Mesoscale Reproducibility in Regional Ocean Modellingwith a Three-Dimensional Stratiﬁcation Estimate Based on
Aviso-Argo Data
Yusuke Uchiyama

1,5,6,*, Ryosuke Kanki2, Akiko Takano3, Hidekatsu Yamazaki3,5, andYasumasa Miyazawa4

1

Department of Civil Engineering, Kobe University, Kobe, Japan
2
Construction Bureau, City of Kobe, Kobe, Japan3
Department of Ocean Sciences, Tokyo University of Marine Science and Technology, Tokyo, Japan
4
Application Laboratory, Japan Agency for Marine-Earth Science and Technology,
Yokohama, Japan
5
Core Research for Evolutionary Science and Technology, Japan Science and Technology
Agency, Tokyo, Japan
6
Coastal and Estuarine Environmental Department, Port and Airport Research Institute,
Yokosuka, Japan[Original manuscript received 31 October 2016; accepted 24 August 2017]

For dynamically consistent, high-resolution, yet cost-effective regional oceanic downscaling modelling, an empirical three-dimensional (3D) density estimate based on publicly available datasets is utilized for the
Regional Oceanic Modeling System (ROMS) with simple data assimilation (i.e., TS nudging, where TS stands fortemperature and salinity). We rely on a method built upon the two-layer model to reconstruct a mesoscale 3D temperature and salinity ﬁeld, referred to as Tokyo University of Marine Science and Technology (TUMSAT)-TS, usingnear real-time altimeter-derived dynamic height along with Argo ﬂoat proﬁling data. The TUMSAT-TS is ﬁrst validated using in situ hydrographic data, then is implemented in the Japan Coastal Ocean Predictability Experiment(JCOPE2)-ROMS downscaling system for the Kuroshio region off Japan. We explore the usability of TUMSAT-TS
by carrying out three comparative simulations with temperature and salinity nudging towards the (i) TUMSAT-TSand (ii) JCOPE2-TS ﬁelds, and (iii) without the nudging. Whereas the unassimilated case fails to properly accountfor the Kuroshio, both datasets individually are found to help reproduce the mesoscale variability of the Kuroshio,
as well as its transient paths, volume transport, associated kinetic energy (KE) and eddy KE, and seasonallyvarying stratiﬁcation.

ABSTRACT[Traduit par la rédaction] Pour effectuer une réduction d’échelle par modélisation océanique régionaleà haute résolution et dynamiquement cohérente, qui reste avantageuse quant au coût, nous utilisons des estimations
empiriques et tridimensionnelles de densité se fondant sur des données offertes publiquement, et le système régionalde modélisation océanique (Regional Oceanic Modeling System; ROMS) combiné à une assimilation simple dedonnées (c.-à-d. un rappel spectral pour la température et la salinité). Nous appliquons une méthode fondée
sur le modèle à deux couches aﬁn de reconstruire à mésoéchelle un champ tridimensionnel de température etde salinité (TS), appelé TUMSAT-TS (Tokyo University of Marine Science and Technology-TS), à partir de hauteurs dynamiques dérivées de mesures d’altimètre en temps quasi réel et de données de ﬂotteurs proﬁlants
Argo. Nous validons d’abord le champ TUMSAT-TS à l’aide de données hydrographiques in situ. Puis nous appliquons le système de mise à l’échelle inférieure Japan Coastal Ocean Predictability Experiment (JCOPE2)-ROMS
pour la région du Kuroshio au large du Japon. Nous explorons la facilité d’exploiter le TUMSAT-TS en menanttrois simulations comparatives qui rappellent la température et la salinité vers les champs i) TUMSAT-TS et ii)
JCOPE2-TS, puis iii) sans rappel spectral. Le cas sans assimilation ne tient pas adéquatement compte du Kuroshio.
En revanche, chacune des deux autres séries de données prises individuellement aide à reproduire tant la variabilité du Kuroshio à mésoéchelle que ses trajectoires transitoires, son volume de transport, l’énergie cinétiqueassociée et ses tourbillons, ainsi que la stratiﬁcation saisonnière.

RÉSUMÉKEYWORDS

mesoscale reproducibility; Kuroshio; Aviso-Argo-derived hydrography; ROMS

*Corresponding author’s email: uchiyama@harbor.kobe-u.ac.jp
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Canadian Meteorological and Oceanographic Society2 / Yusuke Uchiyama et al.
1 Introduction
Oceanic reanalysis and prediction based on ocean models aresocially beneﬁcial to many sectors across a broad spectrum
including logistics, ﬁsheries, meteorological and coastal disaster prevention organizations, and environmental protection
agencies. Data assimilation is a useful technique for improving
the reproducibility of oceanic structure in ocean modelling(e.g., Wunsch, 2001). Agencies such as the European Centre
for Medium-range Weather Forecasts, the National Centers
for Environmental Prediction, and the Global Ocean Data
Assimilation Experiment (GODAE) rely markedly on assimilation in their operational oceanic reanalysis and prediction
systems (e.g., GODAE, 2001). In general, successful data
assimilation depends on many factors including satellite
remote sensing, such as that done by altimeters (Topography
Experiment/Poseidon (TOPEX/Poseidon) and Archiving,
Validation and Interpretation of Satellite Oceanographic data
(Aviso1)) for sea surface height (SSH), and in situ measurements with moorings and buoys (Argo2, expendable bathythermograph (XBT3), Tropical Atmosphere Ocean/Triangle
Trans-Ocean Buoy Network (TAO/TRITON4)) for subsurface, three-dimensional oceanic structure. Many of thesedata assimilation systems account for SSH and sea surface
temperature (SST) variability (e.g., Behringer, Ji, &Leetmaa, 1998; Fujii & Kamachi, 2003). Inclusion of subsurface temperature and salinity is also essential for improving
the reproducibility of a model, while surface salinity is generally of less importance for the density in the upper ocean
except for river mouths and estuaries. For instance, Ji, Reynolds, and Behringer (2000) conducted a reanalysis of the
Paciﬁc Ocean assimilated with both in situ subsurface temperature data from the TAO moorings array data and the
XBT network, as well as the altimetry SSH ﬁeld fromTOPEX/Poseidon for the prediction of the El Niño–Southern
Oscillation (ENSO). The modelled temperature ﬁeld assimilated with both the subsurface temperature and SSH is lessaccurate than that without the TOPEX/Poseidon data
because of inconsistent dynamic height and, thus, the resultant
inaccurate salinity ﬁeld. Troccoli et al. (2002) demonstrated
that assimilation merely with temperature contaminates thesalinity ﬁeld through an undesirable salinity adjustment
arising from an inconsistent density structure. All these previous studies suggest that salinity data are required to conserve
the correct density stratiﬁcation although real-time observations of surface and subsurface salinity are still limited intime and space.
In the last three decades, three-dimensional ocean observations have progressed. Since the 1980s the TAO array ofmoored buoys (Hayes, Mangum, Picaut, Sumi, & Takeuchi,

