Question

Explain the Exactness of Kriging briefly.

Answer 1

in theory, ordinary kriging is exact. However, if you interpolate on a grid, the probability that the center of the pixel (where the interpolated value is computed) falls exactly on an observed point is very very small. Therefore, the interpolated pixel value will not likely be the same as the points that are under it. This difference will be more apparent if you have a large nugget effect and/or large pixels.The kriging interpolation method is usually associated with exact interpolation. When semivariogram and covariance models have a nugget effect there is potential for a discontinuity in the predicted surface at the sample data locations. Kriging predictions change gradually and relatively smoothly in space until they get to a location where data has been collected, at which point there is a "jump" in the prediction to the exact value that was initially measured.

Variations of kriging can produce noise-free predictions. For example, the filtered kriging interpolator produces a map that is smooth and free of "jumps" at the sample data locations. Consequently, the prediction standard errors are smaller because the nugget component of variance, which is probably due to measurement error, is not predicted. The algorithms incorporated in Geostatistical Analyst can provide exact filtered value predictions at sample data locations. This prevents discontinuities in predictions and the associated standard errors, yet retains standard errors that are comparable to those for exact kriging.