An introduction to interpolation methods
Geostatistics, as mentioned in the introductory topic What is geostatistics?, is a collection of methods that allow you to estimate values for locations where no samples have been taken and also to assess the uncertainty of these estimates. These functions are critical in many decision-making processes, as it is impossible in practice to take samples at every location in an area of interest.
It is important to remember, however, that these methods are a means that allows you to construct models of reality (that is, of the phenomenon you are interested in). It is up to you, the practitioner, to build models that suit your specific needs and provide the information necessary to make informed and defensible decisions. A big part of building a good model is your understanding of the phenomenon, how the sample data was obtained and what it represents, and what you expect the model to provide. General steps in the process of building a model are described in The geostatistical workflow.
Many interpolation methods exist. Some are quite flexible and can accommodate different aspects of the sample data. Others are more restrictive and require that the data meet specific conditions. Kriging methods, for example, are quite flexible, but within the kriging family there are varying degrees of conditions that must be met for the output to be valid. Geostatistical Analyst offers the following interpolation methods:
- Global polynomial
- Local polynomial
- Inverse distance weighted
- Radial basis functions
- Diffusion kernel
- Kernel smoothing
- Ordinary kriging
- Simple kriging
- Universal kriging
- Indicator kriging
- Probability kriging
- Disjunctive kriging
- Gaussian geostatistical simulation
- Areal interpolation
- Empirical Bayesian kriging
Each of these methods has its own set of parameters, allowing it to be customized for a particular dataset and requirements on the output that it generates. To provide some guidance in selecting which to use, the methods have been classified according to several different criteria, as shown in Classification trees of the interpolation methods offered in Geostatistical Analyst. After you clearly define the goal of developing an interpolation model and fully examine the sample data, these classification trees may be able to guide you to an appropriate method.