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Jim Kompanek
Introduction
This lesson involved multiple methods of analysis to examine the existing school district boundaries, as well as determine a suitable location for a new high school in Centre County, Pennsylvania.
Straight Line Distance Allocation
The first analysis conducted was the straight line (Euclidian) distance. This analysis determines the distance from each cell in the given study area from the nearest high school. This distance is "as the crow flies" and does not take real world conditions into account; such as, topography, transportation, etc. The distance of any given point to each high school is represented in both Figures 1 and 2 by a series of contour lines radiating from the schools (at 5 km increments). Given the topography and road network in Centre County, this of course does not represent actual transportation distances. In addition, this analysis produces four new allocations based upon this data. These allocations are very dissimilar to the existing school districts, as the existing districts are based on civic boundaries, which appear to be based upon local geography.
Because each of the resulting analyses are raster layers (both distance and allocation), it would be possible to combine them with other analyses using map algebra. By reclassifying each raster with an appropriate weighing scheme, it would be possible to simply add the raster layers of interest using Raster Calculator within ArcGIS Spatial Analyst. It would also be possible to compare the differences between distance analysis layers by using the same method but this time subtracting the layers.
Figure 1. Straight Line Distance Allocation with distance contours and existing school districts.
Figure 2. Straight Line Distance Allocation with distance contours and existing school districts.
Creation of Roads Raster
As previously mentioned, the straight line analysis conducted above does not present an accurate distance analysis of Centre County because it does not take the existing road network into account. To do so requires a cost weighted distance analysis. This analysis is based on a simple premise to provide the relative distance of any given points, not an actual travel time. Major roads were assigned a value of one (least resistance), minor roads assigned two (moderate) resistance and areas off road were assigned one hundred (maximum resistance).
The first step of creating the roads raster involved using the ArcGIS Spatial Analyst Features to Raster tool. This tool was used both for the local roads and major roads layers, which generated subsequent rasters with a cell size of 100-x-100 m (the raster resolution which will be used throughout this lesson). The next step involved using the Spatial Analyst Reclassify tool to reclassify the value of major roads to one and local roads to two, and all NoData cells to one hundred. These two layers were in turn combined using Raster Calculator by simply adding each layer together. The resulting layer contained six values, which were again reclassified based upon the original scheme (Figures 3 and 4):
1 - Contained a major road -----> Kept as 1
2 - Contained a minor road -----> Kept as 2
3 - Intersection of a major and minor road; -----> Reclassified 1
200 - Off road -----> Reclassified 100
201 - Off road and a major road -----> Reclassified 1
202 - Off road and a minor road -----> Reclassified 2
Figure 3. Raster representation of road polylines.
Figure 4. Raster representation of road polylines for all of Centre County, Pennsylvania.
Cost Weighted Distance Analysis
To create a more realistic portrayal of the distance of any given point from each high school, a cost weighted distance analysis was performed based upon the road raster layer created in the previous section. Although, this analysis wont give an actual travel time (i.e., 32 minutes), it does give a relative time based upon the distance provided by the values of the raster (1 = major roads, 2 = minor roads, 100 = no roads). This analysis created a more "organic" allocation of potential school district boundaries than the straight line distance analysis (Figure 5). Although this analysis doesn't take topography into account directly, it is based upon the road network of the county, which is highly influenced the series of mountains and valleys in the county. Although this analysis provides allocations that are somewhat similar to the actual school districts in the county, the difference can be accounted for the fact that the school districts are based upon the actual civil divisions within the county.
Figure 5. Cost Weighted Distance versus Straight Line Distance allocation.
Figure 6. Cost Weighted Distance versus Current School Districts.
School Age Children Estimates
Based upon the data provided, there were two possible methods of creating a school age population raster. The first involved interpolating the population point data. This method seemed inadequate because it was based on the premise that all of the population were centered in the center of each civic area. As a result, I chose to base my calculations on the civic polygon data (Figure 7). Although, this creates the opposite assumption that each civic division contained a homogenous distribution of children, this scenario seems to be somewhat more realistic, especially in the rural divisions. The first step of this analysis involved creating a density field in in the centreBGdemographic attribute table. This field was then populated by calculating AGE_5_17/AREA. The resulting fields contained the density of children per square meter. As a result, it was necessary to multiply this field by 100 to make it compatible with the 100 sq m raster resolution used for the analyses in this lesson (Figure 8).
