Journal of Oceanography, Vol. 53, pp. 585 to 599. 1997
Sea Surface Dynamic Height of the Pacific Ocean Derived
from TOPEX/POSEIDON Altimeter Data: Calculation Method
and Accuracy
TSURANE KURAGANO and AKIRA SHIBATA
Meteorological Research Institute, Nagamine 1-1, Tsukuba 305, Japan
(Received 21 June 1995; in revised form 9 January 1997; accepted 24 June 1997)
The method we developed to calculate annual mean sea surface dynamic height (SSDH)
uses TOPEX/POSEIDON altimeter data, hydrographic data such as XBT and TOGATAO mooring data, and climatological temperature and salinity. The method has the
advantage that annual mean SSDH can be calculated from a set of hydrographic data
observed at least at one time point during the altimeter mission period. As examples, we
calculated the 1993 and 1994 annual mean SSDHs of the Pacific Ocean using our method.
Accuracy of the annual mean SSDH fields is estimated to be below 2 cm in most areas and
2.5 cm at most in the areas where XBT data are sparsely available. SSDH during each
satellite cycle on a reference of the annual mean SSDH is more accurate than that on a
reference of the climatological mean SSDH, so that the sea surface currents detected
from the SSDH field obtained with the present method correspond well to currents
analyzed from ship observations.
briefly explained the present method, but paid little attention
to its accuracy. In this paper, we estimate the accuracy of the
SSDH and the sea surface height anomaly from the annual
mean (SSHA) and annual mean SSDH variability, using tide
gauge and CTD data. Data applied to the method are explained
in Section 2, the calculation method for annual mean SSDH
in Section 3, and annual mean SSDH results in Section 4.
1. Introduction
Since the TOPEX/POSEIDON satellite was launched
in Aug. 1992, the onboard altimeter has been observing sea
surface height with better accuracy than that of preceding
satellites, i.e., GEOS-3, SEASAT and GEOSAT. Combining the accurate sea surface height data with hydrographic
data such as temperature and salinity enables us to obtain
accurate sea surface dynamic height (SSDH) over a large
area. This paper describes a new method of calculating the
annual mean SSDH, taking the 1993 mean analysis as an
example.
In many previous studies, climatological mean SSDHs
were used to approximate the mean surface geopotential
height for the period of an altimeter mission (Willebrand et
al., 1990; Glenn et al., 1991). They indicate differences in
sea surface height between the climatological mean and the
short-term mean for the altimeter mission. Ichikawa and
Imawaki (1992) used SSDH averaged over the same period
as an altimeter mission to reduce this difference. Their
method, however, requires a large number of SSDHs obtained regularly, thus cannot be applied to sparse SSDH
data.
We have solved this problem by introducing a simple
process for obtaining an annual mean SSDH from one SSDH
with altimeter data. From the annual mean SSDHs at each
hydrographic observation stations, we draw a mean SSDH
map for the Pacific Ocean. Kuragano and Shibata (1994)
2. Data and Data Procedure
In our calculation we use the TOPEX/POSEIDON
altimeter data, temperature data from XBT and TOGA-TAO
moorings in 1993 and 1994, and climatological temperature
and salinity. Temperature and salinity data from CTD and
sea level data from tide gauges are used to estimate error.
The TOPEX/POSEIDON altimeter has an excellent
observational accuracy of about 5 cm (Fu et al., 1994). The
TOPEX altimeter was produced by the National Aeronautics and Space Administration (NASA), and the POSEIDON
altimeter by the Centre National D’Etudes Spatiales (CNES).
The TOPEX/POSEIDON altimeter data have been available
since late September 1992. The satellite repeats 127 orbital
circles during one cycle of almost ten days, covering the
ocean between 66°S and 66°N. Data are compiled in the
Merged Geophysical Data Record (MGDR). Because the
satellite attitude was not stable in the early cycles, we deal
with data for cycles 11 to 84 in 1993 and 1994. Sea surface
height data extracted from the MGDR were corrected for
585
Copyright  The Oceanographic Society of Japan.
