Short-Range Prediction Experiments with Operational Data Assimilation System for the Kuroshio South...

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Journal of Oceanography, Vol. 60, pp. 269 to 282, 2004

Keywords:⋅ Data assimilation,⋅ Kuroshio,⋅ short-rangeprediction.

* Corresponding author. E-mail: [email protected]

Copyright © The Oceanographic Society of Japan.

Short-Range Prediction Experiments with OperationalData Assimilation System for the Kuroshio South ofJapan

MASAFUMI KAMACHI1*, TSURANE KURAGANO2, SATOSHI SUGIMOTO2, KUMI YOSHITA2,TOSHIYUKI SAKURAI2, TOSHIYA NAKANO1, NORIHISA USUI1 and FRANCESCO UBOLDI3

1Meteorological Research Institute, Nagamine, Tsukuba 305-0052, Japan2Office of Marine Prediction, Japan Meteorological Agency, Ohtemachi, Tokyo 100-8122, Japan3LEGOS/BRESM, 14, Av. Edouard Belin 31400 Toulouse, France

(Received 12 September 2003; in revised form 19 January 2004; accepted 19 January 2004)

The short-range (one month) variability of the Kuroshio path was predicted in 84experiments (90-day predictions) using a model in an operational data assimilationsystem based on data from 1993 to 1999. The predictions started from an initial con-dition or members of a set of initial conditions, obtained in a reanalysis experiment.The predictions represent the transition from straight to meander of the Kuroshiopath, and the results have been analyzed according to previously proposed mecha-nisms of the transition with eddy propagation and interaction acting as a trigger ofthe meander and self-sustained oscillation. The reanalysis shows that the meanderevolves due to eddy activity. Simulation (no assimilation) shows no meander state,even with the same atmospheric forcing as the prediction. It is suggested thereforethat the initial condition contains information on the meander and the system canrepresent the evolution. Mean (standard deviation) values of the axis error for all 84cases are 13, 17, and 20 (10, 10, and 12) km, in 138.5°E, in the 30-, 60-, and 90-daypredictions respectively. The observed mean deviation from seasonal variation is 30km. The predictive limit of the system is thus about 80 days. The time scale of thelimit depends on which stage in the transition is adopted as the initial condition. Thegradual decrease of the amplitude in a stage from meander to straight paths is alsopredicted. The predictive limit is about 20 days, which is shorter than the predictionof the opposite transition.

sults of the previous studies, modeling and data assimila-tion techniques may be able to answer the above ques-tion.

Before conducting prediction experiments, we needto understand the time scales of the variability. Typicaltime scales of the variability, the doubling time scale ofinitial relative error, and the time scale in which predictedroot-mean-square value is the same as persistency orclimatological value have been studied in some situationsin oceanography.

Spectrum peaks have been calculated with observeddata (such as temperature, velocity and altimeter data) inorder to obtain a typical time scale of the Kuroshio vari-ability. Taira and Teramoto (1981) and Kikuchi (1987)reported 10, 15, 20 to 50 days of the spectrum peaks inthe velocity data of moored current meters in theKuroshio. The decorrelation (e-folding) scale has alsobeen calculated as an index of the ocean’s variability

1. IntroductionCan the variability of the ocean state south of Japan,

especially the Kuroshio path, be predicted? Observationsso far have revealed that the Kuroshio path has signifi-cant variabilities south of Japan. Previous studies (e.g.,Kawabe, 1985, 1995) showed that the Kuroshio takesthree typical paths: nearshore non-large-meander, offshorenon-large-meander, and typical large-meander (see Fig.1 for the paths and geographic names). Many observa-tional, theoretical and numerical studies have reporteddescriptions and mechanisms of the variabilities (see, e.g.,Kawabe, 2003 for a review and references to studies ofthe Kuroshio path). Given due consideration to the re-

270 M. Kamachi et al.

(OOSDP, 1995). Recent TOPEX/Poseidon satellite altim-eter data show typical space-time decorrelation scales of200 km and 30 days in the area south of Japan (Kuraganoand Kamachi, 2000). The scales of 200 km and 30 dayswere thus selected as the target of the short-range predic-tion in this paper. We selected Kuroshio path variabilityas a typical variability for the prediction, although wecan predict and estimate the distributions of usual oceanstate variables such as temperature, salinity, velocity, seasurface height and volume transport.

The doubling time scale has been adopted as an in-dex of predictability in numerical weather prediction,according to the original idea proposed by Lorenz (1982).The time scale is a statistical scale in which the initialrelative forecast error grows and doubles its value in anensemble forecast run. The scale is calculated from a timegrowth curve in a diagram presenting statistical values ofthe root mean square difference of the forecast error withdifferent lead times. Examples in the oceanography arefew, but see Carton (1987), Brasseur et al. (1996) andKamachi et al. (2001).

Carton (1987) used a quasi-geostrophic model witha regional square ocean, 500 km × 500 km, with opti-mum interpolation assimilation of POLYMODE data. Heused the stream function and obtained 10 to 30 days ofpredictability. Brasseur et al. (1996) obtained 27 days ofpredictability from the stream function in the North At-lantic using a technique of nudging TOPEX/Poseidonaltimetry data into a quasi-geostrophic model. Kamachiet al. (2001) report an example of a predictability experi-ment on the Kuroshio south of Japan using the same op-erational data assimilation system as discussed here. Theensemble forecast experiment is started from February

15, 1994 with 28 ensemble members (i.e., the number ofthe initial conditions of the ensemble forecast). Kamachiet al. (2001) adopted the temperature value at 100 m depthalong the ASUKA line as the predictability variable. Ac-cording to the method detailed by Lorenz (1982), the dou-bling time is about 17 days. The time scales in this study,which are for predicting a local (ASUKA line) subsur-face temperature, are smaller than in previous studies byMellor and Ezer (1991) and Brasseur et al. (1996) in theGulf Stream region. This may depend on the differentpredicted variabilities, model, observed data, time stepsize for the ensemble members, area (global or local) andassimilation method. A more comprehensive examinationusing different conditions will be needed in future.

