Kriging with variable spatial precision?

Question

I have a data-set comprised of hydraulic conductivity estimates measured at groundwater monitoring wells, as seen here:

Exact GPS coordinates are available for some wells, while for others I only have the legal land description (LSD), which corresponds to a 0.25 mile square. In the latter case I have derived the center coordinate of this square, which varies from the actual well location by .1 miles on average.

What kriging methods exist that can account for the differing positional errors within my data?

Answer 1

The simplest thing to do to take into account the positional uncertainty would be to simulate from it, and see how that affects your measurements.

So do a thousand (or maybe fewer or more...) iterations of:

• for each well with an imprecise location:
  • position it uniformly at random within the grid cell
• compute the variogram
• do kriging and save the estimates and standard errors

Now the variance of the 1000 estimates gives you an idea of the variability due to the positional uncertainty. With any luck it will be small enough to be ignored - this will depend on how large those cells are compared to the whole space.