Chapter 13

High Resolution Kuroshio Forecast System:
Description and its Applications
Takashi Kagimoto, Yasumasa Miyazawa, Xinyu Guo, and Hideyuki Kawajiri

Summary We have developed a forecast system for the Kuroshio large meanderwith a high horizontal resolution (approximately 10 km). Using the system, we succeeded in predicting the path transitions of the Kuroshio from the nearshore nonlarge
meander path to the offshore nonlarge meander path in 2003, and from the nearshore
nonlarge meander path to the typical large meander path in 2004 as well as the occurrence of its triggering small meander south of Kyushu Island. We have also beendeveloping a higher resolution forecast model for coastal oceans and bays south ofJapan, where physical and biological states of the ocean are much affected by thepath variation of the Kuroshio. This model, although the development is still underway, represents tides and tidal currents in two bays south of Japan in a realistic way.

13.1

Introduction

The Kuroshio, one of the strongest surface currents in the world oceans, ﬂows northeastward or eastward near Japan as a part of the subtropical gyre in the North Paciﬁc.
Because it carries enormous amounts of heat to the high latitude (e.g., 0.76 Peta
Watt (PW) by Bryden et al.’s (1991) observation and 0.25–0.46 PW by Ichikawa and
Chaen’s (2000)), it plays a crucial role in maintaining and changing the global climate system. In particular the heat ﬂux by the geostrophic advection of the Kuroshio
has a substantial contribution to the local heat balance in the Kuroshio Extension
region of the central North Paciﬁc (Qiu and Kelly, 1993). Changes in the sea surface
temperature associated with the Kuroshio path variations cause the surface wind tochange (Nonaka and Xie, 2003), leading to some inﬂuence on the Paciﬁc storm track(Inatsu et al., 2002). Thus in order to know climate variations in the North Paciﬁc, it
is important to grasp how the Kuroshio is and will be.
In addition the Kuroshio also affects coastal (local) areas because of its peculiar path variations. For example, the 100 m-depth temperature in Sagami Bay1 is
1 Reader may be unfamiliar to the names of those places. The locations of Enshu-nada Sea, Shikoku,

Kyushu and Hachijo-jima Islands, and the Kii Peninsula are denoted by E, S, Q, H, and K, respectively, in the upper left panel of Fig. 13.6, that of Sagami Bay is by Sa in the left panel of Fig. 13.12,
and that of the Izu Peninsula is in Fig. 13.14.

210

13 High Resolution Kuroshio Forecast System

remarkably higher during the typical large meander path of the Kuroshio than otherpaths (Kawabe and Yoneno, 1987). The large meander of the Kuroshio may enhancethe onshore intrusion of the warm water into the shelf region of the Enshu-nada Sea1
and thereby contribute toward increasing the temperature in spawning habitats of sardine, leading to increase of postlarval sardine but to decrease of postlarval Japanese
anchovy there (Nakata et al., 2000). Recent observations based on the long-term current measurements (Iwata and Matsuyama, 1989) and the HF radars (Hinata et al.,2005) indicate that the warm water intrusion into Sagami Bay is enhanced when the
Kuroshio is located near the Izu Peninsula,1 corresponding to either the nearshore
nonlarge meander path or the typical large meander path. In addition to the physicaland biological aspects, the location of the Kuroshio may have an inﬂuence on engineering activities such as the determination of optimal routes for ferries and cargovessels. Thus the path variation of the Kuroshio is a general concern of many people
as well as oceanographers.
In order to respond to their concerns it is necessary to predict the path variations of
the Kuroshio. Several previous studies on development of a nowcast/forecast system
for the Kuroshio have been accomplished. Komori et al. (2003) examine a capability
for short-range forecast of the Kuroshio path variations south of Japan using a 1.5
layer primitive equation model with 1/12◦ resolution into which an objective analysis data of the sea surface height (Kuragano and Shibata, 1997) is assimilated witha variational method. The analysis ﬁelds obtained from the model are quite reasonable because the root-mean-square (RMS) differences with regard to the Kuroshio
axis location south of the Enshu-nada Sea and the sea level at Hachijo-jima Island1
between the reanalysis and the observations are less than the observed variances.
The prediction errors are kept within the variances during 75-day prediction period,
suggesting that the model has a predictability skill up to 75 days for the Kuroshio
path variations. Ishikawa et al. (2004) point out, using the same forecast system,that an appropriate assimilation of a shoaling of the thermocline associated with asmall meander of the Kuroshio south of Shikoku Island1 into the model is of great
importance in predicting the transition from the nearshore nonlarge meander path tothe large meander path. Kamachi et al. (2004a) develop an operational ocean data
assimilation system for the Kuroshio region using a more sophisticated ocean general circulation model with 1/4◦ resolution but with the simpler assimilation schemeof a time-retrospective nudging method than Komori et al.’s, and conﬁrm that thereanalysis represents the real ocean reasonably well by comparing with individual
observation data. The system, which has been operated in the Japan Meteorological
Agency since January 2001, can predict the Kuroshio axis in 30- to 80-day prediction period in a manner that depends upon the ocean state in the initial condition(Kamachi et al., 2004b).
Previous studies have indicated several important factors in predicting the pathtransition of the Kuroshio: anticyclonic mesoscale eddies that appear in the subtropical frontal zone and move all the way to the south of Japan along the Kuroshio(Akitomo and Kurogi, 2001; Miyazawa et al., 2004), mesoscale eddies propagating
westward from the Kuroshio Extension region to the southeast of Kyushu Island1(Ichikawa and Imawaki, 1994; Ebuchi and Hanawa, 2000; Akitomo and Kurogi,

13.2 Description of Forecast System

211

2001; Mitsudera et al., 2001), the baroclinic instability process leading to thedevelopment of the small meander and the subsequent typical large meander (Endohand Hibiya, 2000; Qiu and Miao, 2000), and a small seamount and associate abyssal
circulation (Hurlburt et al., 1996; Endoh and Hibiya, 2000; Miyazawa et al., 2004).
All of them suggest that numerical models are required to have a ﬁne horizontal grid
spacing so as to represent those factors reasonably well. Moreover, only a numericalmodel with a ﬁne horizontal resolution can represent the realistic vertical structureof the velocity and the associated density structure in the Kuroshio region (Guoet al., 2003).
On the basis of the implications of previous studies, we developed a high resolution
Kuroshio forecast system, called the Japan Coastal Ocean Predictability Experiment(JCOPE) ocean forecast system. The JCOPE project2 has begun in October 1997
under an initiative of the Frontier Research Center for Global Change (FRCGC) /Japan Agency for Marine-Earth Science and Technology (JAMSTEC). As a part ofthe project, we have carried out fundamental simulation studies. Guo et al. (2003)
examined effectiveness of a one-way nesting technique for the simulation of theKuroshio. Miyazawa et al. (2004) pointed out the role of mesoscale eddies in the pathvariations of the Kuroshio using an eddy-resolving POM. Recently Miyazawa et al.
(2005) indicated using a prototype of the forecast system that an initialization processwith mesoscale eddies taken into account is crucial in predicting the path variationsof the Kuroshio accurately. The present JCOPE forecast system ﬁnally reaches a
stage of near-operational level using almost all available data obtained from satellites, ARGO (the Array for Real-time Geostrophic Oceanography) ﬂoats and ships,
and its outcome is available on the Web site of the JCOPE project.2 In this chapter wewill describe details of the JCOPE ocean forecast system that is currently operated.
This chapter is organized as follows. In Sect. 13.2, we describe the numericalmodel, surface forcing data, and data assimilation scheme that we use for the forecast system in great detail. A couple of examples to show the forecast of the Kuroshio
path transition are shown in Sect. 13.3. We also describe the sensitivity of the forecast to the parameters used in the data assimilation scheme. In Sect. 13.4, we brieﬂy
introduce our recent study toward downscaling of the Kuroshio forecast for coastal
oceans and bays. Section 13.5 is devoted to summary and exempliﬁcation of some
applications of the JCOPE outcome.

