[18643] in s-news-athena
[S] Zonal anisotropy
daemon@ATHENA.MIT.EDU (Caroline Dilks (in5))
Fri Jul 16 09:08:02 1999
Message-Id: <199907161302.IAA05328@wubios.wustl.edu>
From: "Caroline Dilks (in5)" <caroline.dilks@unn.ac.uk>
To: "'GEOSTATS DISCUSION GROUP'" <s-news@wubios.wustl.edu>
Date: Fri, 16 Jul 1999 14:00:36 +0100
Mime-Version: 1.0
Content-Type: text/plain
Following our purchase of S-plus with the spatial statistics module, I would
appreciate some advise on a 'problem' I that have encountered with my data.
I am looking at variation of heavy metals within a small soil plot, for
which I have 121 sample points set out in a regular grid pattern. I have
managed to determine by directional variogram (0,45,90,135 degrees)
analysis, following the optimisation of all parameters (lag, nlag,tol.lag
tol.azimuth etc) that I have both geometric and zonal anisotropy within my
plot.
For example
0 degree directional variogram - range ~ 1.0m, sill ~ 0.15 gamma
45 degree directional variogram - range ~ 2.0m, sill ~ 0.15 gamma
90 degree directional variogram - range ~ 2.0m, sill ~ 0.10 gamma
135 degree directional variogram - range ~ 2.0m, sill ~ 0.15 gamma
3 of the directional variograms (0,45,135) therefore exhibit similar sills
although one of these has a different range (i.e. GEOMETRIC ANISOTROPY). I
am able to correct or this anisotropy with a linear transformation, hence
producing an 'average' variogram for these three directions.
The 90 degree direction (EW) has on the other hand proved to be more
problematic, displaying a markedly different sill (approximately 2/3 of the
other directions), although the 90 degree variogram does display the same
range as the 45 and 135 degree directional variograms. The 90 degree
variogram is therefore exhibiting ZONAL ANISOTROPY.
The zonal anisotropy does not appear to be the result of a trend within my
data (shown by analysis of row and column means / medians etc). As I
understand it, the way your S+spatial Statistics manual suggests that you
cope with zonal anisotropy is by de-trending your data by producing
variograms from loess residuals, and therefore producing variograms with the
same height of sill. Although for my data this method produces directional
variograms of the same sill, they all appear to be nugget and hence not
really modellable. My original variograms were well-behaved, displaying
good structure. I take this to further suggest that I have no trends within
my data.
Would it therefore be possible to produce a nested variogram model for my
data using the following two variograms ?
1) An 'average' variogram for the 3 directions (0,90,135degrees) adjusted
for geometric anisotropy.
2) The original variogram for 90degree direction which exhibits the zonal
anisotropy.
Firstly, am I allowed to do this as I am aware that a nested model is very
flexible but at the same time must not be misused. I am unsure whether my
anisotropy is well enough defined ( there appears to be no underlying reason
for the zonal anisotropy in the 90degree (EW) direction). Secondly, if this
model is appropriate how would I conduct such an analysis using S-Plus.
Finally, if a nested model is inappropriate for the solving of this problem,
how would I incorporate the structure of the 90degree direction into my
final variogram model for kriging. If I cannot incorporate this structure
could I justify not including this direction.
I would very much appreciate anyones the help on this matter. Thank you
very much for your time.
Caroline Dilks
(Research Assistant
University of Northumbria)
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