Adding or removing new sites to assess changes in the kriging standard error

Question

Hi,

Sorry, I was wondering whether somebody might be able to help provide a brief summary of how to calculate potential improvements in the kriging prediction error by adding or removing sample sites. I would like to use Geostatistical Analyst to optimize my monitoring network. The first step I would like to do is calculate the average standard kriging error for a range of different sized networks so I can create something called a Network Density Graph (attached). From this graph I plan on selecting the optimum number of wells and then using the Densify Sample Network tool to locate my site.

Kind regards,

Simon

Network density graph.JPG

SimonHarper · Answer

Hi Eric,

That response was very useful - thanks for your explanation.

EricKrause · Answer

If you employ any kind of transformation (Normal Score, logarithmic, etc), then the standard errors and the predictions will be dependent, and you will get different standard errors for different values you assign to the new point.  There is no perfect methodology for assigning a value to the new points, but interpolating the value from the original measured points is what is done in practice (this is what Densify Sampling Network does automatically).  Using GA Layer To Points just ensures that the value will be justifiable no matter the kriging model.

The issue about predictions and standard errors being independent can definitely be confusing, as you'll often see statements along the lines of "the predicted values of ordinary kriging are independent of the standard errors," with no qualifying statements or hints that there is more to the story.  While the statement is technically true, it is very easy to misunderstand due to terminology.  You might read that statement and assume that you can use Ordinary Kriging with a logarithmic transformation, and the standard errors will be independent of the predictions, but they won't be.  The problem is that the actual name for ordinary kriging with a log transformation is "Ordinary Lognormal Kriging", not just "Ordinary Kriging."  So the previous statement about predictions and standard errors being independent for ordinary kriging models was not meant to apply to ordinary lognormal kriging models.

SimonHarper · Answer

Hey Eric,

Thanks for the reply again.  One question - why do you need to have predicted values for the new points? Sorry, sounds like a silly question but I thought the kriging standard error is independent of the measured value.  I'm noticing that with some of these kriging methods the value makes a difference.

Thanks again,

Simon