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

Transcription

1 Journal of Oceanography, Vol. 60, pp. 269 to 282, 2004 Short-Range Prediction Experiments with Operational Data Assimilation System for the Kuroshio South of Japan MASAFUMI KAMACHI 1 *, TSURANE KURAGANO 2, SATOSHI SUGIMOTO 2, KUMI YOSHITA 2, TOSHIYUKI SAKURAI 2, TOSHIYA NAKANO 1, NORIHISA USUI 1 and FRANCESCO UBOLDI 3 1 Meteorological Research Institute, Nagamine, Tsukuba , Japan 2 Office of Marine Prediction, Japan Meteorological Agency, Ohtemachi, Tokyo , Japan 3 LEGOS/BRESM, 14, Av. Edouard Belin 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 84 experiments (90-day predictions) using a model in an operational data assimilation system based on data from 1993 to The predictions started from an initial condition or members of a set of initial conditions, obtained in a reanalysis experiment. The predictions represent the transition from straight to meander of the Kuroshio path, and the results have been analyzed according to previously proposed mechanisms of the transition with eddy propagation and interaction acting as a trigger of the meander and self-sustained oscillation. The reanalysis shows that the meander evolves due to eddy activity. Simulation (no assimilation) shows no meander state, even with the same atmospheric forcing as the prediction. It is suggested therefore that the initial condition contains information on the meander and the system can represent the evolution. Mean (standard deviation) values of the axis error for all 84 cases are 13, 17, and 20 (10, 10, and 12) km, in E, in the 30-, 60-, and 90-day predictions respectively. The observed mean deviation from seasonal variation is 30 km. The predictive limit of the system is thus about 80 days. The time scale of the limit depends on which stage in the transition is adopted as the initial condition. The gradual decrease of the amplitude in a stage from meander to straight paths is also predicted. The predictive limit is about 20 days, which is shorter than the prediction of the opposite transition. Keywords: Data assimilation, Kuroshio, short-range prediction. 1. Introduction Can the variability of the ocean state south of Japan, especially the Kuroshio path, be predicted? Observations so far have revealed that the Kuroshio path has significant variabilities south of Japan. Previous studies (e.g., Kawabe, 1985, 1995) showed that the Kuroshio takes three typical paths: nearshore non-large-meander, offshore non-large-meander, and typical large-meander (see Fig. 1 for the paths and geographic names). Many observational, theoretical and numerical studies have reported descriptions and mechanisms of the variabilities (see, e.g., Kawabe, 2003 for a review and references to studies of the Kuroshio path). Given due consideration to the re- * Corresponding author. mkamachi@mri-jma.go.jp Copyright The Oceanographic Society of Japan. sults of the previous studies, modeling and data assimilation techniques may be able to answer the above question. Before conducting prediction experiments, we need to understand the time scales of the variability. Typical time scales of the variability, the doubling time scale of initial relative error, and the time scale in which predicted root-mean-square value is the same as persistency or climatological value have been studied in some situations in oceanography. Spectrum peaks have been calculated with observed data (such as temperature, velocity and altimeter data) in order to obtain a typical time scale of the Kuroshio variability. Taira and Teramoto (1981) and Kikuchi (1987) reported 10, 15, 20 to 50 days of the spectrum peaks in the velocity data of moored current meters in the Kuroshio. The decorrelation (e-folding) scale has also been calculated as an index of the ocean s variability 269

2 Fig. 1. Geographic names and three typical paths of the Kuroshio: nearshore non-large-meander (nnlm), offshore non-large-meander (onlm), and typical large-meander (tlm) (see Kawabe, 1995). (OOSDP, 1995). Recent TOPEX/Poseidon satellite altimeter data show typical space-time decorrelation scales of 200 km and 30 days in the area south of Japan (Kuragano and Kamachi, 2000). The scales of 200 km and 30 days were thus selected as the target of the short-range prediction in this paper. We selected Kuroshio path variability as a typical variability for the prediction, although we can predict and estimate the distributions of usual ocean state variables such as temperature, salinity, velocity, sea surface height and volume transport. The doubling time scale has been adopted as an index 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 initial relative forecast error grows and doubles its value in an ensemble forecast run. The scale is calculated from a time growth curve in a diagram presenting statistical values of the root mean square difference of the forecast error with different lead times. Examples in the oceanography are few, but see Carton (1987), Brasseur et al. (1996) and Kamachi et al. (2001). Carton (1987) used a quasi-geostrophic model with a regional square ocean, 500 km 500 km, with optimum interpolation assimilation of POLYMODE data. He used the stream function and obtained 10 to 30 days of predictability. Brasseur et al. (1996) obtained 27 days of predictability from the stream function in the North Atlantic using a technique of nudging TOPEX/Poseidon altimetry data into a quasi-geostrophic model. Kamachi et al. (2001) report an example of a predictability experiment on the Kuroshio south of Japan using the same operational data assimilation system as discussed here. The ensemble forecast experiment is started from February 15, 1994 with 28 ensemble members (i.e., the number of the initial conditions of the ensemble forecast). Kamachi et al. (2001) adopted the temperature value at 100 m depth along the ASUKA line as the predictability variable. According to the method detailed by Lorenz (1982), the doubling time is about 17 days. The time scales in this study, which are for predicting a local (ASUKA line) subsurface temperature, are smaller than in previous studies by Mellor and