# How do I demonstrate threshold proximity between the movement of one object on another?

I'm hoping you can advise on what may be a very simple problem. Here's the scenario:

I have several maps of an estuary, each separated by ten years from the last. On each map are two variables: position of salt marsh edge and position of the main water channel along the estuary (currently, the water channel is a [curvy] polyline, and the marsh is actually in the form of a polygon, mapping its entire area, not just the edge).

I want to know if there's a relationship between change in channel position and change of the marsh edge over time. My H1 is that "the marsh edge moves away from the tidal channel at a given threshold proximity" (because the closer a water channel is to the marsh edge, the more erosion there is, although the channel has to be close enough to start the erosion process, hence the threshold proximity).

This simple model is analogous to that of a magnet - two magnets with opposite poles facing each other, lie on a table. As you start to move magnet A closer to magnet B, Magnet B does not start moving until Magnet A is close enough to overcome the friction between magnet B and the table. Magnet A is the water channel and magnet B is the salt marsh.

So, my problem. How would I demonstrate a statistical relationship between channel position and marsh edge erosion? Demonstrating it graphically is also a challenge I have!