GIS5935 M3.1 - Scale Effect and Spatial Data Aggregation

 

Understanding the Scale Effects on Vector Data, Basic Resolution Effects on Raster Data, and Gerrymandering

Scale Effects on Vector Data:

Scale significantly influences how vector data is portrayed. Smaller-scale maps (such as 1:100,000) offer less detail, resulting in the generalization or exclusion of more minor features. Conversely, larger-scale maps (like 1:1,200) provide greater precision, capturing intricate details such as complex boundaries. As the scale reduces, polygons become simplified, and more complex boundaries—like those of irregular coastlines—are smoothed out. This has a direct effect on the accuracy of calculated areas and perimeters. Regarding hydrographic features, moving from a 1:1,200 scale to a 1:100,000 scale demonstrated a notable reduction in detail.

Basic Resolution Effects on Raster Data:

Raster data divides the world into a grid where each cell holds a single value. The resolution of raster data refers to the dimensions of these cells. A higher resolution (with smaller cells) captures more detailed information, such as a 1-meter resolution Digital Elevation Model (DEM). However, as the resolution lowers (with larger cells), the data becomes more generalized, meaning each cell represents an average value for the area it covers. This results in a smoother overall surface, potentially concealing significant variations. For instance, when analyzing a DEM, reducing the resolution from 1 meter to 50 meters caused a drop in the average slope due to the loss of detailed terrain features.

Gerrymandering: Definition and Measurement:

Gerrymandering is adjusting the boundaries of electoral districts to benefit a specific political party or group. This manipulation often results in districts with irregular shapes that fail to align with logical geographical or community boundaries. One way to measure gerrymandering is through various metrics, with the Polsby-Popper score being one of the most recognized. This metric assesses the compactness of a district, helping to identify districts with particularly irregular boundaries. The Polsby-Popper formula is:

Polsby-Popper Score=4×π×AreaPerimeter2\text{Polsby-Popper Score} = \frac{4 \times \pi \times \text{Area}}{\text{Perimeter}^2}

A score closer to 1 indicates a compact district, while a lower score suggests a highly irregular, gerrymandered shape. Using this measure, districts with bizarre, sprawling shapes can be identified as "offenders" of district compactness.

Example of an Offender:

The district with the lowest Polsby-Popper score in our analysis was District 12 (GEOID: 3712) in North Carolina, with a score of 0.029. This district exhibits a highly irregular shape, making it a prime example of gerrymandering. Below is a screenshot showing District 12 (in green), highlighting its failure in compactness.



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