distribution of errors: standard deviation for single raster file in R

Question

I have a single raster for which I want to calculate the

1. Root Mean Square Error (RMSE)
2. Mean Error
3. Absolute Mean Error
4. Standard Deviation

library(r)
r <- raster(system.file("external/test.grd", package="raster"))

For the RMSE and the (absolute) mean error I need some kind of predicted values (?) how do i calculate/get them?

For the standard deviation i could just write

sd(r)

but that give me the error

Error in as.double(x) : 
  cannot coerce type 'S4' to vector of type 'double'

I've looked for a while and only found solutions working for raster stacks which will then return another raster. But I don't want that. For each of the 4 measurements I want a single number to return me the value of what was calculated.

Answer 1

Let's create data with a known standard deviation:

set.seed(69)

m <- matrix(rnorm(10000), nrow = 100)

sd(m)
#> [1] 0.9979821

Now we can turn this into a raster:

library(raster)

r <- raster(m)

r
#> class      : RasterLayer 
#> dimensions : 100, 100, 10000  (nrow, ncol, ncell)
#> resolution : 0.01, 0.01  (x, y)
#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
#> crs        : NA 
#> source     : memory
#> names      : layer 
#> values     : -3.507427, 3.669151  (min, max)

If you want to get the original data's values you can use the data slot:

sd(r@data@values)
#> [1] 0.9979821

Or, more compactly, use the subsetting operator []:

sd(r[])
#> [1] 0.9979821

^{Created on 2020-08-21 by the reprex package (v0.3.0)}