MSE: Compute mean square error

In s2dv: A Set of Common Tools for Seasonal to Decadal Verification

Compute mean square error

Description

Compute the mean square error for an array of forecasts and an array of observations. The MSEs are computed along time_dim, the dimension which corresponds to the start date dimension. If comp_dim is given, the MSEs are computed only if obs along the comp_dim dimension are complete between limits[1] and limits[2], i.e. there are no NAs between limits[1] and limits[2]. This option can be activated if the user wants to account only for the forecasts for which the corresponding observations are available at all leadtimes.
The confidence interval is computed by the chi2 distribution.

Usage

MSE(
  exp,
  obs,
  time_dim = "sdate",
  dat_dim = NULL,
  memb_dim = NULL,
  comp_dim = NULL,
  limits = NULL,
  conf = TRUE,
  alpha = 0.05,
  ncores = NULL
)

Arguments

exp	A named numeric array of experimental data, with at least 'time_dim' dimension. It can also be a vector with the same length as 'obs'.
obs	A named numeric array of observational data, same dimensions as parameter 'exp' except along 'dat_dim' and 'memb_dim'. It can also be a vector with the same length as 'exp'.
time_dim	A character string indicating the name of dimension along which the correlations are computed. The default value is 'sdate'.
dat_dim	A character string indicating the name of dataset or member (nobs/nexp) dimension. The datasets of exp and obs will be paired and computed MSE for each pair. The default value is NULL.
memb_dim	A character string indicating the name of the member dimension to compute the ensemble mean; it should be set to NULL if the input data are already the ensemble mean. The default value is NULL.
comp_dim	A character string indicating the name of dimension along which obs is taken into account only if it is complete. The default value is NULL.
limits	A vector of two integers indicating the range along comp_dim to be completed. The default value is c(1, length(comp_dim dimension)).
conf	A logical value indicating whether to retrieve the confidence intervals or not. The default value is TRUE.
alpha	A numeric indicating the significance level for the statistical significance test. The default value is 0.05.
ncores	An integer indicating the number of cores to use for parallel computation. The default value is NULL.

Value

A list containing the numeric arrays with dimension:
c(nexp, nobs, all other dimensions of exp except time_dim).
nexp is the number of experiment (i.e., dat_dim in exp), and nobs is the number of observation (i.e., dat_dim in obs).

$mse	The mean square error.
$conf.lower	The lower confidence interval. Only present if conf = TRUE.
$conf.upper	The upper confidence interval. Only present if conf = TRUE.

Examples

# Load sample data as in Load() example:
example(Load)
clim <- Clim(sampleData$mod, sampleData$obs)
ano_exp <- Ano(sampleData$mod, clim$clim_exp)
ano_obs <- Ano(sampleData$obs, clim$clim_obs)
smooth_ano_exp <- Smoothing(ano_exp, runmeanlen = 12, time_dim = 'ftime')
smooth_ano_obs <- Smoothing(ano_obs, runmeanlen = 12, time_dim = 'ftime')
res <- MSE(smooth_ano_exp, smooth_ano_obs, memb_dim = 'member', 
          comp_dim = 'ftime', limits = c(7, 54))

# Synthetic data:
exp1 <- array(rnorm(120), dim = c(dat = 3, sdate = 10, ftime = 4))
obs1 <- array(rnorm(80),  dim = c(dat = 2, sdate = 10, ftime = 4))
res1 <- MSE(exp1, obs1, comp_dim = 'ftime', dat_dim = 'dat')
 
exp2 <- array(rnorm(20), dim = c(sdate = 5, member = 4))
obs2 <- array(rnorm(10),  dim = c(sdate = 5, member = 2))
res2 <- MSE(exp2, obs2, memb_dim = 'member')

s2dv documentation built on Oct. 13, 2024, 9:07 a.m.