well. For the first time the errors of global ocean
models have been assessed against a global data
set with a specified error estimate. One should
note, however, that the error estimates are approximate and heavily dependent on the geoid errors,
which are often not well determined.
The map of the difference between the T/P topography and the model (T/P9model) (Fig. 3.3.4c)
reveals a few large discrepancies: 962 cm in the
Banda Sea (between Australia and Indonesia and
to the east of the Timor Sea); from 36 cm
to 937 cm in the South Pacific sector of the
Antarctic Circumpolar Current. The large discrepancy in the Banda Sea is puzzling, because the
estimated geoid error in the area is only about
8 cm to degree 14. However, there are large highwavenumber geoid features in the region that are
not well modelled and might have aliasing effects
on the low-degree representations of the ocean
topography (Rapp et al., 1996).
There are indications suggesting that the discrepancies in the Southern Ocean might be caused
by problems in the ocean model. The difference
between the Semtner and Chervin’s model and the
model of Smith et al. (1992a) denoted as POP (96)
in Fig. 3.3.3, shows large values (20–30 cm) in the
same region of the Southern Ocean (Rapp et al.,
1996; their Fig. 3.3.2). The rms difference by
degree between the two models is also shown in
Figure 3.3.3. Although the two models are not
totally independent, their difference perhaps
reflects a lower bound for the errors in both
models. The reader is also referred to Park and
Gambéroni (1995) for a regional study of the
Indian Ocean sector of the Southern Ocean. They
reported agreement between the T/P ocean topography and the simulations by the Fine Resolution
Antarctic Model (FRAM Group, 1991) in revealing several gyre-scale circulation patterns that
were absent in historical hydrographic data.
The error of the JGM-3 geoid becomes larger
than the signal in ocean topography (Fig. 3.3.3) at
degrees higher than 14 (corresponding to a wavelength of about 3000 km), where the rms difference between the T/P topography and the model
becomes comparable to the signal magnitude. The
correlation between the T/P topography and the
model drops from the high values of 0.8–0.9 at
low degrees to below 0.5 at degrees higher than
14. The utility of the JGM-3 model is thus limited
to degrees lower than 14. Another slightly more
recent model, called EGM96 (Lemoine et al.,
1998), was constructed using a more extensive
database than JGM-3. Preliminary assessment
suggests that EGM96 has about a-factor-of-two
improvement over JGM-3 up to degree 20. With
this increased accuracy, the utility of altimetryderived ocean topography may be extended to
degree 18 (Lemoine et al., 1998).
Ganachaud et al. (1997) conducted a linear
inverse calculation to evaluate whether the T/P
ocean topography is useful for improving the
estimate of the oceanic general circulation relative
to a previous estimate based on historical hydrographic data (Macdonald and Wunsch, 1996).
They first found that after certain spatial smoothing (excluding wavelengths shorter than 1600 km),
altimetrically determined velocities were consistent
with hydrographic estimates within the error bars
of each. After this consistency check, they further
combined the two estimates using a recursive
inverse procedure and obtained a new solution
that is fully consistent with both altimetry and
hydrography. However, the resulting solution
did not reduce the error in the circulation and its
associated heat transport in any significant way
because the geoid (JGM-3) error was still too
large. They further concluded that in order to
obtain a geoid model sufficiently accurate to
improve upon the hydrographic estimate of ocean
topography, specifically designed gravity missions
meeting very demanding requirements would be
required (also see National Research Council,
1997; Tapley and Kim, 2000). The planned
missions such as GRACE and GOCE mentioned in
Section 3.3.1 are designed to fulfil these roles.
The study of Gananchaud et al. (1997) has provided a particular view of the utility of altimetry
through the perspective of a linear inverse calculation based on hydrographic data and geostrophic
dynamics (also see LeGrand et al., 1998). One
could argue that the prior error estimates assigned
to the hydrographic solution might be too optimistic. Given the difference in the sampling (in
both space and time) of the circulation between
hydrography and altimetry, the combination of
the two data sets using a linear inverse model is
quite tricky. It is expected that when the continuous global altimetry data are combined with a
state-of-the-art general circulation model, one
should be able to obtain an optimal estimate of the
time-evolving global circulation, from which a
3.3 Ocean Circulation and Variability from Satellite Altimetry
147
Fu
models have been assessed against a global data
set with a specified error estimate. One should
note, however, that the error estimates are approximate and heavily dependent on the geoid errors,
which are often not well determined.
