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% Please edit documentation in R/CST_Calibration.R
\name{CST_Calibration}
\alias{CST_Calibration}
exp_cor = NULL,
cal.method = "mse_min",
eval.method = "leave-one-out",
memb_dim = "member",
sdate_dim = "sdate",
\item{exp}{An object of class \code{s2dv_cube} as returned by \code{CST_Start}
function with at least 'sdate' and 'member' dimensions, containing the
seasonal hindcast experiment data in the element named \code{data}. The
hindcast is used to calibrate the forecast in case the forecast is provided;
if not, the same hindcast will be calibrated instead.}
\item{obs}{An object of class \code{s2dv_cube} as returned by \code{CST_Start}
function with at least 'sdate' dimension, containing the observed data in
the element named \code{$data}.}
\item{exp_cor}{An optional object of class \code{s2dv_cube} as returned by
\code{CST_Start} function with at least 'sdate' and 'member' dimensions,
containing the seasonal forecast experiment data in the element named
\code{data}. If the forecast is provided, it will be calibrated using the
hindcast and observations; if not, the hindcast will be calibrated instead.
If there is only one corrected dataset, it should not have dataset dimension.
If there is a corresponding corrected dataset for each 'exp' forecast, the
dataset dimension must have the same length as in 'exp'. The default value
is NULL.}
\item{cal.method}{A character string indicating the calibration method used,
can be either \code{bias}, \code{evmos}, \code{mse_min}, \code{crps_min} or
\code{rpc-based}. Default value is \code{mse_min}.}
\item{eval.method}{A character string indicating the sampling method used, it
can be either \code{in-sample} or \code{leave-one-out}. Default value is the
\code{leave-one-out} cross validation. In case the forecast is provided, any
chosen eval.method is over-ruled and a third option is used.}
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\item{multi.model}{A boolean that is used only for the \code{mse_min}
method. If multi-model ensembles or ensembles of different sizes are used,
it must be set to \code{TRUE}. By default it is \code{FALSE}. Differences
between the two approaches are generally small but may become large when
using small ensemble sizes. Using multi.model when the calibration method is
\code{bias}, \code{evmos} or \code{crps_min} will not affect the result.}
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\item{na.fill}{A boolean that indicates what happens in case calibration is
not possible or will yield unreliable results. This happens when three or
less forecasts-observation pairs are available to perform the training phase
of the calibration. By default \code{na.fill} is set to true such that NA
values will be returned. If \code{na.fill} is set to false, the uncorrected
data will be returned.}
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\item{na.rm}{A boolean that indicates whether to remove the NA values or not.
The default value is \code{TRUE}. See Details section for further
information about its use and compatibility with \code{na.fill}.}
\item{apply_to}{A character string that indicates whether to apply the
calibration to all the forecast (\code{"all"}) or only to those where the
correlation between the ensemble mean and the observations is statistically
significant (\code{"sign"}). Only useful if \code{cal.method == "rpc-based"}.}
\item{alpha}{A numeric value indicating the significance level for the
correlation test. Only useful if \code{cal.method == "rpc-based" & apply_to
== "sign"}.}
\item{memb_dim}{A character string indicating the name of the member dimension.
By default, it is set to 'member'.}
\item{sdate_dim}{A character string indicating the name of the start date
dimension. By default, it is set to 'sdate'.}
\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{ncores}{An integer that indicates the number of cores for parallel
computations using multiApply function. The default value is one.}
An object of class \code{s2dv_cube} containing the calibrated
forecasts in the element \code{data} with the dimensions nexp, nobs and same
dimensions as in the 'exp' object. 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. If 'exp_cor'
is provided the returned array will be with the same dimensions as 'exp_cor'.
Five types of member-by-member bias correction can be performed.
The \code{"bias"} method corrects the bias only, the \code{"evmos"} method
applies a variance inflation technique to ensure the correction of the bias
and the correspondence of variance between forecast and observation (Van
Schaeybroeck and Vannitsem, 2011). The ensemble calibration methods
\code{"mse_min"} and \code{"crps_min"} correct the bias, the overall forecast
variance and the ensemble spread as described in Doblas-Reyes et al. (2005)
and Van Schaeybroeck and Vannitsem (2015), respectively. While the
\code{"mse_min"} method minimizes a constrained mean-squared error using three
parameters, the \code{"crps_min"} method features four parameters and
minimizes the Continuous Ranked Probability Score (CRPS). The
\code{"rpc-based"} method adjusts the forecast variance ensuring that the
ratio of predictable components (RPC) is equal to one, as in Eade et al.
