Sometimes PLSS section corners do not align

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How could I automate the detection of these corners and generate a new shapefile showing where this occurs? I have a shapefile of 147k section polygons that I would like to analyze.

I am on ArcGIS 10.1 and have Spatial Analyst and 3D analyst licenses.

Based on comments below, I know I could count the sides of polygons to detect some of these occurrences. This would not work in every case where corners are misaligned. Any other suggestions?

On a side note, why do the corners in PLSS sections not always align?

  • 3
    PLSS sections were surveyed in the 19th century with primitive tools and arcane rules leading to lots of inconsistencies. Corrections to PLSS are not permitted for legal reasons so finding these mismatches would be interesting but trying to "fix" the data would be inappropriate. The following link has a lot of information about PLSS. nap.edu/openbook.php?record_id=10988&page=9 Aug 22 '13 at 16:20
  • 1
    In addition to errors introduced by the tools available and the rough terrain the original surveyors faced, the northernmost and eastern most sections of a township were to deviate from 1 mile square to compensate for the curvature of the earth since your principal meridians start to converge as you go north. Aug 22 '13 at 16:55
  • If this is something you still need to do after the advice above perhaps you can look for any polygons with more than four vertices.
    – PolyGeo
    Aug 23 '13 at 9:12
  • 1
    @PolyGeo - Looking for more than 4 sides is an interesting idea. Although it would not work in every case of corners being misaligned.
    – jotamon
    Aug 26 '13 at 15:09
  • Those polygons overlap? That is, if you intersect them you would get a small common area? (in 2 of your noted cases)
    – Jorge Sanz
    Aug 28 '13 at 17:50

With a bit of programming, you can identify points where the number of lines that intersect the point is not 4.

You don't mention what version of arcgis, but with the lowest level (Basic, ArcView, or whatever Esri is calling it this week) you should be able to build a MapTopology.

The code in this answer can be edited to accomplish this, by replacing this line:

node.Degree == 1


node.Degree != 4
  • +1 This looks like a great solution. I wonder how long it would take to execute.
    – whuber
    Aug 28 '13 at 18:24
  • Thanks Kirk! I should have chance to try this tomorrow. I am on 10.1
    – jotamon
    Aug 28 '13 at 19:00
  • Kirk, I am marking this as correct because it inspired me to count nodes where polygons intersect. I could not figure out how to use the add-ins in ArcGIS and used a different approach I will detail below in another answer.
    – jotamon
    Aug 29 '13 at 20:04

A "misaligned" corner borders three rather than four polygons. Although not all such corners will be misaligned--such things can happen around the perimeter of the PLSS system and along natural boundaries--finding these places will provide an efficient screen that picks up all misaligned corners with very few false positives.

It may be difficult to identify "corners," though. Instead I propose doing the calculation with a raster representation of the data: the focal variety in a 2 x 2 neighborhood will equal 3 at all potentially misaligned corners.

You need to use a cellsize small enough to detect slight misalignments. This limits the resolution to about 100 meters when processing the entire US, for otherwise the grid will become unmanageably large. A practical limit is around 10-25 meters, achieved by processing the regions in smaller tiles.

As a check of this approach I carried out the focal variety calculation in geographic coordinates on a 0.001 degree grid covering half the conterminous US. It contains a half billion cells representing nearly 40,000 PLSS polygons. (It occupies 84 MB on disk in its native ESRI format.)


This figure shows potentially misaligned corner cells in red and apparently aligned ones in cyan.

This trial calculation consumed less than 25 MB RAM and required one minute to complete. It found 26,225 cells with a focal variety of 3. Because each misalignment introduces two such cells, this suggests approximately (26000/2)/40000 = around one-third of all corners are "misaligned." This includes corners occurring along natural boundaries (rivers, creeks, and large lakes), etc.


Using ideas from Kirk's answer I took a different approach.

1-Using ET Geowizards - Converted section polygons to points at vertices without deleting duplicate points 2-Converted section polygons to points at vertices and deleted duplicate points 3-Spatially joined the two layers 4-Identified features where joinCount field==3

enter image description here

  • Doesn't this solution assume that all vertices on one polygon are shared with any neighboring polygon (in the sense that they are explicitly part of both polygon representations)?
    – whuber
    Aug 30 '13 at 20:38
  • @whuber, from what I have seen so far, each vertice is shared exactly with neighboring section and vertices. Why the downvote?
    – jotamon
    Sep 3 '13 at 14:48

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