Ezer (1991) and Brasseur et al. (1996) in the Gulf Stream region. This may depend on the different predicted variabilities, model, observed data, time step size for the ensemble members, area (global or local) and assimilation method. A more comprehensive examination using different conditions will be needed in future. Other studies have analyzed the prediction error in single trajectory experiments in which a single prediction run started from an initial condition. The error of the prediction results (e.g., root-mean-square, RMS, or mean deviation value) has been compared to error growths of climatogical conditions and persistency prediction and to variability of observation. The time scale within which the error of the single trajectory reaches the variability of observations or errors of climatology/persistency has been adopted as the predictability in some oceanography studies. Adamec (1989) obtained 13 days from stream function in the double gyre model ocean, 2000 km 2000 km, using an identical twin experiment with a quasigeostrophic model. Mellor and Ezer (1991) used a primitive equation model (Princeton ocean model) in the Gulf Stream region (western North Atlantic) with a nudging assimilation technique. They obtained a time scale of 20 days. The US Navy group has made extensive use of operational layered primitive equation models in the North Pacific with optimum interpolation and high horizontal resolution. 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 prediction experiments in the North Pacific using a 1 1/2 layer shallow water equation model with the weak constraint, two-dimensional variational assimilation method. They obtained a time scale that depends on the transition stages from straight to meander (90 days) and vice versa (30 days). They clearly showed that the difference depends on the vorticity balance. It may also relate to processes (effects of bottom topography and baroclinic instability) that are absent from their shallow water model. Estimation of a similar time scale can be done from a scale analysis about the Kuroshio path using the following simple, rough calculation. We assume that there is 10% initial error (as an example value) in a propagation speed c of disturbance (meander) in the Kuroshio. If the major source of the error is a growth rate of the meander, the speed c may also be changed. If the Kuroshio path has a meander state, its phase has an error ct/10 in 270 M. Kamachi et al.

3 the prediction period T. When the error grows in the prediction period and the predicted phase has the error of half the typical wavelength L of the meander, the prediction is considered to have failed. The limit of the prediction is therefore estimated to be the time scale T which satisfies a relation ct/10 = L/2. If we assume that the disturbance (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 we obtain T = 23 days. From this simple estimation, about one month is thought to be the limit of the predictability of the Kuroshio path. We therefore tried to predict the Kuroshio path with all model state variables in one month using the prediction model used in the operational data assimilation system described in Kamachi et al. (2004), which we call a short-range prediction. As well as the prediction of all model state variables in all space-time grids, a statistical quantity such as prediction skill (or statistic) may also be useful. We then examine the predicted states and some statistics (prediction skills). This paper is organized as follows: Prediction condition is mentioned in Section 2. Predicted results are mentioned in Section 3. Section 4 is devoted to results and discussion. 2. Conditions of Prediction Experiments We produced outputs every 5 days from the reanalysis experiment, from 1993 to 1999, with the operational data assimilation system described in Kamachi et al. (2001, 2004). We selected the initial conditions once a month for this study from the outputs. The prediction experiments started from the initial conditions and were integrated for 90 days. We therefore had 84 cases of 90-day prediction experiments for the Kuroshio path. Current numerical weather prediction systems are not able to provide a reliable prediction of the surface boundary conditions for the ocean models for more than a onemonth period. We thus performed our prediction with the ocean model using prescribed boundary forcing in the prediction period from 1993 to 1999, rather than adopting the output of the numerical weather prediction. In the prediction period we adopted climatological sea surface temperature and sea surface salinity. For momentum forcing, we used the wind field that is the sum of the climatological wind field and 30-day mean value of the anomaly from the climatology in the previous 30 days from the initial time (day of the initial condition) for each prediction experiment. The model was integrated for a multi-year run, without assimilation, under the historical forcing (wind stress of the reanalysis data set by the National Center for Environmental Prediction, sea surface temperature and salinity by the Japan Meteorological Agency) from 1993 to This multi-year run also produced a time series of the output. In each prediction period, the model has been driven for 90 days by the same forcing as the prediction experiments, but its initial condition is produced from the time series of the multi-year run. We call this model integration in the prediction period model simulation. The result of the model simulation is also compared with the prediction. The prediction and the model simulation have different initial conditions at the starting time of each prediction period. Though our aim is a short-range, one month, prediction of the ocean state south of Japan, we calculated the predicted fields for 90 days, because we examine time evolution (especially the increasing rate) of prediction errors beyond one month. The prediction experiments are conducted from 1993 to We report three particular cases to asses the property of the prediction: Case 1: From April to July in The Kuroshio path was initially straight, had a meander, and returned to straight (single trajectory). Case 2: From January to March in The Kuroshio path changed from meander to straight (single trajectory). Case 3: Same as the period of Case 1. Prediction started from members of the initial conditions (ensemble prediction). 