#
`reof` documentation

reof reconstructs a time series of eof anomalies from specified EOF modes.

See also: `eof`.

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## Contents

## Syntax

A = reof(eof_maps,pc,modes)

## Description

`A = reof(eof_maps,pc,modes)` reconstructs a gridded time series of the specified modes, from eigenmode maps `eof_maps` and principal component time series `pc`, which are both outputs of the `eof` function.

## Example

Let's say we have some big gridded dataset, and the modes associated with the first 75% of variance are desirable, but all the higher-order modes that make up the last 25% percent of variance we assume (for this exampe) are just noise. We want to filter out all that noise, and we can do such filtering with `reof`.

Start by very quickly running through the steps of EOF analysis which are described in excruciating detail in the `eof` documentation:

```
load pacific_sst
sst = deseason(detrend3(sst,t),t);
[eof_maps,pc,expv] = eof(sst);
```

We said we want to keep the first modes, because they're the most significant, but how many modes does it take to explain 75% of the variance of the dataset? For that, we'll have to plot the cumulative variance explained, as a function of mode number:

figure plot(cumsum(expv)) axis tight box off xlabel mode ylabel 'cumulative variance explained (%)'

As you can see, it only takes a few of the 802 modes to explain 75% of the sst dataset, and we'll assume that means all the other modes are just noise. Zooming in, it looks like only takes 11 modes to explain 75% of the variance:

xlim([0 20]) hline(75) % 75% variance explained vline(11) % corresponds to about mode 11

Let's check. The sum of the variance explained by the first 11 modes is

sum(expv(1:11))

ans = 75.3165

Perfect, 75%. So let's "filter out" that last 25% of noisy variance with `reof`. Just give it the `eof_maps` and `pc` array we calculated earlier:, and specify modes 1:11, like this:

sst_f = reof(eof_maps,pc,1:11);

Now we can make a side-by-side animation, showing the original (detrended and deseasoned) time series, next to our filtered one. Start by plotting the first frame, save it with the `gif` function, and then loop through the remaining frames, updating the data and saving each frame with `gif`.

To keep the filesize small, I'm just plotting frames 200 to 300, which correspond to 1966 to 1974, and we'll only plot every other month.

figure subplot(1,2,1) h = imagescn(lon,lat,sst(:,:,200)); caxis([-3 3]) cmocean bal title 'all modes' axis image off

subplot(1,2,2) h_f = imagescn(lon,lat,sst_f(:,:,200)); caxis([-3 3]) cmocean bal title 'modes 1-11' axis image off

% Save the first frame: gif('eof_filtering.gif','frame',gcf,'nodither')

for k = 202:2:300 h.CData = sst(:,:,k); % updates raw data h_f.CData = sst_f(:,:,k); % updates filtered data gif % saves this frame end

And you can see, in the animation above, that keeping only first 11 modes preserves the large-scale, large-magnitude variability, but eliminates the smaller-scale noisiness.

## Author Info

This function is part of the Climate Data Toolbox for Matlab. The function and supporting documentation were written by Chad A. Greene of the University of Texas at Austin.