition, the heattransport into the ECS also showed interannual variations [27], which potentially regulated
the interannual variation of OHC in the ECS.
To better understand warming in the ECS, the OHC, and BYECS shelf heat budgets
were calculated using the Japan Coastal Ocean Predictability Experiment 2 (JCOPE2M)
reanalysis data. The interannual variation and warming trend of the BYECS from 1993 to2019 were discussed from the perspective of OHC.
2. Materials and Methods
2.1. JCOPE2M Reanalysis Data
In this study, daily hydrodynamic data were obtained from JCOPE2M, which isoperated by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC).
This model, based on the Princeton Ocean Model with a generalized sigma coordinate(POMgcs) [28], is a three-dimensional, eddy-resolving, and data-assimilative ocean model.
The model domain covers the Northwest Pacific (10.5–62◦ N, 108–180◦ E) with a horizontal
resolution of 1/12◦ for meridional and zonal directions and a vertical resolution of 47 sigma
layers, which could reproduce the Kuroshio, a strong western boundary current in thenorthwestern Pacific. The bottom topography is from 1/12◦ global height data, referred to
as GETECH DTM5, with an additional boundary condition for which the minimum andmaximum depths are 10 m and 6500 m, respectively. Notably, the 1/12◦ bottom topography
data used by Uehara et al. [29] are embedded in the Eastern China Seas.
The JCOPE2M model was driven by the atmospheric forcing of wind stresses, heat,and salt fluxes at the sea surface. The wind stress and heat flux fields were calculated from
6-hourly National Centers for Environmental Prediction/National Center for AtmosphericResearch (NCEP/NCAR) reanalysis data using bulk formulas [30,31]. The merged satellite
and in-situ global daily SST (MGDSST) data were employed for surface heat flux correction.
The salinity at the surface was restored to the monthly mean climatology data on a 30-day
timescale after importing precipitation and evaporation data from the NCEP/NCAR reanalysis data. Using the one-way nesting method [32], the lateral boundary condition ofthis model was determined by an outer model, which has a 1/4◦ horizontal resolution and21 sigma levels in the vertical direction. It encompasses almost the entire North Pacific
Ocean (30◦ S–62◦ N, 100◦ E–90◦ W). Sea surface temperature data from remote sensing andtemperature/salinity profiles from in situ observations were assimilated into the JCOPE2M
model through the multi-scale three-dimensional variational scheme method. This method
promises effective simulation of ocean conditions in the western North Pacific. Notably,
there is no assimilation of in-situ profiles in the shelf region of the BYECS [33].
The JCOPE2M and its outer model were spun up for 5 and 15 years, respectively.
Reanalysis calculations from November 1992 were performed for both models using data
assimilation and external forcing. More details on the model parameters are described byMiyazawa et al. [33,34]. In this study, the daily mean water temperature, salinity, and two
horizontal velocity components from 1993 to 2019 were provided for the following analysis.
2.2. Methods
2.2.1. Calculating the OHC
The OHC in the BYECS is vertically integrated from the sea surface to the sea bottom,
as follows:
Z
0

OHC =

−H

c p ρ( x, y, z)t( x, y, z)dz

(1)

where H is the maximum water depth at each grid point, cp = 3996 J kg−1 ◦ C−1 is the
specific heat capacity of seawater, and ρ (kg m−3 ) and t (◦ C) are the potential density andtemperature of seawater, respectively. The terms x and y are the horizontal coordinates andz is the vertical coordinate. dz is the vertical interval of the grid points. After obtaining the
OHC in each grid point, the total OHC (OHCT ) in the BYECS is then calculated by an area
integral of OHC.

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The change in the total OHC over the BYECS (OHCT ) is defined as the sum of the
air-sea heat flux (QN ) and heat transport through the lateral boundaries (QV ):∂OHCT= − Q N + QV
∂t(2)

