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  Replace probability distribution Conditional Weibull  GPD

February 3, 2010 Background II: Stations Station NameAbbreviation Water Depth (m) Schiermonnikoog NoordSON19 Eierlandse GatELD26 Platform K13AK1330 IJmuiden-06YM621 Meetpost NoordwijkMPN18 Euro platformEUR32 Lichteiland GoereeLEG21 SchouwenbankSWB20 Scheur WestSCW15

February 3, 2010 Background III: Wave parameters 1.Significant wave height H m0  2.Mean wave period T m-1,0  3.Peak wave period T pb  equal to T m-1,0 with frequency limits restricted to a window around the peak s(f) = energy density as a function of frequency n = the order of the moment (0,1,2,…or -1,-2,…) df = frequency step f1 = lower frequency limit f2 = upper frequency limit

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 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: each station Extreme Value Analysis  Selection of peaks (iid)  Fitting a GPD  GPD threshold selection

February 3, /- 48 hrs Threshold Selection of peaks [v1] Independence of peaks

February 3, 2010 Fitting a GPD  Choose threshold, u  Fit shape and scale parameter (ξ and σ)  large sample  maximum likelihood  small sample  probability-weighted moments

February 3, 2010 Treshold selection

February 3, 2010 Treshold selection

February 3, 2010

Initial Fit Per 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

February 3, 2010 Refit GPD Have Fixed shape parameters - ξ RFA Need Threshold Scale parameter

February 3, 2010 Final Fit

February 3, 2010 Results – GPD vs CW

February 3, 2010 Results – extension of time series

February 3, 2010

Discussion – Thresholds and Curvature Return periods of the highest observations GPD Series length: 30 years

February 3, 2010 Wrapping up  ANALYSIS  EVA was carried out at each of nine offshore stations for parameters H m0, T m-1,0, and T p.  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?