i carried out an field soil sampling campaign recent years in a certain region, and measured the soil organic carbon (soc) content. when i was to calculate the soc stock of this region, i used kriging interpolation method make this come true.
here is my question, i want use Monte Carlo method to analysis the uncertainty of the kriging interpolation process and the uncertainty of my field survey, here is an article that i want to follow, but i didn't know how to make it out specifically, does anyone help? thanks very much.
p.s. the article was attached.
http://onlinelibrary.wiley.com/doi/10.1111/gcb.12025/abstract
[attached PDF removed due to copyright]
If you have been using a kriging interpolation then you should have access to the semi variogram analysis. The variographic analysis give you all information to qualify your uncertainty
thanks for your answer, i know i should conduct a semivariogram analysis, while the viewer of my manuscript ask me to add the uncertainty analysis by using Monte Carlo Method, like the articles that i attached.
Kriging gives you a measure of uncertinaty: the kriging variance. If the focus is a complete picture of uncertainty, geostatistical simulation sould be used instead kriging.
Hi
I advice you to see these documents. You will find what you need.
Best regards
ftp://131.252.97.79/Transfer/Treg/WFRE_Articles/phillips_96_EvalSpaceUncertainty_InterpolatedMeasures.pdf
https://www.google.fr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0CDcQFjACahUKEwjfnofozfnIAhVMWhoKHYqlAzY&url=http%3A%2F%2Flup.lub.lu.se%2Fstudent-papers%2Frecord%2F3411964%2Ffile%2F3411965.pdf&usg=AFQjCNG-Ckk02M6Uy7tySvRCFvplgklMaQ&sig2=Z8cGokqFsmCMp_4_QLF7OQ
There are several sources of uncertainty and you need to recognize that these affect the results in different ways. there is also the question of exactly what you mean by "uncertainty"
1. Even with a very large data set, there is always some uncertainty with respect to fitting the variogram ("semivariogram" is older terminology and not used by most authors, there is also the risk of using the terms interchangeably if you use the older terminology) See for example "Geostatistics" by Chiles and Delfiner, the older terminology only appears once and that is in the index where the reader is referred to "variogram". The kriging variance does not incorporate any uncertainty pertaining to the fitting of the variogram.
2. The kriging variance is not a true "variance", i.e. except to the extent that the data is used to estimate/fit the variogram the data does not affect the kriging variiance. It is determined by the variogram model and its parameters, user decisions such as the search neighborhood and its parameters as well as the spatial pattern of the data locations. That is not to say that the kriging variance is not a useful quantity.
3. Cross validation and various statistics that you can obtain from cross validation will give you useful information about uncertainties
4. Geostatistics, in particular kriging is based on certain statistical assumptions and these are not fully statistically testable (because the data is only a non-random sample from one partial realization of the random function. If by chance you are transforming the data, e.g. a log transform, that affects the uncertainty since it is only a univariate transform and you really need information about the multivariate distribution.
A key question at the end is whether the results are useful to you in the context of the particular application based on your understanding of the phenomenon that generated the data. The suggestion to consider conditional simulation is a good one but note that to use that algorithm you need to estimate/model the variogram or covariance function and there is unspecified uncertainty associated with that, moreover there are several different possible algorithms for conditional simulation and they don't produce the same results (even when the variogram/covariance function is the same and with the same data). Don't confuse random sampling of data locations with random sampling of the probability distribution of the data values.
THANK YOU VERY MUCH FOR YOUR HELPFUL SUGGESTIONS, I HAVE SOLVED THE PROBLEM. THANKS AGAIN.
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