Comparison of Kuroshio Surface Velocities Derived from Satellite Altimeter and Drifting Buoy Data

Transcription

1 Journal of Oceanography, Vol. 54, pp. 115 to Comparison of Kuroshio Surface Velocities Derived from Satellite Altimeter and Drifting Buoy Data HIROSHI UCHIDA 1, SHIRO IMAWAKI 2 and JIAN-HWA HU 3 1 Department of Earth System Science and Technology, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816, Japan 2 Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka 816, Japan 3 Department of Oceanography, National Taiwan Ocean University, Keelung 202, Taiwan, R.O.C. (Received 19 September 1997; in revised form 1 November 1997; accepted 1 November 1997) Sea-surface geostrophic velocities for the Kuroshio region calculated from TOPEX/ POSEIDON altimetry data together with in situ oceanographic data are compared with surface velocities derived from drifting buoy trajectories. The geostrophic velocities agree well with the observed velocities, suggesting that the Kuroshio surface layer is essentially in geostrophic balance, within measurement error. The comparison is improved a little when the centrifugal acceleration is taken into account. The observed velocities are divided into the temporal mean and fluctuation components, and the partitioning of velocities between these two components is examined. For the Kuroshio region, most of the fluctuation components of the velocities derived from drifting buoys are found to be positive. This result suggests that Eulerian mean velocities for the Kuroshio region estimated from drifting buoy data tend to be larger than actual means, due to the buoy s tendency to sample preferentially in the high-velocity Kuroshio. Keywords: TOPEX/ POSEIDON, satellite altimeter, drifting buoy, geostrophic velocity, gradient-wind velocity, Kuroshio. 1. Introduction Satellite altimetry has been recognized as one of the most useful methods to observe variations of the sea-surface topography and velocity fields globally, with high spatial resolution at short time intervals. A microwave radar altimeter on board a satellite measures the sea-surface height (hereafter SSH) which consists of large-amplitude undulations of the geoid and small-amplitude undulations of the sea-surface dynamic topography (SSDT). In practice, however, only the temporal fluctuation component of the SSDT can be accurately determined because the present geoid model is not accurate enough for the SSDT to be extracted from the SSH (Imawaki, 1995). In order to determine the absolute SSDT and geostrophic velocity fields, the temporal mean SSDT lost in the analysis must be determined by some other method. Verification of the altimeter data has been done mostly for the SSDT, but several studies have also been done to verify the altimetry-derived geostrophic velocity field. Willebrand et al. (1990), Ichikawa et al. (1995), and Yu et al. (1995) compared two-dimensional velocity fields derived from altimetry data with surface velocity fields derived from drifting buoy data. In their comparison, altimetry-derived velocity fields were considerably smoothed in time and space with optimal interpolation to obtain gridded data, and observed velocity fields were also smoothed. Ebuchi and Hanawa (1995) compared cross-track velocity anomalies (i.e., departures from some temporal mean) derived from altimetry data with velocity anomalies obtained from repeated shipboard acoustic Doppler current profiler (ADCP) measurements across the Kuroshio. In their comparison, the ship track was oblique to subsatellite tracks and altimetry-derived velocities had to be interpolated with reference to the ship track position. Those previous works are described in detail in the discussion section below. It is important to avoid smoothing in time and space, especially for the Kuroshio region, where fluctuations with short time scales and small spatial scales are large. To our knowledge, no studies have been carried out on a nearly instantaneous comparison between altimetry-derived velocities and observed velocities without notable smoothing in space. The altimetry satellite TOPEX/POSEIDON (hereafter T/P) has been collecting SSH data since late September 1992 (Fu et al., 1994). A group entitled Affiliated Surveys of the Kuroshio off Cape Ashizuri (ASUKA) carried out oceanographic surveys along a subsatellite track of T/P crossing the Kuroshio south of Shikoku, Japan (Fig. 1), during (Imawaki et al., 1997a, b). Horizontal SSDT profiles estimated from in situ oceanographic data along the ASUKA line were combined with fluctuation SSDT profiles derived from the T/P data, in order to obtain the temporal mean SSDT profile. The sum of the mean SSDT profile so obtained with each of the fluctuation SSDT profiles gave accurate absolute SSDT profiles along the Copyright The Oceanographic Society of Japan. 115