13.2
13.2.1

Description of Forecast System
Numerical Model

The numerical model that we adopt for the Kuroshio forecast system is a threedimensional primitive-equation ocean general circulation model based on the POM
with a generalized vertical coordinate (Mellor et al., 2002). The forecast system
2 See http://www.jamstec.go.jp/frcgc/jcope/

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13 High Resolution Kuroshio Forecast System

Fig. 13.1 Bottom topography used in the coarse model. Contour interval is 1,000 m. The small
rectangle region delineated by solid straight lines is the computational domain for the ﬁne model

consists of two models with different computational domains and resolutions: one
is for the North Paciﬁc basin with the variable horizontal resolution (1/4◦ near Japanand 1/2◦ in the east of basin) and 21 vertical levels; and the other is for the western
North Paciﬁc basin with 1/12◦ resolution and 45 levels (Fig. 13.1). The former model(hereafter coarse model) provides the boundary conditions for all prognostic variables described below to the latter (hereafter ﬁne model), but the latter does not affectthe former (no feedback).
The prognostic variables in the governing equations of the model are the surface
elevation (η), the zonal and meridional components of the vertically averaged velocity (ū, v̄), the zonal and meridional velocity (u, v), potential temperature (T ), salinity(S), twice the turbulent kinetic energy (q 2 ), and turbulent length scale (l). A set ofthe equations for the latter two variables is a turbulent closure submodel (Mellor and
Yamada, 1982), which is used for the estimation of the vertical eddy mixing coefﬁcients. Mellor (2001) modiﬁed the treatment of the turbulent dissipation term in thesubmodel in such a way that the surface mixed layer did not become shallow overly
in summer. With this correction Ezer (2000) succeeded in simulating the realistic vertical temperature proﬁle in the North Atlantic, but Kagimoto (2003) pointed out thatthe correction caused overly mixing in the surface equatorial region where the vertical shear was strong and thereby the Equatorial Undercurrent almost disappeared.
Hence we do not employ this modiﬁcation. The horizontal eddy mixing coefﬁcientis, on the other hand, evaluated by Smagorinsky’s (1963) nonlinear formulation withconstant coefﬁcients of 0.1 for the coarse model and 0.075 for the ﬁne model.3 The
coefﬁcient for tracers is half of that for momentum, meaning that the turbulent Prandtl
number is two.
The horizontal coordinate system is a conventional longitude–latitude grid,whereas the vertical one is a generalized “z-plus-sigma” grid. The depth of layer
3 Those values correspond approximately to the so-called Smagorinsky’s constants of 0.2659 and
0.23, respectively.

13.2 Description of Forecast System213

1 ≤ k ≤ kb at location (x, y) and time t is deﬁned by z = η(x, y, t) + s(x, y, k, t),where kb is the number of vertical levels. A z-level system is s (z) = σ (k)[Hmax +η(x, y, t)], and a sigma coordinate system is s (σ ) = σ (k)[H (x, y) + η(x, y, t)],where Hmax is the maximum depth and the relative distribution of vertical layers is
0 ≤ σ (k) ≤ −1 (Ezer and Mellor, 2004). In our formulation for the vertical grid,z-level grids are aligned on sigma grids. The boundary between the z-level systemand the sigma-level system is located at ke , the minimum value of indices that satisfy
the following inequality,|s (z) (x, y, ke , t)| > 0.5H (x, y)(13.1)

Note that this formulation keeps surface layers from being over-resolved particularly
in shallow areas (Mellor et al., 2002) and then prevents the sea surface temperature(SST) from being overestimated there. We also note that the bottom topography canbe represented with the terrain following grid system more realistically than the zlevel grids. In fact, the bottom relief is crucial to the representation of the Kuroshio
because the bottom pressure torque plays a major role in the vorticity budget over thecontinental slope region at which the main axis of the Kuroshio is located (Kagimoto
and Yamagata, 1997).
The bottom topography used in the model is based on the global DTM5 (Digital
Terrain Models) with 1/12◦ resolution. For the ﬁne model, the topography data with
500 m resolution archived by Hydrographic and Oceanographic Department, Japan
Coastal Guard is also used for the area near Japan. In order to reduce the error incomputing the pressure gradient force near steep topography, the topography data
is smoothed out using two kinds of smoothing ﬁlters: the Gaussian smoothing withthe 1/8◦ length scale, and the ﬁlter based on Mellor et al. (1994). The latter ﬁlter is
continuously applied to the data until the depth satisﬁes the inequality δ H/ H̄ ≤ 0.35,
where δ H is the depth difference between two neighboring grid points and H̄ is theaverage depth between them. Note that the former ﬁlter is useful particularly forthe variable grid system, which is adopted in our coarse model, because an effectof the ﬁlter that is not based on the local depth gradient but depth “difference” isinhomogeneous in space, thereby the bottom relief in areas with coarser resolutions
is heavily smoothed out rather than with ﬁner ones. The depths near the boundary of
the ﬁne model are calculated from the smoothed topography data used in the coarse
model by using a bilinear interpolation in such a way that solutions of the ﬁne model
may be connected smoothly with those of the coarse model.
In the original POM, a partial slip condition is applied to the tangential component of the velocity at the boundary. We change it to the no-slip boundary condition,
because the positive vorticity supply may be important to the development of theKuroshio large meander (Akitomo et al., 1991). The temperature and salinity near
the artiﬁcial boundaries in the coarse model are restored to the monthly mean climatology (Levitus and Boyer, 1994; Levitus et al., 1994) in such a way that ﬁctitious
waves neither propagate along nor reﬂect at the boundaries. Since sea ice processes
are not taken into account in the forecast system, both the temperature and salinityof the coarse model in the Sea of Okhotsk and the Bering Sea are also restored to the214

13 High Resolution Kuroshio Forecast Systemmonthly mean climatology. In the ﬁne model, they are restored to the climatology
only in the Sea of Okhotsk.
The initial condition is a state of rest with the 1/4◦ annual mean climatologicaltemperature and salinity ﬁelds (Boyer and Levitus, 1997). The coarse model is spunup for 10 years from the initial state with the use of the monthly mean surface forcings
described below. Then it is further driven by 6 hourly surface forcings covering from
September 1999 to December 2001. The ﬁne model is also forced from the initialstate with the monthly mean surface forcings but for 5 years, and is continued to
be forced with the 6 hourly forcings from September 1999 to December 2001. The
data assimilation scheme described in Sects. 13.2.5 and 13.2.7 is introduced from
September 1999. Then the forecast experiment together with the data assimilation isstarted in December 2001.

13.2.2

Nesting

As described earlier, the coarse model provides the boundary values of the prognostic
variables to the ﬁne model. All prognostic variables except for two turbulent properties in the coarse model are linearly interpolated on to the boundary grid points of
the ﬁne model. In order to reduce noise caused by a mismatch between two models,
we modify the vertically averaged velocity normal to the boundary with the use of
the following radiation condition (Flather, 1976; Guo et al., 2003),
g(ηf − ηc )(13.2)ū f = ū c − crf
Hwhere ū c and ηc are, respectively, the interpolated values of the normal componentof the velocity and the surface elevation, g is the gravity constant, ηf is the surface
elevation of the ﬁne model at a grid inside the open boundary, and crf is an adjustableparameter (0 < crf ≤ 1), for which we select 0.1. The turbulent properties, q 2 andq 2 l, are set to be a constant of 10−10 , meaning that the turbulent energy advectedfrom the outside is ignored.

