When performing kriging with anisotropy it can be the case that a very high length-to-width-ratio of my sampling points can pretend an anisotropy which is in reality not existent. So my question is if there is a recommended ratio of the longest and shortest sampling axis for kriging to avoid this effect? Or how can I deal with this situation?
There is the golden ratio:
https://en.wikipedia.org/wiki/Golden_ratio
according to California EPA document ("information advisory clean imported fill material" by DTSC), an area of 2 acres or less needs minimum of 4 samples. 2-4 acres need 1 sample for every 1/2 acre. 4-10 acres need minimum of 8 samples. And more than 10 acres need 8 locations with 4 samples in each location.
There is no way of determining that absent some knowledge of the phenomena that generates the data and at least some information on the spatial correlation for the variable of interest.
This is a little like asking what the minimum number of data locations is necessary to apply kriging and again without some preliminary information you can't say. Moreover the problem is different for the variogram estimation/modeling step vs using the variogram for kriging
Note that for a given data set, the total number of data location pairs (used in the sample variogram(s) is fixed, all of which might be used in an omni-directional sample variogram but fewer in each of the directional sample variograms (but not necessarily the same number for different directions).
One of the consequences is that the directional sample variograms may be difficult to interpret (too few pairs) and/or for one direction the sample variogram is moderately good but for one or more other directions it is not good. The spatial pattern of the data locations can also cause effects in the sample variograms as you have noted.
You might find the following interesting
1987, A. Warrick and D.E. Myers, Optimization of Sampling Locations for Variogram Calculations Water Resources Research 23, 496-500
Thank you for your answers. What I forgot to mention was that I assume a regular sampling grid. For instance I take all 10 m one sample in north-south direction and east-west direction that I get a regular sampling pattern.
The described problem in my question arises in line construction works or buildings with a high length to width ratio. There I have these biases in my experimental directional variogram.
How much I have to extend my sampling pattern in width that this distortions get minimal assuming no trend in the data and other factors which can influence the variogram estimation?
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