for western boundary currents and lead to a 4-year
record being required to reduce the sampling error
to 1 cm s
91 in strong 10 cm s
91 variability. In the
interior the two empirical laws diverge and predict
a range between 2.5 and 7.5 years of record to
achieve 3 mm s
91 accuracy. Thus the sampling
requirements for a global array to determine a
level of known motion on the 500 km scale boils
down to obtaining a 5-year record in every 500 km
by 500 km region, which translates to 1000 floats
with 5-year lives distributed over the ice-free ocean.
An aspect of the WOCE Float Programme’s
design that deserves comment is the goal of
deploying floats uniformly, rather than concentrating them in special regions such as western boundary currents. In part this design reflects the fact
that concentrated deployments in strong currents
are not very effective because the floats are quickly
swept through the region of interest. When longterm averages are sought at reasonable cost it is
necessary to rely on new floats being recruited into
the region of interest as fast as others exit it, and
this requires that floats be deployed into the
source waters of the current as well as the current
itself. Another, more subtle reason for seeking a
uniform sampling array is the bias of the mean
velocity measured by non-uniform Lagrangian
arrays in an eddy field. Just as tracers diffuse
down their concentration gradient, there is an
average transport of floats from a region where,
on average, there is a high concentration of floats
to regions with low average concentration. If C is
the float concentration averaged over the time
used to find the mean velocity U, then the mean
float velocity will be in error by
␦U:9K grad ln C
(3.2.4)
(Davis, 1991). Imagine floats deployed preferentially into a strong current so that the average concentration of floats roughly doubled over 200 km.
A typical boundary current K of O(410
3 m
2 s
91 )
would lead to a significant 2 cm s
91 cross-stream
error in the float-measured mean flow.
Diffusion bias is an example of a characteristic
of quasi-Lagrangian float sampling: because the
velocity being measured determines the location at
which samples are taken, the velocities observed
may not be typical of the field as a whole. The
classical Stokes drift of particles on a material surface in a surface wave field is an example of this
phenomenon. Because the time- or area-averaged
velocity on the measured surface differs from the
average velocity at the average depth of that surface, and because floats tend to stay longer in the
forward flow under crests than in the reverse flow
under troughs, the average velocity of floats can
differ from the Eulerian mean velocity. Indeed
recent theoretical discussions (e.g. Gent and
McWilliams, 1990) indicate that the appropriate
advection velocity for passive tracers in a layer of
thickness h is
U ADV :U;:uЈhЈ9/:h9
(3.2.5)
where U is the Eulerian mean velocity and primes
represent fluctuations around the mean. Floats that
follow the vertical fluid flow (which are then nondiffusive tracers) move at U ADV while isobaric
floats, which respond to part of the Stokes drift
process but not all of it, will follow neither U nor
U ADV exactly. In most of today’s float arrays sampling noise probably masks these relatively small
effects but a comparison of Lagrangian and Eulerian
mean velocities may ultimately be the most direct
way to test theories parameterizing U ADV 9U.
In addition to their sampling biases, pseudoLagrangian observations can be more difficult
to interpret than an equivalent number of fixedposition time series. Because time and space
changes cannot be separated along a single float
trajectory, successful analysis of variability from
float data depends critically on having high enough
sampling density to determine both space and time
structure. In regions with large temporal variability
a few Eulerian measurements (like moorings) are
much more effective in determining temporal variability than are a few floats. On the other hand,
the wandering nature of float trajectories eliminates the topographic biases that can confuse
moored observations and floats are quite effective
in mapping spatial structures if temporal variability is small.
3.2.4 WOCE float observations
3.2.4.1 Implementation and instrumentation
The WOCE Float Programme was undertaken by
scientists from many different nations. Generally a
nation, or a few collaborating nations, took responsibility for observations in a selected region.
