spacetime EOF implementation - interpretation question

Thanks for bringing this up, Andrew, for the note, and for the example.
I looked into the note, into Wilks, and into Cressie & Wikle, which I
tried to follow when I wrote EOF.

I decided to deprecate spacetime::EOF. It computes principle component
scores from the m x p space-time matrix or its transpose, which might be
useful to some, but what it does is too far from the EOF literature to
be helpful. In particular, it confused "spatial" and "temporal" modes,
as C & W use these terms.

I added a new function, spacetime::eof, which should do what the
literature describes as EOF: return the eigenvector coefficients of the
rotation matrix. Argument returnEOFs = FALSE gives back the prcomp
object, feeding that to predict() gives the scores.

Reproducing the figures in C & W Ch 5 looks now better, up to expected
sign changes, but the numerical ranges are still different.

Please reinstall spacetime from github, use eof, and see if things now
work as expected. demo(CressieWikle) is now updated as well.

In your example below, you normalize by

PCs = apply(seof$rotation, 2, function(x) (x - mean(x)) / sd(x))

but why? Eigenvectors are already standardized, but to unit length; is
this another convention of the EOF world?

With best regards,

On 10/24/2014 12:04 AM, Andrew Vitale wrote:

Hello,

I'm performing an empirical orthogonal function analysis on sea level
pressure using the spacetime package, and I'm having trouble determining
which elements of the function output I should use to interpret the

results.

It seems that most examples in the literature calculate empirical
orthogonal functions (EOFs) and their associated principle component (PC)
time series (e.g.

http://www.met.reading.ac.uk/~han/Monitor/eofprimer.pdf ,

pp 11-12, Fig. 2, 3).  As far as I can tell, I should be able to extract
all of the relevant information using only the spatial mode in the
spacetime:::EOF function.  However, the ambiguous terminology in the
literature and the availability of the "temporal" mode in spacetime:::EOF
have me uncertain of my interpretation.

I have been treating the output of spacetime:::EOF with
returnPredictions=TRUE as the EOFs, and I have been treating the
spacetime:::EOF $rotation element with returnPredictions=FALSE as the

PCs.

Am I extracting the proper information from the spacetime:::EOF results?
Are the results of the spatial and temporal modes of spacetime:::EOF both
required to perform an EOF analysis of a sea level pressure field, or are
these two separate analyses?

Below is a small example of how I am currently extracting the spatial

EOFs

and their associated PCs.

Thanks for any comments,
Andrew Vitale


library(raster)
library(spacetime)

## Create a raster object that mimics my data
## which is actually a raster stack of 20,718
## daily sea level pressure anomolies
a = array(rnorm(9*9*100), c(9,9,100))
b = brick(a)
b = setValues(b, a)
z = seq(as.Date('1980-01-01'), as.Date('1980-04-09'),
        by = 'day')
b = setZ(b, z)

## coerce the raster stack to an STFDF object
st = as(b, 'STFDF')

## calculate EOFs in spatial mode using spacetime
seof = EOF(st, how='spatial', returnPredictions=FALSE, scale.=TRUE)
seof_preds = EOF(st, how='spatial', returnPredictions=TRUE, scale.=TRUE)

## Create a raster stack of the predictions, which seem to be
## generally referred to as EOFs in the literature
EOFs = stack(seof_preds)
## extract and standardize the rotation element of the
## seof object, which seems to be the eigenvectors, which seem
## to also be referred to as PCs in the literature
PCs = apply(seof$rotation, 2, function(x) (x - mean(x)) / sd(x))

## Plot the EOFs as maps (seof_preds)
plot(EOFs)

## Plot the first PC (seof$rotation [standardized])
x11(height=7, width=10)
plot(x=as.Date(row.names(PCs), format='X%Y.%m.%d'),
     y=PCs[ , 1], type='l', xlab='Date', ylab='Standardized PC1')

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