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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, C04023, doi:10.1029/2009JC005818, 2010

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ArticleHindcast and predictability of sporadic Kuroshio‐water
intrusion (kyucho in the Bungo Channel) into the shelfand coastal waters
Atsuhiko Isobe,1 Xinyu Guo,1 and Hidetaka Takeoka1
Received 18 September 2009; revised 20 November 2009; accepted 7 December 2009; published 28 April 2010.

[1] Prerequisite(s) for ocean circulation models capable of hindcasting “kyucho” occurrence(a sudden coastal temperature rise induced by Kuroshio frontal waves) in the Bungo
Channel, Japan, is investigated using long‐term observed temperature and sea level timeseries, archived hydrographic data, and reanalysis data provided by the Japanese Coastal
Ocean Predictability Experiment (JCOPE) group. Anticyclonic mesoscale eddies impinging
on the Kuroshio front south of the Bungo Channel enhance the frontal sharpness, frontal
wave growth, and activity of kyucho phenomena. A kyucho hindcast is carried out toexamine the reliability of a numerical model including realistic anticyclonic eddies
propagating south of Japan. The Finite Volume Coastal Ocean Model (FVCOM) for whichboundary conditions are given by daily JCOPE2 reanalysis data is adopted in the present
study. This numerical model does a reasonable job of hindcasting kyucho occurrence in
2003. It is therefore considered that forecasts of kyucho occurrence up to 2 or 3 months ahead
are possible by using the FVCOM in conjunction with JCOPE2 forecast data.
Citation: Isobe, A., X. Guo, and H. Takeoka (2010), Hindcast and predictability of sporadic Kuroshio‐water intrusion (kyucho
in the Bungo Channel) into the shelf and coastal waters, J. Geophys. Res., 115, C04023, doi:10.1029/2009JC005818.

1. Introduction[2] Western boundary currents such as the Kuroshio in the
East China Sea are often accompanied by frontal waves (orfrontal eddies) on their onshore side because these currents
are dynamically unstable along shelf breaks [Qiu et al., 1990;
James et al., 1999]. These frontal waves may contributesignificantly to biological variability over shelves because
growing frontal waves play a key role to uplift offshore
nutrient‐rich intermediate water onto shallow shelves asshown in the well‐known schematic of Lee et al. [1981]. In
fact, Isobe and Beardsley [2006] demonstrate that the onshore
volume transport across the East China Sea shelf break ismaintained stably in a finely gridded numerical ocean circulation model where unstable Kuroshio frontal waves arecomputed realistically, and that the stable transport disappears in the absence of sufficiently growing frontal waves
in a coarsely gridded model. Furthermore, on the basis of abox model approach to evaluate the nutrient budget over the
East China Sea shelf, Chen and Wang [1999] show that amajor nutrient source is Kuroshio subsurface water transported across the shelf break. Hence, field measurements
on shelves to monitor a nutrient (hence, biological) transition after passage of Kuroshio frontal waves have beenof particular interests. However, it is difficult to monitor
1

Center for Marine Environmental Studies, Ehime University, Matsuyama,
Japan.
Copyright 2010 by the American Geophysical Union.
0148‐0227/10/2009JC005818

the transition directly because neither locations nor times
at which frontal waves grow sufficiently can be predetermined along the East China Sea shelf break with the length O(1000 km).
[3] An area south of Japan is free from one of the above
difficulties in monitoring the nutrient and biological transitions induced by growing frontal waves. The growth ofKuroshio frontal waves south of Japan causes sporadic
Kuroshio water intrusions into the shelf and coastal waters
between Shikoku and Kyushu Islands, Japan [Akiyama andSaitoh, 1993; Arai, 2005], which are called “kyucho” by
Takeoka and Yoshimura [1988], a pioneering work in this
Bungo Channel (Figure 1). Figure 2 demonstrates a satellite‐
derived sea surface temperature (SST) snapshot of a kyucho
onset, where part of a growing Kuroshio frontal wave starts to
intrude into the Bungo Channel. The occurrence of kyucho,
which stands for “sudden stormy currents” in Japanese[Takeoka et al., 2000], results in fishery damages by sudden(within several days) temperature rises harmful to cultured
fishes as well as by strong currents that can break fishery nets
[Takeoka and Yoshimura, 1988]. However, it also provides
us with an opportunity to monitor the nutrient and biologicaltransitions induced by growing Kuroshio frontal waves
because field measurements can be limited in space to within
the narrow Bungo Channel of width about 50 km. In fact,kyucho induced transitions of phytoplankton biomass and/or
species have been pointed out in Bungo Channel research[Koizumi and Kohno, 1994; Katano et al., 2007; Hirose et al.,2008]. Hence, we are able to predetermine the location where
nutrient and biological transitions may occur after the passageof growing frontal waves (i.e., kyucho).

