Optimising monitoring networks using Kriging

SimonHarper

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.

Cheers,

Simon 

Eric6346

Hi Simon,

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.

-Eric