JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110, C10026, doi:10.1029/2004JC002426, 2005

Ensemble forecast of the Kuroshio meandering
Yasumasa Miyazawa, Shozo Yamane,1 Xinyu Guo,2 and Toshio Yamagata3
Frontier Research Center for Global Change/Japan Agency for Marine-Earth Science and Technology (JAMSTEC),
Kanagawa, Japan
Received 10 April 2004; revised 10 July 2005; accepted 28 July 2005; published 26 October 2005.

[1] Focusing on predictability of the Kuroshio meandering, we have done an ensemble

forecast experiment; the application of the method to the problem addressed seems to be
the first comprehensive attempt in the community of physical oceanography. By
assimilating sea surface height anomaly into an ocean general circulation model in thepreceding 40-day period, the observed Kuroshio meandering manifested south of Japan inNovember 1999 was successfully predicted 2 months before the event. The
experiment yields a forecasting skill of the Kuroshio meander position for 60 days in thesense that the RMS error does not exceed the magnitude of the model climatic
variation and those obtained from the non-assimilated simulation and persistence. In
addition to a single trajectory forecast experiment, ensemble forecasts were conductedusing 10 perturbed initial states generated by the breeding method. The predictedstates realized as the ensemble members of the 80-day forecast are classified into two
categories: large and non-large meander. It is found that the intensity of an anticycloniceddy in the initial state seems to play a key role in selecting one of the two states.
Citation: Miyazawa, Y., S. Yamane, X. Guo, and T. Yamagata (2005), Ensemble forecast of the Kuroshio meandering, J. Geophys.
Res., 110, C10026, doi:10.1029/2004JC002426.

1. Introduction[2] The transition of the Kuroshio path between the largemeander state and the non-large-meander one has been
extensively investigated by both theoretical and observational studies. The theoretical studies [e.g., Masuda, 1982]
suggest that the Kuroshio can possess multiple equilibria
under the same external conditions. Kawabe [1995] discussed the equilibrium states of the Kuroshio system andshowed that the large meander appears when the upstream
volume transport is relatively large.
[3] As in the atmospheric blocking, we may classify thetheoretical studies into two categories: nonlocal [e.g., Whiteand McCreary, 1976; Masuda, 1982] and local approaches[Yamagata and Umatani, 1989]. The former adopts the leewave theory for Rossby wave and formulates the Kuroshio
bimodality problem as a boundary value problem in which
the phase speed C of Rossby wave satisfies suitable inlet
and outlet conditions imposed at respective boundaries near
the strait south of Kyushu and the one at the Izu-Ogasawara
Ridge. In this case, the large-meander state exists when the
upstream current U satisfies either subcritical (U + C < 0) or
critical (U + C = 0) conditions. On the other hand,
Yamagata and Umatani [1987, 1989] demonstrated that1
Also at Department of Environmental Security, Faculty of Risk andCrisis Management, Chiba Institute of Science, Chiba, Japan.
2
Also at Center for Marine Environmental Studies, Ehime University,
Ehime, Japan.
3
Also at Department of Earth and Planetary Science, Graduate Schoolof Science, University of Tokyo, Tokyo, Japan.

Copyright 2005 by the American Geophysical Union.
0148-0227/05/2004JC002426$09.00

for a supercritical condition (U + C > 0), the observed large
meander can be interpreted as a manifestation of thegeometrically trapped nonlinear solitary wave. Mitsudera
and Grimshaw [1994] extended the theory into a baroclinic
case and showed that the specified local topography cangenerate a stationary large-amplitude wave through baroclinic instability process satisfying a supercritical condition.
The observational study of Kawabe [1995] supports
the local approach at least for the meander formation[Mitsudera and Grimshaw, 1994]. Recent modeling studies
using realistic topography suggest that even a local seamount south of Japan is important for the formation of theKuroshio large meander [Hurlburt et al., 1996; Endoh andHibiya, 2001; Miyazawa et al., 2004].
[4] In the framework of the above local approach, transitions between multiple equilibria are governed by initial
disturbances if the given state is within the appropriate
dynamical regime [Yamagata and Umatani, 1987;
Mitsudera and Grimshaw, 1994]. In fact, this conjecture
was tested numerically and the transitions between different
states are successfully simulated in some modeling studies[e.g., Endoh and Hibiya, 2001]. The Kuroshio volumetransport has been either large or intermediate since 1975;
however, the stable large meander has not occurred in thelast decade (see Quick Bulletin of Ocean Conditions by theJapan Coast Guard) [see also Qiu and Miao, 2000]. Therefore, if the real Kuroshio state falls in one of the multiple
equilibrium states since 1975, it is interesting to investigate,
on the basis of hindcast experiments using a realistic ocean
general circulation model (OGCM), how the Kuroshio pathvariation is sensitive to the initial disturbances.
[ 5 ] Recent observational studies using the satellite
altimeter and the in situ Acoustic Doppler Current Profilers

