CST_Analogs.R

#'@rdname CST_Analogs
#'@title Downscaling using Analogs based on large scale fields.
#' 
#'@author Carmen Alvarez-Castro, \email{carmen.alvarez-castro@cmcc.it}
#'@author Nuria Perez-Zanon \email{nuria.perez@bsc.es}
#'
#'@description This function perform a downscaling using Analogs. To compute 
#'the analogs, the function search for days with similar large scale conditions
#'to downscaled fields in the local scale. 
#'The large scale and the local scale regions are defined by the user.
#'The large scale is usually given by atmospheric circulation as sea level 
#'pressure or geopotential height (Yiou et al, 2013) but the function gives the
#' possibility to use another field. The local scale will be usually given by 
#' precipitation or temperature fields, but might be another variable. 
#' The analogs function will find the best analogs based in three criterias:
#' (1) Minimal distance in the large scale pattern (i.e. SLP)
#' (2) Minimal distance in the large scale pattern (i.e. SLP) and minimal 
#' distance in the local scale pattern (i.e. SLP). 
#' (3) Minimal distance in the large scale pattern (i.e. SLP), minimal 
#' distance in the local scale pattern (i.e. SLP) and maxima correlation in the 
#' local variable to downscale (i.e Precipitation).
#' The search of analogs must be done in the longest dataset posible. This is 
#' important since it is necessary to have a good representation of the 
#' possible states of the field in the past, and therefore, to get better 
#' analogs. Once the search of the analogs is complete, and in order to used the 
#' three criterias the user can select a number of analogsi, using parameter 'nAnalogs' to restrict 
#' the selection of the best analogs in a short number of posibilities, the best
#' ones.
#' This function has not constrains of specific regions, variables to downscale,
#' or data to be used (seasonal forecast data, climate projections data, 
#' reanalyses data). 
#' The regrid into a finner scale is done interpolating with CST_Load. 
#' Then, this interpolation is corrected selecting the analogs in the large 
#' and local scale in based of the observations. 
#' The function is an adapted version of the method of Yiou et al 2013.       
#'
#'@references Yiou, P., T. Salameh, P. Drobinski, L. Menut, R. Vautard,
#' and M. Vrac, 2013 : Ensemble reconstruction of the atmospheric column 
#' from surface pressure using analogues.  Clim. Dyn., 41, 1419-1437. 
#' \email{pascal.yiou@lsce.ipsl.fr}
#'
#'@param expL an 's2dv_cube' object containing the experimental field on the large scale for which the analog is aimed. This field is used to in all the criterias. If parameter 'expVar' is not provided, the function will return the expL analog. The element 'data' in the 's2dv_cube' object must have, at least, latitudinal and longitudinal dimensions. The object is expect to be already subset for the desired large scale region.
#'@param obsL an 's2dv_cube' object containing the observational field on the large scale. The element 'data' in the 's2dv_cube' object must have the same latitudinal and longitudinal dimensions as parameter 'expL' and a temporal dimension with the maximum number of available observations.
#'@param time_obsL a character string indicating the date of the observations in the format "dd/mm/yyyy"
#'@param expVar an 's2dv_cube' object containing the experimental field on the local scale, usually a different variable to the parameter 'expL'. If it is not NULL (by default, NULL), the returned field by this function will be the analog of parameter 'expVar'.
#'@param obsVar an 's2dv_cube' containing the field of the same variable as the passed in parameter 'expVar' for the same region.
#'@param region a vector of length four indicating the minimum longitude, the maximum longitude, the minimum latitude and the maximum latitude.
#'@param criteria a character string indicating the criteria to be used for the selection of analogs:
#'\itemize{
#'\item{Large_dist} minimal distance in the large scale pattern;
#'\item{Local_dist} minimal distance in the large scale pattern and minimal 
#' distance in the local scale pattern; and
#'\item{Local_cor} minimal distance in the large scale pattern, minimal 
#' distance in the local scale pattern and maxima correlation in the 
#' local variable to downscale.}
#' 
#'@import multiApply
#'@import ClimProjDiags
#'@import abind
#'
#'@seealso code{\link{CST_Load}}, \code{\link[s2dverification]{Load}} and \code{\link[s2dverification]{CDORemap}}
#'
#'@return An 's2dv_cube' object containing the dowscaled values of the best analogs in the criteria selected. 
#'@examples
#'res <- CST_Analogs(expL = lonlat_data$exp, obsL = lonlat_data$obs)
CST_Analogs <- function(expL, obsL, time_obsL, expVar = NULL, obsVar = NULL,
                        region = NULL, criteria = "Large_dist") {
  if (!inherits(expL, 's2dv_cube') || !inherits(obsL, 's2dv_cube')) {
    stop("Parameter 'expL' and 'obsL' must be of the class 's2dv_cube', ",
         "as output by CSTools::CST_Load.")
  }
  if (!is.null(expVar) || !is.null(obsVar)) {
    if (!inherits(expVar, 's2dv_cube') || !inherits(obsVar, 's2dv_cube')) {
      stop("Parameter 'expVar' and 'obsVar' must be of the class 's2dv_cube', ",
           "as output by CSTools::CST_Load.")
