diff --git a/R/ACC.R b/R/ACC.R
index 44c724c927675295ee54f26d7768380aaf96fc7a..ceb1e94e5257ef85de5b97ed97a19733c8e8d6ef 100644
--- a/R/ACC.R
+++ b/R/ACC.R
@@ -276,7 +276,7 @@ ACC <- function(exp, obs, dat_dim = 'dataset', lat_dim = 'lat', lon_dim = 'lon',
   }
   if (!all(dim(exp)[name_exp] == dim(obs)[name_obs])) {
     stop(paste0("Parameter 'exp' and 'obs' must have same length of ",
-                "all the dimensions expect 'dat_dim' and 'memb_dim'."))
+                "all the dimensions except 'dat_dim' and 'memb_dim'."))
   }
 
 #-----------------------------------------------------------------
diff --git a/R/Ano_CrossValid.R b/R/Ano_CrossValid.R
index 99205020b7412afdf90513ad18dedf0b9302320d..d1996b9cd84023e8dc37e11af20b32b6e1cedd0f 100644
--- a/R/Ano_CrossValid.R
+++ b/R/Ano_CrossValid.R
@@ -18,7 +18,8 @@
 #'@param dat_dim A character vector indicating the name of the dataset and 
 #'  member dimensions. When calculating the climatology, if data at one 
 #'  startdate (i.e., 'time_dim') is not complete along 'dat_dim', this startdate
-#'  along 'dat_dim' will be discarded. The default value is 
+#'  along 'dat_dim' will be discarded. If there is no dataset dimension, it can be NULL.
+#' The default value is 
 #'  "c('dataset', 'member')".
 #'@param memb_dim A character string indicating the name of the member 
 #'  dimension. Only used when parameter 'memb' is FALSE. It must be one element
@@ -83,11 +84,25 @@ Ano_CrossValid <- function(exp, obs, time_dim = 'sdate', dat_dim = c('dataset',
     stop("Parameter 'time_dim' is not found in 'exp' or 'obs' dimension.")
   }
   ## dat_dim
-  if (!is.character(dat_dim)) {
-    stop("Parameter 'dat_dim' must be a character vector.")
-  }
-  if (!all(dat_dim %in% names(dim(exp))) | !all(dat_dim %in% names(dim(obs)))) {
-    stop("Parameter 'dat_dim' is not found in 'exp' or 'obs' dimension.")
+  if (!is.null(dat_dim)) {
+    if (!is.character(dat_dim)) {
+      stop("Parameter 'dat_dim' must be a character vector.")
+    }
+    if (!all(dat_dim %in% names(dim(exp))) | !all(dat_dim %in% names(dim(obs)))) {
+      stop("Parameter 'dat_dim' is not found in 'exp' or 'obs' dimension.",
+           " Set it as NULL if there is no dataset dimension.")
+    }
+    # If dat_dim is not in obs, add it in
+    if (any(!dat_dim %in% names(dim(obs)))) {
+      reset_obs_dim <- TRUE
+      ori_obs_dim <- dim(obs)
+      dim(obs) <- c(dim(obs), rep(1, length(dat_dim[which(!dat_dim %in% names(dim(obs)))])))
+      names(dim(obs)) <- c(names(ori_obs_dim), dat_dim[which(!dat_dim %in% names(dim(obs)))])
+    } else {
+      reset_obs_dim <- FALSE
+    }
+  } else {
+    reset_obs_dim <- FALSE
   }
   ## memb
   if (!is.logical(memb) | length(memb) > 1) {
@@ -115,9 +130,11 @@ Ano_CrossValid <- function(exp, obs, time_dim = 'sdate', dat_dim = c('dataset',
   ## exp and obs (2)
   name_exp <- sort(names(dim(exp)))
   name_obs <- sort(names(dim(obs)))
-  for (i in 1:length(dat_dim)) {
-    name_exp <- name_exp[-which(name_exp == dat_dim[i])]
-    name_obs <- name_obs[-which(name_obs == dat_dim[i])]
+  if (!is.null(dat_dim)) {
+    for (i in 1:length(dat_dim)) {
+      name_exp <- name_exp[-which(name_exp == dat_dim[i])]
+      name_obs <- name_obs[-which(name_obs == dat_dim[i])]
+    }
   }
   if(!all(dim(exp)[name_exp] == dim(obs)[name_obs])) {
     stop(paste0("Parameter 'exp' and 'obs' must have the same length of ",
@@ -135,36 +152,65 @@ Ano_CrossValid <- function(exp, obs, time_dim = 'sdate', dat_dim = c('dataset',
 
   #-----------------------------------
   # Per-paired method: If any sdate along dat_dim is NA, turn all sdate points along dat_dim into NA.
-   pos <- rep(0, length(dat_dim))  # dat_dim: [dataset, member]
-   for (i in 1:length(dat_dim)) {
-     pos[i] <- which(names(dim(obs)) == dat_dim[i])
-   }
-   outrows_exp <- MeanDims(exp, pos, na.rm = FALSE) +
-                  MeanDims(obs, pos, na.rm = FALSE)
-   outrows_obs <- outrows_exp
-
-   for (i in 1:length(pos)) {
-     outrows_exp <- InsertDim(outrows_exp, pos[i], dim(exp)[pos[i]])
-     outrows_obs <- InsertDim(outrows_obs, pos[i], dim(obs)[pos[i]])
-   }
-   exp_for_clim <- exp
-   obs_for_clim <- obs
-   exp_for_clim[which(is.na(outrows_exp))] <- NA
-   obs_for_clim[which(is.na(outrows_obs))] <- NA
+  if (!is.null(dat_dim)) {
+    pos <- rep(0, length(dat_dim))  # dat_dim: [dataset, member]
+    for (i in 1:length(dat_dim)) {
+        pos[i] <- which(names(dim(obs)) == dat_dim[i])
+    }
+    outrows_exp <- MeanDims(exp, pos, na.rm = FALSE) +
+                    MeanDims(obs, pos, na.rm = FALSE)
+    outrows_obs <- outrows_exp
+
+    for (i in 1:length(pos)) {
+        outrows_exp <- InsertDim(outrows_exp, pos[i], dim(exp)[pos[i]])
+        outrows_obs <- InsertDim(outrows_obs, pos[i], dim(obs)[pos[i]])
+    }
+    exp_for_clim <- exp
+    obs_for_clim <- obs
+    exp_for_clim[which(is.na(outrows_exp))] <- NA
+    obs_for_clim[which(is.na(outrows_obs))] <- NA
+  } else {
+    exp_for_clim <- exp
+    obs_for_clim <- obs
+  }
+
 
   #-----------------------------------
+  res <- Apply(list(exp, obs, exp_for_clim, obs_for_clim),
+                    target_dims = c(time_dim, dat_dim),
+                    fun = .Ano_CrossValid, dat_dim = dat_dim, 
+                    memb_dim = memb_dim, memb = memb,
+                    ncores = ncores)
 
-    res <- Apply(list(exp, obs, exp_for_clim, obs_for_clim),
-                  target_dims = c(time_dim, dat_dim),
-                  fun = .Ano_CrossValid,
-                  memb_dim = memb_dim, memb = memb,
-                  ncores = ncores)
+  # Remove dat_dim in obs if obs doesn't have at first place
+  if (reset_obs_dim) {
+    res_obs_dim <- ori_obs_dim[-which(names(ori_obs_dim) == time_dim)]
+    if (!memb & memb_dim %in% names(res_obs_dim)) {
+      res_obs_dim <- res_obs_dim[-which(names(res_obs_dim) == memb_dim)]
+    }
+    if (is.integer(res_obs_dim) & length(res_obs_dim) == 0) {
+      res$obs <- as.vector(res$obs)
+    } else {
+      res$obs <- array(res$obs, dim = res_obs_dim)
+    }
+  }
 
   return(res)
 }
 
-.Ano_CrossValid <- function(exp, obs, exp_for_clim, obs_for_clim,
+.Ano_CrossValid <- function(exp, obs, exp_for_clim, obs_for_clim, dat_dim = c('dataset', 'member'),
                             memb_dim = 'member', memb = TRUE, ncores = NULL) {
+  if (is.null(dat_dim)) {
+    ini_dims_exp <- dim(exp)
+    ini_dims_obs <- dim(obs)
+    ini_dims_exp_for_clim <- dim(exp)
+    ini_dims_obs_for_clim <- dim(exp)
+    exp <- InsertDim(exp, posdim = 2, lendim = 1, name = 'dataset')
+    exp_for_clim <- InsertDim(exp_for_clim, posdim = 2, lendim = 1, name = 'dataset')
+    obs <- InsertDim(obs, posdim = 2, lendim = 1, name = 'dataset')
+    obs_for_clim <- InsertDim(obs_for_clim, posdim = 2, lendim = 1, name = 'dataset')
+  }
+
   # exp: [sdate, dat_dim, memb_dim]
   # obs: [sdate, dat_dim, memb_dim]
   ano_exp_list <- vector('list', length = dim(exp)[1])  #length: [sdate]
@@ -222,5 +268,10 @@ Ano_CrossValid <- function(exp, obs, time_dim = 'sdate', dat_dim = c('dataset',
   ano_obs <- array(unlist(ano_obs_list), dim = c(dim(obs)[-1], dim(obs)[1]))
   ano_obs <- Reorder(ano_obs, c(length(dim(obs)), 1:(length(dim(obs)) - 1)))
 
+  if (is.null(dat_dim)) {
+    ano_exp <- array(ano_exp, dim = ini_dims_exp)
+    ano_obs <- array(ano_obs, dim = ini_dims_obs)
+  }
+
   return(list(exp = ano_exp, obs = ano_obs))
 }
diff --git a/R/BrierScore.R b/R/BrierScore.R
index c3673ad4273089059f13debc91d244554c2f90cd..22f497d18553240f67693d3891c912cc43be059a 100644
--- a/R/BrierScore.R
+++ b/R/BrierScore.R
@@ -57,13 +57,13 @@
 #''bs_check_gres', 'bss_gres', 'rel_bias_corrected', 'gres_bias_corrected', 
 #''unc_bias_corrected', and 'bss_bias_corrected' are (a) a number (b) an array
 #'with dimensions c(nexp, nobs, all the rest dimensions in 'exp' and 'obs' 
-#'expect 'time_dim' and 'memb_dim') (c) an array with dimensions of
+#'except 'time_dim' and 'memb_dim') (c) an array with dimensions of
 #''exp' and 'obs' except 'time_dim' and 'memb_dim'\cr
 #'Items 'nk', 'fkbar', and 'okbar' are (a) a vector of length of bin number 
 #'determined by 'threshold' (b) an array with dimensions c(nexp, nobs, 
-#'no. of bins, all the rest dimensions in 'exp' and 'obs' expect 'time_dim' and
+#'no. of bins, all the rest dimensions in 'exp' and 'obs' except 'time_dim' and
 #''memb_dim') (c) an array with dimensions c(no. of bin, all the rest dimensions
-#'in 'exp' and 'obs' expect 'time_dim' and 'memb_dim')
+#'in 'exp' and 'obs' except 'time_dim' and 'memb_dim')
 #' 
 #'@references
 #'Wilks (2006) Statistical Methods in the Atmospheric Sciences.\cr
@@ -176,11 +176,11 @@ BrierScore <- function(exp, obs, thresholds = seq(0.1, 0.9, 0.1), time_dim = 'sd
   }
   if (any(!name_exp %in% name_obs) | any(!name_obs %in% name_exp)) {
     stop(paste0("Parameter 'exp' and 'obs' must have the same names and lengths ",
-                "of all the dimensions expect 'dat_dim' and 'memb_dim'."))
+                "of all the dimensions except 'dat_dim' and 'memb_dim'."))
   }
   if (!all(dim(exp)[name_exp] == dim(obs)[name_obs])) {
     stop(paste0("Parameter 'exp' and 'obs' must have the same names and lengths ",
-                "of all the dimensions expect 'dat_dim' and 'memb_dim'."))
+                "of all the dimensions except 'dat_dim' and 'memb_dim'."))
   }
   ## ncores
   if (!is.null(ncores)) {
diff --git a/R/Clim.R b/R/Clim.R
index ce9ba2ed17b283d9a137df32e8b06275e7691f2e..c144025c1f8af795bb06afb31884949f868cb08f 100644
--- a/R/Clim.R
+++ b/R/Clim.R
@@ -173,7 +173,7 @@ Clim <- function(exp, obs, time_dim = 'sdate', dat_dim = c('dataset', 'member'),
   }
   if(!all(dim(exp)[name_exp] == dim(obs)[name_obs])) {
     stop(paste0("Parameter 'exp' and 'obs' must have the same dimensions ",
-                "expect 'dat_dim'."))
+                "except 'dat_dim'."))
   }
 