13.2.3

Surface Forcings

The zonal and meridional components of the momentum ﬂux (τx , τ y ) are parameterized with the following bulk formula,2 (u(τx , τy ) = ρa CD u 210m + v 10m(13.3)
10m , v 10m )where ρa = 1.225 kg m−3 is the air density at sea level, u 10m and v 10 m are, respectively, the zonal and meridional components of wind velocity at 10 m above sea level13.2 Description of Forecast System215(m s−1 ), and CD is the drag coefﬁcient based on Large and Pond’s (1981) formula,that is,
⎧

2
⎪
⎪
1.14,
(
u 210m + v 10m
< 10)
⎪
⎨


3
2 , (10 ≤ u 2
2
10 × CD = 0.49 + 0.067 u 210m + v 10m+ v 10m< 26) (13.4)
⎪
 10m
⎪
⎪
⎩ 0.49 + 0.065 × 26,
2 )(26 ≤ u 210m + v 10m
For u 10m and v 10m , we adopt the QuikSCAT Near-Realtime data products (Liu et al.,1998), whose spatial and temporal resolutions are half a degree and 12 h, respectively.
Although the resolutions are coarser than the intrinsic ones in the NASA/JPL’s SeaWinds Scatterometer, the products have the advantage of less sampling error along
the satellite track than others.
The turbulent heat ﬂux w  T  is evaluated using the following equation,
ρa Cp w  T  = (Q L + Q E + Q H ) −dQ(Ts − Tobs )dT(13.5)

where Cp = 1.005 × 103 J kg−1 K−1 is the speciﬁc heat capacity, Q L is the longwave radiation, Q E is the latent heat ﬂux, Q H is the sensible heat ﬂux, dQ/dT =−35 W m−2 K−1 is the coupling coefﬁcient, and Ts and Tobs are the model andobserved SST, respectively. The last term of (13.5) is the correction term to reduce
SST biases. The ﬁrst three terms are parameterized with the bulk formulas,√
4
3
Q L = σ Tobs
(0.39 − 0.05 ea )(1 − 0.8C) + 4 σ Tobs
(Tobs − Ta )(13.6)

2 (q (T ) − q )Q E = ρa CE L u 22m + v 2m
(13.7)
sat obsa
2 (TQ H = ρa Cp CH u 22m + v 2m
(13.8)
obs − Ta )where = 0.97 is the emissivity of the ocean, σ = 5.67 × 10−8 W m−2 K−4 is the
Stefan-Boltzmann constant, C is the fraction cloud cover, Ta is the air temperature,
L = 2.501 × 106 J kg−1 is the latent heat of fusion, qsat (Tobs ) is the saturated speciﬁc
humidity at Tobs , and qa is the speciﬁc humidity. The saturated speciﬁc humidity isrelated to the saturated vapor pressure, which is approximately a polynomial functionof temperature (Tetens, 1930). The vapor pressure, ea , is calculated from qa using
the same relationship. The zonal and meridional wind velocities at 2 m above sea
level, (u 2m , v 2m ), are estimated from u 10m and v 10m using the logarithmic law. The
turbulent exchange coefﬁcients, CE and CH , are based on Kondo’s (1975) formulas.
The incoming shortwave radiation at the sea surface, Q s , is estimated with anempirical formula,sky
Q s = Q s (0.77 − 0.5C 2 )(1 − α)(13.9)sky

where Q s is the solar radiation incident on the ocean under clear skies, and
α = 0.08 is the ocean surface albedo. Equation (13.9) is different from numerous empirical relations proposed in previous studies (e.g., Reed, 1977). The factor,

216

13 High Resolution Kuroshio Forecast System(0.77 − 0.5C 2 ), is found out with trial and error in such a way that the climatological model SST becomes close to the observed one. The penetration of the shortwave
radiation into the ocean is taken into account on the basis of Paulson and Simpson’s(1977) formulation,

 
 
z
z
+ (1 − γ ) exp(13.10)I (z) = Q s γ exp
ζ1ζ2
where I (z) is the penetrated solar radiation ﬂux at depth z, ζ1 and ζ2 are, respectively,
the e-folding depths of the long (ζ1 ), and short visible and ultra violet (ζ2 ) wavelengths, and γ is a fraction for the former part. We select γ = 0.58, ζ1 = 0.35 m,
and ζ2 = 23.0 m, corresponding to the type I water of Jerlov’s (1976) classiﬁcation.4
Those ﬂuxes require the observed SST, surface air temperature, speciﬁc humidity,
the fraction cloud cover, and the solar radiation incident on the ocean under clear
skies. We adopt the 6 hourly NCEP/NCAR reanalysis product (Kalnay et al., 1996)
for them.
The sea surface salinity, Ss , is restored to the monthly climatology (Levitus et al.,1994), Sobs , in the form of the salinity ﬂux,
w  s  = γs (Ss − Sobs )(13.11)

where γs = 10 m month−1 is the restoring speed.

13.2.4

Observational Data

The observations assimilated into the model are the satellite altimeter data obtained
from the TOPEX/POSEIDON and ERS-1 during September 1999 to June 2002 andfrom the Jason-1 and the GeoSat Follow-On during June 2002 to the present, thesea surface temperature from the advanced very high resolution radiometer/multichannel sea surface temperature (AVHRR/MCSST) Level 2 products, and vertical
proﬁle data of the temperature and salinity provided by the Global TemperatureSalinity Proﬁle Program (GTSPP). From these data, we build up 7 days interval dataon 1/4◦ grids using the optimal interpolation technique described later. The sampling
period for the satellite data is 7 days (before and after 3 days of an analysis time),
while that for the temperature and salinity proﬁle is 31 days. The spatial extent ofsampling data is 360 km.
The gridded anomaly of a variable, ag , is calculated using a linear combination of
the observed anomaly of the variable, ao ,ag = W T ao

(13.12)4 The type II or IA is better for the water off Japan, but the use of the e-folding depths corresponding
to the waters resulted in a warm bias of the SST. Hence we chose the type I water.

13.2 Description of Forecast System

217

where ag and ao are, respectively, the column vectors with N and M elements, W
is a M × N matrix of weights,5 M is the number of observation points, and N is
the number of grid points. The superscript of W , T , denotes the transpose of thematrix. The matrix, W , is found by minimizing the variance of interpolation errors,
and obtained from solving the algebraic equation (Gandin, 1963),(P oo + λI )W = P og

(13.13)where I is the unit matrix. The M × M matrix of the autocorrelation of the observed
values, P oo , is parameterized with a Gaussian model,
P oo = (Pi,ooj )= P oo (x i ; x j )= C0 (xi , yi , z i ) exp −x−cx t
Lx

2

−

y
Ly

2

−

t
Lt

2 

(13.14)

where x i = (xi , yi , z i , ti ) and x j are two observation points, C0 is the autocorrelation
at lag 0, x = xi − x j , y = yi − y j , t = ti − t j , cx is a phase speed in thezonal direction, and L x , L y , and L t , respectively, denote the zonal, meridional, andtemporal decorrelation scales. The M × N matrix of the autocorrelation between
the observed and interpolated values, P og , is also calculated from (13.14), but x j isreplaced with x g , which denotes a grid point to which the data are interpolated. The
signal-to-noise ratio, λ in (13.13), is calculated with C0 ,λ=

1 − C0C0(13.15)The parameters, C0 , L x , L y , L t , and cx , required by the optimal interpolation
are calculated from the following procedures using the observation data listed inTable 13.1.
1. Create a mean ﬁeld during a period
2. Calculate the autocorrelation at observation points and average the correlation
matrices within 5◦ × 5◦ regions
Table 13.1 Data used to estimate the parameters in (13.14)
Data
Instruments
Distributor
PeriodTOPEX/POSEIDON,
SSH
CCAR
Sep 1999–Jun 2002
ERS-2
JPL, NAVOSST
AVHRR
Oct 2001–Aug 2002
CEANO
T &S
CTD, XBT, MBT, etc.
GTSPP
Mar 1990–Mar 2002
(0–400 m)

Mean
None
Mean during
the periodBoyer and
Levitus (1997)

5 For the sake of convenience, (13.12) is expressed with the matrix form, but in the numericalcalculation W is evaluated at each grid point. Thus in practice ag is a scalar, W is an M elements
column vector.

