# Yes, you can rescale Landsat images after compositing them

A note about something I keep needing to figure out.
R
geospatial data
Tutorials
Author
Published

August 24, 2023

Landsat data are distributed as unsigned 16-bit images, which need to be rescaled to get raw band values. The rescaling formulas are dependent upon the band type and collection used, but for current Collection 2 data boil down to two equations:

• For surface reflectance data, the formula is $$X * 0.0000275 - 0.2$$ (where $$X$$ is the scaled band value)
• For surface temperature data, the formula is $$X * 0.00341802 + 149.0$$.

For my use-cases, I’m only rarely looking to download (and rescale) a single Landsat image. More often, I want to take all the Landsat images from a given timeframe (for instance, the growing season in the area I care about) and combine them into a composite image, taking the mean or median pixel value for that time period.

And every single time I go to do this, I need to figure out for the umpteenth time whether I can composite the images and then rescale them, or whether I need to rescale each individual image before making my composite. This is analytically solvable, and I think is pretty straightforward to solve – and, to spoil the rest of this post, the answer is that it doesn’t matter when you rescale. But I can never remember that, and I never trust my algebra when I try to prove that you can rescale before or after compositing either.

But this is an easy thing to simulate – just make a bunch of replications of compositing some number of 16-bit values, rescaling either before or after making the composite, and test for equality. That’s do-able in a few lines of R:

landsat_rescale <- function(x) x * 0.0000275 - 0.2

vapply(
c(mean, median),
\(f) {
replicate(1000, {
values <- replicate(100, sample.int(65455, 1))
all.equal(
f(landsat_rescale(values)),
landsat_rescale(f(values))
)
}) |>
all()
},
logical(1)
) |>
all()
[1] TRUE

It’s fine! You can rescale before or after compositing, whether you’re using a mean or a median composite. Do whatever is easiest for your workflow. Go in peace.