    }
  }
  timevector <- obsL$Dates$start
  if (!is.null(expVar)) {
    region <- c(min(expVar$lon), max(expVar$lon), min(expVar$lat), max(expVar$lon))
    lonVar <- expVar$lon
    latVar <- expVar$lat
  } else {
    region <- c(min(expL$lon), max(expL$lon), min(expL$lat), max(expL$lon))
    lonVar <- expL$lon
    latVar <- expL$lat
  }      
  result <- Analogs(expL$data, obsL$data, time_obsL = timevector, 
                    expVar = expVar$data, obsVar = obsVar$data,
                    criteria = criteria, 
                    lonVar = expVar$lon, latVar = expVar$lat, 
                    region = region, nAnalogs = 1, return_list = FALSE)
  if (!is.null(obsVar)) {
    obsVar$data <- result$AnalogsFields
    return(obsVar)
  } else {
    obsL$data <- result$AnalogsFields
    return(obsL)
  }
}
#'@rdname Analogs
#'@title Analogs based on large scale fields.
#' 
#'@author Carmen Alvarez-Castro, \email{carmen.alvarez-castro@cmcc.it}
#'@author Nuria Perez-Zanon \email{nuria.perez@bsc.es}
#'        
#'@description This function perform a downscaling using Analogs. To compute 
#'the analogs, the function search for days with similar large scale conditions
#'to downscaled fields in the local scale. 
#'The large scale and the local scale regions are defined by the user.
#'The large scale is usually given by atmospheric circulation as sea level 
#'pressure or geopotential height (Yiou et al, 2013) but the function gives the
#' possibility to use another field. The local scale will be usually given by 
#' precipitation or temperature fields, but might be another variable. 
#' The analogs function will find the best analogs based in three criterias:
#' (1) Minimal distance in the large scale pattern (i.e. SLP)
#' (2) Minimal distance in the large scale pattern (i.e. SLP) and minimal 
#' distance in the local scale pattern (i.e. SLP). 
#' (3) Minimal distance in the large scale pattern (i.e. SLP), minimal 
#' distance in the local scale pattern (i.e. SLP) and maxima correlation in the 
#' local variable to downscale (i.e Precipitation).
#' The search of analogs must be done in the longest dataset posible. This is 
#' important since it is necessary to have a good representation of the 
#' possible states of the field in the past, and therefore, to get better 
#' analogs. Once the search of the analogs is complete, and in order to used the 
#' three criterias the user can select a number of analogsi, using parameter 
#' 'nAnalogs' to restrict 
#' the selection of the best analogs in a short number of posibilities, the best
#' ones.
#' This function has not constrains of specific regions, variables to downscale,
#' or data to be used (seasonal forecast data, climate projections data, 
#' reanalyses data). 
#' The regrid into a finner scale is done interpolating with CST_Load. 
#' Then, this interpolation is corrected selecting the analogs in the large 
#' and local scale in based of the observations. 
#' The function is an adapted version of the method of Yiou et al 2013.       
#'
#'@references Yiou, P., T. Salameh, P. Drobinski, L. Menut, R. Vautard,
#' and M. Vrac, 2013 : Ensemble reconstruction of the atmospheric column 
#' from surface pressure using analogues.  Clim. Dyn., 41, 1419-1437. 
#' \email{pascal.yiou@lsce.ipsl.fr}
#'
#'@param expL an array of N named dimensions containing the experimental field
#' on the large scale for which the analog is aimed. This field is used to in 
#' all the criterias. If parameter 'expVar' is not provided, the function will
#'  return the expL analog. The element 'data' in the 's2dv_cube' object must 
#'  have, at least, latitudinal and longitudinal dimensions. The object is 
#'  expect to be already subset for the desired large scale region.
#'@param obsL an array of N named dimensions containing the observational field 
#'on the large scale. The element 'data' in the 's2dv_cube' object must have 
#'the same latitudinal and longitudinal dimensions as parameter 'expL' and a
#' temporal dimension with the maximum number of available observations.
#'@param time_obsL a character string indicating the date of the observations in the format "dd/mm/yyyy"
#'@param expVar an array of N named dimensions containing the experimental 
#'field on the local scale, usually a different variable to the parameter 
#''expL'. If it is not NULL (by default, NULL), the returned field by this 
#'function will be the analog of parameter 'expVar'.
#'@param obsVar an array of N named dimensions containing the field of the same variable as the passed in parameter 'expVar' for the same region.
#'@param criteria a character string indicating the criteria to be used for the selection of analogs:
#'\itemize{
#'\item{Large_dist} minimal distance in the large scale pattern; 
#'\item{Local_dist} minimal distance in the large scale pattern and minimal 
#' distance in the local scale pattern; and
#'\item{Local_cor} minimal distance in the large scale pattern, minimal 
#' distance in the local scale pattern and maxima correlation in the 
#' local variable to downscale.} 
#'@param lonVar a vector containing the longitude of parameter 'expVar'.