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C04023Figure 1. Study area. The area within the square in the inset map is enlarged. The Kuroshio path is shown
schematically in the inset map. Also shown are isobaths in meters.
[4] Nevertheless, it is not yet possible to monitor kyucho
influences on biological variability over the Bungo Channel
because onsets of kyucho need to be predicted before monitoring. The present physical oceanographic study, one partof a research project to elucidate kyucho influences on biological variability over the Bungo Channel, attempts toanswer two questions: Is reliable kyucho forecast possible byusing a numerical ocean circulation model? What are theprerequisites for a numerical model capable of forecasting the
kyucho? First, we address the latter question using long‐term
observed temperature and sea level time series along thewestern coast of Shikoku Island, hydrographic data archived
in the Japan Oceanographic Data Center (hereinafter, referred
to as JODC), and reanalysis data provided by Japanese
Coastal Ocean Predictability Experiment (JCOPE2 reanalysisdata) [Miyazawa et al., 2008, 2009] group. We thereafter
attempt to hindcast kyucho events in a specific year to
examine the reliability of the numerical model including theprerequisite(s) detected in the above analyses. The Finite
Volume Coastal Ocean Model (FVCOM) [Chen et al., 2003]
of which boundary conditions are given by daily JCOPE2
reanalysis data is adopted in the present study. Last, we
discuss the predictability of kyucho occurrence using thenumerical model available for the kyucho hindcast.

2. Data[5] An observed temperature record at the Shitaba station(Figure 1) during the period May 2001 through the end of2007 is analyzed to provide a plausible scenario of kyucho
occurrence. A temperature sensor (MDS‐MkV/t of JFE‐
ALEC Co. Ltd) was set at 5 m depth over the course of theabove period. Sequential data were subsampled once per hourfor the subsequent analyses because various time intervals
less than 1 hour were used for the observations. The timeseries was thereafter band passed using a 5 day Butterworth
filter to remove the perturbation induced meteorologicallyafter removal of the seasonal variation by fitting an annual
sinusoidal curve.
[6] Tide gauge data at the Uwajima station (Figure 1) are
analyzed in conjunction with the above mentioned temperature
data because these data might record steric‐height variations
caused by warm water intrusions during kyucho events. An
advantage of tide gauge data is that, in general, a long‐term
data set is available for analyses; in fact, we use tide gauge data
for the years 1967 through 2007 in the present study. Hourly
data downloaded on the JODC website (JODC Data Online
Service System: http://www.jodc.go.jp) were band passed in
the same manner as that for the temperature data. In addition,
the inverse barometric effect was compensated for by hourly
air‐pressure data at the Uwajima meteorological observatory.
[7] In addition to the above two data sets at the fixed stations,temperature data archived for the years 1900 through 2000
were downloaded from the JODC website to investigate climatological temperature patterns south of Japan, which may
uncover the plausible scenario for kyucho occurrence. Thesetemperature data at standard depths were converted into 0.5°
latitude by 0.5° longitude gridded data using a Gaussian filter
with an e‐folding scale of 0.25° and a tail length of 0.5°. Before
averaging the data in each cell grid, data that exceed three times
the standard deviation from their average value were removed.
In addition, any cell grid that has less than 10 data values wasomitted. A combination of median and Laplacian filters wasused to remove “noisy” patterns after gridding.
[8] Furthermore, using JCOPE2 reanalysis data, we examine a spatiotemporal variation of hydrographic properties

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C04023Figure 2. Satellite‐derived SST maps in the study area on 24 May 2006. The area within the square isenlarged in the inset. Temperature is indicated by the gray scale at the bottom. The 23°C isotherm line is
added to emphasize a folded‐wave pattern of a Kuroshio frontal wave south of the Bungo Channel. Contour
interval is 0.5°C in the inset. The area with temperature higher than 23°C is stippled to emphasize theKuroshio frontal wave. The SST data are downloaded on the North Pacific Region Environmental Cooperation Center website (http://www.npec.or.jp/).
south of Japan during the period with intense kyucho events.
The JCOPE2 reanalysis data are generated by using a general ocean circulation model to which satellite‐derived sea
surface height anomalies, satellite‐derived SST, and verticalprofile data of temperature and salinity obtained from the
Global Temperature‐Salinity Profile Program are assimilated[Miyazawa et al., 2008, 2009]. Miyazawa et al. [2008]
demonstrate that their reanalysis data for the years 2003
through 2004 reproduce well the mesoscale eddies propagated south of Japan and Kuroshio meandering triggered bythese eddies. Daily data sets of temperature, salinity, sea
surface height, and horizontal currents are used in the present
study. Besides seeking kyucho‐related phenomena south ofJapan, these data are used for boundary and initial conditions
in a numerical ocean circulation model to hindcast kyucho
events in a specific year. The detailed description of thismodel is provided later in section 4.