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MIYAZAWA ET AL.: ENSEMBLE FORECAST OF THE KUROSHIO MEANDERING(ADCPs) showed that meso-scale eddies are very active
south of Japan [Ebuchi and Hanawa, 2000]. Regional
numerical studies [Mitsudera et al., 2001; Endoh andHibiya, 2001] employing the inflow-outflow boundary
conditions also demonstrated that a meso-scale eddy
triggers the Kuroshio large meander or offshore non-large
meander. Ebuchi and Hanawa [2003], using the satellite
altimetry data, reported that three offshore non-large meanders in 1993, 1998, and 1999 were triggered by anticycloniceddies. Miyazawa et al. [2004] were successful in simulating the Kuroshio path variation induced by the eddyKuroshio interaction using a basin-wide eddy-resolving
OGCM.
[6] So far, a few studies have examined possibility ofoperational numerical predictions of the Kuroshio pathsouth of Japan. Komori et al. [2003], using a reduced gravity
model initialized by assimilating the TOPEX/Poseidon
altimetry data, estimated the predictability limit which falls
within the range extending from 30 to 90 days and theyfurther pointed out that the estimate of this kind would
heavily depend on the model dynamics employed. Kamachi
et al. [2004] conducted hindcast experiments of theKuroshio path during from 1993 to 1999 using an eddypermitting (1/4 grid) OGCM with the assimilated TOPEX/
Poseidon data. The predictability limit of their forecast
system is reported to be about 80 days. They suggest thatthe eddy-Kuroshio interaction is an important potential
mediator causing the transition from the nearshore to offshore
non-large meander. However, they have not discussed thegeneration mechanism of the large meander.
[7] In addition to a single trajectory forecast experiment,
Kamachi et al. [2004] performed an ensemble forecast withfive ensemble members accompanying the transition fromnearshore to offshore non-large meander. Their ensemble
mean forecast yielded slightly better forecasting skill thanthe unperturbed forecast. However, since their experiment
was very preliminary, neither detailed features of the spreadin their ensemble experiment nor sensitivity of the prediction
on the imposed initial errors was discussed in their study.
[8] No conventional method on ensemble generation has
been established yet for multimodal dynamical systems
such as the Kuroshio path south of Japan. For a simple
dynamical system with multiple attractors, Miller and Ehret[2002] evaluated the performance of ensemble runs withseveral different methods of generation, however, the performance of such a complex dynamical system as the one
under consideration remains to be investigated further. As
the first step toward such studies, we utilize here an iterative
ensemble generation process called ‘‘breeding method’’[Toth and Kalnay, 1993]. The breeding method may wellsimulate the development of growing errors in the assimilation cycle.
[9] In the present study, we discuss the event in the year
1999 using an eddy-resolving OGCM with the TOPEX/
Poseidon altimetry data assimilated into the initial field. We
conduct a hindcast experiment of the Kuroshio path for aperiod of 80 days after the last cycle of the assimilated
initialization. To the best of our knowledge, the present
work is the first comprehensive attempt to investigate thepredictability of the Kuroshio meandering using the ensemble forecast approach. Since the eddy dynamics is an
important factor in the Kuroshio path variation [Miyazawa

C10026et al., 2004], the present use of the eddy-resolving OGCM
is vital and enables us to examine meaningful case-by-casevariation in the model ensemble.
[10] This paper is organized as follows. In section 2, ahindcast experiment of the event in 1999 as a single
trajectory forecast is described. Section 3 covers the resultsof the ensemble forecast experiment, in particular, thecharacteristics relating to both the skill and spread in
the ensemble run are argued. In section 4, looking into
the ensemble forecast of 80 days, we discuss the possible
dynamical roles played by eddies in triggering the bifurcation of the bimodal Kuroshio paths. Final section 5 isdevoted to summary.

2. Hindcast Experiment of the Kuroshio
Meandering
2.1. Ocean Model[11] The present ocean model is based on Princeton
Ocean Model (POM) [Mellor, 1998], one of the mostpopular community models in the world. A high-resolution
regional model with spatial grid of 1/12 degree and 35
sigma levels is embedded in a low-resolution basin-wide
model with a spatial grid of about 1/4 degree and 21 sigma
levels. The inner model domain covers the northwest Pacific(12N –56N, 117E– 180E) and its lateral boundary conditions are determined from the basin-wide model using theone-way nesting method [Guo et al., 2003]. Details of themodel configuration are described in our previous paper[Miyazawa et al., 2004].
[12] The model is driven by wind stresses, and heat andsalt fluxes. Both wind stress and heat flux fields arecalculated from the 6-hourly NCEP/NCAR reanalysis data
[Kalnay et al., 1996] using the bulk formula [Rosati and
Miyakoda, 1988]. Salinity at the ocean surface is restored tomonthly mean climatology data [Levitus et al., 1994] with atimescale of 30 days. Simulation of the low-resolution
model is started from a state of rest with the annual-meantemperature and salinity fields created from a 1/4 degree
climatology data [Boyer and Levitus, 1997]. The lowresolution model is spun up by the monthly mean surface
forcing for 10 years. Then the model is further driven by
6-hourly surface forcing covering from 1 January 1991 to
30 November 1999. The high-resolution model is also
forced from a state of rest with the climatological temperature and salinity fields but with 6-hourly surface forcing
applied from 8 August 1996 to 30 November 1999.
2.2. Hindcast of the Kuroshio Meandering in 1999[13] According to Quick Bulletin of Ocean Conditions
published by the Japan Coast Guard (Figure 1, left), the real
Kuroshio took an offshore non-large-meander path from
November 1999 to June 2001. A hindcast experiment
without initialization failed to reproduce this offshore nonlarge-meander episode. Therefore TOPEX/Poseidon sea
surface height anomaly (SSHA) data in the period startingfrom 26 July to 7 September 1999 have been successively
assimilated to the simulated fields in the high-resolution
model with the time interval of 10 days.
[14] For indirect estimation of temperature and salinity
fields, we adopt a practical approach similar to the optimal
analysis equation proposed by Mellor and Ezer [1991]. The