#'@param latVar a vector containing the latitude of parameter 'expVar'.
#'@param region a vector of length four indicating the minimum longitude, 
#'the maximum longitude, the minimum latitude and the maximum latitude.
#'@param return_list TRUE if you want to get a list with the best analogs FALSE
#' if not. For Downscaling return_list must be FALSE. 
#'@param nAnalogs  number of Analogs to be selected to apply the criterias (this
#' is not the necessary the number of analogs that the user can get, but the number
#' of events with minimal distance in which perform the search of the best Analog.
#' The default value for the Large_dist criteria is 1, the default value for 
#' the Local_dist criteria is 10 and same for Local_cor. If return_list is 
#' False you will get just the first one for downscaling purposes. If return_list
#' is True you will get the list of the best analogs that were searched in nAnalogs
#' under the selected criterias.
#'@import multiApply
#'@import ClimProjDiags
#'@import abind
#'@return DatesAnalogs, A character string with the date of the best analogs (time, distance) 
#'@return AnalogsFields, dowscaled values of the best analogs for the criteria selected.
#'@examples
#'require(zeallot)
#'
#'# Example 1:Downscaling using criteria 'Large_dist' and a single variable:
#'# The best analog is found using a single variable (i.e. Sea level pressure, SLP)
#'# The downscaling will be done in the same variable used to study the minimal distance 
#'# (i.e. SLP). obsVar and expVar NULLS or equal to obsL and expL respectively
#'# region, lonVar and latVar not necessary here. return_list=FALSE 
#'
#'expSLP <- rnorm(1:20)
#'dim(expSLP) <- c(lat = 4, lon = 5)
#'obsSLP <- c(rnorm(1:180),expSLP*1.2)
#'dim(obsSLP) <- c(lat = 4, lon = 5, time = 10)
#'time_obsSLP <- paste(rep("01", 10), rep("01", 10), 1994 : 2003, sep = "-")
#'downscale_field <- Analogs(expL=expSLP, obsL=obsSLP, time_obsL=time_obsSLP)
#'str(downscale_field)
#'
#'# Example 2: Downscaling using criteria 'Large_dist' and 2 variables:
#'# The best analog is found using 2 variables (i.e. Sea Level Pressure, 
#'# SLP and precipitation, pr): one variable (i.e. sea level pressure, expL) 
#'# to find the best analog day (defined in criteria 'Large_dist' as the day, in obsL,
#'# with the minimum Euclidean distance to the day of interest in expL) 
#'# The second variable will be the variable to donwscale (i.e. precipitation, obsVar)
#'# Parameter obsVar must be different to obsL.The downscaled precipitation
#'# will be the precipitation that belongs to the best analog day in SLP. 
#'# Region not needed here since will be the same for both variables.
#'
#'expSLP <- rnorm(1:20)
#'dim(expSLP) <- c(lat = 4, lon = 5)
#'obsSLP <- c(rnorm(1:180),expSLP*2)
#'dim(obsSLP) <- c(lat = 4, lon = 5, time = 10)
#'time_obsSLP <- paste(rep("01", 10), rep("01", 10), 1994 : 2003, sep = "-")
#'obs.pr <- c(rnorm(1:200)*0.001)
#'dim(obs.pr)=dim(obsSLP)
#'downscale_field <- Analogs(expL=expSLP, obsL=obsSLP, 
#'                           obsVar=obs.pr,
#'                           time_obsL=time_obsSLP)
#'str(downscale_field)
#'
#'# Example 3:List of best Analogs using criteria 'Large_dist' and a single variable:
#'# same as Example 1 but getting a list of best analogs (return_list =TRUE) with the 
#'# corresponding downscaled values, instead of only 1 single donwscaled value
#'# instead of 1 single downscaled value. Imposing nAnalogs (number of analogs to do the 
#'# search of the best Analogs).obsVar and expVar NULL or equal to obsL and expL,respectively.
#'
#'expSLP <- rnorm(1:20)
#'dim(expSLP) <- c(lat = 4, lon = 5)
#'obsSLP <- c(rnorm(1:1980),expSLP*1.5)
#'dim(obsSLP) <- c(lat = 4, lon = 5, time = 100)
#'time_obsSLP <- paste(rep("01", 100), rep("01", 100), 1920 : 2019, sep = "-")
#'downscale_field<- Analogs(expL=expSLP, obsL=obsSLP, time_obsSLP,
#'                          nAnalogs=5,return_list = TRUE)
#'str(downscale_field)
#'
#'# Example 4:List of best Analogs using criteria 'Large_dist' and 2 variables:
#'# same as example 2 but getting a list of best analogs (return_list =TRUE) with the values
#'# instead of only a single downscaled value. Imposing nAnalogs (number of analogs to do the 
#'# search of the best Analogs). obsVar and expVar must be different to obsL and expL.
