Acoust. Sci. & Tech. 23, 2 (2002) PAPER
Estimate method for frontal position of Kuroshio extension using ocean acoustic tomography data
Tomio Shinke1;*, Yasushi Yoshikawa2, Takashi Kamoshida1 and Iwao Nakano2 1Oki Electric Industry Co., Ltd., 4–10–3, Shibaura, Minato-ku, Tokyo, 108–8551 Japan 2Ocean Research Department, Japan Marine Science and Technology Center, 2–15, Natsushima-cho, Yokosuka, 237–0061 Japan ( Received 13 June 2001, Accepted for publication 26 October 2001 )
Abstract: In the present study, a simple and efficient method for estimating frontal positions of the Kuroshio extension (KE) is proposed using relationship between meridional shifts of the KE and acoustic travel time propagating through the SOFAR channel. Effectiveness of the proposed method is estimated by sound propagation simulation using the temperature and salinity fields from observations in the KE, and demonstrates propriety of this method. Applying this method to in situ ocean acoustic tomography data in the KE region in summer 1997 provides the proper estimates of the KE positions. This simple method may be utilized in determining ‘‘initial guess of the KE position’’ and ‘‘reference sound speed field’’ that are necessary for ocean acoustic tomographic inversion which is much more complicated and time-consuming data analysis.
Keywords: Ocean acoustic tomography, Kuroshio extension, SOFAR channel, Acoustic front PACS number: 43.30.Pc
time between acoustic transceivers, using the dependency 1. INTRODUCTION of sound speed upon temperature, salinity, pressure and The Kuroshio flows along the East China sea and ocean currents. channels through the Tokara strait, then continues along the Here, in order to utilize the OAT system efficiently, we south coast of Honshu. Finally, it separates from the coast propose a simple method for estimating the KE’s frontal near the Boso peninsula and flows father eastward, forming position using the acoustic travel time variability. Of an inertial jet called the Kuroshio extension (KE). Figure 1 course one can derive the frontal position from a shows the map of the study area indicating the current path temperature field obtained by three-dimensional tomo- of the Kuroshio. The KE is the boundary between the cold graphic inversion, but this method tends to be too water mass of the mixed water region and the warm water complicated to efficiently analyze the field. In Section 2, mass of the subtropical region. The position of the KE we first show that acoustic signals propagating through the changes with various time scales longer than a few days. sound fixing and ranging (SOFAR) channel, which exists Recently, the KE variability has been studied using the near 1,000 m deep in mid-latitudes [4], are useful in satellite remote sensing actively [1,2]. Satellite remote detecting meridional variability of the KE position. Also in sensing enables us to collect ocean surface data both this section, we developed a method for estimating frontal rapidly and globally. Nevertheless, only in situ observa- positions in case of the following three conditions; 1) the tions, such as thermometer, current meter, etc., can provide OAT section has only one intersection point with the KE; direct subsurface information. In particular, observation 2) stable averaged sound speeds in the SOFAR channel methods using underwater acoustic techniques have been both in the mixed water and the subtropical regions are developed for large scale subsurface observation. known; and 3) There are no huge warm/cold eddies on the Ocean acoustic tomography (OAT) [3] is one of the OAT section. This estimation method is evaluated using underwater acoustic techniques and estimates temperature sound propagation simulations in which observed tempera- and current velocity fields by measuring accurate travel ture, salinity and pressure fields are used in Section 3. In Section 4, this method was applied to the data that were *e-mail: [email protected] obtained from the OAT field experiment during the
