PUBLICATIONSJournal of Geophysical Research: Oceans
RESEARCH ARTICLE
10.1002/2015JC010739
Key Points:
 Concurrent simulation of tide andocean circulation in the North
Western Paciﬁc
 Modulation of M2 baroclinic tide byocean circulation
 Energy cycle analysis of baroclinic
tide

Correspondence to:Y. Miyazawa,
miyazawa@jamstec.go.jp
Citation:
Varlamov, S. M., X. Guo, T. Miyama,
K. Ichikawa, T. Waseda, and
Y. Miyazawa (2015), M2 baroclinic tidevariability modulated by the ocean
circulation south of Japan, J. Geophys.
Res. Oceans, 120, 3681–3710,
doi:10.1002/2015JC010739.
Received 20 JAN 2015
Accepted 13 APR 2015
Accepted article online 25 APR 2015
Published online 25 MAY 2015

M2 baroclinic tide variability modulated by the ocean
circulation south of Japan
Sergey M. Varlamov1, Xinyu Guo1,2, Toru Miyama1, Kaoru Ichikawa3, Takuji Waseda1,4,
and Yasumasa Miyazawa1
1

Application Laboratory, Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan, 2Center for Marine
Environmental Studies, Ehime University, Matsuyama, Japan, 3Research Institute for Applied Mechanics, Kyushu
University, Kasuga, Japan, 4Graduate School of Frontier Science, University of Tokyo, Kashiwa, Japan

Abstract We analyze a concurrent simulation result of the ocean circulation and tidal currents using adata-assimilative ocean general circulation model covering the Western North Paciﬁc with horizontal resolution of 1/368 to investigate possible interactions between them. Four sites of active M2 internal tide variability in open ocean (hot spots), such as Tokara Strait, Izu Ridge, Luzon Strait, and Ogasawara Ridge, aredetected from both the satellite observation and the simulation. Energy cycle analysis of the simulated M2
baroclinic tide indicates two types of the hot spots: dissipation (Tokara Strait and Izu Ridge) and radiation(Luzon Strait and Ogasawara Ridge) dominant sites. Energy conversion from barotropic to baroclinic M2
tides at the hot spots is modulated considerably by the lower-frequency changes in the density ﬁeld. Modulation at the two spots (Tokara Strait and Izu Ridge) is affected by the Kuroshio path variation together withthe seasonal variation of the shallow thermocline. At the other two sites, inﬂuence from changes in the relatively deep stratiﬁcation through the Kuroshio intrusion into South China Sea (Luzon Strat) and mesoscale
eddy activity (Ogasawara Ridge) is dominant in the modulation.

1. Introduction
The baroclinic (internal) tides, which involve vertical oscillations of the isopycnal surfaces, are activated by
the interaction between the barotropic (external) tide and bottom topography [Cox and Sandstrom, 1962;
Baines, 1973; Wunsch, 1975; Kantha and Tiereney, 1997]. They play a key role in dissipation of the barotropic
tides and mixing in the deep layer through their wave breaking and dissipation [Munk and Wunsh, 1998;
Qiu et al., 2012]. The satellite altimetry analysis reveals the wide distribution of the baroclinic tide by focusing on the stationary periodic (coherent) sea level variations with M2 semidiurnal tidal frequency [Ray and
Mitchum, 1996]. Some studies based on the ﬁeld observations suggest active interactions between the baroclinic tides and lower-frequency phenomena, which result in the time-dependent (incoherent) nature of thebaroclinic tide. The incoherence of the baroclinic tides is caused by their modulation through the variationsin the background stratiﬁcation and the changes of the phase speed caused by the ambient ﬂows [Eichet al., 2004; Chavanne et al., 2010; Zilverman et al., 2011].
Recent development of the ocean modeling includes concurrent simulations of tides and lower-frequency
ocean circulations in global [Arbic et al., 2010, 2012] and regional [Kartadikaria et al., 2011; Osborne et al.,2011; Jan et al., 2012; Kerry et al., 2014] scales. Those results demonstrate that the baroclinic tide variability
is affected by the spatiotemporally varying stratiﬁcation and ambient currents and it modiﬁes the mesoscalewater mass structures.

C 2015. American Geophysical Union.
V

Motivated by such simulation studies, using a state of art tide-resolving ocean general circulation model:
JCOPE-T, we examine the incoherence of the baroclinic tide variability south of Japan where both the baroclinic tide [Niwa and Hibiya, 2001, 2004, 2011] and mesoscale eddy [Pascual et al., 2006] variations are very
active. JCOPE-T is operationally utilized for the ocean state prediction at Japan Agency for Marine-Earth Sciences and Technology (JAMSTEC), and the visualization of the real-time prediction based on the latest version of JCOPE-T is available from the website: http://www.jamstec.go.jp/jcope/vwp/. This model
demonstrates some skills representing the complicated ocean current variations associated with the interactions among the wind-driven, tidal, river discharge, and open ocean currents [Miyazawa et al., 2012, 2013].

All Rights Reserved.

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We focus on the modulation of the baroclinic tideenergetics in some areasof their active generationby the lower-frequency
ocean circulation processes, which topic has
not been fully investigated until now. The previous studies analyzing
the baroclinic tide energetics in the Western
North Paciﬁc did notinclude the ocean general circulation dynamics
in their simulations [Niwaand Hibiya, 2001, 2004,
2011; Kerry et al., 2013]. A
few studies recently
showed that the presence of Kuroshio and/or
mesoscale eddies [e.g.,
Jan et al., 2012; Kerryet al., 2014] modulate
both the generation andpropagation of the baroclinic tidal energy undersome idealized situations.
In this study, we elucidate
the temporal dependFigure 1. Topography of the JCOPE-T model domain. Thick (thin) contours denote shorelines (isoence of the M2 baroclinic
depth line with 200 and 2000 m). The abbreviations represents locations (S, South China Sea; Ls,
Luzon Strait; Ry, Ryukyu Islands Chain; Og, Ogasawara Ridge; Es, East China Sea; Tk, Tokara Strait; Iz,
tide energy budget in
Izu Ridge; Ys, Yellow Sea; and Js, Japan Sea).
active generation sites ofthe baroclinic tide southof Japan on the spatiotemporal changes in the background stratiﬁcation, which are driven by the lowerfrequency ocean general circulation processes including the Kuroshio and mesoscale eddies representing
the realistic behaviors allowed by the data assimilation.
This paper is organized as follows. Section 2 provides a description on the tide-resolving, operational ocean
general circulation model for the Western North Paciﬁc, JCOPE-T, and reports the validation of the M2 baroclinic tide using the Jason-2 satellite altimeter data. Section 3 describes the M2 baroclinic tide energetics
using the simulation data from sensitivity experiment simulations designed for investigation of the modulation of M2 baroclinic tide. The incoherent M2 baroclinic tide variability induced by changes in the background stratiﬁcation is discussed in section 4. The ﬁnal section is devoted to summary. Appendices describe
the tidal forcing scheme of our model (Appendix A) and the validation of the simulated M2 tide using theJason-2 data, a barotropic tide model used for providing the tidal forcing of our model, and the tide gauge
data (Appendix B).

2. Tide-Resolving Ocean Circulation Simulation
We conducted a 1 year reanalysis simulation using a tide-resolving general circulation model (JCOPE-T) thatwas developed based on the Princeton Ocean Model with a general coordinate of sigma (POMgcs) [Mellor
et al., 2002]. JCOPE-T has a horizontal resolution of 1/368 and 46 generalized sigma layers and covers a partof the Western North Paciﬁc: 178N–508N and 1178E–1508E (Figure 1) nested in an outer model, JCOPE2[Miyazawa et al., 2009]. Note that another version of JCOPE-T covering a smaller region: 288N–448N, and 1258E–

