Whether NUMERICAL MODELS have really become
the ARTIFACTs of inversion of field data
to estimate hydraulic parameters
in the context of
modeling fluid flow through porous media?
[First, it is very good topic!]
The detail of how to re-build a space from a set of limited known points can become very tricky (inverse problem solving) and the answer is not unique, so your method and even the details of you numerical implementation would make (sometime big) difference.
However, in groundwater modeling, the field of hydraulic conductivity will be used in a model, and outcome of the model cannot be improved much with changing the method of solving your inverse problem. In simple words with 10 known points there is no magic! your resolution of hydraulic conductivity and the uncertainty which leak into your results would be a certain amount. To reduce that your best bet it either distribute the points in space in a more informative setting or increase number of points. Your inverse problem solution scheme cannot perform a magical spell!
Please read my articles on this, especially one I uploaded today entitled, "The Usefulness of Multi-Well Aquifer Tests in Heterogeneous Aquifers.pdf" There are several examples, graphics, and software on my web page http://dudleybenton.altervista.org/ Follow the Project Descriptions link and then the Welltest. The principles apply to parameters besides transmissivity and storativity. I've used these same concepts in fields having nothing to do with hydraulics. It's important to design the test and apply the right analysis to avoid unwanted numerical artifacts, which are all too common in the open literature.
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