From d1e614c7edf1415e59f72a210e9fa467c8b0260e Mon Sep 17 00:00:00 2001 From: Carlos Delgado Date: Tue, 6 Jul 2021 17:58:06 +0200 Subject: [PATCH 01/59] included the posibility to take into account the effective degrees of freedom --- R/RandomWalkTest.R | 37 +++++++++++++++++++++++-------------- 1 file changed, 23 insertions(+), 14 deletions(-) diff --git a/R/RandomWalkTest.R b/R/RandomWalkTest.R index 494be65..f747f87 100644 --- a/R/RandomWalkTest.R +++ b/R/RandomWalkTest.R @@ -10,6 +10,9 @@ #' forecaster B's. The dimensions should be identical as parameter 'skill_A'. #'@param time_dim A character string indicating the name of the dimension along #' which the tests are computed. The default value is 'sdate'. +#'@param N.eff A numerical array with the number of effective degrees of freedom. +#' The dimensions should be the same as 'skill_A' and 'skill_B' but without the 'time_dim' dimension. +#' If NA (default), the length of the 'time_dim' dimension is used. #'@param ncores An integer indicating the number of cores to use for parallel #' computation. The default value is NULL. #' @@ -34,11 +37,11 @@ #' reference <- array(1:40, dim = c(sdate = 10, lat = 2, lon = 2)) #' skill_A <- abs(fcst_A - reference) #' skill_B <- abs(fcst_B - reference) -#' RandomWalkTest(skill_A = skill_A, skill_B = skill_B, time_dim = 'sdate', ncores = 1) +#' RandomWalkTest(skill_A = skill_A, skill_B = skill_B, time_dim = 'sdate', N.eff = NA, ncores = 1) #' #'@import multiApply #'@export -RandomWalkTest <- function(skill_A, skill_B, time_dim = 'sdate', ncores = NULL){ +RandomWalkTest <- function(skill_A, skill_B, time_dim = 'sdate', N.eff = NA, ncores = NULL){ ## Check inputs if (is.null(skill_A) | is.null(skill_B)){ @@ -56,6 +59,11 @@ RandomWalkTest <- function(skill_A, skill_B, time_dim = 'sdate', ncores = NULL){ if(!time_dim %in% names(dim(skill_A)) | !time_dim %in% names(dim(skill_B))){ stop("Parameter 'time_dim' is not found in 'skill_A' or 'skill_B' dimensions.") } + if(!identical(N.eff,NA)){ + if (!identical(dim(N.eff), dim(skill_A)[-which(names(dim(skill_A)) == time_dim)]) | !is.numeric(N.eff)){ + stop("Parameter 'N.eff' must be NA, or an array with the same dimensions as 'skill_A' and 'skill_B' but without the 'time_dim' dimension") + } + } if (!is.null(ncores)){ if (!is.numeric(ncores) | ncores %% 1 != 0 | ncores <= 0 | length(ncores) > 1){ stop("Parameter 'ncores' must be a positive integer.") @@ -63,20 +71,21 @@ RandomWalkTest <- function(skill_A, skill_B, time_dim = 'sdate', ncores = NULL){ } ## Compute the Random Walk Test - res <- multiApply::Apply(data = list(skill_A, skill_B), - target_dims = time_dim, - fun = .RandomWalkTest, - ncores = ncores) + res <- multiApply::Apply(data = list(skill_A = skill_A, skill_B = skill_B, N.eff = N.eff), + target_dims = list(skill_A = time_dim, skill_B = time_dim, N.eff = NULL), + fun = .RandomWalkTest, ncores = ncores) return(res) } -.RandomWalkTest <- function(skill_A, skill_B){ +.RandomWalkTest <- function(skill_A, skill_B, N.eff){ + + N <- ifelse(test = is.na(N.eff), yes = length(skill_A), no = N.eff) + + score <- cumsum(skill_A > skill_B) - cumsum(skill_A < skill_B) + + ## TRUE if significant (if last value is above or below 2*sqrt(N)) + signif<- ifelse(test = (score[length(skill_A)] < (-2)*sqrt(N)) | (score[length(skill_A)] > 2*sqrt(N)), + yes = TRUE, no = FALSE) - score <- cumsum(skill_A > skill_B) - cumsum(skill_A < skill_B) - - ## TRUE if significant (if last value is above or below 2*sqrt(N)) - signif<- ifelse(test = (score[length(skill_A)] < (-2)*sqrt(length(skill_A))) | (score[length(skill_A)] > 2*sqrt(length(skill_A))), - yes = TRUE, no = FALSE) - - return(list("score"=score[length(skill_A)],"signif"=signif)) + return(list("score"=score[length(skill_A)],"signif"=signif)) } -- GitLab From 5306c9f72399dacb2c87b491948110b39e260df0 Mon Sep 17 00:00:00 2001 From: Victoria Agudetse Roures Date: Tue, 8 Nov 2022 15:30:07 +0100 Subject: [PATCH 02/59] Add parameters 'sign' and 'alpha' to RMSSS() --- R/RMSSS.R | 41 ++++++++++++++++++++++++++++------------- 1 file changed, 28 insertions(+), 13 deletions(-) diff --git a/R/RMSSS.R b/R/RMSSS.R index e44105c..0a0d98d 100644 --- a/R/RMSSS.R +++ b/R/RMSSS.R @@ -56,7 +56,7 @@ #'@importFrom stats pf #'@export RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', - pval = TRUE, ncores = NULL) { + pval = TRUE, sign = FALSE, alpha = 0.5, ncores = NULL) { # Check inputs ## exp and obs (1) @@ -109,6 +109,14 @@ RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', if (!is.logical(pval) | length(pval) > 1) { stop("Parameter 'pval' must be one logical value.") } + ## sign + if (!is.logical(sign) | length(sign) > 1) { + stop("Parameter 'sign' must be one logical value.") + } + ## alpha + if (!is.numeric(alpha) | length(alpha) > 1) { + stop("Parameter 'alpha' must be one numeric value.") + } ## ncores if (!is.null(ncores)) { if (!is.numeric(ncores) | ncores %% 1 != 0 | ncores <= 0 | @@ -148,14 +156,15 @@ RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', c(time_dim, dat_dim)), fun = .RMSSS, time_dim = time_dim, dat_dim = dat_dim, - pval = pval, ncores_input = ncores, + pval = pval, sign = sign, alpha = alpha, + ncores_input = ncores, ncores = ncores) return(res) } .RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', pval = TRUE, - ncores_input = NULL) { + sign = FALSE, alpha = 0.05, ncores_input = NULL) { if (is.null(dat_dim)) { # exp: [sdate] # obs: [sdate] @@ -188,7 +197,6 @@ RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', dif1[, , i] <- sapply(1:nexp, function(x) {exp[, x] - obs[, i]}) } - # rms1 and eno1 rms1 <- apply(dif1^2, c(2, 3), mean, na.rm = TRUE)^0.5 #array(dim = c(nexp, nobs)) # rms2 and eno2 rms2 <- array(colMeans(obs^2, na.rm = TRUE)^0.5, dim = c(nobs = nobs)) @@ -204,22 +212,25 @@ RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', rmsss <- 1 - rms1/rms2 ## pval and conf - if (pval) { - eno1 <- Eno(dif1, time_dim, ncores = ncores_input) - eno2 <- Eno(obs, time_dim, ncores = ncores_input) + if (pval || sign) { + eno1 <- Eno(dif1, time_dim, ncores = ncores_input) + eno2 <- Eno(obs, time_dim, ncores = ncores_input) eno2 <- array(eno2, dim = c(nobs = nobs, nexp = nexp)) eno2 <- Reorder(eno2, c(2, 1)) } # pval - if (pval) { + if (pval || sign) { F.stat <- (eno2 * rms2^2 / (eno2- 1)) / ((eno1 * rms1^2 / (eno1- 1))) tmp <- !is.na(eno1) & !is.na(eno2) & eno1 > 2 & eno2 > 2 p_val <- 1 - pf(F.stat, eno1 - 1, eno2 - 1) + signif <- (p_val <= 0.05) ## TODO: change to alpha + # If there isn't enough valid data, return NA p_val[which(!tmp)] <- NA + signif[which(!tmp)] <- NA - # change not significant rmsss to NA + # change not significan rmsss to NA rmsss[which(!tmp)] <- NA } @@ -228,15 +239,19 @@ RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', if (is.null(dat_dim)) { dim(rmsss) <- NULL dim(p_val) <- NULL + dim(signif) <- NULL } ################################### # output + res <- list(rmsss = rmsss) if (pval) { - res <- list(rmsss = rmsss, p.val = p_val) - - } else { - res <- list(rmsss = rmsss) + p.val <- list(p.val = p_val) + res <- c(res, p.val) + } + if (sign) { + signif <- list(sign = signif) + res <- c(res, signif) } return(res) -- GitLab From 78a8c337469ad581517352331ec71a469e0f16b7 Mon Sep 17 00:00:00 2001 From: Victoria Agudetse Roures Date: Tue, 8 Nov 2022 15:48:31 +0100 Subject: [PATCH 03/59] Update RMSSS() documentation --- R/RMSSS.R | 17 +++++++++++++---- 1 file changed, 13 insertions(+), 4 deletions(-) diff --git a/R/RMSSS.R b/R/RMSSS.R index 0a0d98d..ba749f4 100644 --- a/R/RMSSS.R +++ b/R/RMSSS.R @@ -27,8 +27,12 @@ #'@param time_dim A character string indicating the name of dimension along #' which the RMSSS are computed. The default value is 'sdate'. #'@param pval A logical value indicating whether to compute or not the p-value -#' of the test Ho: RMSSS = 0. If pval = TRUE, the insignificant RMSSS will -#' return NA. The default value is TRUE. +#' of the test Ho: RMSSS = 0. The default value is TRUE. +#'@param sign A logical value indicating whether to compute or not the +#' statistical significance of the test Ho: RMSSS = 0. The default value is +#' FALSE. +#'@param alpha A numeric of the significance level to be used in the +#' statistical significance test. The default value is 0.05. #'@param ncores An integer indicating the number of cores to use for parallel #' computation. The default value is NULL. #' @@ -38,10 +42,15 @@ #'nexp is the number of experiment (i.e., dat_dim in exp), and nobs is the #'number of observation (i.e., dat_dim in obs).\cr #'\item{$rmsss}{ -#' The root mean square error skill score. +#' A numerical array of the root mean square error skill score. #'} #'\item{$p.val}{ -#' The p-value. Only present if \code{pval = TRUE}. +#' A numerical array of the p-value with the same dimensions as $rmsss. +#' Only present if \code{pval = TRUE}. +#'} +#'\item{sign}{ +#' A logical array of the statistical significance of the RMSSS with the same +#' dimensions as $rmsss. Only present if \code{sign = TRUE}. #'} #' #'@examples -- GitLab From 40577b5720ec891199d38c949d25dc16a7173994 Mon Sep 17 00:00:00 2001 From: Victoria Agudetse Roures Date: Tue, 8 Nov 2022 15:49:51 +0100 Subject: [PATCH 04/59] Fix bug in default value of alpha --- R/RMSSS.R | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/R/RMSSS.R b/R/RMSSS.R index ba749f4..2f17c28 100644 --- a/R/RMSSS.R +++ b/R/RMSSS.R @@ -65,7 +65,7 @@ #'@importFrom stats pf #'@export RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', - pval = TRUE, sign = FALSE, alpha = 0.5, ncores = NULL) { + pval = TRUE, sign = FALSE, alpha = 0.05, ncores = NULL) { # Check inputs ## exp and obs (1) -- GitLab From 61df5023cb780dbe485764875bb7767b1303a7bc Mon Sep 17 00:00:00 2001 From: aho Date: Fri, 11 Nov 2022 15:37:05 +0100 Subject: [PATCH 05/59] Remove ncores_inputs and modify unit tests --- R/RMSSS.R | 37 +++++++------- man/RMSSS.Rd | 37 +++++++++----- tests/testthat/test-RMSSS.R | 96 ++++++++++++++++++++++++++----------- 3 files changed, 113 insertions(+), 57 deletions(-) diff --git a/R/RMSSS.R b/R/RMSSS.R index 2f17c28..9c47da4 100644 --- a/R/RMSSS.R +++ b/R/RMSSS.R @@ -6,11 +6,12 @@ #'different, with the number of experiments/models (nexp) and the number of #'observational datasets (nobs).\cr #'RMSSS computes the root mean square error skill score of each jexp in 1:nexp -#'against each jobs in 1:nobs which gives nexp * nobs RMSSS for each other -#'grid point of the array.\cr -#'The RMSSS are computed along the time_dim dimension which should corresponds -#'to the startdate dimension.\cr -#'The p-value is optionally provided by an one-sided Fisher test.\cr +#'against each job in 1:nobs which gives nexp * nobs RMSSS for each grid point +#'of the array.\cr +#'The RMSSS are computed along the time_dim dimension which should correspond +#'to the start date dimension.\cr +#'The p-value and significance test are optionally provided by an one-sided +#'Fisher test.\cr #' #'@param exp A named numeric array of experimental data which contains at least #' two dimensions for dat_dim and time_dim. It can also be a vector with the @@ -40,7 +41,8 @@ #'A list containing the numeric arrays with dimension:\cr #' c(nexp, nobs, all other dimensions of exp except time_dim).\cr #'nexp is the number of experiment (i.e., dat_dim in exp), and nobs is the -#'number of observation (i.e., dat_dim in obs).\cr +#'number of observation (i.e., dat_dim in obs). If dat_dim is NULL, nexp and +#'nobs are omitted.\cr #'\item{$rmsss}{ #' A numerical array of the root mean square error skill score. #'} @@ -58,7 +60,7 @@ #' exp <- array(rnorm(30), dim = c(dataset = 2, time = 3, memb = 5)) #' set.seed(2) #' obs <- array(rnorm(15), dim = c(time = 3, memb = 5, dataset = 1)) -#' res <- RMSSS(exp, obs, time_dim = 'time') +#' res <- RMSSS(exp, obs, time_dim = 'time', dat_dim = 'dataset') #' #'@rdname RMSSS #'@import multiApply @@ -166,14 +168,16 @@ RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', fun = .RMSSS, time_dim = time_dim, dat_dim = dat_dim, pval = pval, sign = sign, alpha = alpha, - ncores_input = ncores, ncores = ncores) return(res) } .RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', pval = TRUE, - sign = FALSE, alpha = 0.05, ncores_input = NULL) { + sign = FALSE, alpha = 0.05) { + # exp: [sdate, (dat)] + # obs: [sdate, (dat)] + if (is.null(dat_dim)) { # exp: [sdate] # obs: [sdate] @@ -207,7 +211,6 @@ RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', } rms1 <- apply(dif1^2, c(2, 3), mean, na.rm = TRUE)^0.5 #array(dim = c(nexp, nobs)) - # rms2 and eno2 rms2 <- array(colMeans(obs^2, na.rm = TRUE)^0.5, dim = c(nobs = nobs)) rms2[which(abs(rms2) <= (max(abs(rms2), na.rm = TRUE) / 1000))] <- max(abs( rms2), na.rm = TRUE) / 1000 @@ -220,10 +223,10 @@ RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', # use rms1 and rms2 to calculate rmsss rmsss <- 1 - rms1/rms2 - ## pval and conf + ## pval and sign if (pval || sign) { - eno1 <- Eno(dif1, time_dim, ncores = ncores_input) - eno2 <- Eno(obs, time_dim, ncores = ncores_input) + eno1 <- Eno(dif1, time_dim) + eno2 <- Eno(obs, time_dim) eno2 <- array(eno2, dim = c(nobs = nobs, nexp = nexp)) eno2 <- Reorder(eno2, c(2, 1)) } @@ -234,12 +237,12 @@ RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', F.stat <- (eno2 * rms2^2 / (eno2- 1)) / ((eno1 * rms1^2 / (eno1- 1))) tmp <- !is.na(eno1) & !is.na(eno2) & eno1 > 2 & eno2 > 2 p_val <- 1 - pf(F.stat, eno1 - 1, eno2 - 1) - signif <- (p_val <= 0.05) ## TODO: change to alpha + if (sign) signif <- p_val <= alpha # If there isn't enough valid data, return NA p_val[which(!tmp)] <- NA - signif[which(!tmp)] <- NA + if (sign) signif[which(!tmp)] <- NA - # change not significan rmsss to NA + # change not significant rmsss to NA rmsss[which(!tmp)] <- NA } @@ -248,7 +251,7 @@ RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', if (is.null(dat_dim)) { dim(rmsss) <- NULL dim(p_val) <- NULL - dim(signif) <- NULL + if (sign) dim(signif) <- NULL } ################################### diff --git a/man/RMSSS.Rd b/man/RMSSS.Rd index 9ebcf65..05dfb1b 100644 --- a/man/RMSSS.Rd +++ b/man/RMSSS.Rd @@ -10,6 +10,8 @@ RMSSS( time_dim = "sdate", dat_dim = "dataset", pval = TRUE, + sign = FALSE, + alpha = 0.05, ncores = NULL ) } @@ -33,8 +35,14 @@ which the RMSSS are computed. The default value is 'sdate'.} dimension. The default value is 'dataset'.} \item{pval}{A logical value indicating whether to compute or not the p-value -of the test Ho: RMSSS = 0. If pval = TRUE, the insignificant RMSSS will -return NA. The default value is TRUE.} +of the test Ho: RMSSS = 0. The default value is TRUE.} + +\item{sign}{A logical value indicating whether to compute or not the +statistical significance of the test Ho: RMSSS = 0. The default value is +FALSE.} + +\item{alpha}{A numeric of the significance level to be used in the +statistical significance test. The default value is 0.05.} \item{ncores}{An integer indicating the number of cores to use for parallel computation. The default value is NULL.} @@ -43,12 +51,18 @@ computation. The default value is NULL.} A list containing the numeric arrays with dimension:\cr c(nexp, nobs, all other dimensions of exp except time_dim).\cr nexp is the number of experiment (i.e., dat_dim in exp), and nobs is the -number of observation (i.e., dat_dim in obs).\cr +number of observation (i.e., dat_dim in obs). If dat_dim is NULL, nexp and +nobs are omitted.\cr \item{$rmsss}{ - The root mean square error skill score. + A numerical array of the root mean square error skill score. } \item{$p.val}{ - The p-value. Only present if \code{pval = TRUE}. + A numerical array of the p-value with the same dimensions as $rmsss. + Only present if \code{pval = TRUE}. +} +\item{sign}{ + A logical array of the statistical significance of the RMSSS with the same + dimensions as $rmsss. Only present if \code{sign = TRUE}. } } \description{ @@ -58,17 +72,18 @@ have the same dimensions except along dat_dim, where the length can be different, with the number of experiments/models (nexp) and the number of observational datasets (nobs).\cr RMSSS computes the root mean square error skill score of each jexp in 1:nexp -against each jobs in 1:nobs which gives nexp * nobs RMSSS for each other -grid point of the array.\cr -The RMSSS are computed along the time_dim dimension which should corresponds -to the startdate dimension.\cr -The p-value is optionally provided by an one-sided Fisher test.\cr +against each job in 1:nobs which gives nexp * nobs RMSSS for each grid point +of the array.\cr +The RMSSS are computed along the time_dim dimension which should correspond +to the start date dimension.