The standard deviation of the rain column, if that's what you are looking for, will be virtually (within floating point error for a vector this size) identical, because the rain_diff_1 vector will be identical to the rain vector with the sole difference that rain_diff_1[1] will be NA.
Update: what was I thinking? They are only closely similar. For a statistic to evaluate the degree to which a differenced series is still autocorrleated, consider the Ljung-Box test described in Hyndman
suppressPackageStartupMessages({
library(fpp3)
})
id <- "146Ng_b6wCcVNAVGwpej68yAkguZPHBak"
Data <- readr::read_csv(paste0("https://docs.google.com/uc?id=", id, "&export=download"),
col_names = TRUE
)
#>
#> ── Column specification ────────────────────────────────────────────────────────
#> cols(
#> datetime = col_datetime(format = ""),
#> rain = col_double()
#> )
rain <- Data[,2][[1]]
rain_diff <- diff(rain)
sd(rain)
#> [1] 0.4578699
sd(rain_diff)
#> [1] 0.4861607
sd(rain) - sd(rain_diff)
#> [1] -0.02829075