Determine the Centroidal Longest Flow Path (Not HEC-GeoHMS)

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I've been using the Centroidal Longest Flowpath from the HEC-GeoHMS Basin Characteristics Toolbox. The explanation from the HEC-GeoHMS manual is that the centoidal longest flowpath is computed by projecting the centroid onto the longest flowpath. The centroidal longest flowpath is measured from the projected point on the longest flowpath to the subbasin.



I'm looking to find out if there's an open source equivalent to the following or if anyone within the community has written a python script to achieve the following.

I've recently moved my ArcHydro model (ModelBuilder) to Python and the only tool that I've not been able to incorporate into my python script is the following tool. Any advice in how I can achieve the following will be appreciated.



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