Kriging

Overview

Kriging is advanced geostatistical procedure that generates surface from a scattered set of points with z-values

• to use Kriging effectively involves an interactive investigation of the spatial behavior of the phenomenom
  • represented by the z-values before you select the best estimation method for generating the output surface
• IDW and Spline interpolation are deterministic interpolation methods
  • because they are directly based on the surrounding measured values
  • or on specified mathematical formulas that determine the smoothness of the resulting surface
• Kriging is in another family of interpolation methods
  • based on statistical models that include autocorrelation
  • provides some measure of the certainty or accuracy of the predictions
• Kriging assumes the distance or direction between sample points reflects a spatial correlation that can be used to explain variation in the surface

Kriging is a mult-step process; including exploratory data analysis, variogram modeling, creating the surface, and optionally exploring a variance surface

Kriging is most appropriate when you know there is a spatially correlated distance or directional bias in the data

Definition

\(\hat{Z}(s_0) = \sum_{i=1}^N \lambda_i Z(s_i)\)

• where \(Z(s_i)\) = the measured value at the i-th location
  • \(\lambda_i\) = an unknown weight for the measured value at the i-th location
    • \(s_0\) = the predicted location
      • \(N\) = the number of measured values