clean

%  Change to working directory - you'll have to edit this line.  Just
%  change it to the directory where you dump all of the files that you
%  downloaded from the website (including this file).
cd /Users/dvimont/Class/aos760/Notes/WES/WES_modes

%%%   Define model paramters  %%%
%  Now, set up parameters:  Note that if you want to change anything,
%  like the amplitude of Kq or the WES parameter, you can do so in the
%  "wes_model_gill" routine, or here.  If you do it here, you'll have to
%  comment out the appropriate line in wes_model_gill.m .

Lx = 240;        %  Zonal wavelength in degrees.  Try changing this.
wesh = 15;       %  Amplitude of WES feedback (W m^-2 K^-1).  Try
                 %  changing this


%%%  Obtain linear model (a matrix M)  %%%
wes_model_gill;

%%%  Now, get normal modes of 'M'  %%%
[vc, lamc] = eig(M);          %  Eigenvectors (v) and eigenvalues (lam)
lamc = diag(lamc);

%%%  Now, note that we could obtain the uncoupled modes by eliminating
%%%  every fourth row or column of M - this eliminates coupling with the
%%%  temperature equaiton (every fourth column) as well as the
%%%  temperature equation itself (every fourth row).  Take a look at the
%%%  in Question (4) of the writeup.

ny = length(y);
ind = sort([1:4:(4*ny) 2:4:(4*ny) 3:4:(4*ny)]);
Mu = M(ind,ind);            %  Uncoupled model

[vu, lamu] = eig(Mu);       %  e-vect. / e-val. of uncoupled system 
lamu = diag(lamu);

%%%  Organize coupled modes in terms of stability
[tem, ind] = sort(-real(lamc));

%  Try changing which mode you'll plot, by changing 'ii'.
ii = 2;
plot_struct_lin_gill2

%  Now, plot the eigenspectrum
plot_spect_gill

%  Use the 'zoom' tool, or the 'axis' command to zoom in on the set of
%  coupled SST modes.  Note that the remaining modes look pretty similar
%  to the uncoupled modes - these are just the standard gravity and
%  Rossby waves that emerge as in Matsuno.  The blue dots are the
%  uncoupled eigenvalues, the red circles are the coupled eigenvalues.
%  Another way to see this is to gradually decrease Lx from planetary
%  wave-lengths to about the Rossby radius (about 10 degrees).  Note that
%  the gravity wave phase speed increases considerably - this reminds us
%  of the dispersion relationship, no?