Home > wafo > wavemodels > thvpdf2.m

thvpdf2

PURPOSE ^

Joint (Vcf,Hd) PDF for linear waves with Torsethaugen spectra.

SYNOPSIS ^

[f,varargout] = thvpdf2(Hd,Vcf,Hm0,Tp,normalizedInput)

DESCRIPTION ^

 THVPDF2 Joint (Vcf,Hd) PDF for linear waves with Torsethaugen spectra. 
  
   CALL: f = thvpdf2(Hd,Vcf,Hm0,Tp) 
   
   f   = pdf structure evaluated at meshgrid(Vcf,Hd). 
   Hd  = zero down crossing wave height 
   Vcf = crest front velocity 
   Hm0 = significant wave height [m]. 
   Tp  = Spectral peak period    [s]. 
  
  THVPDF2 approximates the joint PDF of (Vcf, Hd), i.e., crest 
  front velocity (Ac/Tcf) and wave height, for a Gaussian process with a 
  Torsethaugen spectral density. The empirical parameters of the model is 
  fitted by least squares to simulated (Vcf,Hd) data for 600 classes of 
  Hm0 and Tp. Between 50000 and 150000 zero-downcrossing waves were 
  simulated for each class of Hm0 and Tp. 
  THVPDF2 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(0,4*2*Hm0/Tp)'; 
   f  = thvpdf2(h,v,Hm0,Tp); 
   w  = linspace(0,40,5*1024+1).'; 
   S  = torsethaugen(w,[Hm0 Tp]); 
   dt = 0.3; 
   x  = spec2sdat(S,80000,.2); 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, thsspdf

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function [f,varargout] = thvpdf2(Hd,Vcf,Hm0,Tp,normalizedInput) 
002 %THVPDF2 Joint (Vcf,Hd) PDF for linear waves with Torsethaugen spectra. 
003 % 
004 %  CALL: f = thvpdf2(Hd,Vcf,Hm0,Tp) 
005 %  
006 %  f   = pdf structure evaluated at meshgrid(Vcf,Hd). 
007 %  Hd  = zero down crossing wave height 
008 %  Vcf = crest front velocity 
009 %  Hm0 = significant wave height [m]. 
010 %  Tp  = Spectral peak period    [s]. 
011 % 
012 % THVPDF2 approximates the joint PDF of (Vcf, Hd), i.e., crest 
013 % front velocity (Ac/Tcf) and wave height, for a Gaussian process with a 
014 % Torsethaugen spectral density. The empirical parameters of the model is 
015 % fitted by least squares to simulated (Vcf,Hd) data for 600 classes of 
016 % Hm0 and Tp. Between 50000 and 150000 zero-downcrossing waves were 
017 % simulated for each class of Hm0 and Tp. 
018 % THVPDF2 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; 
023 %  Tp = 8; 
024 %  h  = linspace(0,4*Hm0/sqrt(2))';  
025 %  v  = linspace(0,4*2*Hm0/Tp)'; 
026 %  f  = thvpdf2(h,v,Hm0,Tp); 
027 %  w  = linspace(0,40,5*1024+1).'; 
028 %  S  = torsethaugen(w,[Hm0 Tp]); 
029 %  dt = 0.3; 
030 %  x  = spec2sdat(S,80000,.2); 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),pdfplot(fk,'r'),hold off 
036 % 
037 % See also  thspdf, thsspdf 
038  
039 % Reference   
040 % P. A. Brodtkorb (2004),   
041 % The Probability of Occurrence of Dangerous Wave Situations at Sea. 
042 % Dr.Ing thesis, Norwegian University of Science and Technolgy, NTNU, 
043 % Trondheim, Norway.    
044    
045 % History 
046 % revised pab 10.08.2003   
047 % -revised pab 28.11.2002 
048 %   extended the example 
049 % By pab 20.12.2000 
050  
051 error(nargchk(3,5,nargin)) 
052  
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 [V,H] = meshgrid(Vcf,Hd); 
058  
059 f = createpdf(2); 
060 [f.f,Hrms,Vrms,varargout{1:nargout-1}]  = thvpdf(H,V,Hm0,Tp,normalizedInput); 
061 f.x = {Vcf(:),Hd(:)}; 
062   
063 if (normalizedInput) 
064   f.labx = {'Vcf', 'Hd'}; 
065   f.norm = 1; 
066 else 
067   f.norm = 0; 
068   f.labx = {'Vcf [m/s]', 'Hd [m]'}; 
069 end 
070 f.title = 'Joint distribution of (Hd,Vcf) in time'; 
071 f.note = ['Torsethaugen Hm0=' num2str(Hm0) ' Tp = ' num2str(Tp)]; 
072 [f.cl,f.pl] = qlevels(f.f); 
073 return 
074

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

Comments or corrections to the WAFO group


Generated on Thu 06-Oct-2005 02:21:16 for WAFO by m2html © 2003