\cr +The p-value and significance test are optionally provided by an one-sided +Fisher test.\cr } \examples{ set.seed(1) exp <- array(rnorm(30), dim = c(dataset = 2, time = 3, memb = 5)) set.seed(2) obs <- array(rnorm(15), dim = c(time = 3, memb = 5, dataset = 1)) -res <- RMSSS(exp, obs, time_dim = 'time') +res <- RMSSS(exp, obs, time_dim = 'time', dat_dim = 'dataset') } diff --git a/tests/testthat/test-RMSSS.R b/tests/testthat/test-RMSSS.R index d592130..0a4916e 100644 --- a/tests/testthat/test-RMSSS.R +++ b/tests/testthat/test-RMSSS.R @@ -1,23 +1,17 @@ context("s2dv::RMSSS tests") ############################################## - # case 0 - set.seed(1) - exp0 <- array(rnorm(15), dim = c(sdate = 3, dataset = 5)) - set.seed(2) - obs0 <- array(rnorm(6), dim = c(sdate = 3, dataset = 2)) - # case 1 set.seed(1) - exp1 <- array(rnorm(15), dim = c(time = 3, memb = 5)) + exp1 <- array(rnorm(15), dim = c(sdate = 3, dataset = 5)) set.seed(2) - obs1 <- array(rnorm(6), dim = c(time = 3, memb = 2)) + obs1 <- array(rnorm(6), dim = c(sdate = 3, dataset = 2)) # case 2 set.seed(3) - exp2 <- array(rnorm(120), dim = c(sdate = 10, dat = 1, lon = 3, lat = 2, dataset = 2)) + exp2 <- array(rnorm(120), dim = c(time = 10, dat = 1, lon = 3, lat = 2, dataset = 2)) set.seed(4) - obs2 <- array(rnorm(60), dim = c(dat = 1, sdate = 10, dataset = 1, lat = 2, lon = 3)) + obs2 <- array(rnorm(60), dim = c(dat = 1, time = 10, dataset = 1, lat = 2, lon = 3)) # case 3: vector set.seed(5) @@ -27,14 +21,14 @@ context("s2dv::RMSSS tests") # case 4 set.seed(7) - exp4 <- array(rnorm(120), dim = c(sdate = 10, dat = 1, lon = 3, lat = 2)) + exp4 <- array(rnorm(60), dim = c(sdate = 10, lon = 3, lat = 2)) set.seed(8) - obs4 <- array(rnorm(60), dim = c(dat = 1, sdate = 10, lat = 2, lon = 3)) + obs4 <- array(exp4 + rnorm(60) / 2, dim = dim(exp4)) ############################################## test_that("1. Input checks", { - + ## exp and obs (1) expect_error( RMSSS(c(), c()), "Parameter 'exp' and 'obs' cannot be NULL." @@ -56,31 +50,46 @@ test_that("1. Input checks", { RMSSS(array(1:10, dim = c(a = 2, c = 5)), array(1:4, dim = c(a = 2, b = 2))), "Parameter 'exp' and 'obs' must have same dimension name" ) + ## time_dim expect_error( RMSSS(exp1, obs1, time_dim = 1), "Parameter 'time_dim' must be a character string." ) expect_error( - RMSSS(exp0, obs0, time_dim = 'a'), + RMSSS(exp1, obs1, time_dim = 'a'), "Parameter 'time_dim' is not found in 'exp' or 'obs' dimension." ) + ## dat_dim expect_error( - RMSSS(exp0, obs0, dat_dim = NA), + RMSSS(exp1, obs1, dat_dim = NA), "Parameter 'dat_dim' must be a character string." ) expect_error( - RMSSS(exp0, obs0, dat_dim = 'memb'), + RMSSS(exp1, obs1, dat_dim = 'memb'), paste0("Parameter 'dat_dim' is not found in 'exp' or 'obs' dimension.", " Set it as NULL if there is no dataset dimension.") ) + ## pval expect_error( - RMSSS(exp0, obs0, pval = c(T, T)), + RMSSS(exp1, obs1, pval = c(T, T)), "Parameter 'pval' must be one logical value." ) + ## sign + expect_error( + RMSSS(exp1, obs1, sign = 0.05), + "Parameter 'sign' must be one logical value." + ) + ## alpha expect_error( - RMSSS(exp0, obs0, ncores = 1.4), + RMSSS(exp1, obs1, alpha = T), + "Parameter 'alpha' must be one numeric value." + ) + ## ncores + expect_error( + RMSSS(exp1, obs1, ncores = 1.4), "Parameter 'ncores' must be a positive integer." ) + ## exp and obs (2) expect_error( RMSSS(exp = array(1:10, dim = c(sdate = 1, dataset = 5, a = 1)), obs = array(1:4, dim = c(a = 1, sdate = 2, dataset = 2))), @@ -96,7 +105,7 @@ test_that("1. Input checks", { ############################################## test_that("2. Output checks: case 1", { - res1_1 <- RMSSS(exp1, obs1, time_dim = 'time', dat_dim = 'memb') + res1_1 <- RMSSS(exp1, obs1, dat_dim = 'dataset') expect_equal( dim(res1_1$rmsss), c(nexp = 5, nobs = 2) @@ -110,12 +119,17 @@ test_that("2. Output checks: case 1", { -0.5449538, tolerance = 0.00001 ) + expect_equal( + as.vector(res1_1$p.val)[3:7], + c(0.4914588, 0.5134658, 0.6428701, 0.4919943, 0.8672634), + tolerance = 0.001 + ) exp1_2 <- exp1 exp1_2[2:4] <- NA obs1_2 <- obs1 obs1_2[1:2] <- NA - res1_2 <- RMSSS(exp1_2, obs1_2, time_dim = 'time', dat_dim = 'memb', pval = TRUE) + res1_2 <- RMSSS(exp1_2, obs1_2, dat_dim = 'dataset', pval = TRUE) expect_equal( length(res1_2$rmsss[which(is.na(res1_2$rmsss))]), @@ -134,16 +148,16 @@ test_that("2. Output checks: case 1", { test_that("3. Output checks: case 2", { expect_equal( - dim(RMSSS(exp2, obs2)$rmsss), + dim(RMSSS(exp2, obs2, time_dim = 'time')$rmsss), c(nexp = 2, nobs = 1, dat = 1, lon = 3, lat = 2) ) expect_equal( - mean(RMSSS(exp2, obs2)$rmsss), + mean(RMSSS(exp2, obs2, time_dim = 'time')$rmsss), -0.3912208, tolerance = 0.00001 ) expect_equal( - range(RMSSS(exp2, obs2)$p.val), + range(RMSSS(exp2, obs2, time_dim = 'time')$p.val), c(0.2627770, 0.9868412), tolerance = 0.00001 ) @@ -171,17 +185,41 @@ test_that("5. Output checks: case 4", { expect_equal( dim(RMSSS(exp4, obs4, dat_dim = NULL)$rmsss), - c(dat = 1, lon = 3, lat = 2) + c(lon = 3, lat = 2) + ) + expect_equal( + dim(RMSSS(exp4, obs4, dat_dim = NULL)$p.val), + c(lon = 3, lat = 2) ) expect_equal( - mean(RMSSS(exp4, obs4, dat_dim = NULL)$rmsss), - -0.3114424, + as.vector(RMSSS(exp4, obs4, dat_dim = NULL)$rmsss), + c(0.5393823, 0.6818405, 0.4953423, 0.4093817, 0.5972085, 0.5861135), tolerance = 0.00001 ) expect_equal( - range(RMSSS(exp4, obs4, dat_dim = NULL)$p.val), - c(0.3560534, 0.9192801), + as.vector(RMSSS(exp4, obs4, dat_dim = NULL)$p.val), + c(0.015203983, 0.001091360, 0.026987112, 0.066279877, 0.006161059, 0.007437649), tolerance = 0.00001 ) - + expect_equal( + names(RMSSS(exp4, obs4, dat_dim = NULL)), + c('rmsss', 'p.val') + ) + expect_equal( + names(RMSSS(exp4, obs4, dat_dim = NULL, sign = T, pval = F)), + c('rmsss', 'sign') + ) + expect_equal( + names(RMSSS(exp4, obs4, dat_dim = NULL, sign = T, pval = T)), + c('rmsss', 'p.val', 'sign') + ) + expect_equal( + as.vector(RMSSS(exp4, obs4, dat_dim = NULL, sign = T, pval = F)$sign), + c(T, T, T, F, T, T) + ) + expect_equal( + as.vector(RMSSS(exp4, obs4, dat_dim = NULL, sign = T, pval = F, alpha = 0.01)$sign), + c(F, T, F, F, T, T) + ) + }) -- GitLab From 05f8c82432f8f6219c9f63d341f3ce657243327f Mon Sep 17 00:00:00 2001 From: aho Date: Wed, 16 Nov 2022 13:36:15 +0100 Subject: [PATCH 06/59] Reorder the largest other dim to the last dim as unlimited dim --- R/CDORemap.R | 12 +++++++--- tests/testthat/test-CDORemap.R | 44 ++++++++++++++++++++++++++++++++++ 2 files changed, 53 insertions(+), 3 deletions(-) diff --git a/R/CDORemap.R b/R/CDORemap.R index f0044cb..927b107 100644 --- a/R/CDORemap.R +++ b/R/CDORemap.R @@ -666,7 +666,10 @@ CDORemap <- function(data_array = NULL, lons, lats, grid, method, total_slices <- 1 other_dims_per_chunk <- ifelse(is_irregular, 1, 2) # 4 (the maximum accepted by CDO) - 2 (lon, lat) = 2. if (length(other_dims) > 1 || (length(other_dims) > 0 && (is_irregular))) { - if (!(length(dim(data_array)) %in% other_dims)) { + # If lat/lon is the last dimension OR the largest other_dims is not the last one, + # reorder the largest other dimension to the last as unlimited dim. + if (!(length(dim(data_array)) %in% other_dims) | + which.max(dim(data_array)[other_dims]) != length(other_dims)) { if (avoid_writes || is_irregular) { dims_mod <- dim(data_array) dims_mod[which(names(dim(data_array)) %in% @@ -675,9 +678,9 @@ CDORemap <- function(data_array = NULL, lons, lats, grid, method, permutation <- (1:length(dim(data_array)))[-dim_to_move] permutation <- c(permutation, dim_to_move) permutation_back <- sort(permutation, index.return = TRUE)$ix - dim_backup <- dim(data_array) +# dim_backup <- dim(data_array) data_array <- aperm(data_array, permutation) - dim(data_array) <- dim_backup[permutation] +# dim(data_array) <- dim_backup[permutation] other_dims <- which(!(names(dim(data_array)) %in% c(lon_dim, lat_dim))) } else { # We allow only lon, lat and 1 more dimension per chunk, so @@ -695,6 +698,9 @@ CDORemap <- function(data_array = NULL, lons, lats, grid, method, total_slices <- prod(dim(slices_to_iterate)) } if ((other_dims_per_chunk > 1) || (other_dims_per_chunk > 0 && is_irregular)) { + #NOTE: Why don't we use the second line here? In history, that line was never used. + # The first line sort() can cause problems. If the largest other_dims is always + # the last dim, tail(other_dims) is enough. unlimited_dim <- tail(sort(tail(other_dims_ordered_by_size, other_dims_per_chunk)), 1) #unlimited_dim <- tail(other_dims) } diff --git a/tests/testthat/test-CDORemap.R b/tests/testthat/test-CDORemap.R index 16da1b0..1ace086 100644 --- a/tests/testthat/test-CDORemap.R +++ b/tests/testthat/test-CDORemap.R @@ -39,6 +39,10 @@ data4_1 <- drop(data4) data4_2 <- ClimProjDiags::Subset(data4, c(1,2,3,4,8), list(1,1,1,1,1), drop = 'selected') data4_3 <- .aperm2(data4_2, c(1, 3, 2)) + # data5: regular grid, more dimensions + data5 <- array(1:(4*10*8*3*2), dim = c(dat = 1, var = 1, memb = 4, lon = 10, lat = 8, sdate = 3, sweek = 2)) + data5_1 <- aperm(data5, c(1,2,3,6,4,5,7)) + ############################################## test_that("1. Input checks", { @@ -269,3 +273,43 @@ c(-88.2, -84.6, -81.0, -77.4, -73.8) ) }) + + +############################################################ + +test_that("6. dat5: regular regrid, more dimensions", { +suppressWarnings( +res5 <- CDORemap(data5, lons = seq(1, 5.5, by = 0.5), lats = seq(10, 13.5, by = 0.5), + grid = 'r360x181', method = 'bil', crop = T) +) +expect_equal( +as.vector(res5$lons), +1:5 +) +expect_equal( +as.vector(res5$lats), +10:13 +) +expect_equal( +as.vector(res5$data_array[1, 1, 1, , , 2, 1]), +c(seq(321, 353, by = 8), seq(401, 433, by = 8), seq(481, 513, by = 8), seq(561, 593, by = 8)) +) + +suppressWarnings( +res5_1 <- CDORemap(data5_1, lons = seq(1, 5.5, by = 0.5), lats = seq(10, 13.5, by = 0.5), + grid = 'r360x181', method = 'bil', crop = T) +) +expect_equal( +aperm(res5_1$data_array, c(1, 2, 3, 5, 6, 4, 7)), +res5$data_array +) +expect_equal( +as.vector(res5_1$lons), +1:5 +) +expect_equal( +as.vector(res5_1$lats), +10:13 +) +}) + -- GitLab From c88492d7dcd209b1b193e641f387abfd533ec6c8 Mon Sep 17 00:00:00 2001 From: Victoria Agudetse Roures Date: Thu, 17 Nov 2022 12:33:29 +0100 Subject: [PATCH 07/59] Add 'sign' parameter to Corr --- R/Corr.R | 55 ++++++++++++++++++++++++++++++++----------------------- 1 file changed, 32 insertions(+), 23 deletions(-) diff --git a/R/Corr.R b/R/Corr.R index 67efb09..1cee56d 100644 --- a/R/Corr.R +++ b/R/Corr.R @@ -42,8 +42,10 @@ #' of the test Ho: Corr = 0. The default value is TRUE. #'@param conf A logical value indicating whether to retrieve the confidence #' intervals or not. The default value is TRUE. -#'@param conf.lev A numeric indicating the confidence level for the -#' regression computation. The default value is 0.95. +#'@param sign A logical value indicating whether to retrieve the statistical +#' significance of the test Ho: Corr = 0. The default value is FALSE. +#'@param alpha A numeric indicating the significance level for the +#' regression computation. The default value is 0.05. #'@param ncores An integer indicating the number of cores to use for parallel #' computation. The default value is NULL. #' @@ -100,8 +102,8 @@ Corr <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', comp_dim = NULL, limits = NULL, method = 'pearson', memb_dim = NULL, memb = TRUE, - pval = TRUE, conf = TRUE, - conf.lev = 0.95, ncores = NULL) { + pval = TRUE, conf = TRUE, sign = FALSE, + alpha = 0.05, ncores = NULL) { # Check inputs ## exp and obs (1) @@ -185,9 +187,13 @@ Corr <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', if (!is.logical(conf) | length(conf) > 1) { stop("Parameter 'conf' must be one logical value.") } - ## conf.lev - if (!is.numeric(conf.lev) | conf.lev < 0 | conf.lev > 1 | length(conf.lev) > 1) { - stop("Parameter 'conf.lev' must be a numeric number between 0 and 1.") + ## sign + if (!is.logical(sign) | length(sign) > 1) { + stop("Parameter 'sign' must be one logical value.") + } + ## alpha + if (!is.numeric(alpha) | alpha < 0 | alpha > 1 | length(alpha) > 1) { + stop("Parameter 'alpha' must be a numeric number between 0 and 1.") } ## ncores if (!is.null(ncores)) { @@ -259,14 +265,17 @@ Corr <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', fun = .Corr, dat_dim = dat_dim, memb_dim = memb_dim, time_dim = time_dim, method = method, - pval = pval, conf = conf, conf.lev = conf.lev, ncores_input = ncores, + pval = pval, conf = conf, sign = sign, alpha = alpha, + ncores_input = ncores, ncores = ncores) return(res) } -.Corr <- function(exp, obs, dat_dim = 'dataset', memb_dim = 'member', time_dim = 'sdate', method = 'pearson', - conf = TRUE, pval = TRUE, conf.lev = 0.95, ncores_input = NULL) { +.Corr <- function(exp, obs, dat_dim = 'dataset', memb_dim = 'member', + time_dim = 'sdate', method = 'pearson', + conf = TRUE, pval = TRUE, sign = FALSE, alpha = 0.05, + ncores_input = NULL) { if (is.null(memb_dim)) { if (is.null(dat_dim)) { # exp: [sdate] @@ -372,7 +381,7 @@ Corr <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', # } # } - if (pval | conf) { + if (pval || conf || sign) { if (method == "kendall" | method == "spearman") { if (!is.null(dat_dim) | !is.null(memb_dim)) { tmp <- apply(obs, c(1:length(dim(obs)))[-1], rank) # for memb_dim = NULL, 2; for memb_dim, c(2, 3) @@ -406,13 +415,14 @@ Corr <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', #############old################# #This doesn't return error but it's diff from cor.test() when method is spearman and kendall - if (pval) { + if (pval || sign) { t <-sqrt(CORR * CORR * (eno_expand - 2) / (1 - (CORR ^ 2))) p.val <- pt(t, eno_expand - 2, lower.tail = FALSE) + if (sign) signif <- p.val <= alpha } ################################### if (conf) { - conf.lower <- (1 - conf.lev) / 2 + conf.lower <- (1 - alpha) / 2 conf.upper <- 1 - conf.lower conflow <- tanh(atanh(CORR) + qnorm(conf.lower) / sqrt(eno_expand - 3)) confhigh <- tanh(atanh(CORR) + qnorm(conf.upper) / sqrt(eno_expand - 3)) @@ -433,16 +443,15 @@ Corr <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', ################################### - if (pval & conf) { - res <- list(corr = CORR, p.val = p.val, - conf.lower = conflow, conf.upper = confhigh) - } else if (pval & !conf) { - res <- list(corr = CORR, p.val = p.val) - } else if (!pval & conf) { - res <- list(corr = CORR, - conf.lower = conflow, conf.upper = confhigh) - } else { - res <- list(corr = CORR) + res <- list(corr = CORR) + if (pval) { + res <- c(res, list(p.val = p.val)) + } + if (conf) { + res <- c(res, list(conf.lower = conflow, conf.upper = confhigh)) + } + if (sign) { + res <- c(res, list(sign = signif)) } return(res) -- GitLab From 13d802653e185c6fa9d3a4b59e406596e36ca0ec Mon Sep 17 00:00:00 2001 From: Victoria Agudetse Roures Date: Thu, 17 Nov 2022 12:52:22 +0100 Subject: [PATCH 08/59] Fix computation of confidence level (alpha = 1 - conf.lev) --- R/Corr.R | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/R/Corr.R b/R/Corr.R index 1cee56d..01237a1 100644 --- a/R/Corr.R +++ b/R/Corr.R @@ -422,7 +422,7 @@ Corr <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', } ################################### if (conf) { - conf.lower <- (1 - alpha) / 2 + conf.lower <- alpha / 2 conf.upper <- 1 - conf.lower conflow <- tanh(atanh(CORR) + qnorm(conf.lower) / sqrt(eno_expand - 3)) confhigh <- tanh(atanh(CORR) + qnorm(conf.upper) / sqrt(eno_expand - 3)) -- GitLab From 956dc25405fc035659ca9d621956e40a28ad2c53 Mon Sep 17 00:00:00 2001 From: aho Date: Thu, 17 Nov 2022 17:51:02 +0100 Subject: [PATCH 09/59] Refine doc and add unit tests --- R/Corr.R | 32 ++++++++++++++++++-------------- man/Corr.Rd | 20 ++++++++++++++------ tests/testthat/test-Corr.R | 35 ++++++++++++++++++++++++++++++++--- 3 files changed, 64 insertions(+), 23 deletions(-) diff --git a/R/Corr.R b/R/Corr.R index 01237a1..c95b103 100644 --- a/R/Corr.R +++ b/R/Corr.R @@ -38,14 +38,15 @@ #'@param memb A logical value indicating whether to remain 'memb_dim' dimension #' (TRUE) or do ensemble mean over 'memb_dim' (FALSE). Only functional when #' 'memb_dim' is not NULL. The default value is TRUE. -#'@param pval A logical value indicating whether to compute or not the p-value +#'@param pval A logical value indicating whether to return or not the p-value #' of the test Ho: Corr = 0. The default value is TRUE. -#'@param conf A logical value indicating whether to retrieve the confidence -#' intervals or not. The default value is TRUE. +#'@param conf A logical value indicating whether to return or not the confidence +#' intervals. The default value