JHVCDF Joint (Vcf,Hd) CDF for linear waves with JONSWAP spectrum. CALL: f = jhvcdf(Hd,Vcf,Hm0,Tp,Gamma,tail) f = CDF evaluated at (Vcf,Hd) Hd = zero down crossing wave height [m] Vcf = crest front velocity [m/s] 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) JHVCDF approximates the joint CDF of (Vcf, Hd), i.e., crest front velocity (Ac/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 (Vcf,Hd) data for 13 classes of GAMMA between 1 and 7. About 100000 zero-downcrossing waves were simulated for each class of GAMMA. JHVCDF is restricted to the following range for GAMMA: 1 <= GAMMA <= 7 Example: Hm0 = 6;Tp = 8; gam = 3.5; vc = 3; hc = 3; lowerTail = 0; upperTail = ~lowerTail jhvcdf(hc,vc,Hm0,Tp,gam) % Prob(Hd<Hc,Vcf<Vc) jhvcdf(hc,vc,Hm0,Tp,gam,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 = jhvcdf(hc,vc,H,T,gam,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. | |
Peakedness factor Gamma given Hm0 and Tp for JONSWAP | |
Joint (Vcf,Hd) PDF for linear waves with a JONSWAP spectrum. | |
Check if all input arguments are either scalar or of common size. | |
Display message and abort function. | |
Average or mean value. | |
Evaluate polynomial. | |
Display warning message; disable or enable warning messages. |
001 function f = jhvcdf(Hd,Vcf,Hm0,Tp,gam,tail) 002 %JHVCDF Joint (Vcf,Hd) CDF for linear waves with JONSWAP spectrum. 003 % 004 % CALL: f = jhvcdf(Hd,Vcf,Hm0,Tp,Gamma,tail) 005 % 006 % f = CDF evaluated at (Vcf,Hd) 007 % Hd = zero down crossing wave height [m] 008 % Vcf = crest front velocity [m/s] 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 % JHVCDF approximates the joint CDF of (Vcf, Hd), i.e., crest front 016 % velocity (Ac/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 (Vcf,Hd) data for 13 classes of 019 % GAMMA between 1 and 7. About 100000 zero-downcrossing waves were 020 % simulated for each class of GAMMA. 021 % JHVCDF is restricted to the following range for GAMMA: 022 % 1 <= GAMMA <= 7 023 % 024 % Example: 025 % Hm0 = 6;Tp = 8; gam = 3.5; 026 % vc = 3; 027 % hc = 3; 028 % lowerTail = 0; 029 % upperTail = ~lowerTail 030 % jhvcdf(hc,vc,Hm0,Tp,gam) % Prob(Hd<Hc,Vcf<Vc) 031 % jhvcdf(hc,vc,Hm0,Tp,gam,upperTail) % Prob(Hd>Hc,Vcf>Vc) 032 % 033 % % Conditional probability of steep and high waves given seastates 034 % % i.e., Prob(Hd>hc,Vcf>vc|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 = jhvcdf(hc,vc,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 thvpdf 047 048 049 % Reference 050 % P. A. Brodtkorb (2004), 051 % The Probability of Occurrence of Dangerous Wave Situations at Sea. 052 % Dr.Ing thesis, Norwegian University of Science and Technolgy, NTNU, 053 % Trondheim, Norway. 054 055 % History 056 % revised pab 09.08.2003 057 % changed input 058 % validated 20.11.2002 059 % By pab 20.12.2000 060 061 062 error(nargchk(2,6,nargin)) 063 064 if (nargin < 6|isempty(tail)),tail = 0; end 065 if (nargin < 4|isempty(Tp)),Tp = 8; end 066 if (nargin < 3|isempty(Hm0)), Hm0 = 6; end 067 if (nargin < 5|isempty(gam)), 068 gam = getjonswappeakedness(Hm0,Tp); 069 end 070 071 multipleSeaStates = any(prod(size(Hm0))>1|prod(size(Tp))>1); 072 if multipleSeaStates 073 [errorcode, Vcf,Hd,Hm0,Tp,gam] = comnsize(Vcf,Hd,Hm0,Tp,gam); 074 else 075 [errorcode, Vcf,Hd] = comnsize(Vcf,Hd); 076 end 077 if errorcode > 0 078 error('Requires non-scalar arguments to match in size.'); 079 end 080 displayWarning = 0; 081 if displayWarning 082 if any(any(Tp>5*sqrt(Hm0) | Tp<3.6*sqrt(Hm0))) 083 disp('Warning: Hm0,Tp is outside the JONSWAP range') 084 disp('The validity of the parameters returned are questionable') 085 end 086 end 087 %dev = 2e-5; 088 c1 =[ 0.16183666835624 1.53691936441548 1.55852759524555]; 089 c2 =[ 0.15659478203944 1.15736959972513 1]; 090 Tm02 = Tp.*(polyval(c2,gam)./polyval(c1,gam)); 091 092 Hrms = Hm0/sqrt(2); 093 Vrms = 2*Hm0./Tm02; % Erms 094 095 v = Vcf./Vrms; 096 097 hMax = 6; 098 eps2 = 1e-6; 099 normalizedInput = 1; 100 101 102 h = min(Hd./Hrms,hMax); 103 f = zeros(size(Hd)); 104 % Only compute 105 k0 = find((Tp<5*sqrt(Hm0)) & (3.6*sqrt(Hm0)<Tp)); 106 if any(k0) 107 if multipleSeaStates 108 h = h(k0); 109 v = v(k0); 110 Hm0 = Hm0(k0); 111 Tp = Tp(k0); 112 gam = gam(k0); 113 else 114 k0 = 1:prod(size(Hd)); 115 end 116 utprb = gaussq('jhvpdf',hMax,2*hMax,eps2/2,[],mean(v(:)),mean(Hm0(:)),mean(Tp(:)),mean(gam(:)),normalizedInput,7); 117 if eps2<utprb 118 warning('Check the accuracy of integration!') 119 end 120 121 if 0 122 % This is a trick to get the html documentation correct. 123 k = jhvpdf(1,1,2,3); 124 end 125 126 hlim = h; 127 128 129 lowerTail = 0; 130 if tail==lowerTail, 131 k = find(h>2*v); 132 hlim(k) = 2*v(k); 133 f(k0) = gaussq('jhvpdf',0,hlim,eps2/2,[],v,Hm0,Tp,gam,normalizedInput,5)... 134 + gaussq('jhvpdf',hlim,h,eps2/2,[],v,Hm0,Tp,gam,normalizedInput,5); 135 else % upper tail 136 k = find(h<2*v); 137 hlim(k) = 2*v(k); 138 f(k0) = gaussq('jhvpdf',h,hlim,eps2/2,[],v,Hm0,Tp,gam,normalizedInput,7)... 139 + gaussq('jhvpdf',hlim,hMax,eps2/2,[],v,Hm0,Tp,gam,normalizedInput,7); 140 end 141 end 142 return 143 144
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