2 Fig. 1. Trajectories of surface drifting buoys (thin lines) in the WOCE-TOGA SVP during September 1992 through November 1995 and their estimated velocities (arrows) on the ASUKA line (thick line). The open circle at 29 N indicates the location of Ocean Data Buoy No. B The triangle at the northern end of the ASUKA line shows the tide gauge location. See text for label A near the northern end. ASUKA line, which compared very well with the individual in situ SSDT profiles obtained repeatedly (Uchida and Imawaki, in preparation). In the present paper we compare cross-track surface geostrophic velocities, derived from the above-mentioned absolute SSDT profiles, with surface velocities determined from drifting buoy trajectories. Additionally, we take the centrifugal acceleration into account in this comparison. Observed velocities are divided into temporal mean and fluctuation components, and the partitioning of velocities between these two components is examined; the result suggests that there is a sampling problem for drifting buoy data from the Kuroshio region. The present paper aims to verify the accuracy of the absolute SSDT derived from the T/P altimeter data and to examine how geostrophy holds at the sea surface in the Kuroshio region. 2. Data and Data Processing The altimeter data used in the present study were taken from the T/P Merged Geophysical Data Record (M-GDR), which consists of scientific data from the National Aeronautics and Space Administration (NASA) altimeter system, TOPEX, and from the Centre National d Etudes Spatiales (CNES) altimeter system, POSEIDON. We used data from subsatellite pass No. 112, which is almost identical with the ASUKA line (Fig. 1), with 10-day repeat cycles from September 1992 to April 1996 (Cycles 1 to 132). The sampling interval was 1 s, corresponding to 6.2 km along the subsatellite track. We applied standard geophysical data corrections (Benada, 1993) as follows. The SSH was corrected using electromagnetic bias, ionospheric, dry and wet tropospheric, and inverse barometer corrections. The solid earth and pole tides were removed. These correction data were provided in M-GDR. The CSR3.0 tidal model (Eanes and Bettadpur, 1995) was used to remove the ocean tides. The JGM-3 gravity model (Tapley et al., 1996) was used to determine the satellite orbit height. We corrected for an error in the algorithm used in correction for TOPEX oscillator drift, which was found in summer The relative bias between TOPEX and POSEIDON altimeters was not taken into account, because it is estimated to be fairly small (less than 2 cm; Haines, personal communication, 1996). We processed the data to obtain fluctuation SSDT, using the collinear method (Cheney et al., 1983). The effect of the cross-track and along-track geoid gradients was removed by using the mean sea-surface data provided in M- GDR. After this correction, the SSH data were collocated onto a set of latitudes and longitudes during Cycle 48, which was chosen as a reference. The temporal mean SSH over three years (Cycles 6 to 116) was calculated at each reference point. The fluctuation SSDT was determined by subtracting the temporal mean SSH from the individual SSH for each cycle. To remove small scale measurement errors, the fluctuation SSDT was low-pass-filtered twice along the track with a 3-point Hanning filter with a half power gain at 48 km wavelength. The temporal mean SSDT profile along the track was estimated by a similar method to that of Imawaki and Uchida (1995). At location x and time t, the absolute SSDT ζ(x, t) is written as follows; ζ( x,t)= ζ( x)+ ζ ( x,t) () 1 where ζ( x) is the temporal mean SSDT, and ζ (x, t) the fluctuation SSDT. The absolute profile ζ(x, t) was estimated repeatedly from a combination of moored current meter data and repeated hydrographic data along the ASUKA line, referred to the tide gauge data (see Fig. 1 for location). The fluctuation profile ζ (x, t) was derived from the T/P altimeter data together with the tide gauge data which were used to improve the SSDT profiles near the coast (Uchida and Imawaki, 1996). Using those profiles, the unknown temporal mean SSDT profile ζ( x) was estimated from Eq. (1), using the least-squares method. The sum of the resulting mean SSDT profile and a fluctuation SSDT profile from the T/P altimeter data gave a very accurate individual absolute 116 H. Uchida et al.

