03 wave measurement and analysis

8/7/2019 03 Wave Measurement and Analysis

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Wave Analysis

Short Term and Long Term Analysis

Haryo Dwito Armono. PhDUpdated 4 March 2009


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Introduction

n Short term analysis: analyse of wave

that occurs withinone wave train

n Long term analysis derivation of

statisticaldistributions thatcover manyyears

-0.04

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-0.01

0

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0 5 10 15 20 25 30

Time (sec)

WaterLevel(m)

www.aviso.oseanobs.com


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Why collect wave data?n Monitoring of coastal processes

such as beach erosion andsediment transport.

n Baseline design statistics forcoastal projects.

n Operational assistance in coastalconstruction projects.

n Monitoring of severe weatherconditions.

n Oceanographic research. (Manly Hydraulic Lab : http://mhl.nsw.gov.au/)


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How to measured wave?n Use wave recorder : i.e:

Wave staffsn e.g: www.oceansensorsystem.com

Wave rider / wave buoyn e.g: www.datawell.nl

Pressure sensorn e.g : www.civiltek.com

Satellite imagesn e.g : GFO (Geosat Follow On)

n Place wave recorder in deepwater (>0.5L)

n Record wave height, period and direction (duration 15 60)n Links http://cdip.ucsd.edu, http://mhl.nsw.gov.au/,

http://www.coastal.udel.edu/coastal/comps.html, etc

n Assignment 2 :

n Find more info on wave recorder (product detail, vendors, measurement and analysismethods, etc)

n


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Wave Animation


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Typical wave recorder

http://www.scienceprog.com/wp-content/uploads/2007i/Ocean_embedded/wave_heigh_measurement.jpg

www.datawell.nl

www.civiltek.com

www.oceansensorsystem.com

TRITON-ADVwww.sontek.com

AWACwww.nortek.com


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Typical recorded samples

File created by:Device: Model

Serial No: 1752File Type: WAV

Operating Mod

Contract Refere

Site Reference:


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Triton Webinar


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Termsn Realization

Representative recordat particular timerange

n Ensemble Compilation of several

realization Each ensemble has

parameters such asmean, standarddeviation, skewness,

kurtosis, etcn

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Time (sec)

WaterLevel(m

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0

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0 5 10 15 20 25 30

Time (sec)

WaterLevel(

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0

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0 5 10 15 20 25 30

Time (sec)

WaterLevel(

Ensemble of Three Realizations

1

2

3


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Termsn Stationary

If none of theensemblesparameter (z) vary intimeexp:

2a= 2b

=

2c a = b = c 3a = 3b =

3c 4a = 4b =

4c

n

n ErgodicTime

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0

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0 5 10 15 20 25 30

Time (sec)

WaterLevel(m

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0

0.01

0.02

0.03

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0 5 10 15 20 25 30

Time (sec)

WaterLevel(

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0

0.01

0.02

0.03

0.04

0 5 10 15 20 25 30

Time (sec)

WaterLevel(

a

b

c( )

( ) ( ) ( )

1 1

3

1 1

k a k b k c

k

K N

k k jk j

z z z

zharus sama

z zK N = =

+ +

= =

Assume ergodicity in wave recordsKamphuis, Intro to Coastal Eng & Management


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Short Term Analysis

n Height of waves ( ) are randomn It is impossible to predict exact value of at any

time or locationn Probability that has a certain value is called

PDF (Probability Density Function), p( ).n p( ) can be described by normal distribution.

n

22 2

21

1 1( ) exp ,

22

N

j

j

pN

=

= =

Ntt1 1


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Short Term Analysis contd

n Assumed that H = 2 max , then PDF for H(Probability that H has a certain value)

n

n Rayleigh Distribution

n

n

n

2 2

2 2( ) exp

4 8

H Hp H

=

=

=

===

j

j

tt

tR

t2

Ndt

t

1=

R

R

1

2

0

22 1lim

=

=N

j

jN 1

22 1


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n The Cumulative Distribution Function (CDF) of waveheight: probability that any individual wave height H isless than a specified wave height H

n

n

n

n The Probability of Exceedance: the probability that any

individual wave of height H is greater than a specifiedwave height H :

n

n

2 2 2

2 2 2

0

( ' ) exp 1 exp4 8 8

HH H H

P H H dH

< = =

2

2( ' ) 1 ( ' ) exp 8

H

Q H H P H H

> = < =


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N NE E SE S

Total % 15,51 5,90 6,85 5,82 10,33

6.0 - 6.5 0,01 0,01 0,01 0,01

5.5 - 6.0 0 01 0 02 0 06 0 10

Omnidirectional Percentage Excee

Annual Directional Perc


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0

0.1

0.2

0.3

0.4

0.5

0.60.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8

H/Sigma

(H).p(H),P,Q

(H).p(H)