Other studies have analyzed the prediction error insingle trajectory experiments in which a single predic-tion run started from an initial condition. The error of theprediction results (e.g., root-mean-square, RMS, or meandeviation value) has been compared to error growths ofclimatogical conditions and persistency prediction and tovariability of observation. The time scale within whichthe error of the single trajectory reaches the variability ofobservations or errors of climatology/persistency has beenadopted as the predictability in some oceanography stud-ies. Adamec (1989) obtained 13 days from stream func-tion in the double gyre model ocean, 2000 km × 2000km, using an identical twin experiment with a quasi-geostrophic model. Mellor and Ezer (1991) used a primi-tive equation model (Princeton ocean model) in the GulfStream region (western North Atlantic) with a nudgingassimilation technique. They obtained a time scale of 20days. The US Navy group has made extensive use of op-erational layered primitive equation models in the NorthPacific with optimum interpolation and high horizontalresolution. They showed the time scale is about 30 days,derived from sea surface height (e.g., Hurlburt et al., 2000;Rhodes et al., 2002). Komori et al. (2003) conducted pre-diction experiments in the North Pacific using a 1–1/2layer shallow water equation model with the weak con-straint, two-dimensional variational assimilation method.They obtained a time scale that depends on the transitionstages from straight to meander (90 days) and vice versa(30 days). They clearly showed that the difference de-pends on the vorticity balance. It may also relate to proc-esses (effects of bottom topography and baroclinic insta-bility) that are absent from their shallow water model.

Estimation of a similar time scale can be done froma scale analysis about the Kuroshio path using the fol-lowing simple, rough calculation. We assume that thereis 10% initial error (as an example value) in a propaga-tion speed c of disturbance (meander) in the Kuroshio. Ifthe major source of the error is a growth rate of the me-ander, the speed c may also be changed. If the Kuroshiopath has a meander state, its phase has an error cT/10 in

Fig. 1. Geographic names and three typical paths of theKuroshio: nearshore non-large-meander (nNLM), offshorenon-large-meander (oNLM), and typical large-meander(tLM) (see Kawabe, 1995).

Operational Kuroshio Assimilation and Prediction 271

the prediction period T. When the error grows in the pre-diction period and the predicted phase has the error ofhalf the typical wavelength L of the meander, the predic-tion is considered to have failed. The limit of the predic-tion is therefore estimated to be the time scale T whichsatisfies a relation cT/10 = L/2. If we assume that thedisturbance (or meander) appears with a wavelength scale(L = 200 km) in the south of Kii peninsula (134°E–136°E)and insert a typical value of about c = 0.5 m/sec, then weobtain T = 23 days. From this simple estimation, aboutone month is thought to be the limit of the predictabilityof the Kuroshio path.

We therefore tried to predict the Kuroshio path withall model state variables in one month using the predic-tion model used in the operational data assimilation sys-tem described in Kamachi et al. (2004), which we call ashort-range prediction. As well as the prediction of allmodel state variables in all space-time grids, a statisticalquantity such as prediction skill (or statistic) may also beuseful. We then examine the predicted states and somestatistics (prediction skills). This paper is organized asfollows: Prediction condition is mentioned in Section 2.Predicted results are mentioned in Section 3. Section 4 isdevoted to results and discussion.

2. Conditions of Prediction ExperimentsWe produced outputs every 5 days from the reanalysis

experiment, from 1993 to 1999, with the operational dataassimilation system described in Kamachi et al. (2001,2004). We selected the initial conditions once a monthfor this study from the outputs. The prediction experi-ments started from the initial conditions and were inte-grated for 90 days. We therefore had 84 cases of 90-dayprediction experiments for the Kuroshio path.

Current numerical weather prediction systems are notable to provide a reliable prediction of the surface bound-ary conditions for the ocean models for more than a one-month period. We thus performed our prediction with theocean model using prescribed boundary forcing in theprediction period from 1993 to 1999, rather than adopt-ing the output of the numerical weather prediction. In theprediction period we adopted climatological sea surfacetemperature and sea surface salinity. For momentum forc-ing, we used the wind field that is the sum of theclimatological wind field and 30-day mean value of theanomaly from the climatology in the previous 30 daysfrom the initial time (day of the initial condition) for eachprediction experiment.

The model was integrated for a multi-year run, with-out assimilation, under the historical forcing (wind stressof the reanalysis data set by the National Center for En-vironmental Prediction, sea surface temperature and sa-linity by the Japan Meteorological Agency) from 1993 to1999. This multi-year run also produced a time series of

the output. In each prediction period, the model has beendriven for 90 days by the same forcing as the predictionexperiments, but its initial condition is produced from thetime series of the multi-year run. We call this model inte-gration in the prediction period model simulation. Theresult of the model simulation is also compared with theprediction. The prediction and the model simulation havedifferent initial conditions at the starting time of eachprediction period.

Though our aim is a short-range, one month, predic-tion of the ocean state south of Japan, we calculated thepredicted fields for 90 days, because we examine timeevolution (especially the increasing rate) of predictionerrors beyond one month. The prediction experiments areconducted from 1993 to 1999. We report three particularcases to asses the property of the prediction:

Case 1: From April to July in 1998. The Kuroshiopath was initially straight, had a meander, and returnedto straight (single trajectory).

