JHNLWPARFUN Wave height, Hd, distribution parameters for Stokes waves with Jonswap spectrum. CALL [a b c] = jhnlwparfun(Hm0,Tp,gamma,dim) Hm0 = significant wave height [m]. Tp = peak period [s] gamma = Peakedness parameter of the JONSWAP spectrum dim = 'time' : Hd distribution parameters in time (default) JHNLWPARFUN returns the truncated Weibull distribution parameters which approximates the marginal PDF of Hd/Hrms, i.e., zero-downcrossing wave height, for 2nd order Stokes waves with a Jonswap spectral density. The empirical parameters of the model is fitted by least squares to simulated Hd data for 13 classes of GAMMA between 1 and 7, given Hm0 = 7 and Tp = 11;. About 50000 zero-downcrossing waves were simulated for each class of GAMMA for DIM=='time'. JHNLWPARFUN is restricted to the following range for GAMMA and Tp: 1 <= GAMMA <= 7, and 3.6*sqrt(Hm0) < Tp < 5*sqrt(Hm0) Example: Hm0 = 6;Tp = 9;Hrms = Hm0/sqrt(2); gam = getjonswappeakedness(Hm0,Tp); [a b c] = jhnlwparfun(Hm0,Tp,gam); h = linspace(0,4*Hrms)'; F = wtweibcdf(h/Hrms,a,b,c); f = wtweibpdf(h/Hrms,a,b,c)/Hrms; dt = 0.4; w = linspace(0,2*pi/dt,256)'; S = jonswap(w,[Hm0 Tp,gam]); xs = spec2nlsdat(S,80000,dt); rate=8; method=1; [S,H] = dat2steep(xs,rate,method); fk = kdebin(H,'epan',[],[],.5,128); subplot(2,1,1) empdistr(H,[h,F],1) subplot(2,1,2) plot(h,f), hold on, pdfplot(fk,'r'), hold off See also jhvnlpdf
Peakedness factor Gamma given Hm0 and Tp for JONSWAP | |
Display message and abort function. | |
Compare first N characters of strings ignoring case. |
Joint (Scf,Hd) PDF for nonlinear waves with a JONSWAP spectra. | |
Joint (Vcf,Hd) PDF for linear waves with a JONSWAP spectrum. |
001 function [A0,B0,C0]= jhnlwparfun(Hm0,Tp,gam,dim) 002 %JHNLWPARFUN Wave height, Hd, distribution parameters for Stokes waves with Jonswap spectrum. 003 % 004 % CALL [a b c] = jhnlwparfun(Hm0,Tp,gamma,dim) 005 % 006 % Hm0 = significant wave height [m]. 007 % Tp = peak period [s] 008 % gamma = Peakedness parameter of the JONSWAP spectrum 009 % dim = 'time' : Hd distribution parameters in time (default) 010 % 011 % JHNLWPARFUN returns the truncated Weibull distribution parameters which 012 % approximates the marginal PDF of Hd/Hrms, i.e., 013 % zero-downcrossing wave height, for 2nd order Stokes waves with a 014 % Jonswap spectral density. 015 % 016 % The empirical parameters of the model is 017 % fitted by least squares to simulated Hd data for 13 classes of 018 % GAMMA between 1 and 7, given Hm0 = 7 and Tp = 11;. 019 % About 50000 zero-downcrossing waves were simulated for 020 % each class of GAMMA for DIM=='time'. 021 % JHNLWPARFUN is restricted to the following range for GAMMA and Tp: 022 % 1 <= GAMMA <= 7, and 3.6*sqrt(Hm0) < Tp < 5*sqrt(Hm0) 023 % 024 % Example: 025 % Hm0 = 6;Tp = 9;Hrms = Hm0/sqrt(2); 026 % gam = getjonswappeakedness(Hm0,Tp); 027 % [a b c] = jhnlwparfun(Hm0,Tp,gam); 028 % h = linspace(0,4*Hrms)'; 029 % F = wtweibcdf(h/Hrms,a,b,c); 030 % f = wtweibpdf(h/Hrms,a,b,c)/Hrms; 031 % dt = 0.4; w = linspace(0,2*pi/dt,256)'; 032 % S = jonswap(w,[Hm0 Tp,gam]); 033 % xs = spec2nlsdat(S,80000,dt); rate=8; method=1; 034 % [S,H] = dat2steep(xs,rate,method); 035 % fk = kdebin(H,'epan',[],[],.5,128); 036 % subplot(2,1,1) 037 % empdistr(H,[h,F],1) 038 % subplot(2,1,2) 039 % plot(h,f), hold on, pdfplot(fk,'r'), hold off 040 % 041 % See also jhvnlpdf 042 043 044 % History: 045 % revised pab 10 jan 2004 046 % by pab 29.11.2002 047 048 error(nargchk(2,4,nargin)) 049 if nargin<3|isempty(gam), 050 gam = getjonswappeakedness(Hm0,Tp) 051 end 052 if nargin<4|isempty(dim), dim = 'time';end 053 054 displayWarning = 0; 055 if displayWarning 056 if any(any(Tp>5*sqrt(Hm0) | Tp<3.6*sqrt(Hm0))) 057 disp('Warning: Hm0,Tp is outside the JONSWAP range') 058 disp('The validity of the parameters returned are questionable') 059 end 060 if any(any(gam>7|gam<1)) 061 disp('Warning: gamma is outside the valid range') 062 disp('The validity of the parameters returned are questionable') 063 end 064 end 065 066 if strncmpi(dim,'t',1) 067 % LS fit to data 068 % best fit to jonswap for gamma = 1:.5:7 069 A0 = -0.01243795213128.*gam + 1.08025514722235; 070 B0 = -0.03043834819688.*gam + 2.27161821064622; 071 C0 = -0.01342959276544.*gam + 0.10353423379696; 072 073 else % not implemented yet 074 075 A0 = []; 076 B0 = []; 077 C0 = []; 078 end 079 080 return 081 082
Comments or corrections to the WAFO group