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1488E has been used forthe investigation of theradionuclide
dispersion
around Japan [Miyazawa
et al., 2012, 2013]. The
outer model (JCOPE2)
with no-tide provides thedaily mean information on
the open boundary of
JCOPE-T using a one-way
nesting technique [Guoet al., 2003; also see
Appendix A].
We modify the original
POMgcs to implement a
fourth order baroclinicpressure gradient scheme[McCalpin, 1994; Berntsen
and Oey, 2010] and a
ﬂux-corrected transport
scheme for tracer advection [Boris and Book, 1973]
instead of the second
order pressure gradientand the central difference
advection schemes, respectively. In addition, we
include the lateral horizontal diffusion along not a
sigma-level but along a zFigure 2. Amplitude (in m) of M2 surface tidal elevation in the JCOPE-T simulation. Black lines denote
level to avoid formation oflines of constant phase with 308 interval.
erroneoustemperatureand salinity values near the steep bottom topography. The horizontal viscosity coefﬁcient for the harmonic
schemes is evaluated using the Smagorinsky’s [1963] formula with a constant of 0.3, and horizontal diffusion
coefﬁcient is ﬁxed as 50 m2 s21. The vertical viscosity and diffusion processes are also described by the harmonic
schemes with the coefﬁcients calculated using the Mellor-Yamada’s level 2.5 turbulent closure model [Mellor
and Yamada, 1982] modiﬁed by the inclusion of the surface wave breaking effects [Mellor and Blumberg, 2004].
The usual bottom stress scheme originally included in the Princeton Ocean Model [see Mellor, 2002, equation(14)] effectively works for reasonable representation of the bottom friction except for biases to the observed sea
level amplitude of the tide in some part of the nearshore region (Appendix B).
The model is driven by the surface momentum, heat, and freshwater ﬂuxes calculated by an algorithm proposed by Li et al. [2010] with use of modeled sea surface temperature and hourly atmospheric data provided from National Centers for Environmental Prediction Global Forecast System (NCEP GFS) as 6 hanalyses and hourly forecasts. Details of the tidal forcing are described in Appendix A. Lateral freshwater
inputs from 47 major Japanese rivers, 3 rivers on the Korean Peninsular, 1 Taiwan river, and 7 Chinese main
land rivers are accounted by JCOPE-T. Monthly mean volume ﬂuxes of the river discharges [Ministry of Land,
Infrastructure, Transport, and Tourism, 2002; Wang et al., 2008; see the Global River Discharge Database,
http://www.sage.wisc.edu/riverdata/] are speciﬁed for the grid boxes corresponding to the river mouths.
River water is assumed to have zero salt content and temperature equal to maximum of air temperature orwater freezing temperature (08C). Inﬂow is going to upper model layers corresponding to river mouth depth(default 5 m).
Observed features of geostrophic phenomena including the Kuroshio and mesoscale eddies are involved in
JCOPE-T through a nudging of temperature and salinity ﬁelds to those provided by the data-assimilative

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JCOPE2 model [Miyazawa
et al., 2009] with the relaxation time scale of 5 day[Miyazawa et al., 2013]. The
JCOPE2 model, which represents no tidal current, assimilates the detided sea
surface height anomaly
obtained from the satellite
altimetry, satellite sea surface temperature, and insitu temperature and salinity
proﬁles [Miyazawa et al.,2009]. To avoid suppressing
the high-frequency variability including tide, we add
the nudging term proportional to the difference
between the 5 day runningmean values of JCOPE-T and
the daily mean values of
JCOPE2 interpolated on the
JCOPE-T grids to the original
temperature and salinity
equations, which could beconsidered as a variant of
the spectral nudging methods [e.g., Waldron et al.,1996]. The model was initialized with the ﬂow, temperaFigure 3. Amplitude (in m) of M2 surface tidal elevation evaluated from the high-pass ﬁltered sea
ture and salinity interpolated
surface height anomaly of the JCOPE-T simulation. The amplitude larger than 0.109 m is excluded
from the shading. Black lines denote the Jason-2 satellite altimeter tracks. Numerics with three
from JCOPE2 on 1 Decemdigits indicate the pass numbers.
ber 2010. Hourly results ofsea level, current, temperature, and salinity of JCOPE-T for a period from 1 March 2011 to 1 March 2012 are used for analyses.
A corange and cophase map of the M2 tidal constituent of the simulated SSHA (Figure 2) shows the westward propagation of the M2 tidal wave from the central part of the Western North Paciﬁc, and increase(decrease) of the amplitude in the marginal seas including the East China, and Yellow Seas (Japan Sea).
Those features are similar to the previous results of barotropic and baroclinic tides simulations [Egbert et al.,
1994; Guo and Yanagi, 1998; Niwa and Hibiya, 2001]. In addition, O (100 km) short wavelength ﬂuctuations
in both amplitude and phase are apparent in South China Sea and east of Taiwan. These are related to thebaroclinic tide variability [Niwa and Hibiya, 2001; Arbic et al., 2012]. Detailed comparison of the simulated M2tide with that evaluated from the satellite altimetry (Jason-2), from the barotropic tide model used for the
tidal forcing at the open boundaries, and from the tide gauge data is described in Appendix B.
The surface manifestation of the baroclinic tide is detected by a high-pass ﬁlter of SSHA [Ray and Mitchum,
1996; Matsumoto et al., 2000; Niwa and Hibiya, 2001]. Figure 3 depicts the amplitude of M2 harmonic constituent evaluated from the high-pass ﬁltered SSHA of the simulation. We set cutoff scale of 200 km of theGaussian ﬁlter based on the consideration on a typical wavelength of 110 km for the semidiurnal baroclinic
tide assuming a ﬁrst mode baroclinic wave speed of 2.5 m/s [Kantha and Tierney, 1997]. The distribution ofsmaller spatial scale M2 amplitude indicates localized intense variability around the steep topographic
slopes in the Western North Paciﬁc including Ryukyu Islands Chain, Tokara Strait, Izu and Ogasawara Ridges,
and Luzon Strait (see Figure 1 for locations). The M2 amplitude estimated from the variation of 26.7 Sigma-t
isopycnal surface also shows the similar patterns (not shown), suggesting that the high-pass ﬁltering of the

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(b)

(c)

(d)

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Figure 4. (a) M2 tidal amplitudes (in m) evaluated from the high-pass ﬁltered sea surface height anomaly along the Jason-2 tracks averaged in square regions of 58 by 58. (b) As in Figure
4a except for the JCOPE-T simulation data. (c) Correlation between the M2 tidal amplitude of the Jason-2 observation and JCOPE-T simulation evaluated from the high-pass ﬁltered sea
surface height anomaly along the Jason-2 tracks within square regions of 58 by 58. Statistically insigniﬁcant regions are excluded from the shading. (d) As in Figure 4c except for phase.

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M2 track 036

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Figure 5. M2 tidal amplitude from the high-pass ﬁlter sea surface height anomaly along the Jason-2 satellite altimeter tracks. Closed(open) circles denote the JCOPE-T simulation (the Jason-2 observation). Around (a) Tokara Strait, (b) Izu Ridge, (c) Luzon Strait, and(d) Ogasawara Ridge.

simulated SSHA is an effective way for detection of the M2 baroclinic tide variability. Note that the simulation shows comparatively larger amplitude in East China Sea and Yellow Sea.
The M2 amplitude distributions of the satellite observed (Appendix B) and simulated high-pass ﬁltered
SSHA also exhibit good agreement with each other, and both demonstrate a smaller magnitude (Figures 4a

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and 4b) as compared to those of
the nonﬁltered SSHA (Figures
A1a and A1b). A correlation map
for the amplitude (Figure 4c) indicates that the simulation has askill representing the observed
amplitude distributions; however,it basically fails to reproduce theobserved phase distribution (Figure 4d). The relatively simple spatial ﬁlter used in the present
study might be sensitive tonoises included in the phase
information.
The distribution of the M2 amplitude estimated from the highpass ﬁltered SSHA (Figure 3) represents the localized intense variability (hot spots) in theWestern North Paciﬁc. Comparison of the observed and simulated M2 amplitudes along the
tracks (Figure 3) around some
hot spots: Tokara Strait, Izu
Ridge, Ogasawara Ridge, andLuzon Strait (for locations, see
22
Figure 6. Depth-integrated BEC rate (in W m ) evaluated from the ‘‘M2-Tide’’ simulation.
Figures 1 and 5) suggests that
Boxes indicate the regions of the active generation sites of the baroclinic tides (hot spots):
Tokara Strait, Izu Ridge, Luzon Strait, and Ogasawara Ridge (see Figure 1 for locations).
the simulation generally represents the amplitudes around there as observed though it tends to slightly overestimate them in shallower
part of the model region (Figures 5a2 and 5c2; also see Figure 3).