3 SSDT profile (Uchida and Imawaki, in preparation). Cross-track surface geostrophic velocities are calculated from the along-track gradient of this absolute SSDT profile, with a horizontal resolution of 12.4 km. The shorter interval of finite difference gives sharper velocity structures, but noisier velocity profiles. The chosen interval of 12.4 km is a compromise with stable estimates. The geostrophic velocities obtained every 10 days are interpolated to the time when a drifting buoy crossed the ASUKA line. Drifting buoy data have been collected by the World Ocean Circulation Experiment-Tropical Oceans Global Atmosphere (WOCE-TOGA) Surface Velocity Program (SVP), using the ARGOS system to locate positions of freely-drifting surface buoys. The data used in the present study were quality-controlled and optimally interpolated to uniform six-hour interval trajectories (Hansen and Poulain, 1996). All buoys were attached to drogues centered at 15-m depth and transmitted signals continuously. The velocities of drifting buoys are computed from the six-hourly position data by finite difference, and then linearly interpolated onto the ASUKA line. Figure 1 shows the twenty drifting buoy trajectories (thin lines) which are used in this study. The figure also shows the drifting buoy-derived surface velocities (arrows) which are compared with the T/P altimetry-derived geostrophic velocities on the ASUKA line; twenty-eight cases are shown. Here one drifting buoy (No ) has been excluded from the present comparison (and Fig. 1) because the velocity of that drifting buoy changed abruptly near the ASUKA line and its spatial interpolation onto that line is inappropriate. The sea-surface wind data used in the present study were obtained by Ocean Data Buoy No. B21004 off Shikoku, which has been collecting marine meteorological and oceanographic data (Fig. 1). We used the wind data at threehour intervals for three years ( ). These data were low-pass-filtered with a one-day running mean. 3. Results In the present study, we compare the two surface velocities, estimated from the T/P altimeter and drifting buoy data, for the cross-track component (east-northeastward flow). Figure 2 shows the scatter plot of geostrophic velocities (V g ) derived from the absolute SSDT profiles (estimated from T/P altimeter data) against surface velocities derived from the drifting buoy trajectories. Closed circles show the results for velocities associated with the Kuroshio, so judged subjectively on the basis of altimetry-derived geostrophic velocity profiles. The dotted circle shows the result for the velocity labeled A near the northern end of the ASUKA line in Fig. 1, which was observed in the Kuroshio region but located considerably distant from the Kuroshio at that time. Open circles show the results for velocities measured south of the Kuroshio region (south of 31 N), including a fairly Fig. 2. Scatter plot of geostrophic velocities derived from altimeter data against surface velocities derived from drifting buoy data. Closed circles are for the Kuroshio, the dotted circle is for the velocity labeled A in Fig. 1 (see text for details) and open circles are for the region south of the Kuroshio. Twentyeight cases are shown. The correlation coefficient (C.C.) and the slope of the regression line (thick solid line) are also shown. Thin dashed lines represent one standard deviation from the regression line. The rms difference between the two quantities is 16 cm sec 1. strong eastward flow near 25 N (Fig. 1). The agreement of these cross-track velocities is excellent. The correlation coefficient (0.92) is high, the slope (0.92) of the regression line is close to unity, and the rms (root-mean-square) difference (16 cm sec 1 ) between the two quantities is fairly small. This fact suggests that flows in the surface layer of the Kuroshio region and adjacent area are essentially in geostrophic balance. The Kuroshio changes its location and strength temporally. The velocities used in the present comparison were observed opportunistically at the time and location when and where drifting buoys crossed the ASUKA line. Therefore, two interesting questions arise regarding this data sampling. First, what is the partition between the temporal mean and fluctuation components of the observed velocities? If the fluctuation component is small, the altimeter data are not important in the present comparison. Second, can averaged velocities derived from drifting buoys give true longterm Eulerian mean velocities? These questions can be answered with the aid of the altimetry-derived geostrophic velocities, instead of the drifting buoy-derived velocities, because the former are originally formed as sums of mean and fluctuation components as described in the previous section, while the latter are not readily separable into mean and fluctuation components. The first question about the partition of the temporal Kuroshio Velocities from Altimeter and Drifting Buoy 117