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Figure 1. (left) Bi-weakly mean observed Kuroshio path during the period from September 1999 toNovember 1999, reported in the Quick Bulletin Ocean Conditions provided by Hydrographic andOceanographic Department, Japan Coast Guard. The gray path corresponds to the last and the white pathto the current path. (Right) Model sea surface height in 5-day mean of the unperturbed forecast. Contour
interval of sea surface height is 0.1 m.
analyzed estimate of the forecast variable T f at depths from50 m to 2000 m is calculated as follows:
T a ¼ T f þ PT h FTh Dho  Dh f ;ð1Þ

where Ta and T f are analyzed and forecast quantities; PTh isa weight of correction and FTh is a regression coefficient
calculated statistically from the model results without
assimilation; Dho and Dh f denote the observed and thesimulated SSHA, respectively. Dh f in equation (1) is
calculated by subtracting the temporal mean from the SSH
obtained through the one year model simulation in 1998.
The observed along-track SSHA referencing to the Ohio
University Mean Sea Surface, provided by the Colorado
Center for Astrodynamics Research Real-Time Altimeter
Data Group [Lillibridge et al., 1997], is interpolated to themodel grid with an interval of 10-days using an optimum
interpolation method [Kuragano and Kamachi, 2000]. The
latitudinal mean value of the SSHA corresponding to thelarge-scale, seasonal variation is subtracted from the SSHA
to assimilate only meso-scale variation (Y. Wakata, personalcommunication, 1999). The weight of correction PTh inequation (1) is calculated so that it minimizes the analyzed
error h(T a  T t )2i, where brackets denote an expected value
and Tt represents a true state. PTh has the following form:
PT h ¼Es;
2 1
Eo þ Es þ 1=CTh2ð2Þwhere Es = h(Dh f 2  Dht)2i=hDht i and Eo =h(Dho  Dht)2i=hDht i are the normalized simulation and observation error variances of SSHA, respectively.
The quantity CTh is the correlation coefficient between
the SSHA and the temperature/salinity. Derivation ofequation (2) is described in Appendix A. The normalized
simulation error variance Es is empirically determined to be
2.8 in the region south of Japan (27N –38N, 130E–
145E) and 1.5 in the other. We conduct ensemble forecasts

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Figure 1. (continued)
to reduce this uncertainty of error estimate. The observation
error variance of SSHA may include various types of error(error in the mean SSH used to compute the SSHA, realmeasurement error of the along-track SSH, interpolation
error, etc.), although we simply specify interpolation error
variance obtained from the optimum interpolation ofalong2
track SSHA as Eo. The normalizing factor hDht i as thevariance of true SSHA is to be substituted by the varianceof observed SSHA, since there is no other way to give anapproximate estimate of this quantity.
[15] In order to achieve smooth assimilation, both temperature and salinity fields are nudged to the analyzed
variables in equation (1) with a restoring timescale of
0.3 days during a tentatively set time span of 6 days inthe middle of which observational data are provided. The
nudging toward both the analyzed temperature and salinity
gradually would modify velocities and sea surface height
through geostrophic adjustment. The analysis (1) is calculated using the temperature/salinity and SSHA fields forecasted at 3 days before the observation time. The grid dataof SSHA created from 26 July 1999 to 7 September 1999
were assimilated into the original simulation. Then the time
integration proceeded with constant surface forcing andlateral boundary condition evaluated at the last initializationtime.
[16] Figure 1 (right) shows evolution of the assimilated sea
surface height after the last initialization. The anticycloniceddy stays southeast of the Kyushu Island in the initial state.
Then it propagates eastward toward the Kii Peninsula in
October 1999 and generates the meander in November 1999
as observed (left panel of Figure 1, left). Thus we see that theinitialization with the aforementioned data assimilation processes leads to a successful prediction of the meander of theKuroshio, though the predicted field on 26 November 1999
underestimates the meander amplitude with its position
shifted to the east compared with the observation.
forecasting[17] To measure theq
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃskill quantitatively, we useðh f  hr Þ2 and anomaly correlation
Dh f Dhrof sea surface height c1 = qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ for a reference sea
Dh f 2  Dh r2
N
1X
surface height hr, where A
Aj (N denotes number
N j¼1
of grid points in the Kuroshio region; 28N – 35N, 130E–
140E); the RMS error is normalized by the value 0.19 m
both RMS error e1 =4 of 14

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C10026The skill improvement of the forecast, however, measured
by the RMS error seems to be smaller than that by theanomaly correlation. Although the pattern of the forecast
SSHA is generally similar to the reference SSHA even in
the late period, stronger signal of the reference SSHA thanthat of the forecast, especially in the meandering region(not shown), tends to increase the RMS error. The RMS
error exceeds the level of the modeled climatic variation
more than 70 days after the last initialization, while thepersistence reaches the level at 60 days. Therefore theforecast only improves on the persistence by 10 days.
Skills of both the unperturbed and ensemble mean forecasts
for SSHA and other variables (temperature, salinity, andthe Kuroshio meander position) are further discussed in thenext section.