   ###############################
diff --git a/R/Consist_Trend.R b/R/Consist_Trend.R
index b02aa5fe10cf64b6c574fb2314dd3ad91ab38029..ee956840bf613fc25b4d9ca65760a86e2f9bb4b3 100644
--- a/R/Consist_Trend.R
+++ b/R/Consist_Trend.R
@@ -124,7 +124,7 @@ Consist_Trend <- function(exp, obs, dat_dim = 'dataset', time_dim = 'sdate', int
   }
   if(!all(dim(exp)[name_exp] == dim(obs)[name_obs])) {
     stop(paste0("Parameter 'exp' and 'obs' must have same length of ",
-                "all dimension expect 'dat_dim'."))
+                "all dimension except 'dat_dim'."))
   }
   ## interval
   if (!is.numeric(interval) | interval <= 0 | length(interval) > 1) {
diff --git a/R/Corr.R b/R/Corr.R
index 0382a393266a7b021a7aab39e69f9e7382e1155c..67efb09c0a1119c0970682de43518a32368f48a1 100644
--- a/R/Corr.R
+++ b/R/Corr.R
@@ -2,28 +2,29 @@
 #'
 #'Calculate the correlation coefficient (Pearson, Kendall or Spearman) for 
 #'an array of forecast and an array of observation. The correlations are 
-#'computed along time_dim, the startdate dimension. If comp_dim is given, 
-#'the correlations are computed only if obs along the comp_dim dimension are 
-#'complete between limits[1] and limits[2], i.e., there is no NA between 
-#'limits[1] and limits[2]. This option can be activated if the user wants to 
-#'account only for the forecasts which the corresponding observations are 
-#'available at all leadtimes.\cr 
+#'computed along 'time_dim' that usually refers to the start date dimension. If
+#''comp_dim' is given, the correlations are computed only if obs along comp_dim
+#'dimension are complete between limits[1] and limits[2], i.e., there is no NA 
+#'between limits[1] and limits[2]. This option can be activated if the user 
+#'wants to account only for the forecasts which the corresponding observations 
+#'are available at all leadtimes.\cr 
 #'The confidence interval is computed by the Fisher transformation and the 
 #'significance level relies on an one-sided student-T distribution.\cr 
-#'If the dataset has more than one member, ensemble mean is necessary necessary
-#'before using this function since it only allows one dimension 'dat_dim' to
-#'have inconsistent length between 'exp' and 'obs'. If all the dimensions of
-#''exp' and 'obs' are identical, you can simply use apply() and cor() to 
+#'The function can calculate ensemble mean before correlation by 'memb_dim' 
+#'specified and 'memb = F'. If ensemble mean is not calculated, correlation will
+#'be calculated for each member.
+#'If there is only one dataset for exp and obs, you can simply use cor() to 
 #'compute the correlation.
 #'
-#'@param exp A named numeric array of experimental data, with at least two 
-#'  dimensions 'time_dim' and 'dat_dim'.
+#'@param exp A named numeric array of experimental data, with at least dimension
+#'  'time_dim'.
 #'@param obs A named numeric array of observational data, same dimensions as  
 #'  parameter 'exp' except along 'dat_dim' and 'memb_dim'.
 #'@param time_dim A character string indicating the name of dimension along  
 #'  which the correlations are computed. The default value is 'sdate'.
 #'@param dat_dim A character string indicating the name of dataset (nobs/nexp) 
-#'  dimension. The default value is 'dataset'.
+#'  dimension. The default value is 'dataset'. If there is no dataset 
+#'  dimension, set NULL.
 #'@param comp_dim A character string indicating the name of dimension along which
 #'  obs is taken into account only if it is complete. The default value
 #'  is NULL.
@@ -51,9 +52,10 @@
 #'  c(nexp, nobs, exp_memb, obs_memb, all other dimensions of exp except 
 #'  time_dim and memb_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). exp_memb is the number of
-#'member in experiment (i.e., 'memb_dim' in exp) and obs_memb is the number of 
-#'member in observation (i.e., 'memb_dim' in obs).\cr\cr
+#'number of observation (i.e., 'dat_dim' in obs). If dat_dim is NULL, nexp and 
+#'nobs are omitted. exp_memb is the number of member in experiment (i.e., 
+#''memb_dim' in exp) and obs_memb is the number of member in observation (i.e.,
+#''memb_dim' in obs). If memb = F, exp_memb and obs_memb are omitted.\cr\cr
 #'\item{$corr}{
 #'  The correlation coefficient. 
 #'}
@@ -129,11 +131,14 @@ Corr <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset',
     stop("Parameter 'time_dim' is not found in 'exp' or 'obs' dimension.")
   }
   ## dat_dim
-  if (!is.character(dat_dim) | length(dat_dim) > 1) {
-    stop("Parameter 'dat_dim' must be a character string.")
-  }
-  if (!dat_dim %in% names(dim(exp)) | !dat_dim %in% names(dim(obs))) {
-    stop("Parameter 'dat_dim' is not found in 'exp' or 'obs' dimension.")
+  if (!is.null(dat_dim)) {
+    if (!is.character(dat_dim) | length(dat_dim) > 1) {
+      stop("Parameter 'dat_dim' must be a character string or NULL.")
+    }
+    if (!dat_dim %in% names(dim(exp)) | !dat_dim %in% names(dim(obs))) {
+      stop("Parameter 'dat_dim' is not found in 'exp' or 'obs' dimension.",
+           " Set it as NULL if there is no dataset dimension.")
+    }
   }
   ## comp_dim
   if (!is.null(comp_dim)) {
@@ -194,15 +199,17 @@ Corr <- 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)))
-  name_exp <- name_exp[-which(name_exp == dat_dim)]
-  name_obs <- name_obs[-which(name_obs == dat_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 (!is.null(memb_dim)) {
     name_exp <- name_exp[-which(name_exp == memb_dim)]
     name_obs <- name_obs[-which(name_obs == memb_dim)]
   }
   if(!all(dim(exp)[name_exp] == dim(obs)[name_obs])) {
     stop(paste0("Parameter 'exp' and 'obs' must have same length of ",
-                "all dimension expect 'dat_dim' and 'memb_dim'."))
+                "all dimension except 'dat_dim' and 'memb_dim'."))
   }
   if (dim(exp)[time_dim] < 3) {
     stop("The length of time_dim must be at least 3 to compute correlation.")
@@ -234,152 +241,121 @@ Corr <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset',
     rm(obs_sub, outrows)
   }
 
-  if (is.null(memb_dim)) {
-    # Define output_dims
-    if (conf & pval) {
-      output_dims <- list(corr = c('nexp', 'nobs'),
-                          p.val = c('nexp', 'nobs'),
-                          conf.lower = c('nexp', 'nobs'),
-                          conf.upper = c('nexp', 'nobs'))
-    } else if (conf & !pval) {
-      output_dims <- list(corr = c('nexp', 'nobs'),
-                          conf.lower = c('nexp', 'nobs'),
-                          conf.upper = c('nexp', 'nobs'))
-    } else if (!conf & pval) {
-      output_dims <- list(corr = c('nexp', 'nobs'),
-                          p.val = c('nexp', 'nobs'))
-    } else {
-      output_dims <- list(corr = c('nexp', 'nobs'))
-    }
-
-    res <- Apply(list(exp, obs), 
-                 target_dims = list(c(time_dim, dat_dim), 
-                                    c(time_dim, dat_dim)),
-                 output_dims = output_dims, 
-                 fun = .Corr, 
-                 time_dim = time_dim, method = method,
-                 pval = pval, conf = conf, conf.lev = conf.lev, 
-                 ncores = ncores)
-
-  } else {
+  if (!is.null(memb_dim)) {
     if (!memb) { #ensemble mean
-      name_exp <- names(dim(exp))
-      margin_dims_ind <- c(1:length(name_exp))[-which(name_exp == memb_dim)]
-      exp <- apply(exp, margin_dims_ind, mean, na.rm = TRUE) #NOTE: remove NAs here 
-      obs <- apply(obs, margin_dims_ind, mean, na.rm = TRUE)
-
-      # Define output_dims
-      if (conf & pval) {
-        output_dims <- list(corr = c('nexp', 'nobs'),
-                            p.val = c('nexp', 'nobs'),
-                            conf.lower = c('nexp', 'nobs'),
-                            conf.upper = c('nexp', 'nobs'))
-      } else if (conf & !pval) {
-        output_dims <- list(corr = c('nexp', 'nobs'),
-                            conf.lower = c('nexp', 'nobs'),
-                            conf.upper = c('nexp', 'nobs'))
-      } else if (!conf & pval) {
-        output_dims <- list(corr = c('nexp', 'nobs'),
-                            p.val = c('nexp', 'nobs'))
-      } else {
-        output_dims <- list(corr = c('nexp', 'nobs'))
-      }
-
-      res <- Apply(list(exp, obs),
-                   target_dims = list(c(time_dim, dat_dim),
-                                      c(time_dim, dat_dim)),
-                   output_dims = output_dims,
-                   fun = .Corr,
-                   time_dim = time_dim, method = method,
-                   pval = pval, conf = conf, conf.lev = conf.lev, ncores_input = ncores,
-                   ncores = ncores)
-
-    } else {  # correlation for each member
-
-      # Define output_dims
-      if (conf & pval) {
-        output_dims <- list(corr = c('nexp', 'nobs', 'exp_memb', 'obs_memb'),
-                            p.val = c('nexp', 'nobs', 'exp_memb', 'obs_memb'),
-                            conf.lower = c('nexp', 'nobs', 'exp_memb', 'obs_memb'),
-                            conf.upper = c('nexp', 'nobs', 'exp_memb', 'obs_memb'))
-      } else if (conf & !pval) {
-        output_dims <- list(corr = c('nexp', 'nobs', 'exp_memb', 'obs_memb'),
-                            conf.lower = c('nexp', 'nobs', 'exp_memb', 'obs_memb'),
-                            conf.upper = c('nexp', 'nobs', 'exp_memb', 'obs_memb'))
-      } else if (!conf & pval) {
-        output_dims <- list(corr = c('nexp', 'nobs', 'exp_memb', 'obs_memb'),
-                            p.val = c('nexp', 'nobs', 'exp_memb', 'obs_memb'))
-      } else {
-        output_dims <- list(corr = c('nexp', 'nobs', 'exp_memb', 'obs_memb'))
-      }
+      exp <- MeanDims(exp, memb_dim, na.rm = TRUE)
+      obs <- MeanDims(obs, memb_dim, na.rm = TRUE)
+#      name_exp <- names(dim(exp))
+#      margin_dims_ind <- c(1:length(name_exp))[-which(name_exp == memb_dim)]
+#      exp <- apply(exp, margin_dims_ind, mean, na.rm = TRUE) #NOTE: remove NAs here 
+#      obs <- apply(obs, margin_dims_ind, mean, na.rm = TRUE)
+      memb_dim <- NULL
+    }
+  }
 
-      res <- Apply(list(exp, obs),
+  res <- Apply(list(exp, obs),
                    target_dims = list(c(time_dim, dat_dim, memb_dim),
                                       c(time_dim, dat_dim, memb_dim)),
-                   output_dims = output_dims,
                    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,
-                   ncores = ncores) 
-    } 
-  }
+                   ncores = ncores)
 
  return(res)
 }
 
-.Corr <- function(exp, obs, time_dim = 'sdate', method = 'pearson',
+.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) {
-
-  if (length(dim(exp)) == 2) {
-  # exp: [sdate, dat_exp]
-  # obs: [sdate, dat_obs]
-  nexp <- as.numeric(dim(exp)[2])
-  nobs <- as.numeric(dim(obs)[2])
-  
-# NOTE: Use sapply to replace the for loop 
-  CORR <- sapply(1:nobs, function(i) {
-                           sapply(1:nexp, function (x) {
-      if (any(!is.na(exp[, x])) && sum(!is.na(obs[, i])) > 2) { #NOTE: Is this necessary?
-        cor(exp[, x], obs[, i],
-            use = "pairwise.complete.obs",
-            method = method)
-      } else {
-        NA #CORR[, i] <- NA
+  if (is.null(memb_dim)) {
+    if (is.null(dat_dim)) {
+      # exp: [sdate]
+      # obs: [sdate]
+      nexp <- 1
+      nobs <- 1
+      CORR <- array(dim = c(nexp = nexp, nobs = nobs))
+      if (any(!is.na(exp)) && sum(!is.na(obs)) > 2) {
+        CORR <- cor(exp, obs, use = "pairwise.complete.obs", method = method)
       }
-    })
-  })
-  if (is.null(dim(CORR))) {
-  CORR <- array(CORR, dim = c(1, 1))
-  }
-
-  } else {  # member
-
-  # exp: [sdate, dat_exp, memb_exp]
-  # obs: [sdate, dat_obs, memb_obs]
-  nexp <- as.numeric(dim(exp)[2])
-  nobs <- as.numeric(dim(obs)[2])
-  exp_memb <- as.numeric(dim(exp)[3])
-  obs_memb <- as.numeric(dim(obs)[3])
+    } else {
+      # exp: [sdate, dat_exp]
+      # obs: [sdate, dat_obs]
+      nexp <- as.numeric(dim(exp)[dat_dim])
+      nobs <- as.numeric(dim(obs)[dat_dim])
+      CORR <- array(dim = c(nexp = nexp, nobs = nobs))
+      for (j in 1:nobs) {
+        for (y in 1:nexp) {            
+          if (any(!is.na(exp[, y])) && sum(!is.na(obs[, j])) > 2) {
+            CORR[y, j] <- cor(exp[, y], obs[, j],
+                              use = "pairwise.complete.obs",
+                              method = method)
+          } 
+        }
+      }
+#----------------------------------------
+# Same as above calculation. 
+#TODO: Compare which is faster.
+#    CORR <- sapply(1:nobs, function(i) {
+#              sapply(1:nexp, function (x) {
+#                if (any(!is.na(exp[, x])) && sum(!is.na(obs[, i])) > 2) {
+#                  cor(exp[, x], obs[, i],
+#                      use = "pairwise.complete.obs",
+#                      method = method)
+#                } else {
+#                  NA 
+#                }
+#              })
+#            })
+#-----------------------------------------
+    }
 