#'
#'expSLP <- rnorm(1:20)
#'dim(expSLP) <- c(lat = 4, lon = 5)
#'obsSLP <- c(rnorm(1:180),expSLP*2)
#'dim(obsSLP) <- c(lat = 4, lon = 5, time = 10)
#'time_obsSLP <- paste(rep("01", 10), rep("01", 10), 1994 : 2003, sep = "-")
#'obs.pr <- c(rnorm(1:200)*0.001)
#'dim(obs.pr)=dim(obsSLP)
#'downscale_field <- Analogs(expL=expSLP, obsL=obsSLP, 
#'                           obsVar=obs.pr,
#'                           time_obsL=time_obsSLP,nAnalogs=5,return_list = TRUE)
#'str(downscale_field)
#'
#'# Example 5: Downscaling using criteria 'Local_dist' and 2 variables:
#'# The best analog is found using 2 variables (i.e. Sea Level Pressure, 
#'# SLP and precipitation, pr). Parameter obsVar must be different to obsL.The 
#'# downscaled precipitation will be the precipitation that belongs to the best 
#'# analog day in SLP. lonVar, latVar and Region must be given here to select the local scale
#'
#'expSLP <- rnorm(1:20)
#'dim(expSLP) <- c(lat = 4, lon = 5)
#'obsSLP <- c(rnorm(1:180),expSLP*2)
#'dim(obsSLP) <- c(lat = 4, lon = 5, time = 10)
#'time_obsSLP <- paste(rep("01", 10), rep("01", 10), 1994 : 2003, sep = "-")
#'obs.pr <- c(rnorm(1:200)*0.001)
#'dim(obs.pr)=dim(obsSLP)
#'# analogs of local scale using criteria 2
#'lonmin=-1
#'lonmax=2
#'latmin=30
#'latmax=33
#'region=c(lonmin,lonmax,latmin,latmax)
#'Local_scale <- Analogs(expL=expSLP,
#'                       obsL=obsSLP, time_obsL=time_obsSLP,
#'                       obsVar=obs.pr,
#'                       criteria="Local_dist",lonVar=seq(-1,5,1.5),
#'                       latVar=seq(30,35,1.5),region=region, 
#'                       nAnalogs = 10, return_list = FALSE)
#'str(Local_scale)
#'
#'# Example 6: list of best analogs using criteria 'Local_dist' and 2 variables:
#'# The best analog is found using 2 variables. Parameter obsVar must be different to obsL in this case.The 
#'# downscaled precipitation will be the precipitation that belongs to the best 
#'# analog day in SLP. lonVar, latVar and Region needed. return_list=TRUE
#'
#'expSLP <- rnorm(1:20)
#'dim(expSLP) <- c(lat = 4, lon = 5)
#'obsSLP <- c(rnorm(1:180),expSLP*2)
#'dim(obsSLP) <- c(lat = 4, lon = 5, time = 10)
#'time_obsSLP <- paste(rep("01", 10), rep("01", 10), 1994 : 2003, sep = "-")
#'obs.pr <- c(rnorm(1:200)*0.001)
#'dim(obs.pr)=dim(obsSLP)
#'# analogs of local scale using criteria 2
#'lonmin=-1
#'lonmax=2
#'latmin=30
#'latmax=33
#'region=c(lonmin,lonmax,latmin,latmax)
#'Local_scale <- Analogs(expL=expSLP,
#'                       obsL=obsSLP, time_obsL=time_obsSLP,
#'                       obsVar=obs.pr,
#'                       criteria="Local_dist",lonVar=seq(-1,5,1.5),
#'                       latVar=seq(30,35,1.5),region=region, 
#'                       nAnalogs = 10, return_list = TRUE)
#'str(Local_scale)
#'
#'# Example 7: Downscaling using Local_dist criteria
#'# without parameters obsVar and expVar. return list =FALSE 
#'
#'expSLP <- rnorm(1:20)
#'dim(expSLP) <- c(lat = 4, lon = 5)
#'obsSLP <- c(rnorm(1:180),expSLP*2)
#'dim(obsSLP) <- c(lat = 4, lon = 5, time = 10)
#'time_obsSLP <- paste(rep("01", 10), rep("01", 10), 1994 : 2003, sep = "-")
#'# analogs of local scale using criteria 2
#'lonmin=-1
#'lonmax=2
#'latmin=30
#'latmax=33
#'region=c(lonmin,lonmax,latmin,latmax)
#'Local_scale <- Analogs(expL=expSLP,
#'                       obsL=obsSLP, time_obsL=time_obsSLP,
#'                       criteria="Local_dist",lonVar=seq(-1,5,1.5),
#'                       latVar=seq(30,35,1.5),region=region, 
#'                       nAnalogs = 10, return_list = TRUE)
#'str(Local_scale)
#'
#'# Example 8: Downscaling using criteria 'Local_cor' and 2 variables:
#'# The best analog is found using 2 variables. Parameter obsVar and expVar are necessary and must be different 
#'# to obsL and expL, respectively.The downscaled precipitation will be the 
#'# precipitation that belongs to the best analog day in SLP large and local scales,
#'# and to the day with the higher correlation in precipitation. return_list=FALSE
#'
#'expSLP <- rnorm(1:20)
#'dim(expSLP) <- c(lat = 4, lon = 5)
#'obsSLP <- c(rnorm(1:180),expSLP*2)
#'dim(obsSLP) <- c(lat = 4, lon = 5, time = 10)
#'time_obsSLP <- paste(rep("01", 10), rep("01", 10), 1994 : 2003, sep = "-")
