Partitionnement de spectres et statistiques sur Partitionnement de spectres et statistiques sur l’acuité (l’acuité () des systèmes de vagues observés ) des systèmes de vagues observés sur le site d’expérimentation EMR SEM-REVsur le site d’expérimentation EMR SEM-REV

J-Baptiste SAULNIEREcole Centrale de Nantes, LHEEA (France)

Ile de Berder – 05/07/2013

(Comm. OMAE2013-11470)

Introduction

• Marine Renewable Energy needs fine characterisation of environmental parameters, and sea state ones in particular (design, survivability, commissioning/decommissioning…) Wave spectra from in situ measurements (wave buoys, ADCPs…)

• Statistics of Hs, Tp… and spectral peakedness (bandwidth/narrowness) required in particular for simulating extreme sea states (fatigue and survivability) using e.g. JONSWAP spectra effect of wave groups

• A sea state is the combination of several independent wave systems (swell(s) and wind-sea) Sea state partitioning for considering wave systems individually and the peakedness characterising each system

- I -

WAVE SYSTEM IDENTIFICATION AND MODELLING

Goal

Complex sea state

Hm0

Tp, T02…

θp, θm…

γ (shape)...???… Not relevant if more than 1 peak in the spectrum

Individual components ‘i’

(swells, wind-sea) i , Hm0,i

Tp,i, T02,i…

θp,i, θm,i…

γi

…More relevant physically

(simulations, design…)

Simple methodology

SWELL

WIND-SEA

Ŝ(f,θ)

Bimodal directional spectrum estimated from buoy

measurements (with smoothing)

Watershed partitioning algorithm= path of steepest ascent technique

(e.g. Hanson & Phillips, 2001)

Partitioning of the discrete spectral matrix Ŝ(fi,θj)

(source: dir. wave buoy, ADCP, array of sensors… or numerical models)

Simplified watershed technique [Hanson et Phillips, 2001]

STEP 1

Partitions grouping:Partitions with fp > fs PARTITION 1 = WIND-SEA

Partitions with fp <= fs & Hm0 >= Hmin PARTITION = SWELL j

Partitions with fp <= fs & Hm0 < Hmin GROUPED WITH SWELL WITH CLOSEST fp

Fitting of analytical shapes (least-squares minimisation)JONSWAP for Sj (f) (∫partition_j(f,θ) dθ) [Hasselmann et al., 1973]

Cos^2s for Dj (θ) (∫partition_j(f,θ) df) [e.g. Mitsuyasu et al., 1975]

Set of parameters for each identified

wave system

JONSWAP

Cos^2s

STEP 2

STEP 3

fs = separation frequency

P partitions identified (1 wind-sea + (P-1) swells)

0.05 0.1 0.15 0.2 0.25 0.30

2

4

6

8

10

12

Frequency[Hz]

Wa

ve s

pe

ctra

l de

nsi

ty[m

2 /Hz]

= 1 = 3.3 = 7

0 45 90 135 180 225 270 315 3600

0.5

1

1.5

2

Direction[°]

Dir.

sp

rea

din

g fu

nct

ion

[1/r

ad

]

s = 2s = 10s = 50

JONSWAP spectra(gamma = 1, 3.3, 7)

Cos^2s function(s = 2, 10, 50)

Frequency fitting shapes…

… Directional fitting shapes(not crucial here)

0 0.1 0.2 0.3 0.4 0.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Frequency[Hz]

Spec

tral

den

sity

[m2 /Hz]

SEM-REV - 05-Jan-2011 07:00:00

OriginalNot corrected fitCorrected fit

SCΣ ˆ

nnn fff

fff

fff

p21

2p2221

1p1211

SSS

SSS

SSS

Σ

%100

ˆ

ˆ

1

1

n

iii

i

n

iii

ffS

ffSfSeGoodness-of-fit estimator:

Correction of mutual influences [Kerbiriou et al., 2007]

Correction of Hm0,j so as to minimise the area difference of the total reconstructed density S(f) with target Ŝ(f)

STEP 4

e ~ 25%

- II -

SEM-REV WAVE DATA

SEM-REV location

Nantes(50km)

Loire estuary

SEM-REV location

ADCP

W WAVE BUOY E WAVE BUOY

BMTO2

Datawell directional buoy and spectral processing:

•Measurements of {x,y,z} motions (continuous)•1.28Hz sampling rate•HF radio transmission + onboard storage•1h-based signals for cross-spectral analysis•36 non-overlapping 100s periodograms (72 dof)•Cos^2s directional reconstruction (based on 1st- and 2nd-order dir. Fourier coefficients)•Δf = 0.01Hz, Δθ = 10°•Spectral smoothing (3x3 cell moving average)

8748 hourly directional spectra in 2011 (easternmost buoy) over 8760 expected (99.9% success rate)

- III -

RESULTS AND DISCUSSION

Processing of SEM-REV 2011 hourly dir. spectra

Separation frequency swell/wind-sea:

Interpolated (1h) ECMWF ERA-Interim 10m-height wind speed for location (4.75°N, 3.0°W) close to SEM-REV In practice here: fs = min(g/2πβU10 , 0.20Hz)

Min. threshold for swell partition grouping : Hmin = 0.20m

00.10.20.30.40.5

f p, f

s[H

z]

01234

Hm

0[m

],

Uw

,10/2

[m/s

]0

90180270360

p,

w,1

0[º]

012345

[-]

015304560

[º]

07/02 08/02 09/02 10/02 11/02 12/02 13/02 14/02 15/020

15304560

e[%

]

Time evolution of wave system

parameters(~18600 systems

extracted,~2.1 syst./s.s.)

