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SSA.m
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SSA.m
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Created: 21-May-2012 12:18:18
% Computer: GLNX86
% Matlab: 7.9
% Author: NK
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function SSA
close all
clear all
%% ##########################INPUT#########################################
%netcdf data
nc.file='./sst.mon.anom.nc';
%variable key
nc.var='sst';
%lat/long keys
nc.lat='lat';
nc.lon='lon';
%time key
nc.time='time';
%days since 'YYYYMMDD'
nc.ds='18000101';
%chosen dimensions file
input='./input.txt';
%##########################################################################
%% begin
main(input,nc)
end
function main(input,nc)
dims=dlmread(input);
%% get data
D=readData(nc);
%% get time
[T]=getTime(D.time,nc.ds,dims);
%% get space
[S]=getspace(D,dims);
%% cut piece
[D]=cutPiece(D,S,T);
%% create mean
[D]=lat_weighted_mean(D);
%% build lag shifet matrix Y, toeplitz covariance matrix C and get
%EOFs (rho) and eigenvalues
[eof]=Toep_cov(detrend(D.cut.sstm)',dims);
%% build reconstructed components
[RC]=RCs(eof,dims);
%%
plotStuff(eof,RC,D,T)
printall2eps
end
function [p,freq]=fourierm(sstm,time)
% perform fft on monthly data
f = sstm;
N = length(f); %% number of points
T = (time(end)-time(1))/(365.25/12); %% define time of interval, days to months
%t = (0:N-1)/N; %% define time
%t = t*T; %% define time in seconds
p = abs(fft(f))/(N/2); %% absolute value of the fft
warning('off','MATLAB:colon:nonIntegerIndex')
p = p(1:N/2).^2; %% take the power of positve freq. half
freq = (0:N/2-1)/T*12; %% find the corresponding frequency in Hz
end
function [RC]=RCs(eof,dims)
% build RCs
[pcl,pcn]=size(eof.PC);
M=pcn;
rcn=dims(4,2);
%% build Z
%Z size of PC times number of eigenvectors
Z=zeros(pcl,M,rcn);
%loop over PCs
for z=1:rcn
for x=1:M
Z(1+x-1:end,x,z)=eof.PC(1:end-x+1,M-z+1); %we need the pcn-lon end part of PC
end
end
%% build RCs
RC=nan(pcl,rcn);
for r=1:rcn
RC(:,r)=squeeze(Z(:,:,r))*eof.rho(:,M-r+1)/M;
end
end
function [eof]=Toep_cov(in,dims)
%lag
M=dims(4,1);
%autocorrelation
C=autocorr(in,M-1);
%toeplitz form
C=toeplitz(C);
%EOFs
[rho,lambda]=eig(C);
lambda=diag(lambda);
%Y
[I,~]=size(in);
Y=zeros(I,M);
[~,L]=size(Y);
for x=1:L
Y(1:end-x+1,x)=in(x:end);
end
%% build principal components
eof.PC=Y*rho;
%% pack bag
eof.Y=Y;
eof.C=C;
eof.rho=rho;
eof.lambda=lambda;
end
function [D]=lat_weighted_mean(D)
D.cut.sstW=nan(size(D.cut.sst));
%% create weight
D.weight=nan(D.dim.cut.y,D.dim.cut.x);
for y=1:D.dim.cut.y
D.weight(y,:)=cosd(D.cut.lat(y));
end
%% "total number" of values
N=nansum(D.weight(:));
for t=1:D.dim.cut.t
% kill land
D.weight(isnan(squeeze(D.cut.sst(t,:,:))))=nan;
% weighted in
D.cut.sstW(t,:,:)=squeeze(D.cut.sst(t,:,:)).*D.weight;
% build mean
D.cut.sstm(t)=nansum(nansum(D.cut.sstW(t,:,:)))/N;
end
end
function [D]=cutPiece(D,S,T)
D.cut.sst=D.sst(T.from:T.till,S.s:S.n,S.w:S.e);
D.cut.lat=D.lat(S.s:S.n);
D.cut.lon=D.lon(S.w:S.e)- 180;
[D.dim.cut.t,D.dim.cut.y,D.dim.cut.x]=size(D.cut.sst);
end
function [T]=getTime(timein,ds,dims)
% get time info, ask time window
% time(f:t)
disp('getting time..')
T.time=timein+datenum(ds,'yyyymmdd');
disp(['data spans ',datestr(T.time(1)),' through ',datestr(T.time(end))])
disp('reading time coordinates from input file..')
from=datenum(num2str(dims(1,1)),'yyyymm');
till=datenum(num2str(dims(1,2)),'yyyymm');
disp([datestr(from),' till ',datestr(till)])
[~,T.from]=min(abs(T.time-from));
[~,T.till]=min(abs(T.time-till));
T.time=T.time(T.from:T.till);
end
function D=readData(nc)
%% read data
nc.info=nc_info(nc.file);
D.lon=double(nc_varget(nc.file,nc.lon));
D.lat=double(nc_varget(nc.file,nc.lat));
D.time=nc_varget(nc.file,nc.time);
D.sst=nc_varget(nc.file,nc.var);
[D.dim.t,D.dim.y,D.dim.x]=size(D.sst);
%make flag nan
D.sst=flag2nan(D.sst,max(D.sst(:)));
end
function printall2eps
%prints all figures into current dir as .eps
figs = findobj('Type','figure');
for l=1:length(figs)
eval(['print -f', num2str(figs(l)),' -r400 -depsc figure_',num2str(figs(l)),'.eps;'])
end
close all
system('evince ./*.eps');
end
function [S]=getspace(D,dims)
disp('organizing space stuff..')