#'exp.pr <- c(rnorm(1:20)*0.001)
#'dim(exp.pr)=dim(expSLP)
#'obs.pr <- c(rnorm(1:200)*0.001)
#'dim(obs.pr)=dim(obsSLP)
#'# analogs of local scale using criteria 2
#'lonmin=-1
#'lonmax=2
#'latmin=30
#'latmax=33
#'region=c(lonmin,lonmax,latmin,latmax)
#'Local_scalecor <- Analogs(expL=expSLP,
#'                          obsL=obsSLP, time_obsL=time_obsSLP,
#'                          obsVar=obs.pr,expVar=exp.pr,
#'                          criteria="Local_cor",lonVar=seq(-1,5,1.5),
#'                          latVar=seq(30,35,1.5),nAnalogs=15,region=region, 
#'                          return_list = FALSE)
#'str(Local_scalecor)
#'
#'# Example 9: List of best analogs in the three criterias Large_dist, Local_dist, and Local_cor 
#'# return list TRUE same variable
#'
#'expSLP <- rnorm(1:20)
#'dim(expSLP) <- c(lat = 4, lon = 5)
#'obsSLP <- c(rnorm(1:180),expSLP*2)
#'dim(obsSLP) <- c(lat = 4, lon = 5, time = 10)
#'time_obsSLP <- paste(rep("01", 10), rep("01", 10), 1994 : 2003, sep = "-")
#'# analogs of large scale using criteria 1
#'Large_scale <- Analogs(expL=expL,
#'                       obsL=obsL, time_obsL=time_obsL,
#'                       criteria="Large_dist", 
#'                       nAnalogs = 15, return_list = TRUE)
#'str(Large_scale)
#'# analogs of local scale using criteria 2
#'lonmin=-1
#'lonmax=2
#'latmin=30
#'latmax=33
#'region=c(lonmin,lonmax,latmin,latmax)
#'Local_scale <- Analogs(expL=expSLP,
#'                       obsL=obsSLP, time_obsL=time_obsSLP,
#'                       criteria="Local_dist",lonVar=seq(-1,5,1.5),
#'                       latVar=seq(30,35,1.5),nAnalogs=15,region=region, 
#'                       return_list = TRUE)
#'str(Local_scale)
#'# analogs of local scale using criteria 3
#'Local_scalecor <- Analogs(expL=expSLP,
#'                          obsL=obsSLP, time_obsL=time_obsSLP,
#'                          obsVar=obsSLP,expVar=expSLP,
#'                          criteria="Local_cor",lonVar=seq(-1,5,1.5),
#'                          latVar=seq(30,35,1.5),nAnalogs=15,region=region, 
#'                          return_list = TRUE)
#'str(Local_scalecor)
#'
#'# Example 10: Downscaling in the three criteria Large_dist, Local_dist, and Local_cor 
#'return list FALSE, different variable
#'
#'expSLP <- rnorm(1:20)
#'dim(expSLP) <- c(lat = 4, lon = 5)
#'obsSLP <- c(rnorm(1:180),expSLP*2)
#'dim(obsSLP) <- c(lat = 4, lon = 5, time = 10)
#'time_obsSLP <- paste(rep("01", 10), rep("01", 10), 1994 : 2003, sep = "-")
#'exp.pr <- c(rnorm(1:20)*0.001)
#'dim(exp.pr)=dim(expSLP)
#'obs.pr <- c(rnorm(1:200)*0.001)
#'dim(obs.pr)=dim(obsSLP)
#'# analogs of large scale using criteria 1
#'Large_scale <- Analogs(expL=expL,
#'                       obsL=obsL, time_obsL=time_obsL,
#'                       criteria="Large_dist", 
#'                       nAnalogs = 15, return_list = FALSE)
#'str(Large_scale)
#'# analogs of local scale using criteria 2
#'lonmin=-1
#'lonmax=2
#'latmin=30
#'latmax=33
#'region=c(lonmin,lonmax,latmin,latmax)
#'Local_scale <- Analogs(expL=expSLP,
#'                       obsL=obsSLP, time_obsL=time_obsSLP,
#'                       obsVar=obs.pr,
#'                       criteria="Local_dist",lonVar=seq(-1,5,1.5),
#'                       latVar=seq(30,35,1.5),nAnalogs=15,region=region, 
#'                       return_list = FALSE)
#'str(Local_scale)
#'# analogs of local scale using criteria 3
#'Local_scalecor <- Analogs(expL=expSLP,
#'                          obsL=obsSLP, time_obsL=time_obsSLP,
#'                          obsVar=obs.pr,expVar=exp.pr,
#'                          criteria="Local_cor",lonVar=seq(-1,5,1.5),
#'                          latVar=seq(30,35,1.5),nAnalogs=15,region=region, 
#'                          return_list = FALSE)
#'str(Local_scalecor)
#'
#'@export 
Analogs <- function(expL, obsL, time_obsL, expVar = NULL, obsVar = NULL, 
                    criteria = "Large_dist",
                    lonVar = NULL, latVar = NULL, region = NULL, 
                    nAnalogs = 1, return_list = FALSE) {
  # checks
  if (!all(c('lon', 'lat') %in% names(dim(expL)))) {
    stop("Parameter 'expL' must have the dimensions 'lat' and 'lon'.")
