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Are the datapoints (34) for this Kriging operation sufficient?

Research Gate recommends > 30. [both -> here and here], while another source [-> here] mentions 30 to 50. All mention Webster and Oliver says at least 100. Another stack question agrees

The challenge is related to the spatial pattern of the dataset. The area is flat (~0-to-100-meters) at ~20*20-km [Cape Town. South Africa]

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I can execute a Generalized Least Squares-Regression Kriging (GLS + Ordinary Kriging) and Universal Kriging and the empirical and fitted variogram (with a Matern model. [Exponential fits a straight line.]) below.

empirical fit
First row

The result [-> here] looks more than okay but is it meaningful? Are these too few datapoints?

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It has "meaning" within the specification of the model, which doesn't depend on the number of points. You can krig with four points but your variogram estimate will be vague and your predictions will be vague. Still meaningful though. It might not be useful, though, since it wont tell you anything much about the value of Z outside the samples.

A model can be meaningful and useful, or neither, or either one of them. I would say "meaningful" means the model is correctly specified and applied, and "useful" means the fitted model provides sufficiently small uncertainties to help any conclusions you'd like to draw.

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  • You are very kind to respond so promptly @Spacedman. Thank you. Okay. I think I understand what you are saying. The 'Matern' is correctly applied and the fit is useful because sufficiently smaĺl uncertianties could create a pretty good trend surface. ---both could be better with more points.
    – arkriger
    Commented Aug 26, 2023 at 16:16
  • Yes, think of the kriged surface as a wobbly surface that's "pinned" at the known sample locations. Every sample pins the surface at that point to a known value, and so decreases the wobbliness in the vicinity of that point. The amount of wobbliness and how flexible the wobbly surface is is estimated by the variogram.
    – Spacedman
    Commented Aug 26, 2023 at 16:38

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