Chapter 10  Geostrophic Currents
10.6 Comments on Geostrophic Currents
Now that we know how to calculate geostrophic currents from hydrographic
data, let's consider some of the limitations of the theory and techniques.
Converting Relative Velocity to Velocity
Hydrographic data give geostrophic
currents relative to geostrophic currents at some reference level. How can
we convert the relative geostrophic velocities to velocities relative to the Earth?
1. Assume a Level of no Motion: Traditionally,
oceanographers assume there is a level of no motion,
sometimes called a reference
surface, roughly 2,000m below the surface. This is the assumption
used to derive the currents in Table
10.4. Currents are assumed to be zero at this depth, and relative
currents are integrated up to the surface and down to the bottom to
obtain current velocity as a function of depth. There is some experimental
evidence that such a level exists on average for mean currents (see for
example, Defant, 1961: 492).
Defant recommends choosing a reference level where the current shear in
the vertical is smallest. This is usually near 2 km. This leads to useful
maps of surface currents because surface currents tend to be faster than
deeper currents. Figure 10.9 shows the geopotential anomaly and surface
currents in the Pacific relative to the 1,000 decibar pressure level. Compare
this with Figure 10.5.

Figure 10.9. Mean depthgeopotential anomaly
of the Pacific Ocean relative to the 1,000dbar surface based on 36,356
observations.
Height is in geopotential centimeters. If the velocity
at 1,000dbar were zero, the map would be the surface topography of the Pacific.
From
Wyrtki (1974). 
2. Use known currents: The known currents
could be measured by current meters or by satellite altimetry. Problems
arise if the currents are not
measured at the same time as the hydrographic data. For example, the
hydrographic data may have been collected over a period of months to
decades, while the currents may have been measured over a period of
only a few months. Hence, the hydrography may not be consistent with
the current measurements. Sometimes currents and hydrographic data are
measured at nearly the same time (Figure 10.10). In this example, currents
were measured continuously by moored current meters (points) in a deep
western boundary currents and from CTD data taken just after the current
meters were deployed and just before they were recovered (smooth curves).
The solid line is the current assuming a level of no motion at 2,000 m,
the dotted line is the current adjusted using the current meter observations
smoothed for various intervals before or after the CTD casts.

Figure 10.10 Current meter measurements can
be used with CTD measurements to determine current as a function of depth
avoiding
the need for assuming a depth of no motion. Solid
line: profile assuming a depth of no motion at 2000 decibars. Dashed line: profile
adjusted
to agree with currents measured by current meters 17 days before the CTD measurements.
(Plots from Tom Whitworth, Texas A&M University) 
3. Use Conservation Equations: Lines of
hydrographic stations across a strait or an ocean basin may be used with
conservation of mass and salt to
calculate currents. This is an example of an inverse problem (see Wunsch,
1996 on how inverse methods are used in oceanography). See Mercier et al.
(2003) for a description of how they determined the circulation in the
upper layers of the eastern basins of the South Atlantic using hydrographic
data from the World Ocean Circulation Experiment and direct measurments
of current in a box model constrained by inverse theory.
Disadvantage of Calculating Currents from Hydrographic Data
Currents calculated from hydrographic data have provided important insights into
the circulation of the ocean over the decades from the turn of the 20th century
to the present. Nevertheless, it is important to review the limitations of the
technique.
 Hydrographic data can be used to calculate only the current relative a
current at another level.
 The assumption of a level of no motion may be suitable in the deep ocean,
but it is usually not a useful assumption when the water is shallow such
as over the continental shelf.
 Geostrophic currents cannot be calculated from hydrographic stations that
are close together. Stations must be tens of kilometers apart.
Limitations of the Geostrophic Equations
We began this section by showing
that the geostrophic balance applies with good accuracy to flows that exceed
a few tens of kilometers in extent and with periods greater than a few days. The
balance cannot, however, be perfect. If it were, the flow in the ocean would never
change because the balance ignores any acceleration of the flow. The important
limitations of the geostrophic assumption are:
 Geostrophic currents cannot evolve with time because the balance ingnores
acceleration of the flow. Acceleration dominates if the horizontal dimensions
are less than roughly 50 km and times are les than a few days. Acceleration
in negligible, but not zero, over longer distances and times.
 The geostrophic balance does not apply near the equator where the Coriolis
force goes to zero because sin j → 0.
 The geostrophic balance ignores the influence of friction.
Accuracy
Strub et
al. (1997) showed that currents calculated from satellite altimeter measurements
of seasurface slope have an accuracy of ±3–5 cm/s. Uchida, Imawaki,
and Hu (1998) compared currents measured by drifters in the Kuroshio with currents
calculated from satellite altimeter measurements of seasurface slope assuming
geostrophic balance. Using slopes over distances of 12.5 km, they found the
difference between the two measurements was ±16 cm/s for currents up to
150 cm/s, or about 10%. Johns, Watts, and Rossby (1989) measured the velocity
of the Gulf Stream northeast of Cape Hatteras and compared the measurements
with velocity calculated from hydrographic data assuming geostrophic balance.
They found that the measured velocity in the core of the stream, at depths
less than 500 m, was 10–25 cm/s faster than the velocity calculated from
the geostrophic equations using measured velocities at a depth of 2000 m. The
maximum velocity in the core was greater than 150 cm/s, so the error was
≈10%. When they added the influence of the
curvature of the Gulf Stream, which adds an acceleration term to the geostrophic
equations, the difference
in
the calculated and observed velocity dropped to less than 5–10 cm/s (≈5%).
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