# Re: [ferret_users] EOF analysis

I wrote this routine a very long time ago, and I'm not in a position to test it now, but I think this is correct.
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The result of the EOF computation (before normalization) has both the EOF and time function dimensionless, and all the amplitude is in the eigenvalues. The result has the valuable property that the original data can be recovered by the sum over all EOFs n=1:N, where N is the min(#space pts,# time points). Using subscript _0 to represent these original fields:
```
data(x,t) = SUM_n[EVALUE(n)*EOF_0(x,n)*TAF_0(t,n)]

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The normalization simply distributes the amplitude-containing eigenvalue over the EOFs and TAFs: It multiplies the original EOFs and time functions by the sqrt(eigenvalue). Thus, for the Ferret EOF output:
```
data(x,t) = SUM_n[EOF(x,n)*TAF(t,n)]

The result of this is that, for output of the Ferret EOF routines:

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The sum over all space of any single EOF^2 equals the corresponding eigenvalue. The sum over all time of any single (time function)^2 equals the number of observations.
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To reverse the normalization, simply reverse this process: divide by the sqrt(eigenvalue). But note that if you want to retain the data- recovery property of EOFs (or if you want to correctly plot or present the EOF results including both the space and time functions), then you must make this change to BOTH the EOF and the time function.
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Billy K

On 16/05/2008, at 7:18 PM, Peter Kim wrote:

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Hi All

According to Ferret documentation, EOF_SPACE returns
the normalized eigenfuctions so that they have the units of data.
I would like to know how it is normalized.
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I want to get dimensionless eigenvectors, in other words, eigenvectors of unit length.
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-Seon Tae-
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