4 mean and fluctuation components is answered by their scatter plot, shown in Fig. 3. For the Kuroshio (closed circles), both components are important, although the mean component is a little larger than the fluctuation component in general. For the region south of the Kuroshio (open circles), the fluctuation component is larger than the mean component. Therefore the good comparison shown in Fig. 2 is not only due to accurate estimates of the mean SSDT profile, but also due to those of the fluctuation SSDT profiles derived from altimeter data. Note that for the case of the velocity labeled A in Fig. 1, the mean and fluctuation components have almost the same amplitudes, but opposite signs. The second question about averaged velocities from drifting buoy data is more important. Figure 3 clearly shows that most of the fluctuation components are positive for the Kuroshio region; namely, most of individual total velocities are larger than the mean components there. This is a reflection of the fact that most drifting buoys tend to continue to follow the Kuroshio very well, even if the Kuroshio fluctuates and shifts its location laterally. In other words, drifting buoys are only rarely expected to measure velocities outside of the fluctuating Kuroshio. Therefore, the data from drifting buoys are likely to be biased due to this sampling tendency for the Kuroshio region, especially in the case where the Kuroshio changes its axis temporally. Drifting buoy-derived velocities are not likely to reflect the fact that the Eulerian mean velocity field is weakened and broadened by lateral shift of a strong current. There is only one exception in the present analysis, the velocity labeled A in Fig. 1 and shown by the dotted circle in Fig. 3, which indicates a large negative fluctuation component. This drifting buoy showed a somewhat different trajectory from the others; it followed a small meander of the Kuroshio southeast of Kyushu, approached the ASUKA line, and then escaped from the Kuroshio to enter the bay (Bay Tosa) south of Shikoku (see Fig. 1). As an example of biased Eulerian means, temporal mean velocities estimated from the present drifting buoy data are compared with the temporal mean geostrophic velocities, which were estimated by combining the in situ oceanographic observation data and T/P altimeter data (see the previous section) and are considered as reference velocities. The results for the Kuroshio region are shown in Fig. 4. Here the averages were taken for bins of 24.8 km width along the ASUKA line. Data distribution in time (Fig. 4(a)) shows that more data were obtained in the early half of this three-year period, but some data were also obtained in the latter half; the data distribution is not homogeneous, but Fig. 3. Scatter plot of fluctuation components against mean components of geostrophic velocities derived from T/P altimeter data, following the present data sampling scheme of drifting buoys. Closed circles are for the Kuroshio, the dotted circle is for the velocity labeled A in Fig. 1 and open circles are for the region south of the Kuroshio. Twenty-eight cases are shown. Fig. 4. Eulerian mean velocities derived from drifting buoys in the Kuroshio region. (a) is the data distribution in time (in Julian day from the beginning of 1993) and space along the ASUKA line. (b) is the horizontal distribution of the surface layer velocity. Solid line is the reference three-year Eulerian mean velocity. Open circles and the dotted circle are drifting buoyderived velocities. Closed circles are Eulerian means of drifting buoy-derived velocities within bins of 24.8 km width; vertical bars show their estimated errors. Triangles are threeyear means estimated from combination of the drifting buoy data and fluctuation velocity data from the altimeter. 118 H. Uchida et al.

5 it is acceptable, as shown below. All differences of the mean velocities so obtained (closed circles in Fig. 4(b)) from the mean geostrophic velocities (thick line) are positive and remarkably large; they are as much as cm sec 1. These differences are not due to differences between the drifting buoy velocities and altimetry-derived geostrophic velocities, but due to the data sampling tendency of the drifting buoys mentioned above. This is confirmed by a subsidiary calculation of similar Eulerian means of altimetry-derived velocities with the same data sampling scheme as the drifting buoys, which gives almost the same values as the above-mentioned means. The weak velocity labeled A in Fig. 1 makes a large contribution to reducing the biased Eulerian mean estimates from drifting buoy data in the most coastal bin, centered at N; without this, the estimated mean differs much more from the reference mean. It might be suspected that those departures from the reference mean could be due to the inhomogeneous distribution of drifting buoy data; such results could be obtained if the Kuroshio were stronger in the early half of the three-year period and weaker in the latter half. Indeed, the mean velocity for the most coastal bin is a little larger in the early half than the latter half, and therefore the departure mentioned above (37 cm sec 1 ) may be partly due to the bias