Keywords:
⋅ Sea surface
dynamic height,
⋅ TOPEX/
POSEIDON
altimeter,
⋅ hydrographic data,
⋅ tide gauge data,
⋅ optimum interpolation method,
⋅ Pacific Ocean,
⋅ sea surface current,
⋅ El Niño.
media effects based on Benada (1993), ocean tides using the
model of Cartwright and Ray (1991), and the inverse barometer effect. The ‘Mean Sea Surface Height’ proposed by
Rapp et al. (1991) was also subtracted. Values used for the
corrections are included in the MGDR.
Climatological monthly and seasonal temperature and
salinity data are extracted from the World Ocean Atlas data
set of the National Oceanographic Data Center (NODC,
1994; Levitus et al., 1994; Levitus and Boyer, 1994). The
upper layer temperature is observed by ships with XBT and
by TOGA-TAO moorings in the tropical Pacific (Hayes et
al., 1991) (Fig. 1). The XBT data are extracted from the
BATHY/TESAC data file compiled by the Japan Oceanographic Data Center (JODC). The TOGA-TAO data for
each 00:00 hours (Greenwich time) are obtained from the
TOGA-TAO Project Office.
Most XBT and TOGA-TAO moorings are conducted at
depths shallower than 500 m. Temperatures are extrapolated
below the maximum observation depth to approach the
climatological monthly mean value asymptotically (seasonal
mean temperature at levels deeper than 1000 m) by
[
] [
]
T ( d ) = To ( de ) − Tc ( de ) exp − α ( d − de ) + Tc ( d ),
(1)
where T is temperature (°C), d depth (m), de depth of the
deepest observation level, To observed temperature, Tc climatological monthly or seasonal mean temperature and α a
constant (Fig. 2(a)). We use 0.008 (m–1) as α (see Appendix). Salinity corresponding to the above temperature is
estimated by the following procedure (Fig. 2(b)). A correlation coefficient and a regression equation between temperature and salinity are calculated for climatological monthly
mean values at each depth in an area within 550 km of the
temperature observation. Salinity is estimated from the
regression equation when the correlation coefficient exceeds
0.5, and climatological monthly or seasonal mean salinity is
adopted when the correlation coefficient is below 0.5. There
are no areas where the correlation coefficient exceeds 0.5,
except in the areas near Japan.
The upper layer CTD data observed by R/Vs Ryofumaru and Kofu-maru in 1993 and 1994 (Fig. 3), and CTD
data for the eastern Pacific in the BATHY/TESAC data file
compiled by the JODC are also used. In total there are 244
CTD data points. Monthly sea levels from tide gauges in the
Pacific Ocean corrected for barometric pressure are obtained
from the Sea Level Center in the University of Hawaii
(Mitchum, 1990).
Fig. 1. Temperature data density. Data density of temperature in each 30′ × 30′ grid, composed of 88343 XBT data and 43156 TOGATAO mooring data. The data are available in 10834 grids out of the 45011 grids.
586
T. Kuragano and A. Shibata
Fig. 2. Vertical profile of temperature (a) and salinity (b) at 33.00°N, 135.43°E on Nov. 2, 1992. The thin line shows the climatological
monthly mean profile and the bold broken line the calculated profile. The bold line in (a) shows temperature profile observed with
XBT. See text for the method of calculating the bold broken lines.
Fig. 3. Locations of the CTD observations at 137°E, 144°E, and
155°E by the R/Vs Ryofu-maru and Kofu-maru.
3. Calculation of Sea Surface Height and Accuracy
age value, corresponding to about 6 km spacing. To apply
the collinear method and save computer time, 15′-latitude
averages are calculated. This averaging reduces small-scale
oceanic signals along the track, which are not resolved on
the interpolation between tracks due to the tracks’ coarse
spacing. We calculate SSHA from the 1993 annual mean sea
surface height with the collinear method. We interpolate
SSHA at 30′ × 30′ grid points during each cycle using the
functional fitting method (OD/JMA, 1990) where the grid
value is determined by fitting a linear function of position to
SSHA along tracks within 330 km of the grid (Fig. 4).
