Holes in kriged surface where data points exist??

[GailMillar]

Hello,

I am getting an unexpected result when performing universal kriging. There are holes in the kriged surface where data points exist (see attachment). I am having trouble understanding why this is occurring.

Background:
I have applied universal kriging to a data set of air pollutant measurements that have a high spatial density (collected via mobile monitoring). I am investigating universal kriging because the data give indication of a global spatial trend that can be explained in terms of pollutant pooling along the valley bottom (log transformation, second order trend removal). I am interested in the very local variation so have chosen a focused search neighbourhood  (max 15, min 1). The output layer has holes where data points actually exist. If I click on the areas where the holes are in the Searching Neighbourhood Window, the neighbours do not seem to be identifiable. The points are black and the Identify panes says Neighbours 0, Prediction <Not Calculated> (see attachment). I have checked the original data to see if there is some sort of anomaly but there doesn't seem to be and all of the data have values >0 so the log transformation shouldn't be the issue.

I am relatively new to spatial interpolation and am wondering if there is something I am missing.

Thanks for the help!

[EricKrause]

Is it possible to send the data to ekrause@esri.com? 

I'll need the point feature class, and I'll need the xml file for the kriging layer.  You can get the xml by right-clicking the layer in ArcMap and choosing Method Properties.  This will open the Wizard, then click Finish.  The Method Summary window pops up, and clicking Save... will allow you to save the xml file.

[EricKrause]

I should have noticed this when I first looked at the pdf, but the problem is that the areas of no prediction are surrounded by points that lie on the same line.  For second-order trend removal, you need to have at least three distinct x and three distinct y coordinates in the neighborhood around each prediction location (among other restrictions).  So, if all the neighbors fall on the same two lines, there is instability in the predictions, and the prediction can�??t calculate.  As Gail discovered, if you increase the maximum neighbors, you�??ll force more points in that don�??t fall on the same two lines.