Case 2: From January to March in 1999. TheKuroshio path changed from meander to straight (singletrajectory).

Case 3: Same as the period of Case 1. Predictionstarted from members of the initial conditions (ensembleprediction).

3. ResultsFigure 2 shows the location in latitude of the

Kuroshio path along 138.5°E, calculated from the maxi-mum velocity at 200 m depth in 138.5°E. The period is1998 to early 1999, which contains the period of the threeprediction experiments. We adopted the field of outputsafter assimilation as a reference within a range of analy-sis error (see Kamachi et al. (2004) for the error estima-tion of the path derived from the output after assimila-tion). As a result, the estimation of the predictability ofthe system in this study is somewhat optimistic (see alsoKomori et al., 2003). The thick dotted line in Fig. 2 showsthe position of Kuroshio axis in the reference solution(treated as observations), and solid and dashed lines showthe position in the prediction. The predicted position isdrawn for 90 days, though the target of the experimentperiod is about 30 days. Each prediction depicts the dif-ferent kinds of lines with different prediction time: thicksolid (0–30 days prediction), thin solid (30–60 days) andthin dashed (60–90 days) lines. The prediction skill withthe different prediction period can be seen from the lines.The assimilation system in this study predicts the axisvariability very well (root mean square difference of theaxis along 138.5°E is 34 km) in the prediction period ofone month. The predicted Kuroshio axis, however, has afaster transition than the reference. For example, for themeander from June to July in 1998, when the initial con-dition is April 30, the predicted axis started the meander


5 days sooner than the transition of the reference, whichis due to the model characteristics (i.e., bias) themselves.The model has the faster velocity and stronger north-southgradient of temperature in the Kuroshio region. The me-ander therefore started faster in the prediction period,because the model velocity field tends to be faster. Whenthe prediction started, however, from the initial stage ofmeander, i.e., May 30, the axis position is predicted verywell. If we start the prediction from March 30, the mean-der is predicted, but the starting time is faster (about 40days) and the amplitude of the meander is smaller (seethe discussion about Fig. 7). Therefore, the time scale ofthe predictable limit depends on which stage in the tran-sition is adopted as the initial condition in the variability.

3.1 Single trajectory prediction experiments (Cases 1and 2)In this subsection we examine single trajectory pre-

diction experiments. Predicted fields are described in thissubsection for the period from April to July, 1998. In thisperiod the Kuroshio path changes from straight to mean-der and later back to straight. We compare temperaturefields of the prediction with reference and simulation at115 m depth in Fig. 3, because the steepest gradient ofthe temperature field indicates the Kuroshio path. In Fig.3, the upper panels show the reference (as observation),middle panels prediction, and the lower panels simula-tion. The initial condition for the prediction is the outputof the assimilation on April 30, 1998.

The initial condition (i.e., April, 30) shows thestraight path of the Kuroshio (Fig. 3(a)). Figure 3(b) showsthat the predicted field has a small meander, though thereference (assimilation) field has a starting state of themeander around Ashizuri and Kii Peninsulas in May 20.The prediction progresses about 5 days faster than thereference. After 25 days from the initial condition, May25, both the prediction and reference show a meander of

the Kuroshio path, but the model simulation does not. Themeander progresses further by June 29 (Fig. 3(d)). Thepredicted ocean state shows that the temperature in thecoastal area is lower and the gradient of the temperaturein the northern edge of the Kuroshio path is steeper thanthe reference. These characteristics are due to the modelbias. In this assimilation system, the model used has largervelocity in the Kuroshio region. In the prediction period,the characteristics (due to bias) of the model graduallyappear in the prediction period: the velocity of theKuroshio becomes faster, and then the north-south gradi-ent of the temperature increases and coastal water entersinto the meander region. In order to decrease the velocityamplitude, further tuning of the model will be needed,and the climatological mean state of the model should beconsistent with observation, such as the data set producedby Qu et al. (2001). This is a matter for future work, how-ever.

Next we show prediction skills with relation to oceanstates in the prediction period. Figure 4 shows a time evo-lution of an axis error. The axis error is defined as fol-lows: we first calculate the position of the maximum ve-locity in latitude in each model grid. The Kuroshio pathis a line to which latitudes of the calculation are connected.The axis error is obtained from the area between theKuroshio paths in the reference and prediction (or be-tween reference and simulation) divided by the length ofthe path in the reference (e.g., Ezer and Mellor, 1994).This is better than a mean value of the difference in lati-tude, because the axis error is affected by the differencesof straight and meander states, even if the mean differ-ence in latitude has the same value. Figure 4 shows thetime evolution of the errors calculated from simulation,prediction and persistency. Persistency is a prediction inwhich the initial condition continues, without any changesof state vector, throughout the prediction period. For thecalculation of the skill we adopted the area of 133°E to

Fig. 2. Time series of the latitude of the Kuroshio path along 138.5°E in the reference (thick dotted line) and prediction (thicksolid line for 0–30 day, thin solid line for 30–60 days, and thin dashed line for 60–90 days predictions). Horizontal axis is timefrom January 1998 to March 1999.


