eot: EOT analysis of a predictor and (optionally) a response...
In environmentalinformatics-marburg/Reot: Empirical Orthogonal Teleconnections in R

Description Usage Arguments Details Value References Examples

Calculate a given number of EOT modes either internally or between RasterStacks.

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eot(pred, resp = NULL, n = 1, standardised = TRUE, write.out = FALSE,
  path.out = ".", names.out = NULL, reduce.both = FALSE, type = c("rsq",
  "ioa"), print.console = TRUE, ...)

`pred`	a ratser stack used as predictor
`resp`	a RasterStack used as response. If `resp` is `NULL`, `pred` is used as `resp`
`n`	the number of EOT modes to calculate
`standardised`	logical. If `FALSE` the calculated r-squared values will be multiplied by the variance
`write.out`	logical. If `TRUE` results will be written to disk using `path.out`
`path.out`	the file path for writing results if `write.out` is `TRUE`. Defaults to current working directory
`names.out`	optional prefix to be used for naming of results if `write.out` is `TRUE`
`reduce.both`	logical. If `TRUE` both `pred` and `resp` are reduced after each iteration. If `FALSE` only `resp` is reduced
`type`	the type of the link function. Defaults to `'rsq'` as in original proposed method from Dool2000. If set to `'ioa'` index of agreement is used instead
`print.console`	logical. If `TRUE` some details about the calculation process will be output to the console
`...`	not used at the moment

For a detailed description of the EOT algorithm and the mathematics behind it, see the References section. In brief, the algorithm works as follows: First, the temporal profiles of each pixel xp of the predictor domain are regressed against the profiles of all pixels xr in the response domain (in case of only a single field xr = xp - 1). The calculated coefficients of determination are summed up and the pixel with the highest sum is identified as the 'base point' of the first/leading mode. The temporal profile at this base point is the first/leading EOT. Then, the residuals from the regression are taken to be the basis for the calculation of the next EOT, thus ensuring orthogonality of the identified teleconnections. This procedure is repeated until a predefined amount of n EOTs is calculated. In general, Reot implements a 'brute force' spatial data mining approach to identify locations of enhanced potential to explain spatio-temporal variability within the same or another geographic field.

a list of n EOTs. Each EOT is also a list with the following components:

eot.series - the EOT time series at the identified base point
max.xy - the cell number of the indeified base point
exp.var - the (cumulative) explained variance of the considered EOT
loc.eot - the location of the base point (in original coordinates)
r.predictor - the RasterLayer of the correlation coefficients between the base point and each pixel of the predictor domain
rsq.predictor - as above but for the coefficient of determination
rsq.sums.predictor - as above but for the sums of coefficient of determination
int.predictor - the RasterLayer of the intercept of the regression equation for each pixel of the predictor domain
slp.predictor - same as above but for the slope of the regression equation for each pixel of the predictor domain
p.predictor - the RasterLayer of the significance (p-value) of the the regression equation for each pixel of the predictor domain
resid.predictor - the RasterBrick of the reduced data for the predictor domain

All *.predictor fields are also returned for the *.response domain, even if predictor and response domain are equal. This is due to that fact, that if not both fields are reduced after the first EOT is found, these RasterLayers will differ.

Empirical Orthogonal Teleconnections
H. M. van den Dool, S. Saha, A. Johansson (2000)
Journal of Climate, Volume 13, Issue 8, pp. 1421-1435
http://journals.ametsoc.org/doi/abs/10.1175/1520-0442%282000%29013%3C1421%3AEOT%3E2.0.CO%3B2

Empirical methods in short-term climate prediction
H. M. van den Dool (2007)
Oxford University Press, Oxford, New York
http://www.oup.com/uk/catalogue/?ci=9780199202782

### EXAMPLE I:
### a single field
data(vdendool)

# claculate 2 leading modes
modes <- eot(pred = vdendool, resp = NULL, n = 2, reduce.both = FALSE,
             standardised = FALSE, print.console = TRUE)

plotEot(modes, eot = 1, show.eot.loc = TRUE)
plotEot(modes, eot = 2, show.eot.loc = TRUE)