1991; McPhaden, 1993) has been expanded in the tropicalPaciﬁc within 10° of the equatorial Paciﬁc for ENSO prediction. A broad-scale global array of temperature-salinity proﬁling ﬂoats, known as the Argo project (e.g., Argo Science
Team, 2001), was launched in 2000, and the number ofArgo ﬂoats in the world’s oceans has reached 3,0005. This progress makes in situ subsurface density data available at ahigher spatiotemporal resolution. These efforts promote theavailability of in situ subsurface data for oceanic data assimilation at almost any point in the world’s oceans.
Mesoscale oceanic structure and variability, such as thetransient meandering of the Kuroshio, are necessarily reproduced as accurately as possible in realistic regional ocean
modelling for a broad range of purposes including scientiﬁc,environmental, navigational, military, and engineering
aspects, particularly in coastal marginal seas. Kamachi, Kuragano, Yoshioka, Zhu, and Uboldi (2001, 2004) described an
operational ocean data assimilation system based on the
Meteorological Research Institute Oceanic Global Circulation
Model (MRI-OGCM) used in the Japan Meteorological
Agency (JMA) for the Kuroshio along Japan at the ﬁnest
grid resolution of 1/4°. The TOPEX and in situ (ship andﬂoat) temperature and salinity data are utilized for the assimilation (nudging) using a four-dimensional space-time
optimal interpolation and vertical projection. This system successfully reproduces the mesoscale variability of the Kuroshio
axis and its low-frequency variability, especially around the
Okinawa Islands and the Ryukyu Current System. Uchiyama,
Ishii, and Miyazawa (2012) demonstrated with a submesoscale eddy-resolving Japan Coastal Ocean Predictability Experiment–Regional Ocean Modeling System (JCOPE2-ROMS)
downscaling oceanic modelling system that the mesoscale
reproducibility of the Kuroshio axis along Japan is signiﬁcantly improved by introducing restoration to data (temperature and salinity nudging) where the prognostic temperatureand salinity ﬁelds are weakly nudged four-dimensionally
towards the assimilative JCOPE2 reanalysis6. The dynamic
kernel of JCOPE2 is a Princeton Ocean Model (POM)based, eddy-resolving, operational oceanic reanalysis and prediction system at a horizontal grid spacing of 1/12° developedby Miyazawa et al. (2009) and maintained at the Japan Agency
for Marine-Earth Science and Technology. JCOPE2 has athree-dimensional variational data assimilation (3D-VAR)
scheme with satellite SSH, SST, Argo ﬂoats, mooring, andshipborne data depending on their availability. It also turns
out to be a substantial improvement in reproducibility and predictability around the Kuroshio near Japan and has been
widely used for scientiﬁc research and navigation, as well as
engineering and ﬁshery activities. However, such a reliable,1

http://www.aviso.altimetry.fr/en/home.html
http://www.jamstec.go.jp/J-ARGO/index_e.html
http://www-hrx.ucsd.edu/
4
http://www.pmel.noaa.gov/tao/index.shtml
5
http://www.argo.net
6
http://www.jamstec.go.jp/jcope/htdocs/e/home.html
2
3

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Mesoscale Reproducibility in Regional Ocean Modelling / 3
T ABLE 1.

Numerical conﬁgurations of the ROMS model.

Items

Data

Computational period
Horizontal grid resolution
Grid
Baroclinic time step
Surface wind stress
Other surface ﬂux
SST to restore
Topography
Boundary condition
Temperature and salinity nudging towards:

1 Jan. 2010 to 5 May 2013 (plus one year model spin-up)
3 km
784×864 (× 32 vertical s-layers)
120 s
JMA GPV-GSM (daily average, dx = 20 km)
COADS05 (monthly climatology)
Pathﬁnder-AVHRR (monthly climatology)
JODC J-EGG500 supplemented by SIO SRTM30_Plus
JCOPE2 (daily average, dx = 1/12o)(1) 7-day average TUMSAT-TS (ROMS-TUM)(2) 10-day average JCOPE2-TS (ROMS-JCP)(3) none (ROMS-FREE)

Nudging strength

1/10 (d−1)

high-resolution oceanic reanalysis may only be available
for some limited areas. Therefore, alternative surface and subsurface temperature and salinity data are essential to improving the accuracy of oceanic reanalysis and prediction.
Guinehut, Larnicol, and Le Traon (2002, 2004) reconstructeda three-dimensional monthly mean temperature ﬁeld with a combination of Argo and remotely sensed SSH and SST data at 1/6°
resolution. Takano, Yamazaki, Nagai, and Honda (2009) proposed an empirical method for estimating a three-dimensional
thermal structure from near real-time Aviso altimetry data
along with Argo ﬂoat data based on the two-layer model ofGoni, Kamholz, Garzoli, and Olson (1996). This method
makes use of only currently available data, so no new instrumentation cost is required. In addition, they show improved accuracy
in the estimation of ocean thermal structure with increased
spatial (1/10°) and temporal (every seven days) resolutions.
In the present study, we take advantage of the threedimensional temperature estimate of Takano et al. (2009)
for the assimilative oceanic reanalysis with the JCOPE2ROMS systems. We further expand this method to simultaneously obtain a three-dimesnional salinity ﬁeld in sucha way that the thermal structure is converted into salinity
by using polynomial regression models describing relationships between temperature and salinity from Argo ﬂoat
data. The derived three-dimensional temperature and salinity
estimate (hereafter TUMSAT-TS) are then used for theassimilation. We conducted a synoptic numerical experimentof mesoscale variability of the Kuroshio using the JCOPE2ROMS downscaling system to explore how the empirical
TUMSAT-TS dataset improved the results. We aimed toanalyze the reproducibility of the Kuroshio by carryingout two comparative runs based on ROMS with temperatureand salinity nudging towards (i) the 10-day averaged temperature and salinity ﬁelds from JCOPE2 (hereafter called

JCOPE2-TS data) and (ii) the TUMSAT-TS ﬁelds available
every seven days, along with a supplemental unassimilated
simulation. The modelled ﬂow and stratiﬁcation were compared with several ﬁeld measurements to quantitatively
evaluate the potential usability of TUMSAT-TS data inoperational oceanic reanalysis and prediction.

