february 3, 2010 extreme offshore wave statistics in the north sea
TRANSCRIPT
February 3, 2010
Extreme offshore wave statistics in the North Sea
February 3, 2010
Presentation Structure
Introduction
Background information
Analysis Overview
Analysis
Discussion
Conclusions
Questions
February 3, 2010
Introduction
Flood safety
5-yearly safety assessment of primary water defenses
1. Extreme offshore wave parameters wind, and water levels
2. Translation to nearshore loads
3. Hydraulic load-strength interactions
February 3, 2010
Background I: purpose of the study
1. Extend the time series
1979-2002 1979-2008
2. Replace probability distribution
Conditional Weibull GPD
February 3, 2010
Background II: Stations
Station Name AbbreviationWater Depth
(m)
Schiermonnikoog Noord SON 19
Eierlandse Gat ELD 26
Platform K13A K13 30
IJmuiden-06 YM6 21
Meetpost Noordwijk MPN 18
Euro platform EUR 32
Lichteiland Goeree LEG 21
Schouwenbank SWB 20
Scheur West SCW 15
February 3, 2010
Background III: Wave parameters
1. Significant wave height Hm0
2. Mean wave period Tm-1,0
3. Peak wave period Tpb
equal to Tm-1,0 with frequency limits
restricted to a window around the peak
2
1
fn
n
f
m s f f df s(f) = energy density as a function of frequencyn = the order of the moment (0,1,2,…or -1,-2,…)df = frequency step f1 = lower frequency limitf2 = upper frequency limit
0 04mH m
11,0
0m
mT
m
February 3, 2010
Background IV: EVT
Extreme value theory (EVT) is analogue to the central limit theory:
Central limit theory states that, in the limit, sample means are normally distributed
Extreme value theory states that, in the limit, extreme values (tails of distributions) are distributed by extreme value distributions, regardless of the parent distribution.
For annual peaks, the extreme value distribution is known as the Generalized Extreme Value distribution (GEV). For peaks selected over a threshold, the extreme value distribution is known as the Generalized Pareto Distribution (GPD).
Current study – short time series – GPD
February 3, 2010
Background V: GPD
GPD has three parameters:
ξ = shape parameter
σ = scale parameter
u = threshold
GPD has three tail types
ξ = 0 Type I tail
ξ < 0 Type II tail
ξ > 0 Type III tail
Return period
Ret
urn
valu
e
Tail Type I
Tail Type II
Tail Type III
1
1 1 , for 0( )
1 exp , for 0,u
y
F yy
y = peak excesses over threshold (x-u)
February 3, 2010
Analysis overview
1. Extreme value analysis of wave parameters at each station
2. Regional frequency analysis (RFA): smoothing of GPD shape parameter
3. Refitting of GPD with RFA shape parameters
February 3, 2010
Step 1: EVA @ each station
Extreme Value Analysis Selection of peaks (iid) Fitting a GPD
GPD threshold selection
1
1 1 , for 0( )
1 exp , for 0,u
y
F yy
February 3, 2010
Time
Wa
ve H
eig
ht
+/- 48 hrs
Threshold
Selection of peaks
Independence of peaks
February 3, 2010
Fitting a GPD
1
1 1 , for 0( )
1 exp , for 0,u
y
F yy
Fitting a GPDChoose threshold, uFit shape and scale parameter (ξ and σ)
large sample maximum likelihoodsmall sample probability-weighted moments
0.1 1 10 100 1000 10000Return period (yrs)
Ret
urn
valu
e
selected peaks over threshold I
selected peaks over threshold II
February 3, 2010
Treshold selection
-0.5
0
0.5
1
Threshold
Sha
pe p
aram
eter
6
8
10
12
14
Threshold
Ext
rem