3. Results Figure 2 shows the location in latitude of the Kuroshio path along E, calculated from the maximum velocity at 200 m depth in E. The period is 1998 to early 1999, which contains the period of the three prediction experiments. We adopted the field of outputs after assimilation as a reference within a range of analysis error (see Kamachi et al. (2004) for the error estimation of the path derived from the output after assimilation). As a result, the estimation of the predictability of the system in this study is somewhat optimistic (see also Komori et al., 2003). The thick dotted line in Fig. 2 shows the position of Kuroshio axis in the reference solution (treated as observations), and solid and dashed lines show the position in the prediction. The predicted position is drawn for 90 days, though the target of the experiment period is about 30 days. Each prediction depicts the different kinds of lines with different prediction time: thick solid (0 30 days prediction), thin solid (30 60 days) and thin dashed (60 90 days) lines. The prediction skill with the different prediction period can be seen from the lines. The assimilation system in this study predicts the axis variability very well (root mean square difference of the axis along E is 34 km) in the prediction period of one month. The predicted Kuroshio axis, however, has a faster transition than the reference. For example, for the meander from June to July in 1998, when the initial condition is April 30, the predicted axis started the meander Operational Kuroshio Assimilation and Prediction 271

4 Fig. 2. Time series of the latitude of the Kuroshio path along E in the reference (thick dotted line) and prediction (thick solid line for 0 30 day, thin solid line for days, and thin dashed line for days predictions). Horizontal axis is time from January 1998 to March days sooner than the transition of the reference, which is due to the model characteristics (i.e., bias) themselves. The model has the faster velocity and stronger north-south gradient of temperature in the Kuroshio region. The meander therefore started faster in the prediction period, because the model velocity field tends to be faster. When the prediction started, however, from the initial stage of meander, i.e., May 30, the axis position is predicted very well. If we start the prediction from March 30, the meander is predicted, but the starting time is faster (about 40 days) and the amplitude of the meander is smaller (see the discussion about Fig. 7). Therefore, the time scale of the predictable limit depends on which stage in the transition is adopted as the initial condition in the variability. 3.1 Single trajectory prediction experiments (Cases 1 and 2) In this subsection we examine single trajectory prediction experiments. Predicted fields are described in this subsection for the period from April to July, In this period the Kuroshio path changes from straight to meander and later back to straight. We compare temperature fields of the prediction with reference and simulation at 115 m depth in Fig. 3, because the steepest gradient of the temperature field indicates the Kuroshio path. In Fig. 3, the upper panels show the reference (as observation), middle panels prediction, and the lower panels simulation. The initial condition for the prediction is the output of the assimilation on April 30, The initial condition (i.e., April, 30) shows the straight path of the Kuroshio (Fig. 3(a)). Figure 3(b) shows that the predicted field has a small meander, though the reference (assimilation) field has a starting state of the meander around Ashizuri and Kii Peninsulas in May 20. The prediction progresses about 5 days faster than the reference. After 25 days from the initial condition, May 25, both the prediction and reference show a meander of the Kuroshio path, but the model simulation does not. The meander progresses further by June 29 (Fig. 3(d)). The predicted ocean state shows that the temperature in the coastal area is lower and the gradient of the temperature in the northern edge of the Kuroshio path is steeper than the reference. These characteristics are due to the model bias. In this assimilation system, the model used has larger velocity in the Kuroshio region. In the prediction period, the characteristics (due to bias) of the model gradually appear in the prediction period: the velocity of the Kuroshio becomes faster, and then the north-south gradient of the temperature increases and coastal water enters into the meander region. In order to decrease the velocity amplitude, further tuning of the model will be needed, and the climatological mean state of the model should be consistent with observation, such as the data set produced by Qu et al. (2001). This is a matter for future work, however. Next we show prediction skills with relation to ocean states in the prediction period. Figure 4 shows a time evolution of an axis error. The axis error is defined as follows: we first calculate the position of the maximum velocity in latitude in each model grid. The Kuroshio path is a line to which latitudes of the calculation are connected. The axis error is obtained from the area between the Kuroshio paths in the reference and prediction (or between reference and simulation) divided by the length of the path in the reference (e.g., Ezer and Mellor, 1994). This is better than a mean value of the difference in latitude, because the axis error is affected by the differences of straight and meander states, even if the mean difference in latitude has the same value. Figure 4 shows the time evolution of the errors calculated from simulation, prediction and persistency. Persistency is a prediction in which the initial condition continues, without any changes of state vector, throughout the prediction period. For the calculation of the skill we adopted the area of 133 E to 272 M. Kamachi et al.