2 Methods
a The JCOPE2-ROMS Model
The downscaling oceanic modelling for the Kuroshio region
off Japan is based on the University of California, Los
Angeles (UCLA), version7 of ROMS8, a state-of-the-art
regional oceanic circulation model (Shchepetkin & McWilliams, 2005, 2008). The ROMS conﬁguration is summarizedin Table 1. The boundary condition is provided by the dailymean ﬁeld of the JCOPE2 reanalysis (Miyazawa et al.,2009) at a horizontal grid spacing of 1/12° (dx ≈ 10 km),projected spatiotemporally onto the perimeters of the
ROMS domain at dx = 3 km (Fig. 1). The ROMS model
is designed to encompass the Kuroshio and the Kuroshio
Extension regions off Japan and consists of 784 × 864 horizontal grid cells with 32 bottom-following, stretched vertical
σ-layers. The model topography is taken from the 30 arcsecond global bathymetry based on the Shuttle Radar Topography Mission (SRTM30_Plus9; Becker et al., 2009)
overall, with reﬁnement using the Japan Oceanographic
Data Center (JODC)-Expert Grid data for Geography10(J-EGG500) at a resolution of 500 m for the coastal
regions. We make use of the daily product of the JMA
Grid-Point Values of Global Spectral Model (GPVGSM11) reanalysis for surface wind stresses and the Comprehensive Ocean-Atmosphere Data Set (COADS12) climatological heat, radiation, and freshwater ﬂuxes for the7

http://web.atmos.ucla.edu/roms/Welcome.html
https://www.myroms.org/
http://topex.ucsd.edu/WWW_html/srtm30_plus.html
10
http://www.jodc.go.jp/data_set/jodc/jegg_intro_j.html
11
http://www.jmbsc.or.jp/jp/online/ﬁle/f-online10100.html
12
http://iridl.ldeo.columbia.edu/SOURCES/.COADS/8
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Fig. 2 The blending rate (no dimension, ranging from 0 to 1) of the
TUMSAT-TS data against the JCOPE2-TS data.
Fig. 1 The ROMS domain (dx = 3 km, outlined in black). The red line represents the JMA’s hydrography transect along 137°E. The dotted lines
indicate the cross-sections from Cape Shionomisaki (left) and Cape
Omaezaki (right) used in Fig. 12. The colour bar indicates depth inmetres.

other surface forcing. Monthly climatological PathﬁnderAdvanced Very High Resolution Radiometer (AVHRR13)
is applied to restore the SST with an inverse time scale of
1/90 (d−1) to avoid a long-term bias resulting from the
COADS climatological surface heat ﬂux, while no restoration is conducted for surface salinity. The ROMS includes
K-proﬁle parameterization (KPP), a non-local turbulent
closure scheme for vertical momentum, and tracer mixing
in the surface and bottom planetary boundary layers andin the interior of the ﬂuid (Durski, Glenn, & Haidvogel,
2004; Large, McWilliams, & Doney, 1994). In addition,
ROMS has a numerical hyperdiffusion associated with horizontal advection with an effective diffusivity coefﬁcient that
decreases with the grid scale. The ROMS is initialized withthe spatially interpolated JCOPE2 ﬁeld for 1 January 2009and spun up for one year. The computational period
chosen is January 2010 to May 2013, about three years.
The detailed algorithm and its implementation of thenesting approach based on the UCLA-ROMS are describedin Mason et al. (2010), Buijsman, Uchiyama, McWilliams,
and Hill-Lindsay (2012), Uchiyama, Idica, McWilliams,
and Stolzenbach (2014; 2017), and Kamidaira, Uchiyama,and Mitarai (2017).
In the present study, the two types of data assimilation are
examined based on the temperature and salinity nudging in
ROMS with one towards time-varying three-dimensional TS
ﬁelds of the JCOPE2-TS and the other towards those of the
TUMSAT-TS. We call the former case ROMS-JCP and the13latter ROMS-TUM. A weak nudging strength of 1/10 d−1 isset in both ROMS runs. In the ROMS-JCP, the shallow
coastal areas with depths less than 20 m are not included in
the nudging to allow intrinsic shallow water dynamics thatare not well represented in the JCOPE2 model. TheTUMSAT-TS ﬁeld is optimal for the offshore subsurface
regions on the Paciﬁc side of Japan because a sufﬁcientnumber of Argo ﬂoats have been deployed. Therefore, thetemperature and salinity ﬁelds in the coastal regions and in
the Sea of Japan are supplemented by the JCOPE2-TS at theblending rate shown in Fig. 2. We also exclude surface
water shallower than 80 m (z < −80 m) from the salinity
nudging in ROMS-TUM because the near-surface salinity is
not well quality-controlled. Note that the daily-averaged
results from the models are exploited in the following analyses
unless otherwise stated.
b TUMSAT-TS Model
The TUMSAT-TS was derived from altimeter data and in situ
density data primarily based on the method described in
Takano et al. (2009). Water temperature was estimated fromisothermal depths that are derived from an empirical equation
based on the two-layer model of Goni et al. (1996) with altimetry absolute dynamic height acquired from Aviso data
along with in situ Argo temperature proﬁles:ε(x, y, t, T)h(x, y, t, T) = α(T)η(x, y, t) + β(T),(1)

where ε = (ρ2 – ρ1)/ρ2 so that the reduced gravity is g′ = εg; thesubscripts 1 and 2 correspond to the upper and lower layers
segmented by the user-deﬁned temperature T at the interface
between two layers; x, y, and t are the two horizontal