-  CORR <- array(dim = c(nexp = nexp, nobs = nobs, exp_memb = exp_memb, obs_memb = obs_memb))
+  } else {  # memb_dim != NULL
+    exp_memb <- as.numeric(dim(exp)[memb_dim]) # memb_dim
+    obs_memb <- as.numeric(dim(obs)[memb_dim])
+
+    if (is.null(dat_dim)) {
+      # exp: [sdate, memb_exp]
+      # obs: [sdate, memb_obs]
+      nexp <- 1
+      nobs <- 1
+      CORR <- array(dim = c(nexp = nexp, nobs = nobs, exp_memb = exp_memb, obs_memb = obs_memb))
+
+      for (j in 1:obs_memb) {
+        for (y in 1:exp_memb) {
+              
+          if (any(!is.na(exp[,y])) && sum(!is.na(obs[, j])) > 2) {
+            CORR[, , y, j] <- cor(exp[, y], obs[, j],
+                                  use = "pairwise.complete.obs",
+                                  method = method)
+          }
 
-  for (j in 1:obs_memb) {
-    for (y in 1:exp_memb) {
-      CORR[, , y, j] <- sapply(1:nobs, function(i) {
-                          sapply(1:nexp, function (x) {
-        if (any(!is.na(exp[, x, y])) && sum(!is.na(obs[, i, j])) > 2) {
-          cor(exp[, x, y], obs[, i, j],
-              use = "pairwise.complete.obs",
-              method = method)
-        } else {
-          NA #CORR[, i] <- NA
         }
-        })
-      })
+      }
+    } else {
+      # exp: [sdate, dat_exp, memb_exp]
+      # obs: [sdate, dat_obs, memb_obs]
+      nexp <- as.numeric(dim(exp)[dat_dim])
+      nobs <- as.numeric(dim(obs)[dat_dim])
+      
+      CORR <- array(dim = c(nexp = nexp, nobs = nobs, exp_memb = exp_memb, obs_memb = obs_memb))
+
+      for (j in 1:obs_memb) {
+        for (y in 1:exp_memb) {
+          CORR[, , y, j] <- sapply(1:nobs, function(i) {
+                              sapply(1:nexp, function (x) {
+            if (any(!is.na(exp[, x, y])) && sum(!is.na(obs[, i, j])) > 2) {
+              cor(exp[, x, y], obs[, i, j],
+                  use = "pairwise.complete.obs",
+                  method = method)
+            } else {
+              NA
+            }
+            })
+          })
 
+        }
+      }
     }
-  }
-
 
   }
 
@@ -398,14 +374,21 @@ Corr <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset',
 
   if (pval | conf) {
     if (method == "kendall" | method == "spearman") {
-      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)
+      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)
+      } else {
+        tmp <- rank(obs)
+        tmp <- array(tmp)
+        names(dim(tmp)) <- time_dim
+        eno <- Eno(tmp, time_dim, ncores = ncores_input)
+      }
     } else if (method == "pearson") {
       eno <- Eno(obs, time_dim, ncores = ncores_input)  
     }
 
-    if (length(dim(exp)) == 2) {
+    if (is.null(memb_dim)) {
       eno_expand <- array(dim = c(nexp = nexp, nobs = nobs))
       for (i in 1:nexp) {
         eno_expand[i, ] <- eno
@@ -435,6 +418,21 @@ Corr <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset',
     confhigh <- tanh(atanh(CORR) + qnorm(conf.upper) / sqrt(eno_expand - 3))
   }
 
+###################################  
+  # Remove nexp and nobs if dat_dim = NULL
+  if (is.null(dat_dim) & !is.null(memb_dim)) {
+    dim(CORR) <- dim(CORR)[3:length(dim(CORR))]
+    if (pval) {
+      dim(p.val) <- dim(p.val)[3:length(dim(p.val))]
+    }
+    if (conf) {
+      dim(conflow) <- dim(conflow)[3:length(dim(conflow))]
+      dim(confhigh) <- dim(confhigh)[3:length(dim(confhigh))]
+    }
+  }
+
+###################################
+
   if (pval & conf) {
     res <- list(corr = CORR, p.val = p.val, 
                 conf.lower = conflow, conf.upper = confhigh)
@@ -447,6 +445,6 @@ Corr <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset',
     res <- list(corr = CORR)
   }
 
-  return(res) 
+  return(res)
 
 }
diff --git a/R/NAO.R b/R/NAO.R
index af4893ad0c5b904d0f62893f986282b4883d401d..6d48dba6aaec6eb8fc41dba2462c097e514ccc3f 100644
--- a/R/NAO.R
+++ b/R/NAO.R
@@ -194,7 +194,7 @@ NAO <- function(exp = NULL, obs = NULL, lat, lon, time_dim = 'sdate',
     }
     if (throw_error) {
       stop(paste0("Parameter 'exp' and 'obs' must have the same names and lengths ",
-                  "of all the dimensions expect 'memb_dim'."))
+                  "of all the dimensions except 'memb_dim'."))
     }
   }
   ## ftime_avg
diff --git a/R/RMS.R b/R/RMS.R
index b3c8ad4b016d18cc9f3dfd79ddaeb3bb38ba15b0..b3188fcd045518458cec57415c4bcd7da3b5621a 100644
--- a/R/RMS.R
+++ b/R/RMS.R
@@ -107,11 +107,14 @@ RMS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset',
     stop("Parameter 'time_dim' is not found in 'exp' or 'obs' dimension.")
   }
   ## dat_dim
-  if (!is.character(dat_dim) | length(dat_dim) > 1) {
-    stop("Parameter 'dat_dim' must be a character string.")
-  }
-  if (!dat_dim %in% names(dim(exp)) | !dat_dim %in% names(dim(obs))) {
-    stop("Parameter 'dat_dim' is not found in 'exp' or 'obs' dimension.")
+  if (!is.null(dat_dim)) {
+    if (!is.character(dat_dim) | length(dat_dim) > 1) {
+      stop("Parameter 'dat_dim' must be a character string or NULL.")
+    }
+    if (!dat_dim %in% names(dim(exp)) | !dat_dim %in% names(dim(obs))) {
+      stop("Parameter 'dat_dim' is not found in 'exp' or 'obs' dimension.",
+           "Set it as NULL if there is no dataset dimension.")
+    }
   }
   ## comp_dim
   if (!is.null(comp_dim)) {
@@ -151,11 +154,13 @@ RMS <- 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)))
-  name_exp <- name_exp[-which(name_exp == dat_dim)]
-  name_obs <- name_obs[-which(name_obs == dat_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 expect 'dat_dim'."))
+                "all dimension except 'dat_dim'."))
   }
   if (dim(exp)[time_dim] < 2) {
     stop("The length of time_dim must be at least 2 to compute RMS.")
@@ -196,12 +201,22 @@ RMS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset',
 }
 
 .RMS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset',
-                 conf = TRUE, conf.lev = 0.95, ncores_input = NULL) { 
-
-  # exp: [sdate, dat_exp]
-  # obs: [sdate, dat_obs]
-  nexp <- as.numeric(dim(exp)[2])
-  nobs <- as.numeric(dim(obs)[2])
+                 conf = TRUE, conf.lev = 0.95, ncores_input = NULL) {
+  if (is.null(dat_dim)) {
+    # exp: [sdate]
+    # obs: [sdate]
+    nexp <- 1
+    nobs <- 1
+    ini_dims <- dim(exp)
+    dim(exp) <- c(ini_dims, dat_dim = 1)
+    dim(obs) <- c(ini_dims, dat_dim = 1)
+  } else {
+    # exp: [sdate, dat_exp]
+    # obs: [sdate, dat_obs]
+    nexp <- as.numeric(dim(exp)[2])
+    nobs <- as.numeric(dim(obs)[2])
+  }
+  
   nsdate <- as.numeric(dim(exp)[1])
 
   dif <- array(dim = c(sdate = nsdate, nexp = nexp, nobs = nobs))
@@ -236,6 +251,16 @@ RMS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset',
     conf.upper <- (eno * rms ** 2 / chi) ** 0.5
   }
 
+  ###################################
+  # Remove nexp and nobs if dat_dim = NULL
+  if (is.null(dat_dim)) {
+    dim(rms) <- NULL
+    dim(conf.lower) <- NULL
+    dim(conf.upper) <- NULL
+  }
+
+  ###################################
+
   if (conf) {
     res <- list(rms = rms, conf.lower = conf.lower, conf.upper = conf.upper)
   } else {
diff --git a/R/RMSSS.R b/R/RMSSS.R
index 5fa96596ebacc4a2d46ed4f9e511adf504eb3e04..e44105cea96ba9f14c2e96f8488f4cc986c9826d 100644
--- a/R/RMSSS.R
+++ b/R/RMSSS.R
@@ -96,11 +96,14 @@ RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset',
     stop("Parameter 'time_dim' is not found in 'exp' or 'obs' dimension.")
   }
   ## dat_dim
-  if (!is.character(dat_dim) | length(dat_dim) > 1) {
-    stop("Parameter 'dat_dim' must be a character string.")
-  }
-  if (!dat_dim %in% names(dim(exp)) | !dat_dim %in% names(dim(obs))) {
-    stop("Parameter 'dat_dim' is not found in 'exp' or 'obs' dimension.")
+  if (!is.null(dat_dim)) {
+    if (!is.character(dat_dim) | length(dat_dim) > 1) {
+      stop("Parameter 'dat_dim' must be a character string or NULL.")
+    }
+    if (!dat_dim %in% names(dim(exp)) | !dat_dim %in% names(dim(obs))) {
+      stop("Parameter 'dat_dim' is not found in 'exp' or 'obs' dimension.",
+           " Set it as NULL if there is no dataset dimension.")
+    }
   }
   ## pval
   if (!is.logical(pval) | length(pval) > 1) {
@@ -116,11 +119,13 @@ 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(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 expect 'dat_dim'."))
+                "all dimension except 'dat_dim'."))
   }
   if (dim(exp)[time_dim] <= 2) {
     stop("The length of time_dim must be more than 2 to compute RMSSS.")
@@ -151,10 +156,20 @@ RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset',
 
 .RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset', pval = TRUE, 
                    ncores_input = 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)
+  } else {
   # exp: [sdate, dat_exp]
   # obs: [sdate, dat_obs]
-  nexp <- as.numeric(dim(exp)[2])
-  nobs <- as.numeric(dim(obs)[2])
+    nexp <- as.numeric(dim(exp)[2])
+    nobs <- as.numeric(dim(obs)[2])
+  }
+
   nsdate <- as.numeric(dim(exp)[1])
   
   p_val <- array(dim = c(nexp = nexp, nobs = nobs))
@@ -208,6 +223,14 @@ RMSSS <- function(exp, obs, time_dim = 'sdate', dat_dim = 'dataset',
     rmsss[which(!tmp)] <- NA
   }
 