140°E and 30°N to the south coast of Japan. The initialcondition shows the straight Kuroshio path on April 30.Persistency, simulation and prediction have a similar timeevolution to the error up to day 20–25. An analysis of thefactors resulting in the same growth rates of prediction

and persistency in the same model with “different” ini-tial conditions is actually crucial. This analysis will beneeded in future studies with more cases of prediction.The meander started from May 20 to 25. The errors in themodel simulation (no assimilation) and persistency con-tinue to increase, because both states still show the straightpath. In the prediction, however, the meander started onMay 25, and the growth rate of the error decreases andthe value of the error becomes saturated at June 10, fromwhich date the meander has a mature stage. One of thesimplest ways to estimate the predictable limit of the sys-tem is to compare the error to prediction by using clima-tology. If the ocean state is dynamically balanced and ina quasi-steady (or regularly periodic) state, we may pre-dict the state using annual mean (or seasonal variation)of the axis. Here we compare the axis error to an errorvalue of 30 km, which is the mean deviation of the axisin 138.5°E from its seasonal variation. The axis error oftwo curves of simulation and persistency reaches 30 kmin 50 and 60 days, respectively, as shown in Fig. 4. Theprediction is smaller than 30 km in 60 days, though, whichindicates that the predictive limit is more than 60 days inthis case. We need an analysis using all 84 cases to deter-mine the predictable limit. See the discussion in Section 4.

Fig. 3. Comparison of reference (upper panel), prediction (middle panel), and simulation (lower panel) of Case 1. Contour mapshows the temperature distribution at 115 m depth. (a) Initial condition, April 30, 1998. (b) May 20. (c) June 9. (d) June 29.The unit of the C.I. is degree.

Fig. 4. Time evolution of the axis error of the prediction(Predic.), model simulation (Sim.) and persistency (Init.).Horizontal axis shows the number of days after the initialstate (April 30).


Figure 5 shows the time series of correlation coeffi-cients of prediction, simulation, persistency and clima-tology versus reference. The coefficients are calculatedin the same area as the axis error and used temperaturedata at 115 m depth. The experiment, in this case only,was done for 120 days to calculate the correlation coeffi-cient. The coefficient shows a correlation of a two-di-mensional pattern of the temperature distribution in thearea. The initial condition in April 30 and a state in theperiod between initial and May 20 has the straightKuroshio path. Both the persistency and prediction havethe straight path, but the prediction has higher correla-tion than persistency. The meander started from May 20to 25. In this period prediction is much better than thesimulation and persistency, both of which still have astraight path. However, correlation of the prediction alsodecreases, because the north-south gradient of tempera-ture increases and warm water intrudes along theKuroshio, even if the path is a meander. Prediction has ahigher correlation than not only persistency but also cli-matology and model simulation. Around August 8 theKuroshio path returns to straight, and all correlations in-crease to give similar values.

Why does the prediction have a higher score thanpersistency, climatology and model simulation? In otherwords, why does the prediction experiment well repro-duce the meander state in the prediction period? The dif-ference between the prediction and model simulation isonly the initial condition. The prediction has higher scoreand well reproduces the meander state in the predictionperiod because it starts from the same initial state as thereference solution, while the simulation run starts fromthe initial state, which lacks important features that areresponsible for triggering the meander. The small mean-der south-east of Kyushu (off Cape Toi) has been reported

to be a trigger of the meander (esp., typical large mean-der) in many studies (e.g., Shoji, 1972; Yoon and Yasuda,1987; Akitomo et al., 1991; Endoh and Hibiya, 2000).Figure 6 shows a time evolution of the potential vorticity(PV) distribution at 115 m depth, calculated from theoutput of the reanalysis (assimilation experiment), be-cause we would like to discuss the role of PV as a func-tion of the quality of the initial condition. Figure 6 showsa time series of the state before the initial condition (Fig.6(a), April 20), the initial condition (Fig. 6(b), April 30),before the meander (Fig. 6(c), May 10), starting time ofthe meander (Fig. 6(d), May 20), evolution of the mean-der (Fig. 6(e), May 30), and the mature stage of the me-ander (Fig. 6(f), June 9). Low PV intruded before the ini-tial condition April 30 (east of Amami-Ohshima Islandto Tokara Strait in Fig. 6(a)). Figure 6(b) shows the in-crease of the potential vorticity south-east of Kyushu (off

Fig. 5. Time series of correlation coefficient of the prediction(Predic.), model simulation (Sim.), persistency (Init.) andclimatology (Clim.). Horizontal axis shows the number ofdays after the initial state (April 30).

Fig. 6. Time evolution of the potential vorticity distribution at115 m depth for (a) April 20, (b) the initial condition (April30), (c) before the meander (May 10), (d) starting time ofthe meander (May 20), (e) May 30, and (f) mature stage ofthe meander (June 9). Contour (variable) interval is 3 to 4 ×10–6 m–1s–1.


Cape Toi). The increased PV propagates to the south ofShikoku (off Ashizuri Peninsula in Fig. 6(c): May 10),and reachs the area off Kii Peninsula at the beginning ofthe meander on May 20 (Fig. 6(d)). These stages are thelateral intrusion of high-PV water before and in thebaroclinic instability. The potential vorticity off Kii Pe-ninsula increases more as the meander grows (Figs. 6(e)and (f)). This process is a similar scenario to that givenby Qiu and Miao (2000) for the interannual variation.