3. Prominent Kyucho‐Related Variation in
Temperature Records[9] As in the previous Kuroshio frontal wave studies [Qiuet al., 1990; James et al., 1999; Isobe and Beardsley, 2006]
and kyucho studies [Akiyama and Yanagi, 1984; Akiyama

et al., 1987; Takeoka and Yoshimura, 1988], kyucho eventsare detected as short‐term (less than 1 month) temperaturefluctuations (Figure 3). The growth of Kuroshio frontal waves
south of Japan and subsequent kyucho occurrences are observed at the southern end of the Bungo Channel throughout
the year [Akiyama and Yanagi, 1984; Akiyama et al., 1987],
while the appearance of significant short‐term fluctuations islimited to the seasons spring through autumn in Figure 3. Thisis because Kuroshio water cannot reach the northern part ofthe Bungo Channel over the course of winter due to verticalmixing caused by intense surface cooling [Takeoka et al.,1993]. We therefore investigate the periodicity of the temperature fluctuations using a wavelet analysis [Torrence andCompo, 1998] suitable to analyze time series with prominentand sporadic fluctuations.
[10] The wavelet spectra (Figure 4) show that temperaturefluctuations appear intensely on two different timescales. One
is the period less than about 30 days, the typical timescale ofkyucho occurrence as shown in Figure 3. It seems that thesekyucho‐related temperature fluctuations are revealed only inthe seasons spring through autumn, as mentioned above,
because the intense winter cooling prevents warm Kuroshio
water from moving northward. In addition to this annual
variation, fortnightly fluctuations (15 day period indicated by

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Figure 3. Time series of temperature at the Shitaba station (see Figure 1 for its location) for the years 2001
through 2007. These temperature time series are band passed between 5 days and 1 year. The thin dashedlines indicate the level of 20°C in each year.

Figure 4. Wavelet spectra for temperature time series from 2001 to 2007. The abscissa represents the time,
and the ordinate denotes the period in days. The magnitude of each spectrum is normalized by the varianceof that time series, and is indicated by the gray scale shown in the top left. Wavelet spectra cannot be computed on either end because of the finite‐length time series [see Torrence and Compo, 1998], and so the area
is left blank.
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C04023Figure 5. Temperature time series band passed between 5 and 30 days (solid line) and between 60 and
120 days (dashed line) in 2003, 2005 and 2006. The stippled areas represent scale‐averaged wavelet spectra
between 5 and 30 days. The spectra are normalized by the maximum value in each year. See the right (left)
ordinate for the band‐passed time series of temperature (scale‐averaged wavelet spectra).
a dashed line in Figure 4) are present because the strongly
stratified situation at neap tides intensifies the northwardtransport of warm Kuroshio water in the upper layer [Takeoka
et al., 1993]. Another remarkable fluctuation is visible in the
period longer than 60 days in Figure 4. The wavelet spectra
between 60 and 120 days become energetic when the spectra
shorter than 30 days take large values (2003, 2005, 2006, and2007). On the other hand, the wavelet spectra with both short(<30 days) and long (>60 days) periods weaken together in2004.
[11] The synchronicity of the temperature fluctuations withdifferent periods (T) suggests that the long‐term fluctuation is
also associated with kyucho occurrence, so the phase relationship between these two fluctuations is examined next.
The temperature time series in 2003, 2005 and 2006 aredecomposed into two band‐passed series with short (5 days <T < 30 days) and long (60 days < T < 120 days) periods(Figure 5). These 3 years are chosen because both short‐termand long‐term fluctuations are clearly visible outside the“cone of influence” [Torrence and Compo, 1998] at both ends
in Figure 4. Also shown by stippling are scale‐averaged
wavelet spectra for the short‐term fluctuations for ease ofreference to show the duration with intense kyucho events.
Onsets of the events are detected in May and July of 2003,
in May and July of 2005, and in April and July of 2006,
respectively. The long‐term fluctuations are amplified roughly
but not exactly in phase with the amplification of the short‐term ones (i.e., intense kyucho events). It is however notedthat the phase of the long‐term fluctuations is somewhat
delayed with respect to the amplification of short‐term ones.
[12] Both synchronicity and the phase delay suggestthat the long‐term temperature fluctuations result from theenhancement of the northward heat transport during kyucho
events intensified every several months (i.e., 60 days < T <120 days). If this is the case, the long‐term fluctuation must be
detected not only in the temperature data, but also in the tidegauge data because the enhanced horizontal heat transport
into the Bungo Channel alters the steric height over this area.

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Figure 6. Time series of temperature (solid line; right ordinate) at the Shitaba station and sea level (dashed line; left
ordinate) at the Uwajima station. These time series are band
passed between 60 and 120 days.
A significant correlation is indeed detected between band‐
passed temperature data at Shitaba and tide gauge data at
Uwajima for the years 2001 through 2006 (Figure 6); thecorrelation coefficient is estimated to 0.53, a significant value
suggested by the t test with 99% confidence level.