+  ###################################
+  # Remove extra dimensions if dat_dim = NULL
+  if (is.null(dat_dim)) {
+    dim(rmsss) <- NULL
+    dim(p_val) <- NULL
+  }
+  ###################################
+
   # output  
   if (pval) {
     res <- list(rmsss = rmsss, p.val = p_val)
diff --git a/R/RPS.R b/R/RPS.R
index 8ded53e6d1546373f065bca04f07d12bebfbc73a..200c59c7b04a6c53012143b2317dd4f9d81bae7f 100644
--- a/R/RPS.R
+++ b/R/RPS.R
@@ -88,7 +88,7 @@ RPS <- function(exp, obs, time_dim = 'sdate', memb_dim = 'member',
   if (!identical(length(name_exp), length(name_obs)) |
       !identical(dim(exp)[name_exp], dim(obs)[name_obs])) {
     stop(paste0("Parameter 'exp' and 'obs' must have same length of ",
-                "all dimensions expect 'memb_dim'."))
+                "all dimensions except 'memb_dim'."))
   }
   ## prob_thresholds
   if (!is.numeric(prob_thresholds) | !is.vector(prob_thresholds) |
diff --git a/R/RPSS.R b/R/RPSS.R
index 3b24777ddde51eaab88286ca6479a07724e7eeb3..cbd87bd2eea81ba203f6e40abd5139306752d8bf 100644
--- a/R/RPSS.R
+++ b/R/RPSS.R
@@ -108,7 +108,7 @@ RPSS <- function(exp, obs, ref = NULL, time_dim = 'sdate', memb_dim = 'member',
   if (!identical(length(name_exp), length(name_obs)) |
       !identical(dim(exp)[name_exp], dim(obs)[name_obs])) {
     stop(paste0("Parameter 'exp' and 'obs' must have same length of ",
-                "all dimensions expect 'memb_dim'."))
+                "all dimensions except 'memb_dim'."))
   }
   if (!is.null(ref)) {
     name_ref <- sort(names(dim(ref)))
@@ -116,7 +116,7 @@ RPSS <- function(exp, obs, ref = NULL, time_dim = 'sdate', memb_dim = 'member',
     if (!identical(length(name_exp), length(name_ref)) |
         !identical(dim(exp)[name_exp], dim(ref)[name_ref])) {
       stop(paste0("Parameter 'exp' and 'obs' must have same length of ",
-                  "all dimensions expect 'memb_dim'."))
+                  "all dimensions except 'memb_dim'."))
     }
   }
   ## prob_thresholds
diff --git a/R/RatioRMS.R b/R/RatioRMS.R
index f7e34b42f01fb2893a3d38112b49b69ce7c6d3b1..51f39846e1eb9c8e5a1616627de6c69ae848f8e6 100644
--- a/R/RatioRMS.R
+++ b/R/RatioRMS.R
@@ -21,7 +21,7 @@
 #'  computation. The default value is NULL.
 #'
 #'@return A list containing the numeric arrays with dimensions identical with
-#'  'exp1', 'exp2', and 'obs', expect 'time_dim':
+#'  'exp1', 'exp2', and 'obs', except 'time_dim':
 #'\item{$ratiorms}{
 #'  The ratio between the RMSE (i.e., RMSE1/RMSE2).
 #'}
diff --git a/R/RatioSDRMS.R b/R/RatioSDRMS.R
index 544ca6f8db3b6f85c73788fdecd5caa9c8557586..d527625c2daabfc5fc0fa2366ebec4a5292a46df 100644
--- a/R/RatioSDRMS.R
+++ b/R/RatioSDRMS.R
@@ -109,7 +109,7 @@ RatioSDRMS <- function(exp, obs, dat_dim = 'dataset', memb_dim = 'member',
   name_obs <- name_obs[-which(name_obs == memb_dim)]
   if(!all(dim(exp)[name_exp] == dim(obs)[name_obs])) {
     stop(paste0("Parameter 'exp' and 'obs' must have same length of ",
-                "all the dimensions expect 'dat_dim' and 'memb_dim'."))
+                "all the dimensions except 'dat_dim' and 'memb_dim'."))
   }
   ## pval
   if (!is.logical(pval) | length(pval) > 1) {
diff --git a/R/ResidualCorr.R b/R/ResidualCorr.R
index 7428d1b08be1ab462cbd37750e82835a2c91f797..8d9f0404fbfd1bd50d307da6950e7da4664859c1 100644
--- a/R/ResidualCorr.R
+++ b/R/ResidualCorr.R
@@ -125,7 +125,7 @@ ResidualCorr <- function(exp, obs, ref, N.eff = NA, time_dim = 'sdate',
   if (length(name_exp) != length(name_obs) | length(name_exp) != length(name_ref) |
       any(dim(exp)[name_exp] != dim(obs)[name_obs]) | any(dim(exp)[name_exp] != dim(ref)[name_ref])) {
     stop(paste0("Parameter 'exp', 'obs', and 'ref' must have same length of ",
-                "all dimensions expect 'memb_dim'."))
+                "all dimensions except 'memb_dim'."))
   }
   ## method
   if (!method %in% c("pearson", "kendall", "spearman")) {
diff --git a/R/UltimateBrier.R b/R/UltimateBrier.R
index aeaddcdcadcdd9d25e3a283d1ec8d24534f969d0..d2c4ac936016ef4f663f6005877b6a3220a06e88 100644
--- a/R/UltimateBrier.R
+++ b/R/UltimateBrier.R
@@ -5,14 +5,15 @@
 #'to choose.
 #'
 #'@param exp A numeric array of forecast anomalies with named dimensions that
-#'  at least include 'dat_dim', 'memb_dim', and 'time_dim'. It can be provided
+#'  at least include 'memb_dim', and 'time_dim'. It can be provided
 #'  by \code{Ano()}. 
 #'@param obs A numeric array of observational reference anomalies with named
-#'  dimensions that at least include 'dat_dim' and 'time_dim'. If it has 
+#'  dimensions that at least include 'time_dim'. If it has 
 #'  'memb_dim', the length  must be 1. The dimensions should be consistent with
 #'  'exp' except 'dat_dim' and 'memb_dim'. It can be provided by \code{Ano()}. 
 #'@param dat_dim A character string indicating the name of the dataset 
-#'  dimension in 'exp' and 'obs'. The default value is 'dataset'.
+#'  dimension in 'exp' and 'obs'. The default value is 'dataset'. If there is no dataset 
+#'  dimension, set NULL.
 #'@param memb_dim A character string indicating the name of the member 
 #'  dimension in 'exp' (and 'obs') for ensemble mean calculation. The default
 #'  value is 'member'.
@@ -55,7 +56,7 @@
 #'same dimensions:
 #'c(nexp, nobs, no. of bins, the rest dimensions of 'exp' except 'time_dim' and
 #''memb_dim'). 'nexp' and 'nobs' is the length of dataset dimension in 'exp'
-#'and 'obs' respectively.\cr
+#'and 'obs' respectively. If dat_dim is NULL, nexp and nobs are omitted.\cr
 #'The list of 4 includes: 
 #'  \itemize{
 #'    \item{$bs: Brier Score}
@@ -102,12 +103,15 @@ UltimateBrier <- function(exp, obs, dat_dim = 'dataset', memb_dim = 'member', ti
     stop("Parameter 'exp' and 'obs' must have dimension names.")
   }
   ## dat_dim
-  if (!is.character(dat_dim) | length(dat_dim) > 1) {
-    stop("Parameter 'dat_dim' must be a character string.")
-  }
-  if (!dat_dim %in% names(dim(exp)) | !dat_dim %in% names(dim(obs))) {
-    stop("Parameter 'dat_dim' is not found in 'exp' or 'obs' dimension.")
+  if (!is.null(dat_dim)) {
+    if (!is.character(dat_dim) | length(dat_dim) > 1) {
+      stop("Parameter 'dat_dim' must be a character string or NULL.")
+    }
+    if (!dat_dim %in% names(dim(exp)) | !dat_dim %in% names(dim(obs))) {
+      stop("Parameter 'dat_dim' is not found in 'exp' or 'obs' dimension.")
+    }
   }
+
   ## memb_dim
   if (!is.character(memb_dim) | length(memb_dim) > 1) {
     stop("Parameter 'memb_dim' must be a character string.")
@@ -137,11 +141,11 @@ UltimateBrier <- function(exp, obs, dat_dim = 'dataset', memb_dim = 'member', ti
   name_obs <- name_obs[-which(name_obs == dat_dim)]
   if (any(name_exp != name_obs)) {
     stop(paste0("Parameter 'exp' and 'obs' must have the same names and lengths ",
-                "of all the dimensions expect 'dat_dim' and 'memb_dim'."))
+                "of all the dimensions except 'dat_dim' and 'memb_dim'."))
   }
   if (!all(dim(exp)[name_exp] == dim(obs)[name_obs])) {
     stop(paste0("Parameter 'exp' and 'obs' must have the same names and lengths ",
-                "of all the dimensions expect 'dat_dim' and 'memb_dim'."))
+                "of all the dimensions except 'dat_dim' and 'memb_dim'."))
   }
   ## quantile
   if (!is.logical(quantile) | length(quantile) > 1) {
@@ -183,6 +187,7 @@ UltimateBrier <- function(exp, obs, dat_dim = 'dataset', memb_dim = 'member', ti
                  target_dims = list(c(time_dim, dat_dim, memb_dim),
                                     c(time_dim, dat_dim, memb_dim)),
                  fun = .UltimateBrier,
+                 dat_dim = dat_dim, memb_dim = memb_dim,
                  thr = thr, type = type,
                  decomposition = decomposition,
                  ncores = ncores)$output1
@@ -203,6 +208,7 @@ UltimateBrier <- function(exp, obs, dat_dim = 'dataset', memb_dim = 'member', ti
                  target_dims = list(c(time_dim, dat_dim),
                                     c(time_dim, dat_dim)),
                  fun = .UltimateBrier,
+                 dat_dim = dat_dim, memb_dim = memb_dim,
                  thr = thr, type = type,
                  decomposition = decomposition,
                  ncores = ncores)
@@ -217,8 +223,8 @@ UltimateBrier <- function(exp, obs, dat_dim = 'dataset', memb_dim = 'member', ti
   return(res)
 }
 
-.UltimateBrier <- function(exp, obs, thr = c(5/100, 95/100), type = 'BS',
-                           decomposition = TRUE) {
+.UltimateBrier <- function(exp, obs, dat_dim = 'dataset', memb_dim = 'member', thr = c(5/100, 95/100), 
+                           type = 'BS', decomposition = TRUE) {
   # If exp and obs are probablistics
   # exp: [sdate, nexp]
   # obs: [sdate, nobs]
@@ -229,6 +235,10 @@ UltimateBrier <- function(exp, obs, dat_dim = 'dataset', memb_dim = 'member', ti
   #NOTE: 'thr' is used in 'FairEnsembleBSS' and 'FairEnsembleBS'. But if quantile = F and 
   #      thr is real value, does it work?
   if (type == 'FairEnsembleBSS') {
+    if (is.null(dat_dim)) {
+      obs <- InsertDim(obs, posdim = 2, lendim = 1, name = 'dataset')
+      exp <- InsertDim(exp, posdim = 2, lendim = 1, name = 'dataset')
+    }
     size_ens_ref <- prod(dim(obs)[c(1, 3)])
     res <- array(dim = c(nexp = as.numeric(dim(exp)[2]), 
                          nobs = as.numeric(dim(obs)[2]), 
@@ -245,6 +255,9 @@ UltimateBrier <- function(exp, obs, dat_dim = 'dataset', memb_dim = 'member', ti
         }
       }
     }
+    if (is.null(dat_dim)) {
+      dim(res) <- dim(res)[3:length(dim(res))]
+    }
 
   } else if (type == 'FairEnsembleBS') {
     #NOTE: The calculation in s2dverification::UltimateBrier is wrong. In the final stage,
@@ -252,6 +265,10 @@ UltimateBrier <- function(exp, obs, dat_dim = 'dataset', memb_dim = 'member', ti
     #      but the 3rd dim of result is 'bins' instead of decomposition. 'FairEnsembleBS' does
     #      not have decomposition.
     #      The calculation is fixed here.
+    if (is.null(dat_dim)) {
+      obs <- InsertDim(obs, posdim = 2, lendim = 1, name = 'dataset')
+      exp <- InsertDim(exp, posdim = 2, lendim = 1, name = 'dataset')
+    }
     res <- array(dim = c(nexp = as.numeric(dim(exp)[2]), 
                          nobs = as.numeric(dim(obs)[2]), 
                          bin = length(thr) + 1))
@@ -264,10 +281,17 @@ UltimateBrier <- function(exp, obs, dat_dim = 'dataset', memb_dim = 'member', ti
         }
       }
     }
+    if (is.null(dat_dim)) {
+      dim(res) <- dim(res)[3:length(dim(res))]
+    }
 #    tmp <- res[, , 1] - res[, , 2] + res[, , 3]
 #    res <- array(tmp, dim = c(nexp = as.numeric(dim(exp)[2]), nobs = as.numeric(dim(obs)[2])))
 
