Kriging Residuals

[StephenVitoria]

Hi

Please forgive me if this is a beginner's question, but I am a beginner 🙂

I have a kriging model of rainfall for an area. For each point rainfall station I have a rainfall total and elevation.
Unfortunately, the root mean squared error is not very good - it's around 13. I wanted to know about different ways to improve my model and reduce the rmse.

I have read that the residuals of kriging (i.e. the actual minus predicted values) for each rainfall station can be themselves kriged and the results of this added back to the original model to improve prediction quality. So my questions are:

1. Is this a valid approach to improving a model, and if so, why?
2. If this is a valid approach, can you provide a quick step by step description of how to add the residual kriging results back to the original kriging model?
3. Do you have any other suggestions for techniques which I could use to improve my kriging results? Note that I also have elevation data, but co-kriging with this hardly seems to improve the model.

I hope this is a sensible question.

Many thanks for all your help

Stephen Vitoria

[EricKrause]

This is a complicated question, but the short answer is that it is not valid to krig on residuals of kriging in ArcGIS. 

To get an idea why it is not valid, you need to know a few things:
1) Kriging is a exact interpolator when you do not use measurment error, so without measurement error your residuals will all be zero.  There would be nothing to krig.
2) ArcGIS only supports homogeneous measurement error where the percent of the nugget explained by measurement error is constant and uncorrelated. 
3) Because we assume the measurement error is uncorrelated, it should have no spatial autocorrelation, so kriging would not be valid.  If your residuals do show spatial autocorrelation, it means that your original kriging model was not fitted correctly.

[StephenVitoria]

Dear Eric

Many thanks for the reply. I had no idea it was such a complicated question, and that probably says volumes about my lack of knowledge 🙂

Thank you for the short answer. At least I know not to pursue that avenue anymore.

All the best

Stephen