4. Discussion
4.1. Process by Which Kyucho Occurrence Is Triggered[13] The activity of kyucho phenomena is enhanced every
60–120 days, and so it is reasonable to consider that afavorable condition of baroclinic and barotropic instabilities
leading to the growth of Kuroshio frontal waves occurs southof Japan with a similar period. Climatological temperaturepatterns south of Japan are next investigated to elucidate theconditions favorable for kyucho occurrence. Figure 7 graphs
the tide gauge data band passed between 60 and 120 days
for the years 1967 through 2007 at the Uwajima station. As
suggested in Figure 6, this long‐term fluctuation is anticipatedto be significantly correlated with the long‐term temperaturefluctuation over the course of 41 years. In addition, as suggested by Figure 5, kyucho phenomena are likely to prevail
during the periods with large positive values in Figure 7.
Figure 8 indicates temperature cross sections along the132° 20′ longitude; temperature data obtained in the periods
when positive (negative) sea level anomalies in Figure 7 arelarger (smaller) than the standard deviation are used to define
the top left (bottom left) of Figure 8. Figure 8 (top left) showsthat an anticyclonic mesoscale eddy is located at 32°N close
to the Kuroshio front (32° 30′) when kyucho phenomenaprevail in the Bungo Channel, while Figure 8 (bottom left)
shows that the anticyclonic eddy mostly disappears when thenumber of kyucho events decreases.
[14] The relationship between kyucho phenomena andanticyclonic eddies is clarified by investigating anticycloniceddy behavior south of Japan using the JCOPE2 reanalysis
data. In Figure 9 sea surface height anomaly maps are viewed
during the period 15 March through 15 May (the former
period in Figure 9 (top)), and 15 June through 1 August (theC04023latter period). In the course of the former period, an anticyclonic eddy (positive anomalous area indicated by the letterA) far south of Japan on 15 March gradually moves northward(15 April and 1 May), and thereafter impinges on Shikoku
Island on 15 May. This anticyclonic eddy A remains southof Shikoku Island over the course of the latter period. In
addition, another anticyclonic eddy indicated by the letter B
appears in the study area on 15 June, and thereafter moves
northwestward on 1 July. This eddy B merges into eddy A on
15 July, and it seems likely that eddy A strengthens south of
Shikoku Island on 1 August. Explicitly, the Kuroshio‐front
sharpness increases south of the Bungo Channel at the endof both periods (15 May, and 1 August). Special attention
should be paid to the fact that the scale‐averaged wavelet
spectrum (Figure 9 (top)) indicating the activity of kyucho
phenomena reaches a peak when the frontal sharpness increases
along the northern edge of eddy A.
[15] The relationship between anticyclonic eddies southof Japan and kyucho provides us with a scenario to explain
how intense kyucho events occur. In general, the increaseof frontal sharpness leads to the rapid growth of Kuroshio
frontal waves caused by a hybrid of baroclinic and barotropic instabilities [Qiu et al., 1990; James et al., 1999].
It is therefore plausible that anticyclonic mesoscale eddies
impinging on the Kuroshio front result in the amplificationof frontal waves and an increase of kyucho occurrence in the
Bungo Channel. A timescale between 45 and 180 days istaken for mesoscale eddies to pass by a fixed point in the
Kuroshio recirculation region south and/or southeast of Japan[Ebuchi and Hanawa, 2000]. In particular, using altimeter
data, Ebuchi and Hanawa [2003] detect anticyclonic eddies
carried in the clockwise direction in the region south of
Shikoku Island. Based on a center position vector analysis forthese eddies, they obtain a rotary spectrum with one peak
between 50 and 100 days and another peak on 160 days (seetheir Figure 9); although their attention is placed on the latter
peak, this quasi semiannual spectral peak is unlikely to appear
in kyucho phenomena in the Bungo Channel because intense

Figure 7. Time series of the sea level at the Uwajima station
for the years 1967 through 2007. This time series is band
passed between 60 and 120 days. Two dashed lines indicate
the standard deviation.

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C04023Figure 8. (top left and bottom left) Cross sections of climatological temperature along the dashed line in
Figure 8 (right). Temperature data obtained in the years when the sea level is higher (lower) than the positive(negative) standard deviation in Figure 7 are used to depict Figure 8 top left (bottom left). In Figure 8 (left),
contour interval is 0.5°C. (right) Also shown are isobaths in meters.
cooling prevents Kuroshio water from moving northward on
the winter shelf. The several month timescale with respect tothe anticyclonic eddies south of Japan is consistent with thatof the intense kyucho events in the Bungo Channel.
[16] The JCOPE2 data reproducing realistic eddy motion
may give us a straightforward hindcast method of kyucho
occurrence in the Bungo Channel. We next compute thegrowth rate of baroclinic‐instability waves using an Eady’s
model (Appendix A) applied to daily JCOPE2 data along theline in the 15 March panel of Figure 9. The growth rate ispossibly a good index for examining whether or not instability waves (i.e., kyucho) develop at each location along theline; the rate computed in this simple model is mostly
determined by the horizontal density gradient, that is, thevertical shear of currents. The growth rate (stippling) is
superimposed on the space‐time plot of temperature anomaly(contour map) at 100 m depth in Figure 10 (bottom). The areawith high growth rates moves northwestward as the anticyclonic eddies approach Shikoku Island for the period Marchthrough August (see Figure 9 for eddy motion). It is worth

mentioning that the kyucho phenomena prevail in the period
May through August (Figure 10 (top), the same one as Figure 5)
when the growth rate around Shikoku Island (around 0 km
location in Figure 10 (bottom)) remains high. Thus, the growthrate computed in the linear stability analysis using JCOPE2 data
is an indicator for kyucho occurrence.
[17] Nevertheless, the growth rate computed in the above
procedure is incapable of accurate kyucho hindcasts (hence,
forecasts). The time series of the growth rate nearest to
Shikoku Island (dashed curve in Figure 10 (middle)) indeed
indicates the kyucho event in May. However, the growth ratetakes relatively low values for the months July throughSeptember over which the kyucho events prevail, presumably
because the actual growth rate of kyucho phenomena (i.e.,
Kuroshio frontal waves) is determined by a complex combination of frontal sharpness, distance between the Kuroshio
axis and shelf break, horizontal shear of currents, and so forth[James et al., 1999]. Probably the most reliable method thatshould be taken for practical kyucho hindcasts/forecasts is thenumerical model approach.