To estimate the error of the interpolated SSHA, we
compared the interpolated SSHA with tide gauge data corrected for barometric pressure using monthly mean values
(Fig. 5). The RMS differences are small (1.5–3.5 cm) and
the correlation coefficients are high (0.75–0.95) in the
tropical open ocean, while the RMS difference is larger and
the correlation is slightly worse in the mid-latitudes. In most
of the continental and Japanese coastal areas, the RMS
difference is quite high and the correlation is low. This may
be caused by the tidal correction error in SSHA (Molines et
al., 1994).
Such an error estimation must be done for the whole
region, not only at the tide stations. In general, the error
variance of SSHA (σae2), defined as variance of the difference between the real and interpolated SSHAs, is expressed
as
2
σ ae
= ∫ ( P( k ) ⋅ rk )dk ,
3.1 SSHA
The TOPEX/POSEIDON altimeter data are used to
determine SSHA. The data are given as a one-second aver-
(2)
where P is the wave number power spectrum of SSHA and
rk is the ratio of the error variance of interpolated SSHA to
Sea Surface Dynamic Height Derived from TOPEX/POSEIDON Data
587
the real SSHA at wave number k.
To estimate the error variance ratio, we assumed the
SSHA distribution with a wavelength of 500 km as a real
state (Fig. 6(a)). The interpolated SSHA is calculated from
the values along tracks by the functional fitting (Fig. 6(b)).
In this case, the ratio of the error variance of the interpolated
SSHA to the variance of the assumed SSHA is 0.43. Similar
calculations for 25 different wavelengths of the assumed
patterns were done for nine 10°-latitude zonal areas (Fig. 7).
The results south of 30°N differ little from each other, so
only the result at 10°N–20°N is shown. The interpolation is
less successful for smaller wavelengths. The error variance
is almost entirely composed of wavelengths smaller than
1000 km. The great success for wavelengths longer than
1000 km is because the zonal interval of the satellite track is
sufficiently small to resolve such large-scale variations. The
interpolation for the same wavelength is slightly worse at
lower latitudes, because the spatial interval between satellite tracks is larger. The power spectrum of SSHA is calculated every 5°-latitude with the SSHA data in a 10°-latitude
width along the track. The 10°-latitude width is adopted
because the error variance is almost entirely composed of
wavelengths smaller than 1000 km. Using this power spectrum and the error variance ratio rk in Fig. 7, the error variance of SSHA is calculated from Eq. (2) (Fig. 8).
In a comparison of the errors in Fig. 8 (mean for 10
days) with those in Fig. 5(a) (mean for 30 days), the values
in Fig. 5(a) should be multiplied by 3 , if the errors of the
interpolated SSHA in a month are independent of each other,
and the square of the error changes little over a month. After
this modification, the RMS errors of SSHA for a 10-day cycle
in Fig. 8 coincide well with those in Fig. 5(a) in the tropical
Pacific, and the general coincidence is not bad, except at
some stations at the coast. The error estimation in Fig. 8 is
concluded to be valid. The RMS errors are especially large
in the western mid-latitudes such as the Kuroshio circulation
area. This shows that small spatial scale phenomena have
large variability in these areas.
3.2 SSDH
The geopotential anomaly referred to 1500 db (in
dynamic meters) calculated from temperature profiles of
XBT or TOGA-TAO mooring was linearly converted to
SSDH (in meters). Since most XBT and TOGA-TAO
mooring are conducted at depths shallower than 500 m,
temperatures at greater depths and salinities are determined
by the method given in Section 2. Thus, the estimated SSDH
has an error due to the determination error of salinity and
deep-water temperature. To estimate the error of SSDH,
SSDHs are calculated with the procedure in Section 2 using
Fig. 4. SSHA fields for cycle 25 during May 19 to 28, 1993. The contour interval and the numerical unit are 10 cm. The shaded area
indicates a sea surface height below the annual mean height of 1993.
