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
Hi Simon,
There are probably multiple ways to do this, but if I were going to do it myself, I would do the following:
The workflow is a bit long, but it can be automated. It boils down to sequentially creating a new point at the location of the largest standard error within the study area, merging its predicted value into the original dataset, then recalculating the new average standard error, then repeating the process until the average standard error is smaller than some value you specify.
Please let me know if any of this is unclear or if you have any other questions.
-Eric
Also, if you want to experiment with the location of the new points rather than have them selected at the location of the largest standard error, just create the new point (or multiple new points) anywhere you want in place of running Densify Sampling Network. You should then use GA Layer To Points to predict the value of the new points. Merge these values into the original data before recalculating the new standard errors.
You alluded to wanting to do something like this in this post:
Optimising monitoring networks using Kriging
Similarly, if you want to add, say, 5 new points at a time between calculating the average standard error, just specify 5 new points in Densify Sampling Network, and follow the same workflow.
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
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.
Hi Eric,
That response was very useful - thanks for your explanation.