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jhscdf

PURPOSE ^

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

SYNOPSIS ^

f = jhscdf(Hd,Scf,Hm0,Tp,gam,tail)

DESCRIPTION ^

 JHSCDF Joint (Scf,Hd) CDF for linear waves with a JONSWAP spectrum. 
  
   CALL: f = jhscdf(Hd,Scf,Hm0,Tp,Gamma,tail) 
   
    f   = CDF evaluated at (Scf,Hd) 
    Hd  = zero down crossing wave height [m]  
    Scf = crest front steepness 
    Hm0 = significant wave height [m] 
    Tp  = Spectral peak period    [s] 
  Gamma = Peakedness parameter of the JONSWAP spectrum   
   tail = 1 if upper tail is calculated    
          0 if lower tail is calulated (default) 
    
  JHSCDF approximates the joint CDF 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 of GAMMA. 
  JHSCDF is restricted to the following range for GAMMA:  
   1 <= GAMMA <= 7  
  
  Example: 
  Hm0 = 6;Tp = 9; gam = 3.5; 
  ec = 0.25; 
  hc = 3; 
  lowerTail = 0; 
  upperTail = ~lowerTail   
  jhscdf(hc,ec,Hm0,Tp,gam)           % Prob(Hd<Hc,Scf<ec) 
  jhscdf(hc,ec,Hm0,Tp,gam,upperTail) % Prob(Hd>Hc,Scf>ec)   
    
   % Conditional probability of steep and high waves given seastates 
   % i.e., Prob(Hd>hc,Scf>ec|Hs,Tp)   
   upperTail = 1; 
   Hs = linspace(2.5,11.5,10); 
   Tp = linspace(4.5,19.5,16); 
   [T,H] = meshgrid(Tp,Hs);  
   p = jhscdf(hc,ec,H,T,gam,upperTail); 
   v = 10.^(-6:-1);   
   contourf(Tp,Hs,log10(p),log10(v)) 
   xlabel('Tp') 
   ylabel('Hs')   
   fcolorbar(log10(v))   
    