http://podaac.jpl.nasa.gov/AVHRR-Pathﬁnder
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Mesoscale Reproducibility in Regional Ocean Modelling / 5
coordinates and time, depending on the availability of theAviso data; h is the thickness of the upper-layer, thus is theisothermal depth; α and β are empirical parameters to be determined; η is the absolute dynamic topography from Aviso.
First, the Argo temperature and salinity proﬁles were used todetermine ε(x0, y0, t0, T ) h(x0, y0, t0, T ) on the sparse Argo
ﬂoat locations available at (x0, y0, t0) in the upper layer.
Then α (T ) and β (T ) were derived from a linear regression
analysis between η(x0, y0, t0) and ε(x0, y0, t0, T ) h(x0, y0, t0,
T ). Subsequently we evaluated the ε(x, y, t, T ) distribution
at the resolution of Aviso, (x, y, t), from the monthly mean climatology of temperature and salinity from the forty-ﬁrst to ﬁftieth years of the Modular Ocean Model (MOM)-based highresolution oceanic global circulation model for the Earth
Simulator (OFES) data (Masumoto et al., 2004) instead of
the sparse Argo proﬁles. These procedures enabled us to estimate arbitrary isothermal depth h. In particular, multiple isotherms of 3°, 5°, 10°, 16°, 17°, 18°, 20°, and 25°C were
derived in the present study. Satellite SST data were used
for the surface temperature. The temperature in the subsurface
deeper layer with T < 3°C was replaced with monthly mean
OFES temperature.
After the three-dimensional temperature ﬁeld was obtained,
the three-dimensional salinity ﬁeld was estimated with the predetermined polynomial regression coefﬁcients between thetemperature and salinity data of Argo ﬂoats deployed in thearea (20°–50°N, 136°–180°E) from 1 August 2004 to 31
December 2012. Each proﬁle was interpolated vertically at
100 hPa intervals. The Paciﬁc side of the study area wasdivided into blocks by creating 5o × 5o horizontal grids with
15 vertical levels (25, 50, 100, 150, 200, 300, 400, 500,
600, 700, 800, 900, 1100, 1300, and 1500 m depths). The
regression analysis was conducted for each block by collecting
all available Argo data in the block, removing the highest andlowest 50 temperature data points (and associated salinity
data) to enhance the accuracy. The polynomial order was
selected according to the Akaike information criterion. Then,
to reduce blockwise discontinuity in the salinity estimate, we
computed the horizontal distributions of the salinity on isotherm surfaces from −0.3° to 31°C at intervals of 0.1°C andapplied horizontal bilinear interpolation and vertical linear
interpolation. Even with this smoothing operation, there
were still undesirable block noises in the salinity estimate(see Section 3). Note that we also excluded near-surface (z <−80 m) salinity from the TS nudging because it is not as
precise as the temperature owing to the limited number ofArgo proﬁles. As a consequence, the diagnostic three-dimensional temperature and salinity ﬁelds (viz., TUMSAT-TS)
were available at seven-day intervals with a horizontal resolution of 1/10° for the present ROMS simulation.
c Measures for assessing mesoscale reproducibility
Reproducibility of the mesoscale oceanic structures in the
ROMS results was measured quantitatively with root-meansquare error (RMSE) and a model skill score (e.g., Ralston,Geyer, & Lerczak, 2008; Warner, Geyer, & Lerczak, 2005;

Wilmott, 1981) as represented by the following equations.

1
RMSE =(Xmodel − Xobs )2 ,Nskill = 1 − (2)|Xmodel − Xobs |2(|Xmodel − Xobs | + |Xobs − Xobs |)

2

,

(3)

where Xmodel is the ROMS model result; Xobs is the observed“true” data (e.g., from Aviso, JCOPE2, and JMA); overbars
denote the averaging operation, and the summations aretaken over the number of grid points where the observation
is available. The RMSE has the same units as X (e.g., velocity,
SSH, T, and S) and shows better agreement the closer it is tozero, while the skill is non-dimensional and a value of one
indicates perfect reproducibility. Note that alternative skill
scores exist, such as the one proposed by Murphy (1988),
but we did not ﬁnd any substantial differences in the result.
3 Validity of the TUMSAT-TS estimate
To evaluate the accuracy of the TUMSAT-TS estimate, we
compared the results with the hydrography observations
along 137°E conducted by the JMA. Note that the climatological time averages were taken over three years (2010–2012)
for the ROMS result and ten years (1997–2010) for the
JMA data for comparable accuracy using a limited numberof the observations. This mismatch of the two periods does
not introduce any signiﬁcant error associated with interannual
variability in the following analyses. The seasonally averaged
stratiﬁcation in summer and winter from TUMSAT-TS is ingood agreement with the measurement on the whole(Fig. 3). The modelled thermocline and haloclines are slightly
deeper, and the subsurface salinity minima, at around z =−1000 m, are formed more widely in the vertical than themeasurements. However, except for these minor mismatches,TUMSAT-TS reproduces the stratiﬁcation adequately. Horizontal distributions of the monthly climatology of temperatureand salinity from TUMSAT-TS were then compared with themonthly averaged climatology from the World Ocean Atlas
2005 (WOA05; Levitus, Gurgett, & Boyer, 1994; Antonov,
Locarnini, Boyer, Mishonov, & Garcia, 2006; Locarnini, Mishonov, Antonov, Boyer, & Garcia, 2006) at z = −100 m (Figs 4
and 5). The TUMSAT-TS shows fair agreement with WOA05,
particularly in temperature. The zonal gradient of temperature
is well reproduced in all four seasons. In contrast, the salinity
ﬁeld has an undesirable discontinuity at several locations,arising from the piecewise regression estimate (Section 2.b),and is underestimated, as indicated by the deeper haloclines.
Moreover, warmer and fresher patches are found around the
Izu Ridge (30°–34oN and 138°–141oE), particularly insummer. These spurious noises are artifacts of the
TUMSAT-TS model due mainly to shallow topography,
such as ridges, where dense water does not exist in thelower layer in the two-layer model. This leads to diminishingdensity differences between the two layers thus reducing

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Fig. 3 Comparison of the seasonally averaged stratiﬁcation along the JMA transect at 137°E from the TUMSAT-TS data and JMA observations for summer (upper,
July–September) and winter (lower, January–March).

