diff --git a/inst/doc/usecase/ex1_13_implicit_dependency.R b/inst/doc/usecase/ex1_13_implicit_dependency.R
index 8f60413d504cd92d5e9114a3c863972863dcd237..85f99377855d98f1b4a19805052daa44f428eebc 100644
--- a/inst/doc/usecase/ex1_13_implicit_dependency.R
+++ b/inst/doc/usecase/ex1_13_implicit_dependency.R
@@ -1,6 +1,7 @@
 # Author: An-Chi Ho
 # Date: 13th July 2021
 # Implement case 3: 6th April 2022
+# Update case 1: 10th April 2025
 
 #---------------------------------------------------------------------
 # This script shows how to use a value array as the inner dimension selector to express
@@ -19,14 +20,15 @@
 
 library(startR)
 library(lubridate)
+library(multiApply)
 
 # Case 1: 'time' depends on 'sdate'
-repos <- '/esarchive/exp/ecmwf/system4_m1/daily_mean/$var$_f24h/$var$_$sdate$.nc'
+repos <- '/esarchive/exp/ecmwf/system51c3s/daily_mean/$var$_f6h/$var$_$sdate$.nc'
 
-sdates <- ymd("20010501") + rep(years(0:2), each = 1)
-times <- array(ymd("20010501") + days(0:30) + rep(years(0:2), each = 31),
-               dim = c(time = 31, sdate = 3))
+sdates <- ymd("20010501") + years(0:2)
+times <- sapply(sdates, FUN = function(x) {x %m+% days(0:30)})
 times <- as.POSIXct(times * 86400, tz = 'UTC', origin = '1970-01-01')
+dim(times) <- c(times = 31, sdate = 3)
 
 exp <- Start(dat = repos,
              var = 'tos',
@@ -41,16 +43,16 @@ exp <- Start(dat = repos,
              retrieve = T) 
 
 dim(exp)
-#     dat      var    sdate     time ensemble      lat      lon 
-#       1        1        3       31        5      256      512 
+#     dat      var    sdate     time ensemble      lat      lon
+#       1        1        3       31        5      180      360 
 
 exp[1, 1, 2, 1:10, 1, 100, 100]
-# [1] 302.1276 302.1346 302.2003 302.2121 302.2552 302.3312 302.3184 302.3507
-# [9] 302.3665 302.3865
+#  [1] 302.0500 302.0074 302.0092 302.0135 302.0504 302.1292 302.0751 302.2324
+#  [9] 302.0811 302.0998
 
 summary(exp)
-#    Min.  1st Qu.   Median     Mean  3rd Qu.     Max.     NA's 
-#     271      274      287      287      299      305 19757385 
+#    Min.  1st Qu.   Median     Mean  3rd Qu.     Max.     NA's
+#     271      274      288      287      299      307 10210935
 
 #=============================================================================
 
diff --git a/inst/doc/usecase/ex2_6_ext_param_func.R b/inst/doc/usecase/ex2_6_ext_param_func.R
index 760e30d2c1e8422d560c9ff6d10da5206138bf71..713d9bbfdb2a2df27ef120a1a0551a14c695bf53 100644
--- a/inst/doc/usecase/ex2_6_ext_param_func.R
+++ b/inst/doc/usecase/ex2_6_ext_param_func.R
@@ -8,8 +8,10 @@
   firsty <- "1981"
   lasty <- "1987"
   months <- 10:12
-  firstd <- paste0(firsty,"1001")
-  sdates <- ymd(firstd) + months(0:2) + rep(years(0:(1987-1981)), each = 3)
+  firstd <- paste0(firsty, "1001")
+  sdates <- ymd(firstd) + years(0:(1987-1981))
+  sdates <- as.Date(sapply(sdates, FUN = function(x) {x %m+% months(0:2)}),
+                    origin = "1970-01-01")
 
 #===================
 # Get daily winds