is TRUE. #'@param sign A logical value indicating whether to retrieve the statistical -#' significance of the test Ho: Corr = 0. The default value is FALSE. -#'@param alpha A numeric indicating the significance level for the -#' regression computation. The default value is 0.05. +#' significance of the test Ho: Corr = 0 based on 'alpha'. The default value is +#' FALSE. +#'@param alpha A numeric indicating the significance level for the statistical +#' significance test. The default value is 0.05. #'@param ncores An integer indicating the number of cores to use for parallel #' computation. The default value is NULL. #' @@ -70,6 +71,9 @@ #'\item{$conf.upper}{ #' The upper confidence interval. Only present if \code{conf = TRUE}. #'} +#'\item{$sign}{ +#' The statistical significance. Only present if \code{sign = TRUE}. +#'} #' #'@examples #'# Case 1: Load sample data as in Load() example: @@ -266,7 +270,6 @@ Corr <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', dat_dim = dat_dim, memb_dim = memb_dim, time_dim = time_dim, method = method, pval = pval, conf = conf, sign = sign, alpha = alpha, - ncores_input = ncores, ncores = ncores) return(res) @@ -274,8 +277,7 @@ Corr <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', .Corr <- function(exp, obs, dat_dim = 'dataset', memb_dim = 'member', time_dim = 'sdate', method = 'pearson', - conf = TRUE, pval = TRUE, sign = FALSE, alpha = 0.05, - ncores_input = NULL) { + conf = TRUE, pval = TRUE, sign = FALSE, alpha = 0.05) { if (is.null(memb_dim)) { if (is.null(dat_dim)) { # exp: [sdate] @@ -386,15 +388,15 @@ Corr <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', if (!is.null(dat_dim) | !is.null(memb_dim)) { tmp <- apply(obs, c(1:length(dim(obs)))[-1], rank) # for memb_dim = NULL, 2; for memb_dim, c(2, 3) names(dim(tmp))[1] <- time_dim - eno <- Eno(tmp, time_dim, ncores = ncores_input) + eno <- Eno(tmp, time_dim) } else { tmp <- rank(obs) tmp <- array(tmp) names(dim(tmp)) <- time_dim - eno <- Eno(tmp, time_dim, ncores = ncores_input) + eno <- Eno(tmp, time_dim) } } else if (method == "pearson") { - eno <- Eno(obs, time_dim, ncores = ncores_input) + eno <- Eno(obs, time_dim) } if (is.null(memb_dim)) { @@ -416,16 +418,18 @@ Corr <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', #############old################# #This doesn't return error but it's diff from cor.test() when method is spearman and kendall if (pval || sign) { - t <-sqrt(CORR * CORR * (eno_expand - 2) / (1 - (CORR ^ 2))) + t <- sqrt(CORR * CORR * (eno_expand - 2) / (1 - (CORR ^ 2))) p.val <- pt(t, eno_expand - 2, lower.tail = FALSE) - if (sign) signif <- p.val <= alpha + if (sign) signif <- !is.na(p.val) & p.val <= alpha } ################################### if (conf) { conf.lower <- alpha / 2 conf.upper <- 1 - conf.lower + suppressWarnings({ conflow <- tanh(atanh(CORR) + qnorm(conf.lower) / sqrt(eno_expand - 3)) confhigh <- tanh(atanh(CORR) + qnorm(conf.upper) / sqrt(eno_expand - 3)) + }) } ################################### diff --git a/man/Corr.Rd b/man/Corr.Rd index 4cbd098..10bdf71 100644 --- a/man/Corr.Rd +++ b/man/Corr.Rd @@ -16,7 +16,8 @@ Corr( memb = TRUE, pval = TRUE, conf = TRUE, - conf.lev = 0.95, + sign = FALSE, + alpha = 0.05, ncores = NULL ) } @@ -52,14 +53,18 @@ member dimension, set NULL. The default value is NULL.} (TRUE) or do ensemble mean over 'memb_dim' (FALSE). Only functional when 'memb_dim' is not NULL. The default value is TRUE.} -\item{pval}{A logical value indicating whether to compute or not the p-value +\item{pval}{A logical value indicating whether to return or not the p-value of the test Ho: Corr = 0. The default value is TRUE.} -\item{conf}{A logical value indicating whether to retrieve the confidence -intervals or not. The default value is TRUE.} +\item{conf}{A logical value indicating whether to return or not the confidence +intervals. The default value is TRUE.} -\item{conf.lev}{A numeric indicating the confidence level for the -regression computation. The default value is 0.95.} +\item{sign}{A logical value indicating whether to retrieve the statistical +significance of the test Ho: Corr = 0 based on 'alpha'. The default value is +FALSE.} + +\item{alpha}{A numeric indicating the significance level for the statistical +significance test. The default value is 0.05.} \item{ncores}{An integer indicating the number of cores to use for parallel computation. The default value is NULL.} @@ -85,6 +90,9 @@ nobs are omitted. exp_memb is the number of member in experiment (i.e., \item{$conf.upper}{ The upper confidence interval. Only present if \code{conf = TRUE}. } +\item{$sign}{ + The statistical significance. Only present if \code{sign = TRUE}. +} } \description{ Calculate the correlation coefficient (Pearson, Kendall or Spearman) for diff --git a/tests/testthat/test-Corr.R b/tests/testthat/test-Corr.R index 6e3c016..ef013ca 100644 --- a/tests/testthat/test-Corr.R +++ b/tests/testthat/test-Corr.R @@ -22,6 +22,11 @@ context("s2dv::Corr tests") obs2 <- array(rnorm(30), dim = c(member = 1, dataset = 1, sdate = 5, lat = 2, lon = 3)) + exp2_2 <- exp2 + exp2_2[1, 1, 1, 1, 1] <- NA + obs2_2 <- obs2 + obs2_2[1, 1, 1:3, 1, 1] <- NA + # dat3: memb_dim = member, obs has multiple memb set.seed(1) exp3 <- array(rnorm(180), dim = c(member = 3, dataset = 2, sdate = 5, @@ -121,8 +126,8 @@ test_that("1. Input checks", { "integers smaller than the length of paramter 'comp_dim'.") ) expect_error( - Corr(exp1, obs1, conf.lev = -1), - "Parameter 'conf.lev' must be a numeric number between 0 and 1." + Corr(exp1, obs1, alpha = -1), + "Parameter 'alpha' must be a numeric number between 0 and 1." ) expect_error( Corr(exp1, obs1, method = 1), @@ -207,7 +212,7 @@ suppressWarnings( ) suppressWarnings( expect_equal( - min(Corr(exp1, obs1, conf.lev = 0.99)$conf.upper, na.rm = TRUE), + min(Corr(exp1, obs1, alpha = 0.01)$conf.upper, na.rm = TRUE), 0.2747904, tolerance = 0.0001 ) @@ -253,6 +258,10 @@ test_that("3. Output checks: dat2", { dim(Corr(exp2, obs2, memb_dim = 'member')$corr), c(nexp = 2, nobs = 1, exp_memb = 3, obs_memb = 1, lat = 2, lon = 3) ) + expect_equal( + dim(Corr(exp2, obs2, memb_dim = 'member')$corr), + dim(Corr(exp2, obs2, memb_dim = 'member')$p) + ) expect_equal( names(Corr(exp2, obs2, memb_dim = 'member')), c("corr", "p.val", "conf.lower", "conf.upper") @@ -269,6 +278,11 @@ test_that("3. Output checks: dat2", { names(Corr(exp2, obs2, memb_dim = 'member', pval = FALSE)), c("corr", "conf.lower", "conf.upper") ) + expect_equal( + names(Corr(exp2, obs2, memb_dim = 'member', pval = FALSE, sign = T)), + c("corr", "conf.lower", "conf.upper", "sign") + ) + expect_equal( mean(Corr(exp2, obs2, memb_dim = 'member', pval = FALSE, conf = FALSE)$corr), 0.01645575, @@ -299,6 +313,10 @@ test_that("3. Output checks: dat2", { c(-0.9500121, -0.9547642, -0.9883400, -0.8817478, -0.6879465), tolerance = 0.0001 ) + expect_equal( + which(Corr(exp2, obs2, memb_dim = 'member', pval = FALSE, conf = F, sign = T)$sign), + c(3, 6, 12, 17, 23, 34) + ) # ensemble mean expect_equal( @@ -336,7 +354,18 @@ test_that("3. Output checks: dat2", { tolerance = 0.0001 ) + # exp2_2 + expect_equal( + which(is.na(Corr(exp2_2, obs2_2, memb_dim = 'member', memb = FALSE, pval = FALSE)$corr)), + 1:2 + ) + expect_equal( + Corr(exp2_2, obs2_2, memb_dim = 'member', memb = FALSE, pval = FALSE)$corr[-c(1:2)], + Corr(exp2, obs2, memb_dim = 'member', memb = FALSE, pval = FALSE)$corr[-c(1:2)] + ) + }) + ############################################## test_that("4. Output checks: dat3", { # individual member -- GitLab From 49a1e3495e361431c1ed25c22c3ba833cc0d5009 Mon Sep 17 00:00:00 2001 From: aho Date: Tue, 29 Nov 2022 18:39:36 +0100 Subject: [PATCH 10/59] Bugfix for p.val when output is NA; it should return one NA only --- R/Trend.R | 6 +++-- man/Trend.Rd | 4 +++- tests/testthat/test-Trend.R | 46 ++++++++++++++++++++++++++++++++++--- 3 files changed, 50 insertions(+), 6 deletions(-) diff --git a/R/Trend.R b/R/Trend.R index 1f714a6..d709101 100644 --- a/R/Trend.R +++ b/R/Trend.R @@ -50,7 +50,9 @@ #' \code{conf = TRUE}. #'} #'\item{$p.val}{ -#' The p-value calculated by anova(). Only present if \code{pval = TRUE}. +#' A numeric array of p-value calculated by anova(). The first dimension +#' 'stats' is 1, followed by the same dimensions as parameter 'data' except +#' the 'time_dim' dimension. Only present if \code{pval = TRUE}. #'} #'\item{$detrended}{ #' A numeric array with the same dimensions as paramter 'data', containing the @@ -188,7 +190,7 @@ Trend <- function(data, time_dim = 'ftime', interval = 1, polydeg = 1, } if (pval) { - p.val <- rep(NA, polydeg + 1) + p.val <- as.array(NA) } } diff --git a/man/Trend.Rd b/man/Trend.Rd index d283ee6..7623c36 100644 --- a/man/Trend.Rd +++ b/man/Trend.Rd @@ -66,7 +66,9 @@ A list containing: \code{conf = TRUE}. } \item{$p.val}{ - The p-value calculated by anova(). Only present if \code{pval = TRUE}. + A numeric array of p-value calculated by anova(). The first dimension + 'stats' is 1, followed by the same dimensions as parameter 'data' except + the 'time_dim' dimension. Only present if \code{pval = TRUE}. } \item{$detrended}{ A numeric array with the same dimensions as paramter 'data', containing the diff --git a/tests/testthat/test-Trend.R b/tests/testthat/test-Trend.R index 49a9982..07da6ce 100644 --- a/tests/testthat/test-Trend.R +++ b/tests/testthat/test-Trend.R @@ -112,6 +112,22 @@ test_that("2. Output checks: dat1", { 0.1153846, tolerance = 0.001 ) + expect_equal( + dim(Trend(dat1)$trend), + c(stats = 2, dat = 1, sdate = 2) + ) + expect_equal( + dim(Trend(dat1)$p), + c(stats = 1, dat = 1, sdate = 2) + ) + expect_equal( + dim(Trend(dat1)$detrend), + c(ftime = 13, dat = 1, sdate = 2) + ) + expect_equal( + dim(Trend(dat1, polydeg = 3)$trend), + c(stats = 4, dat = 1, sdate = 2) + ) }) @@ -176,8 +192,32 @@ test_that("5. Output checks: dat4", { as.numeric(rep(NA, 5)) ) expect_equal( - Trend(dat4)$p.val[, 1, 1, 1], - c(NA, 0.01800594), - tolerance = 0.0001 + dim(Trend(dat4)$p.val), + c(stats = 1, lat = 2, lon = 3, lev = 2) + ) + expect_equal( + is.na(Trend(dat4)$p.val[, 1, 1, 1]), + TRUE ) + expect_equal( + as.vector(Trend(dat4)$trend[1, 2, , ]), + as.vector(Trend(dat3)$trend[1, 2, , ]) + ) + expect_equal( + as.vector(Trend(dat4)$p.val[1, 2, , ]), + as.vector(Trend(dat3)$p.val[1, 2, , ]) + ) + expect_equal( + as.vector(Trend(dat4)$conf.l[1, 2, , ]), + as.vector(Trend(dat3)$conf.l[1, 2, , ]) + ) + expect_equal( + as.vector(Trend(dat4)$conf.u[1, 2, , ]), + as.vector(Trend(dat3)$conf.u[1, 2, , ]) + ) + expect_equal( + as.vector(Trend(dat4)$de[1, 2, , ]), + as.vector(Trend(dat3)$de[1, 2, , ]) + ) + }) -- GitLab From bd9171a11e2ecb267571b1101e74d39f46b3f1d6 Mon Sep 17 00:00:00 2001 From: aho Date: Tue, 29 Nov 2022 18:40:19 +0100 Subject: [PATCH 11/59] Don't ignore unit test --- .Rbuildignore | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.Rbuildignore b/.Rbuildignore index 6008b57..4212858 100644 --- a/.Rbuildignore +++ b/.Rbuildignore @@ -10,7 +10,7 @@ README\.md$ vignettes .gitlab-ci.yml # unit tests should be ignored when building the package for CRAN -^tests$ +#^tests$ # CDO is not in windbuilder, so we can test the unit tests by winbuilder # but test-CDORemap.R and test-Load.R needs to be hidden #tests/testthat/test-CDORemap.R -- GitLab From 9386a9cbd635e744228970c88b001436b924b5b0 Mon Sep 17 00:00:00 2001 From: aho Date: Tue, 20 Dec 2022 11:44:27 +0100 Subject: [PATCH 12/59] Add sanity checks to prevent exceeding month selection --- R/Season.R | 25 ++++++++++++++++++------- man/Season.Rd | 17 +++++++++-------- tests/testthat/test-Season.R | 20 ++++++++++++++++++++ 3 files changed, 47 insertions(+), 15 deletions(-) diff --git a/R/Season.R b/R/Season.R index 086dc52..152ebbe 100644 --- a/R/Season.R +++ b/R/Season.R @@ -1,4 +1,4 @@ -#'Compute seasonal mean +#'Compute seasonal mean or other calculations #' #'Compute the seasonal mean (or other methods) on monthly time series along #'one dimension of a named multi-dimensional arrays. Partial season is not @@ -6,13 +6,14 @@ #' #'@param data A named numeric array with at least one dimension 'time_dim'. #'@param time_dim A character string indicating the name of dimension along -#' which the seasonal means are computed. The default value is 'ftime'. +#' which the seasonal mean or other calculations are computed. The default +#' value is 'ftime'. #'@param monini An integer indicating what the first month of the time series is. #' It can be from 1 to 12. -#'@param moninf An integer indicating the starting month of the seasonal mean. +#'@param moninf An integer indicating the starting month of the seasonal +#' calculation. It can be from 1 to 12. +#'@param monsup An integer indicating the end month of the seasonal calculation. #' It can be from 1 to 12. -#'@param monsup An integer indicating the end month of the seasonal mean. It -#' can be from 1 to 12. #'@param method An R function to be applied for seasonal calculation. For #' example, 'sum' can be used for total precipitation. The default value is mean. #'@param na.rm A logical value indicating whether to remove NA values along @@ -26,12 +27,12 @@ #' #'@examples #'set.seed(1) -#'dat1 <- array(rnorm(144*3), dim = c(member = 2, sdate = 2, ftime = 12*3, lon = 3)) +#'dat1 <- array(rnorm(144 * 3), dim = c(member = 2, sdate = 2, ftime = 12*3, lon = 3)) #'res <- Season(data = dat1, monini = 1, moninf = 1, monsup = 2) #'res <- Season(data = dat1, monini = 10, moninf = 12, monsup = 2) #'dat2 <- dat1 #'set.seed(2) -#'na <- floor(runif(30, min = 1, max = 144*3)) +#'na <- floor(runif(30, min = 1, max = 144 * 3)) #'dat2[na] <- NA #'res <- Season(data = dat2, monini = 3, moninf = 1, monsup = 2) #'res <- Season(data = dat2, monini = 3, moninf = 1, monsup = 2, na.rm = FALSE) @@ -86,6 +87,16 @@ Season <- function(data, time_dim = 'ftime', monini, moninf, monsup, stop("Parameter 'monsup' must be a positive integer between 1 and 12.") } } + ## time_dim, monini, moninf, monsup + mon_gap <- ifelse(moninf >= monini, moninf - monini, moninf + 12 - monini) + if ((mon_gap + 1) > dim(data)[time_dim]) { + stop("Parameter 'moninf' is out of the range because 'monini' is ", monini, + " and time dimenision length is ", as.numeric(dim(data)[time_dim]), ".") + } + mon_diff <- ifelse(monsup > moninf, monsup - moninf, monsup + 12 - moninf) + if ((mon_gap + mon_diff + 1) > dim(data)[time_dim]) { + stop("The chosen month length exceeds the time dimension of 'data'.") + } ## method if (!is.function(method)) { stop("Parameter 'method' should be an existing R function, e.g., mean or sum.") diff --git a/man/Season.Rd b/man/Season.Rd index 3c1e3ff..fccd9ff 100644 --- a/man/Season.Rd +++ b/man/Season.Rd @@ -2,7 +2,7 @@ % Please edit documentation in R/Season.R \name{Season} \alias{Season} -\title{Compute seasonal mean} +\title{Compute seasonal mean or other calculations} \usage{ Season( data, @@ -19,16 +19,17 @@ Season( \item{data}{A named numeric array with at least one dimension 'time_dim'.} \item{time_dim}{A character string indicating the name of dimension along -which the seasonal means are computed. The default value is 'ftime'.} +which the seasonal mean or other calculations are computed. The default +value is 'ftime'.} \item{monini}{An integer indicating what the first month of the time series is. It can be from 1 to 12.} -\item{moninf}{An integer indicating the starting month of the seasonal mean. -It can be from 1 to 12.} +\item{moninf}{An integer indicating the starting month of the seasonal +calculation. It can be from 1 to 12.} -\item{monsup}{An integer indicating the end month of the seasonal mean. It -can be from 1 to 12.} +\item{monsup}{An integer indicating the end month of the seasonal calculation. +It can be from 1 to 12.} \item{method}{An R function to be applied for seasonal calculation. For example, 'sum' can be used for total precipitation. The default value is mean.