2.2.2. Calculating the Heat Transport
Heat exchange in the BYECS with the surrounding seas mainly occurs through the
SBS, TAS, and TUS (black lines in Figure 1). The inflow heat transport (IHT), outflow heattransport (OHT), and net heat transport (NHT) were calculated as follows:x
IHT =c p ρ( x, y, z)t( x, z)v+ ( x, z)dxdz
(3)
OHT =

x

NHT =

x

c p ρ( x, y, z)t( x, z)v− ( x, z)dxdz(4)c p ρ( x, y, z)t( x, z)v( x, z)dxdz(5)where dx is the horizontal interval of the grid points, v is the monthly velocity component
normal to the sections, v+ and v− denote the onshore and offshore directions, respectively.
2.2.3. Exacting the Interannual Signal
To characterize the interannual time series of OHC, the heat transport through thelateral boundaries, and the air-sea heat flux, the following steps were conducted on theoriginal daily data: (1) the daily variables were averaged to obtain a monthly-mean timeseries; (2) the anomalies observed in these monthly mean data were obtained by subtracting
the annual mean values; (3) the seasonal variations were removed from the monthly
anomalies by subtracting the climatological monthly mean values; (4) the linear trend,
as captured using least squares method, was removed from the monthly anomalies; andfinally, (5) the intraseasonal variations were removed from the monthly perturbations byapplying a 13-month running mean. The resultant single interannual variations for theoriginal time series were utilized for subsequent analysis.
3. Results and Discussion
3.1. Model Validation
The BYECS study area is shown in Figure 1. The annual mean current at the sea
surface showed a marked contrast in spatial distribution. The Kuroshio Current, with avelocity of ~1 m s−1 , enters the ECS from the east of Taiwan, and the main flow turns
northeastward and flows along the 200 m isobaths (black curve line in Figure 1), veers east
around 30◦ N, 129◦ E, and finally exits the ECS through the Tokara Strait. Meanwhile, thenearshore Kuroshio branch intrudes onshore via the 200 m isobaths and soon returns to the
Kuroshio mainstream. The Kuroshio Current transports large amounts of warm water fromlow latitudes and contributes considerably to the BYECS heating process. Furthermore,currents such as the Taiwan Strait Current, China Coastal Current, and Tsushima Warm
Current can also be identified in the distribution of surface currents.
The validation of the current velocity from the JCOPE2M was performed by comparing
the data on annual mean volume transport through the SBS, TAS, and TUS with thoseobserved in previous studies (Table 1). In the JCOPE2M model, the annual mean net
volume transport was 1.33, 1.30, and 2.67 Sv through the TAS, SBS, and TUS, respectively.
The negligible discrepancy with the observations confirms the reliability of the JCOPE2M
results for the mean-state transport.

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Table 1. Comparison of long-term averaged transport through the SBS, TAS, and TUS observed inprevious studies and modelled by the JCOPE2M.
Model/Sv

Obs./Sv

References

Shelf break section

1.3

1.4

[35]

Tsushima Strait

2.67

2.3–2.7
2.64
2.65

[36]
[37]
[38]

Taiwan Strait

1.33

1.8
1.2

[39]
[35]

We compared the annual mean seawater temperature in the BYECS from JCOPE2M
reanalysis data with WOA2018 data [40], which collected the temperature based on profile
data from the World Ocean Database, at both the sea surface and 124◦ E section (Figure 2).
The JCOPE2M model was skilled at capturing the basic features of the observations of SST
and vertical distribution. The SST was higher in the southeast of the BYECS and decreased
toward the northwest region (Figure 2a,b). The intrusions of warm water from northeast
Taiwan and southwest Kyushu in the observations can also be found in the model results.
The vertical profile in both models and observations indicated an elevated temperaturefrom the sea surface to a depth of −200 m in the Kuroshio mainstream at 25◦ N, andupward cold water from the bottom at 27◦ N and north of 35◦ N (Figure 2c,d).

Figure 2. Climatology of water temperature. (a,c) are the annual-mean (2005–2017) temperature
distributions at the sea surface and 124◦ E from the JCOPE2M reanalysis data, respectively. (b,d) areplots of the same, but from the WOA2018 dataset. The red line in (a) denotes the section at 124◦ E.

3.2. Spatial Distribution of OHC in the BYECSBased on the JCOPE2M reanalysis data, the annual mean (1993–2019) OHC over the
BYECS shelf is 4.25 × 1021 J. Figure 3a,b show the annual mean and standard deviation for
the OHC in the upper 200 m of the BYECS. The spatial pattern of OHC was not uniform
over the BYECS, and the OHC in the southeastern BYECS was greater than that in the innershelf by at least one order of magnitude. The maximum OHC was principally found inareas northeast of Taiwan and southwest of Kyushu, which are the two main pathways forKuroshio intrusion over the shelf [21,22]. The distribution of the standard deviation wasWater 2022, 14, 2763

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similar to the annual mean OHC, indicating a larger interannual fluctuation in the region
where the Kuroshio onshore intrusions occurred.

