Empirical orthogonal functions

Empirical orthogonal functions (EOFs) are a way of understanding patterns in a large set of data. Think of it like a big picture puzzle with many, many pieces. The pieces are like the data points, and we want to understand how they fit together to form a complete picture.

Now, imagine that you have a big stack of these puzzles, each with different pictures. You want to figure out if there are any patterns in how the pieces fit together across all of the different puzzles. This is where EOFs come in.

To create EOFs, we start by looking at all the data points in each puzzle and figuring out which ones are most similar to each other. We then group these similar points together and call them an "empirical mode." Each empirical mode is essentially a pattern that describes how certain data points are related to each other.

Next, we find the most important empirical mode and call it the first EOF. This is the pattern that explains the most variation in the data. We then find the second most important pattern, which is orthogonal (or perpendicular) to the first pattern. This means that it captures a different aspect of the data that the first pattern did not.

We continue this process until we have found all the important patterns, or EOFs, that explain the majority of the variation in the data. Each EOF is like a puzzle piece that helps us understand the big picture of the data.

In summary, EOFs are a way of finding patterns in large sets of data by grouping similar data points together into patterns called empirical modes. These modes are then ranked by importance, and the most important patterns are called empirical orthogonal functions (EOFs). Each EOF is a puzzle piece that helps us understand the big picture of the data.