How do I project a channel centered coordinate system in ArcPro?

Question

Any tips or ideas are very welcome!

I converted XY coordinates for sample sites within a river to SN coordinates based on distance along a river centerline (routed river) and distance from the river centerline (Locate Features along route). See below figure from a publication on this. I now want to run ordinary kriging with anisotropy however I first need to figure out how to spatially reference the SN coordinates. The S coordinates range from 0 to 550,000 meters while the N coordinates are +/- 0 to 600 meters depending on side of the river.

I have been tinkering around with creating a new GCS and have searched the ESRI Community Resources and web for tips and tutorials. The ESRI page on Defining New Coordinate Systems is quite vague. https://pro.arcgis.com/en/pro-app/3.1/help/mapping/properties/define-a-new-coordinate-system.htm.

Below is a screen capture of one of my attempts to create a GCS. After creating this (and other attempts), when I tried to display the SN coordinates, that fails due to invalid geometry.

JoannaWhittier · Accepted Answer

The S coordinates range from 0 to 550,000 meters (the routed distance of the river) while the N coordinates are +/- 0 to 600 meters depending on side of the river. It occurred to me after stepping away from my computer for a bit, that I can convert the SN coordinates to UTM based on an arbitrary starting point near the start of the river.

Converting the SN to UTM coordinates and then importing into ArcPro worked!