No time tracking

Correlation to ECMWF wind data

(ERA-Interim)

ECMWF wind data

e mean = 17,7% (95% | e ≤ 30%)

Algorithm performance

/8748

Sea states may be considered as unimodal

only 25% to 64% of time!(according to threshold)

Sea states type in SEM-REV (2011) for different Hm0 thresholds(i.e., wave systems with Hm0 lower than this value are disregarded in the counting)

0 5 100

10

20

30

[-]

Occ

urrence

rate

[%]

Hm0 > 0.5m, 0.04Hz<f<=0.08Hz

= 1.60

0 5 100

10

20

30

40

[-]

Occ

urrence

rate

[%]

Hm0 > 0.5m, 0.08Hz<f<=0.12Hz

= 1.47

0 5 100

10

20

30

40

[-]

Occ

urrence

rate

[%]

Hm0 > 0.5m, 0.12Hz<f<=0.15Hz

= 1.46

0 5 100

10

20

30

[-]

Occ

urrence

rate

[%]

Hm0 > 0.5m, 0.15Hz<f<=0.2Hz

= 1.81

0 5 100

10

20

30

[-]

Occ

urrence

rate

[%]

Hm0 > 0.5m, 0.2Hz<f<=0.5Hz

= 2.14

0 5 100

10

20

30

40

[-]

Occ

urrence

rate

[%]

Hm0 > 1m, 0.04Hz<f<=0.08Hz

= 1.38

0 5 100

20

40

60

[-]

Occ

urrence

rate

[%]

Hm0 > 1m, 0.08Hz<f<=0.12Hz

= 1.27

0 5 100

10

20

30

40

[-]O

ccurrence

rate

[%]

Hm0 > 1m, 0.12Hz<f<=0.15Hz

= 1.38

0 5 100

10

20

30

[-]

Occ

urrence

rate

[%]

Hm0 > 1m, 0.15Hz<f<=0.2Hz

= 1.65

0 5 100

10

20

30

[-]

Occ

urrence

rate

[%]

Hm0 > 1m, 0.2Hz<f<=0.5Hz

= 2.28

0 5 100

10

20

30

40

[-]

Occ

urrence

rate

[%]

Hm0 > 3m, 0.04Hz<f<=0.08Hz

= 1.36

0 5 100

20

40

60

[-]

Occ

urrence

rate

[%]

Hm0 > 3m, 0.08Hz<f<=0.12Hz

= 1.21

0 5 100

20

40

60

[-]

Occ

urrence

rate

[%]

Hm0 > 3m, 0.12Hz<f<=0.15Hz

= 1.90

[0.04;0.08Hz[ [0.08;0.12Hz[ [0.12;0.15Hz[ [0.15;0.20Hz[ [0.20;0.50Hz[

f

SWELLS WIND-SEAS?

Hm0,i > 0,5m

Hm0,i > 1m

Hm0,i > 3m

Peakedness statistics (γ < 10, -3%)

no data

no data

• Again, statistics vary according to Hm0 threshold

• Mean peakedness values found within [1;2] (except HF)Values range from 1 to 5 mostly, even for swells

• In ]0.04; 0.12Hz] (swells) γ decreases with fp on average consistent with theory of swell evolution

[e.g. Gjevik et al., 1988]

• Above 0.15Hz γ (wind-seas) increases with fp on average consistent with JONSWAP observations as peakedness

decreases during sea growth [Hasselmann et al., 1973]

• [5% bias to be deducted from γ here approx. due to sampling variability in the spectral estimation with 72 dof(see paper OMAE2013-10004, same author)]

2 4 6 8 100

1

2

3

4

5

6

Hm0

[m]

[-]

]0.04;0.08Hz]]0.08;0.12Hz]]0.12;0.15Hz]]0.15;0.20Hz]]0.20;0.50Hz]

= 0.219*Hm0

+0.43

Peakedness in severe sea states

fatigue, survivability, certifications…

Severe sea state: Hm0 > 3m (> 8m Joachim storm in December 2011)

Regression line: γ (biased) against Hm0

for Hm0 > 3m (100% sea states are unimodal)

More data required

Storms with low fp

within ]0.04Hz;0.12Hz]

- IV -

CONCLUSIONS & FURTHER WORKS

• On average, JONSWAP peakedness γ decreases and increases with peak frequency within [1;2] – from swell to wind-sea frequency range (most values within [~1;5] for both)

• Partitioning algorithm successful: In SEM-REV in 2011, sea states could be considered as unimodal 64% of time at best partitioning required for metocean and engineering studies

• Further work 1: JONSWAPs adapted to the spectral modelling of swells?... (preliminary results available now)

• Further work 2: dynamic tracking of wave systems for better system type identification

Merci de votre attention

Contact: jbsaulni@ec-nantes.fr (< août 2013) toupaixil@yahoo.fr (ensuite)

Interval Hm0 min0.2m 0.5m 1m 3m

0.04-0.08Hz 9.2% 7.0% 3.9% 0.2%0.08-0.12Hz 29.6% 21.6% 10.0% 0.6%0.12-0.15Hz 10.5% 7.1% 4.8% <0.1%0.15-0.20Hz 8.5% 6.0% 9.9% 00.20-0.30Hz 16.5% 10.1% 1.1% 00.30-0.50Hz 15.4% 2.3% 0 00.20-0.50Hz 31.9% 12.4% 1.1% 0

Cable routeSEM-REV

Le Croisic town

Salt evaporation ponds of Guérande

SEM-REV location