3. Ensemble Forecast[18] Ensemble forecasts were conducted using 10 perturbed initial states generated by the breeding method [Tothand Kalnay, 1993]. First, on 26 July 1999, two-dimensionalrandom perturbation Dhptb with a horizontal correlation
scale of 0.7 degree [Evensen, 1994] is added to the analyzed
value Tca of the assimilation run described in section 2, in theregion (27N – 38N, 130E– 145E) with upper 1000 m
depth,aTptb¼ Tca þ FhT Dhptb ;ð3Þ

where Dhptb is assumed to have zero mean and RMS
magnitude of 0.05 m. At every assimilation time during the

Figure 2. (a) Evolution of RMS errors of sea surface
height anomaly for the reference run over the Kuroshio
region, 28N–35N, 130E– 140E. The RMS error is
normalized by RMS variability of the simulation in thesame region (0.19 m). Thick line with solid circles
corresponds to the unperturbed forecast. Long dashed linewith crosses corresponds to the non-assimilated simulation
run. Short dashed line with squares corresponds to thepersistence of an initial state. (b) As in Figure 2a except for
anomaly correlation.

which is the RMS variation in the Kuroshio region calculated from the one year model simulation in 1998. In thereference assimilation run, we utilize not only the TOPEX/
Poseidon but also the ERS-2 data to effectively approximate a true state. We call this additional assimilation run
simply as the reference run. Figure 2a exhibits that a skillof the forecast (thick line with solid circles) is superior tothose of non-assimilated simulation (long dashed line withcrosses) and persistence (short dashed line with squares)
during the meander period from 27 October to 26 November. Another measure of skill, anomaly correlation, also
shows some similar feature as the RMS error (Figure 2b).

Figure 3. Evolution of RMS errors of sea surface heightanomaly normalized by RMS variability of the simulation(0.19 m) for the reference run over the Kuroshio region,
28N –35N, 130E– 140E (solid lines with solid circles)
and anomaly correlations (dashed lines with solid circles).
Thick lines with solid circles denote the ensemble mean
and thin lines with solid circles denote the unperturbed
forecast. Thin solidpand
dashed lines denote theoretical
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ð M þ 1Þ=2M he12i1/2 and hcMi =skill, heM2i1/2 =1=2M
hc1i estimated from the unperturbed
1 þ ð M  1Þhc1 i
forecast values, respectively (M = 10).

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Figure 4. Evolution of RMS errors of (left) temperature and (right) salinity normalized by RMS
variability of the simulation for the reference run over the Kuroshio region, 28N–35N, 130E– 140E.
The RMS variability values of temperature at 200 m and 1000 m are 1.1 and 0.28C, respectively. Thoseof salinity are 0.043 and 0.020 psu, respectively. Thick lines with solid circles denote the ensemble mean
and thin lines with solid circles denote the unperturbed forecast. Long dashed line with crosses denotes
the non-assimilated simulation run. Short dashed line with squares denotes the persistence of an initialstate.

period from 5 August to 7 September 1999, the differenceof sea surface height anomaly (SSHA) between theperturbed run Dhfptb and the assimilation run Dhc is added
to the assimilated value as follows:

the initial state. Theoretical estimate of RMS error of
ensemble mean forecast for M ensemble members is

f
a
Tptb
¼ Tca þ FhT C0:05m Dhptb
 Dhc ;

where eM and e1 are RMS errors of an ensemble mean
forecast and a single forecast, respectively; brackets
denote an expected value [e.g., Murphy, 1988]. An
additional assumption that variations in anomaly intensity
are small yields an estimate of anomaly correlation of the
form

ð4Þ

where C0.05m is a coefficient to make RMS value ofC0.05m(Dhfptb  Dhc) equal to 0.05 m. For the sake ofsimplicity, we rescale only SSHA. 10 ensemble members
are created by repeating the breeding method staring from10 random perturbations Dhptb uncorrelated with each other.
[19] Simple analytical relationships between the forecast
skill and properties of our ensemble forecast may be derived
under following assumptions: (1) the model is perfect andforecast error growth is caused only by initial state error
through internal dynamics of the model, (2) each individual
integration in an ensemble is equally likely to represent thetrue state evolution, and (3) an initial ensemble represents
true analysis error distribution within sampling limits[Murphy, 1988]. The ensemble mean forecast is expected
to have better forecasting skill statistically than an unperturbed forecast by smoothing out small-scale features,
which are significantly influenced by the uncertainty of

e2M

1=2

¼

pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 1=2
ð M þ 1Þ=2M e1;


hcM i ¼

1=2M
hc1 i;
1 þ ð M  1Þhc1 i

ð5Þ

ð6Þ

where cM and c1 are anomaly correlations of an ensemble
mean forecast and a single forecast, respectively [Murphy,
1988]. These two theoretical relations indicate thatensemble mean forecast is better in the skill than asingle forecast on average. We investigate the skill
measured by both the RMS error and anomaly correlation
averaged over the Kuroshio region (28N – 35N, 130E–
140E) in an ensemble forecast experiment, where thetheoretical relations are not necessarily satisfied.

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Figure 5. As in Figure 4 except for RMS error of theKuroshio axis (0.4 m contour of sea surface height) along
the meandering region, 135E– 140E. The RMS variabilityof the Kuroshio axis is 49.6 km.

