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thsspdf2

PURPOSE ^

Joint (Scf,Hd) PDF for linear waves in space with Torsethaugen spectra.

SYNOPSIS ^

[f,varargout] = thsspdf2(Hd,Scf,Hm0,Tp,normalizedInput)

DESCRIPTION ^

 THSSPDF2 Joint (Scf,Hd) PDF for linear waves in space with Torsethaugen spectra. 
  
   CALL: f = thsspdf2(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] 
   Tp  = Spectral peak period    [s] 
  
  THSSPDF2 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 Torsethaugen spectral density. The empirical parameters 
  of the model is fitted by least squares to simulated (Scf,Hd) data for 
  600 classes of Hm0 and Tp. Between 100000 and 1000000 zero-downcrossing 
  waves were simulated for each class of Hm0 and Tp. 
  THSSPDF2 is restricted to the following range for Hm0 and Tp:  
   0.5 < Hm0 [m] < 12,  3.5 < Tp [s] < 20,  and  Hm0 < (Tp-2)*12/11. 
  
  Example: 
  Hm0 = 6;Tp = 8; 
  h = linspace(0,4*Hm0/sqrt(2));  
  v = linspace(0,6*1.25*Hm0/Tp^2); 
  f = thsspdf2(h,v,Hm0,Tp); 
  w = linspace(0,10,2*1024+1).';  
  S = torsethaugen(w,[Hm0 Tp]); 
  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  thspdf

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function [f,varargout] = thsspdf2(Hd,Scf,Hm0,Tp,normalizedInput) 
002 %THSSPDF2 Joint (Scf,Hd) PDF for linear waves in space with Torsethaugen spectra. 
003 % 
004 %  CALL: f = thsspdf2(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 %  Tp  = Spectral peak period    [s] 
011 % 
012 % THSSPDF2 approximates the joint distribution of (Scf, Hd), i.e., crest 
013 % front steepness (Ac/Lcf) and wave height in space, for a Gaussian 
014 % process with a Torsethaugen spectral density. The empirical parameters 
015 % of the model is fitted by least squares to simulated (Scf,Hd) data for 
016 % 600 classes of Hm0 and Tp. Between 100000 and 1000000 zero-downcrossing 
017 % waves were simulated for each class of Hm0 and Tp. 
018 % THSSPDF2 is restricted to the following range for Hm0 and Tp:  
019 %  0.5 < Hm0 [m] < 12,  3.5 < Tp [s] < 20,  and  Hm0 < (Tp-2)*12/11. 
020 % 
021 % Example: 
022 % Hm0 = 6;Tp = 8; 
023 % h = linspace(0,4*Hm0/sqrt(2));  
024 % v = linspace(0,6*1.25*Hm0/Tp^2); 
025 % f = thsspdf2(h,v,Hm0,Tp); 
026 % w = linspace(0,10,2*1024+1).';  
027 % S = torsethaugen(w,[Hm0 Tp]); 
028 % Sk = spec2spec(specinterp(S,.55),'k1d'); 
029 % dk = 1; 
030 % x = spec2sdat(Sk,80000,dk); rate = 8; 
031 % [vi,hi] = dat2steep(x,rate,1); 
032 % fk = kdebin([vi,hi],'epan',[],[],.5,128); 
033 % fk.title = f.title; fk.labx = f.labx;  
034 % plot(vi,hi,'.'), hold on 
035 % pdfplot(f) 
036 % pdfplot(fk,'r'), hold off 
037 % 
038 % See also  thspdf 
039  
040  
041 % Reference   
042 % P. A. Brodtkorb (2004),   
043 % The Probability of Occurrence of Dangerous Wave Situations at Sea. 
044 % Dr.Ing thesis, Norwegian University of Science and Technolgy, NTNU, 
045 % Trondheim, Norway.    
046    
047    
048 % History 
049 % revised pab 09.08.2003   
050 % By pab 20.12.2000 
051  
052 error(nargchk(3,5,nargin)) 
053 if (nargin < 5|isempty(normalizedInput)),  normalizedInput  = 0;end 
054 if (nargin < 4|isempty(Tp)),  Tp  = 8;end 
055 if (nargin < 3|isempty(Hm0)), Hm0 = 6;end 
056  
057  
058 [V,H] = meshgrid(Scf,Hd); 
059  
060 f = createpdf(2); 
061 [f.f,varargout{1:nargout-1}]  = thsspdf(H,V,Hm0,Tp,normalizedInput); 
062  
063  f.x = {Scf(:),Hd(:)}; 
064   
065 if (normalizedInput) 
066   f.labx={'Scf', 'Hd'}; 
067   f.norm = 1; 
068 else 
069   f.norm=0; 
070   f.labx={'Scf', 'Hd [m]'}; 
071 end 
072 f.title = 'Joint distribution of (Hd,Scf) in Space'; 
073 f.note = ['Torsethaugen Hm0=' num2str(Hm0) ' Tp = ' num2str(Tp)]; 
074 try 
075   [f.cl,f.pl] = qlevels(f.f); 
076 end

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

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