Re: EOF signs

From: Andrew Dawson <andrew.dawson_at_nyahnyahspammersnyahnyah>
Date: Fri, 11 Sep 2009 13:57:10 +0100

EOF analysis can sometimes be quite confusing. It is important to remember
that the process of finding EOF patterns is purely mathematical, and that
any physical meaning is dependent on your interpretation of the mathematical

EOFs are essentially eigenvectors of the covariance matrix formed from your
input data. Since an eigenvector can be multiplied by any scalar and still
remain an eigenvector, the sign is arbitrary. In a mathematical sense the
sign of an eigenvector is rather unimportant. This is why the EOF analysis
may yield different signed EOFs for slightly different inputs. Sign only
becomes an issue when you wish to interpret the physical meaning (if any) of
an eigenvector.

You should approach the interpretation of EOFs by looking at both the EOF
pattern and the associated time series together. For example, consider an
EOF of sea surface temperature. If your EOF has a positve centre and the
associated time series is increasing then you will interpret this centre as
a warming signal. If your EOF had come out the other sign (ie. a negative
centre) then the associated time series would also be the opposite sign and
you would still interpret the centre as a warming signal.

In essence, the sign flip does not change the physical interpretation of the
result. Hence, it is up to you to choose which sign to associate with your
EOF patterns for visualisation (remembering that any sign change to an EOF
must be applied to the associated time series also). Usually you would
simply adjust the sign so that all your EOF patterns with the same physical
interpretation also look the same.

I hope that my explanation makes sense.

2009/9/11 Aideen Foley <>

> Thank you both for your responses.
> It is useful to know how this point testing can be accomplished, but for my
> purposes it is not ideal. For comparative purposes I would prefer to apply
> the same methodology to all datasets rather than adjusting some and not
> others.
> If you have any further thoughts on the matter, please let me know.
> Regards,
> Aideen
> On Wed, Sep 9, 2009 at 4:19 PM, Dennis Shea <> wrote:
>> To add a bit more information:
>> Consider EOF(neof,lat,lon) and you want the
>> first EOF over (say) Iceland to be negative
>> if (EOF(0,{64},{340}).gt.0) then
>> EOF(0,:,:) = -EOF(0,:,:) ; switch all signs
>> end if
>> Wei Huang wrote:
>>> Aideen,
>>> There is no way to have the EOFs automatically
>>> give the same sign. The EOFs are calculated using
>>> LAPACK's "dspevx" routine.
>>> If there is a location in space that you want a
>>> particular sign, you could test that point and
>>> change the sign accordingly.
>>> Regards,
>>> Wei Huang
>>> <>
>>> National Center for Atmospheric Research
>>> P.O. Box 3000 (1850 Table Mesa Dr.)
>>> Boulder, CO 80307-3000 USA
>>> (303) 497-8924
>>> On Sep 9, 2009, at 7:44 AM, Aideen Foley wrote:
>>> Hello.
>>>> I am applying the same EOF analysis script to output from different
>>>> climate models, and finding that for some datasets, the primary EOF is
>>>> positive, and for others it is negative, with a time amplitude series that
>>>> is the inverse of what I would expect were it positive. I know that that one
>>>> can multiply the EOF and it's time amplitude series by -1 to aid
>>>> interpretation, but I would like to understand why the eofunc routine
>>>> prefers inverted output for some of my data but not for others. I would like
>>>> if it followed the same convention with each. dataset. Can anyone help me
>>>> with this question?
>>>> Many thanks,
>>>> Aideen Foley
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Received on Fri Sep 11 2009 - 06:57:10 MDT

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