Wave Height

7/29/2019 Wave Height

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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.

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Wave Height