} @@ -51,12 +52,12 @@ accounted. } \examples{ set.seed(1) -dat1 <- array(rnorm(144*3), dim = c(member = 2, sdate = 2, ftime = 12*3, lon = 3)) +dat1 <- array(rnorm(144 * 3), dim = c(member = 2, sdate = 2, ftime = 12*3, lon = 3)) res <- Season(data = dat1, monini = 1, moninf = 1, monsup = 2) res <- Season(data = dat1, monini = 10, moninf = 12, monsup = 2) dat2 <- dat1 set.seed(2) -na <- floor(runif(30, min = 1, max = 144*3)) +na <- floor(runif(30, min = 1, max = 144 * 3)) dat2[na] <- NA res <- Season(data = dat2, monini = 3, moninf = 1, monsup = 2) res <- Season(data = dat2, monini = 3, moninf = 1, monsup = 2, na.rm = FALSE) diff --git a/tests/testthat/test-Season.R b/tests/testthat/test-Season.R index 0b009a6..f9bfc43 100644 --- a/tests/testthat/test-Season.R +++ b/tests/testthat/test-Season.R @@ -15,6 +15,10 @@ context("s2dv::Season tests") set.seed(1) dat3 <- array(rnorm(12), dim = c(ftime = 12)) + # dat4 + set.seed(1) + dat4 <- array(rnorm(16), dim = c(sdate = 2, ftime = 8)) + ############################################## test_that("1. Input checks", { @@ -54,6 +58,22 @@ test_that("1. Input checks", { Season(dat1, monini = 1, moninf = 1, monsup = 'Jan'), "Parameter 'monsup' must be a positive integer between 1 and 12." ) + expect_error( + Season(dat4, monini = 1, moninf = 9, monsup = 10), + "Parameter 'moninf' is out of the range because 'monini' is 1 and time dimenision length is 8." + ) + expect_error( + Season(dat4, monini = 11, moninf = 9, monsup = 10), + "Parameter 'moninf' is out of the range because 'monini' is 11 and time dimenision length is 8." + ) + expect_error( + Season(dat4, monini = 1, moninf = 2, monsup = 9), + "The chosen month length exceeds the time dimension of 'data'." + ) + expect_error( + Season(dat4, monini = 11, moninf = 12, monsup = 7), + "The chosen month length exceeds the time dimension of 'data'." + ) expect_error( Season(dat1, monini = 1, moninf = 1, monsup = 2, method = 'mean'), "Parameter 'method' should be an existing R function, e.g., mean or sum." -- GitLab From 21730041c24468150f484eee57d77fee6e46e7c7 Mon Sep 17 00:00:00 2001 From: aho Date: Thu, 22 Dec 2022 05:36:55 +0100 Subject: [PATCH 13/59] Correct check when moninf = monsup --- R/Season.R | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/R/Season.R b/R/Season.R index 152ebbe..1425d59 100644 --- a/R/Season.R +++ b/R/Season.R @@ -93,7 +93,7 @@ Season <- function(data, time_dim = 'ftime', monini, moninf, monsup, stop("Parameter 'moninf' is out of the range because 'monini' is ", monini, " and time dimenision length is ", as.numeric(dim(data)[time_dim]), ".") } - mon_diff <- ifelse(monsup > moninf, monsup - moninf, monsup + 12 - moninf) + mon_diff <- ifelse(monsup >= moninf, monsup - moninf, monsup + 12 - moninf) if ((mon_gap + mon_diff + 1) > dim(data)[time_dim]) { stop("The chosen month length exceeds the time dimension of 'data'.") } -- GitLab From 9b96f58464b9412a46304b60e5785749d2595b29 Mon Sep 17 00:00:00 2001 From: aho Date: Tue, 27 Dec 2022 12:15:45 +0100 Subject: [PATCH 14/59] Add randomwalk test; parameter ''ref', 'sig_method' and 'memb_dim' --- R/RMSSS.R | 257 ++++++++++++++++++++++++++++-------- man/RMSSS.Rd | 20 ++- tests/testthat/test-RMSSS.R | 86 +++++++++++- 3 files changed, 305 insertions(+), 58 deletions(-) diff --git a/R/RMSSS.R b/R/RMSSS.R index 9c47da4..b8f411a 100644 --- a/R/RMSSS.R +++ b/R/RMSSS.R @@ -11,7 +11,7 @@ #'The RMSSS are computed along the time_dim dimension which should correspond #'to the start date dimension.\cr #'The p-value and significance test are optionally provided by an one-sided -#'Fisher test.\cr +#'Fisher test or Random Walk test.\cr #' #'@param exp A named numeric array of experimental data which contains at least #' two dimensions for dat_dim and time_dim. It can also be a vector with the @@ -23,10 +23,20 @@ #' dimension can be different. It can also be a vector with the same length as #' 'exp', then the vector will automatically be 'time_dim' and 'dat_dim' will #' be 1. +#'@param ref A named numerical array of the reference forecast data with at +#' least time dimension. The dimensions must be the same as 'exp' except +#' 'memb_dim' and 'dat_dim'. If there is only one reference dataset, it should +#' not have dataset dimension. If there is corresponding reference for each +#' experiement, the dataset dimension must have the same length as in 'exp'. If +#' 'ref' is NULL, the climatological forecast is used as reference forecast. +#' The default value is NULL. #'@param dat_dim A character string indicating the name of dataset (nobs/nexp) #' dimension. The default value is 'dataset'. #'@param time_dim A character string indicating the name of dimension along #' which the RMSSS are computed. The default value is 'sdate'. +#'@param memb_dim A character string indicating the name of the member dimension +#' to compute the ensemble mean; it should be set to NULL if the parameter 'exp' +#' and 'ref' are already the ensemble mean. The default value is NULL. #'@param pval A logical value indicating whether to compute or not the p-value #' of the test Ho: RMSSS = 0. The default value is TRUE. #'@param sign A logical value indicating whether to compute or not the @@ -34,6 +44,8 @@ #' FALSE. #'@param alpha A numeric of the significance level to be used in the #' statistical significance test. The default value is 0.05. +#'@param sig_method A character string indicating the significance method. The +#' options are "one-sided Fisher" (default) and "Random Walk". #'@param ncores An integer indicating the number of cores to use for parallel #' computation. The default value is NULL. #' @@ -66,8 +78,9 @@ #'@import multiApply #'@importFrom stats pf #'@export -RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', - pval = TRUE, sign = FALSE, alpha = 0.05, ncores = NULL) { +RMSSS <- function(exp, obs, ref = NULL, time_dim = 'sdate', dat_dim = 'dataset', + memb_dim = NULL, pval = TRUE, sign = FALSE, alpha = 0.05, + sig_method = 'one-sided Fisher', ncores = NULL) { # Check inputs ## exp and obs (1) @@ -99,6 +112,14 @@ RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', !all(names(dim(obs)) %in% names(dim(exp)))) { stop("Parameter 'exp' and 'obs' must have same dimension name.") } + if (!is.null(ref)) { + if (!is.array(ref) | !is.numeric(ref)) + stop("Parameter 'ref' must be a numeric array.") + if (any(is.null(names(dim(ref))))| any(nchar(names(dim(ref))) == 0)) { + stop("Parameter 'ref' must have dimension names.") + } + } + ## time_dim if (!is.character(time_dim) | length(time_dim) > 1) { stop("Parameter 'time_dim' must be a character string.") @@ -116,6 +137,23 @@ RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', " Set it as NULL if there is no dataset dimension.") } } + ## memb_dim + if (!is.null(memb_dim)) { + if (!is.character(memb_dim) | length(memb_dim) > 1) { + stop("Parameter 'memb_dim' must be a character string.") + } + if (!memb_dim %in% names(dim(exp))) { + stop("Parameter 'memb_dim' is not found in 'exp' dimension.") + } + if (memb_dim %in% names(dim(obs))) { + if (identical(as.numeric(dim(obs)[memb_dim]), 1)) { + obs <- ClimProjDiags::Subset(x = obs, along = memb_dim, indices = 1, drop = 'selected') + } else { + stop("Not implemented for observations with members ('obs' can have 'memb_dim', ", + "but it should be of length = 1).") + } + } + } ## pval if (!is.logical(pval) | length(pval) > 1) { stop("Parameter 'pval' must be one logical value.") @@ -128,6 +166,14 @@ RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', if (!is.numeric(alpha) | length(alpha) > 1) { stop("Parameter 'alpha' must be one numeric value.") } + ## sig_method + if (length(sig_method) != 1 | !any(sig_method %in% c('one-sided Fisher', 'Random Walk'))) { + stop("Parameter 'sig_meothd' must be one of 'one-sided Fisher' or 'Random Walk'.") + } + if (sig_method == "Random Walk" & pval == T) { + warning("p-value cannot be calculated by significance method 'Random Walk'.") + pval <- FALSE + } ## ncores if (!is.null(ncores)) { if (!is.numeric(ncores) | ncores %% 1 != 0 | ncores <= 0 | @@ -138,66 +184,162 @@ RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', ## exp and obs (2) name_exp <- sort(names(dim(exp))) name_obs <- sort(names(dim(obs))) + if (!is.null(memb_dim)) { + name_exp <- name_exp[-which(name_exp == memb_dim)] + } if (!is.null(dat_dim)) { name_exp <- name_exp[-which(name_exp == dat_dim)] name_obs <- name_obs[-which(name_obs == dat_dim)] } if(!all(dim(exp)[name_exp] == dim(obs)[name_obs])) { stop(paste0("Parameter 'exp' and 'obs' must have same length of ", - "all dimension except 'dat_dim'.")) + "all dimension except 'memb_dim' and 'dat_dim'.")) + } + if (!is.null(ref)) { + name_ref <- sort(names(dim(ref))) + if (!is.null(memb_dim) && memb_dim %in% name_ref) { + name_ref <- name_ref[-which(name_ref == memb_dim)] + } + if (!is.null(dat_dim)) { + if (dat_dim %in% name_ref) { + if (!identical(dim(exp)[dat_dim], dim(ref)[dat_dim])) { + stop(paste0("If parameter 'ref' has dataset dimension, it must be ", + "equal to dataset dimension of 'exp'.")) + } + name_ref <- name_ref[-which(name_ref == dat_dim)] + } + } + if (!identical(length(name_exp), length(name_ref)) | + !identical(dim(exp)[name_exp], dim(ref)[name_ref])) { + stop(paste0("Parameter 'exp' and 'ref' must have the same length of ", + "all dimensions except 'memb_dim' and 'dat_dim' if there is ", + "only one reference dataset.")) + } } + if (dim(exp)[time_dim] <= 2) { stop("The length of time_dim must be more than 2 to compute RMSSS.") } ############################### - # Sort dimension - name_exp <- names(dim(exp)) - name_obs <- names(dim(obs)) - order_obs <- match(name_exp, name_obs) - obs <- Reorder(obs, order_obs) +# # Sort dimension +# name_exp <- names(dim(exp)) +# name_obs <- names(dim(obs)) +# order_obs <- match(name_exp, name_obs) +# obs <- Reorder(obs, order_obs) + ############################### + ## Ensemble mean + if (!is.null(memb_dim)) { + exp <- MeanDims(exp, memb_dim, na.rm = T) + if (!is.null(ref) & memb_dim %in% names(dim(ref))) { + ref <- MeanDims(ref, memb_dim, na.rm = T) + } + } + ############################### # Calculate RMSSS + + if (!is.null(ref)) { # use "ref" as reference forecast + if (!is.null(dat_dim) && dat_dim %in% names(dim(ref))) { + target_dims_ref <- c(time_dim, dat_dim) + } else { + target_dims_ref <- c(time_dim) + } + data <- list(exp = exp, obs = obs, ref = ref) + target_dims = list(exp = c(time_dim, dat_dim), + obs = c(time_dim, dat_dim), + ref = target_dims_ref) + } else { + data <- list(exp = exp, obs = obs) + target_dims = list(exp = c(time_dim, dat_dim), + obs = c(time_dim, dat_dim)) + } - res <- Apply(list(exp, obs), - target_dims = list(c(time_dim, dat_dim), - c(time_dim, dat_dim)), + res <- Apply(data, + target_dims = target_dims, fun = .RMSSS, time_dim = time_dim, dat_dim = dat_dim, pval = pval, sign = sign, alpha = alpha, + sig_method = sig_method, ncores = ncores) return(res) } -.RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', pval = TRUE, - sign = FALSE, alpha = 0.05) { +.RMSSS <- function(exp, obs, ref = NULL, time_dim = 'sdate', dat_dim = 'dataset', pval = TRUE, + sign = FALSE, alpha = 0.05, sig_method = 'one-sided Fisher') { # exp: [sdate, (dat)] # obs: [sdate, (dat)] + # ref: [sdate, (dat)] or NULL if (is.null(dat_dim)) { # exp: [sdate] # obs: [sdate] nexp <- 1 nobs <- 1 - dim(exp) <- c(dim(exp), nexp = nexp) - dim(obs) <- c(dim(obs), nobs = nobs) + # Add dat dim back temporarily + dim(exp) <- c(dim(exp), dat = 1) + dim(obs) <- c(dim(obs), dat = 1) + if (!is.null(ref)) { + dim(ref) <- c(dim(ref), dat = 1) + } +# ref_dat_dim <- FALSE + } else { # exp: [sdate, dat_exp] # obs: [sdate, dat_obs] nexp <- as.numeric(dim(exp)[2]) nobs <- as.numeric(dim(obs)[2]) + if (!is.null(ref)) { + if (dat_dim %in% names(dim(ref))) { + nref <- as.numeric(dim(ref)[2]) + } else { + dim(ref) <- c(dim(ref), dat = 1) + nref <- 1 + } + } } nsdate <- as.numeric(dim(exp)[1]) - - p_val <- array(dim = c(nexp = nexp, nobs = nobs)) + + # RMS of forecast dif1 <- array(dim = c(nsdate, nexp, nobs)) names(dim(dif1)) <- c(time_dim, 'nexp', 'nobs') + for (i in 1:nobs) { + dif1[, , i] <- sapply(1:nexp, function(x) {exp[, x] - obs[, i]}) + } + + rms_exp <- apply(dif1^2, c(2, 3), mean, na.rm = TRUE)^0.5 #array(dim = c(nexp, nobs)) + + # RMS of reference + if (!is.null(ref)) { + dif2 <- array(dim = c(nsdate, nref, nobs)) + names(dim(dif2)) <- c(time_dim, 'nexp', 'nobs') + for (i in 1:nobs) { + dif2[, , i] <- sapply(1:nref, function(x) {ref[, x] - obs[, i]}) + } + rms_ref <- apply(dif2^2, c(2, 3), mean, na.rm = TRUE)^0.5 #array(dim = c(nref, nobs)) + if (nexp != nref) { + # expand rms_ref to nexp (nref is 1) + rms_ref <- array(rms_ref, dim = c(nobs = nobs, nexp = nexp)) + rms_ref <- Reorder(rms_ref, c(2, 1)) + } + } else { + rms_ref <- array(colMeans(obs^2, na.rm = TRUE)^0.5, dim = c(nobs = nobs, nexp = nexp)) +# rms_ref[which(abs(rms_ref) <= (max(abs(rms_ref), na.rm = TRUE) / 1000))] <- max(abs( +# rms_ref), na.rm = TRUE) / 1000 + rms_ref <- Reorder(rms_ref, c(2, 1)) + #rms_ref above: [nexp, nobs] + } + + rmsss <- 1 - rms_exp / rms_ref + +################################################# + # if (conf) { # conflow <- (1 - conf.lev) / 2 # confhigh <- 1 - conflow @@ -205,45 +347,52 @@ RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', # conf_high <- array(dim = c(nexp = nexp, nobs = nobs)) # } - # dif1 - for (i in 1:nobs) { - dif1[, , i] <- sapply(1:nexp, function(x) {exp[, x] - obs[, i]}) - } - - rms1 <- apply(dif1^2, c(2, 3), mean, na.rm = TRUE)^0.5 #array(dim = c(nexp, nobs)) - rms2 <- array(colMeans(obs^2, na.rm = TRUE)^0.5, dim = c(nobs = nobs)) - rms2[which(abs(rms2) <= (max(abs(rms2), na.rm = TRUE) / 1000))] <- max(abs( - rms2), na.rm = TRUE) / 1000 - #rms2 above: [nobs] - rms2 <- array(rms2, dim = c(nobs = nobs, nexp = nexp)) - #rms2 above: [nobs, nexp] - rms2 <- Reorder(rms2, c(2, 1)) - #rms2 above: [nexp, nobs] + if (sig_method == 'one-sided Fisher') { + p_val <- array(dim = c(nexp = nexp, nobs = nobs)) + ## pval and sign + if (pval || sign) { + eno1 <- Eno(dif1, time_dim) + if (is.null(ref)) { + eno2 <- Eno(obs, time_dim) + eno2 <- array(eno2, dim = c(nobs = nobs, nexp = nexp)) + eno2 <- Reorder(eno2, c(2, 1)) + } else { + eno2 <- Eno(dif2, time_dim) + if (nref != nexp) { + eno2 <- array(eno2, dim = c(nobs = nobs, nexp = nexp)) + eno2 <- Reorder(eno2, c(2, 1)) + } + } - # use rms1 and rms2 to calculate rmsss - rmsss <- 1 - rms1/rms2 - - ## pval and sign - if (pval || sign) { - eno1 <- Eno(dif1, time_dim) - eno2 <- Eno(obs, time_dim) - eno2 <- array(eno2, dim = c(nobs = nobs, nexp = nexp)) - eno2 <- Reorder(eno2, c(2, 1)) - } + F.stat <- (eno2 * rms_ref^2 / (eno2 - 1)) / ((eno1 * rms_exp^2 / (eno1- 1))) + tmp <- !is.na(eno1) & !is.na(eno2) & eno1 > 2 & eno2 > 2 + p_val <- 1 - pf(F.stat, eno1 - 1, eno2 - 1) + if (sign) signif <- p_val <= alpha + # If there isn't enough valid data, return NA + p_val[which(!tmp)] <- NA + if (sign) signif[which(!tmp)] <- NA + + # change not enough valid data rmsss to NA + rmsss[which(!tmp)] <- NA + } - # pval - if (pval || sign) { + } else if (sig_method == "Random Walk") { + #TODO: What if ref is NULL? + signif <- array(dim = c(nexp = nexp, nobs = nobs)) + for (i in 1:nexp) { + for (j in 1:nobs) { - F.stat <- (eno2 * rms2^2 / (eno2- 1)) / ((eno1 * rms1^2 / (eno1- 1))) - tmp <- !is.na(eno1) & !is.na(eno2) & eno1 > 2 & eno2 > 2 - p_val <- 1 - pf(F.stat, eno1 - 1, eno2 - 1) - if (sign) signif <- p_val <= alpha - # If there isn't enough valid data, return NA - p_val[which(!tmp)] <- NA - if (sign) signif[which(!tmp)] <- NA - - # change not significant rmsss to NA - rmsss[which(!tmp)] <- NA + # Error + error_exp <- array(data = abs(exp[, i] - obs[, j]), dim = c(time = nsdate)) + if (nref == nexp) { + error_ref <- array(data = abs(ref[, i] - obs[, j]), dim = c(time = nsdate)) + } else { + # nref = 1 + error_ref <- array(data = abs(ref - obs[, j]), dim = c(time = nsdate)) + } + signif[i, j] <- .RandomWalkTest(skill_A = error_exp, skill_B = error_ref)$signif + } + } } ################################### diff --git a/man/RMSSS.Rd b/man/RMSSS.Rd index 05dfb1b..af892cb 100644 --- a/man/RMSSS.Rd +++ b/man/RMSSS.Rd @@ -7,11 +7,14 @@ RMSSS( exp, obs, + ref = NULL, time_dim = "sdate", dat_dim = "dataset", + memb_dim = NULL, pval = TRUE, sign = FALSE, alpha = 0.05, + sig_method = "one-sided Fisher", ncores = NULL ) } @@ -28,12 +31,24 @@ dimension can be different. It can also be a vector with the same length as 'exp', then the vector will automatically be 'time_dim' and 'dat_dim' will be 1.} +\item{ref}{A named numerical array of the reference forecast data with at +least time dimension. The dimensions must be the same as 'exp' except +'memb_dim' and 'dat_dim'. If there is only one reference dataset, it should +not have dataset dimension. If there is corresponding reference for each +experiement, the dataset dimension must have the same length as in 'exp'. If +'ref' is NULL, the climatological forecast is used as reference forecast. +The default value is NULL.} + \item{time_dim}{A character string indicating the name of dimension along which the RMSSS are computed. The default value is 'sdate'.} \item{dat_dim}{A character string indicating the name of dataset (nobs/nexp) dimension. The default value is 'dataset'.