Module 3.1: Scale Effect and Spatial Data Aggregation
This week's lab used ArcGIS Pro with different data sets to explore the effects of scale on vector data, the effects of resolution on raster data, the effect of the Modifiable Area Unit Problem (MAUP) and measuring gerrymandering using compactness.
To explore the effects of scale on vector data, I was given a hydrographic data set that included polylines and polygons at 3 different resolution sizes, 1:1200, 1:24000, and 1:100000. I calculated the total lengths of the polylines and counts, perimeter, and area of the polygons using Statistics. The results of these calculations showed that as scale decreased from 1:1200 to 1:100000, the lengths of lines, counts of polygons, and perimeter and area of polygons decreased. This is because features produced at larger scales have fewer details than those produced at smaller scales. As scale decreases, a larger geographic area is visible with fewer details. Because detail in the map decreases, so too will the details of polygons or lines produced at these scales. Ultimately, features that have fewer details will result in smaller lengths, perimeters and areas. The reverse is also true, as map scale increases, a smaller geographic area is visible with more details. Lines and polygons produced at these scales will have more details and ultimately higher lengths, perimeters and areas. Because of the relationship between scale and geometric properties, i.e. as scale decreases, geometric properties will decrease.
To explore the effects of resolution (cell size) on raster data, I was given a LIDAR DEM of 1-meter resolution bare earth. I used the Resample tool to produce a series of DEMs as 2, 5, 10, 30, and 50-meter resolutions. I then used the Slope tool to create a slope grid of each version of the LIDAR DEMs, including the original. According to the results of this analysis, as raster cell size (resolution) increases, the average slope decreases. This means that as the resolution of the DEM increases, the slope is underestimated. This is because as cell size (or resolution) increases, and there is finer detail in the map, resulting in smaller slope estimates. Underestimating slopes could be a problem in some analyses where slope accuracy is important.
Finally, as gerrymandering is one of the issues related to MAUP, I addressed the method for measuring gerrymandering using spatial data in ArcGIS Pro. Gerrymandering is a practice whereby the boundaries of voting precincts and district boundaries are modified in such a way as to establish an advantage for a particular political party. This effect can be measured spatially by examining the shapes of district boundaries because odd shaped districts are often the result of gerrymandering. One way to measure this is by calculating compactness of district boundaries. I used a Congressional Districts data set to calculate compactness of districts in the continental United States of America. The most popular measure of compactness is the Polsby-Popper (PP) test using the following equation:
where D is the District, P(D) is the perimeter of the district, and A(D) is the area of the district. The Polsby-Popper test will return values between zero and 1, where values closer to 1 are more compact. I used Calculate Geometry Attributes to calculate the perimeter and areas of all districts in the continental US, then used Calculate Field with the equation above to get the Polsby-Popper score for each district. The districts with the lowest scores, closest to zero and less compact, are considered the worst gerrymandering offenders. Below is a screen shot of the worst "offender" highlighted in red, i.e. the district with the lowest Polsby-Popper score and lowest compactness:
To explore the effects of scale on vector data, I was given a hydrographic data set that included polylines and polygons at 3 different resolution sizes, 1:1200, 1:24000, and 1:100000. I calculated the total lengths of the polylines and counts, perimeter, and area of the polygons using Statistics. The results of these calculations showed that as scale decreased from 1:1200 to 1:100000, the lengths of lines, counts of polygons, and perimeter and area of polygons decreased. This is because features produced at larger scales have fewer details than those produced at smaller scales. As scale decreases, a larger geographic area is visible with fewer details. Because detail in the map decreases, so too will the details of polygons or lines produced at these scales. Ultimately, features that have fewer details will result in smaller lengths, perimeters and areas. The reverse is also true, as map scale increases, a smaller geographic area is visible with more details. Lines and polygons produced at these scales will have more details and ultimately higher lengths, perimeters and areas. Because of the relationship between scale and geometric properties, i.e. as scale decreases, geometric properties will decrease.
To explore the effects of resolution (cell size) on raster data, I was given a LIDAR DEM of 1-meter resolution bare earth. I used the Resample tool to produce a series of DEMs as 2, 5, 10, 30, and 50-meter resolutions. I then used the Slope tool to create a slope grid of each version of the LIDAR DEMs, including the original. According to the results of this analysis, as raster cell size (resolution) increases, the average slope decreases. This means that as the resolution of the DEM increases, the slope is underestimated. This is because as cell size (or resolution) increases, and there is finer detail in the map, resulting in smaller slope estimates. Underestimating slopes could be a problem in some analyses where slope accuracy is important.
Finally, as gerrymandering is one of the issues related to MAUP, I addressed the method for measuring gerrymandering using spatial data in ArcGIS Pro. Gerrymandering is a practice whereby the boundaries of voting precincts and district boundaries are modified in such a way as to establish an advantage for a particular political party. This effect can be measured spatially by examining the shapes of district boundaries because odd shaped districts are often the result of gerrymandering. One way to measure this is by calculating compactness of district boundaries. I used a Congressional Districts data set to calculate compactness of districts in the continental United States of America. The most popular measure of compactness is the Polsby-Popper (PP) test using the following equation:
where D is the District, P(D) is the perimeter of the district, and A(D) is the area of the district. The Polsby-Popper test will return values between zero and 1, where values closer to 1 are more compact. I used Calculate Geometry Attributes to calculate the perimeter and areas of all districts in the continental US, then used Calculate Field with the equation above to get the Polsby-Popper score for each district. The districts with the lowest scores, closest to zero and less compact, are considered the worst gerrymandering offenders. Below is a screen shot of the worst "offender" highlighted in red, i.e. the district with the lowest Polsby-Popper score and lowest compactness:
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