function [decorr, dist]=DecorrelationLength(x,y,data, dist);
% % EXAMPLE:
% load DATA
% x=lon_d; y=lat_d; 
% dist=0:0.2:10; % the x-axis of the autocorrelation function
% [decorr, dist]=DecorrelationLength(x,y,data,dist);
% plot(dist, decorr, 'linewidth',2); grid on

d=data;
x1=x;y1=y;
i=length(x(:));
j=length(x1(:));
X=M2d(x,j);
Y=M2d(y,j);
X1=M2d(x1,i)';
Y1=M2d(y1,i)';

DIST = sqrt( (X-X1).*(X-X1) + (Y-Y1).*(Y-Y1)) ;
CDD=d*d'; 
L=size(DIST,1);

% Now interpolate the covariances onto regularly spaced distances
for i=1:L;
  
  % Sort the values based on distance
  tmp=DIST(:,i);
  tmp(:,2)=CDD(:,i);  
  tmp=sortrows(tmp,1);
  
  % Remove duplicate values when distances are the same
  in = find (tmp(2:end,1)-tmp(1:end-1,1) ~=0);
  tmp=tmp(in,:);  
  
  % interpolate onto linearly spaced distances
  % DECORR will hold all the realizations of DECORR
  DECORR(:,i)=interp1(tmp(:,1), tmp(:,2), dist, 'linear');
  
end
 
% Compute spatial autocorrelation function by averaging over
% all realizations and divide by the variance of d to get correlation.
decorr=mean(DECORR,2)/var(d);
 
 
return 
 
 
% Utility function. 
function X=M2d(x,J)
I=length(x(:));
X=zeros(I,1); X(:)=x(:);
X=repmat(X,[1 J]);