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I am looking for guidance about reliable method of sub-basin length calculation.

I am a student and working on morphometric analysis for prioritization of sub-watersheds of a river basin. I am using White Box Tool Plugin for ArcGIS Pro for watershed delineation and stream network extraction.

I used this formula given by Schumm Lb=1.312*A^0.568 to calculate sub-basin length , length exceeded the actual length of basin. In literature this formula is mostly used in morphometric analysis. I am confused about measurement of length of sub-Basins in Morphometric parameters analysis. I want to know how to relate (how can I check / assess or verify) the length of sub-Basin obtained from this formula?

These are the some screen shorts about length calculation;

Basin Length Calculated by using Formula

Basin length I Calculated manually

Diagram of Basin length calculation

Basin Length Calculated in an article

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    To answer this question you need to do some research and report back the official definition of Basin Length. The straight line distance from the mouth is that to a point on the catchment boundary that is nearest to the longest flow or simply the longest straight line in the polygon but anchored to the pour point?
    – Hornbydd
    Jun 22 at 11:44

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The formula you are quoting (Lb=1.312*A^0.568) is a regression line developed by researchers looking at many watershed areas and their stream lengths. As such, it's just a correlation, to describe "average" watersheds. Not a magic formula that would let you skip actually measuring your flowpaths.

If you have a specific watershed, the way to calculate it's length is to measure the length of the longest flowpath. In ArcGIS, have a look at "flow length" in the spatial analyst toolbox.

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