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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   
  
  See also  ohhpdf, thspdf

CROSS-REFERENCE INFORMATION ^

This function calls: 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 % 
041 % See also  ohhpdf, thspdf 
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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