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C04023Figure 9. Horizontal distribution of the JCOPE2‐provided sea surface height anomaly (middle) from
15 March to 15 May and (bottom) from 15 June to 1 August. The dashed lines are used for negativevalues. Contour interval is 5 cm. The areas higher than 10 cm are stippled to emphasize anticycloniceddies. (top) The same as Figure 5 (top) except for eight dots representing the dates shown in the below
anomaly maps. The line in the 15 March map is used for Figure 10.
[18] The above discussion provides two prerequisites forthe development of a numerical model to hindcast kyucho
occurrence. One is the high reproducibility of anticyclonicmesoscale eddies propagated south of Japan because intense
kyucho events are triggered by these eddies every several
months. For instance, JCOPE2 reanalysis data reproduce well
the anticyclonic eddy behavior [Miyazawa et al., 2008] asshown in Figure 9. JCOPE2 data using relatively coarse grids(1/12 degree) are however unsuitable for coastal waters, and sokyucho phenomena are unlikely to be reproduced in the Bungo
Channel (∼50 km; shown later in Figure 14). Hence, anotherrequirement is a fine resolution that allows us to computerealistically the ocean circulation inside the narrow channel.
4.2. Hindcast of Kyucho Occurrence
4.2.1. Model Description[19] We next attempt to reproduce kyucho phenomena in a
specified year to examine whether or not a numerical model iscapable of kyucho hindcasts. Mesoscale eddies, which areapproximately a few hundred km in diameter, should be
reproduced appropriately over the broad model domain southof Japan, while the model resolution should be sufficiently
fine to compute the ocean circulation in the narrow Bungo
Channel. Hence, to overcome this difficulty, it is reasonable
to adopt the FVCOM with unstructured triangle cell grids
to resolve a complex coastal topography using the daily
JCOPE2 reanalysis data for the initial and boundary conditions, which are anticipated to introduce mesoscale eddies
into the FVCOM domain. These eddies propagated in themodel domain enhance the Kuroshio‐front sharpness southof the Bungo Channel when they impinge on the front. The
fine resolution of the FVCOM has the advantage of realistically computing the growth of frontal waves (hence, kyucho
occurrence).
[20] The details for the FVCOM in the present application
are described below. We refer the readers to the work ofMiyazawa et al. [2008] and Miyazawa et al. [2009] for detailsof the JCOPE2 model. Figure 11 demonstrates the model
domain along with an enlarged map of unstructured triangle
cell grids in the FVCOM. The grid size is set to 9 km at lateralboundaries to connect smoothly with the JCOPE2 data using
1/12 degree structured cell grids in both latitude and longi-

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C04023Figure 10. Maximum growth rate computed using an Eady’s model with bottom slope applied to year
2003 daily JCOPE2 data along the line in 15 March map of Figure 9 (middle). (bottom) A contour map
denoting the space‐time plot of temperature at 100 m depth. The ordinate indicates the distance from thenorthernmost grid. The temperature anomaly from the annual mean at each location is depicted in this panel;the dashed lines are used for negative values. Stippling in Figure 10 (bottom) indicates the growth rate (seeAppendix A) of which scale is shown in the lower portion. (top) The same as Figure 5 (top) except foromitting the long‐term fluctuations. (middle) The dashed line shows the growth rate at the northernmost grid(x = 0 km) in Figure 10 (bottom).
tude, and diminishes down to 1 km or less in the channel toresolve the complex coastal geometry. Although the FVCOM
is a s coordinate model like the JCOPE2 model with 45 s
layers, the layer number is reduced to 25 in the present
application because numerical models are likely to becomecomputationally unstable when the layer thickness is too
thin in shallow coastal waters. The topographic data set witha 1/12 degree resolution (ETOPO5) provided by the U.S.
National Geophysical Data Center is used for the area southof 31.5°N, while the 500 m gridded topographic data set
provided by the Marine Information Research Center, Japan,
is used for the area north of 31°N. The depth at each triangle
cell grid is given by an interpolation using the nearest 16
topographic data weighted by the inverse distance. The above
two topographic data sets are blended to interpolate depths in
the area between 31°N and 31.5°N latitudes.
[21] The boundary and initial conditions for the FVCOM
are as follows. The horizontal currents, temperature, salinity,
and sea level heights in the daily JCOPE2 reanalysis data
are given at lateral open boundaries from 15 March 2003 to
30 September 2003. These data sets on 15 March 2003 areused for the initial condition as well. To incorporate JCOPE2‐
derived variables (fJCOPE) into FVCOM ones (fFVCOM) smoothly,a relaxation scheme, a(fJCOPE‐fFVCOM), is added to conservation equations. The constant a−1 changes linearly from 1 hourat the open boundaries to zero at the end of the sponge layer
shown by stippling in Figure 11. In addition, to reduce theinitial disturbance, the above relaxation scheme is used over
the whole region in the course of the first 5 days. The constanta−1 changes linearly from 1 hour at the beginning of thecomputation to zero on day 5. The year 2003 is chosen for thecomputation because the kyucho phenomena this year seemto be most prominent among the 7 year observations (seeFigures 3 and 4). These data are given to each boundary cell
grid using a linear interpolation in both time and space.
[22] The modeled SST over the computation period Marchthrough September 2003 is restored on a timescale of 5 days
to the monthly averaged SST, which is made using the
JCOPE2 reanalysis data for the years 2000 through 2002. The
year 2003 data are excluded in making these monthly SST
maps so that we are able to examine to what extent kyucho
occurrence in this specific year is reproduced using only

