From: Aideen Foley <aideen.m.foley_at_nyahnyahspammersnyahnyah>

Date: Fri, 18 Sep 2009 16:54:11 +0100

Date: Fri, 18 Sep 2009 16:54:11 +0100

Hi Andrew,

Thanks so much for this, it has cleared up a lot of my confusion. Much

appreciated!

Regards,

Aideen

On Fri, Sep 11, 2009 at 1:57 PM, Andrew Dawson <andrew.dawson_at_uea.ac.uk>wrote:

*> 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
*

*> result.
*

*>
*

*> 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 <aideen.m.foley_at_nuim.ie>
*

*>
*

*> 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 <shea_at_ucar.edu> 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
*

*>>>> huangwei_at_ucar.edu <mailto:huangwei_at_ucar.edu>
*

*>>>> VETS/CISL
*

*>>>> 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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*

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*>>>>> http://mailman.ucar.edu/mailman/listinfo/ncl-talk
*

*>>>>>
*

*>>>>
*

*>>>>
*

*>>>> ------------------------------------------------------------------------
*

*>>>>
*

*>>>> _______________________________________________
*

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*

*>>>> List instructions, subscriber options, unsubscribe:
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*>>>>
*

*>>>
*

*>>
*

*>> _______________________________________________
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*>>
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*>
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Received on Fri Sep 18 2009 - 09:54:11 MDT

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