  }
  
  if (!all(c('lat', 'lon') %in% names(dim(obsL)))) {
    stop("Parameter 'obsL' must have the dimension 'lat' and 'lon'.")
  }
  
  if (any(is.na(expL)))  {
    warning("Parameter 'exp' contains NA values.")
  }
  
  if (any(is.na(obsL))) {
    warning("Parameter 'obs' contains NA values.")
  }
  if (!is.null(expVar) & is.null(obsVar)) {
    expVar <- NULL
    warning("Parameter 'expVar' is set to NULL as parameter 'obsVar', large scale field will be returned.")
  }
  if (is.null(expVar) & is.null(obsVar)) {
    warning("Parameter 'expVar' and 'obsVar' are NULLs, downscaling/listing same variable as obsL and expL'.")
  }
  if(!is.null(obsVar) & is.null(expVar) & criteria=="Local_cor"){
    stop("parameter 'expVar' cannot be NULL")
  }
  
  if (any(names(dim(obsL)) %in% 'ftime')) {
    if (any(names(dim(obsL)) %in% 'time')) {
      stop("Multiple temporal dimensions ('ftime' and 'time') found",
           "in parameter 'obsL'.")
    } else {
      time_pos_obsL <-  which(names(dim(obsL)) == 'ftime')
      names(dim(obsL))[time_pos_obsL] <- 'time'
      if (any(names(dim(expL)) %in% 'ftime')) {
        time_pos_expL <-  which(names(dim(expL)) == 'ftime')
        names(dim(expL))[time_pos_expL] <- 'time'
      }
    }
  }
  if (any(names(dim(obsVar)) %in% 'ftime')) {
    if (any(names(dim(obsVar)) %in% 'time')) {
      stop("Multiple temporal dimensions ('ftime' and 'time') found",
           "in parameter 'obsVar'.")
    } else {
      time_pos_obsVar <-  which(names(dim(obsVar)) == 'ftime')
      names(dim(obsVar))[time_pos_obsVar] <- 'time'
      if (any(names(dim(expVar)) %in% 'ftime')) {
        time_pos_expVar <-  which(names(dim(expVar)) == 'ftime')
        names(dim(expVar))[time_pos_expVar] <- 'time'
      }
    }
  }
  if (any(names(dim(obsL)) %in% 'sdate')) {
    if (any(names(dim(obsL)) %in% 'time')) {
      dims_obsL <- dim(obsL)
      pos_sdate <- which(names(dim(obsL)) == 'sdate')
      pos_time <- which(names(dim(obsL)) == 'time')
      pos <- 1 : length(dim(obsL))
      pos <- c(pos_time, pos_sdate, pos[-c(pos_sdate,pos_time)])
      obsL <- aperm(obsL, pos)
      dim(obsL) <- c(time = prod(dims_obsL[c(pos_time, pos_sdate)]),
                     dims_obsL[-c(pos_time, pos_sdate)])
    } else {
      stop("Parameter 'obsL' must have a temporal dimension.")
    }
  }
  if (any(names(dim(obsVar)) %in% 'sdate')) {
    if (any(names(dim(obsVar)) %in% 'time')) {
      dims_obsVar <- dim(obsVar)
      pos_sdate <- which(names(dim(obsVar)) == 'sdate')
      pos_time <- which(names(dim(obsVar)) == 'time')
      pos <- 1 : length(dim(obsVar))
      pos <- c(pos_time, pos_sdate, pos[-c(pos_sdate,pos_time)])
      obsVar <- aperm(obsVar, pos)
      dim(obsVar) <- c(time = prod(dims_obsVar[c(pos_time, pos_sdate)]),
                     dims_obsVar[-c(pos_time, pos_sdate)])
    } else {
      stop("Parameter 'obsVar' must have a temporal dimension.")