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the temperature front in the depth of the SOFAR channel, because sound speed mainly depends on temperature in mid-latitudes. Although the flow of the KE does not reach 1,000 m deep, difference of the sound speed between north and south of the KE is evident at the depth (Fig. 2b). Therefore, it is expected that majority of meridional variabilities across the KE may be estimated from the variation of the sound speed around the depth of the SOFAR channel. In the present study, we thus develop a method that can detect the KE positions from the acoustical signal through the SOFAR channel only. Figure 3 shows an example of the OAT data, i.e., arrival pattern, representing the characteristic of the long- range acoustical signal propagation. The last peak exhibit- ing the highest level is the signal that propagated through the SOFAR channel. This signal can be received stably because the transmission loss is the smallest; influence of reflection in the surface layer to this signal is smallest; and the length of the path is shortest. It is thus highly efficient to use the SOFAR travel time with respect to the signal detection of the KE’s frontal positions. Fig. 1 The map of the study area indicating the current path of the Kuroshio and the observation network of the OAT experiment (July–Sept., 1997). T1–T5 are the 2.2. Method tomography transceiver positions. The averaged sound speed in the SOFAR channel (ASSC) is defined as the value of dividing the distance between transceivers by the acoustic travel time through summer 1997 in the KE region. This demonstrated the the SOFAR channel. Therefore, ASSC values in the same efficient estimation of the KE’s frontal positions and their water region are almost constant. The ASSC in the OAT temporal variation. A summary of the results and some section that crosses the KE should have a value between remarks are given in Section 5. the ASSC of the mixed water region and that of the 2. METHOD FOR ESTIMATING FRONTAL subtropical region. POSITIONOF KE According to the above hypothesis, the KE’s frontal position can be estimated as follows; 1) after removing 2.1. Characteristics of Sound Speed Field in KE disturbances due to the sway of the mooring system, the Region acoustic travel time through the SOFAR channel that have Here, characteristics of sound speed field in the KE maximum acoustic energy is calculated, and it is defined as region were examined using conductivity, temperature and the SOFAR channel passage time; 2) the ASSCnðtÞ is depth (CTD) data taken during the cruise of R/V ‘‘Mirai’’ calculated by dividing the distance between transceivers Ln in July 2000. Based on this analysis we developed a simple by the SOFAR channel passage time, where subscript n is method to estimate the KE’s frontal positions from the the OAT section number and t is the observation time; 3) OAT data. Figure 2a shows a cross section of a sound the ASSC derived from the OAT section that includes only speed field between 30 N and 40 N along 152 300E. The the water mass of the subtropical (mixed water) region is sound speed is calculated from the CTD data using the defined to be ASSCS (ASSCM), then is selected among the sound speed equation of Del Grosso [5]. The KE front all ASSCnðtÞ values derived from 2); 4) the distance of the between 34 N and 35 N is formed at a water mass KE position from the southern transceiver location may be boundary, i.e., north of the KE is the mixed water region, derived as follows; and south of the KE is the subtropical region. The depth of ASSC ðtÞÀASSC the SOFAR channel (sound speed) in the subtropical region KEF ¼ n M L : ð1Þ n À n is greater (faster) than that in the mixed water region. ASSCS ASSCM
Structure of the sound speed field and depth of the SOFAR This equation indicates the ratio between the area of ASSCS channel have sharp transition across the KE from north to and that of ASSCM across the KE. In other words, this south which is referred to as an ‘‘acoustic front’’. The corresponds to the ratio between areas associated with position of the acoustic front almost coincides with that of warm and cold water regions along the section.
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Fig. 2 a) Vertical sections of sound speed field between 30 N and 40 N along 152 300E computed from CTD data. The sound profiles between 28 N and 30 N and between 40 N and 42 N (dash line regions) are filled with the sound speed profile at 30 N and 40 N, respectively. Open circles connected by straight line indicate the section of sound propagation simulation which consists of sound source (south) and receiver (north). The contour interval is 5 m/s; b) Variation of sound speed at 1,000 m deep along 152 300E. The dashed curve indicates the ideal sound speed profile, which consists of a linear decrease from south to north at the KE position and constant values north and south of the KE front.