In order to examine what caused the small meanderwith the increased PV, Fig. 7 shows a time series of seasurface height anomaly derived from TOPEX/Poseidonaltimetry, because the PV map relates to meso-scale ed-dies which are depicted well by the altimetry data. Thefigure contains a series of 12 figures, each ten days, fromJanuary 8 to April 28 just before the initial condition,1998. A negative anomaly south-east of Kyushu is ob-served in April 28, and it propagates downward (figureomitted: see the PV field shown in Fig. 6). The anomaly

Fig. 7. Time series of sea surface height anomaly derived from TOPEX/POSEIDON altimetry. Each figure is drawn every tendays from January 8 to April 28 just before the initial condition, 1998. Time progresses along the broad arrow. (a): Jan. 8,(b): Jan. 18, (c): Jan. 28, (d): Feb. 7, (e): Feb. 17, (f): Feb. 27, (g): Mar. 9, (h): Mar. 19, (i): Mar. 29, (j): Apr. 8, (k): Apr. 18,and (l): Apr. 28, 1998. Circles trace an eddy.

Fig. 8. Space-time evolution of the axis error. Horizontal axisis longitude, and vertical axis is time. Contour interval is0.25 degree in latitude.


can be traced back in time (see the circles that trace theanomaly in the figures). It is due to an eddy that propa-gates westward from the Kuroshio extension along 28°N.The eddy interacts with the Kuroshio around the TokaraStrait. The propagation and interaction with the Kuroshiohave been studied extensively by Ichikawa (2001) andEbuchi and Hanawa (2003). In the series of the panels inFig. 7, it is clear that the eddy propagates westward, in-teracts with the Kuroshio, and causes the meander of thepath. If we start the prediction from March 30 (see Fig.2), the meander is predicted, but the starting time is sooner(about 40 days) and the amplitude of the meander issmaller (see the discussion of Fig. 7). In March 29 (Fig.7(i)) the eddy is near Cape Toi, and the system may notreproduce the interaction of the eddy and Kuroshio. InApril 28 (Fig. 7(l)) the eddy is to the east of Kyushu andthe amplitude is larger than that on March 29. When westarted the prediction, the system predicted a more real-istic state. Therefore, the time scale of the predictablelimit depends on which stage in the transition is adoptedas the initial condition in the variability and on the sys-tem. Because interactions of all eddies with different timescales are not always the same (e.g., Ichikawa, 2001) andthe reproduction of the interaction depends on the modeland assimilation method, we need more studies with anOGCM with finer resolution and an advanced assimila-tion method, such as the adjoint one, which propagatesinformation consistently and continuously in space andtime.

Next we examine two prediction experiments withthe transition from meander to straight. One is the subse-quent period to the experiment Case 1, in which the pre-diction started from April 30, 1998. We examine the vari-ation of the Kuroshio path after July in the predictionexperiment. The Kuroshio has the meander path from Mayto July, and then it starts a gradual transition from themeander to the straight path. A space-time relation of anaxis difference may be useful to understand propagationof error. We calculated the difference of the Kuroshio axis,which is here defined as the latitude of the maximum ve-locity at 200 m depth, between prediction and reference(the unit is degree). Figure 8 shows the longitude-timeevolution or propagation of this axis error in each longi-tude from 125°E to 142°E. The period is chosen fromMay 30 (meander path) to the end of August (straightpath). A typical space scale of the axis error is about 50to 75 km, which is similar to the decorrelation scale de-rived from a correlation map of the temperature predic-tion error (figure is omitted) and from TOPEX/Poseidonaltimetry (e.g., Kuragano and Kamachi, 2000). The east-ward propagation speed of the errors is about 100 to 200km per month, which is similar to the propagation speedof the meander (see e.g., Komori et al., 2003). There isthus a possibility that the error is strongly related to the

variability of the Kuroshio path itself. Such kinds of in-formation about the errors will be helpful in developingan advanced data assimilation system, which controls thescale and propagation of errors. The axis error is small inthe region between 133°E to 140°E, which is the samearea as that shown in Fig. 4. It means that the Kuroshiopath is predicted well to the south of Japan, which is thearea targeted in this study. The Kuroshio path, however,has larger errors in the other areas, e.g., East China Sea(128°E to 130°E), Tokara Strait (130°E), south-east ofKyushu (132°E) and Izu ridge to the Kuroshio extension(139°E to 142°E). Until June 20 (80-day prediction) theerror is smaller than 0.25 degree (or about 30 km: meandeviation from seasonal variation of the axis) in latitudein all regions. Then the error grows gradually. This maybe due to the longer (e.g., longer than 1 or 2 months) pre-diction with the ocean model and prescribed atmosphericforcing, due to the different physics of the transition frommeander to straight paths (see Komori et al., 2003, forexample), or due to model bias in each region. It is alsodue to the following anomalous states in the prediction.A great deal of warm water is advected in the East ChinaSea west of 133°E. The Kuroshio path has a southwardshift in 139°E to 141°E compared to the observation.Moreover, the path has a northward shift in the Kuroshioextension. All of these are due to characteristics of theOGCM adopted in the assimilation system, because theseare similar to the model simulation (figure is omitted).We need to improve the model further to decrease theseerrors. The error distribution discussed above, however,is a result of the prediction from the initial condition inApril 30. The prediction period, in the discussion, is morethan 80 days (June 20 is the state after 80 days from theinitial condition), which is much longer than our targetedperiod (i.e., one month, see analyses in the introduction,Section 1). The system well predicted the transition fromthe straight path to the meander and the following oppo-site transition in 80 days, in which the error is smallerthan 0.25 degree (or 30 km) in latitude (see Section 4 foran analysis of all 84 prediction cases from 1993 to 1999).