[20] Figure 3 compares forecasting skills of sea surface
height anomaly (SSHA) in ensemble mean measured byboth the RMS error (solid line with solid circles) andanomaly correlation (dashed line with solid circles) withthose of the unperturbed forecast. The RMS error of theensemble mean forecast is comparable with that of theunperturbed forecast during the early period from September to October. The disagreement of ensemble meanskill with a theoretical estimate (thin solid line) during theearly period is due to non-satisfaction of the second
assumption mentioned above; that is, the unperturbed
forecast represents the true state evolution better thanthe each perturbed forecast during the early period.
During the late one from the end of October to a month
later, however, the skill of the ensemble mean forecast
shows some improvement; the RMS error almost agrees
with the theoretical estimate (thin solid line). This implies
that the skill of the unperturbed forecast is no longer
better than that of each perturbed forecast during the lateperiod. Anomaly correlation also indicates the improvement of the skill in the ensemble mean forecast during
the late period, though the improvement is not so evident
as that of the RMS error.
[21] We also evaluate the forecasting skill for temperatureand salinity (Figure 4). Both temperature and salinity may
be less predictable than SSHA because, in almost all cases,
the RMS error exceeds the magnitude of the climatic
variation soon after or in the beginning of the forecast.
Introduction of another data (ERS-2) into the data assimilation for the reference run may have more impact on
temperature and salinity than on SSHA. Near the surface,
as shown in upper panels of Figure 4, the forecast shows
better skill than both the persistence and non-assimilated
simulation, and the ensemble mean forecast improves the
skill of the unperturbed forecast. These features are consistent with those discussed in the forecast of SSHA, which isstrongly affected by density in the surface layer. In the depthof 1000 m, the unperturbed and ensemble mean forecastingskills are comparable to the persistence (Figure 4, bottom).
Below 1000 m, both temperature and salinity vary slightly
in time of duration (not shown).

C10026[22] A skill measure of most interest is position of theKuroshio meander. We define sea surface height (SSH)
contour of 0.4 m as the axis of the Kuroshio south of Japan(e.g., see Figure 8 later in this section). 0.4 m contour of
SSH well agrees with 15C contour at depth of 200 m (notshown), which is traditionally used to capture the Kuroshio
path [e.g., Kawai, 1969]. As shown in Figure 5, theforecasting skill of the meander position is clearly better
than that of the persistence. The skill improvement by theensemble mean is also evident. While the error of theunperturbed forecast exceeds those of both the persistence
and non-assimilated simulation after 70 days, the ensemble
mean has some skill at this time.
[23] The spread of the ensemble provides useful information about predictability; the growth of spread indicates loss of forecasting skill. Here we adopt the RMS
difference of individual ensemble members from theensemble mean as a measure of the ensemble spread.
Figure 6 indicates that the spread gradually increases
with reduction of the forecast skill shown in Figure 2.
Theoretical relation between spread and RMS error of aM 1 2he1i under the
single forecast is given by hs2Mi =2Mtheoretical assumptions. Since the relation of RMS error isM þ1 2
given by he 2M i =he 1 i, we have the relation:
2M
s2M ð M þ 1Þ
= 1 [e.g., Takano, 2002]. Figure 7 showse2M ð M  1Þ
s2 ð M þ 1Þ
calculated from RMS
the time sequences of M
e2M ð M  1Þerrors and difference respectively given in Figures 3 and 6.
Roughly speaking, the value of the quantity averaged
through the whole period is nearly one. This quantity,
however, shows temporal variations; the value less than
one in the early period becomes larger in October andexceeds one early in November. Its increasing tendency
may be connected with a relatively rapid increase of
the ensemble spread late in October shown in Figure 6.
The rapid increase of the spread seems to be related to thebifurcation of the Kuroshio path, as is discussed in the next
paragraph.
[24] Figure 8 shows ‘‘spaghetti’’ diagram of the Kuroshio
path on 26 November 1999. The predicted Kuroshio me-

Figure 6. Evolution of ensemble spread, SM, measured by
RMS difference normalized by RMS variability of thesimulation (0.19 m) for the reference run over the Kuroshio
region, 28N–35N, 130E –140E.

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s2M ð M þ 1Þ
(M = 10) in thee2M ð M  1ÞKuroshio region, 28N – 35N, 130E– 140E.

Figure 7. Evolution ofander defined as the ensemble mean of the 80-day forecast(thick curve) has larger amplitude in the region west of140E than the unperturbed forecast (dashed curve), whichmight be consistent with both Quick Bulletin of Ocean
Conditions (lowest left panel of Figure 1) and the referencerun (dash-dotted curve). However, since the Kuroshio
path variation south of Japan has the multimodal structure[e.g., Kawabe, 1995], we must be careful in interpreting theensemble mean forecast. Figure 8 indicates that the 80-day
forecast ensemble members (thin curves) of the Kuroshio
path south of Japan are classified into three patterns:
weak meander (two members), weak meander east of the
Izu Islands (three members), and strong meander (fivemembers). The ensemble mean forecast of the present caseseems to be a mixture of the multimodal states. Exact skill
evaluation of the ensemble mean forecast of the Kuroshio
path variation needs more experiments for more various
situations. In the present study, attention is focused on thevariation of the Kuroshio path generated by the ensemble
forecast.
[25] The resulting Kuroshio paths shown in Figure 8 arecharacterized by indices calculated from sea surface variables. Figure 9a shows the time evolution of the sea level at
32.5N, 138E for each ensemble forecast. The index
exhibits clear difference in the Kuroshio meander amplitude; low (high) level indices correspond to strong (weak)
meander. The unperturbed forecast reproduces a weak
meander east of the Izu Islands.
[26] It is well known that the change of the Kuroshio path
is associated with sea level changes along the southern coastof Japan [Kawabe, 1995]. According to the tide gauge data,
the deviation from long-time mean of the sea level difference between Kushimoto and Uragami (see Figure 8 forlocations) during the large-meander state is negative (about
10 mm) and less susceptible to change. As shown in
Figure 9b, although all ensemble members predict reductionof the sea level difference between Kushimoto and
Uragami, three members corresponding to the weak meander east of the Izu Islands show some rise in the sea level
difference in November. The sea level at Hachijojima (seeFigure 8 for location) is used as another path index of theKuroshio axis which characterizes two non-large-meander

