Example of Fig 6.1 - 6.2 - 6.3
SVD Analysis
function [u,lam,v,ss]=example6123 % % Compute svd of matrices s z % Uses EOF projection method % sflat = [-30 30]; sflon = [120 300]; zflat = [0 90]; zflon = [120 360]; lnorm = 'full'; [st,inds,fcos]=readsst(sflat,sflon,'season','jfm','scaling','yes'); [zt,indz,fcos]=readz500(zflat,zflon,'season','jfm','scaling','yes'); [z,sdz]=anomaly(zt,lnorm); [s,sdz]=anomaly(st,lnorm); xcross=norm(z*s','fro'); disp(['Total Crosscovariance ' num2str(xcross)]); [u,v,lam,varz,vars,projz,projs]=ccsvd(z,s,indz,inds); % PLot EOF ----- titstr=cell(size(1:3)); % Height Component figure(1) clf; modeindex=[ 1 2 3]; for i=1:3 ii=modeindex(i); titstr{i} = [' Z Component Expl TC ' num2str(varz(i)*100,'%-2.0f') '%' ... ' Expl CC ' num2str(lam(ii)*100,'%-2.0f') '%']; end bigtit{1}= [' ' ]; bigtit{2}= ['SVD']; pict3(bigtit,u(:,modeindex(1)),u(:,modeindex(2)), u(:,modeindex(3)), ... zflat,zflon,[-0.06:0.02:0.06],titstr,'shading','off'); print('-dpdf','-painters',[mfilename 'Z.pdf']); % SST Component figure(2) clf; modeindex=[ 1 2 3]; for i=1:3 ii=modeindex(i); titstr{i} = [' S Component Expl TC ' num2str(vars(i)*100,'%-2.0f') '%' ... ' Expl CC ' num2str(lam(ii)*100,'%-2.0f') '%']; end bigtit{1}= [' ' ]; bigtit{2}= ['SVD']; pict3(bigtit,v(:,modeindex(1)),v(:,modeindex(2)), v(:,modeindex(3)), ... sflat,sflon,[-0.06:0.02:0.06],titstr,'shading','off','landcolor',[0.1 0.1 0.1]); print('-dpdf','-painters',[mfilename 'S.pdf']); %Time series of coefficients figure(3) clf; subplot(211) sp=size(projz); tim=max(sp); plot(1:tim,projz(:,1),'k-',1:tim,projz(:,2),'k--',1:tim,projz(:,3),'k:') title('Time series of the first three SVD modes -- Z component'); subplot(212) plot(1:tim,projs(:,1),'k-',1:tim,projs(:,2),'k--',1:tim,projs(:,3),'k:') title('Time series of the first three SVD modes -- S component'); legend('Mode 1','Mode 2','Mode 3'); print('-dpdf','-painters',[mfilename 'proj.pdf']); return
Normalization full Normalization full Total Crosscovariance 10984.0561 ll = 0.3415 0.1247 0.1013 0.0765 0.0574 0.0510 0.0366 0.0279 0.0244 0.0204 0.0181 0.0155 0.0143 0.0128 0.0107 0.0099 0.0087 0.0077 0.0069 0.0062 0.0054 0.0043 0.0039 0.0035 0.0023 0.0021 0.0015 0.0012 0.0011 0.0009 0.0006 0.0005 0.0001 0.0000 lu = 0.3706 0.1728 0.0740 0.0565 0.0532 0.0484 0.0423 0.0378 0.0215 0.0194 0.0164 0.0160 0.0114 0.0095 0.0077 0.0058 0.0055 0.0049 0.0042 0.0035 0.0032 0.0029 0.0021 0.0018 0.0017 0.0016 0.0012 0.0011 0.0009 0.0008 0.0006 0.0005 0.0004 0.0000 Modes for SST 33 --- Variance Retained 1 Modes for Z 33 --- Variance Retained 1 SVD computed Residual/NormZ/Norm of residual normalized by norm of Z 1.508325e+02 2.251400e+02 6.699500e-01 Number of modes computed 5 Variance 0.96577 Expanded Field1 Expanded Field2 Expanded Field3 Expanded Field4 Expanded Field5 Crosscovariance between coefficient of the time series 1.006083e+04 -2.046363e-12 -4.433787e-12 Crosscovariance between coefficient of the time series -2.512479e-11 2.432185e+03 -1.080025e-12 Crosscovariance between coefficient of the time series 6.082246e-12 -2.273737e-13 2.319686e+03 Covariance of Z time series 5.620572e+05 -8.616900e+04 1.122719e+05 Covariance of Z time series -8.616900e+04 1.622980e+05 -1.042896e+05 Covariance of Z time series 1.122719e+05 -1.042896e+05 3.076982e+05 Covariance of S time series 2.566147e+05 2.248385e+04 -1.581266e+04 Covariance of S time series 2.248385e+04 7.401746e+04 2.031292e+04 Covariance of S time series -1.581266e+04 2.031292e+04 4.015918e+04 Shading is off Reshaping for T30 Gaussian grid Contouring from a minimum -0.0600 Contouring to a maximum 0.0600 Contouring interval is 0.0200 Contour values are: -0.0600 -0.0400 -0.0200 0.0000 0.0200 0.0400 0.0600 Maximum field value 0.0476 Minimum field value -0.0424 Shading is off Reshaping for T30 Gaussian grid Contouring from a minimum -0.0600 Contouring to a maximum 0.0600 Contouring interval is 0.0200 Contour values are: -0.0600 -0.0400 -0.0200 0.0000 0.0200 0.0400 0.0600 Maximum field value 0.0362 Minimum field value -0.0748 Shading is off Reshaping for T30 Gaussian grid Contouring from a minimum -0.0600 Contouring to a maximum 0.0600 Contouring interval is 0.0200 Contour values are: -0.0600 -0.0400 -0.0200 0.0000 0.0200 0.0400 0.0600 Maximum field value 0.0473 Minimum field value -0.0534 Shading is off Reshaping for T30 Gaussian grid Contouring from a minimum -0.0600 Contouring to a maximum 0.0600 Contouring interval is 0.0200 Contour values are: -0.0600 -0.0400 -0.0200 0.0000 0.0200 0.0400 0.0600 Maximum field value 0.0640 Minimum field value -0.0544 Shading is off Reshaping for T30 Gaussian grid Contouring from a minimum -0.0600 Contouring to a maximum 0.0600 Contouring interval is 0.0200 Contour values are: -0.0600 -0.0400 -0.0200 0.0000 0.0200 0.0400 0.0600 Maximum field value 0.0595 Minimum field value -0.1050 Shading is off Reshaping for T30 Gaussian grid Contouring from a minimum -0.0600 Contouring to a maximum 0.0600 Contouring interval is 0.0200 Contour values are: -0.0600 -0.0400 -0.0200 0.0000 0.0200 0.0400 0.0600 Maximum field value 0.0653 Minimum field value -0.1298 ans = 1.0e+03 * 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 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