Part 4: Time Series II

Empirical Orthogonal Function Analysis

What Does EOF Analysis do?

Slide 4

An Example

Another View of the Rotation

Rotation of Coordinates

Determine the Projection Coefficients

Slide 9

Covariance Matrix

Covariance Matrix – cont.

Eigenvectors of a Symmetric Matrix

Orthogonal Constrains

Mathematic Background

Some Basic Matrix Operations

Correlation Matrix

Correlation Matrix – cont.

How to Get Principal Components?

Presentations of EOF – Variance Map

Presentations of EOF – Correlation Map

Using SVD to Get EOF&PC

What is SVD?

An Example – with SVD method

An Example – With Eigenanalysis

How Many EOFs Should We Retain?

An Example

Rotated EOF

Criteria for the Rotation

Quartimax and Varimax Rotation

Reference For the Following Examples

Example 1:
North Atlantic SST Variability

Example 2: Indian Ocean SST Variability

Example 3:
SLP Variability
(Arctic Oscillation)

Example 4:
Low-Dimensional Variability
(Variance Based)

Slide 35