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I'm currently trying to use ArcMap 10.5.1 for this analysis:

Thus far, I have taken particulate matter trend estimates at monitoring sites across the U.S. and used Simple (Normal Score - due to slight non-normal distribution) Kriging to interpolate trends in between these sites. While I only have 156 sites, the Krige standard error prediction map shows small standard errors across the region. This suggests to me that the interpolation itself is fairly accurate to the observed data.

However, as was pointed out to me recently, this analysis does not take into account the uncertainty of the trend estimates. In other words, I take a site-specific estimate and then smooth those estimates across locations without accounting for uncertainty at the locations. This seems likely to underestimate uncertainty in the resulting Krige prediction. What I'm looking for is a way to incorporate my uncertainty (I have standard error values for each location) into the trend Krige.

Suggestions I've already received include:

  1. Kriging the standard error at each site as a separate figure to show uncertainty across the region. Ideally, I'd like to find some way to include the standard error into my trend estimate so I only have one Krige prediction map.

  2. Subset my data and cross-validate multiple times to confirm Krige prediction output. This still seems like I am not considering the inherent trend estimate uncertainty though.

Is there any way to include measurement standard error (which is different at each site) in the Krige prediction to reflect uncertainty?

  • You cannot do this in ArcGIS but you may want to look into conditional simulation. Unfortunately, you are at the outside of what is possible in ArcGIS. – Jeffrey Evans Feb 28 '18 at 22:53
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After reaching out to the ESRI community as well, I discovered that you could incorporate uncertainty into a Krige product by using the Gaussian Geostatistical Simulations (GGS) tool in ArcMap. The answer provided by Eric Krause in the following link provides information on how to use this tool to incorporate heterogeneous measurement error into your Krige product.

The replies section has the full answer: https://community.esri.com/thread/87862

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