218

13 High Resolution Kuroshio Forecast System

Fig. 13.2 Autocorrelation of the sea surface height (SSH) anomaly in the region, 20◦ N–25◦ N,
145◦ E–150◦ E. (Left) Time-longitude lag-correlation. (Right) Time-latitude lag-correlation. Contour
interval is 0.1. Solid line denotes positive values and dashed line denotes negative values

3. Estimate the parameters by ﬁtting the Gaussian model described earlier
4. Interpolate/extrapolate the parameters on to 1/4◦ grids
5. Smooth out the parameters using the Gaussian ﬁlter with 3◦ horizontal scale
Figure 13.2 shows an example of the autocorrelation of the sea surface height(SSH) anomaly based on the altimetry data in the region, 20◦ N–25◦ N, 145◦ E–150◦ E,
obtained from procedure 2. By ﬁtting the autocorrelation, in a least square sense, tothe Gaussian model of (13.14) (procedure 3), we obtain the parameters,(C0 , cx , L x , L y , L t ) = (0.626, −0.07 m s−1 , 152 km, 108 km, 53 days) (13.16)
The approximate autocorrelation function with the above parameters is shown in
Fig. 13.3. Both the time-longitude and time-latitude correlation functions are good
approximations, although the negative correlation at 300 km apart from the speciﬁc
point is not represented in the latter (right panels of Figs. 13.2 and 13.3).

13.2.5 Data Assimilation
The SSH anomaly, η̃o , and the vertical proﬁle of the temperature and salinity, T o (z 1 ),T o (z 2 ), · · · , T o (z M ), S o (z 1 ), S o (z 2 ), · · · , S o (z M ), gridded in the way described in
the previous subsection are combined with a forecast data, leading to an analysis
data on the 1/12◦ horizontal grids and the “z-plus-sigma” vertical grids, which is used
for the increment analysis update (IAU) process described in Sect. 13.2.7. In our13.2 Description of Forecast System

219

Fig. 13.3 Approximate autocorrelation function of the SSH anomaly in the region, 20◦ N–25◦ N,
145◦ E–150◦ E ﬁtted to the Gaussian model, (13.14). (Left) Time-longitude lag-correlation. (Right)
Time-latitude lag-correlation. Contour interval is 0.1

system, the number of vertical levels for the gridded observation data, M, is 6, andthe corresponding depths, z k (k = 1, · · · , M), are 0, 50, 100, 200, 300, and 400 m.
For the data assimilation process, we use a multivariate optimal interpolation
scheme described later (Lorenc, 1981; Ezer and Mellor, 1997). Before the interpolation, we subtract basin-wide seasonal variations such as the thermal expansion fromthe SSH anomaly, that is,η̃(13.17)η̃ = η̃ −latitudeThis enables us to assimilate the data of the SSH variations associated with mesoscaleeddies effectively into the model (Y. Wakata, personal comm., 1999).
Deﬁne the analysis state, X a , as a 2N + 1 elements column vector,
X a = (η̃a , T1a , T2a , · · · , TNa , S1a , S2a , · · · , SNa )(13.18)where N denotes the number of vertical “z-plus-sigma” levels. The forecast state,X f , and the observation value, y o , are also deﬁned in the same way,X f = (η̃f , T1f , T2f , · · · , TNf , S1f , S2f , · · · , SNf )(13.19)oy o = (η̃o , T1o , T2o , · · · , TMo , S1o , S2o , · · · , SM)(13.20)

The analysis state is calculated from the best linear invariant estimation,
X a = X f + P H T (H P H T + R)−1 (y o − H X f )(13.21)

where P is the error covariance matrix of the forecast state with (2N + 1) × (2N + 1)
elements, H is the observation matrix with (2M + 1) × (2N + 1) elements that220

13 High Resolution Kuroshio Forecast System

is a linear operator mapping the forecast state into the observed data, and R is theobservation error covariance matrix with (2M +1)×(2M +1) elements. The Kalman
gain matrix, P H T (H P H T + R)−1 , acts as interpolation and/or extrapolation of theinnovation, y o − H X f , to the model state. The error covariance matrix is the functionof time and space that depends upon the model physics. For simplicity, however, we
assume it to be constant in time, and estimate it in advance.
Suppose, for a simple explanation, that M = N = 1. In this case, the observation
matrix becomes the 3 × 3 unit matrix, and the matrix, P H T is expressed as follows,⎞⎛(δ η̃f )2  δ η̃f δT f  δ η̃f δS f (13.22)
P H T = ⎝ δT f δ η̃f  (δT f )2  δT f δS f  ⎠δS f δ η̃f  δS f δT f  (δS f )2 
where δx and x denote, respectively, the error and expectation of a variable, x.
Assuming that each element of the matrix, P H T , can be approximately estimatedfrom the variance of the variables obtained from the model (Mellor and Ezer, 1991).
⎞⎛(η̃f )2 E ηf  η̃f T f E Tf η̃f S f E Sf⎟⎜
P H T ≈ ⎝ T f η̃f E ηf  (T f )2 E Tf T f S f E Sf ⎠
S f η̃f E ηf  S f T f E Tf (S f )2 E Sf⎛⎞⎞⎛ f
E η 0 0
1 Fη T Fη S= ⎝ FT η 1 FT S ⎠ ⎝ 0 E Tf 0 ⎠FSη FST 1
0 0 ⎞
E Sf
⎛
(η̃f )2
0
0⎟⎜(13.23)×⎝ 0(T f )2
0 ⎠
f
2
0
0
(S )
where x and x denote the time mean of a variable, x, and the deviation from it,
respectively. The regression coefﬁcient between variables, x and y, denoted by Fx y ,is expressed as follows,xy(13.24)Fx y =
y 2
In this way, the estimation of the forecast error covariance matrix results in the estimation of the nondimensional parameters, E ηf  , E Tf , and E Sf , which are the forecast
error variances normalized by the variances in the forecast data. Note that the spatial
pattern of the regression coefﬁcients depends strongly upon the model performance,suggesting that the improvement of the model performance is crucial to reﬁnementof the regression coefﬁcients.
Assuming that an observation error of a variable is not correlated to that of another,
R becomes a diagonal matrix,⎞⎞⎛⎛ o(η̃f )200
E η 0 0⎟⎜(13.25)R ≈ ⎝ 0 E To 0 ⎠ ⎝ 0(T f )20 ⎠0 0 E So0
0
(S f )2

13.2 Description of Forecast System

221

where E ηo , E To , and E So are the observation error variances normalized by the variances in the forecast data.
If the probability distributions of the observation and forecast errors are independent of each other, we obtain the innovation covariance matrix,
(y o − H X f )(y o − H X f )T  = H P H T + R(13.26)Comparison of the diagonal components between both sides of (13.26) gives a simple
relation of the observation and forecast errors to the model statistics for each variable,(E ηf  + E ηo )(η̃f )2  = (η̃f − η̃o )2 
(E Tf + E To )(T f )2  = (T f − T o )2 
(E Sf + E So )(S f )2  = (S f − S o )2 

(13.27)

