Is there a way to specify different measurement errors for each point?

[BrianKinlan]

I have an application where point data derive from several different sources, with different associated uncertainties.  I would like to specify a different measurement error for each point.  When I krig, it will be at non-data locations so both nugget and measurement error will be filtered (thus there is no need to know the type of measurement to produce the kriging predictions, it only needs to be known at the data locations).  Is there a way in Geostatistical Analyst to specify the measurement error so that it links to a table with the same number of rows as the input data, where each row specifies the measurement error (in % or absolute units, either is fine) for the corresponding point?

Thanks,
Brian Kinlan
NOAA National Ocean Service

[EricKrause]

We can do this with the Gaussian Geostatistical Simulations tool.

First, create a kriging model in the Geostatistical Wizard, and don't worry about the measurement error.  Then, use this kriging layer as input to the GGS tool.  Condition on the field you want to interpolate, and specify the conditioning measurement error field.  Do a few dozen simulations, and save the MEAN raster. 

This workflow will result in a raster that takes the non-constant measurement error into account.

Let me know if you need any clarifications or have any questions.

[BrianKinlan]

Thanks, Eric.  This is a helpful and clever trick.  Unfortunately, it may not work for the purposes of my current problem because it's computationally prohibitive.  I am kriging 7-10million points and generating 30m prediction rasters over a ~500x500km area, and it takes several days up to a week just to do 1 iteration of the kriging.  I am concerned that the simulations required for your method would take several months.

I am looking instead for a method of directly incorporating the heterogeneous measurement errors directly into the kriging.  Can I take it from your answer that no method of doing this directly currently exists in ArcGIS?

If so, this is definitely a feature I'd be interested in in for future versions.  Browsing through the recent literature I found this article (link, and attached PDF) that may be of interest.  This type of situation arises frequently in the earth sciences (one good example is with bathymetric data deriving from many different instruments):
http://onlinelibrary.wiley.com/doi/10.1111/j.1541-0420.2011.01563.x/full

Anyway, thanks for your help and any additional insights you might be able to provide on how to incorporate heterogeneous measurement error when the computational burden of 20-50 simulations would be too much.

Best regards,
Brian

[EricKrause]

Thanks for the paper.  I'll give it a read.  You're correct that we don't have a way of incorporating heterogeneous measurement error directly into the kriging. 

The only other thing I can suggest is to condition on a subset of the data and use large number of simulations.  But even then, GGS has a limit on the size of the raster it can output, and a 30m grid on a 500km x 500km area is well beyond that limit.

[BrianKinlan]

Thanks for your help Eric!  We may try a work-around involving dividing the data into smaller tiles.  On that note, can GGS be accessed in a moving window mode, like Moving Window Kriging, or is that feature limited to kriging?

[EricKrause]

GGS is limited to Simple Kriging layers.

[BrianKinlan]

Oh okay - thanks.  I have to admit I have not used GGS in ArcGIS yet, I still prefer Gstat, R/Gstat, GSLIB and SGeMS for their speed, flexibility, and ability to handle large datasets.  But I was very excited to see you had added this functionality  in ArcGIS and am looking forward to using it more as it improves and becomes more flexible/able to handle larger datasets and prediction grids.   It saves a step for me when I can do everything inside ArcGIS rather than having to export, process in another program, and re-import.

Thanks again for your helpful suggestions

Brian