# EOF analysis of multiple variables This function performs EOF analysis over multiple variables, accepting in input a list of CSTools objects. Based on Singular Value Decomposition. For each field the EOFs are computed and the corresponding PCs are standardized (unit variance, zero mean); the minimum number of principal components needed to reach the user-defined variance is retained. The function weights the input data for the latitude cosine square root. ```r CST_MultiEOF( datalist, lon_dim = "lon", lat_dim = "lat", time_dim = "ftime", sdate_dim = "sdate", var_dim = "var", neof_max = 40, neof_composed = 5, minvar = 0.6, lon_lim = NULL, lat_lim = NULL, ncores = NULL ) ``` ## Arguments - `datalist`: A list of objects of the class 's2dv_cube', containing the variables to be analysed. Each data object in the list is expected to have an element named `$data` with at least two spatial dimensions named "lon" and "lat", a dimension "ftime" and a dimension "sdate". Latitudinal dimension accepted names: 'lat', 'lats', 'latitude', 'y', 'j', 'nav_lat'. Longitudinal dimension accepted names: 'lon', 'lons','longitude', 'x', 'i', 'nav_lon'. NAs can exist but it should be consistent along 'time_dim'. That is, if one grid point has NAs for each variable, all the time steps at this point should be NAs. - `lon_dim`: A character string indicating the name of the longitudinal dimension. By default, it is set to 'lon'. - `lat_dim`: A character string indicating the name of the latitudinal dimension. By default, it is set to 'lat'. - `time_dim`: A character string indicating the name of the temporal dimension. By default, it is set to 'time'. - `sdate_dim`: A character string indicating the name of the start date dimension. By default, it is set to 'sdate'. - `var_dim`: A character string indicating the name of the variable dimension. By default, it is set to 'var'. - `neof_max`: Maximum number of single eofs considered in the first decomposition. - `neof_composed`: Number of composed eofs to return in output. - `minvar`: Minimum variance fraction to be explained in first decomposition. - `lon_lim`: Vector with longitudinal range limits for the EOF calculation for all input variables. - `lat_lim`: Vector with latitudinal range limits for the EOF calculation for all input variables. - `ncores`: An integer indicating the number of cores to use for parallel computation. The default value is NULL. ## Returns A list containing: - **coeff**: An 's2dv_cube' with the data element being an array of principal components with dimensions 'time_dim', 'sdate_dim', number of eof, rest of the dimensions of 'data' except 'lon_dim' and 'lat_dim'. - **variance**: An 's2dv_cube' with the data element being an array of explained variances with dimensions 'eof' and the rest of the dimensions of 'data' except 'time_dim', 'sdate_dim', 'lon_dim' and 'lat_dim'. - **eof_pattern**: An 's2dv_cube' with the data element being an array of EOF patterns obtained by regression with dimensions: 'eof' and the rest of the dimensions of 'data' except 'time_dim' and 'sdate_dim'. - **mask**: An 's2dv_cube' with the data element being an array of the mask with dimensions ('lon_dim', 'lat_dim', rest of the dimensions of 'data' except 'time_dim'). It is made from 'data', 1 for the positions that 'data' has value and NA for the positions that 'data' has NA. It is used to replace NAs with 0s for EOF calculation and mask the result with NAs again after the calculation. - **coordinates**: Longitudinal and latitudinal coordinates vectors. ## Examples ```r seq <- 1 : (2 * 3 * 4 * 5 * 6 * 8) mod1 <- sin( 0.7 + seq )^2 + cos( seq ^ 2 * 1.22 ) dim(mod1) <- c(dataset = 2, member = 3, sdate = 4, ftime = 5, lat = 6, lon = 8) mod2 <- sin( seq * 2 ) ^ 3 + cos( seq ^ 2 ) dim(mod2) <- c(dataset = 2, member = 3, sdate = 4, ftime = 5, lat = 6, lon = 8) lon <- seq(0, 35, 5) lat <- seq(0, 25, 5) exp1 <- list(data = mod1, coords = list(lat = lat, lon = lon)) exp2 <- list(data = mod2, coords = list(lat = lat, lon = lon)) attr(exp1, 'class') <- 's2dv_cube' attr(exp2, 'class') <- 's2dv_cube' d = as.POSIXct(c("2017/01/01", "2017/01/02", "2017/01/03", "2017/01/04", "2017/01/05", "2018/01/01", "2018/01/02", "2018/01/03", "2018/01/04", "2018/01/05", "2019/01/01", "2019/01/02", "2019/01/03", "2019/01/04", "2019/01/05", "2020/01/01", "2020/01/02", "2020/01/03", "2020/01/04", "2020/01/05")) exp1$attrs$Dates = d exp2$attrs$Dates = d cal <- CST_MultiEOF(datalist = list(exp1, exp2), neof_composed = 2) ``` ## Author(s) Jost von Hardenberg - ISAC-CNR, j.vonhardenberg@isac.cnr.it Paolo Davini - ISAC-CNR, p.davini@isac.cnr.it

CST_MultiEOF function