   } else if (type == 'BS') {
+    if (is.null(dat_dim)) {
+      obs <- InsertDim(obs, posdim = 2, lendim = 1, name = 'dataset')
+      exp <- InsertDim(exp, posdim = 2, lendim = 1, name = 'dataset')
+    }
     comp <- array(dim = c(nexp = as.numeric(dim(exp)[2]),
                           nobs = as.numeric(dim(obs)[2]),
                           comp = 3))
@@ -280,17 +304,28 @@ UltimateBrier <- function(exp, obs, dat_dim = 'dataset', memb_dim = 'member', ti
     }
     if (decomposition) {
       rel <- comp[, , 1]
-      dim(rel) <- c(nexp = as.numeric(dim(exp)[2]), nobs = as.numeric(dim(obs)[2]))
       res <- comp[, , 2]
-      dim(res) <- c(nexp = as.numeric(dim(exp)[2]), nobs = as.numeric(dim(obs)[2]))
       unc <- comp[, , 3]
-      dim(unc) <- c(nexp = as.numeric(dim(exp)[2]), nobs = as.numeric(dim(obs)[2]))
       bs <- rel - res + unc
-      dim(bs) <- c(nexp = as.numeric(dim(exp)[2]), nobs = as.numeric(dim(obs)[2]))
+      if (is.null(dat_dim)) {
+        dim(rel) <- NULL
+        dim(res) <- NULL
+        dim(unc) <- NULL
+        dim(bs) <- NULL
+      } else {
+        dim(rel) <- c(nexp = as.numeric(dim(exp)[2]), nobs = as.numeric(dim(obs)[2]))
+        dim(res) <- c(nexp = as.numeric(dim(exp)[2]), nobs = as.numeric(dim(obs)[2]))
+        dim(unc) <- c(nexp = as.numeric(dim(exp)[2]), nobs = as.numeric(dim(obs)[2]))
+        dim(bs) <- c(nexp = as.numeric(dim(exp)[2]), nobs = as.numeric(dim(obs)[2]))
+      }
       res <- list(bs = bs, rel = rel, res = res, unc = unc)
     } else {
       bs <- comp[, , 1] - comp[, , 2] + comp[, , 3]
-      dim(bs) <- c(nexp = as.numeric(dim(exp)[2]), nobs = as.numeric(dim(obs)[2]))
+      if (is.null(dat_dim)) {
+        dim(bs) <- NULL
+      } else {
+        dim(bs) <- c(nexp = as.numeric(dim(exp)[2]), nobs = as.numeric(dim(obs)[2]))
+      }
       res <- list(bs = bs)
     }
 
diff --git a/man/Ano_CrossValid.Rd b/man/Ano_CrossValid.Rd
index d2234a1623901efa767aba83bbd4c5eb532940a7..2a82713159b5d3357904e190a88486aadea52d1b 100644
--- a/man/Ano_CrossValid.Rd
+++ b/man/Ano_CrossValid.Rd
@@ -25,10 +25,11 @@ parameter 'exp' except along 'dat_dim'.}
 The default value is 'sdate'.}
 
 \item{dat_dim}{A character vector indicating the name of the dataset and 
-member dimensions. When calculating the climatology, if data at one 
-startdate (i.e., 'time_dim') is not complete along 'dat_dim', this startdate
-along 'dat_dim' will be discarded. The default value is 
-"c('dataset', 'member')".}
+ member dimensions. When calculating the climatology, if data at one 
+ startdate (i.e., 'time_dim') is not complete along 'dat_dim', this startdate
+ along 'dat_dim' will be discarded. If there is no dataset dimension, it can be NULL.
+The default value is 
+ "c('dataset', 'member')".}
 
 \item{memb_dim}{A character string indicating the name of the member 
 dimension. Only used when parameter 'memb' is FALSE. It must be one element
diff --git a/man/BrierScore.Rd b/man/BrierScore.Rd
index 9271a2adb8fca99ed95483a36b46545e219cd47c..76fb27eb0106b2a38a4222af784b268abcaa45a2 100644
--- a/man/BrierScore.Rd
+++ b/man/BrierScore.Rd
@@ -73,13 +73,13 @@ Items 'rel', 'res', 'unc', 'bs', 'bs_check_res', 'bss_res', 'gres',
 'bs_check_gres', 'bss_gres', 'rel_bias_corrected', 'gres_bias_corrected', 
 'unc_bias_corrected', and 'bss_bias_corrected' are (a) a number (b) an array
 with dimensions c(nexp, nobs, all the rest dimensions in 'exp' and 'obs' 
-expect 'time_dim' and 'memb_dim') (c) an array with dimensions of
+except 'time_dim' and 'memb_dim') (c) an array with dimensions of
 'exp' and 'obs' except 'time_dim' and 'memb_dim'\cr
 Items 'nk', 'fkbar', and 'okbar' are (a) a vector of length of bin number 
 determined by 'threshold' (b) an array with dimensions c(nexp, nobs, 
-no. of bins, all the rest dimensions in 'exp' and 'obs' expect 'time_dim' and
+no. of bins, all the rest dimensions in 'exp' and 'obs' except 'time_dim' and
 'memb_dim') (c) an array with dimensions c(no. of bin, all the rest dimensions
-in 'exp' and 'obs' expect 'time_dim' and 'memb_dim')
+in 'exp' and 'obs' except 'time_dim' and 'memb_dim')
 }
 \description{
 Compute the Brier score (BS) and the components of its standard decompostion
diff --git a/man/Corr.Rd b/man/Corr.Rd
index 077791fbeeb5e100a18e5b44c26a0b4753772d39..4cbd0986bf3b6dbbca2fc67715ac2f56c18c96a9 100644
--- a/man/Corr.Rd
+++ b/man/Corr.Rd
@@ -21,8 +21,8 @@ Corr(
 )
 }
 \arguments{
-\item{exp}{A named numeric array of experimental data, with at least two 
-dimensions 'time_dim' and 'dat_dim'.}
+\item{exp}{A named numeric array of experimental data, with at least dimension
+'time_dim'.}
 
 \item{obs}{A named numeric array of observational data, same dimensions as
 parameter 'exp' except along 'dat_dim' and 'memb_dim'.}
@@ -31,7 +31,8 @@ parameter 'exp' except along 'dat_dim' and 'memb_dim'.}
 which the correlations 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'.}
+dimension. The default value is 'dataset'. If there is no dataset 
+dimension, set NULL.}
 
 \item{comp_dim}{A character string indicating the name of dimension along which
 obs is taken into account only if it is complete. The default value
@@ -68,9 +69,10 @@ A list containing the numeric arrays with dimension:\cr
  c(nexp, nobs, exp_memb, obs_memb, all other dimensions of exp except 
  time_dim and memb_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). exp_memb is the number of
-member in experiment (i.e., 'memb_dim' in exp) and obs_memb is the number of 
-member in observation (i.e., 'memb_dim' in obs).\cr\cr
+number of observation (i.e., 'dat_dim' in obs). If dat_dim is NULL, nexp and 
+nobs are omitted. exp_memb is the number of member in experiment (i.e., 
+'memb_dim' in exp) and obs_memb is the number of member in observation (i.e.,
+'memb_dim' in obs). If memb = F, exp_memb and obs_memb are omitted.\cr\cr
 \item{$corr}{
  The correlation coefficient. 
 }
@@ -87,18 +89,18 @@ member in observation (i.e., 'memb_dim' in obs).\cr\cr
 \description{
 Calculate the correlation coefficient (Pearson, Kendall or Spearman) for 
 an array of forecast and an array of observation. The correlations are 
-computed along time_dim, the startdate dimension. If comp_dim is given, 
-the correlations are computed only if obs along the comp_dim dimension are 
-complete between limits[1] and limits[2], i.e., there is no NA between 
-limits[1] and limits[2]. This option can be activated if the user wants to 
-account only for the forecasts which the corresponding observations are 
-available at all leadtimes.\cr 
+computed along 'time_dim' that usually refers to the start date dimension. If
+'comp_dim' is given, the correlations are computed only if obs along comp_dim
+dimension are complete between limits[1] and limits[2], i.e., there is no NA 
+between limits[1] and limits[2]. This option can be activated if the user 
+wants to account only for the forecasts which the corresponding observations 
+are available at all leadtimes.\cr 
 The confidence interval is computed by the Fisher transformation and the 
 significance level relies on an one-sided student-T distribution.\cr 
-If the dataset has more than one member, ensemble mean is necessary necessary
-before using this function since it only allows one dimension 'dat_dim' to
-have inconsistent length between 'exp' and 'obs'. If all the dimensions of
-'exp' and 'obs' are identical, you can simply use apply() and cor() to 
+The function can calculate ensemble mean before correlation by 'memb_dim' 
+specified and 'memb = F'. If ensemble mean is not calculated, correlation will
+be calculated for each member.
+If there is only one dataset for exp and obs, you can simply use cor() to 
 compute the correlation.
 }
 \examples{
diff --git a/man/RatioRMS.Rd b/man/RatioRMS.Rd
index 194c6b9899e84dfd1772117cc9eade22d2e1e7b7..3330eb5a31aec9507a6836451f38ef829fcc108d 100644
--- a/man/RatioRMS.Rd
+++ b/man/RatioRMS.Rd
@@ -30,7 +30,7 @@ computation. The default value is NULL.}
 }
 \value{
 A list containing the numeric arrays with dimensions identical with
- 'exp1', 'exp2', and 'obs', expect 'time_dim':
+ 'exp1', 'exp2', and 'obs', except 'time_dim':
 \item{$ratiorms}{
  The ratio between the RMSE (i.e., RMSE1/RMSE2).
 }
diff --git a/man/UltimateBrier.Rd b/man/UltimateBrier.Rd
index 2cad133c23d620eeee9e0a57d7466550da9478cf..0dfa772e00dd9d9efa0679b781fee56a76ae855f 100644
--- a/man/UltimateBrier.Rd
+++ b/man/UltimateBrier.Rd
@@ -19,16 +19,17 @@ UltimateBrier(
 }
 \arguments{
 \item{exp}{A numeric array of forecast anomalies with named dimensions that
-at least include 'dat_dim', 'memb_dim', and 'time_dim'. It can be provided
+at least include 'memb_dim', and 'time_dim'. It can be provided
 by \code{Ano()}.}
 
 \item{obs}{A numeric array of observational reference anomalies with named
-dimensions that at least include 'dat_dim' and 'time_dim'. If it has 
+dimensions that at least include 'time_dim'. If it has 
 'memb_dim', the length  must be 1. The dimensions should be consistent with
 'exp' except 'dat_dim' and 'memb_dim'. It can be provided by \code{Ano()}.}
 
 \item{dat_dim}{A character string indicating the name of the dataset 
-dimension in 'exp' and 'obs'. The default value is 'dataset'.}
+dimension in 'exp' and 'obs'. The default value is 'dataset'. If there is no dataset 
+dimension, set NULL.}
 
 \item{memb_dim}{A character string indicating the name of the member 
 dimension in 'exp' (and 'obs') for ensemble mean calculation. The default
@@ -78,7 +79,7 @@ is an array of Brier scores or Brier skill scores. All the arrays have the
 same dimensions:
 c(nexp, nobs, no. of bins, the rest dimensions of 'exp' except 'time_dim' and
 'memb_dim'). 'nexp' and 'nobs' is the length of dataset dimension in 'exp'
-and 'obs' respectively.\cr
+and 'obs' respectively. If dat_dim is NULL, nexp and nobs are omitted.\cr
 The list of 4 includes: 
  \itemize{
    \item{$bs: Brier Score}
diff --git a/tests/testthat/test-ACC.R b/tests/testthat/test-ACC.R
index 5c3672552930be48e114949fdb2301a8ab429bce..04e60ad0888ee97ed49aa2d310fa814d9d87cd4c 100644
--- a/tests/testthat/test-ACC.R
+++ b/tests/testthat/test-ACC.R
@@ -152,7 +152,7 @@ test_that("1. Input checks", {
       obs = array(1:4, dim = c(dataset = 2, member = 2, lat = 1, lon = 1)),
       lat = c(1, 2), lon = c(1),
       avg_dim = NULL),
-  "Parameter 'exp' and 'obs' must have same length of all the dimensions expect 'dat_dim' and 'memb_dim'."
+  "Parameter 'exp' and 'obs' must have same length of all the dimensions except 'dat_dim' and 'memb_dim'."
   )
 