of the temporal sampling scheme. But the difference (36 cm sec 1 ) between these two mean velocities during the subperiods would introduce only a small departure (11 cm sec 1 ) from the three-year reference mean, on average, and the results are not seriously affected. No remarkable differences are detected for the other four bins and therefore most departures are not due to bias of the temporal sampling scheme. an example of the estimation of the curvature of the flow. The radius of curvature is estimated assuming a circle through three positions of a drifting buoy which were located immediately before crossing the ASUKA line, 12 hours before that, and 12 hours after that. To avoid large error in the estimates, the drifting buoy positions were lowpass-filtered with a Hamming filter designed to have a half power gain at 80 hour period. From the altimetry-derived geostrophic velocity V g and the radius R of curvature, we compute the surface gradient-wind velocity V gr normal to the ASUKA line, using the relations V g = Ṽg cosα and V gr = Ṽ gr cosα, where α is the angle between the ASUKA line and the local radius of the drifting buoy track. In this example, the radius R is 320 km and the ratio V g /V gr is Figure 5(b) shows the histogram of this ratio for the Kuroshio. The ratio has a mode centered at The radius R is estimated to be 200 to 600 km for most cases. Figure 6 shows a comparison of the surface gradientwind velocities estimated from the altimeter data with the surface velocities derived from drifting buoy trajectories, as a revision of Fig. 2. Agreement is a little improved in comparison with the geostrophic velocity case. In particu- 4. Sources of Discrepancy Agreement between the geostrophic velocities and the observed velocities is excellent (Fig. 2), but the slope of the regression line is slightly smaller than unity. As can be seen from the drifting buoy trajectories in the Kuroshio (Fig. 1), this may be due to the effect of centrifugal acceleration. The curvature of the flow can be estimated from the drifting buoy trajectories, and therefore gradient-wind velocities can be estimated. The cross-stream momentum balance is written as follows; fṽgr + Ṽ gr 2 R = g ζ n = fṽg 2 ( ) where f is the Coriolis parameter, g the acceleration due to gravity, ζ the SSDT, n the distance normal to the stream, R the radius of curvature, and Ṽgr and Ṽg are the down-stream components of the gradient-wind velocity and geostrophic velocity, respectively. The radius R is positive (negative) when the flow is cyclonic (anticyclonic). Figure 5(a) shows Fig. 5. Ratio of V g /V gr for the Kuroshio. Panel (a) shows an example of estimating a radius of curvature. Closed circles indicate six-hourly positions of a drifting buoy. Solid line is the ASUKA line. The center of curvature (open circle) is estimated by using three drifting buoy positions. Selected bottom topography contours (m) are also shown. (b) is the histogram of the ratio V g /V gr. Twenty-one cases are shown. Kuroshio Velocities from Altimeter and Drifting Buoy 119

6 Fig. 6. Same as Fig. 2, except for gradient-wind velocities. The rms difference is 16 cm sec 1. lar, the slope (0.96) is much closer to unity. The correlation coefficient (0.93) is slightly improved, although the rms difference (16 cm sec 1 ) between the two quantities is almost the same as the previous comparison. The sea-surface velocities estimated from the altimeter data compare well with the surface velocities obtained by drifting buoys. There are, however, some differences between them. Possible sources of this discrepancy are discussed below. First we discuss errors in drifting buoy measurements. Satellite ranging with the ARGOS system can locate positions globally within a 1-km radius (Niiler et al., 1995). Therefore the rms error of velocities derived from the sixhour averaged drifting buoy trajectory is estimated to be less than 7 cm sec 1. The drifting buoy has wind-produced slip of as much as 0.1% of wind speed (Niiler et al., 1995). Ocean Data Buoy B21004 (Fig. 1) south of Shikoku provides an estimate of the three-year ( ) mean surface wind speed of 5.6 m sec 1. Therefore the wind-produced slip in this region is estimated to be less than 1 cm sec 1 on average. The overall error of the present drifting buoy-derived velocity is estimated to be about 7 cm sec 1. Second we discuss possible errors of the T/P altimetryderived geostrophic velocities. Measurement errors of SSH with relatively large horizontal scales hardly affect geostrophic velocities. The total SSH measurement error with small horizontal scale is estimated to be 2.1 cm (including instrument noise of 1.7 cm, ionospheric correction error of 0.5 cm and wet tropospheric correction error of 1.1 cm; Fu et al., 1994), with decorrelation distances of km (Tapley et al., 1994). The rms error is reduced to 1.1 cm by applying an along-track low-pass filter, if we assume that the error is white noise. Therefore the rms error of the altimetry-derived geostrophic velocities is estimated to be 17 cm sec 1 in finite difference over 12.4 km. This