Thus the amplitude of the observation and forecast errors are not determined independently, but the ratio between them is. Note that the ratio strongly affects forecast
skills, because when E xo is bigger (smaller) than E xf the forecast (observation) data
are set above the observation (forecast) in determining the analysis data used in the
IAU process described in Sect. 13.2.7. In fact we realize that the prediction of theKuroshio large meander is sensitive particularly to the error ratio associated with the
SSH anomaly. Now we introduce an adaptive assimilation scheme (Fox et al., 2000)
in order to estimate the adequate forecast error variance in (13.27),6
E ηf  G[(η̃f )2 ] = G[(η̃f − η̃o )2  − αη ei2 (η̃o )]E ηo G[(η̃f )2 ] = G[αη ei2 (η̃o )](13.28)E Tf 0 G[(T0f )2 ] = G[(T0f − T0o )2  − αT0 ei2 (T0o )]E To 0 G[(T0f )2 ] = G[αT0 ei2 (T0o )](13.29)ei2 = Vs2 (1 − W T P og )(13.30)where G[·] is the spatial ﬁlter of the Gaussian shape with a zonal scale of 1.4◦ (theequator)–0.7◦ (60◦ N) and a meridional scale of 0.4◦ (the equator)–0.2◦ (60◦ N), andT0 is the SST. The interpolation error covariance of a variable x, ei2 (x), is deﬁned bywhere Vs2 is a signal variance of the variable. The difference between the original
adaptive assimilation scheme proposed by Fox et al. (2000) and ours is the existenceof the adjustable parameters, αη and αT0 , which are found out from the sensitivity
experiments in such a way that the predicted Kuroshio large meander is as close to
the observation as possible. If there are sufﬁcient data to interpolate on to the model
grids, αx should be unity. In our case, however, the amount of satellite data is insufﬁcient particularly on the onshore side of the Kuroshio, and then the interpolation error
6 Because the satellite data has much information due to high spatio-temporal resolutions, the error
variances of the SSH and SST obtained from the adaptive assimilation scheme are more reliable thanthose of the temperature and salinity from hydrographic observations. Hence we apply the scheme
to the SSH and SST data, although the forecast is not so sensitive to the choice of the SST error
variance.

222

13 High Resolution Kuroshio Forecast System

covariance has a large uncertainty. Hence we introduce the adjustable parameter in(13.28) and (13.29). Note that there is a constraint on the sensitivity experiments.
Since the distribution of the following variable,(y o − H X f )T (H P H T + R)−1 (y o − H X f )asymptotically approaches to the normal distribution with mean M and variance 2M,
as M goes to inﬁnity (Lupton, 1993), we need to conﬁrm that the sum of the above
variable over the computational domain is close to the unity (Menard and Chang,
2000),
1LM

L(yio − H X if )T (H Pi H T + Ri )−1 (yio − H X if ) ≈ 1(13.31)i=1where L is the number of horizontal grid points.
Several parameters listed in Table 13.2 are introduced into the data assimilation
scheme described above. The adaptive assimilation scheme is applied only in the
Kuroshio region of isadpt ≤ longitude ≤ ieadpt and jsadpt ≤ latitude ≤jeadpt, because our main target to predict is the Kuroshio path variations. Hencethe normalized error variances for the SSH and SST out of the region are set tobe constants. Those for the temperature below the surface and the salinity are also
assumed to be constants because their effect on the forecast skill is not so large.
The values of E xo and E xf for a variable x are, respectively, listed in the lines ofvobsadj0 and vmodeladj0 of Table 13.2. The parameter, vobsieadj, corresponds to αx for a variable x.
The data assimilation (the estimation of the analysis values) does not take place inthe whole of the computational domain. If the depth at a grid point is out of rangeof hup to hlow or less than hassim, the observation data is not assimilated, thatis, the Kalman gain in (13.21) is set to be zero. The parameter, vobsiemax0, isTable 13.2 Parameters used for the data assimilation
Parameters
SSH
SST
T
S
hup
0m
0m
50 m
0m
hlow
3 000 m 200 m 3 000 m 3 000 m
hassim
200 m
10 m
50 m
10 m
vobsiemax0
0.9
0.9
0.8 7
0.8 7
vobsadj0
0.48
0.01
0.192
0.192
vmodeladj0
0.036
0.01
0.048
0.048
vcorimpt
1.0
1.0
1.0
0.0
vcorimps
0.1
0.0
0.0
1.0
117◦ E
isadpt117◦ E180◦ E
ieadpt141◦ E
jsadpt
12◦ N
12◦ N
62◦ N
jeadpt44◦ N
vobsieadj
0.6
1.0
-

7 The value of 0.6 is used for the temperature at 50 and 100 m and the salinity at 0, 50, and 100 m.

13.2 Description of Forecast System223

the acceptable maximum interpolation error, implying that if ei /Vs is larger thanthe value the observation data is not assimilated. Additionally all data except for the
SST are not unconditionally assimilated in the region of 117◦ E to 180◦ and 44◦ N
to 62◦ N. In fact the data assimilation in this area is not signiﬁcant, partly because
the temperature and salinity are restored to the monthly mean climatology in the
Okhotsk Sea described in Sect. 13.2.1, partly because the number of hydrographic
observation data in the northern North Paciﬁc is quite few, and partly because therelationship between the SSH anomaly and the in-situ temperature and salinity isunclear there, meaning that the regression coefﬁcient is small.
In the data assimilation process, the regression coefﬁcients between the temperature at the depth k and a variable x, FTk x , and between the salinity at the depth kand the variable, FSk x , are factorized by the adjustable parameters, vcorimpt andvcorimps, respectively, because we realize that the forecast skill got worse when
the temperature and salinity are assimilated with the same weight as each other. These
parameters are empirically determined.

13.2.6 Quality Control
Both the raw and gridded data of the observation are quality controlled in a simple way. They are required to be within the range of valmin to valmax, and theabsolute value of their anomaly to be less than valamax. If the data value is out ofrange, it is converted to be a missing value. Even if within the range, the raw data at
the depth shallower than hobsmin are excluded in the optimal interpolation process.
Additionally the gridded data at the depth shallower than hmin are discarded before
the subsequent multivariate optimal interpolation process is carried out. The exclusion process is due to the worse accuracy of the satellite altimetry data particularly
in shallow coastal areas and marginal seas than in open oceans. The parameters usedin the data quality control process for each variable are listed in Table 13.3.
The analysis data obtained from the multivariate optimal interpolation scheme isalso quality controlled. The analysis value of the temperature, T a , and the salinity,
S a , is required to be within the range,|T a − T f | ≤ 8,
Table 13.3
controlhmin
hobsminvalminvalmaxvalamax−1 ≤ T a ≤ 32

Parameter values for the data quality
SSH
200 m
100 m
−1 m
1 m
1 m

SST
10 m
10 m
−2◦ C
32◦ C
10◦ C

T
10 m
10 m
−2◦ C
32◦ C
7◦ C

S
10 m
10 m
0 psu
36 psu1 psu(13.32)

224

13 High Resolution Kuroshio Forecast System|S a − S f | ≤ 1,

25 ≤ S a ≤ 36

(13.33)where T f and S f are the forecast values of the temperature and salinity, respectively.

13.2.7

Incremental Analysis Update

The analysis data estimated using an optimal interpolation scheme is generally usedas the initial condition of the next forecast experiment (e.g., Mellor and Ezer 1991;
Ezer and Mellor 1994). The estimated data, however, does not satisfy governing
equations of the model because the optimal interpolation scheme doest not takeaccount of them. Hence the forecast result might be infected by ﬁctitious inertiogravity waves. Mellor and Ezer (1991) modiﬁed the velocity ﬁeld through a diagnostic calculation in such a way that it is geostrophically balanced with the density ﬁeld
based on the analysis data.
Another simple initialization scheme is nudging technique. In the scheme, the forecast data is continuously restored to the analysis data,
X n+1 = X n +Xa − Xntτnudge(13.34)

where X n+1 and X n are values of a variable at time level n +1 and n, respectively, X a
is an analysis value of the variable at an analysis time, τnudge is e-folding time scale
during which the forecast value approaches to the analysis value, and t is the modeltime step. It is well known that the nudging scheme tends to impose more ﬁctitious
inertio-gravity waves on the model than the optimal interpolation scheme. Moreover
the response of the model to the nudging, as shown in the end of this subsection,
depends strongly upon the e-folding time scale.
In our forecast system we introduce, instead of the above schemes, an incremental
analysis update (IAU) scheme (Bloom et al., 1996). The formulation is similar to thenudging scheme,
Xa − Xft(13.35)
X n+1 = X n +τ I AU
where X f is a forecast data at the same analysis time as for X a and τ I AU = 7 days is aperiod of the IAU cycle. Equation (13.35) indicates that the analysis increments thatare differences between the analysis and the forecast data are gradually incorporated
into the model over the period. The increments are constants during each IAU cycle.
Figure 13.4 illustrates the ﬂow of the IAU scheme. (1) A previous IAU cycle provides an initial condition of a forecast. (2) The forecast experiment is conducted forτ I AU /2 (=3.5 days).8 (3) The output data of the forecast process is provided to the
8 The forecast experiment is, in fact, conducted for 60 days in each cycle as shown in Fig. 13.4
in order to provide the information about the Kuroshio path variation for public people. Miyazawa
et al. (2005) suggest that the model has a predictability skill up to approximately 2 months for thevariation.

