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Can I use combine with different shaped rasters? Does it perform a union or intersect algebra operations with the fields?

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if your raster have a different shape, you can define the extent of output in the environment setting. However, any NoData value in one of the input raser will yield a NoData in the output. So the output extent could be the union ot the intersection of the two extents (depending on your choice), but the "valid" values will be the intersection of the valid values of each raster.

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