} +\item{memb_dim}{A character string indicating the name of the member dimension +to compute the ensemble mean; it should be set to NULL if the parameter 'exp' +and 'ref' are already the ensemble mean. The default value is NULL.} + \item{pval}{A logical value indicating whether to compute or not the p-value of the test Ho: RMSSS = 0. The default value is TRUE.} @@ -44,6 +59,9 @@ FALSE.} \item{alpha}{A numeric of the significance level to be used in the statistical significance test. The default value is 0.05.} +\item{sig_method}{A character string indicating the significance method. The +options are "one-sided Fisher" (default) and "Random Walk".} + \item{ncores}{An integer indicating the number of cores to use for parallel computation. The default value is NULL.} } @@ -77,7 +95,7 @@ of the array.\cr The RMSSS are computed along the time_dim dimension which should correspond to the start date dimension.\cr The p-value and significance test are optionally provided by an one-sided -Fisher test.\cr +Fisher test or Random Walk test.\cr } \examples{ set.seed(1) diff --git a/tests/testthat/test-RMSSS.R b/tests/testthat/test-RMSSS.R index 0a4916e..fa5ca33 100644 --- a/tests/testthat/test-RMSSS.R +++ b/tests/testthat/test-RMSSS.R @@ -6,7 +6,11 @@ context("s2dv::RMSSS tests") exp1 <- array(rnorm(15), dim = c(sdate = 3, dataset = 5)) set.seed(2) obs1 <- array(rnorm(6), dim = c(sdate = 3, dataset = 2)) - + set.seed(3) + ref1_1 <- array(rnorm(15), dim = c(sdate = 3, dataset = 5)) + ref1_2 <- exp1[, 3] + dim(ref1_2) <- c(sdate = 3) + # case 2 set.seed(3) exp2 <- array(rnorm(120), dim = c(time = 10, dat = 1, lon = 3, lat = 2, dataset = 2)) @@ -25,6 +29,15 @@ context("s2dv::RMSSS tests") set.seed(8) obs4 <- array(exp4 + rnorm(60) / 2, dim = dim(exp4)) + # case 5: memb_dim + set.seed(1) + exp5 <- array(rnorm(45), dim = c(sdate = 3, dataset = 5, member = 3)) + set.seed(2) + obs5 <- array(rnorm(3), dim = c(sdate = 3, dataset = 1, member = 1)) + set.seed(3) + ref5 <- array(rnorm(6), dim = c(sdate = 3, member = 2)) + + ############################################## test_that("1. Input checks", { @@ -47,7 +60,7 @@ test_that("1. Input checks", { "Parameter 'exp' and 'obs' must have dimension names." ) expect_error( - RMSSS(array(1:10, dim = c(a = 2, c = 5)), array(1:4, dim = c(a = 2, b = 2))), + RMSSS(array(1:10, dim = c(a = 3, c = 5)), array(1:4, dim = c(a = 3, b = 5)), time_dim = 'a', dat_dim = NULL), "Parameter 'exp' and 'obs' must have same dimension name" ) ## time_dim @@ -93,7 +106,7 @@ test_that("1. Input checks", { expect_error( RMSSS(exp = array(1:10, dim = c(sdate = 1, dataset = 5, a = 1)), obs = array(1:4, dim = c(a = 1, sdate = 2, dataset = 2))), - "Parameter 'exp' and 'obs' must have same length of all dimension except 'dat_dim'." + "Parameter 'exp' and 'obs' must have same length of all dimension except 'memb_dim' and 'dat_dim'." ) expect_error( RMSSS(exp = array(1:10, dim = c(sdate = 1, dataset = 5, a = 1)), @@ -141,6 +154,59 @@ test_that("2. Output checks: case 1", { tolerance = 0.00001 ) + #ref + res1_3 <- RMSSS(exp1, obs1, ref = ref1_1, dat_dim = 'dataset') + expect_equal( + dim(res1_3$rmsss), + c(nexp = 5, nobs = 2) + ) + expect_equal( + dim(res1_3$p.val), + c(nexp = 5, nobs = 2) + ) + expect_equal( + as.vector(res1_3$rmsss[2, ]), + c(-1.197432, -8.879809), + tolerance = 0.0001 + ) + expect_equal( + as.vector(res1_3$p.val[2, ]), + c(0.8284354, 0.9898591), + tolerance = 0.0001 + ) + res1_4 <- RMSSS(exp1, obs1, ref = ref1_2, dat_dim = 'dataset', sign = T, alpha = 0.3) + expect_equal( + dim(res1_4$rmsss), + c(nexp = 5, nobs = 2) + ) + expect_equal( + dim(res1_4$sign), + c(nexp = 5, nobs = 2) + ) + expect_equal( + as.vector(res1_4$rmsss[2, ]), + c(-0.9249772, -0.5624465), + tolerance = 0.0001 + ) + expect_equal( + as.vector(res1_4$p[2, ]), + c(0.7874844, 0.7094070), + tolerance = 0.0001 + ) + expect_equal( + as.vector(res1_4$sign), + c(rep(F, 5), T, rep(F, 4)) + ) + + # Random Walk + suppressWarnings({ + res1_5 <- RMSSS(exp1, obs1, ref = ref1_1, dat_dim = 'dataset', sig_method = "Random Walk", pval = F, sign = T) + }) + expect_equal( + as.vector(res1_5$sign), + rep(F, 10) + ) + }) @@ -223,3 +289,17 @@ test_that("5. Output checks: case 4", { ) }) + +############################################## +test_that("6. Output checks: case 5", { + res5_1 <- RMSSS(exp5, obs5, ref = ref5, dat_dim = 'dataset', memb_dim = 'member') + res5_2 <- RMSSS(s2dv::MeanDims(exp5, 'member'), s2dv::MeanDims(obs5, 'member'), + ref = s2dv::MeanDims(ref5, 'member'), dat_dim = 'dataset') + expect_equal( + res5_1, + res5_2 + ) + + +}) + -- GitLab From fa23886d4b44ecaff9c2ccb95022103b7a7e3f76 Mon Sep 17 00:00:00 2001 From: aho Date: Tue, 27 Dec 2022 12:33:52 +0100 Subject: [PATCH 15/59] Correct typo --- R/RMSSS.R | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/R/RMSSS.R b/R/RMSSS.R index b8f411a..6f1958f 100644 --- a/R/RMSSS.R +++ b/R/RMSSS.R @@ -168,7 +168,7 @@ RMSSS <- function(exp, obs, ref = NULL, time_dim = 'sdate', dat_dim = 'dataset', } ## sig_method if (length(sig_method) != 1 | !any(sig_method %in% c('one-sided Fisher', 'Random Walk'))) { - stop("Parameter 'sig_meothd' must be one of 'one-sided Fisher' or 'Random Walk'.") + stop("Parameter 'sig_method' must be one of 'one-sided Fisher' or 'Random Walk'.") } if (sig_method == "Random Walk" & pval == T) { warning("p-value cannot be calculated by significance method 'Random Walk'.") -- GitLab From a4d22f82fc447b944786001709af9db2cb3eb767 Mon Sep 17 00:00:00 2001 From: aho Date: Thu, 29 Dec 2022 09:08:47 +0100 Subject: [PATCH 16/59] Move s2dverification vignettes here --- vignettes/NAOindex_81to91.png | Bin 0 -> 50688 bytes vignettes/NAOpredictions.png | Bin 0 -> 33781 bytes vignettes/RMSSSforNAOprediction.png | Bin 0 -> 85982 bytes vignettes/ScoringForecast.md | 255 ++++++ vignettes/data_retrieval.md | 668 +++++++++++++++ vignettes/ex_ano_expA_obsX.png | Bin 0 -> 22516 bytes vignettes/ex_ano_expB_obsX.png | Bin 0 -> 22448 bytes vignettes/ex_clim_expA_expB_obsX.png | Bin 0 -> 11836 bytes vignettes/ex_corr_expA_expB_obsX.png | Bin 0 -> 14071 bytes vignettes/ex_raw_expA_obsX.png | Bin 0 -> 13892 bytes vignettes/ex_raw_expB_obsX.png | Bin 0 -> 14418 bytes vignettes/example.md | 263 ++++++ vignettes/s2dv_modules.png | Bin 0 -> 385333 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libraries: + +- libssl-dev +- libnecdf-dev +- cdo + + +The **s2dv R package** should be loaded by running the following lines in R, onces it is integrated into CRAN mirror. + +```r +library(s2dv) +``` + + + +### 2-Define the problem and loading the data with the corresponding parameters + +In this vignette we will quantify how skilled a seasonal forecast is. The model will be the EUROSIP multi-model seasonal forecasting system and our real truth will be observations represented by the ERAinterim reanalysis dataset. + +For more information about both datasets see the next documentation: +- [**ERAinterim**](https://www.ecmwf.int/en/forecasts/datasets/archive-datasets/reanalysis-datasets/era-interim). +- [**EUROSIP system**](https://www.ecmwf.int/en/forecasts/documentation-and-support/long-range/seasonal-forecast-documentation/eurosip-user-guide/multi-model). + +Both datasets can be downloaded from the corresponding server. However in this example we will use the BSC esarchive database. Files path parameters for the Load() function are defined as follows: + +```r +path_exp_EUROSIP <- list(name = 'system4_m1', + path = file.path('/esarchive/exp/EUROSIP/ecmwf', + '$EXP_NAME$/monthly_mean', + '$VAR_NAME$_f6h/$VAR_NAME$_$START_DATE$.nc')) + +path_obs_eraI <- list(name = 'erainterim', + path = file.path('/esarchive/recon/ecmwf', + '$OBS_NAME$/monthly_mean', + '$VAR_NAME$_f6h/$VAR_NAME$_$YEAR$$MONTH$.nc')) +``` + +Our case of study will be predicting the North Atlantic Oscillation index ([**NAO**](https://en.wikipedia.org/wiki/North_Atlantic_oscillation)), usually defined as the difference in the sea level pressure anomaly between the permanent High pressure system over the Azores Island and the Low pressure system over Iceland. Changes in the NAO index have a direct impact on European season weather since it controls the intensity and pathways of the storms in the continent; Positive NAO values are related with stronger storms and thus wet winters in Central and Northern Europe and its Atlantic facade. Negative NAO values correspond to reduced storm activity and rainfall in Northern Europe but increased in the South and Mediterranean Sea. Especially during the months of November to April, the NAO is responsible for much of the variability of weather in the North Atlantic region, affecting wind speed and wind direction changes, changes in temperature and moisture distribution and the intensity, number and track of storms. + +For this vignette we will use the whole North Atlantic as geographical domain and we will select all forecasts starting in November for the 1981 - 1991 time period. The EUROSIP system provides 7-months long window forecast inluding 51 different members. + +```r +#North Atlantic domain definition +lonNA <- c(-90, 40) +latNA <- c(20, 80) + +#Selected time periods: +startDates <- paste(1981:1991, '1101', sep = '') + +#Loading sea level pressure maps for the whole North Atlantic and for the specific period +data <- Load(var = 'psl', + exp = list(path_exp_EUROSIP), + obs = list(path_obs_eraI), + sdates = startDates, + output = 'lonlat', + lonmin = lonNA[1], lonmax = lonNA[2], + latmin = latNA[1], latmax = latNA[2]) + + +#Retrieving observational and forecast data +obs <- data$obs +exp <- data$mod + +``` + + +### 3-NAO index, Forecast vs Observations + +As a first step we will compare the predicted intensity of the NAO index for observations and for the forecast system. + +In s2dv the NAO index is computed using a common alternative definition; The NAO is defined as the first mode of variability (computed using Single Value Decomposition method) for the sea level pressure in the North Atlantic region [20N-80N, 80W-40E]. The `NAO()` function requires as input anomalies that are previously computed using `Ano_CrossValid()` function. + +```r +#Computing anomalies along sdates dimension +ano <- Ano_CrossValid(exp, obs) + +#Computing NAO index as the first mode of slp variability in the North Atlantic +## Change lon from range [0, 360] to [-180, 180] +nao <- NAO(ano$exp[, , , , , c(73:185, 1:57)], ano$obs[, , , , , c(73:185, 1:57)], lon = data$lon[c(73:185, 1:57)], lat = data$lat) + +#For clarification, we normalize the NAO index for each member dividing by the corresponding standard deviation +nao_exp_sd <- apply(nao$exp, MARGIN = 1, sd, na.rm = T) +nao_obs_sd <- sd(nao$obs) +nao_exp_n <- nao$exp / nao_exp_sd +nao_obs_n <- nao$obs / nao_obs_sd + + +# Finally plot the NAO index using Box plots for all decembers. +PlotBoxWhisker(t(nao_exp_n), nao_obs_n, toptitle = "NAO index, DJF", + monini = 12, yearini = 1981, freq = 1, + drawleg = F, fileout = NULL) +legend(x = 3.8, y = 2.6, c('EUROSIP', 'EraInterim'), col = c(2, 4), pch = 15) +``` + + + +The figure above does not represent a good agreement between observations (blue line) and forecast (whisker boxes) due to the large dispersion through the 51 model members. The NAO signal is too weak due to the large dispersion among ensemble members thus almost disappearing (close to 0). + + +### 4-Quantifying the skillfulness of the prediction. The RMSSS + +Let's quantify how good or bad it is this prediction looking also for a better understanding of what is happening. To do so, we will use the Root Mean Square Error (RMSE), that it is just the squared and then rooted difference between the predicted and the true value. + +s2dv includes the `RMS()` function to directly calculate the RMSE, however, in order to get a better understanding of the output values we will use the `RMSSS()` function (Root Mean Square Error Skill Score). The RMSSS equals the RMSE but it is normalized by a reference RMSE, usually asociated with the intrinsic variability of the system (for example the standard deviation of the climatology). In s2dv the score is computed such that the best RMSSS score would be 1 (RMSE equals 0), while if RMSSS equals 0, the RMSE equals the variability reference of the system (i.e. the standard deviation). RMSSS can also be negative, meaning RMSE is greater than the variability reference. + +```r +#Defining NAO events +Lmember <- length(exp[1, , 1, 1, 1, 1]) + +#Calculating a RMSSS for the ensemble of members average from the mean NAO timeseries of all members +rmsss_m <- RMSSS(exp = MeanDims(nao_exp_n, 'member'), + obs = nao_obs_n, dat_dim = NULL, pval = F)$rmsss + +#Computing the RMSSS for each member +rmsss <- RMSSS(exp = nao_exp_n, obs = array(nao_obs_n, dim = c(sdate = 11, member = 1)), dat_dim = 'member', pval = F)$rmsss + +#Plotting..... +layout(matrix(c(1, 2), 1 , 2, byrow = TRUE)) + +#Plotting RMSSS for all members +plot(rmsss, type = 'h', lwd = 5, col = 'grey', xlab = 'Members', mgp = c(3,1,0), + main = sprintf('RMSSS for each member (RMSSS average %1.3f )', rmsss_m), + ylim = c(-1,1), cex.lab=2, cex.axis=2, cex.main = 1.9) +grid(col ='grey') +lines(rep(0, Lmember), lwd = 1, col = 'black') + +#Plotting boxplot for selected members with higher rmsss +isel <- which(rmsss > 0.1) +rmsss_m_sel <- RMSSS(exp = MeanDims(nao_exp_n[, isel], 'member'), + obs = nao_obs_n, + dat_dim = NULL, pval = F) + +PlotBoxWhisker(t(nao_exp_n[, isel]), nao_obs_n, + toptitle = sprintf('NAO index, selected-members (RMSSS=%1.2f)', rmsss_m_sel), + monini = 12, yearini = 1981, freq = 1, + drawleg = F, fileout = NULL) +legend(x = 4.95, y = 2.4, c('EUROSIP', 'EraInterim'), + col = c(2, 4), pch = 15, cex = 0.9, lty = 0) +``` + + + + +The above figure shows very different RMSSS for different members (left plot). Most of them have RMSSS close to 0, thus the prediction error is close to the system variability. **The RMSSS for the whole ensemble is 0.091**, what means a not very useful ensemble prediction. + +However, we can select the members that present a better RMSSS, i.e. those closer to 1, and recompute the ensemble RMSSS. This is shown in the right plot where only members 8th, 23rd, 40th and 45th are used. Now most marked NAO events are correctly predicted giving a **RMSSS of 0.66 for this selected-members ensemble**. + + +### 5-Quantifying the skillfulness of the prediction. The Brier Score + +Another option to quantify the goodness of this prediction is using the `BrierScore()` function. The BS measures the accuracy of a probabilistic categorical prediction calculating the mean squared difference between the predicted probability and the actual observation. BS scores perfect prediction when BS equals 0 (no difference between prediction and observation) and worst score corresponds to value of 1. + +Moreover, the BS can be descomposed in 3 terms: BS = Reliability - Resolution + Uncertainty. Reliability refers to how close the predicted probabilities are to the true probabilities (i.e. the lower the reliability, the lower the difference between prediction and observation and the better the score). Resolution relates with the difference between the predicted observation and the climatology (i.e. the higher the resolution, the greater the ability of the forecast to predict events different from the climatology). Uncertainty represents the inherent uncertainty of ocurring the event (i.e. the higher the uncertainty, the more difficult to correctly predict the event). + +In the case of the NAO index, we can discretize it in to a categorical variable defining a NAO event always that the index is greater than 0 and asociating the event with the value 1. Negative NAO index values then correspond to the non-ocurrence of a NAO event and thus they are assigned the value 0. For the forecast, we can convert the NAO index prediction of all ensemble members in to a NAO prediction probability computing the proportion of members with a positive NAO prediction. For comparison we do the same for the good scored selected-members ensemble of previous section. + + +```r + +#Defining number of sdates +Lsdates <- length(startDates) + +#For observations +nao_event_obs <- rep(0, Lsdates) +nao_event_obs[which(nao_obs_n > 0)] <- 1 + +#For all members +nao_event_exp <- array(0, dim = c(sdate = Lsdates, member = Lmember)) +nao_event_exp[which(nao_exp_n > 0)] <- 1 +nao_event_exp_prob <- MeanDims(nao_event_exp, 'member') + +BS <- BrierScore(obs = nao_event_obs, exp = nao_event_exp_prob) + +BSscore <- BS$bs +BSrel <- BS$rel +BSres <- BS$res +BSunc <- BS$unc + +#For selected members only +nao_event_exp_sel <- array(0, dim = c(sdate = Lsdates, member = length(isel))) +nao_event_exp_sel[which(nao_exp_n[, isel] > 0)] <- 1 +nao_event_exp_sel_prob <- MeanDims(nao_event_exp_sel, 'member') + +BS_sel <- BrierScore(obs = nao_event_obs, exp = nao_event_exp_sel_prob) + +BSscore_sel <- BS_sel$bs +BSrel_sel <- BS_sel$rel +BSres_sel <- BS_sel$res +BSunc_sel <- BS_sel$unc + + +#Plotting NAO events and prediction probabilities +layout(matrix(c(1, 2), 1, 2, byrow = TRUE)) + +#For all ensemble members +plot(nao_event_obs - 0.5, type='p', lwd = 5, col = 'red', + xlab = 'NAO events', yaxt = 'n', ylab = 'NAO probabilities', mgp = c(3,1,0)) +grid(col = 'grey') +lines(nao_event_obs - 0.5, type = 'h', lwd = 5, col = 'red', yaxt = 'n') +lines(nao_event_exp_prob - 0.5, type = 'h', lwd = 4, col = 'blue', yaxt = 'n') +lines(nao_event_exp_prob - 0.5, type = 'p', lwd = 3, col = 'blue', yaxt = 'n') +axis(2, at = seq(-0.5, 0.5, 0.25), labels = seq(0, 1, 0.25), mgp = c(3,1,0)) +lines(rep(0, Lmember), lwd=2, col = 'black') +title('Predictions for all-members ensemble') + +#For selected-member ensemble only +plot(nao_event_obs - 0.5, type = 'p', lwd = 5, col = 'red', + xlab = 'NAO events', yaxt = 'n', ylab = 'NAO probabilities', mgp = c(3,1,0)) +grid(col = 'grey') +lines(nao_event_obs - 0.5, type = 'h', lwd = 5, col = 'red', yaxt = 'n') +lines(nao_event_exp_sel_prob - 0.5, type = 'h', lwd = 4, col = 'blue', yaxt = 'n') +lines(nao_event_exp_sel_prob - 0.5, type = 'p', lwd = 3, col = 'blue', yaxt = 'n') +axis(2, at = seq(-0.5, 0.5, 0.25), labels = seq(0, 1, 0.25), mgp = c(3, 1, 0)) +lines(rep(0, Lmember), lwd = 2, col = 'black') +title('Predictions for selected-members ensemble') + +``` + + + + +For the all-members ensemble, the results are: +**Total BS = 0.213,** +Reliability = 0.138, +Resolution = 0.172, +Uncertainty = 0.248. + +For the selected-members ensemble, the results are: +**Total BS = 0.136,** +Reliability = 0.015, +Resolution = 0.127, +Uncertainty = 0.248. + +To put the total Brier Score values in to context, note that the BS definition is such that in general a forecast that always gives a 50% probability prediction for all cases would have a BS of 0.25. + +Taking this into account, the all-members ensemble prediction with a BS of 0.213 seems only a bit better than flipping a coin in terms of Brier Scoring. The selected-members ensemble instead presents a clear improvement in the total Brier Score (lower value). This is due to the better scoring (lower value) achieved by the reliability term in this ensemble, in agreement with the previous RMSSS results and also shown in the right plot of the figure above; The prediction probabilities are much closer to the NAO ocurrence distribution. However, the resolution scores are not that different between the all-members and the selected-members ensemble. This is due to the fact that even with a notable difference in RMSSS and reliability, the two ensembles mostly predict equally the correct occurrence of positive/negative NAO events (left plot). Finally, the uncertainty is obviously the same for the two cases, since the observations to compare with are the same. + + +### 6-Appendix: Forecast scores ranges + +| SCORE | RMSSS | BS (total) | Reliability | Resolution | Uncertainty | +|:-----:|:-----:|:----------:|:-----------:|:----------:|:--------------:| +| Best | 1 | 0 | 0 | 1 | Obs. dependant | +| Worst | -Inf | 1 | 1 | 0 | Obs. dependant | diff --git a/vignettes/data_retrieval.md b/vignettes/data_retrieval.md new file mode 100644 index 0000000..ec2d127 --- /dev/null +++ b/vignettes/data_retrieval.md @@ -0,0 +1,668 @@ +--- +title: "Data Retrieval" +author: "Nicolau Manubens" +reviser: "An-Chi Ho" +date: "`r Sys.Date()`" +output: pdf_document +vignette: > + %\VignetteEngine{R.rsp::md} + %\VignetteIndexEntry{Data Retrieval} + %\usepackage[utf8]{inputenc} +--- + +Data retrieval +============== +One of the strong points of s2dv is its data retrieval module. +Its aim is to load and homogenize forecast or hindcast data generated by +climate models, usually in multiple runs and multiple ensemble members per +run, as well as the corresponding observational time series obtained from +either pure observations or reanalyses. + +A climate model run simulates a time period starting at a **starting date** +and generates data for a series of time steps regularly spaced along the +**forecast time** that conform the simulated time period. A model run is +also usually referred to as starting date. +The **lead-time** at each forecast time step is the amount of simulated time +since the beginning of the simulation, e.g., the first value of a +monthly-averaged forecast has a lead-time of 0 months, the second value has a +lead-time of 1 month and so on. In the context of s2dv, however, +the concept lead-time is used to make reference to the forecast time steps: +the first lead-time of a forecast is the value with a lead-time of 0 time units +(the first time step), the second lead-time is the one with a lead-time of 1 +time unit (the second time step) and so on. +Data at one forecast time (or lead-time) from different runs or starting dates +conform a time series defined along the **actual time**. + +`Load()` is the interface function to the data retrieval module. Through it +you can request previously monthly-averaged or daily-averaged 2-dimensional +variables or global mean variables from as many experimental and observational +multi-member datasets as needed, at the selected starting dates and forecast +time steps, over any longitude-latitude region of the Earth surface. + +`Load()` automatically fetches the selected starting dates of the requested +experimental datasets and the date-corresponding observational data, +homogenizes it and loads it into an R object ready to be processed. +If done manually this homogenization procedure can be time-consuming and +become a hurdle in the verification process. + +The object returned by `Load()` contains, among others, two arrays with the +requested data, one for the experimental data and the other for observational +data, with a disctintive dimension structure of s2dv: +```r +c(n. of datasets, n. of members, n. of starting dates, n. of lead-times, n. of latitudes, n. of longitudes) +``` + +The homogenization process consists of the following steps: + 1. Regridding data. `Load()` relies on CDO tools for this task (see +[**Installation**](../README.md)). + 2. Applying masks to disable certain grid cells. + 3. Disabling values beyond certain thresholds. + 4. Computing area-weighted averages. + +(The 1st, 2nd and 4th steps only apply if loading 2-dimensional variables.) + +Supported file formats +---------------------- +There are some guidelines that the files of the datasets must follow so that +`Load()` is able to recognize, fetch and process them: + - Data files must be in NetCDF 3/4 local or remote files or indexed in NCML +catalogs provided by THREDDS servers. + - Data files must contain monthly or daily time series. Data in other +frequencies can also be loaded as experimental data, but the automatical fetch +of date-corresponding observations will fail. + - The only supported source (and target) grids are regular and gaussian grids +(those definable with the CDO grid names that follow the patterns 'rx' +or 'tgrid'). + - The variable of interest must be defined over the dimensions +(time[, members]) if is a global means time-series or (time[, members], +latitudes, longitudes) if is a 2-dimensional field. These dimensions +can be named at will and can be in any order. The less time-consuming orders +to load are, however, (time[, members]) or (time[, members], latitudes, +longitudes). Here, the dimension time makes reference to forecast time. + - If the data is 2-dimensional, a variable with the grid latitudes and a +variable with the grid longitudes must be defined, with the same name as their +corresponding dimension. + - The files of an experimental dataset must be distributed in either of the +following two ways: + - File per starting date: each file must contain the starting date\* +somewhere in its path. + - File per starting date per member: each file must contain the the +starting date\* and the member number\*\* somewhere in its path. + - The files of an observational dataset must be distributed in either of the +following three ways: + - File per month: each file must contain the year and month\*\*\* somewhere +in its path. + - File per month per member: each file must contain the member +number\*\* and the year and month\*\*\* somewhere in its path. + - Single file: the time axis must be properly defined to work with +`cdo showmon` and `cdo showyear`. + +\*: starting dates in the format YYYYMMDD. +\*\*: member number, from 0 to total_number_of_members - 1, with as many +preceding 0s as needed to reach the needed number of digits to represent +total_number_of_members - 1. +\*\*\*: year in the format YYYY and month in the format MM. + +Load() options +-------------- + +`Load()` has 27 parameters. +14 of them are for selecting the data of interest, 8 of them are for adjusting +the homogenization steps and the other 5 are for general adjustments of +`Load()`. See them explained in 3 sections: + - [**Selection parameters**](#selection) + - [**Homogenization parameters**](#homogenization) + - [**General parameters**](#general) + +### Selection parameters +The selection parameters are `var`, `exp`, `obs`, `sdates`, `nmember`, +`nmemberobs`, `nleadtime` (deprecated), `leadtimemin`, `leadtimemax`, +`sampleperiod`, `lonmin`, `lonmax`, `latmin` and `latmax`. You can see most of +them in use in the [**Example**](example.md) except for `nmember`, +`nmemberobs`, `nleadtime` and `sampleperiod`. The first part of that example +is reproduced in more detail below in this section. + +`var` must be provided with the short name of a 2-dimensional or global mean +variable of interest, for example `var = 'tas'` (most usually the provided +name must be the same as the variable name inside the NetCDF data files). +`exp` and `obs` contain the information on the location of the requested +datasets, `sdates` and `leadtimemin`/ `leadtimemax` tell `Load()` which +starting dates and lead-times to pick and so on. +Check the [**user manual**](../s2dv-manual.pdf) or `?Load` for a +thorough explanation. + +Now, as an example, let's consider we have two experimental datasets and one +observational datasets, both with data for the variable 'tas' and with the +files distributed as depicted in the following directory tree: +``` + /path/to/ + |--experiments/ + | |--experimentA/ + | | |--monthly_mean/ + | | |--tas/ + | | |--tas_19911101.nc + | | |--tas_19921101.nc + | | | · + | | | · + | | | · + | | |--tas_20001101.nc + | |--experimentB/ + | |--monthly_mean/ + | |--tas/ + | |--tas_19911101.nc + | |--tas_19921101.nc + | | · + | | · + | | · + | |--tas_20001101.nc + |--observations/ + |--observationX/ + |--monthly_mean/ + |--tas/ + |--tas_199101.nc + |--tas_199102.nc + |--tas_199103.nc + |--tas_199104.nc + |--tas_199105.nc + |--tas_199106.nc + |--tas_199107.nc + |--tas_199108.nc + |--tas_199109.nc + |--tas_199110.nc + |--tas_199111.nc + |--tas_199112.nc + |--tas_199201.nc + |--tas_199202.nc + | · + | · + | · + |--tas_199401.nc + |--tas_199402.nc + |--tas_199403.nc +``` +We assume these files are NetCDF 3/4 compliant and have the variable 'tas' +defined inside, fulfilling the guidelines explained above in the previous +section. + +We can now build the information blocks of each dataset as follows: +```r +library(s2dv) + +expA <- list( + name = 'experimentA', + path = file.path('/path/to/experiments/$EXP_NAME$/monthly_mean', + '$VAR_NAME$/$VAR_NAME$_$START_DATE$.nc') + ) +expB <- list( + name = 'experimentB', + path = file.path('/path/to/experiments/$EXP_NAME$/monthly_mean', + '$VAR_NAME$/$VAR_NAME$_$START_DATE$.nc') + ) +obsX <- list( + name = 'observationX', + path = file.path('/path/to/observations/$OBS_NAME$/monthly_mean', + '$VAR_NAME$/$VAR_NAME$_$YEAR$$MONTH$.nc') + ) +``` +`Load()` will automatically replace the wildcards (keywords starting and +ending with '$') with the corresponding starting dates, variable name, etc. +See help on parameters `exp` and `obs` in `?Load` for a full explanation. + +Now time to issue the `Load()` call: the target variable name will be `'tas'` +and the parameters `exp` and `obs` can be built from the previous information +blocks. Apart from that we just need to specify a set of starting dates for +`Load()` to work: + +```r +sdates <- paste0(1991:2000, '1101') +data <- Load(var = 'tas', exp = list(expA, expB), obs = list(obsX), + sdates = sdates) +``` + +This will pick by default as many members and lead-times of each experimental +dataset as found in the first one ('expA'), and as many members and lead-times +of each observational dataset (only 1 in this example) as found in the first +one ('obsX'). + +All the data will be returned in a named list with many components, in a +format similar to that used in the packages 'downscaleR' and 'loadR' (see +`?Load` for a full description of the returned metadata). +The two components that contain the experimental and observational data are +`$mod` and `$obs`. These are two arrays with the dimensions in the following +order: +```r +c(n. of datasets, n. of members, n. of starting dates, n. of lead-times, n. of latitudes, n. of longitudes) +``` +The presence of the last two dimensions will depend on whether the requested +variable is 2-dimensional or global mean and on the selected `output` type +(see below or in `?Load`). See +[**Normalizing fields**](statistics.md#normalizing) +for the array structure for observational data. + +In the case of the example, if 'expA' has 5 members but 'expB' has 8, the +resulting size of the members dimension will be 5 and the last 3 members of +'expB' will be missed. Besides, if 'expB' has only 2 members, the 3 remaining +members will be filled up with NA values. It happens exactly the same with the +lead-times. +To avoid this default behaviour you can specify the expected maximum number of +members in `nmember` and `nmemberobs` and the expected maximum number of +lead-times in `leadtimemax`. + +Also, if not interested in the few first lead-times of the starting dates, you +can discard them specifying the first lead-time of interest with the parameter +`leadtimemin`, and even pick one lead-time of each `sampleperiod` lead-times +starting from `leadtimemin`. + +The following code will pick the lead-times corresponding to a time period of +one year, starting from December, since the first month of the starting dates +is November and `leadtimemin` is 2: + +```r +sdates <- paste0(1991:2000, '1101') +data <- Load(var = 'tas', exp = list(expA, expB), obs = list(obsX), + sdates = sdates, leadtimemin = 2, leadtimemax = 13) +``` + +It is possible to load experimental data only or observational data only by +providing `NULL` to `exp` or `obs`. + +In the example just above, the loaded variable is 'tas', a 2-dimensional +variable. However though, `Load()` computes by default an area-weighted +average, hence the component `data$mod` will have dimensions +`c(2, 5, 3, 6)` and the component `data$obs` will have dimensions +`c(1, 1, 3, 6)`. Read below in **Homogenization parameters** on how to change +the `output` type of `Load()`. + +If willing to work with averages of a specific region of the Earth surface +you can specify the limits of its bounding box via the parameters `latmin`, +`latmax`, `lonmin` and `lonmax`. For example, for the North Pacific region: + +```r +sdates <- paste0(1991:2000, '1101') +data <- Load(var = 'tas', exp = list(expA, expB), obs = list(obsX), + sdates = sdates, leadtimemin = 2, leadtimemax = 13, + latmin = -10, latmax = 60, lonmin = 100, lonmax = 250) +``` + +### Homogenization parameters +This group of parameters is conformed by all the parameters that have effects +in any of the homogenization steps mentioned in the introduction of +[**Data retrieval**](data_retrieval.md) namely: `output`, `method`, `grid`, +`maskmod`, `maskobs`, `varmin`, `varmax` and `remapcells`. + +When loading 2-dimensional variables, `Load()` calculates and returns by +default area-weighted averages of the values in the grid cells that fall +inside the requested region. The area averages are computed from the original +datasets in their original grids. `Load()`, however, prior to computing the +averages, can remap all the data to a common grid if you specify it via the +`grid` argument. The grid specification must be a character string that follows +one of the patterns 'rx' or 'tgrid', where '' and '' are +the number of longitudes and latitudes