% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/RPSS.R
\name{RPSS}
\alias{RPSS}
\title{Compute the Ranked Probability Skill Score}
\usage{
RPSS(
  exp,
  obs,
  ref = NULL,
  time_dim = "sdate",
  memb_dim = "member",
  dat_dim = NULL,
  prob_thresholds = c(1/3, 2/3),
  indices_for_clim = NULL,
  Fair = FALSE,
  weights = NULL,
  weights_exp = NULL,
  weights_ref = NULL,
  ncores = NULL
)
}
\arguments{
\item{exp}{A named numerical array of the forecast with at least time and
member dimension.}

\item{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'.}

\item{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.}

\item{time_dim}{A character string indicating the name of the time dimension.
The default value is 'sdate'.}

\item{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'.}

\item{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.}

\item{prob_thresholds}{A numeric vector of the relative thresholds (from 0 to
1) between the categories. The default value is c(1/3, 2/3), which 
corresponds to tercile equiprobable categories.}

\item{indices_for_clim}{A vector of the indices to be taken along 'time_dim' 
for computing the thresholds between the probabilistic categories. If NULL,
the whole period is used. The default value is NULL.}

\item{Fair}{A logical indicating whether to compute the FairRPSS (the 
potential RPSS that the forecast would have with an infinite ensemble size).
The default value is FALSE.}

\item{weights}{Deprecated and will be removed in the next release. Please use
'weights_exp' and 'weights_ref' instead.}

\item{weights_exp}{A named numerical array of the forecast ensemble weights.
The dimension should include 'memb_dim', 'time_dim' and 'dat_dim' if there
are multiple datasets. All dimension lengths must be equal to 'exp' 
dimension lengths. The default value is NULL, which means no weighting is 
applied. The ensemble should have at least 70 members or span at least 10 
time steps and have more than 45 members if consistency between the weighted
 and unweighted methodologies is desired.}

\item{weights_ref}{Same as 'weights_exp' but for the reference forecast.}

\item{ncores}{An integer indicating the number of cores to use for parallel 
computation. The default value is NULL.}
}
\value{
\item{$rpss}{
 A numerical array of RPSS with dimensions c(nexp, nobs, the rest dimensions 
 of 'exp' except 'time_dim' and 'memb_dim' dimensions). nexp is the number of 
 experiment (i.e., dat_dim in exp), and nobs is the number of observation 
 i.e., dat_dim in obs). If dat_dim is NULL, nexp and nobs are omitted.
}
\item{$sign}{
 A logical array of the statistical significance of the RPSS with the same 
 dimensions as $rpss.
}
}
\description{
The Ranked Probability Skill Score (RPSS; Wilks, 2011) is the skill score 
based on the Ranked Probability Score (RPS; Wilks, 2011). It can be used to 
assess whether a forecast presents an improvement or worsening with respect to
a reference forecast. The RPSS ranges between minus infinite and 1. If the 
RPSS 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, and another model. It is computed as 
\code{RPSS = 1 - RPS_exp / RPS_ref}. The statistical significance is obtained 
based on a Random Walk test at the 95% confidence level (DelSole and Tippett, 
2016). If there is more than one dataset, RPS will be computed for each pair 
of exp and obs data.
}
\examples{
set.seed(1)
exp <- array(rnorm(3000), dim = c(lat = 3, lon = 2, member = 10, sdate = 50))
set.seed(2)
obs <- array(rnorm(300), dim = c(lat = 3, lon = 2, sdate = 50))
set.seed(3)
ref <- array(rnorm(3000), dim = c(lat = 3, lon = 2, member = 10, sdate = 50))
weights <- sapply(1:dim(exp)['sdate'], function(i) {
            n <- abs(rnorm(10))
            n/sum(n)
          })
dim(weights) <- c(member = 10, sdate = 50)
res <- RPSS(exp = exp, obs = obs) ## climatology as reference forecast
res <- RPSS(exp = exp, obs = obs, ref = ref) ## ref as reference forecast
res <- RPSS(exp = exp, obs = obs, ref = ref, weights_exp = weights, weights_ref = weights)
}
\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
}
