I have recently been looking at the issue of dealing with a non-stationary
mean in kriging. Attendence at the recent Geostats-UK meeting indicated
that there was some disagreement concerning the use of terminology. In
particular, universal kriging (or kriging with a trend, KT) is outlined in
many major texts as a technique which may estimate the trend (or drift)
on a moving window basis and the variogram is not estimated as part of
this process (unlike IRF-k kriging where the generalised variogram is
estimated as a part of the whole process). I would be interested
to know if this definition of KT is actually disputed between researchers.
For KT, many researchers consider it unwise to use the variogram of
residuals from a global polynomial trend. This is presumably because of
(i) bias in the estimated variogram and (ii) the fact that the modelled
trend used for the variogram estimation is different to that used for KT.
However, I am under the impression that some researchers use the variogram
of residuals from a polynomial trend in this manner. I would be interested
to know what approaches list members are using to estimate variograms
where there is a marked trend effect for KT. A more specific issue
concerns the perceived problems with using median polishing (as outlined in
Cressie's 'Statistics for Spatial Data') to estimate the variogram in the
presense of a trend for use with KT (as opposed to median polish kriging).
This email is really a general attempt at creating a discussion about what
is clearly a major issue in geostatistics.
I look forward to comments from list members.
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