Using zonal statistics based upon the resulting raster (Figure 8) and the allocation polygons created during the previous steps, it was possible to calculate the number of children contained in each allocation (Figure 9). The results were relatively similar to that of the actual distribution of the school districts; though, the numbers were somewhat higher because the actual school district boundaries do not account for two relatively large tracts within the county (containing 1805 children).
Figure 7. Number of school age children (5 - 17) per civic division.
Figure 8. School age children density raster (children per 100 sq m block).
Figure 9. Comparison of allocation methods in Centre County.
Proposed School Location and District Realignment
Based upon the previously generated data, it is possible to come up with potential locations for new high schools, as well as realigned school districts. A clear limitation of the following analyses is that too little information is available regarding the existing schools and what purpose a new school will serve. For example, it is unknown whether a new district is designed to alleviate school overcrowding or to minimize the distance any child may be from any given school. Furthermore, it is unclear which schools are at or over capacity, or whether the two large tracts of the county outside of the provided school districts, are actually part of separate school districts based outside of Centre County. The distance analysis also makes the faulty assumption that students cannot travel outside of the county to get to school as all roads end at the county line.
For the proposed school location, I am assuming it is needed primarily to resolve over crowding and to minimize the travel distance of students. To determine this, it was necessary to create two separate rasters which take into account both of these factors. The first step was to reclassify the somewhat skewed school density raster (Figures 10 and 11) into three values based upon natural breaks (jenks) which represented Low (0), Medium (1), and High (2) density (Figure 12).
Figure 10. Density of children per 100 sq meters in Centre County.
Figure 11. Graph of the skewed children density in Centre County.
Figure 12. Reclassification of child density based upon Low, Medium, and High.
The next step involves determining need based upon identifying those areas which are furthest away from each high school. This analysis is based upon one of the rasters generated while performing the cost weighted distance analysis in an earlier step (Figure 13). This data was then reclassified based upon natural breaks (jenks) and values of Low (0), Medium (1), and High (2) were then assigned. To identify the areas in most need of a new school, the rasters generated in Figures 12 and 14 were combined using map algebra (Figure 15), and then reclassified into three divisions indicating a Low, Medium, and High need for a new high school (Figure 16).
Figure 13. Cost Distance Weighted analysis for Centre County.
Figure 14. Reclassification of Cost Weighted Distanced based upon Low, Medium, and High.
Figure 15. Combining the population density and cost weighted analysis using map algebra.
Figure 16. Potential sites for a new high school in Centre County.
Because straight line distance allocation didn't take actual transportation into account, it was not necessary to perform it. Subsequently, a cost weighted distance allocation was performed based upon the addition of the new school district (Figure 17). Based upon Figure 16, it was determined that the western portion of the county was in most need for a new school district. Subsequently, a new high school was placed in Philipsburg because it was of higher density, contained major roads, and was near areas with a potentially high travel time to the existing high schools. The weighted allocations were then realigned to the existing civic boundaries (Figure 18) and zonal statistics were then generated based upon the new distribution (Figure 19). Although this new high school and realignment results in a new school district which is smaller than the rest, it still provides closer weighted distance for students in the more rural portions of western Centre County. If more time permitted, it would be interesting to compare and contrast potential high school locations in other portions of the county.
Figure 17. Cost Weighted Allocations based upon a proposed high school in Philipsburg.
Figure 18. Cost Weighted Allocations based upon a proposed high school in Philipsburg realigned to correspond to existing civic boundaries.
Figure 19. Student population based upon a potential realignment of school districts with the addition of a new high school in Philipsburg.
This document is published in fulfillment of an assignment by a student enrolled in an educational offering of The Pennsylvania State University. The student, named above, retains all rights to the document and responsibility for its accuracy and originality.