of a rectangular grid and '' is the +factor of truncation of spherical harmonics of a gaussian grid. + E.g.: 'r320x160' or 't73grid'. + +Internally, `Load()` will dispatch CDO calls to interpolate the original files. +One of four methods of interpolation can be chosen through the parameter +`method`: 'conservative', 'bilinear', 'bicubic' or 'distance-weighted'. The +parameter `remapcells` is related to the precision of grid interpolations, you +can read more in `?Load`. + +Additionally, any grid cells of your choice can be disabled before computing +the averages by providing a mask for each dataset in `exp` and `obs`. These +masks must be provided with the arguments `maskmod` and `maskobs` and can +simply be a pointer to a NetCDF mask or an R array with the proper size. +Read more on the arguments `maskmod` and `maskobs` in `?Load` to see the +guidelines the mask files must follow or how to provide a mask as an R array. + +It is also possible to work directly with 2-dimensional data without averaging +by setting the parameter `output = 'lonlat'`. With this option the parameters +`grid`, `method`, `maskmod` and `maskobs` keep applying: you can request your +data to be in a common rectangular or gaussian grid of your choice and disable +some values with a mask. + +To summarize the homogenization parameters mentioned so far, we could dispatch the +following `Load()` call: + +```r +mask <- list(path = '/path/to/masks/land_mask_r320x160.nc') +sdates <- paste0(1991:2000, '1101') +data <- Load(var = 'tas', exp = list(expA, expB), obs = list(obsX), + sdates = sdates, leadtimemin = 2, leadtimemax = 13, + latmin = -10, latmax = 60, lonmin = 100, lonmax = 250, + output = 'lonlat', grid = 'r320x160', method = 'bicubic', + maskmod = list(mask, mask), maskobs = list(mask)) +``` + +Finally, extreme values can be disabled by setting a upper and a lower +threshold via the parameters `varmin` and `varmax`. + +### General parameters +The general parameters are `storefreq`, `configfile`, `silent`, `nprocs` and +`dimnames`. + +#### Loading daily data +It is possible to load not only monthly data but also daily data with exactly +the same funcionalities available in both modes. `storefreq` tells `Load()` +whether the experimental data to load is stored in a monthly frequency or in a +daily frequency. This way it will be able to work out the dates of the +corresponding observational data and fetch the corresponding files. The only +supported values for this parameter currently are 'monthly' (the default) and +'daily'. +Note that in the case that only experimental datasets are requested +(via `exp`) any storage frequency is be supported, since `Load()` doesn't +have to make date-correspondences. It is the user's responsibility in these +cases to ensure that the experimental datasets are stored in a common time +frequency. + +#### Adjusting dimension names +Regarding the guidelines that the files of a dataset must follow, the variable +of interest inside the NetCDF files must be defined over the dimensions +(time[, members][, latitudes, longitudes]). These dimensions can be named at +will but, by default, the expected names are 'ensemble', 'latitude' +and 'longitude' (the time dimension can take any name). If the name of any of +the dimensions in all the datasets to load is different to this default, it +can be adjusted with the parameter `dimnames` as in the following example: +```r +dimnames = list(member = 'members', lat = 'j', lon = 'i') +``` +However, if only one of the datasets breaks the rules or each dataset has its +own naming convention, you can adjust individually when building the +information blocks of each dataset as in the following example: +```r +expA <- list( + name = 'experimentA', + path = file.path('/path/to/experiments/$EXP_NAME$/monthly_mean', + '$VAR_NAME$/$VAR_NAME$_$START_DATE$.nc'), + dimnames = list(member = 'members') + ) +expB <- list( + name = 'experimentB', + path = file.path('/path/to/experiments/$EXP_NAME$/monthly_mean', + '$VAR_NAME$/$VAR_NAME$_$START_DATE$.nc'), + dimnames = list(lat = 'j', lon = 'i') + ) +obsX <- list( + name = 'observationX', + path = file.path('/path/to/observations/$OBS_NAME$/monthly_mean', + '$VAR_NAME$/$VAR_NAME$_$YEAR$$MONTH$.nc'), + dimnames = list(member = 'ens', lat = 'y', lon = 'x') + ) +``` + +#### Workflow of `Load()` and parallelism +The workflow of `Load()` consists of 3 steps: + 1. Building up work pieces +Each work piece is a packet of information that describes the location of a +**single** data file requested in a `Load()` call (e.g. 'tas_19901101.nc') and +the homogenization and arranging operations to be applied to that file. + 2. Setting up a cluster +A multi-core cluster is set up. As of now `Load()` can only make the most of +multiple cores in a single processor but not of multiple processors. +The number of nodes in the multi-core cluster can be adjusted via `nprocs` +(number of processes, as each node is a full new R process). Note that the +number of nodes does not necessarly have to coincide with the number of cores: +if `nprocs` is lower than the number of cores, probably some of the available +cores will remain unused and if `nprocs` is higher, a single core will have +more than one task assigned at a time. Depending on the environment this may +be convenient. +Three aspects to take into account when selecting the appropriate `nprocs` are: + - Whether hyperthreading is activated in the system + - The fact that each node will dispatch parallel blocking calls to CDO +along its execution + - A 'bigmemory' shared memory region will be set up for the multiple cores +to arrange the resulting data of each work piece. +Setting `nprocs = 1` will avoid creating a cluster and all the workload will +be carried out in a single process (that may dispatch parallel blocking CDO +calls). + 3. Dispatching the work pieces to the cluster +Once the work pieces and the cluster are ready, `Load()` dispatches the work +pieces with load balancing to the nodes of the cluster. Each node will keep +applying the internal function `LoadDataFile()` to each work piece. + +#### Running `Load()` silently +All along the process `Load()` keeps informing about the status and any +detected potential issues. When run in batch mode it may be of your interest +to turn the messages off by setting `silent = TRUE`. + +#### Using a configuration file +When using `Load()` frequently, one may end up repeating many times the code +to build the same information blocks to load certain specific datasets. +Besides, when using `Load()` in a team, one of its members may be interested +in using datasets that other members usually work with or may want to make +accessible his datasets to the colleagues. + +To help in these two situations `Load()` has a built in mechanism to read +**configuration files** that contain, in a tabular and compact format, the +information blocks of the datasets of interest. This way, by defining the +information of a dataset only once in a configuration file, `Load()` will be +able to read its information as needed. Also, the members of a team can share +a configuration file to put the information of their datasets at others' +disposal. + +A configuration file can be created by hand, following the specifications in +`?ConfigFileOpen`, or can be created and edited through a set of functions +included in s2dv: `ConfigFileCreate()`, `ConfigFileOpen()`, +`ConfigAddEntry()`, `ConfigEditEntry()`, `ConfigRemoveEntry()`, +`ConfigEditDefinition()`, `ConfigRemoveDefinition()`, `ConfigFileSave()`, +`ConfigShowTable()`, `ConfigShowDefinitions()`, `ConfigShowSimilarEntries()` +and `ConfigApplyMatchingEntries()`. + +The first option can be faster for experienced users but the second option is +safer and useful to automatise the creation of configuration files. The +second option will be used in the following examples but the raw file will +also be displayed to show the internals of the configuration files and to +give some hints on how to create them manually. + +A blank new configuration file can be created as follows: +```r +conf_path <- '/path/to/configfile.conf' +ConfigFileCreate(conf_path) +``` +This will generate a file at the specified path with all the boilerplate: +``` +# s2dv configuration file +# +# Check ?ConfigFileOpen after loading s2dv for detailed +# documentation on this configuration file. + +############# +!!definitions +############# +DEFAULT_EXP_MAIN_PATH = $EXP_NAME$ +DEFAULT_EXP_FILE_PATH = $STORE_FREQ$/$VAR_NAME$_$START_DATE$.nc +DEFAULT_NC_VAR_NAME = $VAR_NAME$ +DEFAULT_SUFFIX = +DEFAULT_VAR_MIN = +DEFAULT_VAR_MAX = +DEFAULT_OBS_MAIN_PATH = $OBS_NAME$ +DEFAULT_OBS_FILE_PATH = $STORE_FREQ$/$VAR_NAME$_$YEAR$$MONTH$.nc +DEFAULT_DIM_NAME_LONGITUDES = longitude +DEFAULT_DIM_NAME_LATITUDES = latitude +DEFAULT_DIM_NAME_MEMBERS = ensemble + + +###################### +!!table of experiments +###################### +#exp_name, var_name[, exp_main_path[, exp_file_path[, nc_var_name[, suffix[, var_min[, var_max]]]]]] + +####################### +!!table of observations +####################### +#obs_name, var_name[, obs_main_path[, obs_file_path[, nc_var_name[, suffix[, var_min[, var_max]]]]]] +``` +The lines starting with '#' are comments and the ones starting with '!' are +key lines that can't be moved or removed. + +As just shown, the configuration file consists of a list of definitions and of +two tables, one to keep information on experimental datasets and the other +for observational datasets. + +The rows or entries of the tables will be filled up each with information +relative to a dataset. An entry will associate a pair of dataset name and +variable name to a set of information pieces. +Each entry keeps 8 columns, the pair of keys and 6 information pieces +associated to a dataset: the dataset short name or identifier, the variable +short name, the main path or path to the dataset main folder, the file path or +path to the NetCDF files of the dataset, the actual variable name inside the +files, a suffix (read further) and a lower and uper thresholds to disable +values of the dataset beyond them. +The list of definitions contains, initially, the default values for the columns +of the tables. It can be extended with other definitions that can be accessed +from throughout the configuration file, which is useful to avoid repeating +certain paths, for example, in multiple entries. A definition follows the +format `VARIABLE = value` and its value can be invoked with `$VARIABLE$`. +Apart from these explicit definitions, there are some implicit key definitions: + - `$EXP_NAME$` to retrieve, from an experimental dataset entry, the +identifier name of an experimenal dataset, as requested to `Load()`. + - `$OBS_NAME$`, similar to `$OBS_NAME$`. + - `$VAR_NAME$`, the short name of the variable, as requested to `Load()`. + - `$START_DATE$`, one of the starting dates, as requested to `Load()`. + - `$YEAR$`, `$MONTH$`, `$DAY$`, taken from the `$START_DATE$`. + - `$MEMBER_NUMBER$`, the number of the member in loadin process, from 0 to +total_number_of_members - 1 and with padding zeros. + - `$STORE_FREQ$`, the frequency of the experimental data in disk, as +specified to `Load()` via `storefreq`. + +The next step is to add the entries of the datasets of interest. It can be +achieved with a combination of the functions `ConfigFileOpen()`, +`ConfigAddEntry()` and `ConfigFileSave()`: +```r +c <- ConfigFileOpen(conf_path) +c <- ConfigAddEntry(c, 'experiments', dataset_name = 'expA', var_name = 'tas', + main_path = '/path/to/experiments/$EXP_NAME$/', + file_path = 'monthly_mean/$VAR_NAME$/$VAR_NAME$_$START_DATE$.nc') +c <- ConfigAddEntry(c, 'experiments', dataset_name = 'expB', var_name = 'tas', + main_path = '/path/to/experiments/$EXP_NAME$/', + file_path = 'monthly_mean/$VAR_NAME$/$VAR_NAME$_$START_DATE$.nc') +c <- ConfigAddEntry(c, 'observations', dataset_name = 'obsX', var_name = 'tas', + main_path = '/path/to/observations/$OBS_NAME$/', + file_path = 'monthly_mean/$VAR_NAME$/$VAR_NAME$_$YEAR$$MONTH$.nc') +ConfigFileSave(c, conf_path) +``` + +The tables in the file, at this point, are shown next: +``` +###################### +!!table of experiments +###################### +#exp_name, var_name[, exp_main_path[, exp_file_path[, nc_var_name[, suffix[, var_min[, var_max]]]]]] +expA, tas, /path/to/experiments/$EXP_NAME$/, monthly_mean/$VAR_NAME$/$VAR_NAME$_$START_DATE$.nc, *, *, *, * +expB, tas, /path/to/experiments/$EXP_NAME$/, monthly_mean/$VAR_NAME$/$VAR_NAME$_$START_DATE$.nc, *, *, *, * + +####################### +!!table of observations +####################### +#obs_name, var_name[, obs_main_path[, obs_file_path[, nc_var_name[, suffix[, var_min[, var_max]]]]]] +obsX, tas, /path/to/observations/$OBS_NAME$/, monthly_mean/$VAR_NAME$/$VAR_NAME$_$YEAR$$MONTH$.nc, *, *, *, * +``` + +An asterisk ('*') means that the cell will take the default value defined in +the defaults for the corresponding column. So the column 'nc_var_name' takes +'$VAR_NAME$' which is then replaced by 'tas' in this case. The other default +values are all empty. + +Once the file is ready it can be used from `Load()` by specifying its path via +the parameter `configfile`. Then, `exp` and `obs` can be used in its simple +format: a vector of character strings that tell the name of the datasets of +interest. For example: +```r +sdates <- paste0(1991:2000, '1101') +data <- Load(var = 'tas', exp = c('expA', 'expB'), obs = c('obsX'), + sdates = sdates, configfile = '/path/to/configfile.conf') +``` + +From this point on, one could create files with entries for each pair of +(dataset name, variable name) of interest. + +However, the first two columns of the tables in a configuration file can also +take regular expressions to match more than one dataset name or variable name. +This way, a more compact and generalized table can be obtained: +```r +c <- ConfigFileOpen(conf_path) +c <- ConfigAddEntry(c, 'experiments', dataset_name = '.*', var_name = '.*', + main_path = '/path/to/experiments/$EXP_NAME$/', + file_path = 'monthly_mean/$VAR_NAME$/$VAR_NAME$_$START_DATE$.nc') +c <- ConfigAddEntry(c, 'observations', dataset_name = '.*', var_name = '.*', + main_path = '/path/to/observations/$OBS_NAME$/', + file_path = 'monthly_mean/$VAR_NAME$/$VAR_NAME$_$YEAR$$MONTH$.nc') +ConfigFileSave(c, conf_path) +``` + +The corresponding tables are: +``` +###################### +!!table of experiments +###################### +#exp_name, var_name[, exp_main_path[, exp_file_path[, nc_var_name[, suffix[, var_min[, var_max]]]]]] +.*, .*, /path/to/experiments/$EXP_NAME$/, monthly_mean/$VAR_NAME$/$VAR_NAME$_$START_DATE$.nc, *, *, *, * + +####################### +!!table of observations +####################### +#obs_name, var_name[, obs_main_path[, obs_file_path[, nc_var_name[, suffix[, var_min[, var_max]]]]]] +.*, .*, /path/to/observations/$OBS_NAME$/, monthly_mean/$VAR_NAME$/$VAR_NAME$_$YEAR$$MONTH$.nc, *, *, *, * +``` + +The regular expression '.*' matches any sequence of characters, so these +entries will assign to all the (experiment name, variable name) pairs a path +with the pattern +`/path/to/experiments/$EXP_NAME$/monthly_mean/$VAR_NAME$/$VAR_NAME$_$START_DATE$.nc` +or, to all the (observation name, variable name) pairs a path with the pattern +`/path/to/observations/$OBS_NAME$/monthly_mean/$VAR_NAME$/$VAR_NAME$_$YEAR$$MONTH$.nc`. +In other words, with only two entries in the configuration file you will be +able to load many variables from many datasets, as long as they follow a +common convention. + +If more than one entry match a pair (dataset name, variable name) all of +them will be applied from more general to more specific to obtain a value +for each of the 6 information pieces that, at the end, will tell the location +and information of the requested variable for the requested dataset. + +The configuration file, all in all, is a complex but powerful mechanism. +Read `?ConfigFileOpen` for a complete explanation of the details of the tables +in the configuration files and how multiple matches are applied to build up the +final information. Also see there why the 'suffix' column can be useful. + +#### Re-arranging long runs +Sometimes it can happen that one needs to compare data from two experimental +datasets, one stored in multiple files (one per starting dates) and the other +stored in a single long run (one file with one starting date). + +In this case running one single `Load()` call won't be enough since the +`sdates` argument has to take different values in function of the distribution +of the starting dates of the dataset to load. Besides, running two separate +`Load()` calls with different starting dates yields two non-comparable data +sets. + +To solve this, it is possible to re-arrange the long run into multiple starting +dates with `Histo2Hindcast()` by just specifying the original starting date, +the series of target starting dates and the number of target lead-times: + +Loading the multiple run experiment: +``` +expA <- list( + name = 'experimentA', + path = file.path('/path/to/experiments/$EXP_NAME$/monthly_mean', + '$VAR_NAME$/$VAR_NAME$_$START_DATE$.nc') + ) +sdatesA <- paste0(1991:2000, '1101') +leadtimesA <- 12 +data <- Load(var = 'tas', exp = list(expA), obs = NULL, sdates = sdatesA, + leadtimemax = leadtimesA) +``` + +Loading the single run experiment: +``` +expC <- list( + name = 'experimentC', + path = file.path('/path/to/experiments/$EXP_NAME$/monthly_mean', + '$VAR_NAME$/$VAR_NAME$_$START_DATE$.nc') + ) +sdatesC <- '19501101' +leadtimemin <- (1991 - 1950) * 12 + 1 +leadtimemax <- leadtimemin + (2000 - 1991 + 1) * 12 +data <- Load(var = 'tas', exp = list(expC), obs = NULL, sdates = sdatesC, + leadtimemin = leadtimemin, leadtimemax = leadtimemax) +data <- Histo2Hindcast(data, sdatesA[1], sdatesA, leadtimesA) +``` diff --git a/vignettes/ex_ano_expA_obsX.png b/vignettes/ex_ano_expA_obsX.png new file mode 100644 index 0000000000000000000000000000000000000000..cbb43565f8d978f0b0957822422226f306005a74 GIT binary patch literal 22516 zcmeFZcTiL9*Dj0|6%lD7T|tUe=^X?q(rXAMfOG^Q(mVKw^d?dw2!!4VH9$gB=^%vO zi}cV-=p{M(dEa?