588
T. Kuragano and A. Shibata
Fig. 5. Comparison of SSHA with monthly mean sea level data. (a) RMS differences (cm). (b) Correlation coefficients (in 0.01).
Sea Surface Dynamic Height Derived from TOPEX/POSEIDON Data
589
temperatures in the upper 400 m of 179 CTD data, and are
compared to those calculated from the CTD data of temperature and salinity above 1500 m depth (Fig. 9). The RMS
difference between these SSDHs is 7.7 cm at 137°E and
155°E and 8.0 cm at 144°E (see Fig. 3 for locations). A
similar result of 7.4 cm was obtained from a similar study of
65 CTD data for two areas (48°N–51°N, 125°W–145°W and
equator–13°N, 95°W–170°W) in the eastern Pacific. We
therefore adopt 8.0 cm as the SSDH RMS error for the whole
Pacific.
3.3 Annual mean SSDH: SSDH
We assume that the SSHA represents the SSDH anomaly
from the annual mean as
Fig. 6 Test of the functional fitting method for the region of 5°S-5°N, 170°W–150°W. (a) SSHA assumed to test the functional fitting.
The wavelength is 500 km. (b) SSHA interpolated from satellite tracking values using the functional fitting. The contour interval
and the numerical unit are 10 cm. The shaded area indicates a sea surface height below the annual mean.
590
T. Kuragano and A. Shibata
SSHA = SSDH − SSDH,
(3)
where the bar indicates the annual mean. Substituting SSDH
from hydrographic data and SSHA from altimeter data into
Eq. (3) yields SSDH (Fig. 10).
Our method has the advantage that SSDH can be cal-
culated from a set of temperature data observed at one time
point during the altimeter mission period. The SSDH s are
obtained with all temperature data shown in Fig. 1. Blank
SSDH areas still remain, however, and we get an optimum
SSDH at each grid, using the optimum interpolation method
(Hollingsworth, 1987). The optimum interpolation requires
error covariances of data and a first guess. The datum in the
Fig. 7. Ratio of the error variance of the interpolated SSHA to the variance of the real (assumed) SSHA, showing the result of the
functional fitting test.
Fig. 8. SSHA RMS error field. The contour interval and numerical unit are 1 cm. Sea text for the calculation.
Sea Surface Dynamic Height Derived from TOPEX/POSEIDON Data
591
Fig. 9. Comparison of the SSDH derived from observed temperature of the upper 400 m, extrapolated deeper temperature, and calculated
salinity according to the procedure given in Section 2 (cross) with the SSDH derived from temperature and salinity observed to 1500m depth (open circle) in the sections at 137°E (a) and 144°E (b). Note that the scale on the abscissa is different between (a) and (b).
The SSDHs calculated with the method proposed in this paper, i.e., the sum of the 1993 annual mean SSDH and SSHA of the simultaneous altimetry cycle, is shown by a solid line for reference.
present case is the SSDH obtained from Eq. (3). The first
guess is a climatological mean SSDH.
3.4 SSDH error covariance
Error covariance is the correlation coefficient multiplied
by RMS error. The SSDH RMS error (σme) is composed of
the SSHA RMS error (σae) and SSDH RMS error (σie),
2
2
σ me
= σ ae
+ σ ie2 .
( 4)
Equation (4) assumes no correlation between the errors of
SSHA and SSDH. The SSHA RMS error (σae) is shown in
Fig. 8, and the SSDH RMS error (σie ) is 8.0 cm (Subsection
3.2). To validate the estimation of Eq. (4), we compared the
estimation with the SSDH RMS variability. The SSDH
RMS error was estimated at each grid where over 30 XBTs
592
T. Kuragano and A. Shibata
( SSDH s) were obtained. The mean of the estimated values
in 280 grids around Japan (25°N–45°N, 120°E–150°E) is
12.0 cm, and is almost equal to the value of 12.1 cm which
is estimated for the same grids from the right-hand side of
Eq. (4). This shows that Eq. (4) is valid for the RMS error
estimation.
