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ohhcdf

PURPOSE ^

Marginal wave height, Hd, CDF for Ochi-Hubble spectra.

SYNOPSIS ^

f = ohhcdf(h,Hm0,def,dim,norm,pdef)

DESCRIPTION ^

 OHHCDF Marginal wave height, Hd, CDF for Ochi-Hubble spectra. 
  
   CALL: f = ohhcdf(h,Hm0,def,dim) 
   
   f   = cdf evaluated at h. 
   h   = vectors of evaluation points. 
   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 
  dim = 'time'  : Hd distribution in time (default) 
        'space' : Hd distribution in space 
  
  OHHCDF approximates the marginal PDF of Hd, i.e., 
  zero-downcrossing wave height, for a Gaussian process with a Bimodal 
  Ochi-Hubble spectral density (ohspec2). The empirical parameters of 
  the model is fitted by least squares to simulated Hd data for 24 
  classes of Hm0. Between 50000 and 150000 zero-downcrossing waves were 
  simulated for each class of Hm0 in DIM=='time'. 
  Between 50000 and 300000 zero-downcrossing waves were 
  simulated for each class of Hm0 for DIM=='space'. 
  OHHCDF is restricted to the following range for Hm0:  
   0 < Hm0 [m] < 12,  1 <= def < 11,  
  
  Example: 
  Hm0 = 6;def = 8; 
  h = linspace(0,4*Hm0/sqrt(2))';  
  f = ohhcdf(h,Hm0,def); 
  plot(h,f) 
  dt = 0.4; w = linspace(0,2*pi/dt,256)'; 
  xs = spec2sdat(ohspec2(w,[Hm0, def]),6000); rate=8; method=1; 
  [S,H] = dat2steep(xs,rate,method); 
  empdistr(H,[h f],'g') 
  
  See also  ohhvpdf

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function f = ohhcdf(h,Hm0,def,dim,norm,pdef) 
002 %OHHCDF Marginal wave height, Hd, CDF for Ochi-Hubble spectra. 
003 % 
004 %  CALL: f = ohhcdf(h,Hm0,def,dim) 
005 %  
006 %  f   = cdf evaluated at h. 
007 %  h   = vectors of evaluation points. 
008 %  Hm0 = significant wave height [m]. 
009 %  def = defines the parametrization of the spectral density (default 1) 
010 %        1 : The most probable spectrum  (default) 
011 %        2,3,...11 : gives 95% Confidence spectra 
012 % dim = 'time'  : Hd distribution in time (default) 
013 %       'space' : Hd distribution in space 
014 % 
015 % OHHCDF approximates the marginal PDF of Hd, i.e., 
016 % zero-downcrossing wave height, for a Gaussian process with a Bimodal 
017 % Ochi-Hubble spectral density (ohspec2). The empirical parameters of 
018 % the model is fitted by least squares to simulated Hd data for 24 
019 % classes of Hm0. Between 50000 and 150000 zero-downcrossing waves were 
020 % simulated for each class of Hm0 in DIM=='time'. 
021 % Between 50000 and 300000 zero-downcrossing waves were 
022 % simulated for each class of Hm0 for DIM=='space'. 
023 % OHHCDF is restricted to the following range for Hm0:  
024 %  0 < Hm0 [m] < 12,  1 <= def < 11,  
025 % 
026 % Example: 
027 % Hm0 = 6;def = 8; 
028 % h = linspace(0,4*Hm0/sqrt(2))';  
029 % f = ohhcdf(h,Hm0,def); 
030 % plot(h,f) 
031 % dt = 0.4; w = linspace(0,2*pi/dt,256)'; 
032 % xs = spec2sdat(ohspec2(w,[Hm0, def]),6000); rate=8; method=1; 
033 % [S,H] = dat2steep(xs,rate,method); 
034 % empdistr(H,[h f],'g') 
035 % 
036 % See also  ohhvpdf 
037  
038 % Reference  
039 % P. A. Brodtkorb (2004),   
040 % The Probability of Occurrence of Dangerous Wave Situations at Sea. 
041 % Dr.Ing thesis, Norwegian University of Science and Technolgy, NTNU, 
042 % Trondheim, Norway.    
043    
044 % History 
045 % revised pab jan2004   
046 % By pab 20.01.2001 
047  
048  
049 error(nargchk(2,4,nargin)) 
050  
051 if nargin<4|isempty(dim), dim  = 'time';end  
052 if nargin<3|isempty(def), def  = 1;end  
053  
054 if Hm0>12| Hm0<=0  
055   disp('Warning: Hm0 is outside the valid range') 
056   disp('The validity of the Hd distribution is questionable') 
057 end 
058  
059 if def>11|def<1  
060   Warning('DEF is outside the valid range') 
061   def = mod(def-1,11)+1; 
062 end 
063  
064 Hrms = Hm0/sqrt(2); 
065 [A0, B0, C0] = ohhgparfun(Hm0,def,dim); 
066 f    = wggamcdf(h/Hrms,A0,B0,C0); 
067 return 
068 %old calls 
069 % pardef = 7; 
070 % switch pardef 
071 %   case 1 
072 %      w    = linspace(0,100,16*1024+1).'; % original spacing 
073 %      S = ohspec2(w,[Hm0,def]); 
074 %      R  = spec2cov(S); 
075 %      %    A0 = sqrt((1-min(R.R)/R.R(1))/2);% Naess (1985) 
076 %      A0 = sqrt((1-min(R.R)/R.R(1))/2)+0.03;% Modified approach broadbanded time 
077 %      %    A0 = sqrt((1-min(R.R)/R.R(1))/2)+0.1;% Modified approach broadbanded space                                  
078                        
079 %     B0 = 2; 
080 %     C0 = 0; 
081 %   case 7, 
082 %     global OHHWPAR 
083 %     if isempty(OHHWPAR) 
084 %       OHHWPAR = load('thwpar.mat'); 
085 %     end 
086 %     % Truncated Weibull  distribution parameters as a function of Tp, Hm0  
087 %     A00 = OHHWPAR.A00s; 
088 %     B00 = OHHWPAR.B00s; 
089 %     C00 = OHHWPAR.C00s; 
090  
091 %     Hm00 = OHHWPAR.Hm0; 
092 %     if 1, 
093 %       method = '*cubic'; 
094 %       A0 = interp1(Hm00,A00(:,def),Hm0,method); 
095 %       B0 = interp1(Hm00,B00(:,def),Hm0,method); 
096 %       C0 = interp1(Hm00,C00(:,def),Hm0,method); 
097 %     else 
098 %       A0 = smooth(Hm00,A00(:,def),1,Hm0); 
099 %       B0 = smooth(Hm00,B00(:,def),1,Hm0); 
100 %       C0 = smooth(Hm00,C00(:,def),1,Hm0); 
101 %     end 
102   
103 % end 
104  
105 %Hrms = Hm0/sqrt(2); 
106 %f.f    = wtweibcdf(h/Hrms,A0,B0,C0)/Hrms; 
107  
108 return 
109

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

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