s2dv (version 2.1.0)

EOF: Area-weighted empirical orthogonal function analysis using SVD

Description

Perform an area-weighted EOF analysis using single value decomposition (SVD) based on a covariance matrix or a correlation matrix if parameter 'corr' is set to TRUE.

Usage

EOF(
  ano,
  lat,
  lon,
  time_dim = "sdate",
  space_dim = c("lat", "lon"),
  neofs = 15,
  corr = FALSE,
  ncores = NULL
)

Value

A list containing:

EOFs

An array of EOF patterns normalized to 1 (unitless) with dimensions (number of modes, rest of the dimensions of 'ano' except 'time_dim'). Multiplying EOFs by PCs gives the original reconstructed field.

PCs

An array of principal components with the units of the original field to the power of 2, with dimensions (time_dim, number of modes, rest of the dimensions of 'ano' except 'space_dim'). 'PCs' contains already the percentage of explained variance so, to reconstruct the original field it's only needed to multiply 'EOFs' by 'PCs'.

var

An array of the percentage ( explained by each mode (number of modes). The dimensions are (number of modes, rest of the dimensions of 'ano' except 'time_dim' and 'space_dim').

mask

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

wght

An array of the area weighting with dimensions 'space_dim'. It is calculated by cosine of 'lat' and used to compute the fraction of variance explained by each EOFs.

tot_var

A number or a numeric array of the total variance explained by all the modes. The dimensions are same as 'ano' except 'time_dim' and 'space_dim'.

Arguments

ano

A numerical array of anomalies with named dimensions to calculate EOF. The dimensions must have at least 'time_dim' and 'space_dim'. NAs could exist but it should be consistent along time_dim. That is, if one grid point has NAs, all the time steps at this point should be NAs.

lat

A vector of the latitudes of 'ano'.

lon

A vector of the longitudes of 'ano'.

time_dim

A character string indicating the name of the time dimension of 'ano'. The default value is 'sdate'.

space_dim

A vector of two character strings. The first is the dimension name of latitude of 'ano' and the second is the dimension name of longitude of 'ano'. The default value is c('lat', 'lon').

neofs

A positive integer of the modes to be kept. The default value is 15. If time length or the product of the length of space_dim is smaller than neofs, neofs will be changed to the minimum of the three values.

corr

A logical value indicating whether to base on a correlation (TRUE) or on a covariance matrix (FALSE). The default value is FALSE.

ncores

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

See Also

ProjectField, NAO, PlotBoxWhisker

Examples

# This example computes the EOFs along forecast horizons and plots the one 
# that explains the greatest amount of variability. The example data has low  
# resolution so the result may not be explanatory, but it displays how to 
# use this function.
# \dontshow{
startDates <- c('19851101', '19901101', '19951101', '20001101', '20051101')
sampleData <- s2dv:::.LoadSampleData('tos', c('experiment'),
                                    c('observation'), startDates,
                                    leadtimemin = 1,
                                    leadtimemax = 4,
                                    output = 'lonlat',
                                    latmin = 27, latmax = 48,
                                    lonmin = -12, lonmax = 40)
# }
ano <- Ano_CrossValid(sampleData$mod, sampleData$obs)
tmp <- MeanDims(ano$exp, c('dataset', 'member'))
ano <- tmp[1, , ,]
names(dim(ano)) <- names(dim(tmp))[-2]
eof <- EOF(ano, sampleData$lat, sampleData$lon)
if (FALSE) {
PlotEquiMap(eof$EOFs[1, , ], sampleData$lon, sampleData$lat)
}