13.2 Description of Forecast System

IAU

225

cycle: n-1

cycle: ncycle: n+1

Data

Data

Data

IAU

(4)

(1)

(3)

(4)

reanalysis

reanalysis
(3)

(1)

(4)

IAU

reanalysis

(3)

(1)

(2)

Forecast(2)

Forecast(2)

60days

Forecast

Fig. 13.4 Flow chart for the IAU and forecast. Numbers in the parentheses indicate the order ofprocedures

Response function
Response function
IAU
7days scale nudging
1day scale nudging

1.4

1phase(deg.)

amplitude

1.2

0.8
0.6
0.4
0.2
0
0

10

20

30
40
time(days)

50

60

200
180
160
140
120
100
80
60
40
20
0
−20
−40
−60
−80
−100
−120
−140
−160
−180
−200

IAU
7days scale nudging
1day scale nudging

0

10

20

30
time(days)

40

50

60

Fig. 13.5 Comparison of the amplitude (left) and phase (right) response of ﬁlters. Solid: The IAU
with τ I AU =7 days. Dashed: The nudging with τnudge =7 days. Dotted: The nudging with τnudge =1 day

IAU scheme, and the analysis increment is determined. (4) The increment is incorporated into the model by following (13.35). During a cycle of the IAU process, model
results are stored at 2 days interval as shown in Fig. 13.4. We call these output thereanalysis. Then these procedures are continuously carried out.
Finally we will show the superiority of the IAU scheme to the nudging scheme.
Assuming that the governing equations are linear, we can examine the response characteristics of the ﬁlters such as the IAU and the nudging (Bloom et al., 1996). Afterthe IAU with τ I AU =7 days is applied, phenomena on the 20 days time scale willlose 20% of their amplitude, but the decrease of the signal amplitude asymptotically approaches to zero as the time scale of phenomena gets longer (left panel ofFig. 13.5). Moreover the phase error is almost null for phenomena with time scale
longer than 7 days (right panel of Fig. 13.5). On the other hand, although the phaseerror due to the nudging with the same time scale as the IAU is quite small, the amplitude response is terribly bad. Phenomena with the 60 days time scale will lose 40%
of its amplitude because of the nudging. The nudging with the e-folding scale of

226

13 High Resolution Kuroshio Forecast System

1 day is superior to the others in the amplitude response, but inferior in the phase
response. This comparison implicates that the IAU is a better low-pass ﬁlter than the
nudging.

13.3

Predictions of the Kuroshio Large Meander

We have carried out the forecast experiment of the Kuroshio large meander since
December 2001. The forecast lead time is 2 months, which is determined in sucha way that RMS errors of ensemble forecast experiments do not exceed the magnitude of the model climatic variation, and those obtained from nonassimilated
simulations and persistence (Miyazawa et al., 2005). Forecast results and thereanalysis data described in the previous section are distributed from the web site
http://www.jamstec.go.jp/frsgc/jcope/, and updated on every Saturday. In this section, we will take a couple of examples from the recent forecasts of
the Kuroshio path variations. We will also describe the sensitivity of the July–October
2004 forecast to a couple of parameters used in the data assimilation scheme.

13.3.1Case for April to June 2003

In April 2003 the Kuroshio took the nearshore nonlarge-meander path with a small
offshore displacement south of the Kii Peninsula moving approximately 250 km
east from south of Shikoku Island. On the offshore side of the Kuroshio south of thepeninsula a westward surface current is evident between 30.5◦ N and 32.5◦ N, suggesting the existence of an anticyclonic eddy (upper left panel of Fig. 13.6). Existence ofanother small anticyclonic eddy around 140◦ E on the offshore side of the Kuroshio
is also suggested.
The forecast model is initialized with the IAU output on April 26, 2003. The upper
right panel of Fig. 13.6 shows a nowcast of the SSH, indicating that the Kuroshio
ﬂowing along the Japanese coast and the existence of two major anticyclonic eddies
south of the Kii Peninsula are represented well.
In the May 2003 forecast (1-month lead time forecast), the model predicts thedevelopment of the offshore displacement (small meander) of the path southeast of
the Kii Peninsula (middle right panel of Fig. 13.6), in perfect accord with the observation on its zonal and meridional extents: approximately 450 km and 250 km. In themeander, a cyclonic eddy is formed. On the onshore side of the eddy, the speed of the
westward coastal current exceeds 0.5 m s−1 at places based on the one-time observation (middle left panel of Fig. 13.6), while that in the 2-day mean forecast is at most
0.25 m s−1 . The underestimate is partly because the observation ﬁelds are instantaneous, and partly because the model needs more horizontal resolution to resolve such
local phenomena.

13.3 Predictions of the Kuroshio Large Meander227

22-28 Apr., 2003

35N

K
B

S

E
H

Q

30N

25N
130E

135E

140E

145E

20-27 May, 2003
35N

30N

25N
130E

135E

140E

145E

24 Jun.-1 Jul., 2003
35N

30N

25N
130E

135E

140E

145E

Fig. 13.6 Left: Weekly mean observed Kuroshio path during April 22, 2003 to July 1, 2003 reported
in the Quick Bulletin Ocean Conditions provided by Hydrographic and Oceanographic Department,
Japan Coastal Guard. The thin line delineates the Kuroshio path of a week ago and the thick is thecurrent path. Arrows indicate the surface velocity at 0.15–0.5 m s−1 (thin), 0.5–1.0 m s−1 (thick)and 1.1–2.5 m s−1 (open). Right: Model SSH in 2-day mean of the forecast initialized on April
26, 2003. Contour interval is 0.05 m. Solid contours correspond to positive values of the SSH, anddotted contours to negative values. In the upper left panel, K, E, S, Q, H, and B denote the Kii
Peninsula, Enshu-nada Sea, Shikoku, Kyushu, and Hachijo-jima Islands, and the Bungo Channel,
respectively

228

13 High Resolution Kuroshio Forecast System

In the June 2003 forecast (2-month lead time forecast), the small meander moves
eastward, leading to the offshore nonlarge meander path, which is close to the observation, although the observed path is distorted in the W-shaped pattern (lower panelsof Fig. 13.6). Furthermore, our forecast model initialized in the beginning of June
predicts the subsequent eastward movement of the meander, eventually causing theKuroshio to take the nearshore nonlarge meander path in the end of July (not shown).
Note that the model seems to predict well the anticyclonic eddy southeast of Kyushu
Island, which is barely perceptible from the spatially sparse observation (lower left
panel of Fig. 13.6).

