# Re: EOF varimax rotation and data reconstruction

From: Dennis Shea <shea_at_nyahnyahspammersnyahnyah>
Date: Thu Sep 08 2011 - 09:37:33 MDT

On 9/7/11 9:17 PM, Torben Mueller wrote:
> Dear NCL community,
>
> I have two questions regarding EOF analysis with NCL:
>
> (1) For the function "eofunc_varimax", it states in the description:
> "The result of varimax rotation upon standard EOFs are rotated EOFs
> that are orthonormal. However, the temporal patterns derived by
> projecting the rotated spatial patterns onto the data will not be
> orthogonal".
> It is unclear to be on how obtain the corresponding PC time series to
> the rotated EOF pattern?
===
Standard eigenvector analysis results in orthogonal EOF patterns
and PCs.

As the cosine of 90 deg is zero, the dot product of two
orthogonal vectors is always zero. Moreover, two vectors can be
considered orthogonal if and only if their dot product is zero.

Dot product in space ==> 0
Correlation in time ==> 0

====
My understanding is:

Say the max possible number of eigenvalues/vectors is N=100.
Then the 1st EOF is free of constraints but all subsequent EOFs
(N-1) are constrained to be orthogonal to all previous patterns.

When you select an EOF subset, say the 1st M=10, to be rotated,
you are taking these and saying that there will be only (M-1)
constraints rather than N=100. The varimax patterns
will be ortogonal [dot product of zero) but the PCs will be
correlated due to the mixing of previously independent EOFs.

You can certainly rotate the EOFs and then use eofunc_ts
but I'm not sure how to interpret the results.

Others should feel free to comment on this.

>
> (2) There seems to be no equivalent of the old function "eof2data" for
> the new "eofunc" family of functions. Is the "eof2data" function
> compatible with the output from the new function family?

It is just a multiply, so yes.

http://www.ncl.ucar.edu/Document/Functions/Built-in/eof2data.shtml
>
> Thanks!
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Received on Thu Sep 8 09:37:38 2011

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