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C04023Figure 11. Modeled area using the FVCOM. (right) The bold dashed lines denote the lateral open boundaries of the FVCOM domain. Sidewall boundaries are imposed at Hayasui Strait and Awaji Island. Stippling
in indicates “sponge layers” in which FVCOM results are restored to JCOPE2 data to remove artificial disturbances caused by the connection between two different model results. Also shown are 200 and 1000 m
isobaths. (left) The area within the rectangle in Figure 11 (right) is enlarged to illustrate unstructured triangle
cell grids and depths represented by thin white line and stippling, respectively. Light stippling is used forareas shallower than 50 m, while areas deeper than 100 m are represented by dense stippling.
initial and lateral boundary conditions provided by the
JCOPE2 data in the same year. Likewise, other meteorological conditions such as winds and freshwater flux through thesea surface are also omitted in the present application. In
addition, tides are excluded from the FVCOM computation
as well as the JCOPE2 data because tides are completely predictable, and because the kyucho‐favorable condition causedby the weak stratification during neap tides [Takeoka et al.,1993] is also predictable, regardless of which model is used
for kyucho hindcasts/forecasts.
4.2.2. Kyucho Occurrence in the Numerical Model[23] The foregoing analyses show that precise computationof kyucho phenomena in the Bungo Channel requires realistically modeled mesoscale eddies south of Japan, which arerevealed due to “release” from the lateral boundaries, existencein the initial field, and generation inside the model domain. The
correlation between the sea surface height anomalies in the
FVCOM domain and those in the JCOPE2 data indicates thatthe modeled heights are consistent with the observed field
reproduced in the reanalysis data (Figure 12). In fact, Figure 12
shows that the significant values suggested by the t test with99% confidence level are mostly maintained from April 2003
to the end of September although the correlation decreases
temporally on 15 May, 30 June, and 20 July. However, it
should be noted that the significant correlation disappears in
the former half on April. It is therefore considered that eddies in
the initial field cannot persist as the computation proceeds, andFigure 12. Time series of the correlation coefficient
between sea surface height anomalies over the modeled andreanalysis areas deeper than 1000 m depth. The time series
is left blank when the coefficient is smaller than a significant
value suggested by the t test with 99% confidence level.

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C04023Figure 13. Model results at 5 m depth on 4, 7, and 10 September. (top) The areas within the stippled
rectangles are enlarged in Figure 13 (bottom). Figure 13 (top) shows isotherm lines with the interval of
1°C. (bottom) Temperature is indicated by the gray scale shown at the bottom. Note that 20°C isotherms
are emphasized using the dashed line. Current vectors are depicted every third cell nodes in Figure 13 (bottom). The 200 m isobath is depicted by the dashed (bold white) line in Figure 13 top (bottom) to indicate theshelf break.
that anticyclonic eddies leading to kyucho occurrence areproduced only by release from lateral boundaries and generation inside the model. This disagreement between the modeled
and observed fields in April results mainly from the Kuroshio
path meandering in the early stage (not shown), presumably
due to the growth of disturbances forced at the beginning of
the computation.
[24] We next demonstrate how Kuroshio water is carried
into the modeled Bungo Channel in the course of a kyucho
event. Figure 13 shows temperature and current maps at 5 m
depth on 4, 7, and 10 September 2003, respectively. Figure 13(top) shows that a Kuroshio frontal wave embedded in the
Bungo Channel is gradually distorted in the course of 7 days.
The 20°C isotherm in the lower enlarged maps indicates moreclearly how Kuroshio water is carried onto the shelf in thissporadic kyucho event. The kyucho onset can be seen on
4 September. Thereafter, part of Kuroshio water is carriednorthward on 7 September when the Kuroshio frontal wave
is distorted because Shikoku Island prevents the frontal
wave from being propagated eastward (Figure 13 (top)). On
10 September, part of the Kuroshio water is shed from theKuroshio mainstream south of the Bungo Channel, andmoves further to the north in the channel. It is noted that, likethe 20°C isotherm in the satellite‐derived SST snapshot(Figure 2), the modeled 20°C isotherm extends northward
at the central portion in the Bungo Channel on days 7 and
10 September. The kyucho studies to date [e.g., Takeoka
et al., 1993], on the basis of the temperature record along
the western coast of Shikoku Island, state that kyucho
phenomena in the Bungo Channel are regarded as a lockexchange flow in the Kelvin wave sense. However, boththe observed SST snapshot (Figure 2) and FVCOM‐derived

