1. Complex Empirical Orthogonal Functions – James River Data Linear combination of spatial predictors or modes that are normal or orthogonal to each other u v

2. Streamwise Cross-stream Rotated 49 degrees

3. >> ul=complex(u,v); >> uc=cov(ul); >> [v,d]=eig(uc);

4. Mode 1 96.5% Mode 1 >> lambda=diag(d)/sum(diag(d)); >> v=fliplr(v);

5. Mode 2 2.5% Mode 2

6. Mode 1 96.5% Streamwise cross-stream >> ts=ul*v;

7. Mode 1 96.5% Principal-axis cross-axis Mode scaling >> ts=ul*v;

8. Mode 2 2.5% Streamwise Cross-stream Mode scaling >> ts=ul*v;

9. Mode scaling Mode 2 2.5% Streamwise cross-stream >> ts=ul*v;

10. Low-pass filtered data in James River m/s Streamwise cross-stream

11. Mode 1 75% m/s Streamwise cross-stream

12. Mode 2 22% m/s Streamwise cross-stream

13. Depth (m) radians Phase of EOFS Mode 1 Mode 2 Mode 1 Mode 2

14. streamwise cross-stream >> ts=ul*v;

15. streamwise cross-stream >> ts=ul*v;

16. Modes 1 + 2 (75% + 22%) Original >> for k=1:nz vt(k,:,:)=ts(:,k)*v(:,k)'; end >> v1=squeeze(vt(1,:,:))’; >> v2=squeeze(vt(2,:,:))’; Original

17. Modes 1 + 2 + 3 + 4 (77%+22% +2% + 0.6%) Original

18. Low-pass filtered data in James River m/s 3 ways to EOFs!