Fig. 4 Climatological monthly averaged temperature at z = −100 m for the four seasons (February, May, August, and November); (left) TUMSAT-TS data and(right) World Ocean Atlas 2005 (WOA05).
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Fig. 5 As in Fig. 4, but for salinity at z = −100 m.

ε (measure of stratiﬁcation; Eq. (1)), resulting in somewhat
deeper isotherm surfaces. This discrepancy in TUMSAT-TS
is mediated by introducing the blending with JCOPE-TS, as
shown in Fig. 2, yet it cannot be completely avoided (seeSection 5 for a more a detailed argument). Nevertheless,these results suggest that although reproducibility in the stratiﬁcation is moderate, the slight deviations in the vertical proﬁles cause nontrivial difference between the TUMSAT-TS
estimate and the WOA05 data, speciﬁcally in horizontal
salinity distribution. In summary, there is room for improvement in the TUMSAT-TS salinity estimate.
4 The assimilative ROMS reproducibility
The two ROMS results with temperature and salinity nudging
are compared with Aviso altimeter data and the JCOPE2 reanalysis to quantitatively assess the model’s reproducibility.
Figure 6 shows the annually averaged surface velocity
14

magnitude, SSH variance, and surface eddy kinetic energy(EKE) evaluated for 2012. The EKE accounts for the variability shorter than the 90-day period with the frequency high-passﬁltered surface horizontal velocity14. These model-derived
variables are basically consistent with the data. The mean Kuroshio paths are approximately the same, and the mesoscalevariability (SSH variances) and EKE are energetic in the Kuroshio Extension region in all the results. The RMSE and skill
for each year during the 2010–2012 period also represent
quantitative agreement with the data for both the assimilative
ROMS runs (Table 2).
To demonstrate the substantial importance of temperatureand salinity nudging, an alternative ROMS run without any
assimilation, called ROMS-FREE, was carried out. Except
for the exclusion of temperature and salinity nudging, theother numerical conﬁgurations in the ROMS-FREE caseremained identical to the ROMS-TUM and ROMS-JCP
cases. Annually averaged velocity magnitude, SSH variance,

There has been an argument on possible errors associated with frequency ﬁlters for the multiscale Reynolds decomposition (Liang, 2016).
ATMOSPHERE-OCEAN iFirst article, 2017, 1–18 https://doi.org/10.1080/07055900.2017.1399858
Canadian Meteorological and Oceanographic Society8 / Yusuke Uchiyama et al.

Fig. 6 Annually averaged velocity magnitude at the surface (top), the SSH variance depicting the mesoscale variability (middle), and the surface eddy kinetic
energy (EKE) for periods shorter than 90 days for 2012 (bottom); (left) ROMS-JCP, (middle) ROMS-TUM, and (right) Aviso data or the JCOPE2
reanalysis.

T ABLE 2.

Model skill scores (dimensionless) and RMSEs of surface velocity (m s−1), SSH variance (m2), and surface eddy kinetic energy (EKE, m2 s−2), surface
kinetic energy (KE, m2 s−2) relative to Aviso (velocity magnitude and SSH variance) or to the JCOPE2 reanalysis (EKE and KE) for the years 2010–2012.
Surface Velocity

SSH Variance

EKE

KE

Model

Year

Skill

RMSE

Skill

RMSE

Skill

RMSE

Skill

RMSE

ROMS-JCP

2010
2011
2012
2010
2011
2012
2010
2011
2012

0.78210.77570.78000.74610.72850.75900.63420.7304
0.55860.05020.05580.05050.05900.06430.05590.0791
0.06330.09050.98180.89070.93730.96710.9117
0.94340.78520.77070.70790.00340.00740.00520.00470.00600.00510.01860.01600.0212

0.97550.99310.96080.96820.95950.9496
0.53340.48550.47410.00220.00130.00320.00250.00290.00350.02650.02970.03400.74960.86270.65110.83540.77220.40130.26180.26750.17420.00250.00250.00330.00240.00340.00470.01520.01620.0258

ROMS-TUM
ROMS-FREE

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Mesoscale Reproducibility in Regional Ocean Modelling / 9

Fig. 7 As in Fig. 6, but for ROMS-FREE (excluding temperature and salinity nudging).

Fig. 8 Comparison of the volume-averaged kinetic energy (KE) in the upper ocean above z = −400 m for ROMS-JCP (blue curve), ROMS-TUM (magenta curve),
ROMS-FREE (green curve), and JCOPE2 reanalysis (black dashed curve).

and EKE at the surface for 2012 from the ROMS-FREE are
shown in Fig. 7. The path of the Kuroshio meanders unrealistically, and the SSH variance and EKE are overly energetic
compared with the cases with data assimilation (Fig. 6). The
result is much lower skill and poorer RMSE (Table 2)
because of the underestimate of the energy dissipation due
to the exclusion of temperature and salinity nudging(Uchiyama et al., 2012). These results provide the solid evidence that ensures the inevitability of the inclusion of temperature and salinity nudging for much better mesoscale
reproducibility in the Kuroshio region.
Time series of the volume-averaged surface kinetic energy(KE) in the upper ocean above z = −400 m on the Paciﬁcside of the model domain is plotted for the two assimilative
ROMS results along with the ROMS-FREE output and the
JCOPE2 data (Fig. 8). The corresponding model skill and
RMSE are summarized in the last two columns of Table 2.
The KE behaves quite similarly for the ROMS-TUM,
ROMS-JCP, and JCOPE2 cases in the ﬁrst year, but afterthat ROMS-TUM and ROMS-JCP start deviating slightly
from the JCOPE2 data, particularly in the third year. In
2011, the KE derived from ROMS-TUM is underestimatedin winter, whereas it is overestimated in summer and fall. In

