Velocity Measurements From Gliders

Transcription

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True innovation makes a difference
Ve l o c i t y M e a s u r e m e n t s F r o m
Gliders
Peter J. Rusello
NortekUSA
Boston, MA
NortekUSA Glider Workshop
Ocean Sciences 2012
Wednesday, April 18, 12
M ov i n g P l a t f o r m s
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• Moving platforms include:
Mooring lines
Vertical profilers
Towed arrays
Gliders
AUVs
• Profilers are nominally fixed
in (x,y) and profile in z. They
are subject to mooring line
motion (passive motion).
• Autonomous underwater
vehicles (AUVs) and gliders
actively move in (x,y,z)
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W h y m ov i n g p l a t f o r m s ?
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• Allow high vertical resolution
in measurements.
• Active motion allows
adaptive sampling of regions
of interest.
• A single instrument can be
used to measure along a
transect line, act as a virtual
mooring, or for Lagrangian
tracking of a water mass.
• Gliders and AUV’s can be
deployed from small vessels
and reduce total ship time for
equivalent surveys.
Nortek Glider ADCP
mounted in iRobot
1KA Seaglider
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ADCPs Measure Relative Motion
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• A Doppler instrument
measures motion
relative to the
instrument.
• Platform motion is
implicitly measured.
umeasured = ucurrent
Um
Um
uglider
Ug
Speed over
ground
A positive platform velocity will appear as a
negative measured velocity and vice versa.
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M e a n f l ow v e r s u s Tu r b u l e n c e
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• To accurately estimate mean flows, the platform
motion must be explicitly removed.
• To estimate turbulent fluctuations, the platform
motion can be implicitly removed.
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A quiescent 2D ocean
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z
x
z0
z1
zi
Um (zi ) =
Ug (z0 )
Wm (zi ) =
Wg (z0 )
Ug
Wg
z2
z3
z4
z5
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A 2D ocean with horizontal
currents
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z
Um (zi ) =
x
Ug (z0 ) + Uc (zi )
Wm (zi ) =
z0
z1
Ug
Wg (z0 )
Uc
Wg
z2
z3
z4
z5
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currents
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z
x
Speed over ground
Assume the glider follows the water
0
Ug (z0 ) = Ug (z0 ) + Uc (z0 )
Where Ug' is the glider motion in a
quiescent ocean
z0
Ug
Uc
Wg
Substitute this into the relative motion equation…
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currents
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The measured velocity becomes:
z
x
0
Um (zi ) = Ug (z0 )
typically U 0 (z0 )
g
z0
z1
U g'
+ [Uc (zi )
Uc (z0 )]
[Uc (zi )
Uc (z0 )]
Uc
Wg
z2
z3
z4
z5
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We h a v e a “ q u i e s c e n t ” 2 D o c e a n
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z
y is into the page
Um (zi ) ⇡
x
Wm (zi ) ⇡
z0
z1
zi
Ug (z0 )
Wg (z0 )
Ug
Wg
Vg is motion in or out of the page
z2
z3
z4
z5
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Glider UVW velocities
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Data from a Rutgers glider off of California
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F a c t o r s a f f e c t i n g U g'
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• Roll is used to change heading, can easily be +/- 10º.
• Pitch changes throughout a dive, leads to changes in
forward velocity.
• Different behavior when ascending and descending
(some of this may be due to the system used).
• Drag is dependent on glider Re (O(104-106)).
• Drag also dependent on mounted instrumentation
and glider orientation to the current.
• Leeway is unknown.
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G l i d e r F l i g h t Pa t h
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GPSend
Expected end
position
GPSstart
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L e e wa y
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Leeway
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Depth Averaged Currents
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159 m
185 m
Actual Position - Dead Reckoned Position
= Depth Averaged Current
Δt
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M ov i n g f r o m U g ' t o U g
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• Methods of measuring glider speed over ground (Ug):
Underwater Positioning Systems
Bottom tracking
• Methods of estimating or compensating for Ug:
Shear profiles
Least squares solutions (global problem)
Inertial navigation systems / optimal state estimation (local
problem)
• Each of these methods has advantages and drawbacks.
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U n d e r wa t e r P o s i t i o n i n g S y s t e m s