Figure 3. (a) Annual mean (×109 J m−2 ), (b) standard deviation (×108 J m−2 ), and (c) linear increasing trend (W m−2 ) of the OHC in the BYECS over the 1993–2019 period from the JCOPE2M
reanalysis data.

To examine the results from the JCOPE2M analysis data, the OHC in the BYECS
shelf was also calculated by another reanalysis data from 1993 to 2015, the FORA-WNP30(http://synthesis.jamstec.go.jp/FORA/index.html, accessed on 11 March 2020), with ahorizontal resolution of 1/10◦ . The annual mean OHC over the shelf was 3.93 × 1021 J, andthe spatial distribution of OHC in the BYECS shelf from the FORA data was similar to thatfrom the JCOPE2M data (the figures were not shown).
Figure 3c showed the linear trend of OHC in the BYECS shelf from 1993 to 2019, andthe annual mean warming trend was 0.13 W m−2 with a confidence level of 95%. The OHC
warming trend in the BYECS shelf from the FORA data (1993–2015) was 0.24 W m−2 , which
was about twice the warming rate calculated by the JCOPE2M. The linear trend in the BYECS
was slightly smaller than that of the global ocean OHC during 1990–2019 (0.61 W m−2 ,Garcia-Soto, et al. [1]).
The spatial pattern for the linear trend indicates inhomogeneous warming and coolingchange in the shelf. The trend showed a positive value in a wide region of the shelf, especially in regions northeast of Taiwan and southwest of Kyushu. The maximum warming
rate was about 0.93 W m−2 , which was approximately greater than that of the Pacific andglobal oceans by a factor of 4–5. In addition, the OHC also has an elevated warming trend in
the central Yellow Sea and to the east of the Yangtze River estuary. The associated warming
rate was approximately greater than that of the Bohai Sea by a factor of three. However, the
OHC in the middle of the 200 m isobaths showed a cooling trend, although the cooling rate
was less than the warming rate in the areas northeast of Taiwan and southwest of Kyushu.
3.3. OHC Heat Budget
3.3.1. Heat Transport across the Lateral Boundaries
The annual mean heat transports are 1.32 × 1014 , 0.87 × 1014 , and −1.92 × 1014 W acrossthe TAS, SBS, and TUS, respectively (Figure 1). The heat transfer by the TAS contributed
more heat to the shelf than the SBS. A previous study showed a similar annual mean
strength of heat transport from 1980–2009 was found across the SBS (1.23 × 1014 W) andTUS (−1.8 × 1014 W) in the results based on the ROMS ocean model, but the heat transport(0.82 ×10 14 W) through the TAS was smaller than that across the SBS [41], which wasreversed in this study.
The SBS followed the 200 m isobaths. The grid point numbers were provided as horizontal coordinates. The vertical variation in heat transport across the SBS was smaller thanthat in the horizontal direction (Figure 4a), which was similar to the velocity distribution
at these grid points [24]. The heat transport was from the onshore direction from the sea

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surface to the bottom at grid points 5–40, 80–100, and 135–160 but in the offshore direction
at gird points 42–56, 70–80, and 160–180. These three onshore intrusion locations have beenreported by previous research [22,24,32]. The remarkable heat intrusion occurred in theupper 50 m in the northeast of Taiwan (grid point 5–40) with a maximum onshore velocity
greater than 20 cm s−1 . This was followed by onshore intrusion in the area southwest of
Kyushu (grid point 135–160) and the middle of the shelf break (grid point 80–100).

Figure 4. (a) Vertical distribution of the annual-mean heat transport across the SBS. (b,c) are identicalplots for the TAS and TUS, respectively. The locations of these three sections are provided in Figure 1.