C10026states: the offshore non-large meander (low level) and thenearshore non-large meander (high level). The typical largemeander state is also characterized by high sea level at
Hachijojima. The sea levels at Hachijojima in the ensemble
members bifurcate into low and high states in November
1999 (Figure 8c); the low sea level appears in the threemembers corresponding to the weak meander east of the Izu
Islands. In short, the Kuroshio path indices obtained fromthe members of the strong meander found in Figure 8a havemore similar features to the large meander than thoseobtained from the members of weak meander, whichcorrespond to the nearshore or offshore non-large meander.
In the next section, we will discuss the predictability of theKuroshio meandering south of Japan from the viewpoint ofeddy dynamics triggering and leading to the remarkabledifference found in the 80 days ensemble forecast.

4. Predictability of the Kuroshio Meandering[27] We plot the relation between the intensity of theinitial trigger eddy and resulting meander amplitude of theensemble forecasts in Figure 10. Although the 50 days
ensemble forecasts do not bifurcate into two branches yet(Figure 10a), striking path bimodality manifests itself in the
80 days ensemble forecasts. Therefore the path state within
the 50 days is more predictable. Figure 10b indicates thatstrong anticyclonic eddies may basically induce the large
meander. We note that one member stays at a weak meander
state. In the latter case, the initial anticyclone is distorted
and eventually splits into two weak anticyclones in September 1999. Then the weak anticyclone causes the weak
meandering in November 1999. Note that the bifurcation of
the meander types has no dependence on the upstream
volume transport of two kinds: the Kuroshio mainstream
in the East China Sea and the Ryukyu current east of the
Nansei Islands. For ensemble members, the volume transport of the Kuroshio mainstream measured across the PNline in the East China Sea ranges from 29 to 33 Sv.

Figure 8. ‘‘Spaghetti’’ diagram of the Kuroshio path on
26 November 1999. The Kuroshio path is defined as a
curve on which the value of sea surface height equals
0.4 m. Thick curve denotes ensemble mean. Thin curves
correspond to individual ensemble members. Dashed curve
denotes the unperturbed forecast. Dash-dotted line denotes
the reference run. The numbers denote the tide stations:1, Kushimoto; 2, Uragami; 3, Hachijojima.

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C10026[28] The previous studies [Hurlburt et al., 1996; Endohand Hibiya, 2001; Miyazawa et al., 2004] have suggested
that baroclinic energy conversion is related to the deep
anticyclonic circulation associated with the Kuroshio meander. Figure 11 shows time evolution of the kinetic energy
at the depth of 4000 m averaged in the area of 31N – 33N,
135E –138E. The large kinetic energy associated with the
deep anticyclonic circulation is certainly found in ensemble
members producing the large meander (solid curves) in the
80-day forecast on 26 November 1999. However, the deep
anticyclonic circulation is not yet excited in the 50-day
forecasts on 27 October 1999. This difference is consistent
with the characteristics of the meander growth shown in

Figure 9. (a) Evolution of sea level at 32.5N, 138E.
Thick and thin solid lines correspond to ensemble membersof strong and weak meander, respectively. Solid line withclosed circles denote ensemble mean. Dashed line with
open circles denotes the unperturbed forecast. Dashedline with open squares denotes the reference run. (b) As
in Figure 9a except for sea level difference between
Kushimoto and Uragami. (c) As in Figure 9a except for
sea level of Hachijojima.

Figure 10. (a) Relations between intensity of the trigger
anticyclonic eddy (mean over a region in which sea surface
height exceeds 0.9 m within the Kuroshio region, 28N–
32N, 130E– 136E) and the Kuroshio meander amplitude(sea surface height at 32.5N, 138E) on 27 October 1999.
Solid circles correspond to ensemble members of the large
meander. Crosses correspond to ensemble members of the
non-large meander. A diamond corresponds to theunperturbed forecast. (b) As in Figure 8a on 26 November
1999.

