I'm trying to use Geostatistical Analyst to create a Network Density Graph. This involves evaluating changes in the standard deviation of the estimation error by looking at different sized networks.
From what I understand the standard deviation of the estimation error is independent of the actual measurements so that once the kriging model is determined it can be used to test the effect of new locations on the standard deviation of the estimation error without needing measurements of z.
My question is: How do I use Geostatistical Analyst to do this?
This are the steps I think I should follow:
1. Create a Geostatistical model for testing - In this step I optimize my kriging model
2. Create different sized networks for testing - Here use a range of hexagonal sample arrays to generate samples of increasing size.
3. Create new Geostatistical layers for the different sized networks using the model parameters derived in step one - In this step I create several new Geostatistical layers for each of the different sample configurations.
4. Evaluate the global performance (using the average standard deviation of the estimation error) from each new Geostastical layer created in step 3 by abstracting GA layer to points - here I have sample points across my study area that I use to extract the standard errors from each of the Geostatistical layers.
5. Plot the results on a line graph - this should show that as the network density increases so to will the standard deviation of the estimation error
I'm not sure where I'm going wrong but my prediction errors increase as my network becomes denser.
Any help is appreciated.
It is indeed strange that your standard errors are increasing as the network densifies. In general, this shouldn't happen, but I can think of at least one situation where it could happen.
Predictions and standard errors in kriging are only independent for a fixed mean function (either trend or a constant) and if no transformation is applied. The default kriging model in the Geostatistical Wizard is Simple Kriging with a normal score transformation, so there will generally be dependence between the predicted value and the standard error. Therefore, when you add a new fake point and assign it a value, the resulting standard errors will be depend on that value. I could imagine the standard errors growing larger and larger if the fake value was not given much thought (and especially if the normal score transformation tries to recalculate itself for the invented value).
Try performing your workflow again, but turn off the transformation on the second page of the Geostatistical Wizard (this will make the predictions and standard errors independent). I think you should then see the standard errors decrease for denser networks.
Thanks for the suggestions. I tried a default simple kriging method with a normal score transformation and the concept worked perfectly i.e. the average standard error reduced as my network increased in size. I also further tested my method by evaluating the kriging error on my original data set by: a) using measured values and b) using my location column as the measured field. This demonstrated the standard error was not affected by the measured value. My original test was with Ordinary Kriging, log transformation and a second order trend removal. I will try the Bayesian kriging model to see what happens.
To estimate my average kriging error I am using a dense sample array of wells over my study error to extract the std errors using the GA to points function. I suppose I could possible use a raster to do something similar.
One more thing. I'm guessing the method that I am using is very much similar to the approach of the Densify Sample Network Tool. That is, the DSN tool must add new sites at unknown locations and recalculate the standard error before choosing the next site. I'm assuming they don't face the problem I originally accounted?
The method I'm applying doesn't work with the results using Bayesian Kriging either i.e. my kriging std errors increase as my network densifies. Maybe the method I'm applying is wrong?
Anyone reading this topic and considering performing a similar methodology should also read the following topic, it contains a lot of relevant information: