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ohhscdf

PURPOSE ^

Joint (Scf,Hd) CDF for linear waves with Ochi-Hubble spectra.

SYNOPSIS ^

f = ohhscdf(Hd,Scf,Hm0,def,tail)

DESCRIPTION ^

 OHHSCDF Joint (Scf,Hd) CDF for linear waves with Ochi-Hubble spectra. 
  
   CALL: f = ohhscdf(Hd,Scf,Hm0,def) 
   
   f   = cdf 
   Hd  = zero down crossing wave height 
   Scf = crest front steepness 
   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 
  tail = 1 if upper tail is calculated  
         0 if lower tail is calulated  (default) 
  
  OHHSCDF approximates the joint CDF of (Scf, Hd) in time,  
  i.e., crest front steepness (2*pi*Ac/(g*Td*Tcf)) and 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 
  (Scf,Hd) data for 24 classes of Hm0. Between 50000 and 150000 
  zero-downcrossing waves were simulated for each class of Hm0. 
  OHHSCDF is restricted to the following range for Hm0:  
  0.5 < Hm0 [m] < 12 
  The size of f is the common size of the input arguments, Hd, Scf and 
  Hm0.   
  
  Example: 
  Hm0 = 6; def= 2; 
  Ec = 0.25; 
  Hc = 3; 
  lowerTail = 0; 
  upperTail = ~lowerTail   
  ohhscdf(Hc,Ec,Hm0,def)           % Prob(Hd<Hc,Scf<Ec) 
  ohhscdf(Hc,Ec,Hm0,def,upperTail) % Prob(Hd>Hc,Scf>Ec)   
  
  See also  ohhspdf, thspdf

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function f = ohhscdf(Hd,Scf,Hm0,def,tail) 
002 %OHHSCDF Joint (Scf,Hd) CDF for linear waves with Ochi-Hubble spectra. 
003 % 
004 %  CALL: f = ohhscdf(Hd,Scf,Hm0,def) 
005 %  
006 %  f   = cdf 
007 %  Hd  = zero down crossing wave height 
008 %  Scf = crest front steepness 
009 %  Hm0 = significant wave height [m]. 
010 %  def = defines the parametrization of the spectral density (default 1) 
011 %        1 : The most probable spectrum  (default) 
012 %        2,3,...11 : gives 95% Confidence spectra 
013 % tail = 1 if upper tail is calculated  
014 %        0 if lower tail is calulated  (default) 
015 % 
016 % OHHSCDF approximates the joint CDF of (Scf, Hd) in time,  
017 % i.e., crest front steepness (2*pi*Ac/(g*Td*Tcf)) and wave height, 
018 %  for a Gaussian process with a bimodal Ochi-Hubble spectral density 
019 % (ohspec2). The empirical 
020 % parameters of the model is fitted by least squares to simulated 
021 % (Scf,Hd) data for 24 classes of Hm0. Between 50000 and 150000 
022 % zero-downcrossing waves were simulated for each class of Hm0. 
023 % OHHSCDF is restricted to the following range for Hm0:  
024 % 0.5 < Hm0 [m] < 12 
025 % The size of f is the common size of the input arguments, Hd, Scf and 
026 % Hm0.   
027 % 
028 % Example: 
029 % Hm0 = 6; def= 2; 
030 % Ec = 0.25; 
031 % Hc = 3; 
032 % lowerTail = 0; 
033 % upperTail = ~lowerTail   
034 % ohhscdf(Hc,Ec,Hm0,def)           % Prob(Hd<Hc,Scf<Ec) 
035 % ohhscdf(Hc,Ec,Hm0,def,upperTail) % Prob(Hd>Hc,Scf>Ec)   
036 % 
037 % See also  ohhspdf, thspdf 
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    
046 % History 
047 % revised pab 09.09.2003 
048 % By pab 06.02.2001 
049  
050 error(nargchk(3,5,nargin)) 
051 if (nargin < 5|isempty(tail)),  tail  = 0;end 
052 if (nargin < 4|isempty(def)), def=1;end  
053  
054 multipleSeaStates = any(prod(size(Hm0))>1); 
055 if multipleSeaStates 
056   [errorcode, Scf,Hd,Hm0] = comnsize(Scf,Hd,Hm0); 
057 else 
058   [errorcode, Scf,Hd] = comnsize(Scf,Hd); 
059 end 
060 if errorcode > 0 
061     error('Requires non-scalar arguments to match in size.'); 
062 end 
063  
064 if any(Hm0>12| Hm0<=0.5)  
065   disp('Warning: Hm0 is outside the valid range') 
066   disp('The validity of the Hd distribution is questionable') 
067 end 
068  
069 if def>11|def<1  
070   Warning('DEF is outside the valid range') 
071   def = mod(def-1,11)+1; 
072 end 
073  
074 global OHHSPAR 
075 if isempty(OHHSPAR) 
076   OHHSPAR = load('ohhspar.mat'); 
077 end 
078 method = 'cubic'; 
079 Tm020 = OHHSPAR.Tm02; 
080 Hm00  = OHHSPAR.Hm0; 
081 Hrms = Hm0/sqrt(2); 
082 Tm02 = interp1(Hm00,Tm020(:,def),Hm0,method); 
083 Erms = 1.25*Hm0./(Tm02.^2); % Erms 
084  
085  
086  
087 s = Scf./Erms; 
088 hMax = 10; 
089 h = min(Hd./Hrms,hMax); 
090  
091 eps2 = 1e-6; 
092  
093 hlim    = h; 
094  
095 normalizedInput = 1; 
096 lowerTail = 0; 
097  
098 if 0 
099     % This is a trick to get the html documentation correct. 
100     k = ohhspdf(1,1,2,3); 
101   end 
102  
103 if (tail == lowerTail) 
104   k       = find(h>2.5); 
105   hlim(k) = 2.5; 
106   f = gaussq('ohhspdf',0,hlim,eps2/2,[],s,Hm0,def,normalizedInput,5)... 
107       + gaussq('ohhspdf',hlim,h,eps2/2,[],s,Hm0,def,normalizedInput,5);  
108 else % upper tail 
109   k       = find(h<2.5); 
110   hlim(k) = 2.5; 
111   f = gaussq('ohhspdf',h,hlim,eps2/2,[],s,Hm0,def,normalizedInput,7)... 
112       + gaussq('ohhspdf',hlim,hMax,eps2/2,[],s,Hm0,def,normalizedInput,7);  
113 end 
114 return 
115  
116

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

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