    }
  } 
  
  if (is.null(region) & criteria!="Large_dist") {
    if (!is.null(lonVar) & !is.null(latVar)) {
      region <- c(min(lonVar), max(lonVar), min(latVar), max(latVar))
    }else{
      stop("Parameters 'lonVar' and 'latVar' must be given in criteria 'Local_dist' and 'Local_cor'")
    }
  }
  
  position <- Select(expL = expL, obsL = obsL,  expVar = expVar, obsVar = obsVar, 
                     criteria = criteria, lonVar = lonVar, latVar = latVar,
                     region = region)$position
  best <- Apply(list(position), target_dims = c('time', 'pos'), fun = BestAnalog,
                criteria = criteria, 
                return_list = return_list, nAnalogs = nAnalogs)$output1
  Analogs_dates <- time_obsL[best]
  dim(Analogs_dates) <- dim(best)
  if (all(!is.null(region), !is.null(lonVar), !is.null(latVar))) {
    if (is.null(obsVar)) {
      obsVar <- SelBox(obsL, lon = lonVar, lat = latVar, region = region)$data
      expVar <- SelBox(expL, lon = lonVar, lat = latVar, region=region)$data
      Analogs_fields <- Subset(obsVar, along = which(names(dim(obsVar)) == 'time'),
                               indices = best)
      warning("obsVar is NULL, obsVar will be computed from obsL (same variable)")
      
    } else {
      obslocal <- SelBox(obsVar, lon = lonVar, lat = latVar, region = region)$data
      Analogs_fields <- Subset(obslocal, along = which(names(dim(obslocal)) == 'time'),
                               indices = best)
    }
  } else {
    warning("One or more of the parameter 'region', 'lonVar' and 'latVar'",
            " are NULL and the large scale field will be returned.")
    if (is.null(obsVar)) {
      Analogs_fields <- Subset(obsL, along = which(names(dim(obsL)) == 'time'),
                               indices = best)
    } else {
      Analogs_fields <- Subset(obsVar,
                               along = which(names(dim(obsVar)) == 'time'),
                               indices = best)
    }
  }
  
  lon_dim <- which(names(dim(Analogs_fields)) == 'lon')
  lat_dim <- which(names(dim(Analogs_fields)) == 'lat')
  if (lon_dim < lat_dim) {
    dim(Analogs_fields) <- c(dim(Analogs_fields)[c(lon_dim, lat_dim)], dim(best))
  } else if (lon_dim > lat_dim) {
    dim(Analogs_fields) <- c(dim(Analogs_fields)[c(lat_dim, lon_dim)], dim(best))
  } else {
    stop("Dimensions 'lat' and 'lon' not found.")
  }
  return(list(DatesAnalogs = Analogs_dates,  AnalogsFields = Analogs_fields))
}

BestAnalog <- function(position, criteria = 'Large_dist', return_list = FALSE, 
                       nAnalogs = 10) {
  pos_dim <- which(names(dim(position)) == 'pos')
  if (dim(position)[pos_dim] == 1) {
    pos1 <- Subset(position, along = pos_dim, indices = 1)
    if (criteria != 'Large_dist') {
      warning("Dimension 'pos' in parameter 'position' has length 1,",
              " criteria 'Large_dist' will be used.")
      criteria <- 'Large_dist'
    }
  } else if (dim(position)[pos_dim] == 2) {
    pos1 <- Subset(position, along = pos_dim, indices = 1)
    pos2 <- Subset(position, along = pos_dim, indices = 2)
    if (criteria == 'Local_cor') {
      warning("Dimension 'pos' in parameter 'position' has length 2,",
              " criteria 'Local_dist' will be used.")
      criteria <- 'Local_dist'
    }
  } else if (dim(position)[pos_dim] == 3) {
    pos1 <- Subset(position, along = pos_dim, indices = 1)
    pos2 <- Subset(position, along = pos_dim, indices = 2)
    pos3 <- Subset(position, along = pos_dim, indices = 3)
    if (criteria != 'Local_cor') {
      warning("Parameter 'criteria' is set to", criteria, ".")
    }
  } else {
    stop("Parameter 'position' has dimension 'pos' of different ",
         "length than expected (from 1 to 3).")
  }
  if (criteria == 'Large_dist') {
    if (return_list == FALSE) {
      pos <- pos1[1]
    } else {
      pos <- pos1[1 : nAnalogs]
    }
  } else if (criteria== 'Local_dist') {
    pos1 <- pos1[1 : nAnalogs]
    pos2 <- pos2[1 : nAnalogs]
    best <- match(pos1, pos2)
    if(length(best)==1){
      warning("Just 1 best analog matching Large_dist and ", 
              "Local_dist criteria")
    } 
    if(length(best)==1 & is.na(best[1])==TRUE){
      stop("no best analogs matching Large_dist and Local_dist criterias") 
    }
    pos <- pos1[as.logical(best)]
    pos <- pos[which(!is.na(pos))]
    if (return_list == FALSE) { 
      pos <- pos[1]
    }else {
        pos <- pos}
  } else if (criteria == 'Local_cor') {
    pos1 <- pos1[1 : nAnalogs]
    pos2 <- pos2[1 : nAnalogs]
    best <- match(pos1, pos2)
    pos <- pos1[as.logical(best)]
    pos <- pos[which(!is.na(pos))]
    pos3 <- pos3[1 : nAnalogs]
    best <- match(pos, pos3)