The correlation coefficient of the SSDH error is linearly composed of those of SSDH error and SSHA error. There
is little correlation between the SSDH errors at the hydrographic stations. On the other hand, SSHA errors in nearby
grids at the same time are correlated, because the errors are
derived from the interpolation. However, the SSHA errors of
different times are not correlated, and the SSHA errors at the
time of the observations of temperature data used for the
SSDH calculation generally show little correlation. Accordingly, the correlation coefficient of the SSDH error can be
Fig. 10. Conceptual diagram of the calculation of the annual mean
SSDH, D0 -∆H0, using SSHA from the altimeter (shaded line)
and SSDH calculated from hydrographic data observed at a
time of t0 (open circle). The scales on the ordinate at the left
and right are for the SSHA and the SSDH, respectively.
at each 1° × 1° grid. The geopotential anomaly referred to
1500 db (in dynamic meters) of the climatological mean is
linearly converted to SSDH (in meters). An error of the first
guess is a deviation of the climatological mean SSDH from
the SSDH in the year under analysis.
Since hydrographic data are not obtained continuously
at each grid in most cases, the error of the first guess is
estimated from tide gauge data observed at 52 stations over
15 years, as the height deviation of the annual mean sea level
in each year from the long-term mean sea level for over 15
years. Then the standard deviation of the annual mean sea
level is the RMS error of the first guess. The standard
deviation at each tide station is 2.3–9.7 cm, and there is no
obvious area dependency. The average of these standard
deviations for all tide gauges is 5 cm. This value is adopted
as the RMS error of the first guess for whole Pacific.
Correlation coefficients of the first guess error between
the tide stations are shown in Fig. 11 as a function of distance
between two stations, using over 15 values at each tide
station. The zonal and meridional decorrelation scales are
4030 km and 673 km, respectively. Then we assumed the
correlation coefficient between two arbitrary grids as
(
)
µ gs = exp −rz2 / bz2 − rm2 / bm2 ,
(6)
where bz is 4030 km, bm is 673 km, and rz (rm) is the zonal
(meridional) distance between two grids. The error covariance of the first guess is obtained as µgs multiplied by the
RMS error of 5.0 cm.
Fig. 11. Correlation coefficients of tide gauge data between two
stations with small meridional (zonal) distance less than 330
km, called the zonal (meridional) correlation coefficients,
shown by solid circles (crosses). Dots show the correlation
coefficients for the residual pairs of tide stations. The solid
and broken lines represent Gaussian functions fitted to the
meridional and zonal correlation coefficients, respectively.
assumed as
1
µ me = 
0
( for the same observation ),
( for different observations).
( 5)
Therefore, the error covariance of SSDH is σme for the same
observation and zero for different observations.
3.5 Error covariance of the first guess
As the first guess in the optimum interpolation we
adopt the climatological mean SSDH, which is an average of
12 climatological monthly means calculated from the climatological monthly and seasonal mean temperature and salinity
4. Results of the SSDH and SSDH Field
The maps of SSDH interpolated with the optimum interpolation, the deviation from the first guess (i.e., the
climatological mean SSDH), and the error of the interpolated SSDH which is calculated in the optimum interpolation are shown in Fig. 12. The SSDH field is characterized
by the 1993 El Niño event (McPhaden, 1993): the SSDH s in
the eastern equatorial Pacific are about 5 cm higher than the
climatological mean SSDHs, while those in the western
equatorial Pacific are about 10 cm lower. The SSDH s just
south of the Kuroshio and the Kuroshio Extension are 20 cm
higher than the climatological mean. The error of the interpolated SSDH is 2.5 cm at most. It is smaller than the RMS
errors of the data and the first guess of the optimum interpolation, the TOPEX/POSEIDON altimeter measurement
error (about 5 cm RMS error), and the tidal correction error
(~5 cm) (Fu et al., 1994). Such a small analysis error is due
to a large number of XBT and TOGA-TAO mooring data.
