EOT analysis of a predictor and (optionally) a response RasterStack

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Description

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

Usage

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## S4 method for signature 'RasterStackBrick'
eot(x, y = NULL, n = 1, standardised = TRUE,
  write.out = FALSE, path.out = ".", prefix = "remote",
  reduce.both = FALSE, type = c("rsq", "ioa"), verbose = TRUE, ...)

Arguments

x

a RasterStack used as predictor

y

a RasterStack used as response. If y is NULL, x is used as y

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

prefix

optional prefix to be used for naming of results if write.out is TRUE

reduce.both

logical. If TRUE both x and y are reduced after each iteration. If FALSE only y is reduced

type

the type of the link function. Defaults to 'rsq' as in original proposed method from van den Dool 2000. If set to 'ioa' index of agreement is used instead

verbose

logical. If TRUE some details about the calculation process will be output to the console

...

not used at the moment

Details

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. 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, remote 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.

Value

if n = 1 an EotMode, if n > 1 an EotStack of n EotModes. Each EotMode has the following components:

  • mode - the number of the identified mode (1 - n)

  • eot - the EOT (time series) at the identified base point. Note, this is a simple numeric vector, not of class ts

  • coords_bp - the coordinates of the identified base point

  • cell_bp - the cell number of the indeified base point

  • cum_exp_var - the (cumulative) explained variance of the considered EOT

  • 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

Apart from rsq_sums_predictor, 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.

References

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
https://global.oup.com/academic/product/empirical-methods-in-short-term-climate-prediction-9780199202782?cc=de&lang=en&

Examples

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

## claculate 2 leading modes
nh_modes <- eot(x = vdendool, y = NULL, n = 2, 
                standardised = FALSE, 
                verbose = TRUE)

plot(nh_modes, y = 1, show.bp = TRUE)
plot(nh_modes, y = 2, show.bp = TRUE)