Re: [ferret_users] Results of EOF analysis

[Billy Kessler <william.s.kessler@xxxxxxxx>]

Hello Masud -

My suggestion is to build intuition about advanced statistical techniques like EOFs before you can be confident in interpreting them.

- Construct some patterns of known structure (sine waves, exponentials, other analytic patterns or products of such patterns where you know everything about the variability). Do EOFs on them and build your sense about what it does and doesn't represent well. Multiply the results (EOF1*Timefn1 + EOF2*Timefn2 ...). How does the representation improve by including more EOFs? (This will differ depending on the kind of structure).

- Try the same simple patterns but introduce a large value at a single gridpoint, or at a few scattered gridpoints. How does this affect the EOF?

- For your real data, try EOFs on parts of the field, say the eastern or western half of the Bay, or for the first or last half of the time series. Is the result different?

- Always look at the percent variance represented by each EOF (eofsvd_stat, for J=2). Which patterns are well represented by a single EOF, and which take more than one? (Note that a propagating sine wave will always need two EOFs to represent it, as in the time functions of your first two EOFs).

- Try subtracting the average annual cycle from the data, then do EOFs. Is it different?

Remember that there is nothing dynamical about EOFs. They blindly find orthogonal patterns of variability. It is often the case that "orthogonal" means "distinct physical mechanism", but it does not have to be. Similarly, because of the orthogonality constraint, an EOF can mix two dynamical mechanisms in a single EOF. This is why I suggested subtracting the annual cycle: if this is strong, a low-mode EOF will find it, and mix in other variability that happens to fit the spatial pattern). If you know something about the signal (i.e. it has a large annual cycle), extract that first so it doesn't confuse the EOF calculation.

Billy K
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
William S. Kessler
NOAA / Pacific Marine Environmental Laboratory
7600 Sand Point Way NE
Seattle WA 98115 USA

william.s.kessler@xxxxxxxx
Tel: +1 206-526-6221
Fax: +1 206-526-6744
Web: http://faculty.washington.edu/kessler/

> On Mar 12, 2016, at 10:41 PM, Masud OCN_DU <sohelku08@xxxxxxxxx> wrote:
> 
> Dear Ferret users,
> 
> I am new in ferret. I am a Masters student. I have done EOF analysis following the ef_eofsvd_demo.jnl for my masters dissertation. My installed version is ferret 6.93. I have calculated the same things i.e. the spatial and temporal variability of the weekly MSLA data of 1993-2015 from AVISO.
> 
> However, I am not sure whether my calculation is OK or not. Is my calculation correct? How can I discuss about the spatial and the temporal modes of my figures? My interest is meso scale variability. The first and 2nd modes would be the seasonal or sub-seasonal variability in my little knowledge. Are the next mode for the meso-scale variability? 
> 
> What does y axis denote in my time_amplitude figures (attached below)? is it the amplitude? In addition, in the spatial maps of modes (1-4), what is the scale values (e.g. -0.08 to 0.18 for first mode in space). Is it my variable (sla)?  
> 
> Actually, I am from different background and have a little knowledge on EOF. Could anyone please give me a little time on it. 
> 
> I will be grateful to you all. Thank in advance.
> 
> 
> Cheers,
> Masud
> 
> 
> 
> <sla_avisoeof.gif><tfunc_1.ps><tfunc_2.ps><tfunc_3.ps><tfunc_4.ps>