K. Ramanitharan asked,
My research is on heavy metal pollution in water bodies.
As a part of the analysis, I am doing kriging with the pollutant data.
I have couple of problems in doing this task.
1. Though I have the data sets for 90 water bodies, most of them (85) have
less than 10. As one can expect, this 'environment' gives trouble in
Two papers, I came across on similar issue haven't help me much in solving
Is there any consistent tested way to approach such 'not-enough-data'
2. Some data are with 'Hot Spots'. However, when I work with the data sets,
I have the trouble in fitting the variogram. My questions may be trivial ones.
How to distinguish Outliers from Hotspots, if there is a lack of
site-information beyond the data set?
Could it be possible to effectively fit variograms, when the hot spots are
Could a variogram capture the hot spot presence for kriging?
[ For most of the cases I tried with such suspected hotspot data, my
results show that
the linear interpolation works better than the krigged distribution based
on the 'fitted' variograms]
I would appreciate if anyone could provide me some suggestions on the above
difficulties, and relevant
references for my reading
Till now, I have received three responses. I have given them below.
['Till now' means, Other 'yet-to-come' replies to be helpful and welcome;-)]
Rajah Augustinraj wrote,
I am working on lead in groundwater. I had similar problems with "hot
low ranges and clustered data. I don't know if this is the same problem
face, but I found that the data was more willing and amenable to work with
log transform. It was practically impossible to get a covariance before
that. I don't
know if this helps, but looks like we are working on similar problems.
Paulo Justiniano Ribeiro Jr replied,
You problem seems to be a typical example where a non-Gaussian model should
I would check for some transformations first and/or explicitly non-Gaussian
Victor de Oliveira has been done some work on hot-spots detection.
I believe you can download the relevant paper from:
Dr. Isobel Clark responsed,
> My research is on heavy metal pollution in water
Hi, some thoughts (your numbering):
(1) One of the things I have found successful is the
construct your semi-variogram using ALL of your
data but not allowing pairs between samples in
different water bodies;
use cross validation on each water body separately
to see if the 'generic' model works for all of them or
whether some are more variable or harder to predict
use the generic model for kriging with a
variance/sill scaled for each water body.
> Is there any consistent tested way to approach such
> 'not-enough-data' situations?
Not really, but I have found this works if the
'deposition' is similar in the various bodies.
(2) 'Hot spots' are (a) erratic highs due to
distribution being skewed or (b) true outliers
(inhomogeneities). Which? Tackle accordingly. Cross
validation will pick up outliers but not work properly
if data is severely skewed.
> Could it be possible to effectively fit variograms,
> when the hot spots are present?
Try calculating semi-variograms with and without 'hot
spots' and see what happens.
Kriging is based on an assumption of homogeneity and
it is a little unfair to expect it to come back and
say "that's a daft thing to do" ;-)
> [ For most of the cases I tried with such suspected
> hotspot data, my results show that
> the linear interpolation works better than the
> krigged distribution based on the 'fitted'
I find this statement interesting. How do you define
"better" -- prettier? nicer? easier to interpret? less
All of you thank you very much for your responses.
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