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#'Forecast Calibration based on the ensemble inflation
#'
#'@author Verónica Torralba, \email{veronica.torralba@bsc.es}
#'@description This function applies a variance inflation technique described in Doblas-Reyes et al. (2005) in leave-one-out cross-validation. This bias adjustment method produces calibrated forecasts with equivalent mean and variance to that of the reference dataset, but at the same time preserve reliability.
#'@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
#'
#'@param exp an object of class \code{s2dv_cube} containing the seasonal forecat experiment data returned by \code{CST_Load} function or \code{Load} function from s2dverification.
#'@param obs an object of class \code{s2dv_cube} containing the obseved data returned by \code{CST_Load} function.
#'@return an object of class \code{s2dv_cube} containing the calibrated forecasts in the element \code{data}.
#'@seealso \code{\link{CST_Load}} and \code{\link[s2dverification]{Load}}
#'
#'# Load data using CST_Load or use the sample data provided:
#'library(zeallot)
#'c(exp, obs) %<-% lonlat_data
#'exp_calibrated <- CST_Calibration(exp = exp, obs = obs)
#'str(exp_calibrated)
CST_Calibration <- function(exp, obs) {
if (!inherits(exp, 's2dv_cube') || !inherits(exp, 's2dv_cube')) {
stop("Parameter 'exp' and 'obs' must be of the class 's2dv_cube', ",
"as output by CSTools::CST_Load.")
if (dim(obs$data)['member'] != 1) {
stop("The length of the dimension 'member' in the component 'data' ",
"of the parameter 'obs' must be equal to 1.")
Calibrated <- Calibration(exp = exp$data, obs = obs$data)
Calibrated <- aperm(Calibrated, c(3, 1, 2, 4, 5, 6))
names(dim(Calibrated)) <- dimnames[c(3, 1, 2, 4, 5, 6)]
exp$data <- Calibrated
exp$Datasets <- c(exp$Datasets, obs$Datasets)
exp$source_files <- c(exp$source_files, obs$source_files)
return(exp)
}
Calibration <- function(exp, obs) {
if (!all(c('member', 'sdate') %in% names(dim(exp)))) {
stop("Parameter 'exp' must have the dimensions 'member' and 'sdate'.")
}
if (!all(c('sdate') %in% names(dim(obs)))) {
stop("Parameter 'obs' must have the dimension 'sdate'.")
}
if (any(is.na(exp))) {
warning("Parameter 'exp' contains NA values.")
if (any(is.na(obs))) {
warning("Parameter 'obs' contains NA values.")
}
target_dims_obs <- 'sdate'
if ('member' %in% names(dim(obs))) {
target_dims_obs <- c('member', target_dims_obs)
}
Calibrated <- Apply(data = list(var_obs = obs, var_exp = exp),
target_dims = list(target_dims_obs, c('member', 'sdate')),
return(Calibrated)
}
.cal <- function(var_obs, var_exp) {
ntime <- dim(var_exp)[which(names(dim(var_exp)) == 'sdate')][]
nmembers <- dim(var_exp)[which(names(dim(var_exp)) == 'member')][]
if (all(names(dim(var_exp)) != c('member','sdate'))) {
var_exp <- t(var_exp)
}
climObs <- NA * var_obs
climPred <- NA * var_obs
climObs[t] <- mean(var_obs[ , -t])
climPred[t] <- mean(var_exp[ , -t])
# defining forecast,hindcast and observation in cross-validation
fcst <- NA * var_exp[ , t]
hcst <- NA * var_exp[ , -t]
for (i in 1 : nmembers) {
fcst[i] <- var_exp[i, t] - climPred[t]
hcst[i, ] <- var_exp[i, -t]- climPred[t]
obs <- var_obs[-t]
#coefficients
em_fcst <- mean(fcst)
em_hcst <- apply(hcst, c(2), mean)
corr <- cor(em_hcst, obs)
sd_obs <- sd(obs)
sd_em_hcst <- sd(em_hcst)
fcst_diff <- fcst - em_fcst
hcst_diff <- NA * hcst
hcst_diff[n,] <- hcst[n,] - em_hcst
}
sd_hcst_diff <- sd(hcst_diff)
a <- corr * (sd_obs / sd_em_hcst)
b <- (sd_obs / sd_hcst_diff) * sqrt(1 - (corr ^ 2))
calibrated[, t] <- (a * em_fcst) + (b * fcst_diff) + climObs[t]
}
names(dim(calibrated)) <- c('member', 'sdate')
return(calibrated)
}