Re: EOF_SPACE usage

[Ansley Manke <ansley@xxxxxxxxxxxxx>]

Hello Graham,
Let me see if I can help -- the EOF's need a demo script or two in the
Ferret documentation which we'll be getting online soon.   The  function
call you describe looks correct.   Attached are two scripts; eof_coads_clim.jnl
uses the COADS monthly data set, and plots some results, and eof_cos_sin.jnl
generates an analytic function and then decomposes it with the EOF functions.

I hope this will enough to show you how the results are returned, and get you
started.

Ansley Manke

Graham Gladman wrote:

> Hello,
>
> I've just installed Ferret 5.22 so that I am able to use the external EOF
> and FFT functions (with a view to perhaps writing a more general SVD
> external function, depending on difficulty).
>
> I wonder if anyone has used EOF_SPACE, EOF_STAT and EOF_TRUNC on a 4D
> dataset, and has an example script on the input syntax and handling the
> output from these functions.
>
> For example, I have a 4D temperature field TEMP, and I would an EOF of
> TEMP at 250m depth on the first two years of monthly data. Is:
>
> let temp_eofs = eof_space(temp[z=250,l=1:24], 2, 0.8)
>
> sufficient. Or are the command qualifiers described elsewhere. How are the
> eofs stored on the resulting grid, and how would I plot them?
>
> Any help appreciated,
>
> Graham Gladman

--
Ansley Manke  Pacific Marine Environmental Laboratory  Seattle WA  (206)526-6246
!  eof_coads_clim.jnl   Demonstration of the EOF external functions from 
!  Ferret version 5.0 and later.  Ansley Manke  6/00
!
!
!  Implements Chelton's '82 method for finding EOFs of gappy time series.
!  eof_space returns EOF eigenvectors: spatial EOF in x and y with the same
!            units as the incoming data
!  eof_tfunc returns EOF time amplitude functions; dimensionless
!  eof_stat  returns statistics on the EOF computation: number of EOFs 
!            scaled and returned; Percent variance explained by each EOF; 
!            and the eigenvalues.
!  All the functions perform the same computation but return different
!  aspect of the results.  For all functions the arguments are as follows:
!
!  1st argument:  Input Data field, functions of x, y, and time.
!
!  2nd argument is the minimum percent variance explained by the EOF's that
!  are computed and scaled, e.g. to return EOFs that explain at least 2% 
!  variance, use 2.0

!  3nd argument is the fraction of each time series that must be present to 
!  include it in the calculations, e.g. to use all time series that have 
!  at least half the data present, use 0.5

SET MODE VERIFY
USE coads_climatology
SET REGION/X=67w:1w/Y=11S:11N


!  Compute and save the spatial EOF functions.  These have the same units
!  as the data

LET eof_xyfcn = eof_space(sst, 2.0, 0.5)
SAVE/CLOBBER/FILE=sst_clim_eof_space.cdf eof_xyfcn

can region
can variable/all

use sst_clim_eof_space.cdf
set view ul; fill/l=1/title="eof 1" eof_xyfcn; go land
set view ur; fill/l=2/title="eof 2" eof_xyfcn; go land
set view ll; fill/l=3/title="eof 3" eof_xyfcn; go land
!set view lr; fill/l=4/title="eof 4" eof_xyfcn; go land

!  Compute and save statistics on the EOFs: number of EOFs scaled
!  and returned; Percent variance explained by each EOF; and the
!  eigenvalues.

USE coads_climatology
SET REGION/X=67w:1w/Y=11S:11N

LET eofstat = eof_stat(sst[X=67w:1w,Y=11S:11N], 2.0, 0.5)
let nout =  eofstat[i=1,j=1]

SAVE/CLOBBER/FILE=sst_clim_eof_stat.cdf eofstat[i=1:`nout`]

can var/all
can region
use sst_clim_eof_stat.cdf

let nout = eofstat[i=1,j=1,d=sst_clim_eof_stat]
let pcts = eofstat[i=1:`nout`,j=2,d=sst_clim_eof_stat]
let eigenv = eofstat[i=1:`nout`,j=3,d=sst_clim_eof_stat]

list nout
list pcts
list eigenv

!  Compute and save time amplitude functions: they are dimensionless.

USE coads_climatology
LET eoftime = eof_tfunc(sst[X=67w:1w,Y=11S:11N], 2.0, 0.5)

can region
SAVE/CLOBBER/FILE=sst_clim_eof_tfunc.cdf eoftime[i=1:`nout`]

can var/all
use sst_clim_eof_tfunc.cdf
can view

set view ul; plot/i=1/title="time function 1"/ylimits=-2:2:0.5 eoftime
set view ur; plot/i=2/title="time function 2"/ylimits=-2:2:0.5 eoftime
set view ll; plot/i=3/title="time function 3"/ylimits=-2:2:0.5 eoftime

set mode/last verify

! Demo of the EOF functions: generate a function of x,y,time using trig 
! functions.  Decompose into spatial and time EOF's and display statistics.
!
!  ACM  7/30/99
! -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

show func eof_stat
show func eof_space
show func eof_tfunc

pause

let time = t[t=1-jan-1990:10-jan-1990:24]   ! 24 hour resolution time axis

define axis/x=0:10:0.5 x10
define axis/y=0:10:0.5 y10
define grid/x=x10/y=y10/t=time g10x10
set grid g10x10

let fcn1 = 15.* sin(omega1*t)*cos(r)/(r+1)
let fcn2 = 20.* sin(omega2*t)*(sin(s)-.2*sin(q))/(s+1)

let r = ((6.*(xpts-x0)^2 + 7.*(ypts-y0)^2)^0.5)
let s = (((xpts-x1)^2 + 2*(ypts-y1)^2)^0.5)
let q = ((3*(xpts-x0)^2 + (ypts-y1)^2)^0.5)

let x0 = 2; let y0 = 4; let x1 = 5; let y1 = 7

let omega1 = 1/32*2*3.14159
let omega2 = 2 * omega1

let sample_function = fcn1 + fcn2
let xpts = x
let ypts = y

let estat = eof_stat(sample_function, 2., 0.1)

list/i=1/j=1 estat

list/i=1:5/j=2 estat

list/i=1:5/j=3 estat

pause
! -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

define view/xlim=0.,.33/ylim=.6,1./text=0.2 vul
define view/xlim=.33,.66/ylim=.6,1./text=0.2 vuc
define view/xlim=.66,1./ylim=.6,1./text=0.2 vur

define view/xlim=0.,.33/ylim=.1,.5/text=0.2 vll
define view/xlim=.33,.66/ylim=.1,.5/text=0.2 vlc
define view/xlim=.66,1./ylim=.1,.5/text=0.2 vlr

set view vul; contour/title="FCN1" fcn1[l=1:32@ave]
set view vuc; contour/title="FCN2" fcn2[l=1:32@ave]
set view vur; contour/title="FCN1 + FCN2" sample_function[l=1:32@ave]


let exy = eof_space(sample_function, 2., 0.1)

load exy
set view vll
contour/l=1/title="EOF1" exy
set view vlc
contour/l=2/title="EOF 2" exy

pause
cancel view
! -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

let etim = eof_tfunc(sample_function, 2., 0.1)

set view ul
plot/i=1/title=taf1 etim

set view ur
plot/i=2/title=taf2 etim

! should be all bad flags...
set view ll
plot/i=3/title=taf3 etim