Example of Fig 5.1 - 5.4

Simple Structure

function uu=example514
%
%  Simple Structure
%

flat = [0 90];
flon = [0 360];

lnorm = 'anom';
[zt,ind,fcos]=readz500(flat,flon,'season','jfm','scaling','yes');

[z,sdz]=anomaly(zt,lnorm);

clf;
[u,lam,v,proj]=eoffast(z,ind,10,1);
[s,ur,v]=eofrot(z,ind,1:10);
[s,up]=eofpromax(z,ind,1:10,2);
[s,uq]=eofpromax(z,ind,1:10,12);

index=find(u(:,1) < 9999);
display(['Scalar product for EOF'])
u(index,1:3)'*u(index,1:3)
display(['Scalar product for Rotated EOF'])
ur(index,1:3)'*ur(index,1:3)
display(['Scalar product for Promax EOF'])
up(index,1:3)'*up(index,1:3)

% PLot EOF  -----
titstr={'EOF', 'VARIMAX','PROMAX K=2', 'PROMAX K=12'};

index=find(u(:,1) < 9999);
figure(1)
ax=[-0.1 0.1 -0.1 0.1];
subplot(221);plot(u(index,1),u(index,2),'.');title('EOF');axis(ax);
subplot(222);plot(-ur(index,1),ur(index,2),'.');title('VARIMAX');axis(ax)
subplot(223);plot(-up(index,2),up(index,1),'.');title('PROMAX K=2');axis(ax);
subplot(224);plot(-uq(index,2),uq(index,1),'.');title('PROMAX K=12');axis(ax);
print('-dpdf','-adobecset','-painters',[mfilename 'a.pdf']);

figure(2)
clf;

modeindex=[ 1 1 2 2] ;
for i=1:4
ii=modeindex(i);
end
bigtit{1}= '';
bigtit{2}= '';

pict4(bigtit,u(:,modeindex(1)),ur(:,modeindex(2)), up(:,modeindex(3)), uq(:,modeindex(4)), ...
    flat,flon,[-.2:0.01:0.2],titstr,'shading','off');
print('-dpdf','-adobecset','-painters',[mfilename 'b.pdf']);

return
Normalization anom
Expanded Field
  Converging  V  V0 
 0.000000
 0.000000

varexpl =

    0.8799


varexplrot =

    0.8799


zvar =

   2.4955e+07


totvar =

   2.4955e+07


varunrotated =

    0.3287
    0.1476
    0.0970
    0.0698
    0.0622
    0.0474
    0.0403
    0.0343
    0.0313
    0.0213


varrotated =

    0.2417
    0.1997
    0.0838
    0.0634
    0.0594
    0.0584
    0.0567
    0.0546
    0.0349
    0.0272

Expanded Field
  Converging  V  V0 
 0.000000
 0.000000
Expanded Field
  Converging  V  V0 
 0.000000
 0.000000
Expanded Field
Scalar product for EOF

ans =

    1.0000    0.0000   -0.0000
    0.0000    1.0000   -0.0000
   -0.0000   -0.0000    1.0000

Scalar product for Rotated EOF

ans =

    1.0000   -0.0000   -0.0000
   -0.0000    1.0000    0.0000
   -0.0000    0.0000    1.0000

Scalar product for Promax EOF

ans =

    1.0000    0.0070    0.1566
    0.0070    1.0000    0.4690
    0.1566    0.4690    1.0000

Shading is  off 
Reshaping for T30 Gaussian grid
Contouring from a minimum -0.2000 
Contouring to a maximum 0.2000 
Contouring interval is  0.0100 
Contour values are: 
-0.2000 -0.1900 -0.1800 -0.1700 -0.1600 -0.1500 -0.1400 -0.1300 -0.1200 -0.1100 -0.1000 -0.0900 -0.0800 -0.0700 -0.0600 -0.0500 -0.0400 -0.0300 -0.0200 -0.0100 0.0000 0.0100 0.0200 0.0300 0.0400 0.0500 0.0600 0.0700 0.0800 0.0900 0.1000 0.1100 0.1200 0.1300 0.1400 0.1500 0.1600 0.1700 0.1800 0.1900 0.2000 
Maximum field value 0.1081 
Minimum field value -0.0435 
Shading is  off 
Reshaping for T30 Gaussian grid
Contouring from a minimum -0.2000 
Contouring to a maximum 0.2000 
Contouring interval is  0.0100 
Contour values are: 
-0.2000 -0.1900 -0.1800 -0.1700 -0.1600 -0.1500 -0.1400 -0.1300 -0.1200 -0.1100 -0.1000 -0.0900 -0.0800 -0.0700 -0.0600 -0.0500 -0.0400 -0.0300 -0.0200 -0.0100 0.0000 0.0100 0.0200 0.0300 0.0400 0.0500 0.0600 0.0700 0.0800 0.0900 0.1000 0.1100 0.1200 0.1300 0.1400 0.1500 0.1600 0.1700 0.1800 0.1900 0.2000 
Maximum field value 0.0500 
Minimum field value -0.1156 
Shading is  off 
Reshaping for T30 Gaussian grid
Contouring from a minimum -0.2000 
Contouring to a maximum 0.2000 
Contouring interval is  0.0100 
Contour values are: 
-0.2000 -0.1900 -0.1800 -0.1700 -0.1600 -0.1500 -0.1400 -0.1300 -0.1200 -0.1100 -0.1000 -0.0900 -0.0800 -0.0700 -0.0600 -0.0500 -0.0400 -0.0300 -0.0200 -0.0100 0.0000 0.0100 0.0200 0.0300 0.0400 0.0500 0.0600 0.0700 0.0800 0.0900 0.1000 0.1100 0.1200 0.1300 0.1400 0.1500 0.1600 0.1700 0.1800 0.1900 0.2000 
Maximum field value 0.0423 
Minimum field value -0.1019 
Shading is  off 
Reshaping for T30 Gaussian grid
Contouring from a minimum -0.2000 
Contouring to a maximum 0.2000 
Contouring interval is  0.0100 
Contour values are: 
-0.2000 -0.1900 -0.1800 -0.1700 -0.1600 -0.1500 -0.1400 -0.1300 -0.1200 -0.1100 -0.1000 -0.0900 -0.0800 -0.0700 -0.0600 -0.0500 -0.0400 -0.0300 -0.0200 -0.0100 0.0000 0.0100 0.0200 0.0300 0.0400 0.0500 0.0600 0.0700 0.0800 0.0900 0.1000 0.1100 0.1200 0.1300 0.1400 0.1500 0.1600 0.1700 0.1800 0.1900 0.2000 
Maximum field value 0.0421 
Minimum field value -0.1047