3. M2 Baroclinic Tidal Energetics
The M2 baroclinic tide variability can be investigated quantitatively based on the analysis of its energy transformations. We suppose a governing equation for the depth-integrated baroclinic energy as follows [Niwaand Hibiya, 2004]:!
@Ebc D@P0 U0 D @P0 V 0 D(1)52
1
1gq0 w 0 bt D1DISbc 1ADVbc ;@t@x@ywhere the primed variables are the baroclinic components that are deﬁned as the deviation from the vertical mean values, the overbar denotes the average over the entire water column, Ebc is the baroclinic energy
0density, P is the pressure perturbation associated with the density variation, and wbt is the Cartesian verticalvelocity associated with the barotropic ﬂow given by




@D @g
@D @g
@g
wbt 5U r
1
1V r
1
1ðr11Þ ;
(2)
@x @x
@y @y
@t
where D, ðU; VÞ, r, and g are the bottom depth, horizontal velocity, sigma-level, and sea surface height,
respectively, and DISbc and ADVbc denote the dissipation and advection, respectively. Integrating equation(1) over a ﬁxed area and averaging over one tidal period (denoted by an angle bracket) lead to the conservation equation for the baroclinic energy [Niwa and Hibiya, 2004; Lorenzo et al., 2006],
0
1
ð
ðð
ðð
ðð
0
0 0
(3)
hgq wbt Dids ﬃ hP U n Didl2@ hDISbc ids1 hADVbc idsA;
S

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where Un denotes the velocity outward normal to the boundary ofarea C, ds is an inﬁnitesimal element of the area S, and dl is an
inﬁnitesimal element along theboundary C. The term of the lefthand side of equation (3) speciﬁes
the total energy of baroclinic tide
generated through the tidal barotropic to baroclinic energy conversion (BEC). The ﬁrst term of theright-hand side of equation (3)indicates a part of the total energy
radiated from the boundary ofarea C. The remaining part of theenergy is locally advected and dissipated inside of the area S as represented by the second term of
the right-hand side of equation (3).
To investigate the simulated M2
baroclinic tide energetics in detail,
we conducted two additional simulations forced by the tidal forcing
with the M2 constituent alone,which allow a relatively short harFigure 7. As in Figure 6 except for magnitude of the M2 baroclinic energy radiation ﬂux
monic analysis period owing to no(in kW m21). Vectors indicate the direction and magnitude.
need of extracting the M2 signal
from the simulated variations
forced by the similar frequency tidal constituents. For these experiments, our choice of the harmonic
analysis period is 3 days that is long sufﬁcient to distinguish the M2 and inertial motions in the model
region. One additional simulation case (‘‘M2-Tide’’) is almost same as the original simulation with realistic
multi-constituents tide except that tide is limited by a M2 constituent alone. Another simulation (‘‘Only
M2-tide’’) is performed with an initially horizontally uniform temperature and salinity distribution for thewhole domain, forced by only the M2 tide with zero surface momentum, heat and freshwater ﬂuxes andzero lateral boundary nontidal ﬂow. This experiment excludes impacts of variable stratiﬁcation forced by
no-tidal processes including mixed layer variation, and geostrophic and wind-driven currents on tidal
processes though it still allows generation of internal tidal waves and corresponding energy conversion.
This experiment is run for a period from 10 December 2010 to 22 March 2012. Initial vertical temperature and salinity proﬁles are evaluated using the World Ocean Atlas 2001 climatology data [Conkrightet al., 2002].
For the case ‘‘M2-Tide,’’ we examine the time evolution of the M2 tidal energetics by running harmonic analysis for sea surface height, current, and density for different 182 consecutive subperiods with 3 days duration during the 1 year simulation period. Each subperiod overlaps 1 day with the former and succeeding
subperiods. The ﬁrst subperiod begins from 1 March 2011 and the last one begins from 26 February 2012.
We also evaluate the harmonics of the case ‘‘Only M2-Tide’’ for different 25 subperiods with the ﬁrst subperiod beginning from 1 January 2011 and the last one beginning from 14 March 2011. Note that the energy
budget analysis evaluated from the base simulation forced by a multiple tidal constituents, which requires
longer harmonic analysis duration of at least 30 days for distinguishing M2 and S2 signals, shows basicallysimilar results to those discussed below (not shown).
Figure 6 shows the M2 BEC averaged for all subperiods of the case ‘‘M2-Tide.’’ The energy conversion is
active around the steep bottom topography including Tokara Strait, Izu-Ogasawara Ridges, and Luzon Strait
indicated by squares in Figure 6, and the distribution is partly similar to that of the amplitude of M2 harmonic constituent evaluated from the high-pass ﬁltered SSHA (Figure 3).

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conv-hum2
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dsp-hum2

Figure 8. M2 baroclinic tidal energy budgets (see equation (3)) calculated at the hot spots (see Figures 1 and 7 for their locations and areas,
respectively) for the subperiods with 3 day duration (see the text for the deﬁnition). Closed circles: BEC. Open circles: the divergence of theenergy radiation ﬂuxes. Open squares: the dissipation and advection.


A distribution of the energy radiation ﬂux of the M2 baroclinic tide hP0 U0 Di; hP0 V 0 Di averaged for the all
subperiods (Figure 7) represents that the four hot spots intensively radiate the M2 baroclinic tide energy.
Magnitudes of the radiation depend on those of the energy conversion (Figure 6), showing relatively
smaller magnitudes of the radiation in both of Tokara Strait and Izu Ridge as compared to more active radiation around the Ogasawara Ridge and Luzon Strait. Streaks patterns shown between the ridges at west andeast sides are similar to those shown in the high-pass ﬁltered M2 signal (Figure 3), suggesting the possible
remote effects due to the wave propagation [Kerry et al., 2013] together with the intensiﬁcation of theenergy generation caused by the local sea mountains.
Time sequences of the energy budget equation (3) at the four hot spots for the all subperiods are shown in
Figure 8 (also see mean and standard deviation for the all subperiods described in Table 1). BEC rates andcontribution from the radiation in the two hot spots (Tokara Strait and Izu Ridge) are relatively smaller thanthose in the other two spots (Ogasawara Ridge and Luzon Strait). The situation is reverse for the local dissipation and advection term that is larger in the former two spots than that in the latter two spots. Figure 8
shows the results from both the cases of ‘‘M2-Tide’’ and ‘‘Only M2-Tide.’’ The case with only the M2 tide

Table 1. Mean and Standard Deviation (in Parentheses) During the 1 Year Simulation Period of the ‘‘M2-Tide’’ Simulation of BEC Rates
Averaged at the Spots and the Depth-Integrated Tidal Energy Supply Into the Spots

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Tokara Strait

Izu Ridge

Luzon Strait

Ogasawara Ridge

BEC
Supply3.80 (0.39)
46.45 (1.29)

2.37 (0.17)
36.47 (0.80)

10.56 (0.43)
58.27 (1.86)

5.28 (0.20)
33.32 (0.78)

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forcing, ‘‘Only M2-Tide,’’ results in almost stationary
BEC values after some initial adjust-200
ment in the all spots. Driven by a periodic M2-400
forcing alone, the subtidal state of the model-600
slowly evolves together with changing stratiﬁ-800
cation. Stratiﬁcation change is caused by tide-1000
induced mixing generated by vertical shear of
0.008
0.01 0.012 0.014 0.016
tidal currents. Magnitude of each term is gen-1(s )erally similar between ‘‘Only M2-Tide’’ and ‘‘M2OG
HU
TK
Tide’’ except for Ogasawara Ridge (Figure 8d)
IZLSshowing considerably smaller (larger) conversion and radiation (dissipation and advection)
Figure 9. Time-mean horizontally averaged vertical proﬁles of the buoyin ‘‘Only M2-Tide’’ than in ‘‘M2-Tide.’’ This arises
ancy frequency at the spots: TK, Tokara Strait; IZ, Izu Ridge; LS, Luzon
Strait; and OG, Ogasawara Ridge, calculated from the ‘‘M2-Tide’’ simulafrom the difference in the vertical proﬁles oftion result. A proﬁle ‘‘HU’’ denotes a climatological mean proﬁle calcuthe mean stratiﬁcation used in these simulalated from World Ocean Atlas 2001 [Conkright et al., 2002] and it is usedtions; the vertical density proﬁle used in ‘‘Only
for the ‘‘Only M2-Tide’’ simulation.
M2-Tide’’ does not show a local maximum
around 500 m depth at Ogasawara Ridge,
while it is clearly represented in the mean proﬁle in ‘‘Tide-M2’’ case (Figure 9). This local maximum corresponds to the potential vorticity maximum layer associated with an expression of the main thermocline
southeast of Japan [Emery et al., 1984; Qu et al., 2001]. The mean proﬁles at other sites are qualitatively similar to the proﬁle used in ‘‘Only M2-Tide.’’ This issue will be discussed in the next section from a view of possible effects of changing stratiﬁcation forced by the no-tidal processes on the baroclinic tide variability.
(m)0