The heat transport vertical structure from the TAS was uniform, the northward transport mainly occurred to the east of the TAS (grid point 20–25, Figure 4b), and the magnitudeof the heat transport was greater than that in the northeast of Taiwan along the SBS. The
total net heat transport through the TAS was also greater than that through the SBS owing
to the offshore heat transport from the shelf to the open ocean across the SBS in somewater columns.
Heat loss originating from the TUS occurred mainly in the western channel of the TUS(Figure 4c). The strength of the western intrusion across the TUS was significant, and thenet heat loss from the TUS was approximately twice that of the onshore intrusion throughthe SBS.
3.3.2. Air-Sea Heat Exchange
The air-sea heat flux (QN ) is the sum of shortwave radiation, longwave back radiation,and sensible and latent heat fluxes. As an external heat source, QN also modulates the OHCof the BYECS through heat exchange over the air-sea interface. The annual mean air-sea
heat flux in the BYECS calculated from the JCOPE2M is −0.22 × 1014 W, indicating heattransfer from the BYECS to air. Figure 5a presents the annual mean (1993–2019) air-sea heat
flux from the JCOPE2M reanalysis data. QN is positive for almost the entire BYECS, whichindicates net heat loss from the BYECS to the atmosphere on the mean-state timescale. The
net heat loss was especially remarkable in areas northeast of Taiwan and southwest of
Kyushu, which was balanced by the heat gain from the Kuroshio onshore intrusion. The
annual mean standard deviation was also elevated in these two regions (Figure 5b).
Figure 5c shows the linear trend for the air-sea heat flux on the BYECS shelf from1993 to 2019. The spatial pattern of the linear trend had many positive values, whichindicated a heat loss trend for the majority of the BYECS shelf. Air-sea heat exchange inareas northeast of Taiwan and southwest of Kyushu indicated a rapid heat loss trend but
showed a sow heat loss trend in the middle of the SBS. In addition, a downward heat gainof the air-sea heat flux was observed in the central Yellow Sea. The distribution of the linear
trend of the air-sea heat flux was similar to the linear OHC trend.

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Figure 5. (a) Annual mean (W m−2 ), (b) standard deviation (W m−2 ), and (c) linear trend(W m−2 month−1 ) for the air-sea heat flux in the BYECS during the 1993–2019 period from the
JCOPE2M reanalysis data.

The ocean currents through the three lateral boundaries contribute to a net heat gain
for the BYECS, which are balanced by the upward air-sea flux. According to Equation (2),the OHC tendency was dominated by the air-sea heat flux (QN ) and meridional transportof ocean currents (QV ). The net heat loss from air-sea exchange and the net heat gainfrom ocean currents was of the same order of magnitude. The difference between theheat transferred by each mechanism was less than the annual mean OHC by two ordersof magnitude.
3.4. Interannual OHC Variation in the BYECS
Figure 6 showed the interannual variations in the OHC, heat and volume transport
across the lateral boundaries, and the sea heat flux in the BYECS shelf. From the viewof the entire shelf integration, the OHC suggested a remarkable correlation with the airsea heat flux, with a negative correlation coefficient of −0.55. The OHC was apparently
larger in 1998–1999 and 2007, and smaller in 1996 and 2011 (Figure 6a), and these years
corresponded to a downward (negative) and upward (positive) air-sea heat flux (Figure 6d),respectively. The interannual variation in heat transport through the SBS was greater thanthat across the TAS and TUS, particularly during 2004 and 2005 (Figure 6b). The years
with an increase in the Kuroshio onshore intrusion and inflow from the TAS (Figure 6c)
facilitated an OHC increase, although the correlation coefficients between the OHC and thetwo sections were low.
Considering the inhomogeneous OHC spatial distribution, which was approximately
one order of magnitude greater in the outer shelf (between the 100 m and 200 m isobaths)
compared to the inner shelf (shallower than 100 m) (Figure 3a), we inferred that themechanisms responsible of the interannual variations of OHC in the outer and inner
shelves were different. The OHC and air-sea heat flux in the outer and inner shelves
were integrated between 100 m and 200 m isobaths and isobaths shallower than 100 m,
respectively. Correlation analysis showed that the correlation coefficient between the
OHC in the outer shelf and the heat transport across the whole SBS was not high enough(0.3), while the coefficients increased significantly when northeast Taiwan and southwest
Kyushu were analyzed separately. The exchange of inflow of Kuroshio and outflow of
the shelf water in the middle SBS may have an impact on the correlation analysis [24].
Figure 7a indicates that the OHC in the outer shelf showed interannual dependency on theinterannual variation of heat transport through northeast Taiwan and southwest Kyushu.
At a 99% confidence level, the correlation coefficient between the OHC and heat transport
across northeast Taiwan was 0.47 with a lag of three months. The correlation coefficient
between OHC was 0.37 for heat transport across southwest Kyushu which had no timelag. The correlation between the OHC and air-sea heat flux in the outer shelf decreased

Water 2022, 14, 2763

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to −0.14, although the correlation over the entire shelf was greater (−0.55). Therefore, the
OHC interannual variation in the outer shelf was principally modulated by the Kuroshio
onshore intrusion across northeast Taiwan and southwest Kyushu.

