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ohhspdf2

PURPOSE

Joint (Scf,Hd) PDF for linear waves with Ochi-Hubble spectra.

SYNOPSIS

[f,varargout] = ohhspdf2(Hd,Scf,Hm0,def,normalizedInput)

DESCRIPTION

``` OHHSPDF2 Joint (Scf,Hd) PDF for linear waves with Ochi-Hubble spectra.

CALL: f = ohhspdf2(Hd,Scf,Hm0,def)

f   = pdf struct evaluated at meshgrid(Scf,Hd)
Hd  = zero down crossing wave height
Scf = crest front steepness
Hm0 = significant wave height [m].
def = defines the parametrization of the spectral density (default 1)
1 : The most probable spectrum  (default)
2,3,...11 : gives 95% Confidence spectra

OHHSPDF2 approximates the joint distribution of (Scf, Hd) in time,
i.e., crest front steepness (2*pi*Ac/(g*Td*Tcf)) and wave height,
for a Gaussian process with a bimodal Ochi-Hubble spectral density
(ohspec2). The empirical
parameters of the model is fitted by least squares to simulated
(Scf,Hd) data for 24 classes of Hm0. Between 50000 and 150000
zero-downcrossing waves were simulated for each class of Hm0.
OHHSPDF is restricted to the following range for Hm0:
0.5 < Hm0 [m] < 12
The size of f is the common size of the input arguments, Hd, Scf and
Hm0.

Example:
Hm0 = 6;Tp = 8;def= 2;
h = linspace(0,4*Hm0/sqrt(2))';
v = linspace(0,6*1.25*Hm0/Tp^2)';
f = ohhspdf2(h,v,Hm0,def);
w = linspace(0,40,5*1024+1).';
S = ohspec2(w,[Hm0 def]);
dt = 0.3;
x = spec2sdat(S,80000,.2); rate = 8;
[si,hi] = dat2steep(x,rate,2);
fk = kdebin([si,hi],'epan',[],[],.5,128);
fk.title = f.title; fk.labx = f.labx;
plot(si,hi,'.'), hold on
pdfplot(f),pdfplot(fk,'r'),hold off

CROSS-REFERENCE INFORMATION

This function calls:
 createpdf PDF class constructor ohhspdf Joint (Scf,Hd) PDF for linear waves with Ochi-Hubble spectra. qlevels Calculates quantile levels which encloses P% of PDF error Display message and abort function. meshgrid X and Y arrays for 3-D plots. num2str Convert number to string. (Fast version)
This function is called by:

SOURCE CODE

```001 function [f,varargout] = ohhspdf2(Hd,Scf,Hm0,def,normalizedInput)
002 %OHHSPDF2 Joint (Scf,Hd) PDF for linear waves with Ochi-Hubble spectra.
003 %
004 %  CALL: f = ohhspdf2(Hd,Scf,Hm0,def)
005 %
006 %  f   = pdf struct evaluated at meshgrid(Scf,Hd)
007 %  Hd  = zero down crossing wave height
008 %  Scf = crest front steepness
009 %  Hm0 = significant wave height [m].
010 %  def = defines the parametrization of the spectral density (default 1)
011 %        1 : The most probable spectrum  (default)
012 %        2,3,...11 : gives 95% Confidence spectra
013 %
014 % OHHSPDF2 approximates the joint distribution of (Scf, Hd) in time,
015 % i.e., crest front steepness (2*pi*Ac/(g*Td*Tcf)) and wave height,
016 %  for a Gaussian process with a bimodal Ochi-Hubble spectral density
017 % (ohspec2). The empirical
018 % parameters of the model is fitted by least squares to simulated
019 % (Scf,Hd) data for 24 classes of Hm0. Between 50000 and 150000
020 % zero-downcrossing waves were simulated for each class of Hm0.
021 % OHHSPDF is restricted to the following range for Hm0:
022 % 0.5 < Hm0 [m] < 12
023 % The size of f is the common size of the input arguments, Hd, Scf and
024 % Hm0.
025 %
026 % Example:
027 % Hm0 = 6;Tp = 8;def= 2;
028 % h = linspace(0,4*Hm0/sqrt(2))';
029 % v = linspace(0,6*1.25*Hm0/Tp^2)';
030 % f = ohhspdf2(h,v,Hm0,def);
031 % w = linspace(0,40,5*1024+1).';
032 % S = ohspec2(w,[Hm0 def]);
033 % dt = 0.3;
034 % x = spec2sdat(S,80000,.2); rate = 8;
035 % [si,hi] = dat2steep(x,rate,2);
036 % fk = kdebin([si,hi],'epan',[],[],.5,128);
037 %  fk.title = f.title; fk.labx = f.labx;
038 % plot(si,hi,'.'), hold on
039 % pdfplot(f),pdfplot(fk,'r'),hold off
040 %
042
043 % Reference
044 % P. A. Brodtkorb (2004),
045 % The Probability of Occurrence of Dangerous Wave Situations at Sea.
046 % Dr.Ing thesis, Norwegian University of Science and Technolgy, NTNU,
047 % Trondheim, Norway.
048
049
050 % History
051 % revised pab 09.09.2003
052 % By pab 06.02.2001
053
054
055
056 error(nargchk(4,5,nargin))
057
058 if (nargin < 5|isempty(normalizedInput)),  normalizedInput  = 0;end
059 if (nargin < 4|isempty(def)),  def  = 1;end
060 if (nargin < 3|isempty(Hm0)), Hm0 = 6;end
061
062
063 [V,H] = meshgrid(Scf,Hd);
064
065 f = createpdf(2);
066 [f.f,Hrms,Vrms,varargout{1:nargout-1}]  = ohhspdf(H,V,Hm0,def,normalizedInput);
067
068  f.x = {Scf(:),Hd(:)};
069
070 if (normalizedInput)
071   f.labx={'Scf', 'Hd'};
072   f.norm = 1;
073 else
074   f.norm=0;
075   f.labx={'Scf', 'Hd [m]'};
076 end
077 f.title = 'Joint distribution of (Hd,Scf) in time';
078 f.note = ['ohhspec2 Hm0=' num2str(Hm0) ' def = ' num2str(def)];
079 [f.cl,f.pl] = qlevels(f.f);
080
081 return```

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

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