then inverse analyses could be used to infer tracermixing rates.
This reasoning led to a programme of direct
velocity observations in WOCE. Moored arrays
were used to measure the transport of selected, usually concentrated, currents, and the Surface Velocity
Programme (see Niiler, Chapter 4.1) used currentfollowing drifters to measure directly global flow at
15 m depth. A loosely coordinated WOCE Float
Programme was undertaken with the bold objective, made possible by the new technology discussed above, of establishing over the global ocean
a level of well-measured absolute mean velocity
with which to reference geostrophic shear measurements from WOCE hydrographic sampling and
historical data. Additional objectives were characterizing eddy variability and providing visualization
of transport processes such as intergyre or interbasin transport. In addition to the relatively low
sampling resolution of the global programme, it
was understood from the outset that there would
be special regional foci where higher-resolution
regional deployments would be required. The Deep
Basin Experiment (see Hogg, Chapter 4.5) made
particularly powerful use of Lagrangian methods to
measure deep flow in the Brazil Basin and from
that to infer the mixing processes so critical to the
deep circulation.
Design of the global array was based on an
assessment that by the end of WOCE it would be
possible to map global geostrophic shear with a
lateral resolution near 500 km, which dictated the
target resolution for the float-based reference field.
Measurements could be at any depth but, since
errors in the reference field are added to velocities at
all depths, the velocity measurements must be accurate. The main limitation to accurate determination
of average velocity (say over the WOCE decade)
was identified as temporal variability, which was
thought to result primarily from mesoscale eddies.
The velocity accuracy necessary to provide significant assistance in synthesizing the combined hydrographic and float data set was deemed to vary from
O(3 mm s
91
) across most of the interior ocean to
O(1 cm s
91
) in strong western boundary currents
and the Antarctic Circumpolar Current.
From elementary sampling theory, error U
in the average U of velocity u calculated from N
independent measurements is
U : U / N
1/2
(3.2.1)
and from a continuous time series it is
U : U (T INT / T)
1/2
:(2K/T)
1/2
(3.2.2)
where U is the standard deviation of u variability,
T is the length of the record from which the average is computed, T INT is the integral time scale
of the variable part of u, and K is the asymptotic
lateral Taylor particle diffusivity. The integral time
scale is related to the velocity time-lagged covariance, :u(s)u(s;t)9, and the velocity frequency
spectrum, ⌽(), by the following relations (simplified to one-dimensional flow)
T INT : U
92
͵
∞
9∞
:u(s)u(s;t)9dt
: U
92
2K: U
92
2⌽(:0) (3.2.3)
showing the source of sampling error is the lowest
frequency variability. Although (3.2.2) strictly
applies to a single time series, Davis (1991) argued
it also applies to a collection of time series of total
length T so long as they are statistically independent and long compared to T INT .
The WOCE sampling for a ‘level of known
motion’ was focused near 1000 m depth. This
reflected considerations of acoustic propagation
range, the energy for autonomous floats to complete a cycle and a desire to minimize contact
with bathymetry. It also reflected the demand to
minimize sampling errors in the measured velocity
field. According to equations (3.2.1) and (3.2.2),
this recommends a depth where velocity variability
is minimum and, because the evidence is that eddy
energy decreases with depth in the upper 1 or
2 km, the upper ocean was avoided. This was a
bold decision because, rather than focusing on
levels with the greatest intrinsic interest, it made
success of the global array dependent on its ability
to assist in interpreting post-WOCE hydrography.
At intermediate depths in the North Pacific
Schmitz (1988) found that eddy speeds decreased
from about 10 cm s
91 near the Kuroshio to
3 cm s
91 some 2000 km to the east and that they
decreased with depth above 1500 m. Rossby et al.
