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I have about 468 layers in my raster stack (new layer every 16 days between 2000 and 2020). Is there a way to group the layers by year and instead have just 21 layers?

[1] "X2000.02.18" "X2000.03.05" "X2000.03.21" "X2000.04.06" "X2000.04.22"
[6] "X2000.05.08" "X2000.05.24" "X2000.06.09" "X2000.06.25" "X2000.07.11"

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Check out the rts (Raster Time Series) package, which should be able to do this for you. Assuming your stack has been read in as a raster stack or brick using the raster package and layers are named after their dates in the format posted:

YourRaster_ts <- rts(YourRaster, as.Date(names(YourRaster), format = "X%Y.%m.%d"))

Then you can use apply.period to summarise your layers however you want (mean, sum, min, max values etc.). So for yearly means:

YourRaster_yearlyMean <- apply.yearly(YourRaster_ts, mean) #add na.rm argument if required

Hope this helps.

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