THVCDF Joint (Vcf,Hd) CDF for linear waves with Torsethaugen spectra. CALL: f = thvcdf(Hd,Vcf,Hm0,Tp,tail) f = CDF evaluated at (Vcf,Hd) Hd = zero down crossing wave height Vcf = crest front velocity Hm0 = significant wave height [m] Tp = Spectral peak period [s] tail = 1 if upper tail is calculated 0 if lower tail is calulated (default) THVCDF approximates the joint CDF of (Vcf, Hd), i.e., crest front velocity (Ac/Tcf) and wave height, for a Gaussian process with a Torsethaugen spectral density. The empirical parameters of the model is fitted by least squares to simulated (Vcf,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. THVCDF 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; vc = 3; hc = 3; lowerTail = 0; upperTail = ~lowerTail thvcdf(hc,vc,Hm0,Tp) % Prob(Hd<Hc,Vcf<Vc) thvcdf(hc,vc,Hm0,Tp,upperTail) % Prob(Hd>Hc,Vcf>Vc) % Conditional probability of steep and high waves given seastates % i.e., Prob(Hd>hc,Vcf>vc|Hs,Tp) upperTail = 1; Hs = linspace(2.5,11.5,10); Tp = linspace(4.5,19.5,16); [T,H] = meshgrid(Tp,Hs); p = thvcdf(hc,vc,H,T,upperTail); v = 10.^(-6:-1); contourf(Tp,Hs,log10(p),log10(v)) xlabel('Tp') ylabel('Hs') fcolorbar(log10(v)) See also thvpdf
Numerically evaluates a integral using a Gauss quadrature. | |
Joint (Vcf,Hd) PDF for linear waves with Torsethaugen spectra. | |
Check if all input arguments are either scalar or of common size. | |
Display message and abort function. | |
2-D interpolation (table lookup). | |
Average or mean value. | |
X and Y arrays for 3-D plots. | |
Display warning message; disable or enable warning messages. |
001 function f = thvcdf(Hd,Vcf,Hm0,Tp,tail) 002 %THVCDF Joint (Vcf,Hd) CDF for linear waves with Torsethaugen spectra. 003 % 004 % CALL: f = thvcdf(Hd,Vcf,Hm0,Tp,tail) 005 % 006 % f = CDF evaluated at (Vcf,Hd) 007 % Hd = zero down crossing wave height 008 % Vcf = crest front velocity 009 % Hm0 = significant wave height [m] 010 % Tp = Spectral peak period [s] 011 % tail = 1 if upper tail is calculated 012 % 0 if lower tail is calulated (default) 013 % 014 % THVCDF approximates the joint CDF of (Vcf, Hd), i.e., crest front 015 % velocity (Ac/Tcf) and wave height, for a Gaussian process with a 016 % Torsethaugen spectral density. The empirical parameters of the model is 017 % fitted by least squares to simulated (Vcf,Hd) data for 600 classes of 018 % Hm0 and Tp. Between 50000 and 150000 zero-downcrossing waves were 019 % simulated for each class of Hm0 and Tp. 020 % THVCDF is restricted to the following range for Hm0 and Tp: 021 % 0.5 < Hm0 [m] < 12, 3.5 < Tp [s] < 20, and Hm0 < (Tp-2)*12/11. 022 % 023 % Example: 024 % Hm0 = 6;Tp = 8; 025 % vc = 3; 026 % hc = 3; 027 % lowerTail = 0; 028 % upperTail = ~lowerTail 029 % thvcdf(hc,vc,Hm0,Tp) % Prob(Hd<Hc,Vcf<Vc) 030 % thvcdf(hc,vc,Hm0,Tp,upperTail) % Prob(Hd>Hc,Vcf>Vc) 031 % 032 % % Conditional probability of steep and high waves given seastates 033 % % i.e., Prob(Hd>hc,Vcf>vc|Hs,Tp) 034 % upperTail = 1; 035 % Hs = linspace(2.5,11.5,10); 036 % Tp = linspace(4.5,19.5,16); 037 % [T,H] = meshgrid(Tp,Hs); 038 % p = thvcdf(hc,vc,H,T,upperTail); 039 % v = 10.