estimated error may be an overestimate, however, because the rms error of the comparison (Fig. 2) is not much improved, as would be expected when a finite difference distance is chosen to be considerably larger than 12.4 km; the larger finite difference distance should give a smaller estimated error if the altimeter noise is white. The assumption of white noise for the altimeter measurement error may thus not hold. In addition, the mean geostrophic velocity profile also includes an error. Therefore the overall error of the altimetry-derived velocity is estimated to be about 17 cm sec 1. Finally, the discrepancy may be partly due to the difference of sampling scheme in time and space between the T/P altimeter and drifting buoy data. The present altimeter data are instantaneous data at 10-day interval with 12.4 km resolution in space, while the drifting buoy data give, in principle, nearly instantaneous velocities at a selected spot. So the interpolated altimetry-derived velocities may not have resolved fluctuations with short time scale and small spatial scale, which the drifting buoy-derived velocities did resolve. This might be the reason why the slope (0.96) of the regression line is still slightly smaller than unity in the comparison with gradient-wind velocities (Fig. 6), and why the amplitudes of variation (56 cm sec 1 in standard deviation) of the altimetry-derived velocities is slightly smaller than that (58 cm sec 1 ) of the drifting buoy-derived velocities. It may also be partly due to the smoothing of the altimeter data using the Hanning filter (see Section 2). These error estimates show that the discrepancy (16 cm sec 1 in rms difference) found in the present comparison (Figs. 2 and 6) is smaller than the overall measurement error, including a rather large altimeter measurement error. Therefore it is concluded that the T/P altimetry-derived geostrophic velocities as well as the gradient-wind velocities agree with the observed velocities, within measurement error. In fact, no departure from geostrophy is detected in the surface layer of the Kuroshio region and the adjacent area. One possible major source of departure from geostrophic flow is the wind-driven current. For the drifting buoy, the wind-driven current at 15 m depth is statistically estimated to be 0.5% of wind speed and 68 to the right of the wind vector in the northern hemisphere (Niiler and Paduan, 1995). If we use the mean wind speed at the Ocean Data Buoy, the wind-driven current at 15 m depth is estimated to be about 3 cm sec 1 on average. There are other probable nongeostrophic currents, including inertial oscillations, tidal currents and internal waves, which are not discussed here. 5. Discussion In the previous section, the sea-surface geostrophic velocities and gradient-wind velocities estimated from the altimeter data compare well with the surface velocities obtained by drifting buoys. Those results are compared with 120 H. Uchida et al.

7 previous studies as follows. In most previous studies for verification of the altimetry-derived velocities, fluctuation SSDT s from altimeter data were combined with temporal mean SSDT which is approximated with geopotential anomalies determined from hydrographic observations, in order to obtain surface velocity maps (Willebrand et al., 1990; Ichikawa et al., 1995; Yu et al., 1995). Yu et al. (1995) compared geostrophic velocities derived from T/P altimeter data with surface velocities derived from carefully selected drifting buoy data for the western tropical Pacific. The comparison showed a surprisingly good agreement; for the zonal (meridional) component of velocities, the correlation coefficient was 0.92 (0.76) and the rms difference was 5 (5) cm sec 1. Their velocity range (from 40 to 40 cm sec 1 ) was a little smaller than the present study (from 50 to 150 cm sec 1 ). In strong-current regions like the Kuroshio (Ichikawa et al., 1995) and the Gulf Stream Extension (Willebrand et al., 1990), however, comparison of surface velocities derived from Geosat altimeter data with drifting buoy data showed that altimetry-derived velocities were weaker than drifting buoy-derived velocities; the slope of the regression line was 0.41 for the Kuroshio and 0.36 for the Gulf Stream Extension regions. These systematic differences are considered to be the consequence of both the objective analysis procedure, which essentially removed all variabilities of scales less than O (100 km) from the altimetric map, and the error of the mean SSDT field. The comparison was improved when the drifting buoy data were smoothed at the same scale as the altimetric maps for the Gulf Stream Extension region; the correlation coefficient was 0.81 and the rms difference was 10 cm sec 1 for the zonal component of velocities, which ranged from 40 to 50 cm sec 1 (Willebrand et al., 1990). Geostrophic velocity anomalies derived from T/P altimeter data were compared with surface velocity anomalies derived from shipboard ADCP data for the Kuroshio region (Ebuchi and Hanawa, 1995). The result showed that altimetry-derived velocity anomalies