# Multivariate Root Mean Square Error (RMSE) This function calculates the RMSE from multiple variables, as the mean of each variable's RMSE scaled by its observed standard deviation. Variables can be weighted based on their relative importance (defined by the user). ```r CST_MultivarRMSE( exp, obs, weight = NULL, memb_dim = "member", dat_dim = "dataset", sdate_dim = "sdate", ftime_dim = "ftime" ) ``` ## Arguments - `exp`: A list of objects, one for each variable, of class `s2dv_cube` as returned by `CST_Anomaly` function, containing the anomaly of the seasonal forecast experiment data in the element named `$data`. - `obs`: A list of objects, one for each variable (in the same order than the input in 'exp') of class `s2dv_cube` as returned by `CST_Anomaly` function, containing the observed anomaly data in the element named `$data`. - `weight`: (optional) A vector of weight values to assign to each variable. If no weights are defined, a value of 1 is assigned to every variable. - `memb_dim`: A character string indicating the name of the member dimension. It must be one dimension in 'exp' and 'obs'. The default value is 'member'. - `dat_dim`: A character string indicating the name of the dataset dimension. It must be one dimension in 'exp' and 'obs'. If there is no dataset dimension, it can be NULL. The default value is 'dataset'. - `sdate_dim`: A character string indicating the name of the start date dimension. It must be one dimension in 'exp' and 'obs'. The default value is 'sdate'. - `ftime_dim`: A character string indicating the name of the forecast time dimension. It must be one dimension in 'exp' and 'obs'. The default value is 'ftime'. ## Returns An object of class `s2dv_cube` containing the RMSE in the element `$data` which is an array with two datset dimensions equal to the 'dataset' dimension in the `exp$data` and `obs$data` inputs. An array with dimensions: c(number of exp, number of obs, 1 (the multivariate RMSE value), number of lat, number of lon) ## Examples ```r # Example with 2 variables mod1 <- abs(rnorm(1 * 3 * 4 * 5 * 6 * 7)) mod2 <- abs(rnorm(1 * 3 * 4 * 5 * 6 * 7)) dim(mod1) <- c(dataset = 1, member = 3, sdate = 4, ftime = 5, lat = 6, lon = 7) dim(mod2) <- c(dataset = 1, member = 3, sdate = 4, ftime = 5, lat = 6, lon = 7) obs1 <- abs(rnorm(1 * 1 * 4 * 5 * 6 * 7)) obs2 <- abs(rnorm(1 * 1 * 4 * 5 * 6 * 7)) dim(obs1) <- c(dataset = 1, member = 1, sdate = 4, ftime = 5, lat = 6, lon = 7) dim(obs2) <- c(dataset = 1, member = 1, sdate = 4, ftime = 5, lat = 6, lon = 7) lon <- seq(0, 30, 5) lat <- seq(0, 25, 5) coords <- list(lat = lat, lon = lon) exp1 <- list(data = mod1, coords = coords, attrs = list(Datasets = "EXP1", source_files = "file1", Variable = list(varName = 'pre'))) exp2 <- list(data = mod2, coords = coords, attrs = list(Datasets = "EXP2", source_files = "file2", Variable = list(varName = 'tas'))) obs1 <- list(data = obs1, coords = coords, attrs = list(Datasets = "OBS1", source_files = "file1", Variable = list(varName = 'pre'))) obs2 <- list(data = obs2, coords = coords, attrs = list(Datasets = "OBS2", source_files = "file2", Variable = list(varName = 'tas'))) attr(exp1, 'class') <- 's2dv_cube' attr(exp2, 'class') <- 's2dv_cube' attr(obs1, 'class') <- 's2dv_cube' attr(obs2, 'class') <- 's2dv_cube' anom1 <- CST_Anomaly(exp1, obs1, cross = TRUE, memb = TRUE) anom2 <- CST_Anomaly(exp2, obs2, cross = TRUE, memb = TRUE) ano_exp <- list(anom1$exp, anom2$exp) ano_obs <- list(anom1$obs, anom2$obs) a <- CST_MultivarRMSE(exp = ano_exp, obs = ano_obs, weight = c(1, 2)) ``` ## See Also `RMS` and `CST_Load` ## Author(s) Deborah Verfaillie, deborah.verfaillie@bsc.es

CST_MultivarRMSE function