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#'Compute the Mean Bias
#'
#'The Mean Bias or Mean Error (Wilks, 2011) is defined as the mean difference
#'between the ensemble mean forecast and the observations. It is a deterministic
#'metric. Positive values indicate that the forecasts are on average too high
#'and negative values indicate that the forecasts are on average too low.
#'It also allows to compute the Absolute Mean Bias or bias without temporal
#'mean. If there is more than one dataset, the result will be computed for each
#'pair of exp and obs data.
#'
#'@param exp A named numerical array of the forecast with at least time
#' dimension.
#'@param 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'.
#'@param time_dim A character string indicating the name of the time dimension.
#' The default value is 'sdate'.
#'@param 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.
#'@param memb_dim A character string indicating the name of the member dimension
#' to compute the ensemble mean; it should be set to NULL if the parameter
#' 'exp' is already the ensemble mean. The default value is NULL.
#'@param na.rm A logical value indicating if NAs should be removed (TRUE) or
#' kept (FALSE) for computation. The default value is FALSE.
#'@param absolute A logical value indicating whether to compute the absolute
#' bias. The default value is FALSE.
#'@param time_mean A logical value indicating whether to compute the temporal
#' mean of the bias. The default value is TRUE.
#'@param ncores An integer indicating the number of cores to use for parallel
#' computation. The default value is NULL.
#'
#'@return
#'A numerical array of bias with dimensions c(nexp, nobs, the rest dimensions of
#''exp' except 'time_dim' (if time_mean = T) and 'memb_dim'). 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.
#'
#'@references
#'Wilks, 2011; https://doi.org/10.1016/B978-0-12-385022-5.00008-7
#'
#'@examples
#'exp <- array(rnorm(1000), dim = c(dat = 1, lat = 3, lon = 5, member = 10, sdate = 50))
#'obs <- array(rnorm(1000), dim = c(dat = 1, lat = 3, lon = 5, sdate = 50))
#'bias <- Bias(exp = exp, obs = obs, memb_dim = 'member')
Bias <- function(exp, obs, time_dim = 'sdate', memb_dim = NULL, dat_dim = NULL, na.rm = FALSE,
absolute = FALSE, time_mean = TRUE, ncores = NULL) {
# Check inputs
## exp and obs (1)
if (!is.array(exp) | !is.numeric(exp))
stop("Parameter 'exp' must be a numeric array.")
if (!is.array(obs) | !is.numeric(obs))
stop("Parameter 'obs' must be a numeric array.")
if(any(is.null(names(dim(exp))))| any(nchar(names(dim(exp))) == 0) |
any(is.null(names(dim(obs))))| any(nchar(names(dim(obs))) == 0)) {
stop("Parameter 'exp' and 'obs' must have dimension names.")
}
## time_dim
if (!is.character(time_dim) | length(time_dim) != 1)
stop("Parameter 'time_dim' must be a character string.")
if (!time_dim %in% names(dim(exp)) | !time_dim %in% names(dim(obs))) {
stop("Parameter 'time_dim' is not found in 'exp' or 'obs' dimension.")
}
## memb_dim
if (!is.null(memb_dim)) {
if (!is.character(memb_dim) | length(memb_dim) > 1) {
stop("Parameter 'memb_dim' must be a character string.")
}
if (!memb_dim %in% names(dim(exp))) {
stop("Parameter 'memb_dim' is not found in 'exp' dimension.")
}
if (memb_dim %in% names(dim(obs))) {
if (identical(as.numeric(dim(obs)[memb_dim]), 1)) {
obs <- ClimProjDiags::Subset(x = obs, along = memb_dim, indices = 1, drop = 'selected')
} else {
stop("Not implemented for observations with members ('obs' can have 'memb_dim', ",
"but it should be of length = 1).")
}
}
if (!is.null(dat_dim)) {
if (!is.character(dat_dim) | length(dat_dim) > 1) {
stop("Parameter 'dat_dim' must be a character string.")
}
if (!dat_dim %in% names(dim(exp)) | !dat_dim %in% names(dim(obs))) {
stop("Parameter 'dat_dim' is not found in 'exp' or 'obs' dimension.",
" Set it as NULL if there is no dataset dimension.")
}
}
## exp and obs (2)
name_exp <- sort(names(dim(exp)))
name_obs <- sort(names(dim(obs)))
if (!is.null(memb_dim)) {
name_exp <- name_exp[-which(name_exp == memb_dim)]
if (!is.null(dat_dim)) {
name_exp <- name_exp[-which(name_exp == dat_dim)]
name_obs <- name_obs[-which(name_obs == dat_dim)]
}
if (!identical(length(name_exp), length(name_obs)) |
!identical(dim(exp)[name_exp], dim(obs)[name_obs])) {
stop(paste0("Parameter 'exp' and 'obs' must have same length of ",
"all dimensions except 'memb_dim' and 'dat_dim'."))
}
## na.rm
if (!is.logical(na.rm) | length(na.rm) > 1) {
stop("Parameter 'na.rm' must be one logical value.")
}
## absolute
if (!is.logical(absolute) | length(absolute) > 1) {
stop("Parameter 'absolute' must be one logical value.")
}
## time_mean
if (!is.logical(time_mean) | length(time_mean) > 1) {
stop("Parameter 'time_mean' must be one logical value.")
}
## ncores
if (!is.null(ncores)) {
if (!is.numeric(ncores) | ncores %% 1 != 0 | ncores <= 0 |
length(ncores) > 1) {
stop("Parameter 'ncores' must be either NULL or a positive integer.")
}
}
## Ensemble mean
if (!is.null(memb_dim)) {
exp <- MeanDims(exp, memb_dim, na.rm = na.rm)
}
## (Mean) Bias
target_dims = c(time_dim, dat_dim),
fun = .Bias,
dat_dim = dat_dim,
na.rm = na.rm,
absolute = absolute,
time_mean = time_mean,
.Bias <- function(exp, obs, time_dim = 'sdate', dat_dim = NULL, na.rm = FALSE,
absolute = FALSE, time_mean = TRUE) {
# exp and obs: [sdate, (dat)]
if (is.null(dat_dim)) {
bias <- exp - obs
bias <- mean(bias, na.rm = na.rm)
}
} else {
nexp <- as.numeric(dim(exp)[dat_dim])
nobs <- as.numeric(dim(obs)[dat_dim])
bias <- array(dim = c(dim(exp)[time_dim], nexp = nexp, nobs = nobs))
for (i in 1:nexp) {
for (j in 1:nobs) {
bias[, i, j] <- exp[, i] - obs[, j]
bias <- MeanDims(bias, time_dim, na.rm = na.rm)