early 2012, both ROMS-TUM and ROMS-JCP exhibit
lower KE compared with JCOPE2, while ROMS-TUM deviates slightly more than ROMS-JCP in late 2012. The RMSE
and skill in Table 2 partly support this trend. Both the assimilative ROMS models perform quite well in the ﬁrst year after
initialization although they gradually drift from the JCOPE2
data. The temperature and salinity of the TUMSAT-TS are
estimated separately, which could become a source of longterm accumulated errors. In contrast, ROMS-FREE produces
unrealistically large KE for the three years with the worst
skill scores and RMSEs. These results demonstrate thatROMS runs with temperature and salinity nudging towards
either the JCOPE2-TS or TUMSAT-TS data reproduce themesoscale variability in the Kuroshio region reasonably well
for a year or two. We should note that preliminary test simulations were performed with nudging strengths of 1/5, 1/10,
and 1/20 d−1 (see Section 2.a) to ﬁnd that there is no substantial improvement in model skill or RMSE although using
1/10 d−1 results in the best skill and RMSE of the three. The
spectral nudging technique (e.g., Von Storch, Langenberg,& Feser, 2000) is used occasionally in atmospheric downscaling models, in which large-scale variability is constrained by
the nudging while small-scale intrinsic variability is permitted.

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Fig. 9 Comparison of the seasonally averaged stratiﬁcation from (left) ROMS-JCP, (middle) ROMS-TUM, and (right) JMA observations, along the 137°E transect
for summer (upper two rows) and winter (lower two rows).

Such a method may be an alternative for a future approachrather than further tweaking of the nudging strength.
The modelled cross-sectional temperature and salinity ﬁelds
are compared with the JMA data along the 137oE transect forthe summer and winter (Fig. 9). Again, overall consistency is
conﬁrmed in both temperature and salinity in all three cases.
Similar to the input TUMSAT-TS data (Section 2.a andFig. 3), the assimilative ROMS-TUM also produces slightly
thicker thermoclines and haloclines than the observations
with moderate consistency in the near-surface temperatureand subsurface salinity. However, ROMS-JCP has less freshening bias in salinity at around 800 m depth, while ROMSTUM has better agreement at this depth. The corresponding

T ABLE 3.

Model skill scores (dimensionless), RMSEs of temperature, and
RMSEs of salinity for the years 2010–2012 relative to JMA
observations in the cross-section along the 137°E transect asshown in Fig. 9.
Temperature

Salinity

Model

SeasonSkill

RMSE (°C)

Skill

RMSE

ROMS-JCP

summerwintersummerwintersummerwinter

0.99870.99930.99720.99930.99470.99720.41000.28620.62100.45140.78890.57100.98430.98550.98450.98620.92810.93800.03500.03310.03780.03500.0671
0.0621

ROMS-TUM
ROMS-FREE

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Mesoscale Reproducibility in Regional Ocean Modelling / 11

Fig. 10 Comparison of monthly averaged temperature and salinity in the Kuroshio region at z = −100 m from (left) ROMS-JCP, (middle) ROMS-TUM, and (right)
the JCOPE2 reanalysis, for February 2012 (upper two rows) and August 2012 (lower two rows).

RMSE and model skill also indicate good agreement with thedata; in particular, both assimilative ROMS models give comparable scores for temperature and salinity (Table 3). In turn,
ROMS-FREE generally exhibits much poorer reproducibility
than ROMS-JCP and ROMS-TUM.
Next, monthly averaged horizontal density structures forthe two assimilative ROMS results are compared withthose for the JCOPE2. Figure 10 depicts the temperatureand salinity distributions at z = −100 m for Februaryand August 2012 in the Kuroshio region. The temperaturesfrom the two ROMS cases are again in good agreementwith those from JCOPE2, but the ROMS-TUM salinity
is less consistent with the JCOPE2 salinity. The
ROMS-TUM salinity has a weaker meridional gradient

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Fig. 11 Seasonally (upper four rows) and climatologically (bottom row) averaged eastward velocity normal to the 137°E cross-section from (left) ROMS-JCP,(middle) ROMS-TUM, and (right) the geostrophic velocity estimated with JMA hydrographic data. The contour interval is 0.2 m s−1.

with much less freshening in the coastal area on the left
side of the Kuroshio axis than the ROMS-JCP and
JCOPE2 salinity. In addition, the ROMS-TUM salinity inthe southern part of the domain (south of 32°N) is
lower by about 0.2 than in the other two cases, leading
to a weaker northeastward gradient, particularly in
February. The coastal inconsistency in the temperatureand salinity ﬁelds is attributed to a deﬁciency in the
Argo ﬂoats and the altimetry data.
5 Reproducibility of the Kuroshio
Figure 11 shows the eastward velocity normal to the 137°E
cross-section for the two ROMS cases along with theATMOSPHERE-OCEAN iFirst article, 2017, 1–18 https://doi.org/10.1080/07055900.2017.1399858
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Mesoscale Reproducibility in Regional Ocean Modelling / 13

Fig. 12 Temporal variations of the Kuroshio axis as a function of distance from Cape Omaezaki (CO; upper panel) and Cape Shionomisaki (CS; lower panel) for
ROMS-JCP (blue curve), ROMS-TUM (magenta curve), ROMS-FREE (green curve), the JCOPE2 reanalysis (black dashed curve), and JMA’s estimate(open circles).

Fig. 13 Temporal variations of the volume ﬂux (Sv) associated with the Kuroshio for ROMS-JCP (blue curve), ROMS-TUM (magenta curve), ROMS-FREE(green curve), and the JCOPE2 reanalysis (black dashed curve). The cross-sectional integral is taken along 137°E and between 32°N and 33.5°N.

geostrophic velocity estimated from in situ JMA hydrography
data (see Fig. 9). All four seasonal and annual mean velocity
distributions show good agreement with the JMA data interms of the position of the Kuroshio axis approximated by
the maximum velocity that appears at z > −500 m and peaks
near the surface at around 33°N. The two ROMS runs,
especially ROMS-TUM, indicate greater maximum eastward
velocity around the Kuroshio axis than the JMA data. Thisis partly because of the difference in the duration of the time
average between the model and the observations (Section 3).
The approximate area of the Kuroshio main body in ROMSTUM is more widely distributed both in the offshore andvertical directions. In turn, ROMS-TUM yields negative(westward) velocity far into the sea around 30°–31°N. The
ROMS-JCP also yields a westward but lower velocity butwith a smaller value.
Subsequently, for more rigorous mesoscale Kuroshio modelling, the reproducibility of the transient Kuroshio path isquantitatively examined. We introduce the southward distances to the Kuroshio axis from Cape Omaezaki (CO;along about 138.20oE, the black dotted line on the right in
Fig. 1) and from Cape Shionomisaki (CS; along about
135.76°E, the black dotted line on the left in Fig. 1) to investigate the time-dependent behaviour of the position of the Kuroshio. According to the JMA, the Kuroshio axis is deﬁned as
the lateral point with maximum normal velocity at 50 m depth.