    pos <- pos[order(best, decreasing = F)]
    pos <- pos[which(!is.na(pos))]
    if (return_list == FALSE) {
      pos[1]
    } 
    return(pos)
  }
}
Select <- function(expL, obsL,  expVar = NULL, obsVar = NULL, criteria = "Large_dist",
                   lonVar = NULL, latVar = NULL, region = NULL) {
  names(dim(expL)) <- replace_repeat_dimnames(names(dim(expL)), names(dim(obsL)))
  metric1 <- Apply(list(obsL), target_dims = list(c('lat', 'lon')), 
                   fun = .select, expL, metric = "dist")$output1
  if (length(dim(metric1)) > 1) {
    dim_time_obs <- which(names(dim(metric1)) == 'time' | 
                            names(dim(metric1)) == 'ftime')
    dim(metric1) <- c(dim(metric1), metric=1)
    margins <- c(1 : (length(dim(metric1))))[-dim_time_obs]
    pos1 <- apply(metric1, margins, order)      
    names(dim(pos1))[1] <- 'time'
    metric1 <-  apply(metric1, margins, sort)
    names(dim(metric1))[1] <- 'time'
  } else {
    pos1 <- order(metric1)
    dim(pos1) <- c(time = length(pos1))
    metric1 <- sort(metric1)
    dim(metric1) <- c(time = length(metric1))
    dim_time_obs=1
  }
  if (criteria == "Large_dist") {
    dim(metric1) <- c(dim(metric1), metric = 1)
    dim(pos1) <- c(dim(pos1), pos = 1)
    return(list(metric = metric1, position = pos1))
  }
  if (criteria == "Local_dist" | criteria == "Local_cor") {
    obs <- SelBox(obsL, lon = lonVar, lat = latVar, region = region)$data
    exp <- SelBox(expL, lon = lonVar, lat = latVar, region = region)$data
    metric2 <- Apply(list(obs), target_dims = list(c('lat', 'lon')), 
                     fun = .select, exp, metric = "dist")$output1
    dim(metric2) <- c(dim(metric2), metric=1)
    margins <- c(1 : (length(dim(metric2))))[-dim_time_obs]
    pos2 <- apply(metric2, margins, order)
    dim(pos2) <- dim(pos1)
    names(dim(pos2))[1] <- 'time'
    metric2 <-  apply(metric2, margins, sort)
    names(dim(metric2))[1] <- 'time'
    if (criteria == "Local_dist") {
      metric <- abind(metric1, metric2, along = length(dim(metric1))+1)
      position <- abind(pos1, pos2, along = length(dim(pos1))+1) 
      names(dim(metric)) <- c(names(dim(pos1)), 'metric')
      names(dim(position)) <- c(names(dim(pos1)), 'pos')
      return(list(metric = metric, position = position))
    }   
  }
  if (criteria == "Local_cor") {
    obs <- SelBox(obsVar, lon = lonVar, lat = latVar, region = region)$data
    exp <- SelBox(expVar, lon = lonVar, lat = latVar, region = region)$data
    metric3 <- Apply(list(obs), target_dims = list(c('lat', 'lon')), 
                     fun = .select, exp, metric = "cor")$output1
    dim(metric3) <- c(dim(metric3), metric=1)
    margins <- c(1 : (length(dim(metric3))))[-dim_time_obs]
    pos3 <- apply(metric3, margins, order, decreasing = TRUE)
    names(dim(pos3))[1] <- 'time'
    metric3 <-  apply(metric3, margins, sort)
    names(dim(metric3))[1] <- 'time'
    metric <- abind(metric1, metric2, metric3, along = length(dim(metric1)) + 1)
    position <- abind(pos1, pos2, pos3, along = length(dim(pos1)) + 1)   
    names(dim(metric)) <- c(names(dim(metric1)), 'metric')
    names(dim(position)) <- c(names(dim(pos1)), 'pos')
    return(list(metric = metric, position = position))
  }
  else {
    stop("Parameter 'criteria' must to be one of the: 'Large_dist', ",
         "'Local_dist','Local_cor'.")
  }
}
.select <- function(exp, obs, metric = "dist") {
  if (metric == "dist") {
    result <- Apply(list(obs), target_dims = list(c('lat', 'lon')), 
                    fun = function(x) {sum((x - exp) ^ 2)})$output1
  } else if (metric == "cor") {
    result <- Apply(list(obs), target_dims = list(c('lat', 'lon')), 
                    fun = function(x) {cor(as.vector(x), as.vector(exp))})$output1
  } 
  result
}
replace_repeat_dimnames <- function(names_exp, names_obs, lat_name = 'lat', 
                                    lon_name = 'lon') {
  if (!is.character(names_exp)) {
    stop("Parameter 'names_exp' must be a vector of characters.")
  }
  if (!is.character(names_obs)) {
    stop("Parameter 'names_obs' must be a vector of characters.")
  }
  latlon_dim_exp <- which(names_exp == lat_name | names_exp == lon_name)
  latlon_dim_obs <- which(names_obs == lat_name | names_obs == lon_name)
  if (any(unlist(lapply(names_exp[-latlon_dim_exp],
                        function(x){x == names_obs[-latlon_dim_obs]})))) {
    original_pos <- lapply(names_exp, function(x) which(x == names_obs[-latlon_dim_obs]))
    original_pos <- lapply(original_pos, length) > 0
    names_exp[original_pos] <- paste0(names_exp[original_pos], "_exp")
  }
  return(names_exp)
  ## Improvements: other dimensions to avoid replacement for more flexibility.
}