Dear Sven,
you didn't tell us what you meant by "best results", and how the
different results compared. It could for instance mean "the method with
the smallest MSE, but all methods performed quite similar in this
respect anyway". If this is the case, a possible cause might be that you
have a high signal-to-noise ratio, in which case all methods will tell
you the same: the signal (about which your data tell you a lot).
A plea in favour of ordinary kriging when there is a trend is given in
Journel, A.G. and /Rossi/, M.E., When /Do We Need a Trend/ Model in
Kriging. It's a while ago, but IIRC, their point is that trends are not
that much needed when the data say it all.
Best regards,
--
Edzer
Altfelder, Sven wrote:
Dear list,
I have point measurements of soil water tensions on an area of approx. 2m
(width) x 0.8 m (depth) measured on
a regular grid of 10 by 10 cm. In each of the 17 rows of this grid, 20 measurements were made. Every second row
is shifted by 5 cm with regard to the previous row giving a chequerboard type pattern.
My goal is to interpolate this data to a 5 cm grid, which pretty much means
that I try to fill in the gaps.
The data has strong trend which is limited to the depth direction (driving forces are water movement under
gravity and plant uptake of water).
I had to take logarithms of the data because the original data variance is
strongly dependent on the local mean.
After taking logs it looks fine (to me).
After doing this I calculated various variogramms which I fitted using gstat in the R environment. In log space
I interpolated data using Universal Kriging (using a variogramm calculated perpendicular to the trend)
with various polynomial trend functions in depth direction, Ordinary kriging, Ordinary kriging of residuals
after trend removal and an addition of the trend component after kriging, Inverse distance weighting
and finally Ordinary kriging using the variogramm calculated perpendicular to the trend and ignoring
spatial correlation in depth direction by assuming an appropriate anisotropy.
(basically a 1D Kriging in X-direction).
I cross validated the various procedures on data sets that were actually measured on a
5 x 5 cm grid and were simply reduced to a 10 x 10 cm grid by leaving out every second data point.
I achieved by the best results with last method mentioned (Ordinary kriging
using the variogramm calculated perpendicular to the trend and ignoring spatial dependence in depth direction).
>From a practitioners point of view I'm satisfied with the result.
However, after scanning the literature I've not found anybody who has done a 2-D interpolation this awkward way. This
gives me the uneasy feeling that in a subsequent publication my approach will not stand up against the critical
view of a real geostatistician. Is my approach suitable or should I further explore other methods?
Any advice on this issue would be appreciated.
Thanks,
Sven
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--
Edzer Pebesma
Institute for Geoinformatics (ifgi), University of Münster
Weseler Straße 253, 48151 Münster, Germany. Phone: +49 251
8333081, Fax: +49 251 8339763 http://ifgi.uni-muenster.de
http://www.52north.org/geostatistics e.pebe...@wwu.de
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