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Fig. 14 Monthly averaged near-surface velocity vectors and their magnitude (colour) at z = −100 m for February 2012 (upper panels) and August 2012 (lower
panels) for (a) ROMS-JCP, (b) ROMS-TUM, and (c) the JCOPE2 reanalysis.

Figure 12 shows two time series plots of the distance from CO
and CS from the two assimilative ROMS runs, ROMS-FREE,
JCOPE2, and JMA’s model estimate. The ROMS-TUM,
ROMS-JCP, and JCOPE2 behave quite similarly, whereas
the Kuroshio path in ROMS-TUM tends to have a slightly

shorter distance to the capes than the others. The ROMSFREE performs reasonably well, except for large deviationsin the later years.
To further quantify the reproducibility of the Kuroshio, thecross-sectionally integrated eastward volume ﬂuxes along the

Fig. 15 Monthly averaged dynamic height anomaly (m2 s−2) at z = −100 m derived using (left) ROMS-JCP, (middle) ROMS-TUM, and (right) JCOPE2 data for
February (upper panels) and August (lower panels) 2012.
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Fig. 16 As in Fig. 15, but with TUMSAT-TS for (a) February and (b) August 2012.

137°E transect are plotted in Fig. 13 for the two assimilative
ROMS cases, ROMS-FREE, and JCOPE2. The integral istaken from the bottom to the surface between 32° and 33.5°N,
where the ﬂuctuating Kuroshio axis is mainly located. The
ROMS-TUM, ROMS-JCP, and JCOPE2 have similar variability, ranging from 53 to 60 Sv (1 Sv = 106 m3 s−1) that is consistent with measurement (e.g., Nitani, 1972; Qiu & Joyce,
1992). In 2010 and 2012, the ﬂuxes from the three cases
agree quite well except for April 2010 and the second halfof 2012. The ROMS-TUM tends to yield slightly larger
ﬂuxes, while ROMS-JCP slightly underestimates the ﬂuxes
compared with JCOPE2, which is consistent with the crosssectional velocity distributions in Fig. 10. In turn, thevolume ﬂux is overestimated by ROMS-FREE, ranging
from 70 to 140 Sv, with degraded performance in the later
years.
Monthly averaged, near-surface velocity vectors and theirmagnitude at z = −100 m for February and August 2012 aredisplayed in Fig. 14. The velocity ﬁeld around the Kuroshio
axis from ROMS-TUM agrees well with that from JCOPE2,
while the ROMS-JCP results in a slightly more energetic Kuroshio with a more conﬁned narrow main path, which is consistent with the sharpness of the density gradient in the
Kuroshio front (Figs 3, 9, and 10). In addition, a recurring
westward current emerges in the southern section of the Kuroshio path, most prominently in ROMS-TUM (Figs 11 and
14). This westward countercurrent varies spatially with time

but appears consistently throughout the computational
period. The countercurrent is more apparent in summer, corresponding to the warm-core gyre in ROMS-TUM (Fig. 10) but
is weaker in winter. As we have found in the cross-sectionalplots along the 137oE transect (Fig. 11), the velocity of thecountercurrent is westward down to about 800 m depth.
Because the countercurrent may be associated with artifacts
arising from TUMSAT-TS input data (Section 3), we compared the dynamic height anomaly derived from TUMSATTS and JCOPE2-TS, as well as from the two ROMS runs.
The dynamic height anomaly at a given pressure P, ΔD(P),is computed asP0

ΔD(P) =−1
[ρ−1
1 (S, T, P) − ρ2 (35, 0, P)]dP,(4)0where P0 = −ρ0gzr; zr is the reference depth (–100 m); ρ0 =1000 kg m−3; g is acceleration due to gravity (9.81 m s−2);
ρ1 is the density at zr; ρ2 is the reference density at T = 0°C
and S = 35. Figure 15 shows the dynamic height anomaly computed using ROMS-JCP, ROMS-TUM, and JCOPE2-TS data
averaged monthly for February and August 2012. The
dynamic height anomaly ΔD is similarly distributed in
winter, whereas a discrepancy is prominent in summer. In
August, all three cases induce the pressure gradient force(PGF) that promotes the northeastward-drifting Kuroshio inFig. 17 As in Fig. 15, but using (a) JCOPE2-TS, (b) TUMSAT-TS data, and (c) a combination of TUMSAT-T and JCOPE2-S data, averaged over the three-year
computational period.
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a wide area. However, the along-shelf cross-frontal PGF of
ROMS-TUM is weaker than that for the other two cases.
The offshore ΔD for ROMS-TUM has a high centred on the
Izu Ridge (at 140.2°E, 32.8°N), which is consistent with thedensity ﬁeld (Fig. 10), promoting the clockwise gyre andthus the westward countercurrent to the south (Figs 11 and
14). To compare with the forcing ﬁeld associated with thenudging, ΔD computed with TUMSAT-TS data is plotted inFig. 16. Irregularity in ΔD is found around the Izu Ridge, particularly in summer, attributable to the warmer and fresher
patches existing in TUMSAT temperature (Fig. 4) and salinity(Fig. 5). Figure 17 shows the three-year average ΔD calculatedwith JCOPE2-TS, TUMSAT-TS, and a combination of
TUMSAT temperature and JCOPE2 salinity. Again, theweaker along-shelf cross-frontal PGF and the larger ΔD bias
are pronounced using the TUMSAT density estimate. Nevertheless, the apparent similarity in Figs 17b and 17c suggeststhat salinity is much less inﬂuential in ΔD, indicating that
the TUMSAT salinity estimate with the climatologicalregression using Argo data does not hinder reproducibility.
In summary, although TUMSAT-TS leads to good reproducibility, the modest reproducibility in the temperature estimate
near the ridge causes the somewhat inaccurate large-scale
horizontal ﬂow (Fig. 14), as well as the local bias in the
cross-sectional density and current structure (Figs 9 and 11),
particularly in summer. However, the discrepancy is minor
compared with the robust and excellent mesoscale reproducibility of ROMS-TUM over the non-assimilative ROMS-FREE
model demonstrated throughout the paper.
6 Summary and discussion
The TUMSAT-TS dataset was acquired using the empiricalmethod for estimating three-dimensional oceanic thermal
structure proposed by Takano et al. (2009), along with a piecewise regression analysis between temperature and salinity
using Argo proﬁling data. Because this new density estimate
uses only currently available data, there is no new cost for
instrumentation. At ﬁrst, TUMSAT-TS data were examinedby comparison with in situ hydrography. Although the temperature structure agrees well with observations, the salinity
does not indicate a fully satisfactory three-dimensional structure. Subsequently, a twin ROMS downscaling experiment
was conducted with temperature and salinity nudging (orrobust diagnosis), which is essential for reproducing the Kuroshio variability realistically. Weak nudging towards (i)TUMSAT-TS (ROMS-TUM) and towards (ii) the JCOPE2TS reanalysis (ROMS-JCP) was conducted for quantitative
comparison.
A comprehensive assessment was carried out on the model
results with the 3D-Var embedded assimilative JCOPE2 reanalysis, the Aviso SSH, and JMA’s in situ hydrographic
data. The RMSE and model skill score were utilized for quantitative measure of the models’ reproducibility. Both assimilative ROMS models produced good model skill scores and low
RMSEs in the surface velocity, SSH variance, surface EKE,

