Does IDW interpolation in ArcGIS Geostatistical analyst work as exact interpolation method?

Question

As we know, Inverse distance weighted (IDW) is an exact interpolation method, which means the interpolated values of the known samples should be the same with its original observed values. But when I used the IDW in Geostatistical analyst (ArcGIS 10) to interpolate, I found that the interpolated minimum value and maximum value are not the same with the observed minimum value and maximum value. Actually I did get a Predication Map using the interpolation method of Geostatistical analyst, its values seemed to be the same with the observed ones, but when I changed it into a raster layer, the values all changed, why? In ArcGIS software, is the IDW interpolation in Geostatistical analyst the same as that in Spatial analyst? Are their equations the same with each other？

Forgive my poor English.

Answer 1

As far as I know, IDW is implemented as an exact interpolator in ArcGIS Geostatistical Analyst, as reflected in the Prediction Map results. This issue occurs only when you convert to raster, as you point out, and is intended.

The raster resolution is finite, and the values of the cells are either taken as a value in their center or as a mean over their area (I don't know the implementation details).

In the first case, to obtain the exact minimum and maximum, one of the raster cells' centers would have to exactly coincide with the min/max point, which generally does not happen.

In the second case, as IDW does not produce values outside the min/max range of the input (unlike, for example, spline interpolation), the average over any cell must be closer to the surface average value than the min/max.