Example of Fig 4.2

Three independent maps

function example42
flon = [ 0 360];lonbox=flon;
flat = [ -90 90];latbox=flat;
vlat = [ 34 60 30];
vlon = [ 210 220 280];
ilat = [ 34 41 33];
ilon = [ 56 59 75];
k = 3  %      Only threee independent vectors
s = [96 48];
lnorm = 'full';
tit = ' Z500 Geopotential Heights';
[zt,ind,fcos]=readz500(latbox,lonbox,'season','jfm','scaling','yes');

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

if k ~= 34
    ibase=ceil(linspace(1,34,k)), size(zold)
    zbase=zold(:,ibase); size(zbase)
    zcof=2*rand(k,34)-1;size(zcof)
    z = zbase*zcof; size(z)
else
    z=zold;
end

clear zold;

clf;axis on;
% Choose grid
%
%
if s(1) == 96 && s(2) == 48
    llat = [ -87.16    -83.48    -79.78    -76.07    -72.36    -68.65 ...
        -64.94    -61.23    -57.52    -53.81    -50.10    -46.39 ...
        -42.68    -38.97    -35.26    -31.54    -27.83    -24.12 ...
        -20.41    -16.70    -12.99     -9.28     -5.57     -1.86 ...
        1.86      5.57      9.28     12.99     16.70     20.41 ...
        24.12     27.83     31.54     35.26     38.97     42.68 ...
        46.39     50.10     53.81     57.52     61.23     64.94 ...
        68.65     72.36     76.07     79.78     83.48     87.16 ]';
    llon = 0:3.75:(359.+3.76)';

elseif s(1) == 72 && s(2) == 16
    llat = 15:5:90';
    llon = 0:5:(359.+5)';
elseif s(1) == 128 && s(2) == 64
    llat = [  -87.86380     -85.09653     -82.31291     -79.52560 ...
        -76.73690     -73.94751     -71.15775     -68.36775     -65.57760 ...
        -62.78735     -59.99701     -57.20662     -54.41619     -51.62573 ...
        -48.83523     -46.04472     -43.25418     -40.46364     -37.67308 ...
        -34.88251     -32.09193     -29.30135     -26.51076     -23.72016 ...
        -20.92956     -18.13896     -15.34835     -12.55774      -9.76713 ...
        -6.97652      -4.18590      -1.39529       1.39529       4.18590 ...
        6.97652       9.76713      12.55774      15.34835      18.13896 ...
        20.92956      23.72016      26.51076      29.30135      32.09193 ...
        34.88251      37.67308      40.46364      43.25418      46.04472 ...
        48.83523      51.62573      54.41619      57.20662      59.99701 ...
        62.78735      65.57760      68.36775      71.15775      73.94751 ...
        76.73690      79.52560      82.31291      85.09653      87.86380 ]';
    llon = 0:2.8125:(359.+2.82)';
end

%  Coast
load coast;
if lonbox(2) - lonbox(1) < 80;
    dmerid= [];
else
    dmerid=60;
end
if latbox(2) - latbox(1) < 40;
    dpar= [];
else
    dpar=30;
end

[u,lam,v,proj]=eoffast(z,ind,15,1);

subplot(311)
bigtit{1}= ['Case in which there are only ' num2str(k) ' independent maps'];
bigtit{2}= ['EOF 1'];
sdz=expand(u(:,1),ind,[96 48]);
llmap(sdz,flat,flon,[-0.5:0.01:0.05],bigtit,'shading','off');

subplot(312)
bigtit{1}= [''];
bigtit{2}= ['EOF 2'];
sdz=expand(u(:,2),ind,[96 48]);
llmap(sdz,flat,flon,[-0.5:0.01:0.05],bigtit,'shading','off');

subplot(313)
lam=lam/sum(lam);
%plot(1:length(lam),lam,'*','markersize',5);
bar(1:length(lam),lam);
axis([ 0 length(lam)+1 -0.2 1]);
title('Eigenvalues of the Covariance Matrix');

orient tall;
print('-dpdf','-painters','example03.pdf');

return;
k =

     3

Normalization full

ibase =

     1    18    34


ans =

        4608          34


ans =

        4608           3


ans =

     3    34


ans =

        4608          34

Expanded Field
Shading is  off 
Reshaping for T30 Gaussian grid
Contouring from a minimum -0.5000 
Contouring to a maximum 0.0500 
Contouring interval is  0.0100 
Contour values are: 
-0.5000 -0.4900 -0.4800 -0.4700 -0.4600 -0.4500 -0.4400 -0.4300 -0.4200 -0.4100 -0.4000 -0.3900 -0.3800 -0.3700 -0.3600 -0.3500 -0.3400 -0.3300 -0.3200 -0.3100 -0.3000 -0.2900 -0.2800 -0.2700 -0.2600 -0.2500 -0.2400 -0.2300 -0.2200 -0.2100 -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 
Maximum field value 0.0370 
Minimum field value -0.0329 
Shading is  off 
Reshaping for T30 Gaussian grid
Contouring from a minimum -0.5000 
Contouring to a maximum 0.0500 
Contouring interval is  0.0100 
Contour values are: 
-0.5000 -0.4900 -0.4800 -0.4700 -0.4600 -0.4500 -0.4400 -0.4300 -0.4200 -0.4100 -0.4000 -0.3900 -0.3800 -0.3700 -0.3600 -0.3500 -0.3400 -0.3300 -0.3200 -0.3100 -0.3000 -0.2900 -0.2800 -0.2700 -0.2600 -0.2500 -0.2400 -0.2300 -0.2200 -0.2100 -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 
Maximum field value 0.0464 
Minimum field value -0.0501