CRPSS {s2dv}

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, 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 specified confidence level (DelSole and Tippett, 2016).

Usage

CRPSS(
  exp,
  obs,
  ref = NULL,
  time_dim = "sdate",
  memb_dim = "member",
  dat_dim = NULL,
  Fair = FALSE,
  clim.cross.val = TRUE,
  sig_method.type = "two.sided.approx",
  alpha = 0.05,
  ncores = NULL
)

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 experiment, the dataset dimension must have the same length as in 'exp'. If 'ref' is NULL, the climatological forecast is used as reference forecast. To build the climatological forecast, the observed values along the whole time period are used as different members for all time steps. The parameter 'clim.cross.val' controls whether to build it using cross-validation. 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.

clim.cross.val

A logical indicating whether to build the climatological forecast in cross-validation (i.e. excluding the observed value of the time step when building the probabilistic distribution function for that particular time step). Only used if 'ref' is NULL. The default value is TRUE.

sig_method.type

A character string indicating the test type of the significance method. Check RandomWalkTest() parameter test.type for details. The default is 'two.sided.approx', which is the default of RandomWalkTest().

alpha

A numeric of the significance level to be used in 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

$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.

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