MultiEOF {CSTools}

EOF analysis of multiple variables starting from an array (reduced version)

Description

This function performs EOF analysis over multiple variables, accepting in input an array with a dimension "var" for each variable to analyse. Based on Singular Value Decomposition. For each field the EOFs are computed and the corresponding PCs are standardized (unit variance, zero mean); the minimum number of principal components needed to reach the user-defined variance is retained. The function weights the input data for the latitude cosine square root.

Usage

MultiEOF(
  data,
  lon,
  lat,
  dates,
  time = NULL,
  lon_dim = "lon",
  lat_dim = "lat",
  time_dim = "ftime",
  sdate_dim = "sdate",
  var_dim = "var",
  neof_max = 40,
  neof_composed = 5,
  minvar = 0.6,
  lon_lim = NULL,
  lat_lim = NULL,
  ncores = NULL
)

Arguments

data

A multidimensional array with dimension "var", containing the variables to be analysed. The other diemnsions follow the same structure as the "exp" element of a 's2dv_cube' object. Latitudinal dimension accepted names: 'lat', 'lats', 'latitude', 'y', 'j', 'nav_lat'. Longitudinal dimension accepted names: 'lon', 'lons','longitude', 'x', 'i', 'nav_lon'. NAs can exist but it should be consistent along 'time_dim'. That is, if one grid point has NAs for each variable, all the time steps at this point should be NAs.

lon

Vector of longitudes.

lat

Vector of latitudes.

dates

Vector or matrix of dates in POSIXct format.

time

Deprecated parameter, it has been substituted by 'dates'. It will be removed in the next release.

lon_dim

A character string indicating the name of the longitudinal dimension. By default, it is set to 'lon'.

lat_dim

A character string indicating the name of the latitudinal dimension. By default, it is set to 'lat'.

time_dim

A character string indicating the name of the temporal dimension. By default, it is set to 'time'.

sdate_dim

A character string indicating the name of the start date dimension. By default, it is set to 'sdate'.

var_dim

A character string indicating the name of the variable dimension. By default, it is set to 'var'.

neof_max

Maximum number of single eofs considered in the first decomposition.

neof_composed

Number of composed eofs to return in output.

minvar

Minimum variance fraction to be explained in first decomposition.

lon_lim

Vector with longitudinal range limits for the calculation for all input variables.

lat_lim

Vector with latitudinal range limits for the calculation for all input variables.

ncores

An integer indicating the number of cores to use for parallel computation. The default value is NULL.

Value

A list containing:

coeff

An array of principal components with dimensions 'time_dim', 'sdate_dim', number of eof, rest of the dimensions of 'data' except 'lon_dim' and 'lat_dim'.

variance

An array of explained variances with dimensions 'eof' and the rest of the dimensions of 'data' except 'time_dim', 'sdate_dim', 'lon_dim' and 'lat_dim'.

eof_pattern

An array of EOF patterns obtained by regression with dimensions: 'eof' and the rest of the dimensions of 'data' except 'time_dim' and 'sdate_dim'.

mask

An array of the mask with dimensions ('lon_dim', 'lat_dim', rest of the dimensions of 'data' except 'time_dim'). It is made from 'data', 1 for the positions that 'data' has value and NA for the positions that 'data' has NA. It is used to replace NAs with 0s for EOF calculation and mask the result with NAs again after the calculation.

coordinates

Longitudinal and latitudinal coordinates vectors.

Author(s)

Jost von Hardenberg - ISAC-CNR, [e-mail]

Paolo Davini - ISAC-CNR, [e-mail]

Examples

exp <- array(runif(1280)*280, dim = c(dataset = 2, member = 2, sdate = 3, 
                                     ftime = 3, lat = 4, lon = 4, var = 1))
lon <- seq(0, 3)
lat <- seq(47, 44)
dates <- c("2000-11-01", "2000-12-01", "2001-01-01", "2001-11-01", 
          "2001-12-01", "2002-01-01", "2002-11-01", "2002-12-01", "2003-01-01")
Dates <- as.POSIXct(dates, format = "%Y-%m-%d")
dim(Dates) <- c(ftime = 3, sdate = 3)
cal <- MultiEOF(data = exp, lon = lon, lat = lat, dates = Dates)