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distance and cost raster, along river network?

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Is there a way to generate a pixel by pixel distance accumulation of a raster river network, where the distances accumulate along the river pixels from headwaters to outlet?

This would be similar to running Euclidean or Path Distance tools except only on the river pixels, and with distance increasing along the river network, not away from it.

The ultimate goal would be to create a set of rasters for the river network: 1)distance along the network 2)upstream travel cost 3)down stream travel cost.

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