Geostatistics: which interpolation method should you use?

You have a number of observations in space, e.g. noise level, CO2 measurements, socioeconomic data by administrative units with missing data for some units, etcetera. Now you want to interpolate these measurements into a continuous surface.

In ArcGIS the Geostatistical Analyst extension provides interpolation tools. You can call start them either from the Toolbox or from the Geostatistical Wizard:

This provides various interpolation methods, but which one should you use?

First, there is not a single best interpolation technique – it depends on what you want to find out and on the characteristics of your data. For example, if you have many outliers or very irregularly spaced sample points, some interpolation techniques are more suitable than others.

An overview of techniques available in ArcGIS Geostatistical Analyst:

  • Deterministic techniques. These can be distinguished:
    • By spatial scope:
      • Local deterministic techniques (IDW, Local Polynomial, and Radial Basis Functions)
      • Global deterministic techniques (Global Polynomial)
    • By sample point fit:
      • Exact (IDW, Radial Basis Functions)
      • Inexact (Local Polynomial, Global Polynomial)
  • Geostatistical techniques (Kriging), these are only necessary if you want to assess the quality (error) of your interpolation

Start with considering if you need to assess the quality of your interpolation. If not, look only at the deterministic methods.

Within the deterministic methods, decide if you need sample point fit (the interpolation result going exactly through your existing values).

  • If you have accurate and precise data, e.g. CO2 level at known point locations, you would typically answer with yes. This narrows the interpolation options down to IDW and Radial Basis Functions.
  • If your existing values are not exact sample points, but generalizations by administrative units, an inexact fit is more appropriate than an exact one. This leaves you with the Local Polynomial and Global Polynomial interpolators.

Next, look at the spatial scope of your interpolation: should the interpolation take into consideration only existing values in a specific neighbourhood of the interpolated value?

  • If you are dealing with something like CO2 emissions you could argue that every emission source affects the values all over the study area, so a global technique is adequate. This leaves you with the Global Polynomial interpolation as the technique of choice.
  • If your data has only spatially limited impact, e.g. household spending on council tax, which do not affect anything beyond the council area, then you would use one of the Local deterministic techniques.

…and so on. This is not a comprehensive decision tree, but you get the idea how to decide which interpolation to use.

In general, the decision for a specific method depends not only on the characteristics of your data, but even more on your research design.

A good starting point to learn more about interpolation techniques in ArcGIS 9.2 is the ArcGIS documentation at:
http://webhelp.esri.com/arcgisdesktop/9.2/index.cfm?TopicName=Overview_of_the_interpolation_techniques_implemented_in_Geostatistical_Analyst

More documentation about the Geostatistical Analyst tools:
http://webhelp.esri.com/arcgisdesktop/9.2/index.cfm?TopicName=welcome, at the left go to Extensions > Geostatistical Analyst

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One thought on “Geostatistics: which interpolation method should you use?

  1. Test for spatial dependence between measured values in the ordered set. Do not interpolate if the set does not display a significant degree of spatial dependence in the sampling unit or in the sample space. Adding functionally dependent (calculated!) values to a set of measured values creates spatial dependence where it doesn’t exist. Interpolation does not add a single degree of freedom to the original set of measured values.

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