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ohhsspdf2

PURPOSE ^

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

SYNOPSIS ^

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

DESCRIPTION ^

 OHHSSPDF2 Joint (Scf,Hd) PDF linear waves in space with Ochi-Hubble spectra. 
  
   CALL: f = ohhsspdf2(Hd,Scf,Hm0,Tp) 
   
   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 
  
  OHHSSPDF2 approximates the joint distribution of (Scf, Hd), i.e., crest 
  front steepness (Ac/Lcf) and wave height in space, for a Gaussian 
  process with a bimodal Ochi-Hubble spectral density. The empirical 
  parameters of the model is fitted by least squares to simulated 
  (Scf,Hd) data for 24 classes of Hm0. 
  Between 50000 and 300000 zero-downcrossing waves were simulated for 
  each class of Hm0. 
  OHHSSPDF2 is restricted to the following range for Hm0:  
   0.5 < Hm0 [m] < 12 
  
  Example: 
  Hm0 = 6;Tp = 8;def= 2; 
  h = linspace(0,4*Hm0/sqrt(2))';  
  v = linspace(0,Hm0/Tp)'; 
  f = ohhsspdf2(h,v,Hm0,def); 
  w = linspace(0,10,2*1024+1).'; 
  S = ohspec2(w,[Hm0 def]); 
  Sk = spec2spec(specinterp(S,.55),'k1d'); 
  dk = 1; 
  x = spec2sdat(Sk,80000,dk); rate = 8; 
  [vi,hi] = dat2steep(x,rate,1); 
  fk = kdebin([vi,hi],'epan',[],[],.5,128); 
  fk.title = f.title; fk.labx = f.labx;  
  plot(vi,hi,'.'), hold on 
  pdfplot(f), 
  pdfplot(fk,'r'), hold off 
  
  See also  ohhspdf, thvpdf

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function [f,varargout] = ohhsspdf(Hd,Scf,Hm0,def,normalizedInput,condon) 
002 %OHHSSPDF2 Joint (Scf,Hd) PDF linear waves in space with Ochi-Hubble spectra. 
003 % 
004 %  CALL: f = ohhsspdf2(Hd,Scf,Hm0,Tp) 
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 % OHHSSPDF2 approximates the joint distribution of (Scf, Hd), i.e., crest 
015 % front steepness (Ac/Lcf) and wave height in space, for a Gaussian 
016 % process with a bimodal Ochi-Hubble spectral density. The empirical 
017 % parameters of the model is fitted by least squares to simulated 
018 % (Scf,Hd) data for 24 classes of Hm0. 
019 % Between 50000 and 300000 zero-downcrossing waves were simulated for 
020 % each class of Hm0. 
021 % OHHSSPDF2 is restricted to the following range for Hm0:  
022 %  0.5 < Hm0 [m] < 12 
023 % 
024 % Example: 
025 % Hm0 = 6;Tp = 8;def= 2; 
026 % h = linspace(0,4*Hm0/sqrt(2))';  
027 % v = linspace(0,Hm0/Tp)'; 
028 % f = ohhsspdf2(h,v,Hm0,def); 
029 % w = linspace(0,10,2*1024+1).'; 
030 % S = ohspec2(w,[Hm0 def]); 
031 % Sk = spec2spec(specinterp(S,.55),'k1d'); 
032 % dk = 1; 
033 % x = spec2sdat(Sk,80000,dk); rate = 8; 
034 % [vi,hi] = dat2steep(x,rate,1); 
035 % fk = kdebin([vi,hi],'epan',[],[],.5,128); 
036 % fk.title = f.title; fk.labx = f.labx;  
037 % plot(vi,hi,'.'), hold on 
038 % pdfplot(f), 
039 % pdfplot(fk,'r'), hold off 
040 % 
041 % See also  ohhspdf, thvpdf 
042  
043    
044 % Reference   
045 % P. A. Brodtkorb (2004),   
046 % The Probability of Occurrence of Dangerous Wave Situations at Sea. 
047 % Dr.Ing thesis, Norwegian University of Science and Technolgy, NTNU, 
048 % Trondheim, Norway.    
049    
050 % History 
051 % revised pab 09.09.2003 
052 % By pab 20.12.2000 
053  
054  
055 error(nargchk(4,5,nargin)) 
056  
057 if (nargin < 5|isempty(normalizedInput)),  normalizedInput  = 0;end 
058 if (nargin < 4|isempty(def)),  def  = 1;end 
059 if (nargin < 3|isempty(Hm0)), Hm0 = 6;end 
060  
061  
062 [V,H] = meshgrid(Scf,Hd); 
063  
064 f = createpdf(2); 
065 [f.f,Hrms,Vrms,varargout{1:nargout-1}]  = ohhsspdf(H,V,Hm0,def,normalizedInput); 
066  
067  f.x = {Scf(:),Hd(:)}; 
068   
069 if (normalizedInput) 
070   f.labx={'Scf', 'Hd'}; 
071   f.norm = 1; 
072 else 
073   f.norm=0; 
074   f.labx={'Scf', 'Hd [m]'}; 
075 end 
076 f.title = 'Joint distribution of (Hd,Scf) in space'; 
077 f.note = ['ohhspec2 Hm0=' num2str(Hm0) ' def = ' num2str(def)]; 
078 [f.cl,f.pl] = qlevels(f.f); 
079  
080 return

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

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