% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/BEI_PDFBest.R
\name{BEI_PDFBest}
\alias{BEI_PDFBest}
\title{Computing the Best Index PDFs combining Index PDFs from two SFSs}
\usage{
BEI_PDFBest(index_obs, index_hind1, index_hind2, index_fcst1 = NULL,
  index_fcst2 = NULL, method_BC = "none", time_dim_name = "time",
  na.rm = FALSE)
}
\arguments{
\item{index_obs}{Index (e.g. NAO index) array from an observational database
or reanalysis with at least a temporal dimension (by default 'time'), 
which must be greater than 2.}

\item{index_hind1}{Index (e.g. NAO index) array from a SFS (named SFS1)
with at least two dimensions (time , member) or (time, statistic). 
The temporal dimension, by default 'time', must be greater than 2. 
The dimension 'member' must be greater than 1. 
The dimension 'statistic' must be equal to 2, for containing the two paramenters of 
a normal distribution (mean and sd) representing the ensemble of a SFS.
It is not possible to have the dimension 'member' and 'statistic' at the same time.}

\item{index_hind2}{Index (e.g. NAO index) array from a SFS (named SFS2)
with at least two dimensions (time , member) or (time, statistic). 
The temporal dimension, by default 'time', must be greater than 2. 
The dimension 'member' must be greater than 1. 
The dimension 'statistic' must be equal to 2, for containing the two paramenters of 
a normal distribution (mean and sd) representing the ensemble of a SFS.
It is not possible to have the dimension 'member' and  'statistic' together.}

\item{index_fcst1}{(optional, default = NULL) Index (e.g. NAO index) array from forescating of SFS1
with at least two dimensions (time , member) or (time, statistic). 
The temporal dimension, by default 'time', must be equal to 1, the forecast year target. 
The dimension 'member' must be greater than 1. 
The dimension 'statistic' must be equal to 2, for containing the two paramenters of 
a normal distribution (mean and sd) representing the ensemble of a SFS.
It is not possible to have the dimension 'member' and  'statistic' together.}

\item{index_fcst2}{(optional, default = NULL) Index (e.g. NAO index) array from forescating of SFS2
with at least two dimensions (time , member) or (time, statistic). 
The temporal dimension, by default 'time', must be equal to 1, the forecast year target. 
The dimension 'member' must be greater than 1. 
The dimension 'statistic' must be equal to 2, for containing the two paramenters of 
a normal distribution (mean and sd) representing the ensemble of a SFS.
It is not possible to have the dimension 'member' and  'statistic' together.}

\item{method_BC}{A character vector of maximun length 2 indicating the bias 
correction methodology to be applied on each SFS. If it is 'none' or any of 
its elements is 'none', the bias correction won't be applied. 
Available methods developped are "ME" (a bias correction scheme based on the
mean error or bias between observation and predictions to correct the 
predicted values), and "LMEV" (a bias correction scheme based on a linear 
model using ensemble variance of index as predictor). (see Sanchez-Garcia, 
E. et al (2019), https://doi.org/10.5194/asr-16-165-2019 for more details).}

\item{time_dim_name}{A character string indicating the name of the temporal 
dimension, by default 'time'.}

\item{na.rm}{Logical (default = FALSE). Should missing values be removed?}
}
\value{
BEI_PDFBest() returns an array with the parameters that caracterize
the PDFs, with at least a temporal dimension, by default 'time' and dimension 
'statistic' equal to 2.
The firt statistic is the parameter 'mean' of the PDF for the best estimation
combining the two SFSs PDFs.
The second statistic is the parameter 'standard deviation' of the PDF for
the best estimation combining the two SFSs PDFs.
If index_fcst1 and/or index_fcst2 are null, returns the values for hindcast period. 
Otherwise, it returns the values for a forecast year.
}
\description{
This function implements the computation to obtain the index 
Probability Density Functions (PDFs) (e.g. NAO index) obtained to combining 
the Index PDFs for two Seasonal Forecast Systems (SFSs), the Best Index 
estimation (see Sanchez-Garcia, E. et al (2019), 
https://doi.org/10.5194/asr-16-165-2019 for more details about the 
methodology applied to estimate the Best Index).
}
\examples{
# Example 1 for the BEI_PDFBest function
index_obs<- rnorm(10, sd = 3)
dim(index_obs) <- c(time = 5, season = 2)
index_hind1 <- rnorm(40, mean = 0.2, sd = 3)
dim(index_hind1) <- c(time = 5, member = 4, season = 2)
index_hind2 <- rnorm(60, mean = -0.5, sd = 4)
dim(index_hind2) <- c(time = 5, member = 6, season = 2)
index_fcst1 <- rnorm(16, mean = 0.2, sd = 3)
dim(index_fcst1) <- c(time = 1, member = 8, season = 2)
index_fcst2 <- rnorm(18, mean = -0.5, sd = 4)
dim(index_fcst2) <- c(time = 1, member = 9, season = 2)
method_BC <- 'ME'
res <- BEI_PDFBest(index_obs, index_hind1, index_hind2, index_fcst1, 
index_fcst2, method_BC) 
dim(res)
# time statistic    season
#    1         2         2 
# Example 2 for the BEI_PDFBest function
index_obs<- rnorm(10, sd = 3)
dim(index_obs) <- c(time = 5, season = 2)
index_hind1 <- rnorm(40, mean = 0.2, sd = 3)
dim(index_hind1) <- c(time = 5, member = 4, season = 2)
index_hind2 <- rnorm(60, mean = -0.5, sd = 4)
dim(index_hind2) <- c(time = 5, member = 6, season = 2)
index_fcst1 <- rnorm(16, mean = 0.2, sd = 3)
dim(index_fcst1) <- c(time = 1, member = 8, season = 2)
index_fcst2 <- rnorm(18, mean = -0.5, sd = 4)
dim(index_fcst2) <- c(time = 1, member = 9, season = 2)
method_BC <- c('LMEV', 'ME')
res <- BEI_PDFBest(index_obs, index_hind1, index_hind2, index_fcst1, index_fcst2, method_BC) 
dim(res)
# time statistic    season
#    1         2         2 
}
\references{
Regionally improved seasonal forecast of precipitation through 
Best estimation of winter NAO, Sanchez-Garcia, E. et al.,
Adv. Sci. Res., 16, 165174, 2019, https://doi.org/10.5194/asr-16-165-2019
}
\author{
Eroteida Sanchez-Garcia - AEMET, \email{esanchezg@aemet.es}
}
