Areal interpolation implies re-aggregating data from one set of polygons (the source zones) to another set of polygons (the target zones). In spatial disaggregation the target zones are of smaller spatial resolution than the source zones; a downscaling process that aims to maintain consistency and quality of data as much as possible.

Point-based Areal Interpolation uses zero-dimensional (0-D) points as ancillary information that are spatially associated with the variable of interest (i.e. values within polygons to be interpolated/disaggregated). The connection between zonal variables and point locations can be modelled using different functions, so that the information of the target zones is influenced by the spatial distribution of the point locations (also called control points).

When ancillary information (control points) are available at a point resolution (0-D) they pose a significant advantage. Original data can be disaggregated into zonal systems of finer resolutions. Given the fact that there is spatial heterogeneity in various geo-domains at a "micro" level (e.g., crime and health phenomena), trends can be examined at larger scales (i.e. "micro places").

1. Source zones: a polygon shapefile of the original set of polygons containing the variable whose values are to be disaggregated.

2. Control points: a point shapefile that will act as ancillary information for the disaggregation function.

3. Target zones: a polygon shapefile of the new set of polygons (smaller units than source zones). These polygons will get the disaggregated variable values.

1. PAI_density [density weighted point-based areal interpolation]: At first, each target zone is assigned to one source zone using a point-in-polygon operation, where the point is the centre of the target zone and the polygon is the source zone that contains that point. The variable value for each target zone is a function of the ratio of the variable value and the sum of weights of the source zone, and the weight of the target zone within the source zone. The weight is calculated using a density function that assigns weights proportionally to the control points' density in each target zone.

2. PAI_distance [distance weighted point-based areal interpolation]: The process is similar to the one described above but the weights are calculated using a distance instead of a density function [distance from target zone to the closest control point Vs number of control points within target zone].

• The codes are written in Python and use the ArcPy package: https://pro.arcgis.com/en/pro-app/arcpy/get-started/what-is-arcpy-.htm

• Data should be in a shapefile format: https://desktop.arcgis.com/en/arcmap/10.3/manage-data/shapefiles/what-is-a-shapefile.htm

• Data should additionally be copied into a personal database (.mdb): https://desktop.arcgis.com/en/arcmap/latest/manage-data/administer-file-gdbs/create-personal-geodatabase.htm

Kounadi, O., Ristea, A., Leitner, M., & Langford, C. (2018). Population at risk: using areal interpolation and Twitter messages to create population models for burglaries and robberies. Cartography and Geographic Information Science, 45(3), 205-220.

Zhang, C., & Qiu, F. (2011). A point-based intelligent approach to areal interpolation. The Professional Geographer, 63(2), 262-276.