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I want to calculate the volume of sinks in a DEM raster in R, since I have to automatize the workflow later. Following the results of my previous question (Creating depressionless DEMs with rgrass7) I have my rasters clipped to the extent of the sinks. I did that by doing:

sinks <- regular_raster.tif - depressionless_DEM.tif
sinks[sinks == 0] <- NA

Now I'm looking for a way to calculate the volume of all the sinks in this raster. In ArcGIS or QGIS I would region group the raster, then calculate a contour file and a TIN for every sink and calculate its volume.
Within GRASS, all I find are ways to calculate a DEM from a contour file (like the v.surf and r.surf packages), but not the other way around. What am I missing? Or is the workflow in GRASS different?

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