Thanks for the informative answers. This is really a
great forum!!
I feel that I am bit further down the road to
understanding the issue. I will consult the textbooks and return with some
follow up questions.
One issue is (I think) that it is quite difficult to
obtain information as to whether these all purpose software packagesdoes
the filtering or not when I choose a kriging without a nugget. I guess the best
way of obtaining this information is to perform a cross validation. If its not
perfect, then the software uses filtering (is this
correct?).
Another question that comes to mind is the effect of
removing the nugget on interpolated points that do not coincide with the
measured point. Can someone comment on this? Maybe I am just a bit lazy and
should read the the textbooks instead. However, I fell that it is easier to dive
in to the litterature after having had some directions from the
experts.
cheers
Niklas
Från: Isobel Clark
[mailto:[EMAIL PROTECTED] Skickat: den 7 mars 2006
11:28Till: AI Geostats mailing listÄmne: [ai-geostats] RE:
kriging without a nugget
Hello all
The real issue here is not what your philosophy is but what your software
does with the semi-variogram model at zero distance.
There are (to my knowledge) two possibilities in current software packages:
(a) force the model to go through zero at zero distance, that is
gamma(0)=0
(b) allow the model to hit the vertical axis, that is gamma(0)=nugget
effect
Option (a) makes kriging an exact interpolator. If you krige exactly at a
sample location, you will get the sample value and a kriging variance of zero.
This is what Matheron orignally specified and will be found in all of the early
geostatistics text books.
Option (b) means that kriging will not exactly 'honour' your data, but will
put the most weight on the sample and some weights on the other samples.
If you have software that runs on option (b) the only way to honour your
sample values is to have a zero nugget effect.You do not have to remove
the nugget effect from your model, just add another (say spherical) component to
your model whose sill equals the real nugget effect and whose range of influence
is below your closest sample spacing. If you do not know which option is
implemented in your software, run a kriging with nugget effect is and with this
alternative. If there is no difference in the results, your software does option
(a) gamma(0)=0.
As discussed in the other emails, nugget effect includes all 'random'
variation at scales shorter than your inter-sample distances -- measurement
errors, reproducibility issues and short scale variations. Measurement and
reproducibility/replication errors can be quantified by standard statistical
analysis of variance methods such as described in any experimental design
textbooks. Remember, in this case, that it is the 'errors' that need to be
independent of one another -- not the actual sampled values. Small scale
variation can only be addressed by closer sampling, for example the famous
geostatistical crosses.
If you can quantify "sampling errors" and have (b)-type software, you can
use a combination where a short-range spherical (say) replaces the smaller scale
variability and the nugget effect reflects the 'true' replication error. It is
then your choice as to whether you filter out the replication error by removing
that nugget effect from your model.
An important point to bear in mind is that if you use (b)-type software
and/or remove the nugget effect when kriging, your calculated kriging variances
will be too low by a factor of 2*nugget effect. If you divide the nugget effect
as suggested, your kriging variance will be too low by a factor of 2*replication
error.
One more comment: some packages analyse and model the semi-variogram but
use a covariance (sill minus semi-variogram) when kriging. It is odds-on that
these packages will be type (b).
Isobel
http://www.kriging.com/courses
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