The dissipation dominant feature at Tokara Strait and Izu Ridge is attributable to larger friction due to therelatively shallower depth at which BEC actually occurs. Figure 10 compares the horizontal distributions of
BEC averaged for the all subperiods and the bottom topography in the four spots. Large part of BEC around
Tokara Strait and Izu Ridge is shown at the depth shallower than 500 m, and the averaged water depths ofa region in which BEC rates are larger than 0.2 W m22 , indicated by contours in Figure 10, are 852 and1107 m at Tokara Strait and Izu Ridge, respectively. In contrast, the large BEC rate in the other two spots isshown in the region with depths ranging from shallow to deep levels, and the averaged depths of a region
showing the conversion rates larger than 0.2 W m22 are 1889 and 2046 m at Luzon Strait and Ogasawara
Ridge, respectively.
The radiation direction of the baroclinic tidal energy is governed by the characteristic slope deﬁned as
0:5/  ½ðx2 2f 2 Þ=ðN2 2x2 Þ , where x is the tidal frequency, f is the Coriolis parameter, and N is the buoyancy frequency [Wunsch, 1975]. The baroclinic tidal waves incident on the super (sub) critical slope where
the difference between the bottom slope and the characteristic slope angles is positive (negative) will propagate toward deeper (shallower) region. The angle difference estimated around the four hot spots (Figure11) indicates that the large part of the baroclinic tidal energy generated near the subcritical slopes (cf. Figure 10) at the dissipation dominant hot spots (Tokara Strait and Izu Ridge) is radiated into the shallower
regions and dissipated there [Osborne et al., 2011]. At the radiation dominant hot spots (Ogasawara Ridgeand Luzon Strait), the baroclinic tidal energy is actively generated over the supercritical slopes and thus
could be radiated mainly outward into deeper regions from there. Note that the distribution of the angle
difference itself shows no signiﬁcant time dependence (not shown).

4. Modulation of M2 Internal Tide by the Background Oceanic Conditions
Figure 8 depicts that the temporal variations of both BEC and radiation rates at the hot spots are similar toeach other (see correlation between them described in Table 2). The temporal variations are also found intime sequences of supply of depth-integrated (barotropic) tidal energy into four spots (Figure 12 and Table 1),
which is deﬁned as
Xð
Xð
Xð
2
hPbt Ubt n Didl52
hPbt Ubt n Didljpositive 2
hPbt Ubt n Didljnegative ;(4)
i

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Figure 10. Zoom up views of the time-mean depth-integrated BEC rate of 0.2 W m22 denoted by contours around the hot spots. Shade denotes the bottom topography (in m). The
square denotes each hot spot area. Isodepth lines with 500 and 1000 m are indicated by solid contours. (a) Tokara Strait, (b) Izu Ridge, (c) Luzon Strait, and (d) Ogasawara Ridge.

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Figure 11. As in Figure 10 except for the contours denoting the isobath lines of 500 and 1000 m and the shade denoting the angle difference (in degree) between the bottom and characteristic slopes.

PÐwhere 2 i Ci FdljpositiveðnegativeÞ means a summation of integrated ﬂux values with positive (negative) signs(F) among four lateral boundaries, Ci ði51; 2; 3; 4Þ, deﬁning a hot spot region and positive (negative) means
supply of the energy into (radiation of the energy from) the spot through the boundary. Pbt and Unbt denotebarotropic pressure and barotropic (depth-averaged) velocity outward normal to the boundary. BEC seems

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Table 2. Correlation Coefﬁcients for M2 BEC Rate Averaged in the Spots With the Divergence of the Depth-Integrated Tidal Energy Fluxat the Spots (Radiation), the Depth-Integrated Tidal Energy Supply Into the Spots (Supply), the EOF Amplitudes of the Buoyancy Frequency Proﬁles Horizontally Averaged in the Spots (EOF), and Buoyancy Frequency at Selected Depths Averaged in the Spots (BVF)a

Radiation
Supply
EOF1
EOF2
EOF3
EOF4
EOF5
EOF6
BVF50m
BVF100m
BVF200m
BVF500m
BVF800m
BVF1000m

Tokara Strait

Izu Ridge

Luzon Strait

Ogasawara Ridge

0.61
20.42
0.19 (72)0.62 (20)0.62 (5)0.19 (2)0.07 (0.8)
0.00 (0.1)
0.00
0.51
0.79
20.52
20.55
20.24

0.68
0.29
0.50 (77)0.38 (18)0.03 (3)0.12 (1)0.05 (0.5)
0.14 (0.2)
0.50
0.62
0.48
0.05
0.15
0.13

0.68
0.56
20.44 (72)20.40 (22)0.02 (4)0.08 (1)0.27 (0.4)
0.04 (0.1)
20.56
20.50
20.59
20.04
0.34
0.29

0.51
0.24
0.04 (65)0.15 (28)0.04 (4)0.10 (2)0.50 (0.5)
0.40 (0.07)
20.04
20.03
20.52
0.52
0.48
0.38

a
The signiﬁcant correlation level is 0.27 for p < 0.01 and the signiﬁcant correlation values are indicated by the bold font. Numerics inparentheses of the EOF modes cells denote the contribution ratios (in %) of the EOF modes to the total variance.

to temporally vary partly responding to the variation of the supply of the depth-integrated tidal energy at
Luzon Strait (thick curves shown in Figure 12c). The depth-integrated energy supply into the spot converges
to the steady state in after the initial adjustment in ‘‘Only M2-Tide’’ (not shown) since the background stratiﬁcation also converges to the steady state. The signiﬁcant spatiotemporal variation of the stratiﬁcationinduced by the ocean circulation affects the baroclinic tide generation and radiation at all generation sites,
and thus the depth-integrated tidal energy ﬂux experiences the spatiotemporal variation as a result of thevariation in BEC occurring over all generation sites included in the model region. This effect is considered as

conv
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Figure 12. Time sequences of BEC rate (red curves) averaged in the spots and the barotropic tidal energy supply into the spots (bluecurves). (a) Tokara Strait, (b) Izu Ridge, (c) Luzon Strait, and (d) Ogasawara Ridge. Thin curves denote the 3 day subperiod sequences normalized by mean and standard deviation for the all subperiods and thick curves denote their low-pass ﬁltered sequences with a cutoff at
30 day period.

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10.1002/2015JC010739(a) TK1(b) TK2(c) TK3(d) IZ1(e) IZ2(f) IZ3(g) LS1(h) LS2(i) LS3(j) OG1(k) OG2(l) OG3

Figure 13. EOF mode proﬁles obtained from the buoyancy frequency averaged at the hot spots. (a) Mode 1, (b) Mode 2, and (c) Mode 3
for Tokara Strait; (d) Mode 1, (e) Mode 2, and (f) Mode 3 for Izu Ridge; (g) Mode 1, (h) Mode 2, and (i) Mode 3 for Luzon Strait; and (i) Mode
1, (j) Mode 2, (k) Mode 3 for Ogasawara Ridge.

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10.1002/2015JC010739(c) OG6

Figure 14. As in Figure 13 except for (a) Mode 4, (b) Mode 5, and (c) Mode 6 for Ogasawara Ridge.

the remote effect of the varying background stratiﬁcation on the baroclinic tide generation at a local
generation site. Luzon Strait shows the highest correlation value (0.56) between the supply of thedepth-integrated tidal energy and BEC among the four spots (Table 2), suggesting the signiﬁcance of theremote effect there as demonstrated also by Kerry et al. [2011, 2014]. The other spots, however, indicate lowlevels of positive correlation values (Izu Ridge and Ogasawara Ridge) and a negative value (Tokara Strait).
Later we examine this issue by using the multi regression analysis allowing consideration of mutual relationship among all explanatory variables.
Since the intensity of BEC is also affected by the local background stratiﬁcation[Petrelis et al., 2006] at a local
qﬃﬃﬃﬃﬃﬃﬃﬃ
region, we examine relations between the buoyancy frequency, N5 qg @q(zispositive value of depth, g is
0 @z
gravity acceleration, and q0 is reference density), and BEC rate. Temporal variations of the buoyancy frequency proﬁle spatially averaged in each spot are decomposed into Empirical Orthogonal Function (EOF)
modes [Kutzbach, 1967]. The ﬁrst three EOF modes at the four spots indicate similar proﬁles among eachother (Figure 13). The ﬁrst mode represents the variability of the stratiﬁcation in the upper 200 m depth,
and the second and third modes represent the variability in the upper 300 m depths. Although some EOF
modes have multiple local maxima with positive and negative signs, we focus on the positive correlation
for the positive local maximum at the deepest level (see closed diamonds denoted in Figures 13–15),
because BEC occurs around the bottom slope. Results summarized in Table 2 indicate statistically signiﬁcantcorrelation values between BEC and some EOF modes for each spot: second and third modes at Tokara
Strait (Figures 13b and 13c), ﬁrst and second modes at Izu Ridge (Figures 13d and 13e), ﬁrst and second
modes at Luzon Strait (Figures 13g and 13h), and ﬁfth and sixth modes at Ogasawara Ridge (Figures 14a
and 14b). The positive correlation of the lower modes for Tokara Strait and Izu Ridge implies that the(a) LS1(b) LS2(c) LS3

Figure 15. EOF mode proﬁles obtained from the buoyancy frequency below 400 m averaged at Luzon Strait. (a) Mode 1, (b) Mode 2, and(c) Mode 3.