5 Fig. 3. Comparison of reference (upper panel), prediction (middle panel), and simulation (lower panel) of Case 1. Contour map shows the temperature distribution at 115 m depth. (a) Initial condition, April 30, (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 initial state (April 30). 140 E and 30 N to the south coast of Japan. The initial condition shows the straight Kuroshio path on April 30. Persistency, simulation and prediction have a similar time evolution to the error up to day An analysis of the factors resulting in the same growth rates of prediction and persistency in the same model with different initial conditions is actually crucial. This analysis will be needed in future studies with more cases of prediction. The meander started from May 20 to 25. The errors in the model simulation (no assimilation) and persistency continue to increase, because both states still show the straight path. In the prediction, however, the meander started on May 25, and the growth rate of the error decreases and the value of the error becomes saturated at June 10, from which date the meander has a mature stage. One of the simplest ways to estimate the predictable limit of the system is to compare the error to prediction by using climatology. If the ocean state is dynamically balanced and in a quasi-steady (or regularly periodic) state, we may predict the state using annual mean (or seasonal variation) of the axis. Here we compare the axis error to an error value of 30 km, which is the mean deviation of the axis in E from its seasonal variation. The axis error of two curves of simulation and persistency reaches 30 km in 50 and 60 days, respectively, as shown in Fig. 4. The prediction is smaller than 30 km in 60 days, though, which indicates that the predictive limit is more than 60 days in this case. We need an analysis using all 84 cases to determine the predictable limit. See the discussion in Section 4. Operational Kuroshio Assimilation and Prediction 273

6 Fig. 5. Time series of correlation coefficient of the prediction (Predic.), model simulation (Sim.), persistency (Init.) and climatology (Clim.). Horizontal axis shows the number of days after the initial state (April 30). Figure 5 shows the time series of correlation coefficients of prediction, simulation, persistency and climatology versus reference. The coefficients are calculated in the same area as the axis error and used temperature data at 115 m depth. The experiment, in this case only, was done for 120 days to calculate the correlation coefficient. The coefficient shows a correlation of a two-dimensional pattern of the temperature distribution in the area. The initial condition in April 30 and a state in the period between initial and May 20 has the straight Kuroshio path. Both the persistency and prediction have the straight path, but the prediction has higher correlation than persistency. The meander started from May 20 to 25. In this period prediction is much better than the simulation and persistency, both of which still have a straight path. However, correlation of the prediction also decreases, because the north-south gradient of temperature increases and warm water intrudes along the Kuroshio, even if the path is a meander. Prediction has a higher correlation than not only persistency but also climatology and model simulation. Around August 8 the Kuroshio path returns to straight, and all correlations increase to give similar values. Why does the prediction have a higher score than persistency, climatology and model simulation? In other words, why does the prediction experiment well reproduce the meander state in the prediction period? The difference between the prediction and model simulation is only the initial condition. The prediction has higher score and well reproduces the meander state in the prediction period because it starts from the same initial state as the reference solution, while the simulation run starts from the initial state, which lacks important features that are responsible for triggering the meander. The small meander south-east of Kyushu (off Cape Toi) has been reported Fig. 6. Time evolution of the potential vorticity distribution at 115 m depth for (a) April 20, (b) the initial condition (April 30), (c) before the meander (May 10), (d) starting time of the meander (May 20), (e) May 30, and (f) mature stage of the meander (June 9). Contour (variable) interval is 3 to m 1 s 1. to be a trigger of the meander (esp., typical large meander) 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 the output of the reanalysis (assimilation experiment), because we would like to discuss the role of PV as a function of the quality of the initial condition. Figure 6 shows a 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 of the meander (Fig. 6(d), May 20), evolution of the meander (Fig. 6(e), May 30), and the mature stage of the meander (Fig. 6(f), June 9). Low PV intruded before the initial condition April 30 (east of Amami-Ohshima Island to Tokara Strait in Fig. 6(a)). Figure 6(b) shows the increase of the potential vorticity south-east of Kyushu (off 274 M. Kamachi et al.

