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Applied stochastic models for ocean engineering, climate and safe transportation

Supplementary material for the paper
Transformed Gaussian stationary models for ocean waves

J.-M. Azaïs, S. Déjean, J.R. León, F. Zwolska.

Data

Data analysed in the paper are extracted from 2 real time series acquired by buoy during period with high waves (click on the image to enlarge):
Hurricane Camilla located at Station 1 of South Pass 62A, 29 04.50' N, 88 44.30' W, with a water depth of 107m and a sampling frequency of 1Hz. The record begins at 18H on 08-16-1969 and stops at 16H next day. Coastal Data Information Program (CDIP), station 076 (Offshore Diablo Canyon Nuclear Power Plant, California) 35 12.23' N 120 51.60' W with a water depth of 23m and a sampling frequency of 1.28 Hz. The record covers the whole day 12-21-2005.

Implementation

Here are pieces of Matlab codes used for computations mentioned in the paper. A more user-friendly implementation (based on F. Zwolska's programs -- fz_code.m, comments in french -- developped during graduate courses in 2006) is now being developped and will soon be available on this page.
  • Estimation of the parameters of the transformed Gaussian model: as a preliminary step, estimation was computed thanks to a first order approximation through the function estim:
function [b,c]= estim(x)
m = mean(x);
v = var(x);
s = skewness(x);
k = kurtosis(x)-3;
a = 1-(s^2)/18;
b = s/6;
c = (3*k-4*(s^2))/72;
  • Simulation of data according to a Gaussian model with the spectrum of the real data: the code used to perform computation partly relies on the WAFO toolbox for Matlab.
  • Spectrum estimated from the real data
S_cam_low = dat2spec(cam_low);
S_cam_high = dat2spec(cam_high);
S_diab_low = dat2spec(diab_low);
S_diab_high = dat2spec(diab_high);
  • Simulation of Gaussian data from the previous spectrum (in a loop)
% for example 1800 corresponds
% to half an hour at frequency 1Hz
simul = spec2sdat(S_cam_low,1800);
res = estim(simul)
Last modified : July 17th, 2007 --- Maintained by Sébastien Déjean
Laboratoire de Statistique et Probabilités - Institut de Mathématiques de Toulouse UMR CNRS 5219