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Table 3. As in Table 2 Except for the Correlationfor BEC Rate With the EOF Modes of the Buoyancy
Frequency Proﬁles Below 400 m Horizontally Averaged at Luzon Strait
Luzon Strait
EOF1b
EOF2b
EOF3b
EOF4b
EOF5b
EOF6b

20.15 (79)
0.58 (17)0.08 (2)0.31 (0.5)
0.09 (0.2)
0.17 (0.07)

10.1002/2015JC010739

increase of the stratiﬁcation intensity in the layer at somedepths between surface and 300 m corresponds to theincrease of BEC rate (see positive maxima shown in Figures
13b–13e), and this relation is conﬁrmed by the signiﬁcant positive correlation of the buoyancy frequency at the near surface
levels (Table 2). Such correlation representing the effect of thenear surface stratiﬁcation is consistent with the fact that BEC
occurs around relatively shallow slope at Tokara Strait and Izu
Ridge (Figures 10a and 10b).

At Luzon Strait, signiﬁcant negative correlation values arefound for the ﬁrst and second mode amplitudes and the buoyancy frequency values in the near surface layer, while the ﬁfth mode amplitude and the buoyancy frequency in the deeper layer show positive correlation. To detect the effects of the stratiﬁcation in the deeper
layer more clearly, we conduct the EOF analysis of the proﬁle below 400 m (Figure 15). Later we discuss
Table 4. Normalized Partial Regression Coefﬁcients for BEC Rate at the Spots With the Depth-Integrated Tidal Energy Supply Into the
Spots and the EOF Modes of the Buoyancy Frequency Averaged at the Spotsa

Supply (t)EOF1 (t)EOF2 (t)EOF3 (t)EOF4 (t)EOF5 (t)EOF6 (t)AR2 (F)

Tokara Strait

Izu Ridge

Luzon Strait Below 400 m

Ogasawara Ridge

20.05 (21.7)
0.21 (9.4)
0.50 (22)0.58 (16)0.20 (11)0.03 (1.5)
0.11 (4.6)
0.98 (670)0.28 (5.1)
0.46 (9.8)
0.90 (13)0.59 (8.0)
0.36 (6.6)
0.15 (2.6)
0.11 (2.4)
0.87 (85)0.36 (4.2)
0.11 (1.8)
0.61 (11)0.24 (4.2)
0.20 (2.9)
0.09 (1.7)
0.03 (0.52)
0.73 (36)0.09 (1.3)
0.05 (0.59)
0.35 (3.2)
0.23 (1.8)
0.003 (0.034)
0.54 (7.6)
0.30 (3.8)
0.65 (24)aNumerics in parentheses of the cells denote the t-values of the regression coefﬁcients. Cells in the lowest row denote the adjusted R
squared (AR2) and F (in parentheses) values of the multiregression.

03

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Figure 16. As in Figure 12 except for blue curves denoting the amplitude of the selected EOF modes at the spots (see the text for thedeﬁnition).

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Figure 17.

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possible implications suggested by signiﬁcant positive correlation found in the second mode (Table 3). At
Ogasawara Ridge, the ﬁfth and sixth modes with local positive maxima at 500–600 m depths (see closed
diamonds shown in Figures 14b and 14c) show signiﬁcant positive correlation, but the lower modes indicate no signiﬁcant correlation. Later we also discuss roles of the stratiﬁcation around 500 m depth in the
BEC modulation at Ogasawara Ridge, which is also suggested from the comparison of the ‘‘Only M2-Tide’’and ‘‘M2-Tide’’ results (see Figures 8d and 9).
The correlation analysis described above implies that the varying background stratiﬁcation affects BEC
remotely through the supply of the depth-integrated tidal energy into the spot and locally through the local
stratiﬁcation represented by the EOF modes at the spot. To clarify roles of both the remote and local effects inthe temporal variation of the energy conversion, we conduct the multi regression analysis using all relevant
variables (Table 4). High-frequency variations with period shorter than 30 days are removed by low-pass ﬁltering from all variables to focus on the mesoscale and/or seasonal variability. The analysis results for the four
spots generally lead to high values of the determination coefﬁcient (adjusted R squared) and F-statistic. At
Tokara Strait, the negative correlation between the supply of the depth-integrated tidal energy and BEC isstatistically insigniﬁcant. Both second and third modes show the relatively large partial regression coefﬁcientsand t-values compared to the other EOF modes. For Izu Ridge the signiﬁcance of the ﬁrst, second, and thirdmodes is evident. At Luzon Strait, the second EOF mode for the stratiﬁcation below 400 m is most signiﬁcant,and the supply of the depth-integrated tidal energy secondarily contributes to the variability of BEC. At Ogasawara Ridge, the ﬁfth and sixth modes are comparatively signiﬁcant among the all EOF modes.
Based on the statistical analyses described above, we conclude that the most signiﬁcant local stratiﬁcation factors at the four spots are represented by the EOF second mode (Tokara Strait and Izu Ridge), the ﬁfth mode
(Ogasawara Ridge), and the second mode for stratiﬁcation below 400 m depth (Luzon Strait). A typical positive
impact of the local stratiﬁcation factor on BEC is recognized by identifying an oceanic condition at each hot
spot when the BEC rate increases anomalously with intensiﬁed local stratiﬁcation. Using the time sequencesof EOF amplitudes for the stratiﬁcation and the BEC rate (Figure 16), both normalized by temporal means andstandard deviations (Table 1), we deﬁne the locally enhanced (weakened) states as in cases of (1) the normalized conversion rate >11.2 (<21.2) and (2) the normalized EOF amplitude >11.2 (<21.2).
Figures 17a and 17b compare the locally weakened and intensiﬁed states of the stratiﬁcation at 200 m
depth around Tokara Strait. Correspondence between the stratiﬁcation and the activated M2 tidal currents,
which is represented by the band-pass ﬁltered current magnitude with the target period from 11 to 14 h(note that the minimum period of the inertial motion over the model region is approximately 15.6 h), is
exhibited in Figures 17c–17f. The enhanced stratiﬁcation is distributed around the Kuroshio small meander(Figure 17b) formed during the period from September to December 2011. The strong stratiﬁcation is conﬁned in the layer at depths between 50 and 200 m, and the tidal current is activated in the strong stratiﬁcation layer (Figure 17f). In contrast, the activation of the tidal current is attenuated in the weak stratiﬁcation
layer, particularly in the mixed layer enhanced by the winter mixing (Figure 17e). The horizontal distributionof the tidal currents seems to be affected by the Kuroshio path (Figures 17c and 17d).
Similarly, the Kuroshio path variation affects the stratiﬁcation around Izu Ridge (Figure 18). The tidal currents
are enhanced along the Kuroshio small meander path formed during the period from September to October 2011 (Figure 18d), and the enhancement is conﬁned in the strong stratiﬁcation layer (Figures 18f). The
stratiﬁcation in the subsurface layer at both Tokara Strait and Izu Ridge is enhanced by the cyclonic eddy
associated with the Kuroshio small meander. Such enhancement of the stratiﬁcation due to the cycloniceddies is also observed over the North Western Paciﬁc [Kouketsu et al., 2012]. The periods of the positive
maxima shown in the lower-frequency variations of the EOF second mode amplitude at each spot (see blue
thick curves in Figures 16a and 16b) generally correspond to the periods of the Kuroshio small meander
occurrence there (not shown). Note that the not only the Kuroshio path variation but also the seasonal
Figure 17. Time-mean buoyancy frequency (shade; in s21) at 200 m depth for the subperiods showing the (a) typical locally weakened
and (b) enhanced BEC states among the all subperiods. Contours denote the time-mean sea surface height with interval of 0.05 m for thesubperiods. A box indicates the region of the Tokara Strait spot. (c, d) Zoom up views of the Tokara Strait spot showing the time-mean
buoyancy frequency (shade; in s21) at 200 m depth for the subperiods showing the typical locally (Figure 17c) weakened and (Figure 17d)
enhanced BEC states among the all subperiods. Contours denote the root mean square variability (0.02–0.10 m s21) of the band-pass ﬁltered current with the target period from 11 to 14 h. Contour interval is 0.005 m s21 and thick contours denote the values upper 0.05 m
s21. (e) As in Figure 17c except for showing a vertical section along 29.58N, which is denoted by horizontal lines in Figures 17a–17d. (f) As
in Figure 17d except for showing a vertical section along 29.58N.

