Interpreting Crosscovariance Cloud Result

[WilliamForney]

Hello User Community,

I am having difficulty interpreting the meaning of this result--please see attached.

Let me pose what I think I can infer from it, and ask that others correct me where I am wrong:  controlling for unidirectionality and anisotropy, the values two datasets tend to covary (i.e. the positive and negative values of the sill on the Y-axis) to a lag distance between points (i.e. the range) of just under 180 meters.  In other words, up to a range of 180 meters in the search direction of 294 degrees, the results indicate that the value of one dataset correlates well with the other dataset's value.

Thanks in advance for correcting any misunderstanding that I may have.  Also, if there are any other inferences that I can make from this result, I would love to hear about them!

[EricKrause]

This is a very strange looking crosscovariance cloud.  It actually looks like the correlation increases up to about 180 meters, then it decreases from there.  This means that points that are 180 meters apart are more highly correlated than points that are 10 meters apart.  This is problematic because it appears to violate the idea that points that are closer are more similar.

It may be possible to use cokriging, then turn the "Shift" option to True.  This will attempt to correct for asymmetric cross-covariance (which you appear to have here).  If the Shift correction doesn't help, this just may not be a good dataset for interpolation.

I'm also concerned about the Crosscovariance Surface on the bottom-left of the graphic.  Maybe you just need to refresh your screen, but you should be able to see a surface there.

If you're able to send the data to ekrause@esri.com, I'll take a look at it and try to give a more specific recommendation.

[WilliamForney]

Hi Eric,

Thanks for being willing to look at the data of this problem--I will send it to you directly via email.  I was struggling to make sense of the Crosscovariance Cloud result (obviously). 

I agree with you that points closer to each other ought to be more similar.  Without much luck, I have been searching high and low in the literature and on the web for usage and interpretation of this geostatistical technique in ArcGIS.  These data are thermal infrared imagery of section of river, and results of the "area solar radiation"  tool with a high-resolution, LiDAR-based DEM surface.... so it seems likely that there ought to be some relationship between the two... and the raw data suggests this, too.  What I have read about cross covariograms and covariance would support that hypothesis.   

Thanks very much for your assistance with this.  Please let me know if you have any questions.  I look forward to hearing about what you find.

Regards, Will.

P.S. I restarted the software, and the graphic of the Crosscovariance Surface about which you were concerned appeared, so no problem there.