Re: [ferret_users] eof variance

["William S. Kessler" <william.s.kessler@xxxxxxxx>]

The value of the 2nd argument should probably be less than 1 (.2? . 
4?). Do some experimentation.

To explore this, try the routine on a subset of the data (say restrict  
in lat/lon), for a region where you have a good idea of the signal.

plot ssha[x=80e:90e@ave,y=5n:15n@ave]    ! find a region with a clear  
annual signal

let sshaeoftest=eof_tfunc(ssha[x=80e:90e,y=5n:15n]

plot ssheoftest[i=1],ssheoftest[i=2],ssheoftest[i=3]   ! is one of  
these annual?

But a larger point is that it is a bad idea to use EOFs to extract a  
signal of known frequency (e.g. annual and semi-annual), for three  
reasons:
1) EOFs will be less efficient and more cpu-intensive at doing this  
than a simple harmonic decomposition.
2) Your goal is presumably to distinguish the various physical signals  
in the data, ideally by having individual EOFs represent particular  
signals. But EOFs blindly (non-physically) maximize the correlated  
variance in the lowest modes. If the spatial pattern of a large- 
amplitude signal (e.g. annual) has a partial correlation with the  
spatial pattern of another frequency, then the EOF will mix the two,  
providing potentially misleading results (neither the annual nor the  
other signal will be well-represented by a particular EOF, thwarting  
your goal).
3) A propagating signal will be represented by two EOF modes (because  
EOFs are standing waves, decomposing data into a sum over separable  
functions A(x)*B(t)). This can easily be tested with a constructed  
example. Two modes for one signal is less than ideal, since it may not  
be obvious how the two modes fit together (especially in light of  
problem (2) above). Therefore, even aside from the computational  
disadvantages, they are inherently less effective than harmonics when  
there is a propagating wave in the data.

=> Don't use EOFs to extract known facts. First filter the known  
frequencies from the data and describe those separately. For example,  
first remove the annual cycle (with month_reg@mod; see "Modulo  
regridding" in the documentation; or harmonic decomposition - search  
the archives for "harmonic", several scripts have been posted).  
Analyze the annual (and semi-annual?) signal separately, then do EOFs  
on the residual.

=> When trying any kind of analysis, first do some experiments with  
small subsets or cooked examples where you know the answer. Thereby,  
learn what the technique is and is not capable of doing.

BK

On 10 Nov 2011, at 8:36 AM, golla nageswararao wrote:

> Hi all,
>    I am very new to EOF analysis. I did EOF analysis to weekly SSHA  
> data for 954 weeks. I got some 55000 modes and all. But thing the  
> mode variance is less i.e., 17 and 2nd mode -11,...When I saw time  
> series plot of first mode it is mainly biannual peak. I having doubt  
> that usually for Indian ocean the first mode should be annual with  
> variance more than 50. But astonishingly the result different. How  
> can I decrease the spread  of variance over large no. of modes in  
> eof? Since data is huge, I averaged to 1°x1° and subjected to eof  
> analysis, is this will do any thing with the result? I used the  
> command eof_space(ssha,1) is that "1" any culprit? how to choose  
> that variable? Can anybody throw some light on these doubts.
>
> Thanks in advance.
>
> --
> With Best regards,
> G.NageswaraRao,