3. EVALUATIONOF METHOD USING tally and 0–5,000 m (data interval is 10 m) vertically, and SOUND PROPAGATION SIMULATION the bottom topography is assumed to be flat (Fig. 2a). Here, in order to let the whole OAT section L (5 ¼ 555:27 km) 3.1. Sound Propagation Simulation be included in the subtropical region, we artificially expand Effectiveness of the proposed method can be evaluated the section southward; the sound profile at 30 N is added to using relationships between meridional variability of the the section for 2 corresponding to 12 points with 1/6 KE and the ASSC. In this section, using the observed CTD interval from the southern edge of the observed section. data, we calculate the travel time shifting the OAT section Similarly, northern section is expanded by adding the L relative to the KE. This enables us to examine sound speed profile at 40 N. The travel time was relationships between the KE’s frontal positions and the computed, shifting the section L indicated by open circles ASSC for the simple case where the section has only one with a straight line in Fig. 2a from the southern side to the intersection point with the KE. northern side of the whole section by every 1/6 . This The sound speed field used in this computation is means that the frontal position of the KE shifts southward 28 N–42 N (data interval is 1=6 ¼ 18:509 km) horizon- along the OAT section L by 1/6 . This calculation was
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Fig. 3 Example of the arrival pattern, i.e., OAT data derived using two 200 Hz acoustic transceivers which are in the SOFAR channel. The depths of the Fig. 4 The ASSC versus sound source position (corre- transceivers are 1,200 m and 1,150 m, respectively. sponding to the position of the KE across the OAT The distance between the transceivers is 974 km. The section). vertical axis is normalized by the maximum signal. The horizontal axis is the relative travel time of the arrival pattern. the mixed water region, i.e., the sound source exists between 35 N and 37 N. The difference of 4.2 m/s between the ASSC value in the tropical region (1,481.5 m/s) and performed using the acoustic ray theory [6] under the that in the mixed water region (1,477.3 m/s) corresponds to following conditions; the sound sources and receivers are 1.065 s in terms of the SOFAR channel passage time for the set up at 1,000 m deep; the range of vertical launch angle is length of the OAT section L. The transition region from the from À5 through þ5 with the angle interval is 0.01 . subtropical region to the mixed water region, where the KE The calculation using the acoustic ray theory has no exists in the OAT section L, the relationship between the level information of acoustic energy, while eigenrays sound source position corresponding to the position of the propagating through the SOFAR channel arrive at a KE in the OAT section L and the ASSC is approximated by receiver in a group. Therefore, the SOFAR channel passage the straight line. However, Fig. 4 also indicates the time was decided using the number of eigenrays that exist gradient of the ASSC changes near 31 400N due to the in the constant period as a substitute for the level of the existent of the warmer waters both sides of the KE acoustic energy. Here, 20 ms was selected as the constant corresponding to the higher sound speed regions near 33 N period, and moving the period by 1 ms, the number of the and 35 500N in Fig. 2a. eigenrays was counted. Then, the central time of the period The estimate accuracy of the KE position using this when the maximum number of eigenrays arrives was method is investigated as follows. The values of ASSCS and defined as the SOFAR channel passage time. Finally, the ASSCM were set to the simulated values (1,481.5 m/s and ASSC was calculated using Eq. (1) with this SOFAR 1,477.3 m/s) mentioned above, respectively. Figure 5 channel passage time and the length of the OAT section L. shows the estimated frontal position of the KE using the ASSC values within the area where the sound source 3.2. Results position is between 30 N and 34 N, i.e., the KE is located Figure 4 shows a plot of the ASSC versus the sound in the OAT section. The mean KE position is estimated at source position. Note that this corresponds to the position 34 200N where the meridional variation of the sound speed of the KE in the OAT section. In case that the whole OAT has sharp transition, i.e., the center position of the acoustic section is included only in the subtropical region, i.e., the front at 1,000 m deep from Fig. 2b. However, Fig. 5 sound source exists between 28 N and 29 N, the ASSC indicates that the KE position estimated somewhat north- values remain steady at about 1,481.5 m/s. As the OAT ward from 34 200N over the entire section using the present section is shifted northward, the area of the mixed water method. This is because the sound speed does not slow region in the section increases, and the ASSC decreases to down linearly from south to north due to the existent of about 1,477.3 m/s. After that, the ASSC value becomes warm water parts north (range of 1 mainly on 33 N) and steady again, when the whole OAT section exists only in