The 1994 SSDH field is obtained with the SSHA
calculated as an anomaly from the 1994 annual mean of the
TOPEX/POSEIDON altimeter data (Fig. 13). In terms of the
El Niño characteristics, the positive SSDH anomalies in the
eastern equatorial Pacific disappear, but the negative
Sea Surface Dynamic Height Derived from TOPEX/POSEIDON Data
593
(a)
(b)
Fig. 12. Optimum interpolation results for 1993 analysis. (a) Annual mean SSDH field. The numerical unit is 10 cm. Lightly shaded
areas represent 150–200 cm, medium-shaded 200–250 cm, and heavily shaded over 250 cm. (b) Deviation of the annual mean SSDH
from the climatological mean SSDH (the first guess). The interval of solid contours and the numerical unit are 10 cm. The interval
between the solid and broken contours is 5 cm. Negative areas are shaded. (c) Analysis error field. The numerical unit is 1 cm. Lightly
shaded areas represent 1–2 cm, and heavily shaded over 2 cm.
594
T. Kuragano and A. Shibata
(c)
Fig. 12. (continued).
(a)
Fig. 13. Same as Fig. 12 but for 1994.
Sea Surface Dynamic Height Derived from TOPEX/POSEIDON Data
595
(b)
Fig. 13. (continued).
(a)
Fig. 14. (a) SSDH field in the western North Pacific during cycle 28, from June 17 to 27, 1993 (SSHA plus 1993 annual mean SSDH).
(b) Current map during June 21 to 30, 1993 (Monthly Ocean Report, No. 6, JMA). Arrows show surface current velocities observed
by ships and drifting buoys. (c) SSDH field calculated with the climatological mean SSDH instead of 1993 annual mean SSDH. The
climatological mean SSDH is calculated from Levitus’ data. The numerical unit in (a) and (c) is 10 cm.
596
T. Kuragano and A. Shibata
(b)
(c)
Fig. 14. (continued).
Sea Surface Dynamic Height Derived from TOPEX/POSEIDON Data
597
anomalies in the western tropical Pacific still remain. The
SSDH s just south of the Kuroshio and the Kuroshio Extension are 20 cm higher than the climatological mean SSDHs,
as in 1993.
The positive anomalies just south of the Kuroshio and
Kuroshio Extension are much larger than the RMS error of
the first guess in both years. This indicates that the climatological mean SSDH used as the first guess is a large underestimate. This is probably because the climatological mean
temperature and salinity in the World Ocean Atlas data set
are highly smoothed in space using an objective analysis
with a large influence radius of 550 km (Levitus et al., 1994;
Levitus and Boyer, 1994), and the climatological mean
SSDH is deviated from the actual sea surface height. To
obtain a more accurate SSDH field, the RMS error of the
first guess should be estimated by including the deviation of
the climatological mean SSDH from the actual value. The
deviation can be estimated as a difference between the
following two kinds of deviation: the deviation of the 1993
SSDH from the climatological mean SSDH, and the deviation in the tide-gauge sea level of the 1993 mean from the
long-term mean. Using the first guess error plus this deviation, the SSDH s just south of the Kuroshio and the Kuroshio
Extension are higher by ≤5 cm than that in Fig. 12(a), and the
error of the interpolated SSDH is 8% larger than that in Fig.
12(c). The re-processed SSDH and error must be more accurate than those in Fig. 12.
An SSDH field during the cycle 28 from June 17 to 27,
1993 is obtained by adding SSHA to the re-processed SSDH
(Fig. 14(a)). The Kuroshio, the Kuroshio Extension, and the
North Equatorial Current are detected as a steep inclination
of SSDH and correspond well with the currents analyzed
from ship observations during almost the same period as the
satellite measurement (Fig. 14(b)). If we use the climatological mean SSDH as the mean surface dynamic height
during the altimeter mission like many previous studies, the
SSDH field during the same period as Fig. 14(a) is changed
to Fig. 14(c). The major currents can be detected, but the
inclination of SSDH at the currents is smaller than in Fig.
14(a). Moreover, the high sea surface height region extending at 30–33°N from the south of Japan to the east is not
shown.