13.3.2 Case for May to July 2004
A small meander of the Kuroshio occurs southeast of Kyushu in the beginning of2004 (not shown), stays there with growing its size until June 2004 (middle left panelof Fig. 13.7). It starts to move eastward slowly in the second week of June 2004, andgrows into a large meander at the end of July 2004.
In 1-week lead time forecast initialized on May 1, 2004, the small meander moves
to the east and its head reaches the south tip of the Kii Peninsula (upper right panelof Fig. 13.7), showing a pattern similar to the observation on June 1–8, 2004 or in aweek before delineated by the thin line in the middle left panel of Fig. 13.7.
In the June 2004 forecast (1-month lead time forecast), the center of the meander
reaches the south of the peninsula in a way similar to the observation in the end of
July 2004. As the meander moves to the east, the anticyclonic eddies in the east andwest of it develop (middle right panel of Fig. 13.7).
In the July 2004 forecast (2-month lead time forecast), the Kuroshio large meander
reaches its mature state. The anticyclonic eddy east of the meander moves westward
along the path and is merged into another, then the eddy west of the meander further
develops (lower right panel of Fig. 13.7).
This is the ﬁrst success in predicting the Kuroshio large meander as well as theoccurrence of its triggering meander southeast of Kyushu Island (not shown) using
both the numerical model and available observation data, although the model has abias in the eastward movement speed of the small meander along the Japanese coastas described earlier. In the model the small triggering meander takes approximately
4 months to grow into the large meander after its appearance, while it does approximately 7 months in the real ocean. Previous hydrographic observations, however,indicate that the small meander usually takes approximately 4 months to grow into
the large meander after its appearance southeast of Kyushu Island (Kawabe, 1986),
suggesting that its eastward movement speed in the model is consistent with those inpast events. This means that the model will perhaps be able to predict the path transition of the Kuroshio observed in the more past in a relatively accurate way comparedwith the 2004 forecast, but, at the same time that the model perhaps misses somemechanism to explain why the small meander takes approximately 7 months to growinto the large meander after its appearance.

13.3 Predictions of the Kuroshio Large Meander229

4-11 May, 2004

35N
K
B

S

E
H

Q

30N

25N
130E

135E

140E

145E

1-8 Jun., 2004

35N

30N

25N
130E

135E

140E

145E

29 Jun.-6 Jul., 2004

35N

30N

25N
130E

135E

140E

145E

Fig. 13.7 Same as Fig. 13.6 except for the period during May 4, 2004 to July 6, 2004 and theforecast initialized on May 1, 2004

13.3.3

Sensitivity of the Forecast to Parameters

Since the forecast is quite sensitive to parameters used in the data assimilation
scheme (Table 13.2), we have conducted lots of trial-and-error experiments in sucha way that the forecast of the path transition of the Kuroshio that occurred in thepast becomes reasonable. In this subsection, we will take an example to show how

230

13 High Resolution Kuroshio Forecast System

Fig. 13.8 Comparison of the 2-month lead time forecasts initialized on May 6, 2004 obtained withtwo different sets of parameters. Shading and vectors denote the temperature (◦ C) and velocity(m s−1 ) at 200 m, respectively. Left: With parameters listed in Table 13.2. Right: Same as the left
panel except that vcorimps and vobsieadj for the SSH are 1.0 and 0.01, respectively

Fig. 13.9 Same as Fig. 13.8 except for the forecast initialized on June 3, 2004

sensitive the model is to a couple of parameters. The experiment with parameter values listed in Tables 13.2 and 13.3 is called the standard case, while that with the samevalues except for vcorimps and vobsieadj for the SSH is the test case. The former one is the adjustable parameter by which the regression coefﬁcient between thesalinity at the depth k and the SSH, and the latter is αη in (13.28).
The standard case shows that the large meander path is stable in a sense of its
meridional extent, although the path slightly vibrates in the zonal direction (left panels of Figs. 13.8–13.11). On the other hand, in the test case where vcorimps andvobsieadj for the SSH are set to be 1.0 and 0.01, respectively, the meridional
amplitude of the large meander changes drastically in a manner that depends upon theinitialization date. These changes are mainly due to the detachment of anticycloniceddies from the Kuroshio (right panel of Fig. 13.9). Numbers of pinched-off eddies
suggest that the Kuroshio might be under the baroclinically unstable condition.

13.4 Toward the Kuroshio Forecast Downscaling for Coastal Oceans and Bays231

Fig. 13.10 Same as Fig. 13.8 except for the forecast initialized on July 1, 2004

Fig. 13.11 Same as Fig. 13.8 except for the forecast initialized on August 6, 2004

The above example indicates that even a couple of parameters may drasticallychange a dynamical balance in the model, thus that a careful choice of the parameters
is required in such a way that a reasonable forecast is accomplished. The parametersthat we use for the operational forecast of the Kuroshio path variation are not perfect,but better at this moment. We still now explore the parameter sensitivity.

13.4

Toward the Kuroshio Forecast Downscaling for Coastal
Oceans and Bays

As described in Introduction, the coastal waters around Japan are strongly inﬂuenced
by the Kuroshio. The variation in its path such as the large meander has been wellknown to affect the water temperature in some semienclosed bays along the southerncoast of Japan (Kawabe and Yoneno, 1987) and a biological state there (Nakata et al.,2000). Even during the period of the nearshore nonlarge meander path, a short-term
variation in the Kuroshio also affects hydrographic conditions in the enclosed bays.

232

13 High Resolution Kuroshio Forecast System

For example, it has been reported that an abnormally strong warm current (the Kyucho) originating from the Kuroshio intrudes into the Bungo Channel9 (Takeoka et al.
1993) and the Sagami Bay (Uda 1953; Matsuyama and Iwata 1977), and results ina steep temperature rise there. Such local phenomena, however, cannot be resolvedby the present Kuroshio forecast model described in the previous sections, thus weneed to develop a further ﬁne resolution forecast model for coastal oceans and bays
south of Japan in order to understand and predict the inﬂuence of the Kuroshio on
the coastal waters.
As the ﬁrst step of such efforts, which are extensions of the present Kuroshio forecast system, we chose the Suruga Bay, Sagami Bay, and Tokyo Bay as our target
areas (see Fig. 13.12). These bays are surrounded by many important industrial areasin Japan and several big cities such as Tokyo and Yokohama. As a research site foroceanography, they are one of the most active places in Japan. At present, in addition
to the physical problems such as the Kyucho and internal tides, the primary production and the ﬁsheries are also being deeply concerned, for which several big research
projects have been released by the national and local governments and universities.
Therefore, our modeling efforts will provide a framework for the future interdisciplinary researches.
In this section, we will introduce some results of a tidal simulation. Other simulations forced by either the geostrophic currents or the river runoff, or by all of themincluding the tides are still under way, and the results will be reported in other papers.
We note that the basic idea beneath our activities is that the correct prediction of an
oceanic current intrusion into a coastal water depends upon not only the correct open
boundary conditions but also a good background ﬁeld inside the coastal water. The
former has been partly guaranteed by the present Kuroshio forecast system but thelatter still needs more efforts.
The numerical model that we use for the tidal simulation is based on the twodimensional version of the POM. The horizontal resolution is 1/108◦ × 1/108◦ (approximately 0.854 km in the zonal and 1.031 km in the meridional direction).
The bottom topography data with 500 m resolution archived by Hydrographic andOceanographic Department, Japan Coastal Guard is used after smoothed out withthe ﬁlter based on Mellor et al. (1994), as described in Sect. 13.2.1. The bottom
drag coefﬁcient is set to be a constant (=0.0026). The external forcing is only thebarotropic tide listed in the Table 13.4. The tidal constants (amplitude and phase lag)for each tidal constituent are provided by Matsumoto et al.’s (2000) model output
Table 13.4 Four principal components of the tide used as theforcing
Abbreviation Character
Period [h]M2Principal lunar semidiurnal 12.4206
S2
Principal solar semidiurnal
12.0000
Lunar diurnal
25.8193
O1
Lunisolar diurnal
23.9345
K1
9 The location of the Bungo Channel is denoted by B in the upper left panel of Fig. 13.6.

