Ole,

Please note this was several years ago, but:

That was exactly what I told him! Actually, my tool (a kriging spatial interpolator) showed that there was NO spatial relationship BETWEEN points with a 100% random nugget variance. This essentially means that the dataset (a very good one with over 10.000 measurements) may NOT be interpolated.

However, that doesn't mean there isn't a spatial or better said statistical relationship between soil/rock types and Radon measurements. It just means that any two points close together have no spatial relationship. Realizing this, I figured this is simply caused by the fact that soil / bedrock types tend to vary over relatively short distances with one bedrock type being replaced completely by another, meaning that two houses separated by just 100 meter, might have totally different, and spatially unrelated, Radon levels.

Such data may never be interpolated...

I finally advised the guy to forget about a spatial interpolation, which simply is not allowed with such a dataset and 100% nugget variance (this was difficult for him to accept, like many other people, spatial interpolation of point measurements is often considered as the "holy grail" in GIS. "If I can interpolate it, it will be good...")

I than advised him to try and statistically correlate soil / bedrock type with Radon levels in a normal statistical package, like SPSS. Simply by determining at what bedrock type, based on a geological map of Norway, the measurements were made, and to input that data in the statistical package together with the Radon levels. And maybe even include possible other variables as well, like building material of the houses or possible information about ventilation etc.

If that would show a statistical relationship between soil / bedrock type and Radon levels, he could than reclassify his geological map of Norway based on low / high Radon risk or levels to get to a country wide map, which was what he was after...

I don't know if he finally did this, (he sounded actually a little bit desperate at the point I told him he wasn't allowed to interpolate the fantastic dataset collected over years), but I hope so because with such a huge dataset, you can do some very interesting statistical analysis, just not interpolate it.