5. Conclusion
We have developed a method to calculate the annual
mean SSDH (sea surface dynamic height), SSDH , by
eliminating the SSHA (sea surface height anomaly from the
annual mean) from the SSDH, and obtained the SSDH map
for the Pacific Ocean. In our method the SSHA is calculated
from the TOPEX/POSEIDON altimeter data with the collinear method along the satellite tracks, and is interpolated
into the grids (30′ × 30′) with the functional fitting method.
The SSDH referred to 1500 db is calculated from temperature of XBT and TOGA-TAO mooring data at depths shal-
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T. Kuragano and A. Shibata
lower than 400 m, deeper temperatures being extrapolated
to approach the climatological monthly mean temperature
asymptotically, and salinity estimated with the regression
equation with respect to temperature. The SSDH is obtained
by subtracting the SSHA from the SSDH. The method we
have proposed here has the advantage that the SSDH can be
calculated from a set of hydrographic (temperature) data at
one time point during the altimeter mission period.
The SSDH for the Pacific Ocean in 1993 and 1994 have
been calculated, gridded (30′ × 30′) with the optimum interpolation using the SSDH s as the data and the climatological mean SSDH as the first guess. The SSDH field in 1993
is characterized by the 1993 El Niño event, while the 1994
field is not. The SSDH during each cycle is obtained by
adding the SSHA to the SSDH . The SSDH field shows a
distribution of the sea surface current which corresponds
well with that found from ship observations. The SSDH field
obtained here is more accurate than that obtained by adding
the SSHA to the climatological mean SSDH.
The Japan Meteorological Agency (JMA) produces sea
surface current charts in the western North Pacific every 10
days. In the process of drawing the current map, the SSDH
maps produced with our present method are used for reference. The SSHA used in the calculation for the SSDH is
derived from the Interim GDR of the TOPEX/POSEIDON
altimeter data obtained through the Internet from the Jet
Propulsion Laboratory within about ten days after the satellite observation. The sea surface current charts are presented
in the Monthly Ocean Report issued by the El Niño Monitoring Center of JMA (ENMC, 1993), and are broadcasted
via meteorological radio facsimile for ships at sea.
Acknowledgements
We thank Drs. L. L. Fu and S. Imawaki for supporting
this work and the Jet Propulsion Laboratory staff for providing
MGDR data. Tide gauge data were kindly provided by the
University of Hawaii Sea Level Center, under the direction
of Dr. G. T. Mitchum. Mooring time series data were kindly
provided by the TOGA-TAO Project Office, under the
direction of Dr. M. J. McPhaden of NOAA’s Pacific Marine
Environmental Laboratory, Seattle, Washington. Ship observation data were kindly provided by the Japan Oceanographic Data Center. We sincerely thank the reviewers for
their helpful comments and Mr. N. Shikama for his invaluable advice and comments. Special thanks are extended to
Dr. M. Kawabe for his valuable advice on compiling and
finalizing this paper. This work was supported by the Special Coordination Funds for Promoting Science and Technology from the Science and Technology Agency of Japan.
Appendix
Determination of α in Eq. (1).
We define X and Y as:
Table A1. Regression coefficient of Y – Y on X – X and RMS variability of Y – Y for α.
α (m –1 )
0.002
0.004
0.006
0.008
0.010
0.012
0.015
∞
Regres. coef.
RMS var. (cm)
0.217
15.5
0.095
13.1
0.036
12.3
0.007
12.0
–0.009
11.9
–0.020
11.8
–0.029
11.7
–0.061
11.6
X = SSDH + SSHA;
Y = SSDH – SSHA,
and consider the case that the SSDH is calculated from XBT
data, and the SSHA from the altimeter data at the time and
location of XBT observation. The correlation between X –
X and Y – Y , where the overbar represents the mean in each
grid where more than 30 SSDHs are available. The SSDH for
small (large) α responds excessively (little) to the variability
of observed temperature. Since the value of Y – Y should not
depend on the value of X – X , the optimum α results in a
zero regression coefficient of Y – Y on X – X and the
minimum RMS variability of Y – Y . Table A1 shows the
regression coefficient and the RMS variability for various
values of α. When α is 0.008 m–1, the regression coefficient
is close to 0, and the RMS variability is comparably small
with that for α = ∞, although the RMS variability decreases
as α increases. Therefore, we selected α = 0.008 m–1.