Next we examine prediction in the period from Feb-ruary to the end of March in 1999 (Case 2). The Kuroshiois in the meander path state from February to April. Itgradually then returns to the straight path from May toJune. Prediction experiment started from an initial con-dition in January 30, 1999. Figure 9 shows similar com-parisons of temperature distributions at 115 m depth inthe reference and prediction experiments to those givenin Fig. 3. In Fig. 9 the upper figure in each group is thereference solution, and is related to observations withinthe analysis error. The lower figure is the predictionstarted from the initial condition in January 30 (Fig. 9(a)).The predicted Kuroshio has a similar path to the refer-ence in the 10 days prediction period (February 9: Fig.


Fig. 9. Comparison of reference (upper) and prediction (lower) of the Case 2. Contour map shows the temperature distribution at115 m depth. (a) Initial condition, January 30, 1999. (b) Feb. 9. (c) Feb. 19. (d) Feb. 29. The unit of the C.I. is degree.

Fig. 10. Comparison of temperature field at 115 m depth. (a) Reference and (b) prediction in the ensemble prediction experimentcase 3.1 in May 30. (c) Reference, (d) prediction in case 3.1, and (e) prediction in case 3.2, in June 29. The unit of the C.I. isdegree.


9(b)). In the 20 days prediction period (February 19: Fig.9(c)), the predicted Kuroshio path started to attach to thecoast around 140°E. In the following periods (30 daysafter the initial state: Fig. 9(d)), the Kuroshio path is pre-dicted well in the area south of Honshu (132°E to 139°E).The Kuroshio path, however, has a northward shift eastof 139°E, which is similar to that shown in Fig. 8. Thegradual decrease of the amplitude (in a stage from mean-der to straight paths) south of Japan (i.e., targeted area)is predicted well. The limit of the prediction is about 20days, when the axis error is similar to the climatologicalone, 30 km. It is smaller than the result of a predictionusing a simple model of a 1–1/2 layer shallow water equa-tion (Komori et al., 2003), though the model in this studycontains bottom topography and a representation ofbaroclinic instability. This means that the representationmay not be adequate in the system used here, or that thereis another dynamical balance from meander to straightpaths. This is an important matter for future study, andwe encourage analyses using observed and model data.

3.2 Ensemble prediction from straight to meander (Case3)We examine whether the predicted fields are im-

proved in ensemble prediction rather than the single tra-jectory prediction described in the previous section. Weproduced 5(5) reanalysis outputs around April 30 (May30) in 1998, which are stored every day, as the membersof the initial conditions (this method of producing theinitial conditions is called the blagged average method).Some ensemble prediction methods, such as breeding andsingular value methods, have been reported in operationalcenters for numerical weather prediction. The breedingmethod is adopted in the NCEP. It does not work for pre-diction through a critical state (e.g., transition fromstraight to meander). The singular value method has alarge computational burden and needs adjoint coding ofan OGCM. Here we adopted the simplest method as thefirst step. We used 5 members around April 30 (April 28to May 2) for comparing Fig. 3 (case 3.1). We also used 5members around May 30, in which the meander starts(case 3.2). Figure 10 shows the comparison of the tem-perature distribution at 115 m depth in the reference (up-per panels), ensemble prediction (mean value of the 5members, lower panels). Figures 10(a) and (b) show thecomparison of the two figures in May 30, which is 30days after the initial condition. A comparison of the en-semble prediction in Fig. 10(b) and the single trajectoryprediction shows a difference of temperature distributionin one month prediction. Figures 10(c), (d) and (e) showcomparison of temperature distributions at 115 m depthin June 29. The upper panel (c) is the reference (assimi-lation), the lower panel (e) is the 5-member mean of en-semble prediction in case 3.2, and the other lower panel

(d) is the 5-member mean of ensemble prediction in case3.1. The lower panel (d) is the predicted state in case 3.1,and is a two-month prediction (from the initial conditionin April 30). A comparison between the panel and the sin-gle trajectory of prediction (lower panel in Fig. 3(d))shows that the ensemble prediction is slightly better thanthe single trajectory prediction, especially for tempera-ture north of the Kuroshio, in a two-month prediction.The lower-right panel (e) is the prediction in case 3.2,which is one-month prediction (from the initial condi-tion in May 30). The initial condition has the meander ofthe Kuroshio path already; the predicted temperature dis-tribution, Fig. 10(e), is more similar to the reference (up-per panel Fig. 10(c)) than the case 3.1, Fig. 10(d), andthe single trajectory prediction (lower panel in Fig. 3(d)),especially temperature in the coastal area (between coastand Kuroshio path). These results show that the initialcondition affects the prediction even in the ensemble pre-diction.

The time evolution of the axis errors is shown in Fig.11. Case 3.1 started from the initial time (day 0: April30) in the horizontal axis, but case 3.2 started from day30 (May 30). A comparison of the ensemble prediction incase 3.1 to the single trajectory prediction in Fig. 4 showsthat the ensemble prediction has smaller axis error (13km in day 30, and 19 km in day 60). The axis error incase 3.2 (8 km in day 60, i.e., 30-day prediction, and 13km in day 90, i.e., 60-day prediction) is much smallerthan case 3.1, because the initial condition in case 3.2 isthe state of the meander. This means that the ocean state

Fig. 11. Time evolution of the axis error of the prediction(closed circle and solid line: Predict-1 in the case 3.1; closedsquare and solid line: Predict-2 in the case 3.2), model simu-lation (solid line: Sim.), and persistency (open circle andthin solid line: Persist-1 in the case 3.1; open square andthin solid line: Persist-2 in the case 3.2). Horizontal axisshows the number of days after April 30.


in the initial condition has a great affection on the pre-diction, even in the ensemble prediction. Persistency incase 3.1 (i.e., straight) is better than the persistency incase 3.2 (i.e., meander) after 55 days, because theKuroshio path tends to be straight. It is suggested thatthe statistical ensemble of initial condition extends thelimit of the predictability. It is also important to assessnot only the limit of the predictability but also the diver-gence of the model trajectories with time and to make arough estimate of the sensitivity of the prediction withrespect to the errors in the initial state. This is a matterfor future study. In order to obtain a more reliable esti-mation of the errors in the ensemble prediction, ensem-ble experiments in all 84 cases from 1993 to 1999 maybe needed. This is also something for the future.

