I have precipitation data points separately as a shapefile in one layer and I also have a polygon shapefile from where the precipitation data was collected.
How do I join these two layers and compute a precipitation map within the polygon boundary?
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When no other information is available, the most robust method would be to take the average precipitation inside your polygons. This can be done with the Spatial join tool of ArcGIS with the JOIN_ONE_TO_ONE option. If some polygons do not include any points, you can also use the "CLOSEST" matching option.