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Fig. 5 The estimated mean KE position using the ASSC values within the area where the sound source (receiver) position is between 30 N (35 N) and 34 N (39 N). south (range of 300 mainly on 35 500N) of the KE front pentagon, which are indicated as T1–T5 in Fig. 1 [7]. The which causes sound speed increase. The additional curve in transceivers T1 and T2 were distributed in the mixed water Fig. 2b indicating the ideal sound speed profile, which region slightly north of the KE, and the transceivers T3, T4, consists of a linear decrease from south to north at the KE and T5 were arranged in the subtropical region southern position and constant values north and south of the KE side of the KE. The two-days moving average operation front, shows the higher sound speed at 1,000 m deep both was performed on the data to remove the tidal effect. of the warm water parts. Consequently, the ratio of warm Figure 6 indicates four time series of the ASSCs derived water along the OAT section increases, then the position of from the OAT section corresponding respectively to that the KE front is estimated northward from 34 200N. solely in the mixed water region (T1–T2), those across the The estimated frontal position of the KE includes both KE (T1–T5 and T2–T4), and that solely in the subtropical systematic and random errors. The systematic error is the region (T3–T5). The ASSC value in the mixed water region bias component by which the estimated frontal position of (T1–T2) indicates large variability ranging between the KE is always estimated in the north due to the warm 1,474.8 m/s and 1,477.5 m/s, while that in the subtropical water parts existing in the south side of the KE front. region (T3–T5) is almost constant with a value 1,482.3 m/s. Although the magnitude of the bias is influenced by the The value with the section T1–T5 across the KE about angle of the OAT section and the KE, the bias can be 144 E has large temporal variation between 1,479.4 m/s estimated at about 100–200. However, as the KE position at and 1,481.9 m/s, while the variability along the section T2– the surface usually exists in the north than that at the T4 across the KE about 150 E is smaller, i.e., 1,480.7 m/s– SOFAR channel depth, the estimated frontal position of the 1,481.4 m/s. In the western part of the KE (T1–T5), the KE at the SOFAR channel depth gets closer to that at the ASSC increases from Aug. 1 through Aug. 22, while it then surface. tends to decrease afterwards. On the other hand, in the While, the random error is caused by the existence and eastern part of the KE (T2–T4), the ASSC has a small the size of the small warm and/or cold water parts at the oscillation till it begins to increase from Sept. 10. OAT section, which seems to shift the estimated frontal position of the KE at the SOFAR channel depth to the 100– 200 north (south) side. In addition, under the condition of this simulation, the rms error depends on the setting of ASSCS and ASSCM is calculated with 32.2 km/m/s using Eq. (1) and the product of the variance of the ASSC data (0.12 m/s) used for the setting of ASSCS and ASSCM and the rms error is estimated at 3.9 km. Even if the systematic and random errors are considered, supposing that the width of the KE is about 50 km, this accuracy is sufficient to locate the position of the KE only from the OAT data along one section. 4. ESTIMATIONOF KE USINGOAT DATA In this section, we use the method proposed here to derive the ASSC using the OAT data collected during a field experiment in the KE region from July to September in 1997. Five acoustic transceivers were arranged on a Fig. 6 Time series of the ASSC at each OAT observation section.
94 T. SHINKE et al.: ESTIMATES OF KE USING OAT
Fig. 7 Estimated position of the Kuroshio axis. Asterisks indicate tomography transceiver positions and open circles connected by dashed line show the estimated positions of the Kuroshio axis on the observation line.
Figure 7 shows the estimated position of the KE from position of the KE instead of this method for these sections. Eq. (1). The ASSC and ASSC were set to 1,482.5 m/s and S M 5. DISCUSSION AND CONCLUSIONS 1,476.7 m/s, respectively. The ASSCS is the mean value of the all ASSC data along the three OAT sections (T3–T4, In the present study, a method for estimating the frontal T3–T5, and T4–T5) in the subtropical region. While the position of the KE, which uses the averaged sound speed in ASSCM is determined from the ASSC data along the OAT the SOFAR channel (ASSC) between the transceivers, was section (T1–T2). However, as the small cold water part proposed. The acoustic travel time along the section across exists at the section T1–T2 from August 2 to September 10 the KE meridionally contains the information of the ratio of from satellite altimeter data, the ASSCM is the mean value the warm (the subtropical) and cold (the mixed water) of the ASSC data along the section during the periods from regions. The method proposed here provides the frontal July 20 through August 1 (day ¼ 1{13 in Fig. 6) and that position of the KE, which forms the boundary of the warm from September 11 to 20 (day ¼ 53{63 in Fig. 6) when the and