4. Summary and DiscussionWe have reported three cases of prediction experi-

ments: single trajectory predictions from straight to me-ander and vice versa, and ensemble prediction fromstraight to meander paths in order to evaluate the possi-bility of predicting the Kuroshio axis for a short rangeperiod in 84 cases from 1993 to 1999. The initial condi-tions are calculated in a reanalysis experiment. The pre-dictions represent the transition well. The prediction re-sults are analyzed under the mechanisms of transition fromstraight to meander (esp., typical large meander) of theKuroshio path with growing small meander, self-sustainedoscillation related to baroclinic instability, and eddypropagation and interaction that act as a trigger of themeander, as reported in previous studies. The reanalysisdata show the meander evolution induced by the eddy.Simulation (no assimilation) experiments show no me-ander state, even with the same atmospheric forcing asthe prediction. It is therefore suggested that the initialcondition contains information on the mechanisms of theprevious studies and the system can represent them. Not

only the three cases reported above but also all 84 caseswill be analyzed in order to confirm the above results,especially in regard to the predictive limit.

Figure 12 shows a similar time series to Fig. 2 butfor the all period, from 1993 to 1999. The prediction pe-riod is three months. In the figure the time scale is verylong; the difference is not clear, but generally the systempredicted the Kuroshio axis in 30- to 80-day predictionperiod, depending on the ocean state in the initial condi-tion. If we draw each prediction on a similar scale to Fig.2, the predicted state started sooner than the observation,

Fig. 12. Time series of the latitude of the Kuroshio path in the reference (black dotted line) and prediction (broad solid line).Horizontal axis is time from 1993 to 1999.

Fig. 13. Time series of the axis error (mean deviation of theKuroshio axis in 138.5°E) of the all 84 cases of the predic-tion from 1993 to 1999. Thin solid lines: error for each sin-gle trajectory, medium solid lines: averaged axis error, bro-ken lines: standard deviation of the axis error, and thicksolid line: climatological error (mean deviation from theseasonal variation).


due to the same reason as given in Fig. 2. We calculatedthe Kuroshio axis error, which is here defined as the dif-ference in latitudes of the maximum velocity at 200 mdepth and 138.5°E, between prediction and reference (theunit is km) in all 84 cases from 1993 to 1999 and theresults are shown in Fig. 13. Mean values of the axis er-ror (medium solid line in the figure) in all 84 cases are13, 17, 20 km in the 30-, 60-, and 90-day predictions,respectively. The standard deviations of the axis error are10, 10, 12 km in the 30-, 60-, and 90-day predictions re-spectively. On the other hand, the mean deviation fromclimatology (seasonal variation) of the axis in thereanalysis is 30 km, which is shown as the thick solidline in the figure. The value of the sum of the mean andstandard deviation (broken line in the figure) reaches theclimatology on the 76th day. This indicates that the pre-dictive limit of the system descrived in this paper is about80 days. The time scale of the predictive limit dependson which stage in the transition is adopted as the initialcondition. When the eddy is in south-east of Kyushu, thepredicted meander started 40 days sooner than the obser-vation, with smaller amplitude. When the eddy is east ofKyushu and its amplitude is larger, the predicted mean-der started 5 days sooner. When the prediction started fromthe initial stage of meander, the predictable limit is morethan 80 days.

The gradual decrease of the amplitude (in a stagefrom meander to straight paths) south of Japan (i.e., thetarget area) is predicted well. The limit of the predictionis about 20 days, when the axis error is similar to theclimatological one: 30 km. The representation may notbe adequate in the system used in this study, or there maybe another dynamical balance from meander to straightpaths.

A statistical ensemble of initial condition helps tomake a longer time limit of predictability. It should benoted that the system’s characteristics (e.g., model charac-teristics/bias) causes the faster transition of the states ofthe Kuroshio path. Therefore, in order to increase the pre-

diction skill, we need more improvement to the modelitself as well as the assimilation method and analyses ofobserved data. The improvement is greatly assisted by anunderstanding of the Kuroshio variability. The variabil-ity contains the propagation of meso-scale eddy, its in-teraction with the Kuroshio, propagation of the resultingeddy or small meander, its interaction with bottom/coastaltopography, and baroclinic instability to start the mean-der south of Honshu.

The results in the previous section reveal that themeander is affected by the meso-scale eddy propagation,its interaction with Kuroshio, and PV fluctuation. Theserelations of the meso-scale eddies have been examinedintensively by Ichikawa (2001) and Ebuchi and Hanawa(2003). In this study, it is shown that a route of eddy propa-gation affects the initial condition (Fig. 7). The initialcondition includes this eddy after the assimilation methodused in this study, it affects the time evolution of theKuroshio path in the prediction period.

