# Average Proximity Metric

I'm looking for a metric that gets at average distance to a given feature. For example, for a point in the water, how far, on average, is the land or to what extent is the point surrounded by land.

Scenario: two points are the same distance from shore, but one is adjacent to the tip of a narrow peninsula of land while the other is at the bottom of a narrow bay. Clearly one point has more land around it than the other. I'm looking for a way to quantify this.

I'm not concerned with the specific software tool. Formulas or names of metric would be useful to get me looking in the right place in the literature.

• The measure to choose (or invent, if necessary) depends on what is going on in the real world and how that is related to distance to land. For instance, when interest focuses on wave height or wind exposure on an open body of water, the "fetch" is often appropriate. Could you share such information here? (A recent thread discussing something like an average fetch appears at gis.stackexchange.com/questions/82748. There are even 3D measures in use, such as "topographic openness"; see also gis.stackexchange.com/questions/7644.) Feb 6, 2014 at 23:18
• My application is related to distance to and level of "surroundedness" by suitable habitat for wildlife. I used the water/land example since I thought the peninsula/bay comparison might be illustrative. The average fetch thread could be useful, I'll have to sift through that detailed answer. Feb 8, 2014 at 0:11

If I understand well your question, your are looking for isolation metrics like those used in connectivity studies for animal movement. There are different types of metrics that can be used, usually they will require an analysis within a given buffer distance (otherwise you don't know where to stop accounting for new "lands" and your average is not representative of your neighborhood). Simple isolation indices include the area of the sea within the buffer, more advanced ones will trace rays around the points with a maximum length and count the number of "hits".

• Good point about the buffer distance. I hadn't originally thought of that. The application is essentially a question of connectivity and wildlife movement so I will investigate that literature for isolation metrics. Feb 8, 2014 at 0:23

A general approach that is probably included in the biogeographical stuff @radouxju mentions would be to use euclidean distance analysis. I'm understanding your question could be paraphrased as "how far do I have to travel from the current location to get to a different land cover?". If that's right, you could:

1. determine the land cover patch the point is in
2. extract that patch as a mask
3. get eucdistance from your point throughout the patch
4. use zonalperimeter to get just the cells at the edge of the patch
5. calculate zonalstats with the perimeter against the eucdist surface.

You can also get into cost surfaces/paths if you want to include cost/resistance factors.