D.lon=D.lon-180;
south=D.lat(1); north=D.lat(end); west=D.lon(1); east=D.lon(end);
disp(['data spans from ',num2str(south),' south to ',num2str(north),...
' north and from ',num2str(west),' west to ',num2str(east),' east ',...
'at a resolution of ', num2str(length(D.lat)), ' x ',num2str(length(D.lon))])
disp('reading space coordinates from input file..')
so=dims(2,1);
no=dims(2,2);
we=dims(3,1);
ea=dims(3,2);
disp('finding best fit..')
[~,S.s]=min(abs(D.lat-so));
[~,S.n]=min(abs(D.lat-no));
[~,S.w]=min(abs(D.lon-we));
[~,S.e]=min(abs(D.lon-ea));
%%
windowlat=[linspace(so,no,100),no*ones(1,100),linspace(no,so,100),so*ones(1,100)];
windowlon=[we*ones(1,100),linspace(we,ea,100),ea*ones(1,100),linspace(ea,we,100)];
disp('creating snapshot..')
fig=figure('Color','white');
axesm hatano;
coast = load('coast');
axis on; framem on; gridm on; hold on;
plotm(coast.lat,coast.long)
plotm(windowlat,windowlon,'r')
title('close this depiction of the window you have chosen')
tightmap
waitfor(fig)
end
function plotStuff(eof,RC,D,T)
figure(1)
lamnrmd=flipud(eof.lambda./sum(eof.lambda))*100;
if length(lamnrmd)<30
semilogy(lamnrmd,'*')
else
semilogy(lamnrmd(1:30),'*')
end
hold on
semilogy(lamnrmd(1:4),'*r')
text(5,4, ['sum over first 4 =',...
num2str(round(sum(eof.lambda(end-3:end))/sum(eof.lambda)*100)),' %']...
,'fontsize',12)
ylabel('%')
title('\lambda')
set(gca,'xtick',[]);
set(gca,'xticklabel',{});
%%
pm=0;
L=9;
for s=1:L
figure(10)
subplot(3,3,s)
plot(T.time,RC(:,s),'color',rainbow(1,1,1,s,L))
axis([T.time(1) T.time(end) floor(min(RC(:,s))*100)/100 ceil(max(RC(:,s))*100)/100])
set(gca,'xtick',[T.time(1) T.time(1)+50*365+1 T.time(1)+100*365+1 T.time(end)])
if s==1
set(gca,'xticklabel',{datestr(T.time(1),'mm/yyyy') '+50a' ' ' datestr(T.time(end),'mm/yyyy') })
else
set(gca,'xticklabel',{})
end
set(gca,'ytick',[round(min(RC(:,s))*100)/100 round(max(RC(:,s))*100)/100 ])
figure(100)
plot(T.time,RC(:,s),'color',rainbow(1,1,1,s,L))
axis([T.time(1) T.time(end) min(RC(:)) max(RC(:))])
hold on
figure(4)
[pf,freq]=fourierm(RC(:,s),T.time);
loglog(freq,pf,'color',rainbow(1,1,1,s,L)); %% plot on s
hold on
if max(pf)>pm
pm=max(pf);
end
end
figure(4)
set(gca, 'xtick', [1/50,1/23,1/10,1/5.5 ,1/1])
set(gca, 'xticklabel', {'1/50a','1/23a','1/10a','1/5.5a','1/1a'})
axis([freq(1) freq(end) 0 pm])
ylabel('(K months)^2')
figure(100)
ylen=365.25;
xt=round((T.time(1)+4*ylen:ylen*10:T.time(end)));
set(gca,'xtick',xt)
set(gca,'xticklabel',datestr(xt,'yy'))
set(gca,'ytick',[-.1 0 .1])
%%
figure(2)
da=sum(RC(:,1:2),2);
plot(T.time,detrend(D.cut.sstm),'r');
hold on
plot(T.time,da);
axis([T.time(1) T.time(end) min(D.cut.sstm) max(D.cut.sstm)])
set(gca,'xtick',xt)
set(gca,'xticklabel',datestr(xt,'yy'))
ylabel('K')
title('sum of first 2 RCs')
end
function [colors]=rainbow(R, G, B, l, L)
om=2*pi/L;
red=R*sin(l*om-2*pi*(0/3));
green=G*sin(l*om-2*pi*(1/3));
blue=B*sin(l*om-2*pi*(2/3));
colors=[red green blue]/2+.5;
end
function in=flag2nan(in,fl)
disp('making flags nan..')
in(in==fl)=nan;
end