Hello everyone,
I am considering two sampling strategies, the first is locating samples on the three black lines as the first picture shows, the second is random sampling across the whole area as the second picture shows. Both ways will use the same number of samples, the difference is the pattern.
My questions are:
1. will they generate different variograms and produce different kriged maps??
2. which one is better?
3. can I use the two sampling strategies in ONE kriging? I mean if I have two areas, can I use random way in one area and 'line sampling' in another area, and use both data together to generate a variogram and mapping?
Thanks!
The pattern of sampling will affect your result for sure. But the size of the effect depends on the distribution of the variable of interest. I think, random sampling is a better way to avoid any sampling induced structure to your data.
No matter what sampling design you use, you can use kriging to map the variable if spatial structure is detected, but you need to consider if you are going to compare the result, it is better to have everything even in the data collection for all sites.
Hormoz Sohrabi Thanks for your answer. I think the sampling design should be consistent too. Just I was suggested to use both sampling designs in one data analysis...i.e. put the data from two designs and analyse together. I feel that it's not proper, but I don't have the 'evidence' to support me.
Hi, I agree with Dr. Hormoz. Also, I would advice to have more than at least 50-100 sampling points per area if you want to use "variogram" to produce "krigied maps". Generally, a random sampling design distributed all over your study site would produce more robust variograms (of course, if your variable have a dependent spatial structure). - And yes, you can combine the sampling points of both designs and see the variogram results. There is no any limitations. But, you must consider "the minimum number of of sampling points" and "spatial distribution of sampling poitns". Best, Omid,
Your question needs to be more specific. When you refer to variogram, are you asking about a sample variogram or a variogram model used in the kriging equations? The pattern of the data locations has no effect at all on the variogram model but it can effect a sample variogram (which is not unique for a given pattern). The real question is how many "pairs" do you have for each plotted point in the sample variogram, the TOTAL number of pairs is determined by the number of data locations (not by the pattern),. The pattern of the data locations has no effect on the variogram model. The pattern of the data locations does have an effect on the actual kriging results but that effect is also related to the parameters of the moving search neighborhood.
Before you use kriging you need to consider which form (Ordinary, Universal) and which form of stationarity is being assumed, e.g is the mean of the random function constant or is it a polynomial function of the position coordinates, The exploratory analysis you need to do is effected by both the pattern of the data locations and also the number of data locations as well as the geographical extent of the region of interest. There is no magical best choice for either the pattern or the number of data locations. You always need to consider what you know about the phenomenon that generated the data.
See 1987, A. Warrick and D.E. Myers, Optimization of Sampling Locations for Variogram Calculations Water Resources Research 23, 496-500
1991, Myers,D.E., On Variogram Estimation in Proceedings of the First Inter. Conf. Stat. Comp., Cesme, Turkey, 30 Mar.-2 April 1987, Vol II, American Sciences Press, 261-281
Omid's comments about random design are all wrong, there is no benefit from random selection of the data locations. This is not the same as "random sampling"
The sample variogram is a tool for estimating/modeling the variogram model used in the kriging equations, it is not directly used in the kriging equations.
Frequency distribution of data in terms of the impact on earth-projection estimates is significant.In order to conduct ground-based analysis, samples must follow the normal distribution.
.
Hossein
Both of your claims are wrong. The multivariate probability distribution is not a factor in the derivation of the kriging equations and certainly the distribution of the DATA is never used in the derivation. You should read the book "Geostatistics" by J.-P. Chiles and P. Delfiner, John Wiley and sons
Thanks to you all for your kind answers.
Alexandre Wadoux Yes you are correct that I want to collect samples to generate a variogram, and then use the variogram for ordinary kriging.
I finally used the method similar to what you recommended. Grid sampling first, and then relocated about 15% samples to close distance for the reason you mentioned.
Also thanks Donald Myers I like your paper 'Optimization of Sampling Locations for Variogram Calculations'
All of the comments/suggestions about using random sampling are wrong, clearly the responders do not understand geostatistics and in particular variograms and kriging
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