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Figure 18. As in Figure 17 except for showing the similar conditions of the (a, c, e) enhanced and (b, d, f) weakened BEC states around Izu
Ridge.

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Figure 19. As in Figure 17 except for showing the similar conditions of the (a, c, e) enhanced and (b, d, f) weakened BEC states aroundLuzon Strait. Figures 19a–d show the states at 800 m depth.

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Figure 20. As in Figure 17 except for showing the similar conditions of the (a, c, e) enhanced and (b, d, f) weakened BEC states aroundOgasawara Ridge. Figures 20a–20d show the states at 500 m depth.

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thermocline variation also affects the BEC variation; in fact, the enhanced BEC gradually declines as shownin Figures 16a and 16b after the beginning of the cooling season even during the period when the Kuroshio
small meander state continues.
Around Luzon Strait, the Kuroshio path alternatively takes the looping and leaping modes [Sheu et al.,2010]. The former modes represents the westward Kuroshio intrusion into South China Sea through Luzon
Strait, while the Kuroshio tends to ﬂow northward without intrusion during the latter mode period. The
enhanced BEC actually occurs during the two intrusion periods (April 2011 and January 2012), which areindicated by the positive maxima of the EOF second mode amplitude for the stratiﬁcation below 400 m
depth (Figure 16c). Figure 19b represents the locally enhanced state in January 2012, during which theenhanced tidal currents appear around the western part of the ridges, especially at 218N, 1218E (Figure19d). The stratiﬁcation at 800 m depth is strengthened together with the Kuroshio intrusion (Figure 19f). It
is known that the Kuroshio intrusion accompanies the high potential vorticity water (roughly corresponding
to the strong stratiﬁcation) around the bottom of the main thermocline [Qu et al., 2001]. Similar enhancement of the baroclinic tide generation at Luzon Strait is demonstrated using another ocean model [Kerryet al., 2014, Figure 10].
During the leaping mode period of July 2011 (Figure 19a), the tidal current around the western ridge is comparatively suppressed (Figures 19c and 19e). Sheu et al. [2010] suggest that the leaping (looping) mode tends
to appear in summertime (wintertime). The weakened (enhanced) BEC state actually occurs in summertime(wintertime) in the present simulation showing the similar seasonal occurrence of the Kuroshio intrusion.
The negative correlation of the lower EOF modes showing the seasonal variation of the stratiﬁcation in thenear surface layer (enhanced in summertime and weakened in wintertime) might appear owing to the dominant effect of the deep stratiﬁcation controlled by the seasonally phase-locked Kuroshio intrusion.
Although there exist no Kuroshio variability around Ogasawara Ridge, the mesoscale eddy activity affects
the baroclinic tide activity through the varying background stratiﬁcation near the main thermocline there(Figure 20). Comparison of a time sequence of sea surface height anomaly averaged in Ogasawara Ridge(not shown) and that of the ﬁfth EOF mode amplitude (Figure 16d) indicates that the positive high values of
the EOF mode corresponds to the events of the anticyclonic eddies passing around there. The locally intensiﬁed BEC state appears in the beginning of May 2011, and the local stratiﬁcation maximum around the bottom of the main thermocline [Qu et al., 2001] induced by deepening of the thermocline depth associatedwith the passing of an anticyclonic eddy covers the whole spot region (Figure 20b). The tidal current
enhancement is shown in the layer with the local maximum of the stratiﬁcation intensity (Figure 20f). The
role of the stratiﬁcation around the bottom of the main thermocline depth in the energy conversion is alsosuggested from the result of the sensitivity experiment (Figure 8d) with the horizontally uniform stratiﬁcation proﬁle (Figure 9) that has not the local maxima of the buoyancy frequency near the 500 m depth
around Ogasawara Ridge.
Distributions of the radiation ﬂux of M2 baroclinic energy exhibit the variations of the energy ﬂux in the corresponding subperiods with the locally weakened and intensiﬁed states (not shown). The all spots show
considerable differences in the radiation ﬂux distributions between the locally weakened and intensiﬁed
states. The radiation ﬂux distribution represents quite complicated patterns. The energy radiation of the baroclinic tide is locally enhanced even in the generally weakened state, indicating that the energy radiation of
the baroclinic tide is not simply governed by BEC variation but also is affected by the local dissipation andadvection inside of the spot [Pereira et al., 2007; Chavanne et al., 2010; Jan et al., 2012].

5. Summary and Discussion
We conducted a 1 year concurrent simulation of the ocean circulation and tide in the Western North Paciﬁcusing an ocean general circulation model with a horizontal resolution of 1/368 to investigate possible interactions between the circulation and tide. The model reproduces the amplitude and phase of M2 tide as
observed in the open ocean portion. It also reproduces some part of the amplitude of M2 tidal harmonics
evaluated from the high-pass ﬁltered sea surface height anomaly, which could be regarded as the surface
manifestation of the baroclinic tide. In particular, the intense variability of the M2 baroclinic tide harmonics
around Tokara Strait, Izu Ridge, Luzon Strait, and Ogasawara Ridge (the hot spots) are represented by themodel nearly as observed.

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The sensitivity experiment simulations forced by the only M2 tidal constituent allows the calculation of M2
harmonics for a short-term (3 day) period. Intensity of the M2 barotropic to baroclinic energy conversion(BEC) rates at the hot spots evaluated from the harmonics in each 3 day subperiod exhibits the timedependence attributable to the temporal variations of the background stratiﬁcation. The result suggeststhat the temporal variation of the local stratiﬁcation intensity could be a proxy of the bulk estimate of thetemporal variation of BEC in the spot, though the remote ﬂuctuation of the depth-integrated tidal energy
supply into the spot partly affects it.
The EOF analysis of the buoyancy frequency averaged at the spot indicates the temporal variations of some
EOF modes correlate with the variation of BEC averaged there. Characteristics of the most dominantly inﬂuential mode at each spot imply the lower-frequency oceanic phenomena that are mainly responsible formodulating the baroclinic tide variability there through changes in intensity of the local stratiﬁcation. At
Tokara Strait and Izu Ridge, the enhanced stratiﬁcation in the upper thermocline layer caused by the development of the Kuroshio small meander together with the seasonal thermocline variation considerably
affects the temporal variation of BEC. At Luzon Strait and Ogasawara Ridge, the energy conversion is modulated by the variations in the stratiﬁcation around the bottom of the main thermocline governed by the Kuroshio intrusion into the South China Sea (Luzon Strait) and the mesoscale eddy activity (Ogasawara Ridge).
Note that the remote effect due to the temporal variation of the depth-integrated tidal energy supply,
which is caused by BEC occurring over the all baroclinic tide generation sites, is not negligible especially at
Luzon Strait, as suggested also by the previous studies [Kerry et al., 2013, 2014].
BEC mainly occurs over the bottom slope at the relatively shallow depth at Tokara Strait and Izu Ridge, andthus most of the baroclinic tidal energy is locally dissipated and the stratiﬁcation in the relatively shallow
layer is crucial for the modulation of the baroclinic tide generation. At the other two spots, in contrast, theradiation of the baroclinic tidal energy is more active than at the former spots because of the relatively
deep bottom slope where the active energy conversion occurs, and the stratiﬁcation in the relatively deep
layer is inﬂuential in the modulation of the baroclinic tide generation.
The multiregression using the stratiﬁcation intensity and depth-integrated tidal energy supply does notcompletely explain the variance of the found energy conversion; in particular, the explained ratio is relatively low at the radiation dominant hot spots: Luzon Strait and Ogasawara Ridge (Table 4). The roles of the
ﬂuctuation of the depth-integrated energy supply in the energy conversion might be different among the
spots as suggested by the values of the normalized partial regression coefﬁcients. Detailed BEC processes
could be affected by the additional contribution from the local dissipation and advection [Jan et al., 2012].
Divergence of M2 baroclinic energy radiation ﬂux varies in time responding to the variation of the conversion rate, and its variation range is larger than that of the conversion rate at the radiation dominant sites(Figure 8) also due to the effects of the local dissipation and advection [Pereira et al., 2007; Chavanne et al.,2010; Jan et al., 2012]. Evaluation of possible effects of such local processes on the tidal energetics in the
hot spots might be inﬂuenced by the horizontal and vertical resolution used in the model and still has notbeen examined so far, though only the rough estimate of the dependence based on the empirical relationship between BEC rate and the horizontal resolution has been done [Niwa and Hibiya, 2011]. Future studies
await further exploration in these directions.

