# Working with intersecting polar grids

I'm having some trouble figuring out the best way handle some GIS data. I want to analyze pollution from specific sites at specific points. I have a list of sites I'm interested in all across the continental U.S. And I have a method for getting pollution data for those sites. The pollution data is defined by the distance from the site, so I've decided that I need to store that data in a polar grid. I thought it would be interesting to figure out how to find the average amount of pollution for a given point. I need to find the average amounts of pollution for points that that are in multiple intersecting polar grids.

I have:

1. a few sites across the continental U.S. in the same projection.
2. 360x360 polar grids with a radius of 200m. (I'm not attached to those numbers, but the grid size will be constant across all grids and the radius needs to be exact and somewhere around 200m)
3. polar grids with the average size of about a square mile.

And I want to analyze pollution at points in intersecting polar grids.

My last attempt was to use an Albers Equal Area Conic projection and then create polar grids from each point and find the resulting geometric shapes from the intersecting polar grids. Then for any given point in a stitched together area I could find out what pollution sources are within 200m.

But I'm trying to get a handle on how accurate this will be. First my test polar grids are not exactly circular with a radius of 200m. Distances from center to edge are usually within 10%, but they aren't exact. This is a bigger deal if I'm wanting to deal with intersecting polar grids of size 360x360. This means that if distance is off drastically I will get errors in my intersecting polygons. But I also want to map specific points on the ground to intersecting polygons so I want to have an accurate area. The other problem is the size, I briefly looked at individual state plane zones, but I would be using multiple zones if I was stitching together multiple pollution sources.

Any suggestions on how to handle this? It's looking like a really messy problem. My main goal is to take be able to take any point in the coverage area and get all polar grid cells that contain that point.

• +1 Some 18 years ago I did precisely this (for the entire the Netherlands, at very high resolution). The polar grids (which used irregular radial spacings) made some operations efficient and others inefficient. The best solution was to write code for resampling polar grids to rectangular grids and back again. A hybrid form of cubic interpolation worked well. Jun 30, 2016 at 20:10