13.4 Toward the Kuroshio Forecast Downscaling for Coastal Oceans and Bays233

with 1/12◦ resolution, into which the available harmonic constants obtained from thetide gauges around Japan and those over the open ocean calculated directly fromTOPEX/POSEIDON altimetry are assimilated. The tide calculated with the spatiallyinterpolated tidal constants is given at three lateral open boundaries, but the tidal
potential forcing is not taken into account. The barotropic velocity normal to theopen boundary is modiﬁed in the same way as described in Sect. 13.2.2 except that
ηc in (13.2) is the tide, crf = 1 and ū c is the barotropic velocity at a grid inside theopen boundary. The model is integrated for 7 days from a state of rest with the time
step of 0.5 s, and the output from the last 2 days is used for harmonic tidal analysis.
Figures 13.12 and 13.13 show the corange and cotidal lines obtained from themodel forced with M2 and O1 tides, respectively. Both tidal waves propagate fromeast to west. Whereas the amplitude of M2 tide increases from east to west, that of
O1 tide from the offshore side to the onshore side, suggesting a boundary trapped
wave. In fact O1 tide does not have a feature of Poincaré wave, but that of Kelvinwave because its frequency (=0.818 f ) is less than the inertial frequency, f . Comparison between the tide gauge observation and the model result indicates that theirdifferences with regard to both the amplitude and phase are within a reasonable range(the amplitude error of M2 tide is less than 5% of the observed amplitude in most ofplaces) at all observation points except for those around the Tokyo Bay. The large
difference in the Tokyo Bay may be due to the lack of the horizontal resolution compared to the least width of the bay mouth (approximately 7 km).
The tidal current is generally parallel to the coast line, as shown by ﬂat ellipses
in Fig. 13.14. It is, however, intriguing that M2 tidal current indicates an obvious

10%

5 deg.

Sa
Su

Fig. 13.12 Comparison of M2 tide amplitude (left) and phase (right) between the model and observation based on the tide gauge. The area of circles is proportional to the difference between them.
Black (Gray) circles indicates that the model amplitude is larger (smaller) than the observation, andthat the model (observation) lags the observation (model). Contour lines delineate the corange in m
(left) and cotide in degree (right) obtained from the model. Contour interval is 0.01 m for corange
and 2◦ for cotide. Su and Sa denote Suruga Bay and Sagami Bay, respectively. Dashed line denotes
the area in which the tidal ellipse is delineated (Fig. 13.14)

234

13 High Resolution Kuroshio Forecast System

10%

5 deg.

Fig. 13.13 Same as Fig. 13.12 except for the O1 tide. Contour interval is 0.002 m for corange and0.5◦ for cotide

clockwise rotation over the Izu-Ogasawara Ridge, particularly near the Izu Islands,
whereas the tidal current rotates anticlockwise in the south of Japan apart from theridge (not shown). Although the observed basic features of the tidal current are represented well in the model, the tidal current speed is underestimated particularly in thehead of Sagami Bay and Suruga Bay. This is because of the presence of strong internal tide in these bays (Ohwaki et al. 1991; Takeuchi and Hibiya 1997). At present,
we have ﬁnished simulations of the internal tide and conﬁrmed the reproduction of
the observed strong tidal currents in Sagami Bay and Suruga Bay with the use of ourcoastal model. Readers can refer to Kawajiri et al. (2006) for the details about the
reproduction of internal tide as well as other aspects of the tidal simulation such as
effects of tidal potential forcing, problems related to the open boundary conditions,and an interaction between four tidal constituents listed in Table 13.4.

13.5

Summary

We have described the detail of the Kuroshio forecast system with approximately
10 km resolution, called the JCOPE (Japan Coastal Ocean Predictability Experiment)
ocean forecast system, speciﬁcally with regard to the spatio-temporal interpolationof the observation data and the data assimilation technique including the incremental
analysis update scheme. Although the system is, as described in Sect. 13.3.3, not perfect particularly in a sense of parameter setting, we believe that this documentation
is useful for readers to develop an ocean forecast system.
Two examples of the prediction of the Kuroshio path variations using the system are introduced. The system successfully predicts the path transitions from thenearshore nonlarge meander path to the offshore nonlarge meander path in 2003, and13.5 Summary

235

Fig. 13.14 M2 tidal current ellipses around the Izu Islands

from the nearshore nonlarge meander path to the typical large meander path in 2004
as well as the occurrence of its triggering small meander south of Kyushu Island.
Note that the success of the 2004 forecast is attributed to the recent establishment ofobservation network (satellites, ships, and ARGO ﬂoats) as well as the sophisticationof both the numerical model and the data assimilation technique, suggesting that they
are just like the wheels of a car. We also note that it enables us to deeply understandhow the path transitions of the Kuroshio occur.
For the purpose of the Kuroshio forecast downscaling for coastal oceans and bay
areas, we have, for the ﬁrst step, conducted the tidal simulation with a state-of-the-art
model. Comparison between the tide gauge observation and the model result indicates that their differences with regard to both amplitude and phase are within areasonable range. It is quite intriguing that M2 tidal current rotates clockwise only
over the Izu-Ogasawara Ridge in our analysis area. Moreover the strong tidal current
at that place, particularly near the Kuroshio path, suggests its nonlinear interaction
with the Kuroshio. It is, however, out of the scope of this manuscript, hence we leavethem as future subjects.
More accurate forecasts require further reduction of model biases shown in
Sect. 13.3. Comparing the JCOPE reanalysis data and the individual hydrographic

236

13 High Resolution Kuroshio Forecast Systemobservation that are not assimilated into the model, we realize that the model temperature tends to have a positive bias in the onshore side of the Kuroshio and a negative
bias in the upper 50 m and the thermocline layer of its offshore side. The representation of the density ﬁeld particularly in the onshore side of the Kuroshio is very crucial in predicting the path transition of the Kuroshio accurately, because the eastward
movement and development of the small trigger meander are related to the baroclinic
instability. Hence we have been investigating causes of the biases through numerous
sensitivity experiments to parameters and numerical schemes, and also developing,on the basis of Hukuda and Guo (2004), a two-way nesting forecast model which
consists of the current ﬁne model and a regional model for the Kuroshio area with
1/36◦ resolution and thereby may represent a sharp density front in the onshore sideof the Kuroshio more accurately than the current model.
Outputs of the current JCOPE ocean forecast system can be utilized as pseudo-data
for many purposes. Because of the ﬁneness of the horizontal resolution, the JCOPE
reanalysis data have been used for the lateral boundary condition of a regional ocean
model (e.g., Suzuki et al. 2004; Uchimoto et al. 2006) and for the bottom boundary condition of a regional atmospheric model (e.g., Yamaguchi et al. 2005). In thelatter case, the short-term variations of the rainfall and surface wind associated withthe typhoon passing are represented consistently with the observation by a hindcast experiment with the SST obtained from the JCOPE model compared to anotherexperiment with the surface skin temperature from NCEP Global Forecast System,suggesting that the predicted SST by the JCOPE system may be useful to local severe
weather forecasting and notiﬁcation. Recently the Fisheries Research Agency has
started to investigate dispersal of eggs and larvae of anchovy and horse mackerel
using the velocity ﬁeld of the JCOPE reanalysis data to attain the goal of evaluatingﬁsheries resources and predicting ﬁshing grounds. The JAMSTEC has tentatively utilized the velocity data for the operation of the Deep Sea Drilling Vessels “CHIKYU”
because the strong current has a particularly serious impact on the ability of a drilling
rig to maintain its position. We expect that the JCOPE ocean forecast system maycontribute to as many societies as possible because of its wide availability.
Acknowledgments We are greatly indebted to Prof. Toshio Yamagata and Dr. Hirofumi Sakuma for
their encouragement and the management of our research activity. The JCOPE project is supported by
the Frontier Research Center for Global Change/JAMSTEC. The QuikSCAT data is obtained from theNASA/NOAA sponsored data system Seaﬂux, at JPL through the courtesy of Dr. W. Timothy Liu and
Dr. Wenqing Tang. The comparison study between the JCOPE output and the hydrographic data and thesensitivity study are supported by Dr. Kosei Komatsu, Dr. Takashi Setou, and many collaborators in the
Fisheries Research Agency.

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