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[Helena Mitasova]

I hope that this is not getting too boring, but here are some
of my comments:

>To the spline software 
>developed by Mike Hutchinson which allows the use of independent variables 
>.and/or covariates to "improve" the quality of a surface where something is 
>known about the relationship between your target data, and another 
>variable for which you have more data points, or even a grid.

After talking to Mike Hutchinson, I have tried to do the similar thing 
with our version of splines - we have presented interpolation of
precipitation with the influence of terrain at Grass users conference
at Denver, back in 1992 but the computation was done outside GRASS.
As a part of developments for volume modeling we have now a prototype 
of s.surf.3d program linked to grass which has this type of interpolation
(you input the site data and the third variable given by grid)
as an option.
Mike Hutchinson has some other things in his software, which we haven't
tried to work out yet, like the general crossvalidation for finding
the optimal smoothing parameter and drainage enforcement for interpolation
of DEM.


and one comment to Simon's very well written tutorial:

>Splines are one of a class of interpolators base on physical principles which
>include the "minimum curvature" interpolators.  They are expected to give
>.....
>Kriging, on the other hand, is a purely statistical method, based on
>reducing an objective function allowing for the consideration of local
>correlation lengths.  On its own terms, I think that Kriging, particularly

As probably some of you know, the relationship between splines
and kriging has been proved both by Wahba  and by Matheron about
ten years ago. In fact, besides physical and geometrical interpretation,
 splines have also statistical interpretation (and yes Chris, the general
 form of the equation in kriging and splines is the same). Well written
and not too difficult to understand is a paper:
Hutchinson and Gessler, 1992: Splines - more than just a smooth interpolator
which was supposed to appear in Geoderma, which compares splines and
kriging and explaines the statistics of splines.

Helena