P

Q


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n Wave height with Probability of Exceedance Q:

n

n 2

2 2

1

18 ( ln ) 2 2 ln

1

Q

N

j

j

H QQ

N

=

= =

=


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Short Term Analysis contdn Example 3.1 Calculation of Short-Term Wave Heightsn

n To analyze a wave record it must be stationary. Hence, it is normalto record waves for relatively short time durations (10 to 20minutes). A longer record would not be stationary because windand water level variations would change the waves. Thus it is

usual to record, for example, 15 minutes every three hours. It issubsequently assumed that the 15 min. record is representativeof the complete three hour recording interval.

n

n Suppose the analysis of such a record yieldsn

n

n We want to calculate significant wave height Hs, average waveheight , average of the highest 1% of the waves , and themaximum wave height in the record.

mandT 0.1sec10 ==

01.0HH


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Long Term Analysis

n Purpose :To organise wave height data

To extrapolate data set to extreme valuesof wave height occuring at low probabilityof exceedance

n Methods

Statistical Analysis of grouped wave dataExtreme Value Analysis from ordered data

n


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Nov 01 - Nov 30, 1983

0

0.51

1.5

2

2.5

3

3.5

4

4.5

0 100 200 300 400 500 600 700 800

Time (hrs from Nov 01, 0:00, 1983)

WaveHeight(m)

Ht = 1.5 m

(2)

(4)

(3)

(1)

(6)

(5)

(8)(7)

Grouped wave data


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Grouped wave data contd

Data in the left table obtainedfrom 34,9 years of record.

= number of data points / yr

= 282306 / 34.9 = 8089

= 2738 / 34.9 = 78.45


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Grouped wave data contd( ' )

1019( ' 1.75) 0.372

2738

1019 549( ' 2.00) 0.573

2738

1019 549 382( ' 2.25) 0.712

2738

( ' ) 1

P P H H

P H

P H

P H

Q Q H H P

=

= =

+ = =

+ + = =

= > =

Curveline is difficult to interpolate! transformed into straightline


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Curve Transformation

n Normal Probability Distribution

n Transferred to:

Log-Normal Probability

Distribution

Gumbel Distribution

Weibull Distribution

Cumulative Distribution Function

Normal Distribution

Log Normal Distribution

Gumbel Distribution

Weibul Distribution

y=A.x + B


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Distribution Models

sH = standard deviation,

H = mean wave height and = Weibull and Gumbel Parameter

= lower limit of H = threshold value in a Peak over Threshold data set


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Probability Table

z = -3.4 P = 3.37 x 10 -4

z = +3.4 P =1 - 3.37 x 10-4

= 0.999663

In Excel : NORMINV

z =0

z = -3.4

Normal Distribution Curve


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(1) (2) (3) (4) (5) (6) (7) (8) (9)

H N P Q z ln H G W

=0.8W

=1.31.75 1019 0.372 0.628 -0.326 0.560 0.012 0.384 0.555

2.00 549 0.573 0.427 0.183 0.693 0.584 0.816 0.883

2.25 382 0.712 0.288 0.560 0.811 1.081 1.316 1.184

2.50 254 0.805 0.195 0.859 0.916 1.528 1.848 1.459

2.75 174 0.869 0.131 1.119 1.012 1.959 2.421 1.723

3.00 113 0.910 0.090 1.339 1.099 2.359 2.996 1.964

3.25 81 0.939 0.061 1.550 1.179 2.772 3.627 2.210

3.50 60 0.961 0.039 1.766 1.253 3.232 4.366 2.477

3.75 40 0.976 0.024 1.976 1.322 3.713 5.176 2.7504.00 27 0.986 0.014 2.190 1.386 4.244 6.105 3.044

4.25 19 0.993 0.007 2.442 1.447 4.916 7.326 3.406

4.50 10 0.996 0.004 2.683 1.504 5.611 8.638 3.769

4.75 4 0.998 0.002 2.849 1.558 6.122 9.632 4.031

5.00 2 0.99854 0.00146 2.976 1.609 6.528 10.436 4.234

5.25 1 0.99890 0.00110 3.063 1.658 6.816 11.014 4.377

5.50 2 0.99963 0.00037 3.378 1.705 7.915 13.276 4.9105.75 0 0.99963 0.00037 3.378 1.749 7.915 13.276 4.910