Appendix A: Details of the Tidal Forcing in the Simulation
Tidal processes are introduced into the regional JCOPE-T model by counting both the tidal gravity force inthe model momentum equations and the open boundary condition including the tidal volume ﬂuxes andtidal sea level elevations provided from existing barotropic tidal models. The equilibrium surface pressure
gradient induced by 21 tidal potential constituents: Q1, O1, M1, P1, K1, J1, OO1, 2N2, MU2, N2, NU2, M2, I2, T2,
S2, K2, MM, MF, SSA, SA, MTM, and MSQM is added to the surface pressure gradient term for the operational
ocean forecasting. Tidal forcing composed of eight constituents: Q1, O1, P1, K1, N2, M2, S2, and K2, is included
in JCOPE-T as volume ﬂuxes and sea level anomaly provided from Oregon State University Tidal Inversion
Software (OTIS) [Egbert and Erofeeva, 2002] at lateral boundaries.
Tidal gravity force is estimated using the tidal potential provided as an equilibrium tide sea surface elevation amplitudes for major tidal harmonics. Total equilibrium tide height is estimated integrating potentials
of selected tide harmonics and using corresponding analytical formulas for the space distribution and time

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(a)

(b)

(c)

(d)

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Figure A1. (a) M2 tidal amplitudes (in m) evaluated from sea surface height anomaly along the Jason-2 tracks averaged in square regions of 58 by 58. (b) The Jason-2 observation data.
(right) The JCOPE-T simulation data. (c) Correlation between the M2 tidal amplitude of the Jason-2 observation and JCOPE-T simulation evaluated along the Jason-2 tracks within squareregions of 58 by 58. Statistically insigniﬁcant regions are excluded from the shading. (d) As in Figure A1c except for phase.

variability (frequency and phases) of considered harmonics [e.g., Kantha and Clayson, 2000]. Then the pressure gradient term in the model momentum conservation equations related with the sea level distribution
is replaced by the term that counts for the presence of tidal gravity force provided as distribution of thetotal equilibrium sea surface height,

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10.1002/2015JC010739@g@ðg2getÞ
!
;
@xi
@xi

(A1)

where xi correspond to two model horizontal axes (i 5 1,2), g is the model sea surface height, get is an equilibrium tide height deﬁned as function of time and location using analytical astronomical relations. We use
an equilibrium tide height values for the considered tidal harmonics taken from Kantha and Clayson [2000].
Although the tidal gravity force is the main reason for the tide generation in the world ocean, the impact oftidal gravity force in (A1) usually is not signiﬁcant for the regional models including JCOPE-T owing to therelatively long tidal wavelength of over 1000 km.
We have complex superposition of the tidal gravity waves entering and leaving model domain throughopen boundaries, and hence need to utilize both tidal volume ﬂuxes and elevations information for getting
the best practical solution. Some existing tidal models like OTIS [Egbert and Erofeeva, 2002] provide information on tidal volume ﬂuxes and sea level elevations for the world ocean.
The tidal sea level anomalies along open boundaries estimated one step forward in time t 1 1 (gt11tide ) are
included as a Newtonian smoother relaxation form with a relaxation parameter aE ,
t11
t11
t11
gt11 5gt11
 1aE ½ðgtide 1gno2tide Þ2g ;(A2)where gt11
and gt11 are the ﬁrst guess and corrected estimates for the forward time step t 1 1, respectively,t11
and gno2tide is the external nontidal model sea level at the boundary point for the same time step. The tidal
sea level boundary conditions (A2) must be speciﬁed in the model internal points closest to the open
boundary because sea levels deﬁned at the external model boundary have no impact on the model variables. At each time step the sea level in the model cell adjacent to the open boundary is changed from its
ﬁrst guess volume’s conservative predicted value (gt11
 ) found by integration of the continuity equation to avalue (gt11 ) closer to the prescribed sea levels by adding the adjustment term of equation (A2),t11
t11
Dgadj 5aE ½ðgt11
tide 1gno2tide Þ2g .
For restoring the volume conservation, the boundary volume inﬂow at time step t that was used for sea
level forward-estimation should be corrected to balance the boundary cell volume change Dgadj  dS where
dS is a model cell surface area. Required normal to open boundary barotropic velocity correction is
DUadj 56

Dgadj  dS;
ðH1gt11 Þ  dlb  Dt

(A3)

where H and dlb are the undisturbed depth and linear cell size along the open boundary, respectively, and
Dt is the integration time step. The sign in (A3) depends on the position of the open boundary; for standard
Cartesian coordinate system we will have plus at the western and southern boundaries of domain andminus at the eastern and northern boundaries. The corrected value Ub for the normal to the boundary
inﬂow velocity becomes
Ub 5Uno2tide 1Utide 1DUadj ;(A4)where Uno2tide is the external mode (barotropic) velocity interpolated from the external non-tidal ocean
model, and Utide denotes the barotropic velocity provided by the barotropic tidal model. The correctedboundary velocity value Ub at the time step t is then used for the momentum and tracer equations forward
integration.
Equation (A4) is similar to the Flather’s [1976] boundary condition for the regional tide simulation,rﬃﬃﬃﬃﬃﬃg ðgtide 1gno2tide 2gÞ;Ub 5Uno2tide 1Utide 6
Hb

(A5)

where the sign of the correction term is positive for the western and southern, and negative for the easternand northern open boundaries. The elevation relaxation parameter in equation (A5) is proportional to thefree long gravity wave phase speed at each location instead of been a constant value. If we take the relaxation coefﬁcient aE in equation (A2) asrﬃﬃﬃﬃﬃﬃ
g ðHb 1gt11 Þ  dlb  Dt pﬃﬃﬃﬃﬃﬃﬃﬃ Dt
aE 56
;
(A6)
 gHb
Hb
dS
dnb

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where dnb is boundary cell linear
size in normal to the open
boundary direction, both theFlather’s [1976] formulation (A5)and our approach (A2), (A3), (A4)become equivalent with possible
differences only in numericalrealization, like using forward
predicted value of sea level for
estimation of adjustment terms.
In the described all numericalexperiments, the boundary conditions: (A2), (A3), (A4), and (A6)
are used.
Strong internal gravity waves are
generated at topography slopes
inside of the JCOPE-T model.
Since the external model used
for specifying boundary conditions (JCOPE2) does not include
the tidal internal waves, we
could expect that such waves
must not be emitted or reﬂectedfrom open boundaries into theinterior of the nested model. We
adopt a boundary sponge layer
scheme for dumping of internal
gravity waves coming to theopen boundaries from the interior of the model domain. We
apply a simple three points
smoothing method to temperature, salinity, and baroclinic components of currents at the grids
Figure A2. Difference of the (a) M2 harmonic amplitude (in m) and (b) phase (in 8) between
JCOPE-T and OTIS models.
within six grid points inside fromthe open boundary with thesmoothing weight decreasing linearly from it maximum value of 0.05 for the ﬁrst model point near the
open boundary to zero just outside of the sponge layer. Smoothing is done only in direction normal toopen boundary that seems to be enough for not reﬂecting the internal waves at the boundary. We conﬁrm
that the sponge layer scheme effectively prevents propagation of the noisy disturbances generated near
the open boundary toward the interior of the model region (not shown).

Appendix B: Validation of the Sea Level Variability in the Coastal Regions
To validate the simulated M2 tide variations, we perform the harmonic analysis of both simulated andobserved sea surface height anomaly data to extract four tidal constituents: O1, K1, M2, and S2. We analyze
an along-track altimeter product of a satellite altimeter, Jason-2, with approximately 9.9 days interval for a
4.5 year period from July 2008 to January 2013. Note that the 4.5 year period is not long enough to separate
the all eight constituents (e.g., O1 and K2) [Schrama and Ray, 1994] used as the major tidal driving force of
JCOPE-T. The Jason-2 SSHA along-track product was produced by Ssalto/Duacs and distributed by Aviso,
with support from the Centre National d’Etudes Spatiales. The data estimated from the Jason-2 altimeterare gridded on the JCOPE-T model grid for comparison.
Both of the satellite-observed and simulated M2 amplitudes estimated on the model grids are averaged insquare regions of 58 by 58 (Figures A1a and A1b). The spatial contrast of the simulated amplitude generally

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Figure A3. Location and reference numbers of the tide gauge stations used for the models validation.

agrees with the observation. Similar maps showing temporal correlation between observed and simulated
M2 amplitude and phase averaged in the square regions (Figures A1c and A1d) indicate that the model wellsimulates the M2 tide variability as observed in the model domain except for some regions in the marginalseas such as Japan Sea, East China Sea, and Yellow Sea.
Tides in JCOPE-T model are introduced using the OTIS tidal model solution [Egbert and Erofeeva, 2002]
through the forcing along open boundaries, and thus we compare the M2 tide in JCOPE-T and OTIS models
itself. For both JCOPE-T and OTIS models the harmonic analysis is performed for annual hourly reconstructed/simulated elevations from the base case experiment interpolated/extrapolated to the tidal gauge
locations. Nearest grid point extrapolation is used for both models if interpolation is not possible. Figure A2a
depicts the difference of M2 tidal
amplitudes in JCOPE-T minus OTIS.
Around open boundaries and in deepsea, the difference is basically small
and does not exceed 2–5 cm, but inmarginal seas and coastal bays, it
could be signiﬁcant and exceeds 1 m.
Distribution of the differences is also
very irregular: close located could beareas of large positive and negative
differences (near Chinese coast in the
Yellow Sea, for example). Difference isalso small over the M2 tide amphidromic points that is especially clear
in the Yellow and Bohai seas. It meansthat both models have an amphidromic points with the tidal amplitude
going to zero in similar locations. Over
Figure A4. Distribution of absolute error of M2 harmonic amplitude (in m) deﬁned
the deep ocean, wave-like signal
as difference in that between JCOPE-T and the tide gauge observation.

