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thcdf

PURPOSE ^

Marginal wave height, Hd, CDF for Torsethaugen spectra.

SYNOPSIS ^

[f,fA,fB] = thcdf(h,Hm0,Tp,dim)

DESCRIPTION ^

 THCDF Marginal wave height, Hd, CDF for Torsethaugen spectra. 
  
   CALL: F = thcdf(h,Hm0,Tp) 
   
   F   = cdf evaluated at h. 
   h   = vector of evaluation points. 
   Hm0 = significant wave height [m]. 
   Tp  = Spectral peak period    [s]. 
   dim = 'time'  : Hd distribution in time (default) 
         'space' : Hd distribution in space 
  
  THCDF approximates the marginal cumulative distribution of Hd, i.e., 
  zero-downcrossing wave height, for a Gaussian process with a Torsethaugen 
  spectral density. The empirical parameters of the model is fitted by 
  least squares to simulated 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. 
  THCDF 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))';  
  F = thcdf(h,Hm0,Tp); 
  dt = 0.4; w = linspace(0,2*pi/dt,256)'; 
  S = torsethaugen(w,[Hm0 Tp]); 
  xs = spec2sdat(S,20000,dt); rate=8; method=1; 
  [S,H] = dat2steep(xs,rate,method); 
  empdistr(H,[h, F],'g') 
  
  See also  thpdf

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function [f,fA,fB] = thcdf(h,Hm0,Tp,dim) 
002 %THCDF Marginal wave height, Hd, CDF for Torsethaugen spectra. 
003 % 
004 %  CALL: F = thcdf(h,Hm0,Tp) 
005 %  
006 %  F   = cdf evaluated at h. 
007 %  h   = vector of evaluation points. 
008 %  Hm0 = significant wave height [m]. 
009 %  Tp  = Spectral peak period    [s]. 
010 %  dim = 'time'  : Hd distribution in time (default) 
011 %        'space' : Hd distribution in space 
012 % 
013 % THCDF approximates the marginal cumulative distribution of Hd, i.e., 
014 % zero-downcrossing wave height, for a Gaussian process with a Torsethaugen 
015 % spectral density. The empirical parameters of the model is fitted by 
016 % least squares to simulated Hd data for 600 classes of Hm0 and 
017 % Tp. Between 50000 and 150000 zero-downcrossing waves were simulated for 
018 % each class of Hm0 and Tp. 
019 % THCDF is restricted to the following range for Hm0 and Tp:  
020 %  0.5 < Hm0 [m] < 12,  3.5 < Tp [s] < 20,  and  Hm0 < (Tp-2)*12/11. 
021 % 
022 % Example: 
023 % Hm0 = 6;Tp = 8; 
024 % h = linspace(0,4*Hm0/sqrt(2))';  
025 % F = thcdf(h,Hm0,Tp); 
026 % dt = 0.4; w = linspace(0,2*pi/dt,256)'; 
027 % S = torsethaugen(w,[Hm0 Tp]); 
028 % xs = spec2sdat(S,20000,dt); rate=8; method=1; 
029 % [S,H] = dat2steep(xs,rate,method); 
030 % empdistr(H,[h, F],'g') 
031 % 
032 % See also  thpdf 
033  
034 % Reference  
035 % P. A. Brodtkorb (2004),   
036 % The Probability of Occurrence of Dangerous Wave Situations at Sea. 
037 % Dr.Ing thesis, Norwegian University of Science and Technolgy, NTNU, 
038 % Trondheim, Norway. 
039    
040 % History 
041 % Revised pab jan2004   
042 % By pab 20.12.2000 
043  
044  
045 error(nargchk(3,4,nargin)) 
046 if nargin<4|isempty(dim), 
047   dim = 'time';% dim='time'->wtweibpdf, dim='space'->wggampdf 
048 end 
049  
050 if Hm0>12| Hm0>(Tp-2)*12/11  
051   disp('Warning: Hm0 is outside the valid range') 
052   disp('The validity of the Hd distribution is questionable') 
053 end 
054 if Tp>20|Tp<3  
055   disp('Warning: Tp is outside the valid range') 
056   disp('The validity of the Hd distribution is questionable') 
057 end 
058 Hrms = Hm0/sqrt(2); 
059 [a b c] = thwparfun(Hm0,Tp,dim); 
060 f = wtweibcdf(h/Hrms,a,b,c); 
061 return 
062  
063 %old call kept just in case 
064 if strncmpi(dim,'t',1)     
065   [a b c] = thwparfun(Hm0,Tp); 
066   f = wtweibcdf(h/Hrms,a,b,c); 
067 else  
068   [a b c] = thgparfun(Hm0,Tp,dim); 
069   f = wggamcdf(h/Hrms,a,b,c); 
070 end 
071 return 
072  
073

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

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