Not all the planned deployments were funded and,
3.2 Subsurface Lagrangian Observations during the 1990s
129
Davis and Zenk
record being required to reduce the sampling error
to 1 cm s
91 in strong 10 cm s
91 variability. In the
interior the two empirical laws diverge and predict
a range between 2.5 and 7.5 years of record to
achieve 3 mm s
91 accuracy. Thus the sampling
requirements for a global array to determine a
level of known motion on the 500 km scale boils
down to obtaining a 5-year record in every 500 km
by 500 km region, which translates to 1000 floats
with 5-year lives distributed over the ice-free ocean.
An aspect of the WOCE Float Programme’s
design that deserves comment is the goal of
deploying floats uniformly, rather than concentrating them in special regions such as western boundary currents. In part this design reflects the fact
that concentrated deployments in strong currents
are not very effective because the floats are quickly
swept through the region of interest. When longterm averages are sought at reasonable cost it is
necessary to rely on new floats being recruited into
the region of interest as fast as others exit it, and
this requires that floats be deployed into the
source waters of the current as well as the current
itself. Another, more subtle reason for seeking a
uniform sampling array is the bias of the mean
velocity measured by non-uniform Lagrangian
arrays in an eddy field. Just as tracers diffuse
down their concentration gradient, there is an
average transport of floats from a region where,
on average, there is a high concentration of floats
to regions with low average concentration. If C is
the float concentration averaged over the time
used to find the mean velocity U, then the mean
float velocity will be in error by
␦U:9K grad ln C
(3.2.4)
(Davis, 1991). Imagine floats deployed preferentially into a strong current so that the average concentration of floats roughly doubled over 200 km.
A typical boundary current K of O(410
3 m
2 s
91 )
would lead to a significant 2 cm s
91 cross-stream
error in the float-measured mean flow.
Diffusion bias is an example of a characteristic
of quasi-Lagrangian float sampling: because the
velocity being measured determines the location at
which samples are taken, the velocities observed
may not be typical of the field as a whole. The
classical Stokes drift of particles on a material surface in a surface wave field is an example of this
phenomenon. Because the time- or area-averaged
velocity on the measured surface differs from the
average velocity at the average depth of that surface, and because floats tend to stay longer in the
forward flow under crests than in the reverse flow
under troughs, the average velocity of floats can
differ from the Eulerian mean velocity. Indeed
recent theoretical discussions (e.g. Gent and
McWilliams, 1990) indicate that the appropriate
advection velocity for passive tracers in a layer of
thickness h is
U ADV :U;:uЈhЈ9/:h9
(3.2.5)
where U is the Eulerian mean velocity and primes
represent fluctuations around the mean. Floats that
follow the vertical fluid flow (which are then nondiffusive tracers) move at U ADV while isobaric
floats, which respond to part of the Stokes drift
process but not all of it, will follow neither U nor
U ADV exactly. In most of today’s float arrays sampling noise probably masks these relatively small
effects but a comparison of Lagrangian and Eulerian
mean velocities may ultimately be the most direct
way to test theories parameterizing U ADV 9U.
In addition to their sampling biases, pseudoLagrangian observations can be more difficult
to interpret than an equivalent number of fixedposition time series. Because time and space
changes cannot be separated along a single float
trajectory, successful analysis of variability from
float data depends critically on having high enough
sampling density to determine both space and time
structure. In regions with large temporal variability
a few Eulerian measurements (like moorings) are
much more effective in determining temporal variability than are a few floats. On the other hand,
the wandering nature of float trajectories eliminates the topographic biases that can confuse
moored observations and floats are quite effective
in mapping spatial structures if temporal variability is small.
3.2.4 WOCE float observations
3.2.4.1 Implementation and instrumentation
The WOCE Float Programme was undertaken by
scientists from many different nations. Generally a
nation, or a few collaborating nations, took responsibility for observations in a selected region.
Not all the planned deployments were funded and,
3.2 Subsurface Lagrangian Observations during the 1990s
129
Davis and Zenk