e w
ave
heig
ht (
m)
February 3, 2010
Treshold selection
-0.5
0
0.5
1
Threshold
Sha
pe p
aram
eter
February 3, 2010
February 3, 2010
Initial Fit
0.1 1 10 100 1000 10000Return period (yrs)
Ret
urn
valu
e
selected peaks over thresholdPer station and wave parameter:u, ξ and σ
ξ most influential
Regional Frequency Analysis
February 3, 2010
RFA
Assumptions The parent distribution for the various stations is the same
Differences in shape parameters are due to noise or randomness
The stations belong to a homogeneous region
What is an MRFA? MRFA accounts for inhomogeneity by taking into account
differences in:
Depth
Fetch length
February 3, 2010
Effect of RFA on shape parameters
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
SO
NE
LD K13
YM
6M
PN
EU
RLE
GS
WB
SC
WS
ON
ELD K13
YM
6M
PN
EU
RLE
GS
WB
SC
WS
ON
ELD K13
YM
6M
PN
EU
RLE
GS
WB
SC
W
shap
e pa
ram
eter
February 3, 2010
0 50 100 150 200 250 300 350 400 450 500-0.5
0
0.5
1
1.5
2
number of peaks
GP
D s
hape
par
amet
er ( )
parameter: Hm0 station: LEG
variability - # peaks before RFA
selected in RFA - # peaks after RFA
Refit GPD
Have
Fixed shape parameters - ξRFA
Need
Threshold
Scale parameter
February 3, 2010
Final Fit
10-2
10-1
100
101
102
103
104
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
Return period (year)
Hm
0
Post-RFA Station: LEG Parameter: Hm0
NumPeaks = 253
Thresh = 3.33
shape par = 0.219
All peaks
post-RFA POT
GPD fit
February 3, 2010
Results – GPD vs CW
SON ELD K13 YM6 MPN EUR LEG SWB SCW5
6
7
8
9
10
11
12Hm0: Post-RFA
Hm
0 (m
)
Conditional Weibull
GPD
SON ELD K13 YM6 MPN EUR LEG SWB SCW9
10
11
12
13
14
15
16
17
18
Tm-1,0: Post-RFA
Tm
-1,0
(s)
Conditional Weibull
GPD
SON ELD K13 YM6 MPN EUR LEG SWB SCW10
12
14
16
18
20
22
24Tpb: Post-RFA
Tpb
(s)
Conditional Weibull
GPD
February 3, 2010
Results – extension of time series
SON ELD K13 YM6 MPN EUR LEG SWB SCW4
5
6
7
8
9
10
11Hm0: Post-RFA
Hm
0 (m
)
GPD 2002
GPD 2008
SON ELD K13 YM6 MPN EUR LEG SWB SCW9
10
11
12
13
14
15
16
17
Tm-1,0: Post-RFA
Tm
-1,0
(s)
GPD 2002
GPD 2008
SON ELD K13 YM6 MPN EUR LEG SWB SCW11
12
13
14
15
16
17
18
19
20
21Tpb: Post-RFA
Tpb
(s)
GPD 2002
GPD 2008
February 3, 2010
February 3, 2010
Discussion – Thresholds and Curvature
Return periods of the highest observations
30011.31309.5204.5SCW
2010.5709.4305.5SWB
3011609.6206.1LEG
6011.560010.4606.5EUR
1701431011.7105.9MPN
16015.115012.8307.1YM6
3014.35012.9407.8K13
19015.624013107.5ELD
7016.921014.5608.4SON
Return period
highest peak (s)
Return period
highest peak (s)
Return period
highest peak (m)
Station
TpbTm-1,0Hm0
30011.31309.5204.5SCW
2010.5709.4305.5SWB
3011609.6206.1LEG
6011.560010.4606.5EUR
1701431011.7105.9MPN
16015.115012.8307.1YM6
3014.35012.9407.8K13
19015.624013107.5ELD
7016.921014.5608.4SON
Return period
highest peak (s)
Return period
highest peak (s)
Return period
highest peak (m)
Station
TpbTm-1,0Hm0GPDSeries length: 30 years
February 3, 2010
Wrapping up
ANALYSIS
EVA was carried out at each of nine offshore stations for parameters Hm0, Tm-1,0, and Tp.
The shape parameters from the fitted GPDs were input into an RFA, resulting in spatially-averaged shape parameters
The GPD was fitted to the POT with the fixed post-RFA shape parameters
DISCUSSION
Choice of distribution function
Choice of threshold
February 3, 2010
Questions?