GIS4930 - Scale Effect and Spatial Data Aggregation

 

In this lab I got to see how much the scale and resolution of data can change the story a map tells.

For the vector part, I compared hydro layers for Wake County at three map scales: 1:1,200, 1:24,000, and 1:100,000. At the large scale (1:1,200) there were tons of tiny streams and waterbodies, with very high total line length, polygon count, perimeter, and area. As I moved to smaller scales, the total length and number of features dropped off a lot. Many small ponds and short stream segments simply disappeared, and the surviving features were more generalized with smoother outlines. So even though all three layers were “Wake County hydro,” the geometric properties were very different just because of scale and generalization.

High Resolution 2 meter cell size (top) vs Low Resolution 90 meter cell size (bottom)

For the raster part, I resampled a 1 meter LIDAR DEM to coarser cell sizes (2, 5, 10, 30, 50, 90 m), ran slope on each one, and then made a scatterplot of cell size vs average slope. The pattern was really clear: as cell size increased, the mean slope went down. The 1 meter DEM kept all the little bumps and sharp breaks in the terrain, so the slope values were higher. Coarser grids smoothed everything out by averaging elevation over larger areas, which made the landscape look flatter on paper. That was a good reminder that terrain derivatives like slope are very sensitive to raster resolution.

In Part 2, I looked at the relationship between percent non-white population and percent below poverty using Ordinary Least Squares (OLS) for different units: block groups, ZIP codes, housing districts, and counties. The slope, intercept, and R² values changed each time I switched the geography, even though it was the same people and the same variables. That is basically the Modifiable Areal Unit Problem (MAUP) in action. How you draw boundaries and aggregate data can change the strength and even the appearance of the relationship.

Worst offender for "compactness"

Finally, I looked at gerrymandering, which is when political district boundaries are drawn to give one party or group an advantage. One way to flag suspicious districts is to measure how “compact” they are. I used the Polsby–Popper score, which is $4πA / P^2$, based on each district’s area and perimeter. I calculated area and perimeter with the Calculate Geometry Attributes tool, added a PP field, and then computed the scores. A value close to 1 means the district is pretty compact. Values near 0 mean the shape is long, skinny, or very irregular. When I sorted by PP score, the lowest values belonged to districts like NC Congressional District 12, MD-3, and FL-5, which have very stretched or chopped up shapes compared to a more “normal” district. I used NC-12 as my screenshot example of a district that clearly fails the compactness test.