Re: EOF varimax rotation and data reconstruction

From: Carlos A. F. Marques <cafm_at_nyahnyahspammersnyahnyah>
Date: Thu Sep 08 2011 - 17:16:51 MDT

The properties (spatial orthogonality and temporal
uncorrelatedness) of orthogonally rotated empirical modes
depend on the normalization of the modes, prior to
rotation.

At least one of the properties (spatial orthogonality or
temporal uncorrelatedness) is lost when the EOFs are
rotated, depending on the normalization choice of the
eigenvectors (EOFs). See the following paper:
http://www.aoml.noaa.gov/phod/docs/mestas-00.pdf

Hope it helps,

Carlos

Em Thu, 08 Sep 2011 09:37:33 -0600
Dennis Shea <shea@ucar.edu> escreveu:
>
>
> 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.
>
> ==> From http://en.wikipedia.org/wiki/Dot_product
>
> 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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University of Aveiro.
Campus Universitário de Santiago
3810-193 Aveiro.
Portugal
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Received on Thu Sep 8 17:17:04 2011

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