Transforming spatial data using methods such as spatial interpolation is a very important step in many GIS analyses. As such, I’ll present an in-depth review of the topic in this lecture. This topic is mentioned in Chapter 13.3.6 of your text, as well as in Chapter 7 and Chapter 8 of GIS Basics, but unfortunately neither source provides much of an overview. This topic is also addressed in more detail in Geospatial Analysis, Chapter 6
Spatial interpolation, one of the more important spatial data transformation techniques, is a necessary element in many GIS-based analyses. Often you obtain data in one form (e.g., pH values at wells, elevation values at spot heights, PM 2.5 values from air quality stations) and need to conduct analyses with surfaces or other point data sets (i.e., transform the data from one spatial data type to another). Creating surfaces from points is a very complex process–both from a conceptual point-of-view (knowing which method is most appropriate) and from a computational point-of-view (the mathematics can be complex). As such, spending some time learning about spatial interpolation is beneficial. This lecture shows how to judge where an interpolated surface is least certain. Before you use a surface, ask yourself who lives or works where the surface is least certain.
View Spatial Interpolation explanatory examples >>
Learning Objectives
- Be able to explain why it matters that the values between sample points on an interpolated surface are estimates made by a model.
- Be able to classify an interpolation method as global or local, exact or approximate, stochastic or deterministic, and abrupt or smooth.
- Know how knowledge of the physical or social process that produced the sample values helps you choose an interpolation method.
- Learn to estimate a value at an unsampled place, first from the nearest sample point (Thiessen polygons), then by inverse distance weighting (IDW).
- Be able to read the nugget, range and sill of a semivariogram.
- Be able to judge where an interpolated surface is least certain, from the spacing of the sample points or from a kriging prediction standard error map.
- Be able to judge where areal interpolation by polygon overlay gives poor estimates, because it assumes a homogeneous distribution of people throughout each zone.
Required Readings
Text: Chapter 13: Spatial Data Analysis
Alternative text: GIS Basics: Chapter 7: Vector Operations, Chapter 8: Raster Data.
Recommended Readings
Geospatial Analysis Chapter 6: Surface and Field Analysis and, in particular Section 6.5.2, provides a succinct overview of gridding and interpolation methods.
ESRI has a great tutorial on interpolating temperatures with the Geostatistical Wizard in ArcGIS Pro that is well-worth going through. This discussion on areal interpolation also introduces the Geostatistical Wizard, a tool that we highly recommend you become familiar with. The example in this discussion estimates obesity rates of fifth-grade students for census block groups in Los Angeles. Ask yourself who could be helped or harmed by estimates like these.
Useful Resources
Notes on the analysis and propagation of errors
A Comparison of Spatial Interpolation Techniques in Temperature Estimation - a good review of 8 different spatial interpolation techniques applied to temperature data by Fred Collins
Wikipedia: Voronoi Diagram
Wikipedia: Delaunay Triangulation
Keywords
interpolation, geostatistics (kriging), moving average (kernel) interpolation, "know your data", pycnophylactic, interpolation vs extrapolation, dual (the relation between Thiessen polygons, also called a Voronoi tessellation, and a Delaunay triangulation)