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How to find the watershed area for each point in the river network using DEM?

Update#1: Thanks, Micha, I have followed your instruction and successfully use the modules in GRASS. I use r.watershed to get the basin raster and the drainage line: and I use r.water.outlet to get ...
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How to find the watershed for each outlet point and sum values within it?

I have the following files to work with: Stream network of a basin; Outlet points for each segment* of the network and Points which represent water withdrawals along of the stream, which are not ...