were smaller than ADCPderived velocity anomalies; the slope of the regression line was This is considered to be a consequence of the fact that the ship track was oblique to the subsatellite tracks and therefore the altimetry-derived velocities had to be interpolated with respect to the ship track position. The present study differs from those previous studies in the following two points. First, the absolute SSDT profiles are used after a careful calibration with the in situ oceanographic observation data, including moored current meter data at mid-depth. Second, altimetry-derived geostrophic velocities are compared with observed velocities for a strong current with least smoothing. The effect of the centrifugal force becomes larger as the current becomes stronger. In the Gulf Stream meander, the ratio of the geostrophic velocity to the gradient-wind velocity (V g /V gr ) is typically 1 ± 0.1 (Liu and Rossby, 1993). In the present study, the ratio is typically This relatively stable value of less than unity is explained by the fact that the Kuroshio is located north of the local stationary anticyclonic warm eddy off Shikoku (Hasunuma and Yoshida, 1978), as well as the fact that the geometry of the continental slope favors the anticyclonic flow. The problem of bias of Eulerian mean velocities derived from drifting buoy trajectories is rather serious for the Kuroshio region. Estimated means are times as large as the actual three-year mean velocities in the present example (Fig. 4), although the number of the data used is not sufficiently large to be sure of the statistical significance. This effect has not been taken into account in previous studies of velocity statistics based on drifting buoy data for the Kuroshio (e.g., Hsueh et al., 1996; Maximenko et al., 1997). Problems for estimating Eulerian mean velocities from Lagrangian data to describe the general circulation have been pointed out (Freeland et al., 1975; Davis, 1991; Poulain et al., 1996). The situation could be improved if the fluctuation component of velocity is known at the time when the drifting buoy measures the Kuroshio. For example, T/P altimeter data can give a time series of the fluctuation component of the geostrophic velocity without any in situ oceanographic observation data. The unknown mean velocity can be estimated in the same way as Eq. (1) for velocity instead of SSDT. The mean velocities so estimated (after averaging) are shown by triangles in Fig. 4(b). Generally, the newly estimated mean velocities are much smaller than the original mean velocities and closer to the reference three-year mean velocities (thick line), except for the most offshore bin, where no improvement is obtained for some unknown reason. Therefore this method is useful for estimating Eulerian mean velocities which are less affected by the sampling tendency of the drifting buoys. 6. Conclusion Sea-surface geostrophic velocities for the Kuroshio region calculated from T/P altimeter data combined with in situ oceanographic data are compared with surface velocities derived from drifting buoy trajectories. The geostrophic velocities agree well with the observed velocities; the correlation coefficient between them is 0.92, the rms difference is 16 cm sec 1, and the slope of the regression line is This suggests that the Kuroshio surface layer is essentially in geostrophic balance within measurement error. The comparison is improved a little when the centrifugal acceleration is taken into account and gradient-wind velocities are compared rather than geostrophic velocities; in particular, the slope (0.96) of the regression line becomes closer to unity. The observed velocities are divided into the temporal mean and fluctuation components, and the partitioning of velocities between these two components is examined. Both the temporal mean and fluctuation components are found to be important, and therefore the good comparison is not only due to the accurate estimates of the mean profile, but also Kuroshio Velocities from Altimeter and Drifting Buoy 121

8 due to those of the fluctuation profiles by the altimeter. For the Kuroshio region, most of the fluctuation components of the drifting buoy-derived velocities are found to be positive. This result suggests a problem of data sampling of drifting buoys for the Kuroshio region; namely, Eulerian mean velocities for the Kuroshio region estimated from drifting buoy data tend to be larger than actual means, because of the buoy s tendency to sample preferentially in the high-velocity Kuroshio. Acknowledgements The T/P altimeter data, M-GDR, were provided by the Physical Oceanography Distributed Active Archive Center at the Jet Propulsion Laboratory. The authors wish to thank P. Niiler for allowing them to use WOCE-TOGA drifter data, which were quality-controlled and optimally interpolated at the National Oceanic and Atmospheric Administration, Atlantic Oceanographic and Meteorological Laboratory. The oceanographic observation data along the ASUKA line were obtained by the ASUKA Group. 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