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Drawbacks include:
Increased power requirements,
multiple platforms to support multiple
transducers, increased material cost,
viability for longterm deployments, etc.
• Super Short, Short, and
Long baseline navigation
systems provide
positional information by
measuring distances
between a target and an
array of transducers.
• Accuracy depends on
the array characteristics.
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B o t t o m Tr a c k i n g
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• Bottom tracking provides an
independent measure of the
platform velocity over the
ground.
• Typical glider ADCPs will have a
range of 10-50 m, while dives will
typically occur over 100-1000 m.
• Bottom tracking utility is highly
dependent on deployment
location.
Usually out
of range
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Iner tial Navigation/Optimal State
Estimation
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• Inertial navigation systems are routinely used on
aircraft and ground robots to estimate the current
state (position, attitude, velocity) of a body.
• INS is subject to integration errors, i.e. cumulative
error since the last known position.
• Optimal state estimation is the statistical treatment of
data to forecast the future state of a system (e.g.
Kalman filtering).
• Kalman filtering is implemented already in most glider
mission planning. It’s use here is one a finer scale and
would incorporate more data.
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L ow e r e d A D C P M e t h o d s
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• Shear Method
Implicitly removes platform motion by differentiating
velocity profiles. Platform motion during an individual
measurement is assumed constant.
• Least squares solutions (Inverse Method)
Solve a set of linear equations representing the
observations to determine the unknown platform and
water velocities. To ensure non-trivial solutions, external
constraints are needed.
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Shear Method
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• The platform motion is assumed
constant during an individual
velocity profile.
• Individual velocity profiles are
differentiated to produce a
composite shear profile.
• There is an unknown integration
constant.
• Two surface GPS fixes can be used
to determine the integration
constant.
• This method is sensitive to
integration errors.
Firing, E., & Gordon, R. L. (1990). Deep ocean acoustic Doppler current profiling. In Proc. IEEE Fourth Working Conf. on
Current Measurements (pp. 192–201).
Fischer, J., & Visbeck, M. (1993). Deep velocity profiling with self-contained ADCP's. Journal Of Atmospheric And
Oceanic Technology, 10(5), 764–773.
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Least Squares Solutions
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umeasured = ucurrent
uglider
zi
zg
Measurements
Desired
uc(z)
Profile
• Describe the measurements
as a system of equations.
• This system will be over- or
under-determined depending
on how the measurements
are treated.
• The system is solved in a
least squares sense for uc(z)
and ug(z).
Visbeck, M. (2002). Deep Velocity Profiling Using Lowered Acoustic Doppler Current Profilers: Bottom Track and
Inverse Solutions*. Journal Of Atmospheric And Oceanic Technology.
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Glider Coordinates
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z
x
Xg
zg
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Glider XYZ velocities
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X
Y
Z
Glider Y velocity is near zero
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Acoustic Backscatter
A no cost data stream
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• Many gliders incorporate
an echo sounder for
both range and
backscatter
measurements.
• An ADCP provides
similar data at no
additional cost in power
with velocity
measurements.
Echosounder
ADCP
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Nor tek Glider ADCP
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• 1 Mhz transmit
frequency
• Small, power efficient
design
• 0.25-2 m range cells
(typical)
• 30 m maximum range
With apologies to Pepsi…
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Acoustic scattering
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• Maximum sensitivity
occurs at ka = 1, where k
is acoustic wavenumber
and a is particle radius.
• For 1 MHz this occurs at
2a = 475 μm
• Many zooplankton will
fall within a reasonable
range of this peak value.
• Suspended sediment will
typically be smaller than
this peak value.
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Example Data from Antarctica
cour tesy Rutgers University
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Velocity Measurements From Gliders

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