David,

I recommend that you first look up the difference between spatial statistics and geostatistics. Then you will know how to fit the models for the covariance function.

http://file.scirp.org/Html/7-2800907_52697.htm

Regards,

While the suggestion to consider the "difference" between spatial statistics and geostatistics is pertinent, you also need to be more specific about the question or problem you are wanting to solve.

Exponential, gaussian, spherical, etc all refer to specific mathematical expressions for a spatial covariance function or variogram and are not "models" for variables. They are models for spatial correlation. Covariance functions must be postive definite and variograms must be conditionally negative definite.For a given mathematical expression it is not easy to test whether the function satisfies one of these conditions hence the practical solution is to use a functional form that is known to satisfy the condition. See the book "Geostatistics" by J.-P. Chiles and P. Delfiner, John Wiley & sons (2nd ed). For the broader topic of spatial statistics see the book by N. Cressie with that title.

You also need to consider the underlying statistical assumptions, the paper cited by Faye uses statistical tests and methods that are not really applicable to spatial data, i.e. most assume random sampling and most likely a normal distribution.) There is also the question of the objective(s) for analyzing the data. In geostatistics, one of the principal objectives is generally to interpolate the data or to estimate spatial average values using point data. In the case of Faye's citation the data is multi-attribute in which case one may need to consider cokriging rather than univariate kriging, then you need to consider both covariance functions/variograms but also cross-covariance functions/cross variograms.

If you are looking at groundwater data, you need to look at the hydrology literature and also the environmental sciences literature

please have a look:

https://en.wikipedia.org/wiki/Geostatistics

http://maps.unomaha.edu/Peterson/gisII/ESRImanuals/Ch3_Principles.pdf

http://people.ku.edu/~gbohling/cpe940/Variograms.pdf

On a related question, I was never convinced that the names "spatial statistics" and "geostatistics" meant different things. Could you please elaborate on the rationale?

Thank you for your answers.

The following document recommended by Reza was particularly helpful.

http://people.ku.edu/~gbohling/cpe940/Variograms.pdf

To understand the distinction between "spatial statistics" and "geostatistics" you need to consider the underlying statistical assumptions and in particular the nature of the data as well as the objectives in analyzing the data. It is not really a theoretical distinction but rather a historical one.

If you look at Noel Cressie's book on "spatial statistics" you will see that he does discuss geostatisiics but he also discusses a wide variety of other topics, e.g. "random sets". If you look at the geographical sciences literature you get a rather different perspective although geostatistics is often considered as included.

In part the distinction depends on how the "field" originated, e.g. geostatistics pretty much tracks the work of Georges Matheron and his students (including A. Journel) with applications in geology, mining, hydrology, soil science, petroleum (but over time the list of applicable disciplines has widened considerablly). The interest in random sets was more closely associated with image analysis, at least originally.

It also depends on whether the ideas and developments came primarily from an applied area or more directly from statistics or even from mathematics.

I recommend Faye's answer

Best Regards