^(-6:-1); 040 % contourf(Tp,Hs,log10(p),log10(v)) 041 % xlabel('Tp') 042 % ylabel('Hs') 043 % fcolorbar(log10(v)) 044 % 045 % See also thvpdf 046 047 % Reference 048 % P. A. Brodtkorb (2004), 049 % The Probability of Occurrence of Dangerous Wave Situations at Sea. 050 % Dr.Ing thesis, Norwegian University of Science and Technolgy, NTNU, 051 % Trondheim, Norway. 052 053 % History 054 % revised pab 09.08.2003 055 % changed input 056 % validated 20.11.2002 057 % By pab 20.12.2000 058 059 060 error(nargchk(3,5,nargin)) 061 062 if (nargin < 5|isempty(tail)),tail = 0; end 063 if (nargin < 4|isempty(Tp)),Tp = 8; end 064 if (nargin < 3|isempty(Hm0)), Hm0 = 6; end 065 066 multipleSeaStates = any(prod(size(Hm0))>1|prod(size(Tp))>1); 067 if multipleSeaStates 068 [errorcode, Vcf,Hd,Hm0,Tp] = comnsize(Vcf,Hd,Hm0,Tp); 069 else 070 [errorcode, Vcf,Hd] = comnsize(Vcf,Hd); 071 end 072 if errorcode > 0 073 error('Requires non-scalar arguments to match in size.'); 074 end 075 076 global THVPAR 077 if isempty(THVPAR) 078 THVPAR = load('thvpar.mat'); 079 end 080 081 Tpp = THVPAR.Tp; 082 Hm00 = THVPAR.Hm0; 083 Tm020 = THVPAR.Tm02; 084 % Interpolation method 085 method = '*cubic';% Faster interpolation 086 087 [Tp1,Hs1] = meshgrid(Tpp,Hm00); 088 Tm02 = interp2(Tp1,Hs1,Tm020,Tp,Hm0,method); 089 % w = linspace(0,100,16*1024+1).'; % torsethaugen original spacing 090 %w = linspace(0,10,2*1024+1).'; 091 % St = torsethaugen(w,[Hm0,Tp]); 092 % ch = spec2char(St,{'Tm02','eps2'}); 093 % Tm02 = ch(1); 094 % eps2 = ch(2); 095 Hrms = Hm0/sqrt(2); 096 Vrms = 2*Hm0./Tm02; % Erms 097 098 v = Vcf./Vrms; 099 f = zeros(size(Hd)); 100 101 % Only compute within valid range 102 k0 = find((2<=Tp) & (Tp<=21) & (Hm0<=(Tp-2)*12/11) & (Hm0<=12)); 103 if any(k0) 104 hMax = 5; 105 eps2 = 1e-6; 106 h = min(Hd./Hrms,hMax); 107 108 if multipleSeaStates 109 h = h(k0); 110 v = v(k0); 111 Hm0 = Hm0(k0); 112 Tp = Tp(k0); 113 else 114 k0 = 1:prod(size(Hd)); 115 end 116 if 0 117 % This is a trick to get the html documentation correct. 118 k = thvpdf(1,1,2,3); 119 end 120 normalizedInput = 1; 121 utprb = gaussq('thvpdf',hMax,2*hMax,eps2/2,[],mean(v(:)),mean(Hm0(:)),mean(Tp(:)),normalizedInput,7); 122 if eps2<utprb 123 warning('Check the accuracy of integration!') 124 end 125 126 127 128 hlim = h; 129 130 131 lowerTail = 0; 132 if tail==lowerTail, 133 k = find(h>2.5); 134 hlim(k) = 2.5; 135 k = find(h>1.3*v); 136 hlim(k) = 1.3*v(k); 137 f(k0) = gaussq('thvpdf',0,hlim,eps2/2,[],v,Hm0,Tp,normalizedInput,5)... 138 + gaussq('thvpdf',hlim,h,eps2/2,[],v,Hm0,Tp,normalizedInput,5); 139 else % upper tail 140 k = find(h<1.3*v); 141 hlim(k) = 1.3*v(k); 142 f(k0) = gaussq('thvpdf',h,hlim,eps2/2,[],v,Hm0,Tp,normalizedInput,7)... 143 + gaussq('thvpdf',hlim,hMax,eps2/2,[],v,Hm0,Tp,normalizedInput,7); 144 end 145 end 146 return 147 148
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