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Figure 11. Evolution of kinetic energy (in m2 s2) at thedepth of 4000 m averaged over 31N–33N, 135E–
138E. Thick solid lines correspond to ensemble membersof the large meander. Thin solid lines correspond toindividual ensemble members of the non-large meander.
Dashed line with open circles denotes the unperturbed
forecast.
Figure 10. We note that no difference is found in the kinetic
energy of initial ensemble members.
[29] Figure 12 compares evolution of the anticycloniceddy activities depicted at sea surface height (upper 0.9 m)
and deep flow field in three different paths: the nearshore
non-large meander (nNLM), offshore non-large meander(oNLM), and large meander (LM). We can recognize clear
intensity difference of the anticyclonic eddy southeast of
Kyushu in the initial states. As the Kuroshio meander grows
in November, both the upper and lower layer anticyclones
in the LM case are significantly intensified compared with
the NLM cases. We calculate the barotropic eddy kinetic
1
energy (Figure 13a), (u02 + v02), where u0, v0 are deviations
2of horizontal velocities from time mean, and available
g 2 r0 2
potential energy (Figure 13b),, where g is
2Nb2 r0
gravity acceleration; Nb is background buoyancy frequency;
r0 is deviation of density from time mean; r0 is constantreference density, averaged within the anticyclonic eddy.
The eddy kinetic energy of the trigger eddy in ensemble
members producing the large meander is generally larger
than that in other ensemble members. The available potential energy in the members of the large meander generally
increases after early October, when the anticyclone collides
with the Kuroshio. Figure 13 suggests that the energy of thetrigger eddy is affected by the interaction between the
Kuroshio and the anticyclone, which may be intensified
by stronger anticyclone in the initial state. To guess theenergy source associated with the eddy-Kuroshio interaction, we also calculate both the eddy kinetic energy andavailable potential energy averaged in the Shikoku basin
as shown in Figure 14. After early October, the eddy

C10026kinetic energy increases and the available potential energy
decreases generally in all members. These features seem to
be interestingly emphasized in the ensemble members of
the large meander. However, it is beyond the scope of thepresent study to analyze energy flows in detail related tothe complicated eddy-Kuroshio interaction.
[30] To specify a timescale of the trigger eddy, we
introduce three non-dimensional parameters governing thegeostrophic dynamics on a beta plane: the beta parameter(^b = bL/f ), stratification parameter (^s = (Rd/L)2), and Rossby
number (^e = ^sDH1/H1) [Pedlosky, 1987]. The notations
employed here are as follows: f is the Coriolis parameter(7.3
105 s1), b the meridional gradient of f (2.01011 s1 m1), L the horizontal length scale (120 km), Rd
the internal deformation radius (40 km at 30N according toEmery et al. [1984]), H1 depth of the thermocline (550 m),
and DH1 is variation of the thermocline (50 m to 80 m for
depth of 26.5 sigma-t). For the anticyclonic eddies in theensemble initial states, we have ^b = 0.033, ^s = 0.11, and ^e =0.010  0.016. This suggests that they fall into the subset ofthe planetary geostrophic regime (PG2) of Williams andYamagata [1984] or the frontal geostrophic regime of
Cushman-Roisin [1986]). If we introduce a two-layer
model, the inverse timescale of the frontal geostrophic eddy
is given by w = (H1/H)^e = (P2/P1)^e [Cushman-Roisin et al.,1992], where H is the total depth of 4000 m; P1, P2 arepressure scales of the upper and lower layers, respectively.
For the eddies in the ensemble experiments, this timescale
ranges from 72 days to 115 days. It is determined by theslow lower-layer velocity field related to pressure P2 there.
The timescale might be consistent with the limit of thepredictability in the present study, i.e., 50– 80 days. The
OGCM simulation suggests that the timescale of the trigger
eddy is longer than timescale due to advection by the
Kuroshio mainstream, i.e., 10 days. The timescale of thepredictability is related to behavior of the eddy itself rather
than simple advection of the eddy by the Kuroshio.

5. Summary[31] We have demonstrated that our forecast with a stateof-the-art OGCM initialized on 7 September 1999 by
assimilating sea surface height data successfully predicts
the meandering of the Kuroshio south of Japan as observedin November 1999. The experiment yields a forecastingskill of the Kuroshio meander position for 60 days in thesense that the RMS error does not exceed the magnitude of
the model climatic variation and those obtained from the
non-assimilated simulation and persistence (Figure 5). The
timescale agrees with that evaluated by the previous studies[Komori et al., 2003; Kamachi et al., 2004].
[32] While we obtained the hopeful results from theensemble forecast experiment, further extensive studies ofthis kind are needed to assess the effects of the ensemble
forecast on the forecast skill. In the present study, we
focused our attention on the transitions from the nearshore

Figure 12. Snapshots of sea surface height upper 0.9 m (contour interval is 0.1 m) and horizontal velocity at 4000 m
depth. (left) An ensemble member corresponding to the nearshore non-large meander. (middle) The unperturbed forecast,which realizes the offshore non-large meander. (right) An ensemble member corresponding to the large meander.
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Figure 12
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C10026[33] A novel feature we found in our experiments presented here is a fact that the intensity of an initial anticyclonic eddy plays a key role for the subsequent developmentof the Kuroshio meander classified into two categories, i.e.,a strong anticyclone induces the large meander. Figure 10
suggests that a critical level of the intensity exists. 0.05 m ofthe analysis error of sea surface height anomaly, whichcorresponds to 50 m of the depth variation of 26.5 Sigma-t,
averaged in the upstream region may be enough for thebifurcation of the Kuroshio path forecasts in the ensemble.
[34] The present study suggests the importance of thelocal eddy dynamics in the Kuroshio recirculation region to
the bifurcation of the Kuroshio path. The strong anticycloniceddy may trigger the intensified eddy-Kuroshio interaction
associated with the large-meander formation, whose energy
source might be the available potential energy of theKuroshio and its recirculation system accumulated over
the whole Shikoku Basin. However, detailed mechanism isstill unclear. Further intensive studies are needed on interactions between the Kuroshio and meso-scale eddies.
[35] The ensemble forecast is a promising way to study
predictability of the Kuroshio path. Further development of

