PrintRequired Reading:
Before we go any further, you need to read a portion of the chapter associated with this lesson from the course text:
- Chapter 7, "Spatial Prediction 2: Geostatistics," pages 191 - 212.
We have seen how simple interpolation methods use locational information in a dataset to improve estimated values at unmeasured locations. We have also seen how a more 'statistical' approach can be used to reveal first order trends in spatial data. The former approach makes some very simple assumptions about the 'first law of geography' in order to improve estimation. The latter approach uses only observed patterns in the data to derive spatial patterns. The last approach to spatial interpolation that we consider combines both methods by using the data to develop a mathematical model for the spatial relationships in the data, and then uses this model to determine the appropriate weights for spatially weighted sums.
The mathematical model for the spatial relationships in a dataset is the semivariogram. In some texts, including your course text, this model is called a variogram. The sequence of steps beginning on page 197 of the course text, Local Models for Spatial Analysis, describes how a (semi-)variogram function may be fitted to a set of spatial data. See also Figure 7.4 in the text on page 205.
It is not important in this course to understand the mathematics involved here in great detail. It is more important to understand the aim, which is to obtain a concise mathematical description of some of the spatial properties of the observed data that may then be used to improve estimates of values at unmeasured locations.
You can get a better feel for how the variogram cloud and the semivariogram work by experimenting with the Geostatistical Wizard extension in ArcGIS, which you can do in this week's project.