Dear Kerry and Gustavo,
The kriging variance is a perfect measure for estimation uncertainty as
long as a second order stationary model is a good representation of the
data under study. Obviously, if variability and/or spatial correlation
varies over the field of interest and you have sufficient data to
characterize this, or e.g. do a non-linear transform such as a
log-transform to correct for a proportional effect, than you can and
will do better when taking this into account.
In my opinion papers such as those by Journel and Rossi have
over-shouted their point, and have ignored that for many cases a second
order stationary random field is a suitable model, if not the only possible.
The argument that after rejecting the kriging variance, conditional
simulation is suddenly needed as the solution get some measure of
uncertainty is invalid: if you create a large enough set of conditional
Gaussian simulations, their mean value equals the kriging mean and their
variance equals the kriging variance. Nothing is gained, only an
expensive approximation of something rather cheap is obtained.
You will not find many papers that make this point, as the only point is
that someone else is wrong. Not many people like to write such stuff.
Below is a reference that may be hard to get (but you can google for the
first author). I for instance didn't enjoy writing this email.
Best regards,
--
Edzer
Heuvelink, G.B.M. and E.J. Pebesma, 2002, Is the ordinary kriging
variance a proper measure of interpolation error? In: Proceedings of the
fifth International Symposium on Spatial Accuracy Assessment in Natural
Resources and Environmental Sciences (eds. G. Hunter and K. Lowell).
Melbourne: RMIT University, 179-186.
Gustavo G. Pilger wrote:
Hi,
Indeed the kriging variance is only semi-variogram and spatial data
configuration dependent. The kriging variance is calculated taking
into account only the geometry of the samples, i.e. their spatial
arrangement and the semi-variogram. Basically, kriging variance do not
take into account the value of the samples, but only their location
(and the semi-variogram), consequently ignoring the local variability.
Therefore this parameter is not appropriate to measure uncertainty.
For this purpose you should consider the use of conditional simulation
methods.
I wrote some papers about this subject some years ago. For exemple:
PILGER, Gustavo G.; COSTA, Joao Felipe Coimbra Leite; KOPPE, Jair
Carlos, 2001. Additional Samples: Where they Should be Located?.
Natural Resources Research, New York, v. 10, n. 3, p. 197-207.
I can send you a copy if you wish.
I hope this helps you.
Cheers.
<><><><><><><><><><><><><><><><><><><><><><><>
Gustavo G. Pilger, Mining Engineer, MSc, PhD
Senior Geostatistician
MBR - Brazil
<><><><><><><><><><><><><><><><><><><><><><><>
Hi. I just read through Journel and Rossi's 1999 paper, "When do we
need a trend model in Kriging". In the appendix they say "A kriging
variance is but a variogram-model dependent ranking of data
configurations; being data-value independent, it is generally not a
measure of local accuracy...This fact is unfortunately not yet fully
appreciated by some practitioners". Can someone explain the
implications of this in terms of determining cost-efficiency analysis
for sample designs? Specifically, can we use kriging variance
estimates across potential sampling grids, (from modeled variograms
estimated from say a pilot study) to estimate the variability
associated with different sampling densities/configurations. In
addition, can someone provide some references that address this topic.
Thanks,
Kerry
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