As a nice anecdote about how things can go wrong if you forget that some data sets are unsuitable for interpolation:
About 15 years ago, due to my Kriging Interpolator extension being available on ArcScripts, I was contacted by a fellow working for an environmental agency in one of the Nordic countries here in Europe. They had this fantastic data set with more than 25000 measurements of Radon gas in basements of houses across the country, including detailed data about the age, construction and condition of the house, and on what soils it was located if I remember it all well. All-in-all a treasure trove for a statistician.
Radioactive Radon gas is a health thread, and they wanted to have a country wide map showing the regions with high and low radon in houses. Ergo, they wanted to interpolate the data, at least, that was their first idea of solving this issue.
So why did he contact me then?... Turned out the data showed almost 90-100% nugget variance, and hence virtually no spatial auto-correlation, which they didn't understand.
They had this fantastically detailed data set, and now they couldn't interpolate it?!
After receiving the data, I could confirm their observation, virtually no spatial autocorrelation between Radon measurements. Even measurements in houses separated by only a small distance, could vary wildly in Radon.
So, this set me thinking, why is this? The problem is, Radon is highly correlated with the specific condition of the house: on what soil type is it located, what building materials have been use, how is the ventilation status of the basement? None of these factors are ones that necessarily have high spatial autocorrelation, with smoothly varying changes.
In fact, things like soil type and construction often vary abruptly: a soil or rock type is often abruptly changing from one spot to another, when geological processes like sedimentation, uplifting, volcanic activity etc. have changed the origin of the underground layers.
The same holds true for human influenced factors like building construction.
As a consequence, Radon in houses can vary abruptly and wildly as well in any random selection of buildings, even in the same town or even the same street.
All of this precluded interpolation as the scientific and statistical method to analyze the Radon data! And the 90-100% nugget variance showed it. Yet the fellow that contacted me, had a hard time digesting this: a fantastic data set of Radon measurements across the country, and now they couldn't interpolate it to a country wide map?
I ultimately suggested to him, to use traditional statistical methods with software like R and SPSS, to establish correlations between all the factors and conditions they had so zealously collected, and the corresponding Radon measurements in each house.
After all, this huge data set with all its measurements and ancillary data, still was a treasure trove for a statistician!
After establishing correlations, they could then use this knowledge to assess risk factors and regions at risk based on things like a geological soil map. If one or more soil types showed to be highly correlated with high Radon levels, simply classifying a geological soil map based on the statistically determined relations, might give a coarse, but statistically sound, indication of regions "at risk".
The same could be done for building construction: if some types of buildings were shown to be at risk, classifying the countries buildings based on the statistically determined risk factors, could give them an indication of the status of all buildings in the country.