s2dv (version 1.4.0)

CRPSS: Compute the Continuous Ranked Probability Skill Score

Description

The Continuous Ranked Probability Skill Score (CRPSS; Wilks, 2011) is the skill score based on the Continuous Ranked Probability Score (CRPS; Wilks, 2011). It can be used to assess whether a forecast presents an improvement or worsening with respect to a reference forecast. The CRPSS ranges between minus infinite and 1. If the CRPSS is positive, it indicates that the forecast has higher skill than the reference forecast, while a negative value means that it has a lower skill. Examples of reference forecasts are the climatological forecast (same probabilities for all categories for all time steps), persistence, a previous model version, or another model. It is computed as CRPSS = 1 - CRPS_exp / CRPS_ref. The statistical significance is obtained based on a Random Walk test at the 95 2016).

Usage

CRPSS(
  exp,
  obs,
  ref = NULL,
  time_dim = "sdate",
  memb_dim = "member",
  dat_dim = NULL,
  Fair = FALSE,
  ncores = NULL
)

Value

$crpss

A numerical array of the CRPSS with dimensions c(nexp, nobs, the rest dimensions of 'exp' except 'time_dim' and 'memb_dim' dimensions). 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). If 'dat_dim' is NULL, nexp and nobs are omitted.

$sign

A logical array of the statistical significance of the CRPSS with the same dimensions as $crpss.

Arguments

exp

A named numerical array of the forecast with at least time dimension.

obs

A named numerical array of the observation with at least time dimension. The dimensions must be the same as 'exp' except 'memb_dim' and 'dat_dim'.

ref

A named numerical array of the reference forecast data with at least time and member dimension. The dimensions must be the same as 'exp' except 'memb_dim' and 'dat_dim'. If there is only one reference dataset, it should not have dataset dimension. If there is corresponding reference for each experiement, the dataset dimension must have the same length as in 'exp'. If 'ref' is NULL, the climatological forecast is used as reference forecast. The default value is NULL.

time_dim

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

memb_dim

A character string indicating the name of the member dimension to compute the probabilities of the forecast and the reference forecast. The default value is 'member'.

dat_dim

A character string indicating the name of dataset dimension. The length of this dimension can be different between 'exp' and 'obs'. The default value is NULL.

Fair

A logical indicating whether to compute the FairCRPSS (the potential CRPSS that the forecast would have with an infinite ensemble size). The default value is FALSE.

ncores

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

References

Wilks, 2011; https://doi.org/10.1016/B978-0-12-385022-5.00008-7 DelSole and Tippett, 2016; https://doi.org/10.1175/MWR-D-15-0218.1

Examples

exp <- array(rnorm(1000), dim = c(lat = 3, lon = 2, member = 10, sdate = 50))
obs <- array(rnorm(1000), dim = c(lat = 3, lon = 2, sdate = 50))
ref <- array(rnorm(1000), dim = c(lat = 3, lon = 2, member = 10, sdate = 50))
res <- CRPSS(exp = exp, obs = obs) ## climatology as reference forecast
res <- CRPSS(exp = exp, obs = obs, ref = ref) ## ref as reference forecast