# Computing the Index PDFs for a dataset of SFSs for a hindcats period. This function implements the computation to obtain the index PDFs (e.g. NAO index) to improve the index estimate from SFSs for a hindcast period. ```r PDFIndexHind( index_hind, index_obs, method = "ME", time_dim_name = "time", na.rm = FALSE ) ``` ## Arguments - `index_hind`: Index (e.g. NAO index) array from SFSs 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. - `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. - `method`: A character string indicating which methodology is applied to compute the PDFs. One of "ME" (default) or "LMEV". - `time_dim_name`: A character string indicating the name of the temporal dimension, by default 'time'. - `na.rm`: Logical (default = FALSE). Should missing values be removed? ## Returns An array with at least two dimensions (time, statistic = 4). The firt statistic is the parameter 'mean' of the PDF with not bias corrected. The second statistic is the parameter 'standard deviation' of the PDF with not bias corrected. The third statistic is the parameter 'mean' of the PDF with bias corrected. The fourth statistic is the parameter 'standard deviation' of the PDF with bias corrected. ## Examples ```r # Example for the PDFIndexHind function # Example 1 index_obs <- 1 : (5 * 3 ) dim(index_obs) <- c(time = 5, season = 3) index_hind <- 1 : (5 * 4 * 3) dim(index_hind) <- c(time = 5, member = 4, season = 3) res <- PDFIndexHind(index_hind, index_obs) dim(res) # time statistic season # 5 4 3 # Example 2 index_obs <- 1 : (5 * 3) dim(index_obs) <- c(time = 5, season = 3) index_hind <- 1 : (5 * 2 * 3) dim(index_hind) <- c(time = 5, statistic = 2, season = 3) res <- PDFIndexHind(index_hind, index_obs) ``` ## References Regionally improved seasonal forecast of precipitation through Best estimation of winter NAO, Sanchez-Garcia, E. et al., Adv. Sci. Res., 16, 165174, 2019, tools:::Rd_expr_doi("10.5194/asr-16-165-2019") ## Author(s) Eroteida Sanchez-Garcia - AEMET, esanchezg@aemet.es