The meander is related to baroclinic instability. Qiuand Miao (2000) studied the interannual variation of theKuroshio path, especially the large meander in relationto baroclinic instability as a self-sustained oscillation.They clearly showed that the cycle of the Kuroshio pathvariability (straight to meander and vice versa in theinterannual time scale) is determined by the self-sustainedoscillation, which relates the PV field to baroclinic insta-bility. Our hypothesis is that the self-sustained oscilla-tion, which is related to baroclinic instability, also acts asan important mechanism in the short-range (i.e., aboutone month) variability. If we assume a simple two-layerocean model, changes of upper- and lower-layer kineticenergies reflect vertical energy transfers (i.e., sharp drop/rise of the upper/lower-layer kinetic energy) due tobaroclinic instability (e.g., Holland and Lin, 1975). Thetransition from a straight to meander states is nearly al-ways accompanied by a sharp rise in the lower-layer ki-netic energy. The developments of the meanders are pre-ceded by the occurrence of baroclinic instability (Qiu and

Fig. 14. Time series of the difference of the velocity at 100 m and 200 m, at 138°E, as a vertical shear. The output of thereanalysis (assimilation experiment) is used. Horizontal axis is time from 1993 to 1999.


Miao, 2000). The occurrence of the baroclinic instabilityis also seen in a drop of a vertical shear of the Kuroshio(see also Qiu and Miao, 2000). Does the realistic dataassimilation system reproduce a similar process? As anexample, Fig. 14 shows a time series of the difference ofthe velocity at 100 m and 200 m, at 138°E, as a verticalshear. The horizontal axis is time from 1993 to 1999. Asshown in Figs. 12 and 14, the vertical shear of theKuroshio increases in straight path states. It is likely thatthe Kuroshio with the straight path may eventually be-come baroclinically unstable when the vertical shear ex-ceeds a threshold value. The timing of the decreasing ofthe vertical shear coincides with the southward movementof the Kuroshio path (Fig. 12). The time series of the PVfield also shows a similar self-sustained oscillation (thisfigure is omitted, though part is shown in Fig. 6) to theoscillation addressed by Qiu and Miao (2000) for theinterannual variability. It is likely that the short-rangevariability of the Kuroshio path is also related tobaroclinic instability, though more comprehensive analy-ses will be needed in a future study.

According to the above discussion, Fig. 15 shows aschematic diagram of a scenario for the relation ship be-tween mid-ocean eddy propagation, its interaction withthe Kuroshio, and self-sustained oscillation. The left halfis related to the eddy propagation and interaction, whichact as a trigger of the meander. The right half relates theself-sustained oscillation with the eddy trigger. The sce-nario is not complete. The unsolved process is shown bydotted lines in the figure. For example, not all eddy actsas a trigger of the meander. Other effects, such as volumetransport, wind field, and bottom and coastal topogra-phies, are not also clear in the prediction experiments inthis study, though the effects have been reported (see, e.g.,

Komori et al., 2003; Kawabe, 2003). The transition frommeander to straight, which relates to low PV, is not clearin this study, though the assimilation system can predictthe transition. The transition has a different PV dynamicsfrom that of meander to straight path (Qiu and Miao, 2000;Komori et al., 2003). Further study is needed for an un-derstanding of the mechanism. Understanding of themechanism of the Kuroshio variation will allow an in-crease in the prediction time. This understanding of themechanism and extension of the prediction period can begained with a four-dimensional dataset calculated from ahigh-resolution model with sustained observation and anadvanced data assimilation method.

We focused on the prediction of the Kuroshio pathsouth of Japan, not in other areas such as the Kuroshioextension or the East China Sea. Unfortunately, we haveno experience of the prediction of the typical large-me-ander of the Kuroshio (tLM in Fig. 1), because it did notoccur in the period of this study. Such studies will beneeded in future work.

Historical experience of numerical weather predic-tion in the atmospheric community reveals that opera-tional applications of a model-observation-assimilation-prediction system have a feedback, which improves eachcomponent (i.e., modeling, observation system and as-similation method) and it accelerates further develop-ments of the system and understanding of phenomena.This also holds for oceanography.

AcknowledgementsThe main part of this study was reported in the Ses-

sion B4 “Numerical “Ocean Weather” Prediction and StateEstimation” in the SCOR International Symposium “OurOceanography toward the World Oceanography” in Sap-poro, October 2002. The main part of this work is sup-ported by CREST (Core Research for Evolutional Sci-ence and Technology) of Japan Science and TechnologyCorporation (JST). We appreciate the members of theproject for their helpful discussion. We also appreciatethree anonymous reviewers, guest editor Prof. M. Ikeda,and guest editor in chief Prof. S. Imawaki in this specialsection of the Journal of Oceanography for their fruitfulcomments and encouragements for publication. TheTOPEX/Poseidon altimeter data were provided by theNASA Physical Oceanography Distributed Active ArchiveCenter at the Jet Propulsion Laboratory, California Insti-tute of Technology. We used the free software ‘GrADS(Grid Analysis and Display System) Version 1.7 Beta 6’to produce the figures. One of the authors (MK), of partof this work, is also supported by The Category 7 ofMEXT RR2002 Project for Sustainable Coexistence ofHuman, Nature and the Earth and the Regular ResearchFund in the Meteorological Research Institute.

Fig. 15. Schemtic diagram of a scenario of a relation of mid-ocean eddy and Kuroshio interaction and self-sustained os-cillation. Unresolved process is shown by dotted lines.

A Scenario for short term variability

Advection & interaction

by Kuroshio

Generation of Mid-ocean eddy

In the Kuroshio South of

Japan and its Extension

Eddy-Kuroshio Interaction

Trigger

(not all ddies)

Self-Sustained Oscillation

Westward propagation

Transport (accumulation)

of low-PV water

Intensification of

Recirculation gyre

Decrease of vertical shear,

Baroclinically unstable,

Lateral intrusion of high PV

Straight path

Meander path

Volume Transport

And other effects


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