stratiﬁcation, transient migration of the Kuroshio path, andthe volume ﬂux due to the Kuroshio, at least for one or two
years after the model’s initialization, excluding the one-year
spin-up. On the other hand, a supplemental ROMS run
without assimilation (ROMS-FREE model) totally failed toreplicate the upper ocean dynamics. Therefore, the newly proposed TUMSAT-TS density estimate is potentially a powerful
dataset for improving mesoscale reproducibility in the oceanic
reanalysis.
Nevertheless, TUMSAT-TS has some deﬁciencies andneeds to be further modiﬁed and corrected. The salinity structure and halocline depth moderately agree with JMA data
along the 137°E transect. This slight error in TUMSAT salinity
produced inaccurate horizontal subsurface salinity distribution, whereas it did not impede the mesoscale reproducibility substantially. As Ji et al. (2000) and Troccoli et al. (2002)
suggested, both the temperature and salinity ﬁelds should be
used simultaneously for successful assimilative oceanic reanalysis to avoid density artifacts. In this sense, the proposed
empirical salinity estimate based on the regression works
reasonably well in maintaining overall reproducibility. On
the other hand, a satellite sea surface salinity measurement,such as that from the Aquarius/Satélite de Aplicaciones Cientíﬁcas (SAC)-D mission (e.g., Lagerloef, Swift, & Le Vine,
1995), and an increased number of deployed Argo ﬂoats areprospective in situ datasets for supplementing the salinity estimate. In turn, undesirable dynamic height distribution, thus,
erroneous PGF appears, particularly in summer, to promotespurious westward drifting countercurrents to the south of
the Kuroshio, mainly because of inaccurate temperature estimates near the ridge. Therefore, there is room for improvement
for the quality of both the temperature and salinity estimatesalthough the proposed TUMSAT-TS estimate has proven to
be a strong candidate for the dataset to be used in assimilativemesoscale oceanic downscaling modelling even if reliable reanalyses, such as the JCOPE2 data, were unavailable.
It is worth mentioning that we have conducted similar
downscaling JCOPE2-ROMS modelling runs nudged
towards JCOPE-TS data to examine mesoscale reproducibility for the Japan Sea (Uchiyama, Miyazaki, Kanki, & Miyazawa, 2015) and the East China Sea (Kamidaira et al.,2017). Good agreement with satellite and in situ data was
exhibited, comparable to the results demonstrated here.
Therefore, as long as TUMSAT-TS is reliably producedwith a sufﬁcient amount of Argo data, we may expect successful reanalyses in regions other than the Kuroshio region
off Japan that was investigated in the present study. In
addition, TUMSAT-TS may be exploited for regional
ocean models with other assimilation techniques, such as
the widely used 3D-Var, which requires careful investigations a priori for estimating error covariance and decorrelation length scale to avoid interpolation artifacts inherent
in TUMSAT-TS data.
This study focused on a high-resolution ROMS that fully
resolves mesoscale eddies but under-resolves submesoscalecoherent structures (SCSs). We expect that higher resolution

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Mesoscale Reproducibility in Regional Ocean Modelling / 17
models should, in principle, represent eddies, fronts, andﬁlaments more adequately. However, this is not the casefor the Kuroshio region studied here. At a horizontal resolution of 3 km, ROMS-FREE signiﬁcantly overestimated themeandering of the path of the Kuroshio, which results in aserious mismatch with the data, as shown in Figs 7, 8, 12,
and 13, even though the resolved eddies are seemingly quite
realistic (not shown). At further downscaling to a lateral resolution of 1 km, the behaviour of the Kuroshio becomes muchcloser to that of JCOPE2, even without temperature and salinity nudging (Uchiyama et al., 2012). This implies that if
the model represents SCSs well, then it spontaneously stabilizes the Kuroshio through vigorous energy dissipation due to
SCSs. TS nudging works adequately as if subgrid-scale
eddy-induced mixing had been imposed, where the energy
contained in the available potential energy, KE, and EKE isappropriately extracted through forward energy cascade todissipation.

Disclosure statement
No potential conﬂict of interest was reported by the authors.

Funding
YU and HY appreciate the ﬁnancial support from Japan
Science and Technology Agency Core Research for Evolutional Science and Technology (JST-CREST) program[grant number JPMJCR12A6]. YU also offers thanks for the
support from the Japan Society for the Promotion of Science(JSPS) Grant-in-Aid for Scientiﬁc Research [grant number
24560622], [grant number 15H04049], [grant number
15H00977], and [grant number 15KK0207].

ORCID
Yusuke Uchiyama

http://orcid.org/0000-0002-2234-3608

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