Figure 6. (a) Interannual OHC variation integrated over the BYECS from 1993 to 2019. (b) Interannual
variation of heat transport across the SBS (orange solid line), TUS (gray solid line), and TAS (bluesolid line). (c) Interannual variation of volume transport across the SBS (orange solid line), TUS (graysolid line), and TAS (blue solid line). (d) Interannual variation of air-sea heat flux integrated overthe BYECS.

Figure 7. (a) Interannual OHC variations (×1019 J, black solid line) and air-sea heat flux (×1013 W,
gray dash line) integrated over the outer shelf of the BYECS, heat transport (×1014 W) across the
SBS northeast of Taiwan (orange solid line) and that located southwest of Kyushu (blue solid line).
(b) Interannual OHC variations (×1020 J, purple solid line) and air-sea heat flux (×1013 W, gray dashline) integrated over the inner shelf of the BYECS.

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In the inner shelf, the interannual variation of OHC was highly related to the air-sea
heat flux (Figure 7b), the correlation coefficient was −0.58, and the variation of OHC
lagged the variation of the air-sea heat flux by six months at a 99% confidence level. The
dependency on the air-sea heat exchange increased compared to that over the entire shelf.
The correlation between the OHC in the inner shelf and heat transport through the SBS
was low. Therefore, the interannual OHC variations in the BYECS inner shelf were mainly
associated with air-sea heat exchange. These different mechanisms of the interannual
variations in the outer and inner shelves were consistent with the conclusions from theobservation data and ROMS model results [13].
3.5. Long-Term Trend of OHC in the BYECS Outer Shelf
The linear trend of heat transport through the 200 m isobaths is shown in Figure 8. The
onshore heat transport rates in areas northeast of Taiwan (grid points 1–27) and southwestof Kyushu (grid point 140–168) were remarkably elevated, which enabled rapid warmingof the OHC in the outer shelf (Figure 3c). The trend regarding heat transport in the middleof the SBS indicated slower heat transport into the shelf, which may contribute to the OHC
cooling trend in the middle SBS (Figure 3c).

Figure 8. The trend of vertical-integrated heat transport at each point along the SBS.

The heat transport across these sections was determined by both current velocity
and water temperature. To investigate their contribution to long-term variation in heattransport, we decomposed the temporal variance of heat transport into six terms [42].
The velocity (Vi ) and water temperature (Ti ) across one section can be described as thesum of the annual mean values (V, T) from 1993 to 2019 and anomalies (V’, T’). Vi and Ti
are calculated as follows:
Vi = V + Vi0 , Ti = T + Ti0
(6)
V=

1 N
1 N
Vi , T =Ti∑
N i =1
N i∑
=1

(7)

where N = 324 is the number of months analyzed, and i is the time index. Then the heat
flux (Qi = Vi Ti ) can be expressed as:
Qi = VT + VTi0 + Vi0 T + Vi0 Ti0(8)Then, the annual mean heat flux (Q) is calculated as:
Q = VT +1 N 0 0
Vi Ti
N i∑
=1

(9)

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When defining a new term Gi = Vi ’Ti ’, we have:
1 N 0 0
Vi Ti
N i∑
=1

(10)

Q = VT + G

(11)

G=
Then,
2 ):
The variance of heat flux (σQ
2
=
σQ

1 N
( Q i − Q )2
N i∑
=1

(12)

Substituting Equations (8) and (9) into Equation (12), the heat flux variance may be
expressed as:
2

2

2
2
2
2
σQ
= T σV2 + V σT2 + 2TVσTV+ 2TσVG+ 2VσTG
+ σG2

(13)

where,
1 N
1 N
2 2
V
)
,
σ
=
(
V
−
i
∑ (Ti − T )2
T
N i∑
N
=1
i =1

(14)

1 N
1 N
2
V
−
(Vi − V )( Gi − G )
VT
−
T,
σ
=
i
i
VG
N i∑
N i∑
=1
=1

(15)

1 N
1 N
Ti − TGi − G, σG2 =( Gi − G )2∑
N i =1
N i∑
=1

(16)