The map of the difference between the T/P topography and the model (T/P9model) (Fig. 3.3.4c)
reveals a few large discrepancies: 962 cm in the
Banda Sea (between Australia and Indonesia and
to the east of the Timor Sea); from 36 cm
to 937 cm in the South Pacific sector of the
Antarctic Circumpolar Current. The large discrepancy in the Banda Sea is puzzling, because the
estimated geoid error in the area is only about
8 cm to degree 14. However, there are large highwavenumber geoid features in the region that are
not well modelled and might have aliasing effects
on the low-degree representations of the ocean
topography (Rapp et al., 1996).
There are indications suggesting that the discrepancies in the Southern Ocean might be caused
by problems in the ocean model. The difference
between the Semtner and Chervin’s model and the
model of Smith et al. (1992a) denoted as POP (96)
in Fig. 3.3.3, shows large values (20–30 cm) in the
same region of the Southern Ocean (Rapp et al.,
1996; their Fig. 3.3.2). The rms difference by
degree between the two models is also shown in
Figure 3.3.3. Although the two models are not
totally independent, their difference perhaps
reflects a lower bound for the errors in both
models. The reader is also referred to Park and
Gambéroni (1995) for a regional study of the
Indian Ocean sector of the Southern Ocean. They
reported agreement between the T/P ocean topography and the simulations by the Fine Resolution
Antarctic Model (FRAM Group, 1991) in revealing several gyre-scale circulation patterns that
were absent in historical hydrographic data.
The error of the JGM-3 geoid becomes larger
than the signal in ocean topography (Fig. 3.3.3) at
degrees higher than 14 (corresponding to a wavelength of about 3000 km), where the rms difference between the T/P topography and the model
becomes comparable to the signal magnitude. The
correlation between the T/P topography and the
model drops from the high values of 0.8–0.9 at
low degrees to below 0.5 at degrees higher than
14. The utility of the JGM-3 model is thus limited
to degrees lower than 14. Another slightly more
recent model, called EGM96 (Lemoine et al.,
1998), was constructed using a more extensive
database than JGM-3. Preliminary assessment
suggests that EGM96 has about a-factor-of-two
improvement over JGM-3 up to degree 20. With
this increased accuracy, the utility of altimetryderived ocean topography may be extended to
degree 18 (Lemoine et al., 1998).
Ganachaud et al. (1997) conducted a linear
inverse calculation to evaluate whether the T/P
ocean topography is useful for improving the
estimate of the oceanic general circulation relative
to a previous estimate based on historical hydrographic data (Macdonald and Wunsch, 1996).
They first found that after certain spatial smoothing (excluding wavelengths shorter than 1600 km),
altimetrically determined velocities were consistent
with hydrographic estimates within the error bars
of each. After this consistency check, they further
combined the two estimates using a recursive
inverse procedure and obtained a new solution
that is fully consistent with both altimetry and
hydrography. However, the resulting solution
did not reduce the error in the circulation and its
associated heat transport in any significant way
because the geoid (JGM-3) error was still too
large. They further concluded that in order to
obtain a geoid model sufficiently accurate to
improve upon the hydrographic estimate of ocean
topography, specifically designed gravity missions
meeting very demanding requirements would be
required (also see National Research Council,
1997; Tapley and Kim, 2000). The planned
missions such as GRACE and GOCE mentioned in
Section 3.3.1 are designed to fulfil these roles.
The study of Gananchaud et al. (1997) has provided a particular view of the utility of altimetry
through the perspective of a linear inverse calculation based on hydrographic data and geostrophic
dynamics (also see LeGrand et al., 1998). One
could argue that the prior error estimates assigned
to the hydrographic solution might be too optimistic. Given the difference in the sampling (in
both space and time) of the circulation between
hydrography and altimetry, the combination of
the two data sets using a linear inverse model is
quite tricky. It is expected that when the continuous global altimetry data are combined with a
state-of-the-art general circulation model, one
should be able to obtain an optimal estimate of the
time-evolving global circulation, from which a
3.3 Ocean Circulation and Variability from Satellite Altimetry
147
Fu