6.00 1 1.00000 0.000

Total 2738

X in Distribution Models : [1], [6]

Y in Distribution Models : [5], [7], [8], [9]


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Extrapolation

n The Exceedence Probability of one event in TR

years :

n

n

n

n


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Extreme Value Analysis

n If only few major events are known

n

n Limited number of extreme eventsn

n


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Method

n Rank the data in decreasing ordern Calculate Probability of Exceedence (Q)

n

n

i = ranking of the data point N = total number of points

c1, c2 = constants for unbiased plotting positionn Calculate Probability (P)n Calculate Reduced Variate (z, W, G)

n

2

1

cN

ciQ+=


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Constant for Unbiased Plotting

Distribution c1 c2Normal 0.375 0.375Log Normal 0.250 0.125Gumbel 0.440 0.120Weibull 0.2 + 0.27 0.2 + 0.23


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Distribution Models





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Probability Table

z = -3.4 P = 3.37 x 10-4z = +3.4 P = 1- 3.37 x 10-4

= 0.999663

In Excel : NORMINV

Example: =NORMIV(J38,0,1)

z =0

z = -3.4

Normal Distribution Curve


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i H Q W i H Q W

1 5.95 0.010 6.675 23 4.22 0.505 0.621

2 5.38 0.033 4.642 24 4.21 0.527 0.572

3 5.26 0.055 3.775 25 4.20 0.550 0.526

4 5.03 0.078 3.227 26 4.20 0.572 0.482

5 4.82 0.100 2.832 27 4.17 0.595 0.441

6 4.75 0.123 2.524 28 4.17 0.617 0.402

7 4.71 0.145 2.274 29 4.16 0.640 0.365

8 4.68 0.168 2.064 30 4.16 0.662 0.330

9 4.63 0.190 1.884 31 4.14 0.685 0.297

10 4.54 0.213 1.727 32 4.14 0.707 0.266

11 4.49 0.235 1.588 33 4.13 0.730 0.236

12 4.43 0.258 1.463 34 4.09 0.752 0.208

13 4.40 0.280 1.351 35 4.09 0.775 0.182

14 4.38 0.303 1.250 36 4.08 0.797 0.156

15 4.36 0.325 1.157 37 4.07 0.820 0.13316 4.35 0.348 1.071 38 4.07 0.842 0.111

17 4.34 0.370 0.993 39 4.06 0.865 0.090

18 4.33 0.393 0.920 40 4.05 0.887 0.071

19 4.29 0.415 0.852 41 4.04 0.910 0.053

20 4.25 0.437 0.788 42 4.04 0.932 0.036

21 4.24 0.460 0.729 43 4.03 0.954 0.022

22 4.23 0.482 0.673 44 4.01 0.977 0.009

2

1

cN

ciQ

+

=

1

1ln

=

QW


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Plot Extreme Distribution

y = 3.395x - 13.704

R2 = 0.995

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

4 4.5 5 5.5 6 6.5

Wave Height - H (m)

W

eibullReduced

Variate-

Weibull Distribution for Ordered Data Set ( =0.8).

y=A.x + B

A = 3.395

B = - 13.704


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Log-Normal Distribution for Ordered Data Set

y = 5.270x - 7.180R

2= 0.979

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

1.4 1.5 1.6 1.7 1.8 1.9

ln H

ReducedVar

iate-

y=A.x + B

A = 5.270

B = - 7.180


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Gumbel Distribution for Ordered Data Set

y = 2.211x - 8.591

R2

= 0.992

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

4 4.5 5 5.5 6 6.5

Wave Height - H (m)

G

umbelReduced

Variate- y=A.x + B

A = 2.211

B = - 8.591


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Distribution Models





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Return Period Prediction

Return Period (Yrs)

N 20 50 100 20044 1.26 0.80 0.29 3.97 5.22 5.68 6.05 6.43

Return Period (Yrs)

N 20 50 100 20044 1.26 0.45 3.87 5.31 5.73 6.04 6.36

Return Period (Yrs)

N Hln s 20 50 100 200

44 1.26 1.36 0.19 5.44 5.86 6.16 6.45

Weibull

Gumbel

Log Normal

03 wave measurement and analysis

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