CST_MultiEOF {CSTools}

EOF analysis of multiple variables

Description

This function performs EOF analysis over multiple variables, accepting in input a list of CSTools objects. 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

CST_MultiEOF(
  datalist,
  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

datalist

A list of objects of the class 's2dv_cube', containing the variables to be analysed. Each data object in the list is expected to have an element named $data with at least two spatial dimensions named "lon" and "lat", a dimension "ftime" and a dimension "sdate". 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_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 EOF calculation for all input variables.

lat_lim

Vector with latitudinal range limits for the EOF 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 's2dv_cube' with the data element being 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 's2dv_cube' with the data element being 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 's2dv_cube' with the data element being 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 's2dv_cube' with the data element being 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

seq <- 1 : (2 * 3 * 4 * 5 * 6 * 8)
mod1 <- sin( 0.7 + seq )^2 + cos( seq ^ 2 * 1.22  )
dim(mod1) <- c(dataset = 2, member = 3, sdate = 4, ftime = 5, lat = 6, 
              lon = 8)
mod2 <- sin( seq * 2 ) ^ 3 + cos( seq ^ 2 )
dim(mod2) <- c(dataset = 2, member = 3, sdate = 4, ftime = 5, lat = 6, 
              lon = 8)
lon <- seq(0, 35, 5)
lat <- seq(0, 25, 5)
exp1 <- list(data = mod1, coords = list(lat = lat, lon = lon))
exp2 <- list(data = mod2, coords = list(lat = lat, lon = lon))
attr(exp1, 'class') <- 's2dv_cube'
attr(exp2, 'class') <- 's2dv_cube'
d = as.POSIXct(c("2017/01/01", "2017/01/02", "2017/01/03", "2017/01/04", 
                "2017/01/05", "2018/01/01", "2018/01/02", "2018/01/03",
                "2018/01/04", "2018/01/05", "2019/01/01", "2019/01/02", 
                "2019/01/03", "2019/01/04", "2019/01/05", "2020/01/01", 
                "2020/01/02", "2020/01/03", "2020/01/04", "2020/01/05"))
exp1$attrs$Dates = d
exp2$attrs$Dates = d

cal <- CST_MultiEOF(datalist = list(exp1, exp2), neof_composed = 2)