 })
diff --git a/tests/testthat/test-Ano_CrossValid.R b/tests/testthat/test-Ano_CrossValid.R
index b66fc5fbf54113b71826e7adf79d014890c003e0..2d7c00c127b75ad9e240630bce109fd9b001d904 100644
--- a/tests/testthat/test-Ano_CrossValid.R
+++ b/tests/testthat/test-Ano_CrossValid.R
@@ -13,6 +13,12 @@ exp2 <- array(rnorm(30), dim = c(member = 3, ftime = 2, sdate = 5))
 set.seed(2)
 obs2 <- array(rnorm(20), dim = c(ftime = 2, member = 2, sdate = 5))
 
+# dat3
+set.seed(1)
+exp3 <- array(rnorm(30), dim = c(ftime = 2, sdate = 5))
+set.seed(2)
+obs3 <- array(rnorm(20), dim = c(ftime = 2, sdate = 5))
+
 
 ##############################################
 test_that("1. Input checks", {
@@ -51,7 +57,7 @@ test_that("1. Input checks", {
   )
   expect_error(
     Ano_CrossValid(exp1, obs1, dat_dim = 'dat'),
-    "Parameter 'dat_dim' is not found in 'exp' or 'obs' dimension."
+    "Parameter 'dat_dim' is not found in 'exp' or 'obs' dimension. Set it as NULL if there is no dataset dimension."
   )
   # memb
   expect_error(
@@ -136,6 +142,28 @@ test_that("3. dat2", {
 
 })
 
+##############################################
+test_that("4. dat3", {
+  expect_equal(
+  names(Ano_CrossValid(exp3, obs3, dat_dim = NULL)),
+  c("exp", "obs")
+  )
+  expect_equal(
+  dim(Ano_CrossValid(exp3, obs3, dat_dim = NULL)$exp),
+  c(sdate = 5, ftime = 2)
+  )
+  expect_equal(
+  Ano_CrossValid(exp3, obs3, dat_dim = NULL)$exp[, 2],
+  c(-0.1182939, 1.6462530, -1.3734335, 0.5750579, -0.7295835),
+  tolerance = 0.0001
+  )
+  expect_equal(
+  Ano_CrossValid(exp3, obs3, dat_dim = NULL)$exp[, 2],
+  c(-0.1182939, 1.6462530, -1.3734335, 0.5750579, -0.7295835),
+  tolerance = 0.0001
+  )
+
+})
 
 
 
diff --git a/tests/testthat/test-BrierScore.R b/tests/testthat/test-BrierScore.R
index 5668a089972352b29db2d553acb7134a3ede2203..e2c34f95744114b72ff7f5ac89131bf29f5da250 100644
--- a/tests/testthat/test-BrierScore.R
+++ b/tests/testthat/test-BrierScore.R
@@ -51,7 +51,7 @@ test_that("1. Input checks", {
   expect_error( 
   BrierScore(exp3, obs3),
   paste0("Parameter 'exp' and 'obs' must have the same names and lengths ",
-         "of all the dimensions expect 'dat_dim' and 'memb_dim'.")
+         "of all the dimensions except 'dat_dim' and 'memb_dim'.")
   )
   # thresholds
   expect_error(  
diff --git a/tests/testthat/test-Clim.R b/tests/testthat/test-Clim.R
index 7751afb405c23c4e42cc5587eefa7f670182d14e..f5e288ec2c4b956a44c2494d8ae86f280288a2a1 100644
--- a/tests/testthat/test-Clim.R
+++ b/tests/testthat/test-Clim.R
@@ -134,7 +134,7 @@ test_that("1. Input checks", {
   expect_error(
   Clim(array(1:10, dim = c(dataset = 2, member = 5, sdate = 4, ftime = 3)), 
        array(1:4, dim = c(dataset = 2, member = 2, sdate = 5, ftime = 3))),
-  "Parameter 'exp' and 'obs' must have the same dimensions expect 'dat_dim'."
+  "Parameter 'exp' and 'obs' must have the same dimensions except 'dat_dim'."
   )
 
 })
diff --git a/tests/testthat/test-Consist_Trend.R b/tests/testthat/test-Consist_Trend.R
index aa66f45761c6aa6b8bca1f02d7fbf8649882b038..91dacf7085035a0b16a6ab9689309a517c5ad5a6 100644
--- a/tests/testthat/test-Consist_Trend.R
+++ b/tests/testthat/test-Consist_Trend.R
@@ -62,7 +62,7 @@ test_that("1. Input checks", {
   Consist_Trend(array(1:10, dim = c(dataset = 2, member = 5, sdate = 4, ftime = 3)),
        array(1:4, dim = c(dataset = 2, member = 2, sdate = 5, ftime = 3))),
   paste0("Parameter 'exp' and 'obs' must have same length of ",
-                "all dimension expect 'dat_dim'.")
+                "all dimension except 'dat_dim'.")
   )
   # interval
   expect_error(
diff --git a/tests/testthat/test-Corr.R b/tests/testthat/test-Corr.R
index 9d5d4a3653ca55366919e8cf0bb87676972bf4b9..6e3c0162bb3c50cce3e28d0454c2da1672411ba2 100644
--- a/tests/testthat/test-Corr.R
+++ b/tests/testthat/test-Corr.R
@@ -40,6 +40,29 @@ context("s2dv::Corr tests")
   obs4 <- array(rnorm(10), dim = c(member = 1, dataset = 1, sdate = 5,
                                     lat = 2))
 
+  # dat5: exp and obs have memb_dim and dataset = NULL
+  set.seed(1)
+  exp5 <- array(rnorm(90), dim = c(member = 3, sdate = 5,
+                                    lat = 2, lon = 3))
+
+  set.seed(2)
+  obs5 <- array(rnorm(30), dim = c(member = 1, sdate = 5,
+                                    lat = 2, lon = 3))
+
+  # dat6: exp and obs have memb_dim = NULL and dataset = NULL
+  set.seed(1)
+  exp6 <- array(rnorm(90), dim = c(sdate = 5, lat = 2, lon = 3))
+
+  set.seed(2)
+  obs6 <- array(rnorm(30), dim = c(sdate = 5, lat = 2, lon = 3))
+
+  # dat7: exp and obs have memb_dim = NULL and dataset = 1
+  set.seed(1)
+  exp7 <- array(rnorm(90), dim = c(dataset = 1, sdate = 5, lat = 2, lon = 3))
+
+  set.seed(2)
+  obs7 <- array(rnorm(30), dim = c(dataset = 1, sdate = 5, lat = 2, lon = 3))
+
 ##############################################
 test_that("1. Input checks", {
 
@@ -132,7 +155,7 @@ test_that("1. Input checks", {
   expect_error(
   Corr(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 expect 'dat_dim'."
+  "Parameter 'exp' and 'obs' must have same length of all dimension except 'dat_dim' and 'memb_dim'."
   )
   expect_error(
   Corr(exp = array(1:10, dim = c(sdate = 2, dataset = 5, a = 1)),
@@ -392,4 +415,70 @@ test_that("5. Output checks: dat4", {
   )
 
 })
+
+##############################################
+test_that("6. Output checks: dat5", {
+  expect_equal(
+    dim(Corr(exp5, obs5, dat_dim = NULL, memb_dim = 'member')$corr),
+    c(exp_memb = 3, obs_memb = 1, lat = 2, lon = 3)
+  )
+  expect_equal(
+    names(Corr(exp5, obs5, dat_dim = NULL, memb_dim = 'member')),
+    c("corr", "p.val", "conf.lower", "conf.upper")
+  )
+  expect_equal(
+    names(Corr(exp5, obs5, dat_dim = NULL, memb_dim = 'member', pval = FALSE, conf = FALSE)),
+    c("corr")
+  )
+  expect_equal(
+    mean(Corr(exp5, obs5, dat_dim = NULL, memb_dim = 'member', pval = FALSE, conf = FALSE)$corr),
+    0.1880204,
+    tolerance = 0.0001
+  )
+})
+##############################################
+test_that("7. Output checks: dat6", {
+  expect_equal(
+    dim(Corr(exp6, obs6, dat_dim = NULL, memb_dim = NULL)$corr),
+    c(lat = 2, lon = 3)
+  )
+  expect_equal(
+    names(Corr(exp6, obs6, dat_dim = NULL, memb_dim = NULL)),
+    c("corr", "p.val", "conf.lower", "conf.upper")
+  )
+  expect_equal(
+    names(Corr(exp6, obs6, dat_dim = NULL, memb_dim = NULL, pval = FALSE, conf = FALSE)),
+    c("corr")
+  )
+  expect_equal(
+    mean(Corr(exp6, obs6, dat_dim = NULL, memb_dim = NULL, pval = FALSE, conf = FALSE)$corr),
+    0.1084488,
+    tolerance = 0.0001
+  )
+  # kendall
+  expect_equal(
+  as.vector(Corr(exp6, obs6, dat_dim = NULL, memb_dim = NULL, method = 'kendall')$corr[2:4]),
+  c(0.0, 0.6, 0.2),
+  tolerance = 0.0001
+  )
+  expect_equal(
+  as.vector(Corr(exp6, obs6, dat_dim = NULL, memb_dim = NULL, method = 'kendall')$p[2:4]),
+  c(0.5000000, 0.1423785, 0.3735300),
+  tolerance = 0.0001
+  )
+  expect_equal(
+  as.vector(Corr(exp6, obs6, dat_dim = NULL, memb_dim = NULL, method = 'kendall')$conf.low[2:4]),
+  c(-0.8822664, -0.5997500, -0.8284490),
+  tolerance = 0.0001
+  )
+
+})
+##############################################
+test_that("8. Output checks: dat6 and dat7", {
+  expect_equal(
+    mean(Corr(exp6, obs6, dat_dim = NULL, memb_dim = NULL, pval = FALSE, conf = FALSE)$corr),
+    mean(Corr(exp7, obs7, memb_dim = NULL, pval = FALSE, conf = FALSE)$corr),
+    tolerance = 0.0001
+  )
+})
 ##############################################
diff --git a/tests/testthat/test-NAO.R b/tests/testthat/test-NAO.R
index f3c6d21f5574be54e0b05513d887e927aa6f7a87..2da0d407ea986175a9a3d2c73605bd5aead29451 100644
--- a/tests/testthat/test-NAO.R
+++ b/tests/testthat/test-NAO.R
@@ -95,12 +95,12 @@ test_that("1. Input checks", {
   expect_error(
   NAO(exp1, array(rnorm(10), dim = c(member = 1, sdate = 3, ftime = 4, lat = 2, lon = 2))),
   paste0("Parameter 'exp' and 'obs' must have the same names and lengths ",
-         "of all the dimensions expect 'memb_dim'.")
+         "of all the dimensions except 'memb_dim'.")
   )
   expect_error(
   NAO(exp1, array(rnorm(10), dim = c(dataset = 1, member = 1, sdate = 3, ftime = 4, lat = 1, lon = 2))),
   paste0("Parameter 'exp' and 'obs' must have the same names and lengths ",
-         "of all the dimensions expect 'memb_dim'.")
+         "of all the dimensions except 'memb_dim'.")
   )
   # ftime_avg
   expect_error(
diff --git a/tests/testthat/test-RMS.R b/tests/testthat/test-RMS.R
index 6e18bee447b4397a471350b89a12cf3c1b663f67..f69cfd8a1de8e4db627dcfb5e9d0e0ca2a845080 100644
--- a/tests/testthat/test-RMS.R
+++ b/tests/testthat/test-RMS.R
@@ -17,6 +17,13 @@ context("s2dv::RMS tests")
   set.seed(6)
   obs2 <- rnorm(10)
 
+  # dat3
+  set.seed(1)
+  exp3 <- array(rnorm(120), dim = c(sdate = 5, ftime = 2, lon = 1, lat = 4))
+
+  set.seed(2)
+  obs3 <- array(rnorm(80),  dim = c(sdate = 5, ftime = 2, lon = 1, lat = 4))
+
 
 ##############################################
 test_that("1. Input checks", {
@@ -89,7 +96,7 @@ test_that("1. Input checks", {
   expect_error(
   RMS(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 expect 'dat_dim'."
+  "Parameter 'exp' and 'obs' must have same length of all dimension except 'dat_dim'."
   )
   expect_error(
   RMS(exp = array(1:5, dim = c(sdate = 1, dataset = 5, a = 1)),
@@ -186,3 +193,18 @@ test_that("3. Output checks: dat2", {
 })
 