7 Fig. 7. Time series of sea surface height anomaly derived from TOPEX/POSEIDON altimetry. Each figure is drawn every ten days from January 8 to April 28 just before the initial condition, 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, Circles trace an eddy. Cape Toi). The increased PV propagates to the south of Shikoku (off Ashizuri Peninsula in Fig. 6(c): May 10), and reachs the area off Kii Peninsula at the beginning of the meander on May 20 (Fig. 6(d)). These stages are the lateral intrusion of high-pv water before and in the baroclinic instability. The potential vorticity off Kii Peninsula increases more as the meander grows (Figs. 6(e) and (f)). This process is a similar scenario to that given by Qiu and Miao (2000) for the interannual variation. In order to examine what caused the small meander with the increased PV, Fig. 7 shows a time series of sea surface height anomaly derived from TOPEX/Poseidon altimetry, because the PV map relates to meso-scale eddies which are depicted well by the altimetry data. The figure contains a series of 12 figures, each ten days, from January 8 to April 28 just before the initial condition, A negative anomaly south-east of Kyushu is observed in April 28, and it propagates downward (figure omitted: see the PV field shown in Fig. 6). The anomaly Fig. 8. Space-time evolution of the axis error. Horizontal axis is longitude, and vertical axis is time. Contour interval is 0.25 degree in latitude. Operational Kuroshio Assimilation and Prediction 275

8 can be traced back in time (see the circles that trace the anomaly in the figures). It is due to an eddy that propagates westward from the Kuroshio extension along 28 N. The eddy interacts with the Kuroshio around the Tokara Strait. The propagation and interaction with the Kuroshio have been studied extensively by Ichikawa (2001) and Ebuchi and Hanawa (2003). In the series of the panels in Fig. 7, it is clear that the eddy propagates westward, interacts with the Kuroshio, and causes the meander of the path. 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 is smaller (see the discussion of Fig. 7). In March 29 (Fig. 7(i)) the eddy is near Cape Toi, and the system may not reproduce the interaction of the eddy and Kuroshio. In April 28 (Fig. 7(l)) the eddy is to the east of Kyushu and the amplitude is larger than that on March 29. When we started the prediction, the system predicted a more realistic state. Therefore, the time scale of the predictable limit depends on which stage in the transition is adopted as the initial condition in the variability and on the system. Because interactions of all eddies with different time scales are not always the same (e.g., Ichikawa, 2001) and the reproduction of the interaction depends on the model and assimilation method, we need more studies with an OGCM with finer resolution and an advanced assimilation method, such as the adjoint one, which propagates information consistently and continuously in space and time. Next we examine two prediction experiments with the transition from meander to straight. One is the subsequent period to the experiment Case 1, in which the prediction started from April 30, We examine the variation of the Kuroshio path after July in the prediction experiment. The Kuroshio has the meander path from May to July, and then it starts a gradual transition from the meander to the straight path. A space-time relation of an axis difference may be useful to understand propagation of error. We calculated the difference of the Kuroshio axis, which is here defined as the latitude of the maximum velocity at 200 m depth, between prediction and reference (the unit is degree). Figure 8 shows the longitude-time evolution or propagation of this axis error in each longitude from 125 E to 142 E. The period is chosen from May 30 (meander path) to the end of August (straight path). A typical space scale of the axis error is about 50 to 75 km, which is similar to the decorrelation scale derived from a correlation map of the temperature prediction error (figure is omitted) and from TOPEX/Poseidon altimetry (e.g., Kuragano and Kamachi, 2000). The eastward propagation speed of the errors is about 100 to 200 km per month, which is similar to the propagation speed of the meander (see e.g., Komori et al., 2003). There is thus a possibility that the error is strongly related to the variability of the Kuroshio path itself. Such kinds of information about the errors will be helpful in developing an advanced data assimilation system, which controls the scale and propagation of errors. The axis error is small in the region between 133 E to 140 E, which is the same area as that shown in Fig. 4. It means that the Kuroshio path is predicted well to the south of Japan, which is the area 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 of Kyushu (132 E) and Izu ridge to the Kuroshio extension (139 E to 142 E). Until June 20 (80-day prediction) the error is smaller than 0.25 degree (or about 30 km: mean deviation from seasonal variation of the axis) in latitude in all regions. Then the error grows gradually. This may be due to the longer (e.g., longer than 1 or 2 months) prediction with the ocean model and prescribed atmospheric forcing, due to the different physics of the transition from meander to straight paths (see Komori et al., 2003, for example), or due to model bias in each region. It is also due to the following anomalous states in the prediction. A great deal of warm water is advected in the East China Sea west of 133 E. The Kuroshio path has a southward shift in 139 E to 141 E compared to the observation. Moreover, the path has a northward shift in the Kuroshio extension. All of these are due to characteristics of the OGCM adopted in the assimilation system, because these are similar to the model simulation (figure is omitted). We need to improve the model further to decrease these errors. The error distribution discussed above, however, is a result of the prediction from the initial condition in April 30. The prediction period, in the discussion, is more than 80 days (June 20 is the state after 80 days from the initial condition), which is much longer than our targeted period (i.e., one month, see analyses in the introduction, Section 1). The system well predicted the transition from the straight path to the meander and the following opposite transition in 80 days, in which the error is smaller than 0.25 degree (or 30 km) in latitude (see Section 4 for an analysis of all 84 prediction cases from 1993 to 1999). Next we examine prediction in the period from February to the end of March in 1999 (Case 2). The Kuroshio is in the meander path state from February to April. It gradually then returns to the straight path from May to June. Prediction experiment started from an initial condition in January 30, Figure 9 shows similar comparisons of temperature distributions at 115 m depth in the reference and prediction experiments to those given in Fig. 3. In Fig. 9 the upper figure in each group is the reference solution, and is related to observations within the analysis error. The lower figure is the prediction started from the initial condition in January 30 (Fig. 9(a)). The predicted Kuroshio has a similar path to the reference in the 10 days prediction period (February 9: Fig. 276 M. Kamachi et al.