Figure 13. (a) As in Figure 11 except for eddy kinetic
energy (in m2 s2) of the trigger anticyclonic eddies (aregion in which sea surface height exceeds 0.9 m,
averaged over 28N – 32N, 130E – 136E in September
1999 and over 29N – 32.5N, 133E– 140E in Octoberand November 1999). (b) As in Figure 13a except foravailable potential energy (in m2 s2) of the trigger
anticyclonic eddy.

non-large meander to the large or offshore non-large meander. The meanders occurred in the ensemble members forthe 80-day forecast are classified into two categories: thelarge meander and the non-large meander. The bifurcation
occurs more than 50 days after the initialization. In thepresent case, the ensemble mean of the 80-day forecast
seems to be a mixture of the multimodal states, which might
be similar to climatological mean state of the Kuroshio path.
The theoretical relations (5) and (6) hold when the ensemble
spread agrees with the natural variation owing to loss of
predictability; the ensemble mean corresponds to the climatological mean. Moreover, in the multimodal system such as
the Kuroshio path south of Japan, the ensemble mean may
not be a physically-realizable state. We also notice that thepresent use of the reference assimilation run as the ‘‘truth’’
may lead to either an over- or under-estimation of theforecast skill since the theoretical relations (5) and (6) of
the ensemble forecast pertain to the ‘‘real’’ error variance.
Skill improvement using the ensemble mean forecast would
be validated by conducting many forecast experiments forvarious situations of the Kuroshio path transition.

Figure 14. (a) As in Figure 13a except for averaged
over the Shikoku Basin, 27N – 35N, 131E – 141E.
(b) As in Figure 14a except for available potential
energy (in m2 s2).

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C10026

C10026the ensemble forecast method [e.g., Yamane and Yoden,
2001] would lead us to deeper understanding of theKuroshio path variation.

and Japan Agency for Marine-Earth Science and Technology (JAMSTEC).
We are very thankful to two anonymous reviewers for their constructive
comments on the earlier versions of the manuscript. Comments by Hirofumi
Sakuma also helped in improving the original manuscript.

Appendix A: Weight of Correction for the
Analysis Equation

References[36] Following Mellor and Ezer [1991], we derive theequation (2). The errors of the observed and forecast sea
surface height anomaly (SSHA) are defined according to
Dho  Dht ¼ dho ;Dh f  Dht ¼ dh f :ðA1ÞOn the other hand, the errors arising from our assimilation
adjustment (analysis) described in equation (1) are definedaccording to T a  T t ¼ dT f þ PT h FT h Dho  Dh f þ dT C ;ðA2Þ

where dTC is an error associated with the incomplete
correlation between SSH and temperature/salinity, and dT f =T f  T t. Using equations (A1) and (A2), the assimilation
adjustment error variance h(T a  T t )2i is expressed asfollows:
D2

ðT a  T t ÞE

DE
D 2E D 2E
22¼ dT f þ PTh
FT2 h dho þ dh f
D 2E
þ dT c 2PTh FT h dh f dT f :ðA3ÞIn the derivation of equation (A3), the forecast, observationand correlation errors are assumed to be uncorrelated.
[37] To determine the weight PTh, we minimize theadjustment error(A3) by looking into
D given in equationE@ ðT a  T t Þ2
= 0, which leads tothe condition@PT h
PT h ¼

FT h dh f dT f:2o
FT h ðhdh 2 i þ hdh f 2 iÞ þ hdT c2 iðA4ÞUsing further assumption of the form
D 2E
dh f dT f ¼ FT h dh f

ðA5Þ

and the derivation of the correlation error [Mellor and Ezer,
1991]
D

dT C

2

E

D 2E
1
=CT2 h  1 ;¼ FT2 h Dht

ðA6Þ

we can write
D 2E
dh f
PT h ¼;
hdho2 i þ hdhf 2 i þ hDht2 i 1 =CT2 h  1

ðA7Þ

2

where hDht i is variance of true SSHA. Normalization of theerror variances in equation (A7) gives equation (2).
[38] Acknowledgments. This work is part of the Japan Coastal
Ocean Predictability Experiment (JCOPE) started in October 1997 under
the initiative of the Frontier Research System for Global Change (FRSGC),
which is supported jointly by Japan Aerospace Exploration Agency (JAXA)

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

X. Guo, Center for Marine Environmental Studies, Ehime University, 2-5
Bunkyo-cho, Matsuyama, Ehime, 790-8577, Japan.
Y. Miyazawa, Frontier Research Center for Global Change/JAMSTEC,
3173-25 Showamachi, Kanazawa-ku, Yokohama, Kanagawa 236-0001,
Japan. (miyazawa@jamstec.go.jp)
T. Yamagata, Department of Earth and Planetary Science, Graduate
School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo,
113-0033, Japan.
S. Yamane, Department of Environmental Security, Faculty of Risk andCrisis Management, Chiba Institute of Science, 3 Shiomi-cho, Choshi,
Chiba, 288-0025, Japan.

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