Interpolation in GS⁺

Interpolation means estimating values for points not actually sampled, thereby producing a map or some other spatial model for an area that was not exhaustively sampled. There are many different interpolation techniques, ranging from simple linear techniques that average the values of nearby sampled points, to more complex techniques like kriging that use nearby points weighted by distance from the interpolate location plus  the degree of autocorrelation for those distances.

GS⁺ provides three broad types of interpolation. All are nearest-neighbor techniques in which values at locations close to the interpolation point are used to estimate the interpolation point value. They differ in the way that nearby locations are weighted. The techniques are:

• Kriging, in which interpolation estimates are made based on values at neighboring locations plus knowledge about the underlying spatial relationships in a data set. Variograms provide knowledge about the underlying relationships. Kriging is usually superior to other means of interpolation because it provides an optimal interpolation estimate for a given coordinate location, as well as a variance estimate for the interpolation value.
  
  
• Inverse Distance Weighting (IDW) and Normal Distance Weighting (NDW), in which interpolation estimates are made based on values at nearby locations weighted only by distance from the interpolation location. 

• Conditional Simulation,  in which interpolation estimates are based on a form of stochastic simulation for which measured data values are honored at their locations. This allows one to map sharp spatial discontinuities such as contamination hotspots or fault lines. Punctual and block kriging as well as IDW will smooth out local details of spatial variation, especially as interpolated locations become more distant from measured locations.

 GS⁺ allows you to define the interpolation grid (including any polygon or blanking areas) and other aspects of the analysis, and then GS⁺ runs a 32-bit interpolation engine that cuts hours off of former methods.  The ASCII output file can be written in GS⁺, ArcView^®, or Surfer^® formats.

A Cross Validation command performs a jackknife analysis in which every measured point in the data set is temporarily deleted from the data set then estimated to provide an indication of the appropriateness of a given variogram model.