9 Fig. 9. Comparison of reference (upper) and prediction (lower) of the Case 2. Contour map shows the temperature distribution at 115 m depth. (a) Initial condition, January 30, (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 experiment case 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. is degree. Operational Kuroshio Assimilation and Prediction 277

10 9(b)). In the 20 days prediction period (February 19: Fig. 9(c)), the predicted Kuroshio path started to attach to the coast around 140 E. In the following periods (30 days after the initial state: Fig. 9(d)), the Kuroshio path is predicted well in the area south of Honshu (132 E to 139 E). The Kuroshio path, however, has a northward shift east of 139 E, which is similar to that shown in Fig. 8. The gradual decrease of the amplitude (in a stage from meander to straight paths) south of Japan (i.e., targeted area) is predicted well. The limit of the prediction is about 20 days, when the axis error is similar to the climatological one, 30 km. It is smaller than the result of a prediction using a simple model of a 1 1/2 layer shallow water equation (Komori et al., 2003), though the model in this study contains bottom topography and a representation of baroclinic instability. This means that the representation may not be adequate in the system used here, or that there is another dynamical balance from meander to straight paths. This is an important matter for future study, and we encourage analyses using observed and model data. 3.2 Ensemble prediction from straight to meander (Case 3) We examine whether the predicted fields are improved in ensemble prediction rather than the single trajectory prediction described in the previous section. We produced 5(5) reanalysis outputs around April 30 (May 30) in 1998, which are stored every day, as the members of the initial conditions (this method of producing the initial conditions is called the blagged average method). Some ensemble prediction methods, such as breeding and singular value methods, have been reported in operational centers for numerical weather prediction. The breeding method is adopted in the NCEP. It does not work for prediction through a critical state (e.g., transition from straight to meander). The singular value method has a large computational burden and needs adjoint coding of an OGCM. Here we adopted the simplest method as the first step. We used 5 members around April 30 (April 28 to May 2) for comparing Fig. 3 (case 3.1). We also used 5 members around May 30, in which the meander starts (case 3.2). Figure 10 shows the comparison of the temperature distribution at 115 m depth in the reference (upper panels), ensemble prediction (mean value of the 5 members, lower panels). Figures 10(a) and (b) show the comparison of the two figures in May 30, which is 30 days after the initial condition. A comparison of the ensemble prediction in Fig. 10(b) and the single trajectory prediction shows a difference of temperature distribution in one month prediction. Figures 10(c), (d) and (e) show comparison of temperature distributions at 115 m depth in June 29. The upper panel (c) is the reference (assimilation), the lower panel (e) is the 5-member mean of ensemble prediction in case 3.2, and the other lower panel Fig. 11. Time evolution of the axis error of the prediction (closed circle and solid line: Predict-1 in the case 3.1; closed square and solid line: Predict-2 in the case 3.2), model simulation (solid line: Sim.), and persistency (open circle and thin solid line: Persist-1 in the case 3.1; open square and thin solid line: Persist-2 in the case 3.2). Horizontal axis shows the number of days after April 30. (d) is the 5-member mean of ensemble prediction in case 3.1. The lower panel (d) is the predicted state in case 3.1, and is a two-month prediction (from the initial condition in April 30). A comparison between the panel and the single trajectory of prediction (lower panel in Fig. 3(d)) shows that the ensemble prediction is slightly better than the single trajectory prediction, especially for temperature 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 condition in May 30). The initial condition has the meander of the Kuroshio path already; the predicted temperature distribution, Fig. 10(e), is more similar to the reference (upper panel Fig. 10(c)) than the case 3.1, Fig. 10(d), and the single trajectory prediction (lower panel in Fig. 3(d)), especially temperature in the coastal area (between coast and Kuroshio path). These results show that the initial condition affects the prediction even in the ensemble prediction. The time evolution of the axis errors is shown in Fig. 11. Case 3.1 started from the initial time (day 0: April 30) in the horizontal axis, but case 3.2 started from day 30 (May 30). A comparison of the ensemble prediction in case 3.1 to the single trajectory prediction in Fig. 4 shows that the ensemble prediction has smaller axis error (13 km in day 30, and 19 km in day 60). The axis error in case 3.2 (8 km in day 60, i.e., 30-day prediction, and 13 km in day 90, i.e., 60-day prediction) is much smaller than case 3.1, because the initial condition in case 3.2 is the state of the meander. This means that the ocean state 278 M. Kamachi et al.