References
Benada, R. (1993): PO. DAAC Merged GDR (TOPEX/Poseidon)
Users Handbook, JPL D-11007.
Cartwright, D. E. and R. D. Ray (1991): Energetics of global
ocean tides from Geosat altimetry. J. Geophys. Res., 96, 16897–
16912.
El Niño Monitoring Center (ENMC) (1993): Monthly Ocean
Report—Oceanographic products by the El Niño Monitoring
Center. Oceanogr. Mag., 43, 53–63.
Fu, L. L., E. J. Christensen, C. A. Yamarone, Jr., M. Lefebvre, Y.
Ménard, M. Dorrer and P. Escudier (1994): TOPEX/
POSEIDON mission overview. J. Geophys. Res., 99, 24369–
24381.
Glenn, S. M., D. L. Porter and A. R. Robinson (1991): A synthetic
geoid validation of Geosat mesoscale dynamic topography in
the Gulf Stream region. J. Geophys. Res., 96, 7145–7166.
Hayes, S. P., L. J. Mungum, J. Picaut, A. Sumi and K. Takeuchi
(1991): TOGA-TAO: a moored array for real-time measure-
ments in the tropical Pacific Ocean. Bull. Am. Meteorol. Soc.,
72, 339–347.
Hollingsworth, A. (1987): Objective analysis for numerical weather
prediction. p. 11–59. In Collection of Papers Presented at the
WMO/IUGG NWP Symposium, Tokyo, 4–8 August 1986, ed.
by T. Matsuno.
Ichikawa, K. and S. Imawaki (1992): Fluctuation of the sea
surface dynamic topography southeast of Japan as estimated
from Seasat altimetry data. J. Oceanogr., 49, 155–177.
Kuragano, T. and A. Shibata (1994): Calculation of sea surface
dynamic height from TOPEX altimetry data. Umi to Sora, 70,
123–138 (in Japanese with English abstract).
Levitus, S. and T. P. Boyer (1994): World Ocean Atlas 1994
Volume 4: Temperature. NOAA Atlas NESDIS 3, 117 pp.
Levitus, S., R. Burgett and T. P. Boyer (1994): World Ocean Atlas
1994 Volume 3: Salinity. NOAA Atlas NESDIS 3, 99 pp.
McPhaden, M. J. (1993), TOGA-TAO and the 1991–93 ENSO
event. Oceanography, 6, 36–44.
Mitchum, G. T. (1990): U.S. WOCE supports global sea level data
collection. WOCE Notes, 2(6), pp. 10–12, Tex. A&M Univ.,
College Station, Tex.
Molines, J. M., C. Le Provost, F. Lyard, R. D. Ray, C. K. Shum and
R. J. Eanes (1994): Tidal corrections in the TOPEX/
POSEIDON geophysical data records. J. Geophys. Res., 99,
24,749–24,760.
National Oceanographic Data Center (NODC), Ocean Climate
Laboratory (1994): World Ocean Atlas 1994, National
Oceanographic Data Center Report, 13, 30 pp.
Oceanographical Division, JMA (OD/JMA) (1990): An objective
analysis of subsurface temperature. Weather Service Bull., 57,
271–282 (in Japanese).
Rapp, R. H., Y. Wang and N. K. Pavlis (1991): The Ohio State
1991 geopotential and sea surface topography harmonic coefficient model. Rep. 410, 96 pp., Dep. of Geod. Sci. and
Surv., Ohio State Univ.
Willebrand, J., R. H. Käse, D. Stammer, H.-H. Hinrichsen and W.
Krauss (1990): Verification of Geosat sea surface topography
in the Gulf Stream extension with surface drifting buoys and
hydrographic measurements. J. Geophys. Res., 95, 3007–3014.
Sea Surface Dynamic Height Derived from TOPEX/POSEIDON Data
599