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
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