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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: [email protected] (< août 2013) [email protected] (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