  See also  jhsnlcdf

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function f = jhscdf(Hd,Scf,Hm0,Tp,gam,tail) 
002 %JHSCDF Joint (Scf,Hd) CDF for linear waves with a JONSWAP spectrum. 
003 % 
004 %  CALL: f = jhscdf(Hd,Scf,Hm0,Tp,Gamma,tail) 
005 %  
006 %   f   = CDF evaluated at (Scf,Hd) 
007 %   Hd  = zero down crossing wave height [m]  
008 %   Scf = crest front steepness 
009 %   Hm0 = significant wave height [m] 
010 %   Tp  = Spectral peak period    [s] 
011 % Gamma = Peakedness parameter of the JONSWAP spectrum   
012 %  tail = 1 if upper tail is calculated    
013 %         0 if lower tail is calulated (default) 
014 %   
015 % JHSCDF approximates the joint CDF of (Scf, Hd), i.e., crest front 
016 % steepness (2*pi*Ac/(g*Td*Tcf)) and wave height, for a Gaussian process with a 
017 % JONSWAP spectral density. The empirical parameters of the model is 
018 % fitted by least squares to simulated (Scf,Hd) data for 13 classes of 
019 % GAMMA between 1 and 7. Between 47000 and 55000 zero-downcrossing waves were 
020 % simulated for each class of GAMMA. 
021 % JHSCDF is restricted to the following range for GAMMA:  
022 %  1 <= GAMMA <= 7  
023 % 
024 % Example: 
025 % Hm0 = 6;Tp = 9; gam = 3.5; 
026 % ec = 0.25; 
027 % hc = 3; 
028 % lowerTail = 0; 
029 % upperTail = ~lowerTail   
030 % jhscdf(hc,ec,Hm0,Tp,gam)           % Prob(Hd<Hc,Scf<ec) 
031 % jhscdf(hc,ec,Hm0,Tp,gam,upperTail) % Prob(Hd>Hc,Scf>ec)   
032 %   
033 %  % Conditional probability of steep and high waves given seastates 
034 %  % i.e., Prob(Hd>hc,Scf>ec|Hs,Tp)   
035 %  upperTail = 1; 
036 %  Hs = linspace(2.5,11.5,10); 
037 %  Tp = linspace(4.5,19.5,16); 
038 %  [T,H] = meshgrid(Tp,Hs);  
039 %  p = jhscdf(hc,ec,H,T,gam,upperTail); 
040 %  v = 10.^(-6:-1);   
041 %  contourf(Tp,Hs,log10(p),log10(v)) 
042 %  xlabel('Tp') 
043 %  ylabel('Hs')   
044 %  fcolorbar(log10(v))   
045 %   
046 % See also  jhsnlcdf 
047  
048 % Reference  
049 % P. A. Brodtkorb (2004),   
050 % The Probability of Occurrence of Dangerous Wave Situations at Sea. 
051 % Dr.Ing thesis, Norwegian University of Science and Technolgy, NTNU, 
052 % Trondheim, Norway.      
053    
054 % History 
055 % By pab 20.01.2003 
056  
057  
058 error(nargchk(2,6,nargin))   
059  
060 if (nargin < 6|isempty(tail)),tail = 0; end 
061 if (nargin < 4|isempty(Tp)),Tp = 8; end 
062 if (nargin < 3|isempty(Hm0)), Hm0 = 6; end 
063 if (nargin < 5|isempty(gam)), 
064    gam = getjonswappeakedness(Hm0,Tp); 
065 end 
066  
067 multipleSeaStates = any(prod(size(Hm0))>1|prod(size(Tp))>1); 
068 if multipleSeaStates 
069   [errorcode, Scf,Hd,Hm0,Tp,gam] = comnsize(Scf,Hd,Hm0,Tp,gam); 
070 else 
071   [errorcode, Scf,Hd] = comnsize(Scf,Hd); 
072 end 
073 if errorcode > 0 
074   error('Requires non-scalar arguments to match in size.'); 
075 end 
076 displayWarning = 0; 
077 if displayWarning 
078   if any(any(Tp>5*sqrt(Hm0) | Tp<3.6*sqrt(Hm0))) 
079     disp('Warning: Hm0,Tp is outside the JONSWAP range') 
080     disp('The validity of the parameters returned are questionable') 
081   end 
082 end 
083 %dev = 2e-5; 
084 c1 =[ 0.16183666835624   1.53691936441548   1.55852759524555]; 
085 c2 =[ 0.15659478203944   1.15736959972513   1]; 
086 Tm02 = Tp.*(polyval(c2,gam)./polyval(c1,gam)); 
087  
088 Hrms = Hm0/sqrt(2); 
089 Vrms = 1.25*Hm0./(Tm02.^2); % Erms 
090  
091 v = Scf./Vrms; 
092  
093 hMax = 6; 
094 eps2 = 1e-6; 
095 normalizedInput = 1; 
096 utprb = gaussq('jhspdf',hMax,2*hMax,eps2/2,[],mean(v(:)),mean(Hm0(:)),mean(Tp(:)),mean(gam(:)),normalizedInput,7); 
097 if eps2<utprb 
098   warning('Check the accuracy of integration!') 
099 end 
100  
101 h = min(Hd./Hrms,hMax); 
102  
103 f = zeros(size(Hd)); 
104 % Only compute 
105 if 0, % haver parametrization 
106   loLimit = 3.6; 
107   upLimit = 5; 
108 else 
109   loLimit = 2.5; 
110   upLimit = 6.5; 
111 end 
112  
113 k0 = find( (loLimit*sqrt(Hm0)<Tp) & (Tp<upLimit*sqrt(Hm0)) ); 
114 if any(k0) 
115   if multipleSeaStates 
116     h = h(k0); 
117     v = v(k0); 
118     Hm0 = Hm0(k0); 
119     Tp = Tp(k0); 
120     gam = gam(k0);     
121   else 
122     k0 = 1:prod(size(Hd)); 
123   end 
124 else 
125   return 
126 end 
127  
128 if 0 
129   % This is a trick to get the html documentation correct. 
130   k = jhspdf(1,1,2,3); 
131 end 
132 hlim  = h; 
133 lowerTail = 0; 
134 if tail==lowerTail, 
135   k       = find(h>2.5);%*v); 
136   hlim(k) = 2.5;%*v(k); 
137   f(k0) = gaussq('jhspdf',0,hlim,eps2/2,[],v,Hm0,Tp,gam,normalizedInput,5)... 
138       + gaussq('jhspdf',hlim,h,eps2/2,[],v,Hm0,Tp,gam,normalizedInput,5);  
139 else % upper tail 
140   k       = find(h<2.5);%*v); 
141   hlim(k) = 2.5;%*v(k); 
142    
143   f(k0) = gaussq('jhspdf',h,hlim,eps2/2,[],v,Hm0,Tp,gam,normalizedInput,7)... 
144       + gaussq('jhspdf',hlim,hMax,eps2/2,[],v,Hm0,Tp,gam,normalizedInput,7);  
145 end 
146 return 
147  
148

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

Comments or corrections to the WAFO group


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