With some Gaussian Process Regression/Kriging models, it's possible to specify both a non-zero nugget, and a noise term. For example, in Scikit-learn's GPR model, there is an
alpha parameter, which I think represents the nugget, and a
WhiteKernel that represents noise and can be added to any other kernel.
These two components have very similar effects on the results, as far as I can see (although counter-examples could be very instructive here).
I'm wondering what the two represent. I think (after some discussion on chat) that the nugget basically represents low-distance spatial variability (e.g. variability on scales greater than zero, but smaller than the smallest distance in the dataset), where a noise term would represent uncertainty in the sampled values of each data point (so basically measurement error). Is this a correct interpretation? Can the noise term also represent other things?