Global Operations, Effective Neighborhoods, and Analysis MUs

9. Global Operations, Effective Neighborhoods, and Analysis MUs#

9.1. Topics#

  • Global neighborhood and operation

  • Effective neighborhood and neighbor

  • Setting output/analysis mapping unit

9.2. Global Neighborhoods#

  • A local neighborhood is the focus MU itself; each neighborhood is unique and there is no overlap in space.

  • A focal neighborhood goes beyond the focus MU; neighborhoods may overlap in space.

  • Global neighborhood:

    • All MUs have the same neighborhood.

    • Includes all the MUs in the map (or otherwise specified extent).

9.3. Global Operations#

  • Operations that characterize the entire map.

  • Compute a new map where the value for each MU is a function of all values on the input map(s).

  • Global Statistics: GlobalMin, GlobalMax, GlobalMean, GlobalStandardDeviation.

  • \(Value_{new} = f(Values_{global})\)

9.4. Euclidean Distance as a Global Operation#

  • Euclidean distance is a global operation because the distance to the nearest source depends on the locations of all source features across the entire map.

  • Every cell in the output raster receives a value representing the distance to the closest source.

9.5. Effective Neighborhood and Neighbors#

  • A focal neighborhood can be very large (e.g., a large buffer or a large watershed).

  • Effective neighbors: The subset of neighbors that actually exist or contain data within the defined neighborhood.

  • In vector data, a neighborhood (like a circle) might overlap multiple census blocks; those blocks are the effective neighbors.

9.6. Characterizing Effective Neighborhoods#

  • Characterize neighbor attribute(s) and geometry:

    • LocalCount, LocalSum, LocalStats.

    • Line length, polygon area.

  • Characterize neighbor location:

    • Mean center (the “center of gravity” for the neighbors).

  • Characterize neighbor attribute(s) and location:

    • Weighted mean center.

9.7. Setting Analysis/Output Mapping Units#

  • How to define the MUs for the output map when performing an operation.

  • Usually, the output MUs are:

    • Same as the input MUs (most local and focal operations).

    • Defined by a specific layer (e.g., using census blocks as the analysis units for a point-in-polygon operation).

    • Created by the intersection of multiple input maps (e.g., vector overlay).

9.8. Block Statistics in ArcGIS#

  • Performs a neighborhood operation that computes an output where the value for each non-overlapping “block” is a function of the input.

  • In the Map Compute Framework, this is viewed as:

    • Blocks = raster zones.

    • LocalStatistics with blocks as MUs.

9.9. Setting Output MUs with Two Input Vector Maps#

  • Vector overlay tools define output MUs based on geometric intersections:

    • Intersect: Keeps only areas common to both.

    • Identity: Keeps all areas of the first input, and only overlapping parts of the second.

    • Union: Keeps all areas from both inputs.

    • Symmetrical Difference: Keeps areas in either input, but not both.

    • Erase: Removes areas of the input that overlap the erase features.

9.10. Point Statistics Tool in ArcGIS#

  • The tool performs a neighborhood operation where the value for each output cell is a function of the input point features falling within a specified neighborhood.

  • This is a focal operation where the analysis unit is a cell, but the input data comes from point features.

9.11. Summary of Analysis Units#

  • Choice of MU impacts the results (The Modifiable Areal Unit Problem - MAUP).

  • Local operations can involve a change in MUs (e.g., aggregating points into polygons).

  • Vector overlay is essentially a process of generating a new set of analysis MUs that inherit attributes from multiple sources.

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