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jhspdf2

PURPOSE ^

Joint (Scf,Hd) PDF for linear waves with a JONSWAP spectrum.

SYNOPSIS ^

[f,Hrms,Srms,fA,fB] = jhspdf2(Hd,Scf,Hm0,Tp,gam,normalizedInput)

DESCRIPTION ^

 JHSPDF2 Joint (Scf,Hd) PDF for linear waves with a JONSWAP spectrum. 
  
   CALL: f = jhspdf2(Hd,Scf,Hm0,Tp,gamma) 
   
   f     = pdf struct evaluated at meshgrid(Scf,Hd) 
   Hd    = zero down crossing wave height 
   Scf   = crest front steepness 
   Hm0   = significant wave height 
   Tp    = Spectral peak period  
   Gamma = Peakedness parameter of the JONSWAP spectrum 
  
  JHSPDF2 approximates the joint distribution of (Scf, Hd), i.e., crest 
  front steepness (2*pi*Ac/(g*Td*Tcf)) and wave height, for a Gaussian 
  process with a JONSWAP spectral density. The empirical parameters of 
  the model is fitted by least squares to simulated (Scf,Hd) data for 13 
  classes of GAMMA between 1 and 7. Between 47000 and 55000 
  zero-downcrossing waves were simulated for each class. 
  JHSPDF2 is restricted to the following range for GAMMA:  
   1 <= GAMMA <= 7  
  
  Example: 
  Hm0 = 6;Tp = 9; gam=3.5 
  h = linspace(0,4*Hm0/sqrt(2))';  
  s = linspace(0,6*1.25*Hm0/Tp^2)'; 
  f = jhspdf2(h,s,Hm0,Tp,gam); 
  w = linspace(0,40,5*1024+1).'; 
  S = jonswap(w,[Hm0, Tp, gam]); 
  dt = .3; 
  x = spec2sdat(S,80000,dt); rate = 4; 
  [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  jhspdf

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function [f,Hrms,Srms,fA,fB] = jhspdf2(Hd,Scf,Hm0,Tp,gam,normalizedInput) 
002 %JHSPDF2 Joint (Scf,Hd) PDF for linear waves with a JONSWAP spectrum. 
003 % 
004 %  CALL: f = jhspdf2(Hd,Scf,Hm0,Tp,gamma) 
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 
010 %  Tp    = Spectral peak period  
011 %  Gamma = Peakedness parameter of the JONSWAP spectrum 
012 % 
013 % JHSPDF2 approximates the joint distribution of (Scf, Hd), i.e., crest 
014 % front steepness (2*pi*Ac/(g*Td*Tcf)) and wave height, for a Gaussian 
015 % process with a JONSWAP spectral density. The empirical parameters of 
016 % the model is fitted by least squares to simulated (Scf,Hd) data for 13 
017 % classes of GAMMA between 1 and 7. Between 47000 and 55000 
018 % zero-downcrossing waves were simulated for each class. 
019 % JHSPDF2 is restricted to the following range for GAMMA:  
020 %  1 <= GAMMA <= 7  
021 % 
022 % Example: 
023 % Hm0 = 6;Tp = 9; gam=3.5 
024 % h = linspace(0,4*Hm0/sqrt(2))';  
025 % s = linspace(0,6*1.25*Hm0/Tp^2)'; 
026 % f = jhspdf2(h,s,Hm0,Tp,gam); 
027 % w = linspace(0,40,5*1024+1).'; 
028 % S = jonswap(w,[Hm0, Tp, gam]); 
029 % dt = .3; 
030 % x = spec2sdat(S,80000,dt); rate = 4; 
031 % [si,hi] = dat2steep(x,rate,2); 
032 % fk = kdebin([si,hi],'epan',[],[],.5,128);  
033 % fk.title = f.title; fk.labx = f.labx;   
034 % plot(si,hi,'.'), hold on 
035 % pdfplot(f),pdfplot(fk,'r'),hold off 
036 % 
037 % See also  jhspdf 
038  
039    
040 % Reference   
041 % P. A. Brodtkorb (2004),   
042 % The Probability of Occurrence of Dangerous Wave Situations at Sea. 
043 % Dr.Ing thesis, Norwegian University of Science and Technolgy, NTNU, 
044 % Trondheim, Norway.  
045    
046 error(nargchk(3,6,nargin)) 
047  
048 if (nargin < 6|isempty(normalizedInput)),  normalizedInput  = 0;end 
049 if (nargin < 4|isempty(Tp)),  Tp  = 8;end 
050 if (nargin < 3|isempty(Hm0)), Hm0 = 6;end 
051 if (nargin < 5|isempty(gam)) 
052    gam = getjonswappeakedness(Hm0,Tp); 
053 end 
054 displayWarning = 1; 
055 if displayWarning 
056   if any(any(Tp>5*sqrt(Hm0) | Tp<3.6*sqrt(Hm0))) 
057     disp('Warning: Hm0,Tp is outside the JONSWAP range') 
058     disp('The validity of the parameters returned are questionable') 
059   end 
060 end 
061  
062 [V,H] = meshgrid(Scf,Hd); 
063  
064 f = createpdf(2); 
065 [f.f,Hrms,Srms,varargout{1:nargout-1}]  = jhspdf(H,V,Hm0,Tp,gam,normalizedInput); 
066 f.x = {Scf(:),Hd(:)}; 
067   
068 if (normalizedInput) 
069   f.labx = {'Scf', 'Hd'}; 
070   f.norm = 1; 
071 else 
072   f.norm = 0; 
073   f.labx = {'Scf [m/s]', 'Hd [m]'}; 
074 end 
075 f.title = 'Joint distribution of (Hd,Scf) in time'; 
076 f.note = ['Jonswap Hm0=' num2str(Hm0) ' Tp = ' num2str(Tp) ' Gamma = ' num2str(gam)]; 
077 [f.cl,f.pl] = qlevels(f.f); 
078 return 
079

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

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