 ##############################################
+test_that("4. Output checks: dat3", {
+
+  expect_equal(
+    dim(RMS(exp3, obs3, dat_dim = NULL)$rms),
+    c(ftime = 2, lon = 1, lat = 4)
+  )
+
+  expect_equal(
+  as.vector(RMS(exp3, obs3, dat_dim = NULL)$rms),
+  c(1.6458118, 0.8860392, 0.8261295, 1.1681939, 2.1693538, 1.3064454, 0.5384229, 1.1215333),
+  tolerance = 0.00001
+  )
+})
+
+##############################################
\ No newline at end of file
diff --git a/tests/testthat/test-RMSSS.R b/tests/testthat/test-RMSSS.R
index 7d2a16da9da52c492dad263985f71c042783927b..d592130fc7c8f1ea6478da94a4e5d8677586fdb0 100644
--- a/tests/testthat/test-RMSSS.R
+++ b/tests/testthat/test-RMSSS.R
@@ -25,6 +25,12 @@ context("s2dv::RMSSS tests")
  set.seed(6)
  obs3 <- rnorm(10)
 
+ # case 4
+ set.seed(7)
+ exp4 <- array(rnorm(120), dim = c(sdate = 10, dat = 1, lon = 3, lat = 2))
+ set.seed(8)
+ obs4 <- array(rnorm(60), dim = c(dat = 1, sdate = 10, lat = 2, lon = 3))
+
 ##############################################
 
 test_that("1. Input checks", {
@@ -64,7 +70,8 @@ test_that("1. Input checks", {
   )
   expect_error(
   RMSSS(exp0, obs0, dat_dim = 'memb'),
-  "Parameter 'dat_dim' is not found in 'exp' or 'obs' dimension."
+  paste0("Parameter 'dat_dim' is not found in 'exp' or 'obs' dimension.",
+           " Set it as NULL if there is no dataset dimension.")
   )
   expect_error(
   RMSSS(exp0, obs0, pval = c(T, T)),
@@ -77,7 +84,7 @@ 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 expect 'dat_dim'."
+  "Parameter 'exp' and 'obs' must have same length of all dimension except 'dat_dim'."
   )
   expect_error(
   RMSSS(exp = array(1:10, dim = c(sdate = 1, dataset = 5, a = 1)),
@@ -157,5 +164,24 @@ test_that("4. Output checks: case 3", {
   tolerance = 0.00001
   )
 
+})
+
+##############################################
+test_that("5. Output checks: case 4", {
+
+  expect_equal(
+    dim(RMSSS(exp4, obs4, dat_dim = NULL)$rmsss),
+    c(dat = 1, lon = 3, lat = 2) 
+  )
+  expect_equal(
+    mean(RMSSS(exp4, obs4, dat_dim = NULL)$rmsss),
+    -0.3114424,
+    tolerance = 0.00001
+  )
+  expect_equal(
+    range(RMSSS(exp4, obs4, dat_dim = NULL)$p.val),
+    c(0.3560534, 0.9192801),
+    tolerance = 0.00001
+  )
 
 })
diff --git a/tests/testthat/test-RPS.R b/tests/testthat/test-RPS.R
index 04df1bb397b6906c10a16a5be1f92c1858299103..2029fd981b8efeb13ad18ddb4def4e596c6d37e6 100644
--- a/tests/testthat/test-RPS.R
+++ b/tests/testthat/test-RPS.R
@@ -56,7 +56,7 @@ test_that("1. Input checks", {
   # exp, ref, and obs (2)
   expect_error(
   RPS(exp1, array(1:9, dim = c(sdate = 9))),
-  "Parameter 'exp' and 'obs' must have same length of all dimensions expect 'memb_dim'."
+  "Parameter 'exp' and 'obs' must have same length of all dimensions except 'memb_dim'."
   )
   # prob_thresholds
   expect_error(
diff --git a/tests/testthat/test-RPSS.R b/tests/testthat/test-RPSS.R
index c63add02246ef4980a8c388bed7b54a239e62d24..b8623b6e82cce7d8721a82a4bb4f19fcf2239651 100644
--- a/tests/testthat/test-RPSS.R
+++ b/tests/testthat/test-RPSS.R
@@ -63,11 +63,11 @@ test_that("1. Input checks", {
   # exp, ref, and obs (2)
   expect_error(
   RPSS(exp1, array(1:9, dim = c(sdate = 9))),
-  "Parameter 'exp' and 'obs' must have same length of all dimensions expect 'memb_dim'."
+  "Parameter 'exp' and 'obs' must have same length of all dimensions except 'memb_dim'."
   )
   expect_error(
   RPSS(exp1, obs1, ref2),
-  "Parameter 'exp' and 'obs' must have same length of all dimensions expect 'memb_dim'."
+  "Parameter 'exp' and 'obs' must have same length of all dimensions except 'memb_dim'."
   )
   # prob_thresholds
   expect_error(
diff --git a/tests/testthat/test-RatioSDRMS.R b/tests/testthat/test-RatioSDRMS.R
index 4b93fafa213dcac0e831b7ac59d7646064f8f856..5dbc171337d4bec4fe9db6e2c491ec527511efc3 100644
--- a/tests/testthat/test-RatioSDRMS.R
+++ b/tests/testthat/test-RatioSDRMS.R
@@ -77,7 +77,7 @@ test_that("1. Input checks", {
   expect_error(
   RatioSDRMS(exp = exp3,
              obs = array(1:2, dim = c(member = 1, sdate = 2)), dat_dim = NULL),
-  "Parameter 'exp' and 'obs' must have same length of all the dimensions expect 'dat_dim' and 'memb_dim'."
+  "Parameter 'exp' and 'obs' must have same length of all the dimensions except 'dat_dim' and 'memb_dim'."
   )
 
 })
diff --git a/tests/testthat/test-ResidualCorr.R b/tests/testthat/test-ResidualCorr.R
index c15276c93368322eec48e8b33657474fb8f4a1c4..be71b4748295f70ddc43f7c3d3bccdf1d1f60100 100644
--- a/tests/testthat/test-ResidualCorr.R
+++ b/tests/testthat/test-ResidualCorr.R
@@ -66,7 +66,7 @@ test_that("1. Input checks", {
   # exp, ref, and obs (2)
   expect_error(
   ResidualCorr(exp1, obs1, array(1:10, dim = c(sdate = 10, memb = 1)), memb_dim = 'memb'),
-  "Parameter 'exp', 'obs', and 'ref' must have same length of all dimensions expect 'memb_dim'."
+  "Parameter 'exp', 'obs', and 'ref' must have same length of all dimensions except 'memb_dim'."
   )
   # method
   expect_error(
diff --git a/tests/testthat/test-UltimateBrier.R b/tests/testthat/test-UltimateBrier.R
index 654aad020d5d7df65981316ab1918b3cece94c51..09412f00cf1ce52265328f9da89f2f404081877a 100644
--- a/tests/testthat/test-UltimateBrier.R
+++ b/tests/testthat/test-UltimateBrier.R
@@ -7,7 +7,11 @@ exp1 <- array(rnorm(30), dim = c(dataset = 1, member = 3, sdate = 5, ftime = 2))
 set.seed(2)
 obs1 <- array(round(rnorm(10)), dim = c(dataset = 1, sdate = 5, ftime = 2))
 
-
+# dat2
+set.seed(1)
+exp2 <- array(rnorm(30), dim = c(member = 3, sdate = 5, ftime = 2))
+set.seed(2)
+obs2 <- array(round(rnorm(10)), dim = c(sdate = 5, ftime = 2))
 ##############################################
 test_that("1. Input checks", {
   # exp and obs
@@ -26,7 +30,7 @@ test_that("1. Input checks", {
   # dat_dim
   expect_error(
   UltimateBrier(exp1, obs1, dat_dim = 2),
-  "Parameter 'dat_dim' must be a character string."
+  "Parameter 'dat_dim' must be a character string or NULL."
   )
   expect_error(
   UltimateBrier(exp1, obs1, dat_dim = 'dat'),
@@ -58,12 +62,12 @@ test_that("1. Input checks", {
   expect_error(
   UltimateBrier(exp1, array(1:10, dim = c(dataset = 1, sdate = 6, ftime = 2))),
   paste0("Parameter 'exp' and 'obs' must have the same names and lengths ",
-                "of all the dimensions expect 'dat_dim' and 'memb_dim'.")
+                "of all the dimensions except 'dat_dim' and 'memb_dim'.")
   )
   expect_error(
   UltimateBrier(exp1, array(1:10, dim = c(dataset = 1, sdate = 5, time = 2))),
   paste0("Parameter 'exp' and 'obs' must have the same names and lengths ",
-                "of all the dimensions expect 'dat_dim' and 'memb_dim'.")
+                "of all the dimensions except 'dat_dim' and 'memb_dim'.")
   )
   # quantile
   expect_error(
@@ -105,136 +109,269 @@ test_that("1. Input checks", {
 ##############################################
 test_that("2. Output checks: dat1", {
 
