Re: EOF signs

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