the cold regions, by estimating the ratio of the two OAT section seems to be in the mixed layer region without regions using this acoustic information. To evaluate the the small cold water part. The position of the KE is effectiveness of the estimation method, we conducted the estimated at the sixOAT sections T1–T3, T1–T4, T1–T5, sound propagation simulation using the observed CTD T2–T3, T2–T4 and T2–T5 across the KE. Over the entire data, and demonstrates that the frontal position of the KE observation period, we can see the KE flowed through the can be estimated within an error that is much smaller than northern part of the OAT network between 34 N and 36 N. the width of the KE. In addition, we applied this method to The positions of the KE near 145 E that is the west side of the in situ OAT data gathered during the OAT experiment the OAT network along T1–T5 and that near 149 E have in 1997, and estimated KE positions for the entire period of large temporal variations, where the KE meander occurs the experiment. Consequently, the estimated KE positions frequently. However, as the sections T1–T3 and T2–T5 are located between 34 N and 36 N which are the proper have two intersection points with the KE, the OAT analysis KE positions. using inverse method [8] is necessary to estimate the The proposed method is effective when the OAT
95 Acoust. Sci. & Tech. 23, 2 (2002) transceiver network is arranged in a way such that one were not set up at the depth of minimum sound speed and section of the network is deployed only in the subtropical vertical amplitude of eigenray is fixed at 200 m mainly on region and the other is only in the mixed water region. the depth of the minimum sound speed. Therefore, as the Here, we investigate how to determine the ASSCS and ASSC and the averaged minimum sound speed can be ASSCM using the other methods when the network is not considered to be almost equivalent, ASSCS and ASSCM can arranged shown as above. Same as the method in Section be obtained from a sound speed profile derived from in situ 3.1, we calculated the averaged sound speed in the area CTD data or from historical oceanographic databases. surrounded with the length of the OAT section L In future, the position of the KE estimated by this horizontally and the range of 200 m mainly on the depth method can be used for a precursor information to the OAT of the minimum sound speed vertically shifting the OAT inversion. That is, using this method, we may obtain a section L relative to the KE. This averaged value is referred reference sound speed field even in the KE region where to as an ‘‘averaged minimum sound speed’’. Figure 8a the homogeneous structure cannot be assumed horizon- shows a plot of the averaged minimum sound speed versus tally. Consequently, nonlinear errors in the OAT analysis the sound source position. There is a good agreement should be decreased. Furthermore, if the data can be between Fig. 4 and Fig. 8a. Figure 8b shows the differences transmitted in realtime, this method can be applied to of the ASSC and the averaged minimum sound speed, monitor the Kuroshio variability quickly, due to its large which range from À0:05 m/s through À0:25 m/s. The shortening of the analysis time. average of the differences is À0:105 m/s and the standard deviation is 0.05 m/s. The magnitude of the averaged ACKNOWLEDGMENT minimum sound speed is slightly larger than that of the The authors express their special thanks to Dr. Humio ASSC, however it does not agree with the ASSC Mitsudera of IPRC and Dr. Jun Suwa of Chiba University completely because the sound source and the receiver for their useful comments and suggestions. This study was done as one of the activities of joint research program of Oki Electric Industry Co., Ltd. and Japan Marine Science and Technology Center. REFERENCES [1] K. Ichikawa and S. Imawaki, ‘‘Life history of a cyclonic ring detached from the Kuroshio Extension as seen by the Geosat altimeter’’, J. Geophys. Res., 99, 15953 (1994). [2] J. Suwa, Y. Sugimori, H. Fukushima and P. Thadathil, ‘‘Wave propagation in the north Pacific from Geosat altimeter data using time-space correlation method’’, J. Adv. Mar. Sci. Tech. Soc., 1, 80 (1995). [3] W. H. Munk and C. Wunsch, ‘‘Ocean Acoustic Tomography— A scheme for large scale monitoring—’’, Deep Sea Res., 26, 123 (1979). [4] R. J. Urick, Principles of Underwater Sound, 3rd ed. (McGraw- Hill, New York, 1983), p. 423. [5] V. A. Del Grosso, ‘‘New equation for the speed of sound in natural waters (with comparison to other equations)’’, J. Acoust. Soc. Am., 56, 1084 (1983). [6] W. H. Munk, P. Worcester and C. Wunsch, Ocean Acoustic Tomography (Cambridge University Press, New York, 1995), p. 433. [7] G. Yuan, I. Nakano, H. Fujimori, T. Nakamura, T. Kamoshida and A. Kaya, ‘‘Tomographic measurements of Kuroshio extension mender and its associated eddies’’, Geophys. Res. Lett., 26, 79 (1999). Fig. 8 a) Same as Fig. 4 but for the averaged minimum [8] K. Aki and P. Richards, Quantitative Seismology Theory and sound speed; b) The differences of the ASSC and the Methods (Freeman, San Francisco, 1980), p. 932. averaged minimum sound speed.
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