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A Cooperation Projectwith the
Fugro OCEANOR AS
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Forecasts of Wave Conditions
It is important to all who live, work or travel
on or near sea and ocean
,
measurements of wave parameters are
necessary, which are:
Wave Height
Wave Period
Wave Direction
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Traditional devices for wave
measurements
Ultrasonic: Measures the distance to the surface of
the sea through the emission of ultrasonic wavesfrom an observation device anchored at the sea
bottom. Distance limitations (?)
Accelerometer: With no restriction as to its location
can measure wave parameters by detecting the
horizontal and vertical motions of the buoy.Expensive (?)
GPS Buoy is a cheap alternative
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Analysis of Ocean Wave in the time
domain
Wave height and wave period are commonly used as an
indication of a given wave file.
There are different methods for definition of the wave.
Zero down-crossing method is used to define waveheight and period.
The Permanent International Association of NavigationCongresses (PIANC) and The International Association
of Hydraulic Research (IAHR) use similar definitions.
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Zero Crossing method
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Significant Wave Height
The significant wave height is the value determined by
decomposing a wave record obtained during a certain
period into individual waves, estimating those heights,
rearranging the heights in descending order in size, and
averaging the heights for the top one-third.
3
1
3 N
s ii
H HN =
=
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Maximum Wave Height Maximum wave height is defined as the largest of all
crests to adjacent trough value in the record.
It is possible that the maximum wave height is not the one
causing the maximum crest height.
The most probable maximum wave height in a record can
be estimated from the value of root mean square waveheight (Hrms) or equivalently significant wave height.
max rms
12
2
rms
1
0.2886
ln ln
1 Ni
i
H N HN
H H
N=
= +
=
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Average Wave Period
s
z
z
TT
N=
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Wave Direction
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GPS Measurements Errors
Error Sources Range (1)
Satellite Ephemeris ~2.5m
Satellite clock error ~2m
Expected accuracy (3) of a
single GPS mounted on a buoy
could be around 10 mhorizontally and 20 m
vertically. The error sources are
presented in the Table. It is
Ionospheric effects ~5m
Tropospheric effects ~0.5m
Multipath ~1m
Receiver noise ~1m
error sources, fluctuationscaused by the GPS system, is
on the order of 100 seconds to
several tens of minutes (the time
constant of the GPS errors).
This means that almost allpower of the GPS positioning
error exists in a band less than
0.01 Hz.
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A Single GPS Receiver Height Data
20
25
30
35
vation(m)
0 500 1000 1500 2000 2500 3000 3500 40005
10
15
Time (sec)
Ele
The GPS receiver is Navman Jupiter 21. The sampling rate is 1 Hz and around one
hour of data is recorded for the test experiment. The point positioning using
C/A code pseudorange measurements were performed. Although the GPS antenna isfixed, the positioning results moves on account of GPS errors.
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The Power Spectrum of the GPS Height
Data
7000
8000
9000
10000
This figure shows the
Power spectrum of theGPS positioning data of
the previous slide. This
is the Power spectrum
104
103
102
101
100
101
0
1000
2000
3000
4000
5000
6000
Frequency (Hz)
PowerSpectrum
o e error o
point positioning usingC/A code pseudorange
data. As it was stated in
previous Slides, almost
all of the power of the
GPS positioning error
exists in a band less
than 0.01 Hz.
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A Perfect Harmonic Ocean Wave
MotionWe know that the buoy
movement excited by
ocean wave is rotationalwith a period of 0.1-20
seconds, which
corresponds to 0.05-10 Hz.
shows an experimentperformed in laboratory,
simulating a wave motion
with a period of 11
seconds. The power
spectrum of this wave
data is shown in the next
slide.
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The Power Spectrum of the
Simulated Wave Data
1000
1200
1400
We find an energypeak located at
104
103
102
101
100
0
200
400
600
800
Frequency (Hz)
PowerSpec
tru .
expected.
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Key Principle of Ocean Wave
Measurement using GPS Almost the entire power spectrum of ocean wave data are
in a band higher than 0.05 Hz.
Therefore, a suitably designed high-pass filter can extract
the movement of a GPS e ui ed buo excited b ocean
waves with minimum influence from GPS positioningerrors.
When the high pass filter is adopted, the mean value of theantennas height becomes zero. This is not a problem since
the height of the buoy is not the parameter in question. We
would like to measure the buoys rotational movement.
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Process Algorithm
GPS
Observations
Fourier
High Pass
Filtering
Transfer to
Space Domain
Wave
Parameters
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Laboratory experimentTo test the algorithm in
the previous slide, we
perform a laboratory test
using an apparatus that
consists of a wave simulator
and a GPS receiver. The
wave simulator has a
rotating arm to which a GPS
antenna is fixed. The
rotating arm simulates the
motion of a buoy floating in
the ocean. The diameter of
rotation is 2 meter (wave
height). The rotation speed
can be controlled. The
period is set to 11 seconds
and the direction of the arm
to 266 degrees from the
north.
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Computations
The coordinate system is transformed from latitude, longitude, and height to an
east, north and height local frame. The origin of the local frame is the initial
position from GPS.
The jumps in the GPS position data are removed before high-pass filtering.
Apply the high-pass filter to the pre-processed GPS data by selecting the cut-off
frequency.
Selecting cut-off frequency is very important process as after filtering there will be
very few signals from GPS in a band higher than 0.01 Hz. Therefore results will be
very variable and dependent on the cut-off frequency.
A new procedure to select the cut-off frequency is suggested based on the RMS of
the transformed GPS data back to the time domain from frequency domain after
filtering.
After filtering, the wave parameters are computed by the appropriate equations inthe previous slides.
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High-pass Filtered GPS Data in East
Axis- Lab Test
1
1.5
2
0 500 1000 1500 2000 2500 3000 3500 4000 45001
0.5
0
0.5
Time (sec)
X
Filtered
(m)
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High-pass Filtered GPS Data in North
Axis- Lab Test
0.5
1
0 500 1000 1500 2000 2500 3000 3500 4000 4500
1.5
1
0.5
0
Time (sec)
Y
Filtered(m
)
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High-pass Filtered GPS Data in Height
Axis- Lab Test
0.5
1
1.5
0 500 1000 1500 2000 2500 3000 3500 4000 45001.5
1
0.5
0
Time (sec)
Z
Filtered(
m)
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The Wave Parameters Estimated from
GPS Data- Lab Test
Parameter Experiment result True Value
.
Wave period 11.5 sec 11 sec
Wave direction
264.6 degree 266 degree
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An Open-sea Moored Field Test
A GPS buoy moored along the coast of the An-Ping harborin Tainan, Taiwan.
The same procedure as the
laboratory experiment was carried
out.
A new cut-off frequency was
estimated based on the suggested procedure, which is
different from the laboratory experiment.
Wave parameters were computed using same formulas.
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High-pass Filtered Height GPS Data
Open-sea Moored GPS Buoy
0.4
0.5
0.6
0.7
0 500 1000 1500 2000 2500 3000 3500 4000 4500
0.2
0.1
0
0.1
0.2
0.3
Time (Sec)
Z(m)
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Wave Parameters Estimation
Open-sea Moored GPS BuoyParameter Result
Wave Height 17 cm
Wave period 18.8 sec
Wave direction 226.5 degree
Another study in the north-west coast of Taiwan resulted a wave height
between 20 cm to 4 meter in a two month period. The same study resulted a
wave period between 5 seconds to 15 seconds or more at the same location.