SST maps (Figure 13) demonstrate that the sidewall (i.e.,
Shikoku Island) is not always required for Kuroshio water
intrusions into the Bungo Chanel because a kyucho event
is able to develop northward as a growing instability wave.
In fact, various satellite images shown by Akiyama andSaitoh [1993] also demonstrate kyucho events free fromthe sidewall.
[25] The modeled temperature time series at the Shitaba
station in the FVCOM domain is consistent with the observed
one (Figure 14). The observed time series in Figure 14 (top)shows that the short‐term fluctuation (i.e., kyucho events)
prevails during two periods indicated by bars with the letters
A and B. The JCOPE2 reanalysis data set in the study area ismade using a relatively coarse 1/12 degree grid model, so it isunable to reproduce Kuroshio frontal waves with the spatial
scale of 100 km [see Isobe et al., 2004, Figure 10]. Hence, thetemperature fluctuation in the reanalysis data (dotted line in
Figure 14 (bottom)) is unremarkable over the period Marchthrough September. However, in the FVCOM domain forwhich lateral boundary conditions are provided using thedaily JCOPE2 data set, two periods A and B with intense
kyucho events are visible in the modeled time series at the
Shitaba station. It is therefore concluded both that thenumerical model in the present study is able to reproduce
anticyclonic eddies leading to the growth of frontal waves,and that the modeled kyucho phenomena indeed resemble as
those in the actual ocean. It is however noted that the periods
with intense kyucho events are somewhat delayed withrespect to the observed ones. For instance, the onset of theperiod B in Figure 14 (bottom) is delayed by about two weeks
compared to that in Figure 14 (top) because of the absence

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ISOBE ET AL.: HINDCAST AND PREDICTABILITY OF KYUCHO

C04023consider that this kyucho event would not occur even if thenumerical model included tides.

5. Conclusion: Is Forecasting of the Kyucho
Possible?

Figure 14. Same as 2003 time series in Figure 5, but for(top) the observed and (bottom) modeled ones at the Shitaba
station in the course of FVCOM computation period. The
time series in the JCOPE2 reanalysis data is indicated by thedotted line, while the FVCOM results are represented using
the solid line. See the text for the meaning of the arrow andbars with letters A and B.
of the first kyucho event during this period (see the arrow in
Figure 14 (top)) in the modeled ocean.
[26] It is unlikely that the absence of winds, freshwater
inputs, and tides results in the absence of the first kyucho
event in the period B. The archived wind data show thatmoderate (2∼3 m/s) winds were maintained south of the
Bungo Channel in the latter half of July 2003 (not shown; seeJapan Meteorological Agency website, http://www.jma.go.
jp), and so the kyucho event is unlikely to be triggered bywinds over the actual ocean. Likewise, freshwater supply
must not be critical for kyucho occurrence because large
rivers are absent from the Bungo Channel. Takeoka et al.
[1993] indeed point out that kyucho events prevail every
neap tidal cycles (weak tidal currents). Nevertheless, the firstkyucho event in the period B could not be reproduced in spiteof a nontidal model regime in which a kyucho‐favorable
condition is clearly accomplished. It is therefore reasonable to[27] The present study has addressed two questions: Is areliable kyucho forecast possible using a numerical ocean
circulation model? What are prerequisites for a numericalmodel capable of precise kyucho prediction? The answer
to the latter question is that well‐reproduced anticyclonicmesoscale eddies propagated south of Japan are necessary forthe numerical model to enhance the Kuroshio front sharpness
south of the Bungo Channel. Were it not for these eddies, theunstable growth of frontal waves (hence, kyucho occurrence)
would not appear in the model. In addition, a fine resolution
is required for the numerical model to reproduce kyucho
phenomena in the narrow (∼50 km) Bungo Channel. In thepresent study, the FVCOM with unstructured triangle cell
grids is adopted to compute the ocean circulation using thedaily JCOPE2 reanalysis data for the boundary conditions. As
shown in Figures 13 and 14, this numerical model does areasonable job of hindcasting the kyucho occurrence in 2003.
[28] The successful hindcast gives us confidence in the
kyucho forecast. It is noted that the present model to hindcast
kyucho occurrence is driven only by lateral boundary conditions provided using daily JCOPE2 data in the specific year.
The JCOPE2 group is now providing not only reanalysis data,
but also forecast data (see their website http://www.jamstec.
go.jp/frcgc/jcope/htdocs/distribution/); Miyazawa et al.
[2005] evaluate the limit of reliable predictability of 50–
80 days in forecasting the Kuroshio meander in 1999. Thereby,a forecast system for kyucho occurrence up to 2 or 3 months
ahead is possibly established by using the FVCOM in conjunction with JCOPE2 forecast data.
[29] Last, we have to point out a restriction in forecasting
kyucho occurrence in terms of the numerical model approach.
As shown in Figure 14, the first kyucho event in the period B
is not revealed in the modeled ocean although two periods
during which the number of kyucho occurrences increases
can be identified clearly in both observation and model. It
is indeed difficult to reproduce the magnitude and/or timingof a single kyucho event accurately because the growth ofunstable frontal waves is triggered by small‐scale stochastic
motion in the actual ocean impossible to compute in models.
Therefore, what we are able to forecast in the numericalmodel approach is not a single kyucho event, but periods
during which the number of kyucho occurrences increases.
Nevertheless, the onset of these periods may be delayedcompared to those in the actual ocean because the first kyucho
event in these periods does not always occur in the forecast
model. Possibly probabilistic methods such as the ensemble
forecast by Miyazawa et al. [2005] using JCOPE model will
improve the predictability of kyucho events, and will provide
a practical forecast system available for kyucho in the Bungo
Channel.

