Presentation is loading. Please wait.

Presentation is loading. Please wait.

SVD analysis Singular Value Decomposition (SVD) is usually applied to two combined data filed The method identifies the coupled spatial pattern Example:

Similar presentations


Presentation on theme: "SVD analysis Singular Value Decomposition (SVD) is usually applied to two combined data filed The method identifies the coupled spatial pattern Example:"— Presentation transcript:

1 SVD analysis Singular Value Decomposition (SVD) is usually applied to two combined data filed The method identifies the coupled spatial pattern Example: SST (S, n by p) & SLP (P, n by q) n: time points, p (q): spatial points

2 Forming a covariance matrix: C=StP Apply SVD: C=ULVt U is the left pattern (eigenvector for S) V is the right pattern (eigenvector for P) Diagonal (L) is the eigenvalue The time series (expansion coefficient): A=SU, B=PV

3 In matlab: Input two variables X1 (N by P) and X2 (N by Q), the left pattern EC p, right pattern EC q, and squared covariance fraction scf are obtained. R=cov([X1,X2]); [u1,s1,v1]=svd(R); d=diag(s1); % eigenvalues p=X1*u1; % left EC q=X2*v1; % right EC scf=d.^2/(sum(d.^2)); %squared covarience First mode if mode ==1: For spatial pattern SP: Left pattern: r1=(X1'*p(:,mode)/(ny-1))./(std(X1)*std(p(:,mode)))'; Homogeneous map (Px1) This standard deviation map is also Px1 Right pattern: r2=(X2'*q(:,mode)/(ny-1))./(std(X2)*std(q(:,mode)))'; Homogeneous map (Qx1) This standard deviation map is also Qx1 For expansion coefficient EC: p(:,mode)./std(p(:,mode)) q(:,mode)./std(q(:,mode)) Looks like R has unit = (Deg/m)*(m/s); see B&V, p.24, sec.3.2, 4 th line from below This “r1” (or “r2”) is just the homogeneous correlation map – B&V fig.5.3 caption for S1(SST & S1(SLP) Your EC’s are also the same as B&V fig.5.3 caption for s1(SST & s1(SLP). So all I (we) need to know is just what std(p) & std(q) are B&V: ftp://profs.princeton.edu/leo/journals/EOFandSVD/BjornssonVenegasEOFSVDMatlab2000Report.pdf

4 Dong-Ping’s note for SVD: page1

5 Dong-Ping’s note for SVD: page2

6 Dong-Ping’s note for SVD: page3

7


Download ppt "SVD analysis Singular Value Decomposition (SVD) is usually applied to two combined data filed The method identifies the coupled spatial pattern Example:"

Similar presentations


Ads by Google