Re: [ferret_users] EOF analysis

["William.S.Kessler" <William.S.Kessler@xxxxxxxx>]

I wrote this routine a very long time ago, and I'm not in a position  
to test it now, but I think this is correct.

The result of the EOF computation (before normalization) has both the  
EOF and time function dimensionless, and all the amplitude is in the  
eigenvalues. The result has the valuable property that the original  
data can be recovered by the sum over all EOFs n=1:N, where N is the  
min(#space pts,# time points). Using subscript _0 to represent these  
original fields:

data(x,t) = SUM_n[EVALUE(n)*EOF_0(x,n)*TAF_0(t,n)]

The normalization simply distributes the amplitude-containing  
eigenvalue over the EOFs and TAFs: It multiplies the original EOFs  
and time functions by the sqrt(eigenvalue). Thus, for the Ferret EOF  
output:

data(x,t) = SUM_n[EOF(x,n)*TAF(t,n)]

The result of this is that, for output of the Ferret EOF routines:

The sum over all space of any single EOF^2 equals the corresponding  
eigenvalue.
The sum over all time of any single (time function)^2 equals the  
number of observations.

To reverse the normalization, simply reverse this process: divide by  
the sqrt(eigenvalue). But note that if you want to retain the data- 
recovery property of EOFs (or if you want to correctly plot or  
present the EOF results including both the space and time functions),  
then you must make this change to BOTH the EOF and the time function.

Billy K


On 16/05/2008, at 7:18 PM, Peter Kim wrote:

> Hi All
>
> According to Ferret documentation, EOF_SPACE returns
> the normalized eigenfuctions so that they have the units of data.
> I would like to know how it is normalized.
> I want to get dimensionless eigenvectors, in other words,  
> eigenvectors of unit length.
>
> -Seon Tae-