σV2 =
2
σTV
=

2
σTG
=
2

2

T σV2 denotes the mean water temperature and variance of velocity; V σT2 denotes the2 denotes the mean velocity, mean
mean velocity and variance of water temperature; 2TVσTV
2 denotes thewater temperature, and covariance of velocity and water temperature; 2TσVG
2mean water temperature and covariance of velocity; Gi ; 2VσTG denotes the mean velocity
and covariance of water temperature; and Gi ; σG2 is the variance of Gi .
Figure 9a shows the variance of heat transport across the SBS and Figure 9b–g pre2
sented six terms on the right-hand side of Equation (13). The term of T σV2 accounts for2
the most prominent variation in heat transport (σQ ). In the northeast of Taiwan (gridppoints 5–40), the heat transport from the Kuroshio intrusion is principally determined by
2 and 2TVσ2 also havethe temporal variation of the current velocity. The terms of 2TVσTVTV
2an effect on the heat flux, although they are smaller than the term of T σV2 .
The variances of heat transport across the TAS and TUS and the corresponding six
terms were in Figures 10 and 11. For TAS, the variance of heat flux was large on the east2
side of the TAS (Figure 10a), and it was remarkable that the term of T σV2 (Figure 10b) was
the dominant component in the variance of heat transport. The variance of heat transport
2
through the TUS was remarkable in the west of the TUS (Figure 11a), and the term of T σV2
contributes most of the temporal variation of the heat flux (Figure 11b).
Analysis of the heat transport variance across the SBS, TAS, and TUS confirmed thatthe temporal variation in current velocity played a decisive role in the long-term trends ofheat transport inflow and outflow of the lateral boundaries, and the covariance of velocity
and water temperature also contributed to the temporal heat transport variation.

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Figure 9. (a) denotes the total variance in heat transport across the SBS. (b–g) represent the six terms
decomposed using Equation (13).

Figure 10. (a) denotes the total variance in heat transport across the TAS. (b–g) represent the six terms
decomposed using Equation (13).

Figure 11. (a) denotes the total variance in heat transport across the TUS. (b–g) represent the six
terms decomposed using Equation (13).

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4. Conclusions
This study estimated the OHC for the BYECS shelf and examined its interannual
variation and long-term trends using the JCOPE2M reanalysis data from 1993 to 2019.
The annual mean OHC was 4.25 × 1021 J, with a linearly increasing warming trend of
0.13 W m− 2 . The annual OHC and linear trend in the ECS are distributed inhomogeneous,and a considerable quantity of heat is stored on the outer shelf, which is one order ofmagnitude greater than that on the inner shelf. The warming trend was also much more
rapid in the areas northeast of Taiwan and southwest of Kyushu compared to other regions,with a maximum warming rate of 0.93 W m− 2 , which was approximately greater than thatof the Pacific and global oceans by a factor of 4–5. However, the OHC in the middle of the
200 m isobaths showed a cooling trend. A heat budget calculation indicated that the annual
mean heat transports are 1.32 × 1014 , 0.87 × 1014 , and −1.92 × 1014 W across the TAS, SBS,
and TUS, respectively. Heat transport from the TAS contributes the greatest quantity ofheat to the BYECS. The net heat gain from the lateral boundaries was 0.27 × 1014 W, which
was balanced by the sea heat exchange. The net heat loss from the air-sea heat flux wasparticularly remarkable in areas northeast of Taiwan and southwest of Kyushu.
The interannual variation in OHC is discussed separately in the outer and inner
shelves. In the outer shelf (between 100 m and 200 m isobaths), the OHC interannual
variation was dependent on the Kuroshio onshore intrusion in the northeast of Taiwan
and southwest of Kyushu, whereas, in the inner shelf, the interannual variation of OHC
was highly related to the variation of the air-sea heat flux. The heat gain rate across the
SBS was remarkably high in northeast Taiwan and southwest Kyushu, which favored
rapid warming of the outer shelf. Temporal variance analysis of heat transport throughthe SBS demonstrated that the current velocity variation dominated the temporal variationof heat transport into the shelf. In addition, water temperature also contributed to heattransport variation.
Author Contributions: Conceptualization, X.G. and M.Y.; methodology, Q.S.; validation, M.Y.; formal
analysis, M.Y. and J.Z.; writing—original draft preparation, M.Y.; writing—review and editing, M.Y.
and X.G.; project administration, X.G.; funding acquisition, X.G. All authors have read and agreed tothe published version of the manuscript.
Funding: This study was supported by a Grant-in-Aid for Scientific Research (MEXT KAKENHI,
grant number: 20H04319, 22H05206).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: All sources of data are cited throughout the paper.
Acknowledgments: Yang, M. thanks the Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT) for supporting her stay in Japan.
Conflicts of Interest: All authors declare that they have no conflict of interest to disclose in thecontext of this study.

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