-# 'BS'
-expect_equal(
-is.list(UltimateBrier(exp1, obs1)),
-TRUE
-)
-expect_equal(
-names(UltimateBrier(exp1, obs1)),
-c('bs', 'rel', 'res', 'unc')
-)
-expect_equal(
-is.list(UltimateBrier(exp1, obs1, decomposition = FALSE)),
-FALSE
-)
-expect_equal(
-dim(UltimateBrier(exp1, obs1, decomposition = FALSE)),
-c(nexp = 1, nobs = 1, bin = 3, ftime = 2)
-)
-expect_equal(
-dim(UltimateBrier(exp1, obs1, decomposition = FALSE, thr = c(0.25, 0.5, 0.75))),
-c(nexp = 1, nobs = 1, bin = 4, ftime = 2)
-)
-expect_equal(
-UltimateBrier(exp1, obs1)$bs,
-UltimateBrier(exp1, obs1, decomposition = FALSE)
-)
-expect_equal(
-as.vector(UltimateBrier(exp1, obs1)$bs),
-c(0.42222222, 0.44444444, 0.02222222, 0.48888889, 0.37777778, 0.02222222),
-tolerance = 0.0001
-)
-expect_equal(
-as.vector(UltimateBrier(exp1, obs1)$rel),
-c(0.22222222, 0.31111111, 0.02222222, 0.28888889, 0.24444444, 0.02222222),
-tolerance = 0.0001
-)
-expect_equal(
-as.vector(UltimateBrier(exp1, obs1)$res),
-c(0.0400000, 0.1066667, 0.0000000, 0.0400000, 0.1066667, 0.0000000),
-tolerance = 0.0001
-)
-expect_equal(
-as.vector(UltimateBrier(exp1, obs1)$unc),
-c(0.24, 0.24, 0.00, 0.24, 0.24, 0.00),
-tolerance = 0.0001
-)
-
-# 'BSS'
-expect_equal(
-dim(UltimateBrier(exp1, obs1, type = 'BSS')),
-c(nexp = 1, nobs = 1, bin = 3, ftime = 2)
-)
-expect_equal(
-as.vector(UltimateBrier(exp1, obs1, type = 'BSS')),
-c(-0.7592593, -0.8518519, -Inf, -1.0370370, -0.5740741, -Inf),
-tolerance = 0.0001
-)
-
-# 'FairStartDatesBS'
-expect_equal(
-is.list(UltimateBrier(exp1, obs1, type = 'FairStartDatesBS')),
-TRUE
-)
-expect_equal(
-names(UltimateBrier(exp1, obs1, type = 'FairStartDatesBS')),
-c('bs', 'rel', 'res', 'unc')
-)
-expect_equal(
-is.list(UltimateBrier(exp1, obs1, decomposition = FALSE, type = 'FairStartDatesBS')),
-FALSE
-)
-expect_equal(
-dim(UltimateBrier(exp1, obs1, decomposition = FALSE, type = 'FairStartDatesBS')),
-c(nexp = 1, nobs = 1, bin = 3, ftime = 2)
-)
-expect_equal(
-UltimateBrier(exp1, obs1, type = 'FairStartDatesBS')$bs,
-UltimateBrier(exp1, obs1, decomposition = FALSE, type = 'FairStartDatesBS')
-)
-expect_equal(
-as.vector(UltimateBrier(exp1, obs1, type = 'FairStartDatesBS')$bs),
-c(0.42222222, 0.44444444, 0.02222222, 0.48888889, 0.37777778, 0.02222222),
-tolerance = 0.0001
-)
-expect_equal(
-as.vector(UltimateBrier(exp1, obs1, type = 'FairStartDatesBS')$rel),
-c(0.22222222, 0.31111111, 0.02222222, 0.28888889, 0.24444444, 0.02222222),
-tolerance = 0.0001
-)
-expect_equal(
-as.vector(UltimateBrier(exp1, obs1, type = 'FairStartDatesBS')$res),
-c(0.0400000, 0.1066667, 0.0000000, 0.0400000, 0.1066667, 0.0000000),
-tolerance = 0.0001
-)
-expect_equal(
-as.vector(UltimateBrier(exp1, obs1, type = 'FairStartDatesBS')$unc),
-c(0.24, 0.24, 0.00, 0.24, 0.24, 0.00),
-tolerance = 0.0001
-)
-
-# 'FairStartDatesBSS'
-expect_equal(
-dim(UltimateBrier(exp1, obs1, type = 'FairStartDatesBSS')),
-c(nexp = 1, nobs = 1, bin = 3, ftime = 2)
-)
-expect_equal(
-as.vector(UltimateBrier(exp1, obs1, type = 'FairStartDatesBSS')),
-c(-0.7592593, -0.8518519, -Inf, -1.0370370, -0.5740741, -Inf),
-tolerance = 0.0001
-)
-# 'FairEnsembleBS'
-expect_equal(
-dim(UltimateBrier(exp1, obs1, type = 'FairEnsembleBS')),
-c(nexp = 1, nobs = 1, bin = 3, ftime = 2)
-)
-expect_equal(
-as.vector(UltimateBrier(exp1, obs1, type = 'FairEnsembleBS')),
-c(0.1333333, 0.2000000, 0.2000000, 0.1333333, 0.4000000, 0.2000000),
-tolerance = 0.0001
-)
-# 'FairEnsembleBSS'
-expect_equal(
-dim(UltimateBrier(exp1, obs1, type = 'FairEnsembleBSS')),
-c(nexp = 1, nobs = 1, bin = 3, ftime = 2)
-)
-expect_equal(
-as.vector(UltimateBrier(exp1, obs1, type = 'FairEnsembleBSS')),
-c(-0.1111111, -0.6666667, -0.6666667, 0.2592593, -1.2222222, -0.6666667),
-tolerance = 0.0001
-)
+  # 'BS'
+  expect_equal(
+  is.list(UltimateBrier(exp1, obs1)),
+  TRUE
+  )
+  expect_equal(
+  names(UltimateBrier(exp1, obs1)),
+  c('bs', 'rel', 'res', 'unc')
+  )
+  expect_equal(
+  is.list(UltimateBrier(exp1, obs1, decomposition = FALSE)),
+  FALSE
+  )
+  expect_equal(
+  dim(UltimateBrier(exp1, obs1, decomposition = FALSE)),
+  c(nexp = 1, nobs = 1, bin = 3, ftime = 2)
+  )
+  expect_equal(
+  dim(UltimateBrier(exp1, obs1, decomposition = FALSE, thr = c(0.25, 0.5, 0.75))),
+  c(nexp = 1, nobs = 1, bin = 4, ftime = 2)
+  )
+  expect_equal(
+  UltimateBrier(exp1, obs1)$bs,
+  UltimateBrier(exp1, obs1, decomposition = FALSE)
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp1, obs1)$bs),
+  c(0.42222222, 0.44444444, 0.02222222, 0.48888889, 0.37777778, 0.02222222),
+  tolerance = 0.0001
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp1, obs1)$rel),
+  c(0.22222222, 0.31111111, 0.02222222, 0.28888889, 0.24444444, 0.02222222),
+  tolerance = 0.0001
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp1, obs1)$res),
+  c(0.0400000, 0.1066667, 0.0000000, 0.0400000, 0.1066667, 0.0000000),
+  tolerance = 0.0001
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp1, obs1)$unc),
+  c(0.24, 0.24, 0.00, 0.24, 0.24, 0.00),
+  tolerance = 0.0001
+  )
+
+  # 'BSS'
+  expect_equal(
+  dim(UltimateBrier(exp1, obs1, type = 'BSS')),
+  c(nexp = 1, nobs = 1, bin = 3, ftime = 2)
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp1, obs1, type = 'BSS')),
+  c(-0.7592593, -0.8518519, -Inf, -1.0370370, -0.5740741, -Inf),
+  tolerance = 0.0001
+  )
+
+  # 'FairStartDatesBS'
+  expect_equal(
+  is.list(UltimateBrier(exp1, obs1, type = 'FairStartDatesBS')),
+  TRUE
+  )
+  expect_equal(
+  names(UltimateBrier(exp1, obs1, type = 'FairStartDatesBS')),
+  c('bs', 'rel', 'res', 'unc')
+  )
+  expect_equal(
+  is.list(UltimateBrier(exp1, obs1, decomposition = FALSE, type = 'FairStartDatesBS')),
+  FALSE
+  )
+  expect_equal(
+  dim(UltimateBrier(exp1, obs1, decomposition = FALSE, type = 'FairStartDatesBS')),
+  c(nexp = 1, nobs = 1, bin = 3, ftime = 2)
+  )
+  expect_equal(
+  UltimateBrier(exp1, obs1, type = 'FairStartDatesBS')$bs,
+  UltimateBrier(exp1, obs1, decomposition = FALSE, type = 'FairStartDatesBS')
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp1, obs1, type = 'FairStartDatesBS')$bs),
+  c(0.42222222, 0.44444444, 0.02222222, 0.48888889, 0.37777778, 0.02222222),
+  tolerance = 0.0001
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp1, obs1, type = 'FairStartDatesBS')$rel),
+  c(0.22222222, 0.31111111, 0.02222222, 0.28888889, 0.24444444, 0.02222222),
+  tolerance = 0.0001
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp1, obs1, type = 'FairStartDatesBS')$res),
+  c(0.0400000, 0.1066667, 0.0000000, 0.0400000, 0.1066667, 0.0000000),
+  tolerance = 0.0001
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp1, obs1, type = 'FairStartDatesBS')$unc),
+  c(0.24, 0.24, 0.00, 0.24, 0.24, 0.00),
+  tolerance = 0.0001
+  )
+
+  # 'FairStartDatesBSS'
+  expect_equal(
+  dim(UltimateBrier(exp1, obs1, type = 'FairStartDatesBSS')),
+  c(nexp = 1, nobs = 1, bin = 3, ftime = 2)
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp1, obs1, type = 'FairStartDatesBSS')),
+  c(-0.7592593, -0.8518519, -Inf, -1.0370370, -0.5740741, -Inf),
+  tolerance = 0.0001
+  )
+  # 'FairEnsembleBS'
+  expect_equal(
+  dim(UltimateBrier(exp1, obs1, type = 'FairEnsembleBS')),
+  c(nexp = 1, nobs = 1, bin = 3, ftime = 2)
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp1, obs1, type = 'FairEnsembleBS')),
+  c(0.1333333, 0.2000000, 0.2000000, 0.1333333, 0.4000000, 0.2000000),
+  tolerance = 0.0001
+  )
+  # 'FairEnsembleBSS'
+  expect_equal(
+  dim(UltimateBrier(exp1, obs1, type = 'FairEnsembleBSS')),
+  c(nexp = 1, nobs = 1, bin = 3, ftime = 2)
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp1, obs1, type = 'FairEnsembleBSS')),
+  c(-0.1111111, -0.6666667, -0.6666667, 0.2592593, -1.2222222, -0.6666667),
+  tolerance = 0.0001
+  )
 
 })
 
+##############################################
+test_that("3. Output checks: dat2", {
 
+  # 'BS'
+  expect_equal(
+  is.list(UltimateBrier(exp2, obs2, dat_dim = NULL)),
+  TRUE
+  )
+  expect_equal(
+  names(UltimateBrier(exp2, obs2, dat_dim = NULL)),
+  c('bs', 'rel', 'res', 'unc')
+  )
+  expect_equal(
+  is.list(UltimateBrier(exp2, obs2, dat_dim = NULL, decomposition = FALSE)),
+  FALSE
+  )
+  expect_equal(
+  dim(UltimateBrier(exp2, obs2, dat_dim = NULL, decomposition = FALSE)),
+  c(bin = 3, ftime = 2)
+  )
+  expect_equal(
+  dim(UltimateBrier(exp2, obs2, dat_dim = NULL, decomposition = FALSE, thr = c(0.25, 0.5, 0.75))),
+  c(bin = 4, ftime = 2)
+  )
+  expect_equal(
+  UltimateBrier(exp2, obs2, dat_dim = NULL)$bs,
+  UltimateBrier(exp2, obs2, dat_dim = NULL, decomposition = FALSE)
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp2, obs2, dat_dim = NULL)$bs),
+  c(0.42222222, 0.44444444, 0.02222222, 0.48888889, 0.37777778, 0.02222222),
+  tolerance = 0.0001
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp2, obs2, dat_dim = NULL)$rel),
+  c(0.22222222, 0.31111111, 0.02222222, 0.28888889, 0.24444444, 0.02222222),
+  tolerance = 0.0001
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp2, obs2, dat_dim = NULL)$res),
+  c(0.0400000, 0.1066667, 0.0000000, 0.0400000, 0.1066667, 0.0000000),
+  tolerance = 0.0001
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp2, obs2, dat_dim = NULL)$unc),
+  c(0.24, 0.24, 0.00, 0.24, 0.24, 0.00),
+  tolerance = 0.0001
+  )
+
+  # 'BSS'
+  expect_equal(
+  dim(UltimateBrier(exp2, obs2, dat_dim = NULL, type = 'BSS')),
+  c(bin = 3, ftime = 2)
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp2, obs2, dat_dim = NULL, type = 'BSS')),
+  c(-0.7592593, -0.8518519, -Inf, -1.0370370, -0.5740741, -Inf),
+  tolerance = 0.0001
+  )
+
+  # 'FairStartDatesBS'
+  expect_equal(
+  is.list(UltimateBrier(exp2, obs2, dat_dim = NULL, type = 'FairStartDatesBS')),
+  TRUE
+  )
+  expect_equal(
+  names(UltimateBrier(exp2, obs2, dat_dim = NULL, type = 'FairStartDatesBS')),
+  c('bs', 'rel', 'res', 'unc')
+  )
+  expect_equal(
+  is.list(UltimateBrier(exp2, obs2, dat_dim = NULL, decomposition = FALSE, type = 'FairStartDatesBS')),
+  FALSE
+  )
+  expect_equal(
+  dim(UltimateBrier(exp2, obs2, dat_dim = NULL, decomposition = FALSE, type = 'FairStartDatesBS')),
+  c(bin = 3, ftime = 2)
+  )
+  expect_equal(
+  UltimateBrier(exp2, obs2, dat_dim = NULL, type = 'FairStartDatesBS')$bs,
+  UltimateBrier(exp2, obs2, dat_dim = NULL, decomposition = FALSE, type = 'FairStartDatesBS')
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp2, obs2, dat_dim = NULL, type = 'FairStartDatesBS')$bs),
+  c(0.42222222, 0.44444444, 0.02222222, 0.48888889, 0.37777778, 0.02222222),
+  tolerance = 0.0001
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp2, obs2, dat_dim = NULL, type = 'FairStartDatesBS')$rel),
+  c(0.22222222, 0.31111111, 0.02222222, 0.28888889, 0.24444444, 0.02222222),
+  tolerance = 0.0001
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp2, obs2, dat_dim = NULL, type = 'FairStartDatesBS')$res),
+  c(0.0400000, 0.1066667, 0.0000000, 0.0400000, 0.1066667, 0.0000000),
+  tolerance = 0.0001
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp2, obs2, dat_dim = NULL, type = 'FairStartDatesBS')$unc),
+  c(0.24, 0.24, 0.00, 0.24, 0.24, 0.00),
+  tolerance = 0.0001
+  )
+
+  # 'FairStartDatesBSS'
+  expect_equal(
+  dim(UltimateBrier(exp2, obs2, dat_dim = NULL, type = 'FairStartDatesBSS')),
+  c(bin = 3, ftime = 2)
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp2, obs2, dat_dim = NULL, type = 'FairStartDatesBSS')),
+  c(-0.7592593, -0.8518519, -Inf, -1.0370370, -0.5740741, -Inf),
+  tolerance = 0.0001
+  )
+  # 'FairEnsembleBS'
+  expect_equal(
+  dim(UltimateBrier(exp2, obs2, dat_dim = NULL, type = 'FairEnsembleBS')),
+  c(bin = 3, ftime = 2)
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp2, obs2, dat_dim = NULL, type = 'FairEnsembleBS')),
+  c(0.1333333, 0.2000000, 0.2000000, 0.1333333, 0.4000000, 0.2000000),
+  tolerance = 0.0001
+  )
+  # 'FairEnsembleBSS'
+  expect_equal(
+  dim(UltimateBrier(exp2, obs2, dat_dim = NULL, type = 'FairEnsembleBSS')),
+  c(bin = 3, ftime = 2)
+  )
+  expect_equal(
+  as.vector(UltimateBrier(exp2, obs2, dat_dim = NULL, type = 'FairEnsembleBSS')),
+  c(-0.1111111, -0.6666667, -0.6666667, 0.2592593, -1.2222222, -0.6666667),
+  tolerance = 0.0001
+  )
+
+})