(2014). It is equivalent to function \code{Calibration} but for objects
of class \code{s2dv_cube}.
}
\details{
Both the \code{na.fill} and \code{na.rm} parameters can be used to
indicate how the function has to handle the NA values. The \code{na.fill}
parameter checks whether there are more than three forecast-observations pairs
to perform the computation. In case there are three or less pairs, the
computation is not carried out, and the value returned by the function depends
on the value of this parameter (either NA if \code{na.fill == TRUE} or the
uncorrected value if \code{na.fill == TRUE}). On the other hand, \code{na.rm}
is used to indicate the function whether to remove the missing values during
the computation of the parameters needed to perform the calibration.
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\examples{
# Example 1:
dim(mod1) <- c(dataset = 1, member = 3, sdate = 4, ftime = 5, lat = 6, lon = 7)
dim(obs1) <- c(dataset = 1, member = 1, sdate = 4, ftime = 5, lat = 6, lon = 7)
lon <- seq(0, 30, 5)
lat <- seq(0, 25, 5)
coords <- list(lat = lat, lon = lon)
exp <- list(data = mod1, coords = coords)
obs <- list(data = obs1, coords = coords)
attr(exp, 'class') <- 's2dv_cube'
attr(obs, 'class') <- 's2dv_cube'
a <- CST_Calibration(exp = exp, obs = obs, cal.method = "mse_min", eval.method = "in-sample")
# Example 2:
mod1 <- 1 : (1 * 3 * 4 * 5 * 6 * 7)
mod2 <- 1 : (1 * 3 * 1 * 5 * 6 * 7)
dim(mod1) <- c(dataset = 1, member = 3, sdate = 4, ftime = 5, lat = 6, lon = 7)
dim(mod2) <- c(dataset = 1, member = 3, sdate = 1, ftime = 5, lat = 6, lon = 7)
obs1 <- 1 : (1 * 1 * 4 * 5 * 6 * 7)
dim(obs1) <- c(dataset = 1, member = 1, sdate = 4, ftime = 5, lat = 6, lon = 7)
lon <- seq(0, 30, 5)
lat <- seq(0, 25, 5)
coords <- list(lat = lat, lon = lon)
exp <- list(data = mod1, coords = coords)
obs <- list(data = obs1, coords = coords)
exp_cor <- list(data = mod2, lat = lat, lon = lon)
attr(exp, 'class') <- 's2dv_cube'
attr(obs, 'class') <- 's2dv_cube'
attr(exp_cor, 'class') <- 's2dv_cube'
a <- CST_Calibration(exp = exp, obs = obs, exp_cor = exp_cor, cal.method = "evmos")
}
\references{
Doblas-Reyes F.J, Hagedorn R, Palmer T.N. The rationale behind the
success of multi-model ensembles in seasonal forecasting-II calibration and
combination. Tellus A. 2005;57:234-252. \doi{10.1111/j.1600-0870.2005.00104.x}
Eade, R., Smith, D., Scaife, A., Wallace, E., Dunstone, N.,
Hermanson, L., & Robinson, N. (2014). Do seasonal-to-decadal climate
predictions underestimate the predictability of the read world? Geophysical
Research Letters, 41(15), 5620-5628. \doi{10.1002/2014GL061146}
Van Schaeybroeck, B., & Vannitsem, S. (2011). Post-processing
through linear regression. Nonlinear Processes in Geophysics, 18(2),
147. \doi{10.5194/npg-18-147-2011}
Van Schaeybroeck, B., & Vannitsem, S. (2015). Ensemble
post-processing using member-by-member approaches: theoretical aspects.
Quarterly Journal of the Royal Meteorological Society, 141(688), 807-818.
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\author{
Verónica Torralba, \email{veronica.torralba@bsc.es}
Bert Van Schaeybroeck, \email{bertvs@meteo.be}
}