# Downscaling using Analogs based on large scale fields. This function perform a downscaling using Analogs. To compute the analogs, the function search for days with similar large scale conditions to downscaled fields to a 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 Minimum Euclidean distance in the large scale pattern (i.e.SLP). 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. 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_Start. 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. For an advanced search of Analogs (multiple Analogs, different criterias, further information from the metrics and date of the selected Analogs) use the'Analog' function within 'CSTools' package. ```r CST_Analogs( expL, obsL, expVar = NULL, obsVar = NULL, sdate_dim = "sdate", region = NULL, criteria = "Large_dist", excludeTime = NULL, time_expL = NULL, time_obsL = NULL, nAnalogs = NULL, AnalogsInfo = FALSE, ncores = NULL ) ``` ## Arguments - `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. Latitudinal dimension accepted names: 'lat', 'lats', 'latitude', 'y', 'j', 'nav_lat'. Longitudinal dimension accepted names: 'lon', 'lons','longitude', 'x', 'i', 'nav_lon'. - `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. - `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'. - `obsVar`: An 's2dv_cube' containing the field of the same variable as the passed in parameter 'expVar' for the same region. - `sdate_dim`: A character string indicating the name of the start date dimension. By default, it is set to 'sdate'. - `region`: A vector of length four indicating the minimum longitude, the maximum longitude, the minimum latitude and the maximum latitude. - `criteria`: A character string indicating the criteria to be used for the selection of analogs: * Large_dist minimum Euclidean distance in the large scale pattern; * Local_dist minimum Euclidean distance in the large scale pattern and minimum Euclidean distance in the local scale pattern; and * Local_cor minimum Euclidean distance in the large scale pattern, minimum Euclidean distance in the local scale pattern and highest correlation in the local variable to downscale. Criteria 'Large_dist' is recommended for CST_Analogs, for an advanced use of the criterias 'Local_dist' and 'Local_cor' use 'Analogs' function. - `excludeTime`: An array of N named dimensions (coinciding with time dimensions in expL)of character string(s) indicating the date(s) of the observations in the format "dd/mm/yyyy" to be excluded during the search of analogs. It can be NULL but if expL is not a forecast (time_expL contained in time_obsL), by default time_expL will be removed during the search of analogs. - `time_expL`: A character string indicating the date of the experiment in the same format than time_obsL (i.e. "yyyy-mm-dd"). By default it is NULL and dates are taken from element `$attrs$Dates` from expL. - `time_obsL`: A character string indicating the date of the observations in the date format (i.e. "yyyy-mm-dd"). By default it is NULL and dates are taken from element `$attrs$Dates` from obsL. It must have time dimensions. - `nAnalogs`: Number of Analogs to be selected to apply the criterias 'Local_dist' or 'Local_cor'. This is not the necessary the number of analogs that the user can get, but the number of events with minimum distance in which perform the search of the best Analog. The default value for the 'Large_dist' criteria is 1, for 'Local_dist' and 'Local_cor' criterias must be greater than 1 in order to match with the first criteria, if nAnalogs is NULL for 'Local_dist' and 'Local_cor' the default value will be set at the length of 'time_obsL'. If AnalogsInfo is FALSE the function returns just the best analog. - `AnalogsInfo`: A logical value. TRUE to get a list with two elements: 1) the downscaled field and 2) the AnalogsInfo which contains: a) the number of the best analogs, b) the corresponding value of the metric used in the selected criteria (distance values for Large_dist and Local_dist, correlation values for Local_cor), c)dates of the analogs). The analogs are listed in decreasing order, the first one is the best analog (i.e if the selected criteria is Local_cor the best analog will be the one with highest correlation, while for Large_dist criteria the best analog will be the day with minimum Euclidean distance). Set to FALSE to get a single analog, the best analog, for instance for downscaling. - `ncores`: The number of cores to use in parallel computation ## Returns An 's2dv_cube' object containing an array with the dowscaled values of the best analogs in element 'data'. If 'AnalogsInfo' is TRUE, 'data' is a list with an array of the downscaled fields and the analogs information in elements 'analogs', 'metric' and 'dates'. ## Examples ```r expL <- rnorm(1:200) dim(expL) <- c(member = 10, lat = 4, lon = 5) obsL <- c(rnorm(1:180), expL[1, , ]*1.2) dim(obsL) <- c(time = 10, lat = 4, lon = 5) time_obsL <- as.POSIXct(paste(rep("01", 10), rep("01", 10), 1994:2003, sep = "-"), format = "%d-%m-%y") dim(time_obsL) <- c(time = 10) time_expL <- time_obsL[1] dim(time_expL) <- c(time = 1) lon <- seq(-1, 5, 1.5) lat <- seq(30, 35, 1.5) coords <- list(lon = seq(-1, 5, 1.5), lat = seq(30, 35, 1.5)) attrs_expL <- list(Dates = time_expL) attrs_obsL <- list(Dates = time_obsL) expL <- list(data = expL, coords = coords, attrs = attrs_expL) obsL <- list(data = obsL, coords = coords, attrs = attrs_obsL) class(expL) <- 's2dv_cube' class(obsL) <- 's2dv_cube' region <- c(min(lon), max(lon), min(lat), max(lat)) downscaled_field <- CST_Analogs(expL = expL, obsL = obsL, region = region) ``` ## 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. pascal.yiou@lsce.ipsl.fr ## See Also `CST_Start`, `Start` ## Author(s) M. Carmen Alvarez-Castro, carmen.alvarez-castro@cmcc.it Maria M. Chaves-Montero, mariadm.chaves@cmcc.it Veronica Torralba, veronica.torralba@cmcc.it Nuria Perez-Zanon nuria.perez@bsc.es

CST_Analogs function