11 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 in the initial condition has a great affection on the prediction, even in the ensemble prediction. Persistency in case 3.1 (i.e., straight) is better than the persistency in case 3.2 (i.e., meander) after 55 days, because the Kuroshio path tends to be straight. It is suggested that the statistical ensemble of initial condition extends the limit of the predictability. It is also important to assess not only the limit of the predictability but also the divergence of the model trajectories with time and to make a rough estimate of the sensitivity of the prediction with respect to the errors in the initial state. This is a matter for future study. In order to obtain a more reliable estimation of the errors in the ensemble prediction, ensemble experiments in all 84 cases from 1993 to 1999 may be needed. This is also something for the future. 4. Summary and Discussion We have reported three cases of prediction experiments: single trajectory predictions from straight to meander and vice versa, and ensemble prediction from straight to meander paths in order to evaluate the possibility of predicting the Kuroshio axis for a short range period in 84 cases from 1993 to The initial conditions are calculated in a reanalysis experiment. The predictions represent the transition well. The prediction results are analyzed under the mechanisms of transition from straight to meander (esp., typical large meander) of the Kuroshio path with growing small meander, self-sustained oscillation related to baroclinic instability, and eddy propagation and interaction that act as a trigger of the meander, as reported in previous studies. The reanalysis data show the meander evolution induced by the eddy. Simulation (no assimilation) experiments show no meander state, even with the same atmospheric forcing as the prediction. It is therefore suggested that the initial condition contains information on the mechanisms of the previous studies and the system can represent them. Not Fig. 13. Time series of the axis error (mean deviation of the Kuroshio axis in E) of the all 84 cases of the prediction from 1993 to Thin solid lines: error for each single trajectory, medium solid lines: averaged axis error, broken lines: standard deviation of the axis error, and thick solid line: climatological error (mean deviation from the seasonal variation). only the three cases reported above but also all 84 cases will 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 but for the all period, from 1993 to The prediction period is three months. In the figure the time scale is very long; the difference is not clear, but generally the system predicted the Kuroshio axis in 30- to 80-day prediction period, depending on the ocean state in the initial condition. If we draw each prediction on a similar scale to Fig. 2, the predicted state started sooner than the observation, Operational Kuroshio Assimilation and Prediction 279

12 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 the reanalysis (assimilation experiment) is used. Horizontal axis is time from 1993 to due to the same reason as given in Fig. 2. We calculated the Kuroshio axis error, which is here defined as the difference in latitudes of the maximum velocity at 200 m depth and E, between prediction and reference (the unit is km) in all 84 cases from 1993 to 1999 and the results are shown in Fig. 13. Mean values of the axis error (medium solid line in the figure) in all 84 cases are 13, 17, 20 km in the 30-, 60-, and 90-day predictions, respectively. The standard deviations of the axis error are 10, 10, 12 km in the 30-, 60-, and 90-day predictions respectively. On the other hand, the mean deviation from climatology (seasonal variation) of the axis in the reanalysis is 30 km, which is shown as the thick solid line in the figure. The value of the sum of the mean and standard deviation (broken line in the figure) reaches the climatology on the 76th day. This indicates that the predictive limit of the system descrived in this paper is about 80 days. The time scale of the predictive limit depends on which stage in the transition is adopted as the initial condition. When the eddy is in south-east of Kyushu, the predicted meander started 40 days sooner than the observation, with smaller amplitude. When the eddy is east of Kyushu and its amplitude is larger, the predicted meander started 5 days sooner. When the prediction started from the initial stage of meander, the predictable limit is more than 80 days. The gradual decrease of the amplitude (in a stage from meander to straight paths) south of Japan (i.e., the target area) is predicted well. The limit of the prediction is about 20 days, when the axis error is similar to the climatological one: 30 km. The representation may not be adequate in the system used in this study, or there may be another dynamical balance from meander to straight paths. A statistical ensemble of initial condition helps to make a longer time limit of predictability. It should be noted that the system s characteristics (e.g., model characteristics/bias) causes the faster transition of the states of the Kuroshio path. Therefore, in order to increase the prediction skill, we need more improvement to the model itself as well as the assimilation method and analyses of observed data. The improvement is greatly assisted by an understanding of the Kuroshio variability. The variability contains the propagation of meso-scale eddy, its interaction with the Kuroshio, propagation of the resulting eddy or small meander, its interaction with bottom/coastal topography, and baroclinic instability to start the meander south of Honshu. The results in the previous section reveal that the meander is affected by the meso-scale eddy propagation, its interaction with Kuroshio, and PV fluctuation. These relations of the meso-scale eddies have been examined intensively by Ichikawa (2001) and Ebuchi and Hanawa (2003). In this study, it is shown that a route of eddy propagation affects the initial condition (Fig. 7). The initial condition includes this eddy after the assimilation method used in this study, it affects the time evolution of the Kuroshio path in the prediction period. The meander is related to baroclinic instability. Qiu and Miao (2000) studied the interannual variation of the Kuroshio path, especially the large meander in relation to baroclinic instability as a self-sustained oscillation. They clearly showed that the cycle of the Kuroshio path variability (straight to meander and vice versa in the interannual time scale) is determined by the self-sustained oscillation, which relates the PV field to baroclinic instability. Our hypothesis is that the self-sustained oscillation, which is related to baroclinic instability, also acts as an important mechanism in the short-range (i.e., about one month) variability. If we assume a simple two-layer ocean model, changes of upper- and lower-layer kinetic energies reflect vertical energy transfers (i.e., sharp drop/ rise of the upper/lower-layer kinetic energy) due to baroclinic instability (e.g., Holland and Lin, 1975). The transition from a straight to meander states is nearly always accompanied by a sharp rise in the lower-layer kinetic energy. The developments of the meanders are preceded by the occurrence of baroclinic instability (Qiu and 280 M. Kamachi et al.

