# Is kriging an exact interpolation method?

Can kriging be an exact* method? For example, when optimized with the Geostatistical Wizard? Or in any other way? (as far as I know, "normal" kriging isn't an exact method).

*exact: predictions at known observed values yield exactly the same values again.

• Yes, until you add a nugget (error term). Whereas Kriging is technically an exact interpolator, practically it is not because you never want to specify a Kriging model without the error term. – Jeffrey Evans Apr 3 '15 at 17:38

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.

See this answer from ESRI stating kriging considered exact and this nice description from expert course material that also goes the same route.

Generally, kriging is associated with exactness but according to ESRI:

When semivariogram and covariance models have a nugget effect there is potential for a discontinuity in the predicted surface at the sample data locations.

Although you will see the nugget effect causing inexactness again in actual usage in this hydrology example.

Some authors say it is both! a sound textbook

So pick your answer really. My answer would be that exactness is a vague term (in GIS anyway) that likely should not be used in terms of geostatistical properties. Another question you may want to ask: Is Kriging even an interpolator?

• Thank you. I will review these links in depth and surely say something. – Charly Sep 22 '14 at 18:57

Yes, Ordinary & Simple & Universal kriging are all "exact " interpolators. You simply have to look at the kriging equations for each of those and note that the system of equations has a unique solution,

The comment above about pixels is mis-leading, you have to pay attention to the support of the data and also the support of the interpolated values

• Having a "unique solution" does not appear to be equivalent to the definition of "exact" given in the question. – whuber Dec 26 '15 at 14:55
• I think you are confusing having a unique solution and what exactness is accepted to mean in GIS. – If you do not know- just GIS Jan 20 '16 at 0:15