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presents in the tide amplitudes difference that could be attributed to the manifestation of baroclinic tideon the sea surface discussed earlier in this paper. Phase difference of M2 tidal constituents in both models isshown in Figure A2b, and its behavior has the similar features as has the amplitude differences distribution:
generally large differences found in the marginal seas. Some speciﬁc is related with location of largest differences in phases near to the M2 tide amphidromic points where, due to the small tide amplitude, thephase deﬁnition has large errors because it is related with division on approaching to zero amplitude value.
Moderate phase difference up to 108 can be found in areas where the baroclinic tides are active. These
areas include the spots analyzed in this work (Luzon Strait, Ogasawara Ridge, Tokara strait, and Izu Ridge)
plus an area over the continental slope off the Tsushima strait with the beam of internal tidal waves propagating in to the Japan Sea [Jeon et al., 2014].
For validation of the M2 sea level variability reproduced by the JCOPE-T and OTIS models, we use the sea
level observation data collected by Japan Coastal Guard (JCG), Japan Meteorological Agency (JMA), andKorean Hydrographic and Oceanographic Administration (KHOA) institutions. Data used for comparison
with the model results passed a simple graphical quality control and suspicious spike data were removed.
Location of used tidal gauges with the reference numbers is shown in Figure A3. Numbers given to stations
are arranged so that these increase starting from the Korean stations in Yellow and East China Seas andmoving with the land on the left along the Korean coast to Japan Sea, returning back from north to south
along the Japanese coast of Japan Sea, and then going northward along the Japanese Paciﬁc coast bypassing Seto Inland Sea. Stations in Seto Inland Sea are placed last as stations 105–114.
We compare the results of the two models with sea level observations at the tide gauge locations. To evaluate both amplitude and phase errors in this comparison, we use the absolute tidal harmonic error [Matsumoto et al., 2000] as
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
Err5 a2obs 1a2mod 22  aobs  amod  ðphaseobs 2phasemod Þ;(A7)where aobs and amod are amplitudes (in m), phaseobs and phasemod are phases (in radian) of observed andmodeled M2 tide, respectively. This value corresponds to the presentation of tidal harmonics as complex
numbers or vectors. Average absolute error for M2 tide at all analyzed 114 tidal gauges is 0.172 m for OTIS
model and 0.168 for JCOPE-T that are very close to each other and are large values for some tidal gauges
due to some errors that are not resolved by both models. However, to consider quality of the tide simulations compared to the observations, we examine distribution of JCOPE-T M2 tide absolute error taken withthe sign of M2 amplitude error: it is positive if the model overestimates the observed amplitude of tide andnegative if underestimates. Figure A4 plots ﬁve grades of JCOPE-T M2 tide absolute error. Crosses indicate
stations where relative absolute error does not exceed 5 cm. Such stations in majority are located in the

Figure A5. M2 harmonic amplitude (in m) evaluated from the tide gauge observation (red bars). Horizontal axis denotes the reference
number of the stations (see Figure A2 for locations). Blue cones denote the error deﬁned by equation (A7) for M2 harmonic (in m) with thesign of the M2 amplitude error of JCOPE-T model relative to the observation. Green cones denote the similar error of OTIS model.

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Paciﬁc and Japan Sea coast of Japan and in Ryukyu Islands south of Japan. Unﬁlled triangles indicate stations with absolute errors do not exceeding 10 cm and ﬁlled triangles denote other stations with relative
difference larger 10 cm. Up-looking red triangles indicate stations where the simulated sea M2 tide amplitude exceeds observed when down-looking blue triangles indicate stations where the model underestimates the observed M2 tide. Overestimation by the model takes place at stations facing Tsushima Strait
connecting East China Sea with Japan Sea. Along the Paciﬁc coast of Japan large differences are found fornumber of stations that are located in coastal bays and in the Seto Inland Sea where this difference could
be attributed to complicated coastal topography and coastline shape unresolved by the model with thehorizontal resolution of 1/368 (approximately 3 km). Serious underestimation of M2 barotropic tide takes
place for stations along the western coast of Korean Peninsula. Majority of tidal gauges there are located inshallow bays with very complicated topography that makes it difﬁcult for reproducing tidal variability therewith the 3 km resolution as we already mentioned for small semienclosed seas of Japan.
To check possible model dependence, we plot in Figure A5 the amplitude of M2 sea level tide harmonic at
tidal gauges as red bars, and signed absolute error of M2 JCOPE-T (blue cones) and OTIS (green cones) sea
level tide relative to the observations. For ﬁrst 22 stations located along the Korean coast, JCOPE-T has
mainly larger errors except for some stations where errors are extremely large and which are unresolved byboth OTIS and JCOPE-T. But basically for all stations from No. 27 and forward JCOPE-T errors are very small
and for many Japanese coastal stations clearly smaller compared with these for the OTIS data. Especiallylarge differences are for last stations located in Seto Inland Sea that is very badly resolved by the 1/128 OTIS
model. We conclude that large errors in reproducibility of tidal sea level variability along the western andsouthern coast of Korea is a difﬁcult task not for our model only, but even for the specialized tide simulation
model with the assimilation of the tidal data like OTIS.

Acknowledgments
This work is part of the Japan Coastal
Ocean Predictability Experiment(JCOPE) promoted by the Japan
Agency for Marine-Earth Science andTechnology (JAMSTEC). The altimeterproducts were produced by Ssalto/
Duacs and distributed by Aviso withsupport from CNES (http://www.aviso.
oceanobs.com/duacs/). The sea level
observation data collected by Japan
Coastal Guard (JCG) and Japan
Meteorological Agency (JMA) areavailable from http://www1.kaiho.mlit.
go.jp/KANKYO/TIDE/real_time_tide/sel/ and the data collected by Korean
Hydrographic and Oceanographic
Administration (KHOA) institutions areavailable from http://www.khoa.go.kr/.
The Oregon State University Tidal
Inversion Software (OTIS) model data
are available from http://volkov.oce.
orst.edu/tides/. The simulation data forthis paper are available from theauthors (http://www.jamstec.go.jp/
jcope/vwp/). Computation codes forthe tidal harmonic and energy
analyses were kindly provided by
Takashi Kagimoto and Hideyuki
Kawajiri. We thank two anonymous
reviewers for their suggestive andconstructive comments on the earlier
versions of the manuscript. KI and YM
are supported by JSPS KAKENHI(26400468).

VARLAMOV ET AL.

As shown in the JCOPE-T simulation results, we have both cases of overestimation and underestimation ofsea level variability compared to that observed on the tidal gauges. The problem of overestimated tide
amplitude was reported by Arbic et al. [2010] for their simulation with the global baroclinic tide model. In
the baroclinic tide models, barotropic tide energy has to be transferred to internal tides. Breaking of internal
waves ﬁnally removes the excess of energy from the model. Although our model JCOPE-T has the horizontal
resolution of 1/368 that is ﬁner than 1/12.58 for the HYCOM model of Arbic et al.’s [2010] results, JCOPE-T still
does not completely resolve the processes of generation and breaking of higher vertical mode internal
waves. But this explanation does not cover the cases of underestimated sea level variability for group of
tidal gauges at the western coast of Korean Peninsula, implying that the horizontal resolution of 3 km is still
too coarse to resolve the tidal variability affected by the complicated bottom and coastal topography in thisregion, and/or the dissipation of the tide is overestimated there.

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