13 A Scenario for short term variability Eddy-Kuroshio Interaction Generation of Mid-ocean eddy In the Kuroshio South of Japan and its Extension Westward propagation Advection & interaction by Kuroshio Trigger (not all ddies) Volume Transport And other effects Self-Sustained Oscillation Transport (accumulation) of low-pv water Intensification of Recirculation gyre Straight path Decrease of vertical shear, Baroclinically unstable, Lateral intrusion of high PV Meander path Fig. 15. Schemtic diagram of a scenario of a relation of midocean eddy and Kuroshio interaction and self-sustained oscillation. Unresolved process is shown by dotted lines. Miao, 2000). The occurrence of the baroclinic instability is also seen in a drop of a vertical shear of the Kuroshio (see also Qiu and Miao, 2000). Does the realistic data assimilation system reproduce a similar process? As an example, Fig. 14 shows a time series of the difference of the velocity at 100 m and 200 m, at 138 E, as a vertical shear. The horizontal axis is time from 1993 to As shown in Figs. 12 and 14, the vertical shear of the Kuroshio increases in straight path states. It is likely that the Kuroshio with the straight path may eventually become baroclinically unstable when the vertical shear exceeds a threshold value. The timing of the decreasing of the vertical shear coincides with the southward movement of the Kuroshio path (Fig. 12). The time series of the PV field also shows a similar self-sustained oscillation (this figure is omitted, though part is shown in Fig. 6) to the oscillation addressed by Qiu and Miao (2000) for the interannual variability. It is likely that the short-range variability of the Kuroshio path is also related to baroclinic instability, though more comprehensive analyses will be needed in a future study. According to the above discussion, Fig. 15 shows a schematic diagram of a scenario for the relation ship between mid-ocean eddy propagation, its interaction with the Kuroshio, and self-sustained oscillation. The left half is related to the eddy propagation and interaction, which act as a trigger of the meander. The right half relates the self-sustained oscillation with the eddy trigger. The scenario is not complete. The unsolved process is shown by dotted lines in the figure. For example, not all eddy acts as a trigger of the meander. Other effects, such as volume transport, wind field, and bottom and coastal topographies, are not also clear in the prediction experiments in this study, though the effects have been reported (see, e.g., Komori et al., 2003; Kawabe, 2003). The transition from meander to straight, which relates to low PV, is not clear in this study, though the assimilation system can predict the transition. The transition has a different PV dynamics from that of meander to straight path (Qiu and Miao, 2000; Komori et al., 2003). Further study is needed for an understanding of the mechanism. Understanding of the mechanism of the Kuroshio variation will allow an increase in the prediction time. This understanding of the mechanism and extension of the prediction period can be gained with a four-dimensional dataset calculated from a high-resolution model with sustained observation and an advanced data assimilation method. We focused on the prediction of the Kuroshio path south of Japan, not in other areas such as the Kuroshio extension or the East China Sea. Unfortunately, we have no experience of the prediction of the typical large-meander of the Kuroshio (tlm in Fig. 1), because it did not occur in the period of this study. Such studies will be needed in future work. Historical experience of numerical weather prediction in the atmospheric community reveals that operational applications of a model-observation-assimilationprediction system have a feedback, which improves each component (i.e., modeling, observation system and assimilation method) and it accelerates further developments of the system and understanding of phenomena. This also holds for oceanography. Acknowledgements The main part of this study was reported in the Session B4 Numerical Ocean Weather Prediction and State Estimation in the SCOR International Symposium Our Oceanography toward the World Oceanography in Sapporo, October The main part of this work is supported by CREST (Core Research for Evolutional Science and Technology) of Japan Science and Technology Corporation (JST). We appreciate the members of the project for their helpful discussion. We also appreciate three anonymous reviewers, guest editor Prof. M. Ikeda, and guest editor in chief Prof. S. Imawaki in this special section of the Journal of Oceanography for their fruitful comments and encouragements for publication. The TOPEX/Poseidon altimeter data were provided by the NASA Physical Oceanography Distributed Active Archive Center at the Jet Propulsion Laboratory, California Institute 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 part of this work, is also supported by The Category 7 of MEXT RR2002 Project for Sustainable Coexistence of Human, Nature and the Earth and the Regular Research Fund in the Meteorological Research Institute. Operational Kuroshio Assimilation and Prediction 281