(1983) found from analysis of SOFAR float trajectories that the integral time scale was a relatively
constant 10 days, while Böning (1988) analysed a
larger body of float data to find that T INT varies
inversely as U and is approximately 8 days when
U is 10 cm s
91
. These estimates essentially agree
SECTION 3 NEW WAYS OF OBSERVING THE OCEAN
128
This reasoning led to a programme of direct
velocity observations in WOCE. Moored arrays
were used to measure the transport of selected, usually concentrated, currents, and the Surface Velocity
Programme (see Niiler, Chapter 4.1) used currentfollowing drifters to measure directly global flow at
15 m depth. A loosely coordinated WOCE Float
Programme was undertaken with the bold objective, made possible by the new technology discussed above, of establishing over the global ocean
a level of well-measured absolute mean velocity
with which to reference geostrophic shear measurements from WOCE hydrographic sampling and
historical data. Additional objectives were characterizing eddy variability and providing visualization
of transport processes such as intergyre or interbasin transport. In addition to the relatively low
sampling resolution of the global programme, it
was understood from the outset that there would
be special regional foci where higher-resolution
regional deployments would be required. The Deep
Basin Experiment (see Hogg, Chapter 4.5) made
particularly powerful use of Lagrangian methods to
measure deep flow in the Brazil Basin and from
that to infer the mixing processes so critical to the
deep circulation.
Design of the global array was based on an
assessment that by the end of WOCE it would be
possible to map global geostrophic shear with a
lateral resolution near 500 km, which dictated the
target resolution for the float-based reference field.
Measurements could be at any depth but, since
errors in the reference field are added to velocities at
all depths, the velocity measurements must be accurate. The main limitation to accurate determination
of average velocity (say over the WOCE decade)
was identified as temporal variability, which was
thought to result primarily from mesoscale eddies.
The velocity accuracy necessary to provide significant assistance in synthesizing the combined hydrographic and float data set was deemed to vary from
O(3 mm s
91
) across most of the interior ocean to
O(1 cm s
91
) in strong western boundary currents
and the Antarctic Circumpolar Current.
From elementary sampling theory, error U
in the average U of velocity u calculated from N
independent measurements is
U : U / N
1/2
(3.2.1)
and from a continuous time series it is
U : U (T INT / T)
1/2
:(2K/T)
1/2
(3.2.2)
where U is the standard deviation of u variability,
T is the length of the record from which the average is computed, T INT is the integral time scale
of the variable part of u, and K is the asymptotic
lateral Taylor particle diffusivity. The integral time
scale is related to the velocity time-lagged covariance, :u(s)u(s;t)9, and the velocity frequency
spectrum, ⌽(), by the following relations (simplified to one-dimensional flow)
T INT : U
92
͵
∞
9∞
:u(s)u(s;t)9dt
: U
92
2K: U
92
2⌽(:0) (3.2.3)
showing the source of sampling error is the lowest
frequency variability. Although (3.2.2) strictly
applies to a single time series, Davis (1991) argued
it also applies to a collection of time series of total
length T so long as they are statistically independent and long compared to T INT .
The WOCE sampling for a ‘level of known
motion’ was focused near 1000 m depth. This
reflected considerations of acoustic propagation
range, the energy for autonomous floats to complete a cycle and a desire to minimize contact
with bathymetry. It also reflected the demand to
minimize sampling errors in the measured velocity
field. According to equations (3.2.1) and (3.2.2),
this recommends a depth where velocity variability
is minimum and, because the evidence is that eddy
energy decreases with depth in the upper 1 or
2 km, the upper ocean was avoided. This was a
bold decision because, rather than focusing on
levels with the greatest intrinsic interest, it made
success of the global array dependent on its ability
to assist in interpreting post-WOCE hydrography.
At intermediate depths in the North Pacific
Schmitz (1988) found that eddy speeds decreased
from about 10 cm s
91 near the Kuroshio to
3 cm s
91 some 2000 km to the east and that they
decreased with depth above 1500 m. Rossby et al.
(1983) found from analysis of SOFAR float trajectories that the integral time scale was a relatively
constant 10 days, while Böning (1988) analysed a
larger body of float data to find that T INT varies
inversely as U and is approximately 8 days when
U is 10 cm s
91
. These estimates essentially agree
SECTION 3 NEW WAYS OF OBSERVING THE OCEAN
128