[R-sig-Geo] Spatial interpolation of river network observations

[dan]

Hi there.  I have a similar objective and request as Ulrich but am dealing
with hundreds of observations in groundwater.  

I've been using the EarthVisions software by Dynamic Graphics to generate 3D
conceptual models of contaminant plumes in groundwater for several years
now.  The software provides both a minimum tension algorithm (similar to a
thin-plate spline as far as I can tell) and an implementation of GSLIB's
KT3D.  Both can be used to generate crude estimates of contaminant
distribution that are acceptable for general remedial design considerations
but neither approach has ever generated what I would consider a truly
realistic looking plume.  This is not a slight on the software but instead
due to the fact that every site I've ever worked on involves a heterogeneous
aquifer that results in groundwater plumes that violate the assumption of
stationarity.  

I also perform groundwater modeling for some of the more complex sites and
have attempted to condition universal kriging implementations to the results
of groundwater simulations.  While these results have been slightly more
realistic looking, there is still a large amount of uncertainty associated
with them and most projects cannot afford the added expense of groundwater
flow and contaminant transport modeling.  I am hoping to simultaneously
improve the realism of my conceptual models, the geostatistical rigor of my
analysis, and to alleviate the need for transport modeling.

The tandem approach posed by Rivest and Marcotte, 2012 seems to me a very
reasonable one.  It entails 1) a coordinate transformation to warp the 3D
cartesian grid into a 3D space that describes the location of each grid cell
relative to one or more 3D flow lines (presumably derived through particle
tracking on a calibrated flow model), and 2) covariance functions that
relate observed groundwater concentrations to observations of groundwater
head.  In my case, the 3D head distribution would likely just be a 3D grid
interpolated from numerous water levels in wells completed at a variety of
depths and the flow lines would likely be coarsely digitized from the head
field and adjusted to account for places where the underlying geologic
framework model did not seem to be honored by the head distribution.

The problem is that I'm new to R and only have a couple graduate level
courses in geostatistics under my belt.  I've spent the entire day searching
this forum as well as crantastic for leads on how to accomplish either of
the two improvements to my workflow and haven't come up with much.  I've
bookmarked a couple links to R packages (eg. regress) that I believe will
help me develop the covariance functions but am not seeing anything
regarding tools that will allow me to perform complex 3D coordinate
transformations based on one or more 3D linestrings represents idealized
conceptual groundwater flowpaths.    

My primary question is whether any R packages exist that would enable me to
derive a 3D grid of "flow coordinates" based on multiple 3D line entities. 
I would certainly welcome any input as to packages for deriving the
covariance between concentration and head as well.

Thanks much,
Dan

Rivest, M. and D. Marcotte.  2012.  Kriging groundwater solute
concentrations using flow coordinates and nonstationary covariance
functions.  Journal of Hydrology.  Volumes 472-473. Pg. 238-253.



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