| Why EOFs ? |
| Joe Tribbia | |
| NCAR | |
| Random Matrices TOY 5/9/2007 |
| Why EOFs ? outline |
| Background history of EOFs in meteorology | |
| 1 dimensional example-BurgerÕs eqn | |
| EOFs as a random matrix | |
| EOFs for taxonomy | |
| EOFs for dimension reduction/basis | |
| Summary | |
| Background in meteorology |
| 1956 report by E N Lorenz | |
| Use EOFs to objectively classify Low –frequency weather patterns | |
| Application was to ŌLong range predictionĶ i.e. monthly weather outlooks | |
| Through Don Gilman, John Kutzbach and Bob Livezy became the basis for monthly and seasonal outlooks | |
| E N Lorenz : EOFs and dynamical systems |
| E N Lorenz (continued) |
| 1 dimensional example: sample over time |
| 1 dimensional example BurgerÕs equation |
| 1 dimensional example (cont.) |
| Slide 9 |
| EOFs and PCs |
| Looking for variance structure: taxonomy in climate |
| Looking for structure: taxonomy |
| Looking for dynamical structure: bump hunting |
| Slide 14 |
| Looking for predictable structure |
| 1 dimensional example BurgerÕs equation |
| 1 dimensional example (cont.) |
| Dimension reduction:EOF basis |
| Sampling strategies for small samples in high dimensional systems: dimension reduction |
| Bred vectors and Singular vectors |
| Concluding remarks |
| EOFs can be motivated from a dynamical systems perspective | |
| EOFs useful for elucidating structure ( taxonomy, predictability, non-gaussianity) | |
| EOFs useful for dimension reduction (natural basis, importance sampling) | |
| Limits to utility: intrinsic Gaussianity and linearity, prior information needed |