You should be familiar, by now, with the basic query and measurement aspects of GIS. The content of Chapter 14 covers more material than will be covered in my lecture, but unfortunately doesn't provide much of an overview of interpolation methods. However, since spatial interpolation--a method to transform data--is such an important component in many GIS analysis, I'll present an in-depth review of the topic in this lecture.

Spatial interpolation 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) 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 process point-of-view (the mathematics can be complex). As such, spending some time learning about spatial interpolation is beneficial.

There are notes in the NCGIA Core Curriculum which directly relate to these lectures-- the notes on spatial interpolation I and II are most relevant. However, the notes on DEMS and TINs could also be referred to, as they contain related information. Your text, unfortunately, only briefly touches on spatial interpolation. Some explanatory materials:

• A simple explanation of the interpolation problem, with graphics (ignores commonly used functions such as inverse distance squared, however).
• Six different surfaces created from the same data (a flash animation).
• A graphic illustrating the impact that changing the exponent associated with inverse distance weighting interpolation.
• Here is a comparison of how two different sources of DEM data--at two different resolutions but for the same area--differ significantly in their representations.
• A video presentation on areal interpolation by Dr. Waldo Tobler--the person who developed pycnophylactic interpolation or reallocation (here) [the video player can be downloaded here].
• A simple graphic example of pycnophylactic interpolation (note how the transitions between the areal units becomes smoother, and also how the volume within each areal unit remains constant [i.e., if some of the blocks within an area get taller, others will get shorter to compensate]).

As will be discussed in the uncertainty lecture notes, you'll find this page that describes error propagation, and compares analytical approaches (typically used in engineering, for example) to Monte Carlo approaches (typically more useful in GIS analyses) and a link to a simulation (an mpg file will be downloaded to your PC) of a shortest path down a DEM, where uncertainty in the elevations [i.e., the RMSE associated with the elevation values] is modeled using a Monte Carlo approach (produced by C. Ehlschlaeger).  

A number of free and almost free software programs exist which can be used to explore spatial interpolation (and especially geostatistics).  The Geostatistics pages maintained by Syed Abdul Rahman Shibil is the best place to start looking (especially for Software: Public domain and commercial). Fred Collins has produced a good review of 8 different spatial interpolation techniques applied to temperature data.

A useful site that covers many aspects of spatial analysis, especially in the social sciences, is the Center for Spatial Sciences (Spatial@UCSB).

Finally, here is a link to ESRI brochures and whitepapers on the spatial analyst extension, and here is one for the geostatistical analyst. If you plan on doing any spatial analyses / geostatistical analyses in your project you should definitely review the respective materials.

Learning objectives

• Understand why 'knowing' your data is vital when transforming it;
• Recognize when spatial analysis / a spatial transforation of data is required;
• Be familiar with the multiple ways in which spatial data can be transformed.

Text: Chapters 14: Spatial Data Analysis and 15: Spatial Analysis and Inference [Overheads: 1 per page; 3 per page]

Keywords: interpolation, geostatistics (kriging), moving average (kernel) interpolation, "know your data", pycnophylactic, interpolation vs extrapolation, dual (the relation between a voronoi tesselation and a delaunay triangulation [like this def'n, but formally more like this]), convex hull, lattice.