Appendix A: Computation of the Growth Rateas an Index of Kyucho Occurrence[30] The growth rate of baroclinic instability waves in an
Eady’s model is explained in various text books of geo-

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C04023[32] For simplicity, we next introduce a linearized vertical
shear of the currents as U = az + b. The rigid‐lid approximation justifies that the vertical velocity vanished at thesurface (z = 0), so equation (A5) provides a surface boundary
condition as:
0 ¼ ð!  bk Þz þ ka:ðA6ÞAt the ocean bottom (z = −H), vertical velocities generate
when the currents in the y component impinge on the bottom
slope as:w ¼ y x ðH Þy :ðA7ÞSubstituting equation (A7) into w of equation (A5) yields aboundary condition at the ocean bottom as:

0 ¼ f!  ðb  aH Þk gz þ k a þ N 2 f 1 Hy :

Figure A1. Cartesian coordinate used in the linear stability
analysis to compute the growth rate of kyucho around the
Bungo Channel. The currents (U) with a linear vertical shear
are imposed only in the x direction as shown in this figure.
physical fluid dynamics such as Cushman‐Roisin [1994], so
the essence in computing an index of kyucho occurrence is
described below. Let us consider the Cartesian coordinate
with a sloping ocean floor (Figure A1). Mean currents (U) are
imposed only in the x direction, and have the vertical shear
caused by the horizontal density gradient. We start with aconservation equation of the potential vorticity as:
ð@t þ U @x Þ r2 y þ f 2 N 2 y zz ¼ 0;

ðA1Þwhere f, N, y are the Coriolis parameter, buoyancy frequency,
and stream function for currents (u = −yy, v = yx) deviatedfrom mean ones, respectively; otherwise the notation isstandard. Substituting wavy motion, y = (z)ei(kx−wt), into
equation (A1) yields
ð!  Uk Þ f 2 N 2 zz  k 2  ¼ 0;

ðA2Þwhere w and k denote the frequency and wave number, respectively. A nontrivial solution is readily obtained as:ð zÞ ¼ A coshðnzÞ þ B sinhðnzÞ;ðA3Þ

where A and B are constants and n is expressed as kN/f.
[31] As computed in Chapter 15 of Cushman‐Roisin’s text
book, the linearized form of the vertical velocity (w) in quasi‐
geostrophic dynamics can be written as:
w ¼ fN 2 fy zt þ J ðUy; y z Þ þ J ðy; Uz yÞg:ðA4Þ

Substituting y = (z)ei(kx−wt) into equation (A4), we obtainw ¼ ieiðkx!tÞ fN 2 fð!  Uk Þz þ kUz g:

ðA5Þ

ðA8Þ

[33] We next substitute equation (A3) into equations (A6)and (A8) to remove the constants A and B, and obtain aquadratic equation with respect to w as follows:!2 þ k ðaH  2bÞ  N 2 HT n1 f 2 !
hnoþ ðkaH Þ2 ðnH Þ1 1  N 2 T ðaf Þ2 a1 n1  biðnH Þ2 bðaH Þ1 þb2 ðaH Þ2 ¼ 0;
ðA9Þ

where b T (=fH−1 Hy) denotes the topographic b, and  is coth(nH). The imaginary part of the solution of equation (A9)gives the growth rate as a function of the wave number (k).
[34] Using daily JCOPE2 density data in the upper 200 m
layer, the buoyancy frequency averaged vertically at eachgrid is computed along the line in the 15 March map ofFigure 9. Two coefficients, a and b, representing the verticalstructure of currents perpendicular to the line are computed
using a least square method by fitting daily JCOPE2 current
data in the upper 200 m layer at each grid along the line. The
topographic b is given by ETOPO5 depths at neighboring
grids along the line. The depth (H) at areas deeper than 200 m
is set to 200 m. The maximum growth rate is plotted in
Figure 10 by stippling.
[35] Acknowledgments. This work is supported by the Japan Society
for the Promotion of Science through Grant‐in‐Aid for Scientific Research(21244073). Comments of two anonymous reviewers and the editor are very
helpful in improving the manuscript, and are appreciated.

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X. Guo, A. Isobe, and H. Takeoka, Center for Marine Environmental
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(aisobe@sci.ehime‐u.ac.jp)

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