Re: [ferret_users] eof correlation covariance

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

The Ferret EOF routines use the covariance matrix. You would get the  
correlation matrix by dividing the input variable by its standard  
deviation at each location before calling the EOF routines. (A check  
is that the sum of eigenvalues is the total variance of the field.  
This sum should be [the number of spatial locations] if you are using  
the correlation matrix. Similarly, the sum of the spatial EOFs at  
each point is the variance at that point for the covariance matrix,  
or 1 if the correlation matrix.) If you use the correlation matrix  
for calculation you could reconstruct the full fields by  
remultiplying either the EOF or time function at each location by its  
RMS. Of course, this might change the ordering of EOFs by variance  
represented.

The main reason to use this approach would be to do joint EOFs of  
several variables. For example, you might want to do a joint EOF of  
temperature and salinity. In that case divide each quantity by its  
RMS at each location, then construct a grid twice as large  
(presumably by extending one of the axes and regridding one variable  
onto the extended part of the grid using @shf). Then call the EOF  
routines with the extended grid, and extract the two fields from the  
final result.

Billy K

On Jun 8, 2007, at 8:58 AM, Fabian Lienert wrote:

> Hi Ferreters,
>
>
> Where does the external function eof_space() calculate its EOFs from?
> From a correlation or a covariance matrix?
> How can I switch between the two?
>
> Thanks a lot for any hint,
> Fabian
>
> --
> Fabian Lienert
> PhD Student
> Canadian Centre for Climate Modelling and Analysis
> Meteorological Service of Canada
> School of Earth and Ocean Sciences
> University of Victoria
> P.O. Box 1700
> Victoria, BC  V8W 2Y2
> CANADA
>
> phone:  +1(250)363-8242
> e-mail: cccma-student-003@xxxxxxxx