|b7sz&Z@z!OnePu$?(Ds1-D|IMt!u4Kq>h#f=>xh4L_|cSs&5tb zh=^{n6A|6yzjqT@dBkf(3%uQOS5P&$ckkZJqV`|l>-~>!jopDC+yDK$k<9&wo`~of zk*cD+flvC*946itgd!Yxa^2p(k@HV?Hz$FJHRKj$Q^wb=pAlgzYBwinUmRM0%+~I> zO?{IkvRL1Tc+O$?Pp#_okH^l-uiyLzQ{1Icxw-{ex_1-Ba;sfFWAB}3g*ozM+Nol} zX{ULi!r-m0rz3n0R5)-xT9bKQ)*lqi0*IwEEWbqwyc@}~&=3*5c2(pfBKoux0Rfge z$Wg#+6sy|}A|fi46<}+eaou--Q)WpucRg!TJYBl|vYlwck4bOFkdZeA+5@Ak0A44e?%VXg&y)B~yn(?Xdkh%qhE+OpW>kA&r2X 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ztG=|8zX)%=9Jc281@Me7-%D;P%4mM?e2VSjGkopW+cSBE<~28?yS{^s@ty literal 0 HcmV?d00001 diff --git a/vignettes/example.md b/vignettes/example.md new file mode 100644 index 0000000..9ac470d --- /dev/null +++ b/vignettes/example.md @@ -0,0 +1,263 @@ +--- +author: "Nicolau Manubens" +reviser: "An-Chi Ho" +date: "`r Sys.Date()`" +output: html_document +vignette: > + %\VignetteEngine{R.rsp::md} + %\VignetteIndexEntry{Example} + %\usepackage[utf8]{inputenc} +--- +Example +======= + +Next you can see an example of usage of s2dv spanning its +four modules ([**Data retrieval**](data_retrieval.md), +[**Statistics**](statistics.md), [**Verification**](verification.md) +and [**Visualisation**](visualisation.md)). + +The goal of the example is to load and analyse the skill of two sample +forecasts of the near-surface air temperature over the North Pacific region +and assess their skill against a reference reanalysis. +The data used in this example has gone already through a first post-processing +stage in which the monthly means have been computed. + +Loading data +------------ + +First the package is loaded and attached. + +The goal is to load data for two experimental datasets and one observational +dataset to be used as reference. The distribution in the file system and +details of these datasets are explained in [**Data retrieval**]. + +A list is built with information on the location of each dataset to load. +A path pattern is specified for each dataset, in this case, with the wildcards +'$VAR_NAME$', '$START_DATE$', '$YEAR$', '$MONTH$', '$EXP_NAME$' and +'$OBS_NAME$'. These wildcards will be automatically replaced by `Load()` with +the corresponding values (the requested variable name, the requested starting +dates, years or months, the dataset names, ...). See the available wildcards in `?Load`. + +```r +library(s2dv) + +expA <- list(name = 'experimentA', + path = file.path('/path/to/experiments/$EXP_NAME$/monthly_mean', + '$VAR_NAME$/$VAR_NAME$_$START_DATE$.nc')) +expB <- list(name = 'experimentB', + path = file.path('/path/to/experiments/$EXP_NAME$/monthly_mean', + '$VAR_NAME$/$VAR_NAME$_$START_DATE$.nc')) +obsX <- list(name = 'observationX', + path = file.path('/path/to/observations/$OBS_NAME$/monthly_mean', + '$VAR_NAME$/$VAR_NAME$_$YEAR$$MONTH$.nc')) +``` + +Then the data is loaded with `Load()` providing the previously built lists +-to specify the desired datasets- and other parameters to select the Earth +surface region of interest, starting dates and forecast time steps to load +data from. +In this example, the requested format is 2-dimensional: all the loaded data +will be remapped onto the specified common 'grid' via CDO libraries. + +```r +sdates <- paste0(1991:2000, '1101') +data <- Load('tas', list(expA, expB), list(obsX), + sdates = sdates, + leadtimemin = 2, leadtimemax = 13, + latmin = -10, latmax = 60, + lonmin = 100, lonmax = 250, + output = 'lonlat', grid = 't106grid', + method = 'distance-weighted') +## * The load call you issued is: +## * Load(var = "tas", exp = list(structure(list(name = "experimentA", path = +## * "/path/to/experiments/$EXP_NAME$/monthly_mean/$VAR_NAME$/$VAR_NAME$_$START_DATE$.nc"), +## * .Names = c("name", "path")), structure(list(name = +## * "experimentB", path = +## * "/path/to/experiments/$EXP_NAME$/monthly_mean/$VAR_NAME$/$VAR_NAME$_$START_DATE$.nc"), +## * .Names = c("name", "path"))), obs = list(structure(list(name = +## * "observationX", path = +## * "/path/to/observations/$OBS_NAME$/monthly_mean/$VAR_NAME$/$VAR_NAME$_$YEAR$$MONTH$.nc"), +## * .Names = c("name", "path"))), sdates = c("19911101", +## * "19921101", ..., "20001101"), grid = "t106grid", output = +## * "lonlat", storefreq = "monthly", ...) +## * See the full call in '$load_parameters' after Load() finishes. +## * Fetching first experimental files to work out 'var_exp' size... +## * Exploring dimensions... /path/to/experiments/experimentA/monthly_mean/tas/tas_19911101.nc +## * Success. Detected dimensions of experimental data: 2, 5, 10, 12, 63, 134 +## * Fetching first observational files to work out 'var_obs' size... +## * Exploring dimensions... /path/to/observations/observationX/monthly_mean/tas/tas_199112.nc +## * Success. Detected dimensions of observational data: 1, 1, 10, 12, 63, 134 +## * Will now proceed to read and process 140 data files: +## * The list of files is long. You can check it after Load() finishes in the output '$source_files'. +## * Total size of requested data: 89147520 bytes. +## * - Experimental data: ( 2 x 5 x 10 x 12 x 63 x 134 ) x 8 bytes = 81043200 bytes. +## * - Observational data: ( 1 x 1 x 10 x 12 x 63 x 134 ) x 8 bytes = 8104320 bytes. +## * If size of requested data is close to or above the free shared RAM memory, R will crash. +## starting worker pid=3674 on localhost:11060 at 15:11:26.226 +## starting worker pid=3690 on localhost:11060 at 15:11:26.419 +## starting worker pid=3706 on localhost:11060 at 15:11:26.614 +## starting worker pid=3722 on localhost:11060 at 15:11:26.805 +## starting worker pid=3739 on localhost:11060 at 15:11:26.997 +## starting worker pid=3755 on localhost:11060 at 15:11:27.190 +## starting worker pid=3771 on localhost:11060 at 15:11:27.380 +## starting worker pid=3787 on localhost:11060 at 15:11:27.572 +## * Loading... This may take several minutes... +## * Progress: 0% + 10% + 10% + 10% + 10% + 10% + 10% + 10% + 10% + 10% + 10% +``` + +The output consists of two arrays of data (experimental and observational +data) with labelled dimensions, a list of loaded files, a list of not found +files and a call stamp to exactly reproduce as needed, among others. +See [**Data +retrieval**](data_retrieval.md) +for a full explanation of the capabilities and outputs of `Load()`. + +Keep in mind that the two arrays obtained from `Load()` will have the +following dimensions in the following order: +```r + c(n. of datasets, n. of members, n. of starting dates, n. of lead-times, n. of latitudes, n. of longitudes) +``` + +Checking and summarizing data +----------------------------- + + +Next, the data of the first member, starting date and leadtime of each dataset +can be visualised on a cylindrical equidistant projection with `PlotEquiMap()` +to check that the loaded data is as expected. +```r +PlotEquiMap(data$mod[1, 1, 1, 1, , ], data$lon, data$lat) +PlotEquiMap(data$mod[2, 1, 1, 1, , ], data$lon, data$lat) +PlotEquiMap(data$obs[1, 1, 1, 1, , ], data$lon, data$lat) +``` + + +See the full code used to obtain this figure in +[**Snippet 1**](snippets.md#snippet1). + +The values for some starting dates at a single grid point of an experimental +dataset can be plotted together with the observations with the function +`PlotAno()`: +```r +mod <- data$mod[, , , , 30, 60, drop = FALSE] +dim(mod) <- dim(mod)[1:4] +obs <- data$obs[, , , , 30, 60, drop = FALSE] +dim(obs) <- dim(obs)[1:4] +PlotAno(mod, obs, gsub('1101', '1201', sdates), + toptitle = paste0("Experiment ", c("A", "B"), + ": raw 'tas' at 166.5ºE, 27.47ºN."), + ytitle = "K", + fileout = c('ex_raw_expA_obsX.eps', 'ex_raw_expB_obsX.eps')) +``` + + + + +Each coloured region represents data corresponding to a single starting date. +The bold line represents the mean value and the thin lines represent the values +of each ensemble member. The upper and lower limits of each region are +defined, respectively, by the maximum and minimum values among the members. +The black line represents the reference reanalysis values. + +We can see in the plot how the 'tas' reaches a minimum in February/March. + +We can work out the exact coordinates of the selected grid cell as follows: +```r +data$lon[60] +## 166.5 +data$lat[30] +## 27.47649 +``` + +At this point, additional numerical checks could be carried out to ensure the +data retrieval stage has been sucessful. + +Bias correction +--------------- + +The next common step is to perform statistics on the raw data such as +computing climatologies and subtracting them to the raw data to obtain +anomalies that account for the inherent drift of the forecasts. +This is straightforward with the functions `Clim()` and `Ano()` (or +`Ano_CrossValid()`, see [**Statistics**]). Before, however, it is usual to +average the data over the region of interest instead of focusing on a single +grid cell. This can be done by directly requesting the data to `Load()` with +the 'areave' output type, which will apply area weights and calculate the +total average: +```r +data <- Load('tas', list(expA, expB), list(obsX), + sdates = sdates, + leadtimemin = 2, leadtimemax = 13, + latmin = -10, latmax = 60, + lonmin = 100, lonmax = 250, + output = 'areave', grid = 't106grid', + method = 'distance-weighted') +``` + +Then we calculate and plot the per-pair climatologies with `Clim()` and +`PlotClim()`: +```r +clim <- Clim(data$mod, data$obs) +PlotClim(clim$clim_exp, clim$clim_obs, monini = 12, + toptitle = "Per-pair climatologies of 'tas' over North Pacific region.", + listexp = c('Experiment A', 'Experiment B'), + listobs = c('Observation X'), + ytitle = "K", fileout = 'ex_clim_expA_expB_obsX.eps') +``` + + + +Each line in this plot represents the climatology of each member of the +corresponding dataset. A single climatology of the ensemble mean could be +obtained providing the parameter memb = FALSE to `Clim()`, if distinction +of members is irrelevant. + +We can obtain the anomalies with `Ano()`, which simply subtracts the +climatologies to the corresponding starting dates and members of the raw data. +These can be plotted with `PlotAno()`: +```r +ano_mod <- Ano(data$mod, clim$clim_exp) +ano_obs <- Ano(data$obs, clim$clim_obs) +PlotAno(ano_mod, ano_obs, gsub('1101', '1201', sdates), + toptitle = paste0("Experiment ", c("A", "B"), + ": drift-corrected 'tas' anomalies over North Pacific region."), + ytitle = 'K', linezero = TRUE, + fileout = c('ex_ano_expA_obsX.eps', 'ex_ano_expB_obsX.eps')) +``` + + + + +To fulfill the bias correction we would need to add the observed climatologies +to these anomalies. The working units of the package, however, are the +anomalies so this step is not needed. + +Other statistics such as trends, detrended anomalies, frequency filtering, +EOF/PCA and empirical model generation are implemented in the package. +Check [**Statistics**](statistics.md) for a thorough explanation. +Also see [**Visualisation**](visualisation.md) for details on visualisation +tools. + +Assessing the quality +--------------------- + +As a measure of the skill of the two forecasts we will compute their +correlation against the reanalysis. + +First we compute the ensemble mean and then calculate the Pearson correlation +with `Corr()` and plot the results with `PlotVsLTime()`, which allows to plot +any other computed variable with confidence intervals and signification values. +```r +corr <- Corr(Mean1Dim(ano_mod, 2), Mean1Dim(ano_obs, 2)) +PlotVsLTime(corr, toptitle = "Correlations with Observation X over North Pacific region.", + ytitle = 'corr', monini = 12, + listexp = c('Exp A', 'Exp B'), + fileout = 'ex_corr_expA_expB_obsX.eps') +``` + + + +See [**Verification**](verification.md) for a detailed explanation of the +available deterministic and probabilistic scores or +[**Plotting time series**](visualisation.md#time_series) for quick reference of +how each score can be plotted. diff --git a/vignettes/s2dv_modules.png b/vignettes/s2dv_modules.png new file mode 100644 index 0000000000000000000000000000000000000000..35465c8e0985fe4f08cf7dd0c578de0bd3e8fe04 GIT binary patch literal 385333 zcmeEuWmJ{j_w50ZZjf%Jkx;s&C8fJdy1S)8Kt#Ghkd%_{RzSKtBoEz^cc1tD|Ni6N z5BJL*<9@m0KFV+$4(IUfz1Ny+&bihx@|~hI1}X_E1OmZ$Dh?O~aX2*<^Be6b?8-cbiO49HTI;20C*5*&-PYEni@N%9 zeOVhHyK<}>A{Bs|k4Zk~$X_kwTOiwT)4)gGj`mo8CEm;FgNF-l zO1Jmlpdg{W++r+Sykt`wEalXBP+L^|L%7n5H1dckv{MD=M#Tk9lbv(vehiMkw|t|a z{#R>~gXM;e;yr9*2#G4eTj9j_4GhQ~Lzl7Cx~4dSw@l7E2*<`|;WbrhDjyt?qmG_2 zY#Aywho@{+v)?0`e7ws3btRAEM-Ge$9Vm{&~PW%#8lFdRPoSw zwM3qZ#Jxp6_O9!^DVu*_Vl@=WO_`pU=#O*A3@Xsx=AY4SyjPc)(djP|m%h86CU)iI z*8HMASc>f@L>3>3SzWPw4yU_i7lj46KeF*qyBIy*FP+_$AorxD}k ziY(Hj@IC~D!Yn}@Jh-{sYXdkId4aX?`e8`Xqr%qS)|7^izaMmR26|?_$EPR58}a9( z9Cq>_Q5~nFhm#$+k;8869U%<(*HG^(aSin#mzm2A=ToPz=JYv5oRrlis3~b$U7bxx zE!n6NpGMGAJn$!V!^5`hZWxNkE(Y0}f+LuHoVYH?s!>&x_2|O%3^2}O#kA0x^6C@V z5U+?ex1;A?6nJ@>)~-D7cSBfCy{yT*k2P2fnJlyU^ku8FB_G>f@yW@@Be|XBUe!`) zZQDp$lIEK0qJ2g~%QFu&6{Gh?A>T8bO^0&$h(>MH%55GfE;Da22ovIH44p}Dyb&FL z9E2)Au`qpi#DQ@ruDYO*JmcfHE$i3cRy8>DjqwUmeb%@)2*0bZ@EcPyrhxzEY$eBS6NM^&HVf)JTPlqQcE zQXd##E?_cW=+ZPX?0ICo_{qZbTUyyl7FO)$Q~wqYS@tU~?*>4JSp@M!!&V0bx^AmV`yppnZ42PtgBB+nK{+|{$u2S2$$ZR$FP${&PVVR`Xbo` z1&_ayB9~X2W^SaEEuViN!JT;iY;*ndqJ{_?h>B~kk@omc1jVl^t_`ShC-Og~P=t=w zv>Q$Tltezf#j0I+`@1QM^1+{!Z~dcpy$icD`Lg$=&$%<%D9uHJy1Ehc#KH0IR6|XD zP;HBlz%sv*mlUK{70>mQpn>*|h@lmY9&E_Yp%7`bZ~RAbIV4#$xv8 z1v6W+6AtVd#%(TnG~Z_Jf6mFqX0P>)=9LM63te6b2!M+*JQ@xm)KZVO+)Jd^c`E8F z{4bJyBUq`~&uc1f*vZ7+X-dGPqQb42Zf1mq`MQ?$A6RtbhC zrMg;L+_MFPH~wQw78Qn}@=`jf ztF@j^f05MHjg5{buP#(bD{?22FpFeZiYm`t{5?%bTx*;L^pOAT`JYqkg6b1-0;BT| zKK3I92}NW6X>y&9J?9L)cK|f@c^gU4`T`10wn0EwU0lyFZQgswzPoGvD*uuEn?@xL06c??ga=?~up8XC-jh{E;py`QDQ@ z`nYN>8=~T~FVarH7JH*sfZ0^G5+?OwYtTLedB%8;6#rZkadm7 z=uyFt^ovQR8}{n^?T2p+6Em8A^35RG9#D0I9)zS<|Kd<~40K^CM@m<^KlaPMX)7zi z?Pqi7EQ_b)vVMf#47K948|kbr5D7W5zH&*Za=tBPGG5*?HC(fnMJPmUiQx#IWTOu! zTjN+*d)3!EHxENCo3W|ZT-u{v35iK(P&~)**gVDANrNKhW2m;NLVlx6STE^%tg8>u zVfpCeh`HDLqn>5`CCh$rKm~~3IX;O>P?%|CJE^=eQdGp!T|!;~!?gluyyvPPN!WEc z$WtAW%{OUf2VIZWBWLK!-+k0&sD=h#S=>j=PUKef8>KV%>IB@1U$P)2rAugDxD zjxu>Z5Z&q}TRgO4gL+y~Q6JAd{0{YlV(&p$4V*)6 zLZ}dgp-xjb>koI?kX@D8p?krJbhE3wRqffXw*}|-uNmr0XRgGB`0$9H3ZY+LU;!*; z8Yn3-pAA^^xO2G+cxKMGjy|iymz!6OzL{taTg!P)XjGFTmajCU(bK?&^l$04{`D>u z8?K8hvgVmDn^$Y*bd7XMXIv=b*@V+-Q79`iizc7&0Kk1=sVAn?|KLWU`PPae!*=O- zt7fHJw0&zkF}q&^z>@Lf-&)y01G(1G9sbFSR6idC)6Xk5kU$DdVIrPu^E)rGzb7}P zj5x=8hjG8U_Y4ocw+bxmc=QdA$^mYLB{dO>FbQ&HtawEhEup33g;8zia5p-@_%)B! z%V1QRylE;<9ByN~DQOoNK3!9z;ZsY`3@@FuUzygNr~vgDA#0jwyE!Sv0tOA4WEZywybte+}>=h z_+r25cJYz1tr_YDCb==Fc0IIwvV*?7E`F`qn`Y2L6^(ZpQ)L$d#PzD1@#o-u7(+v_ zQixL5iC4U49j{#qPHQx;m_Bsz$3b)Wq8u-Rg6#9v;WZS(lt$HZMqCT50JBj0psJ8O z_{@^qrg`_q+X17gm51}FRg0X`hthwWHqTvY;ah_a{1Xit@AcZL$0t$}Uu{_R1=afI z775yLk)F?VcK2clHD3g$Pf)p*Ud+}P+Al|T?`1j^kw15|?pQ!R*YIzQYvQ2RC%-9P za;J>1kh)#n=0gd{zA@k+_jygGKBdlHbP?gE_WAS}VxJdOiQ}#+FLEQp331(B)Grw7 z)Txd6{F;r6sM5O$-9~j=!nu#OcKcU;*;7od$2IkG;rx;&)TyagwHuxq0|OxHBCY!p zFC2+=womO9gVhGUTN>COyEJ)Rs4&(%<1hJ=sJS?yy_8{_7_PiyHYR!CJbdX#qW8Te zuS|QPobUTpQsJPFxXW@hl!g=MRDcaf`L)SE?EgF@<<-8zi-Hl!+7{X3763HE`b*(1 znl|3AQHRPnM(yykPW;~5$($DfG_C@O!(^PA`vz%<@{0COkgmAwIpc3tMyQ!_srzl_ zQ+=+I752Edvu=Axk|WKZU!i;+&mZmgVh>E?U^o39&Rl-Bqq`I>d!}A@yI1mt#P8u? 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