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I have about 10 point shapefiles containing a lot of points each. (I would prefer not to join them into one shapefile, it's pain). And I am using interpolation method Topo to Raster to create a DTM. This method can deal with many separate datasets. I'm using ArcGIS 9.3 (and have access to 10).

I would like to get errors of the estimates, to check if they have normal distribution. How can I get the interpolation errors? Like the -e flag option in GRASS.

Is it available only for kriging? Is it the only way, to compute them manually comparing each dataset to the resulting raster? Thank you for advices.

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Although kriging produces a so-called "error map," it is not what it sounds like. To help you appreciate what it is not, I will just remark that once you have specified a variogram model, you can produce that error map with absolutely no data at all. In geostatistics, the errors you are looking for are estimated through conditional simulation. You can do almost the same thing, although it will be painful: you systematically leave out one point from the dataset, recreate the DTM (at least in the neighborhood of the left-out point), and measure its error there. Repeat for all points. –  whuber Jul 2 '13 at 20:13
    
@whuber thank you for the clarification. So what I need is not geostatistical error map, but difference between points and the overlaying cells (the interpolation is not exact). –  nadya Jul 2 '13 at 20:32
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Almost: even when the interpolation is inexact, measuring those differences usually grossly underestimates the errors. To be honest about it, you need to remove some of your data, re-interpolate using the rest, and see how well you did by comparison to the data that had been held out. By doing this many times in a controlled way you can estimate how large the likely errors are when you use all the data. Variants of this are called the "jackknife" (which often is used to cross-validate variogram models for kriging) and, more generally, "bootstrapping." –  whuber Jul 2 '13 at 20:45
    
I'm confused. How do you estimate the error at a point where you don't have the correct value? I don't see how dropping points solves this problem. For the sake of discussion, let's treat this as a 1D problem. Let's say I have data at twice the raster spacing with values 0,1,0,1,0,1,... Linearly interpolating, I'll get .5 at the missing points. Now let's say I drop one of my points, one of the 1s. If I interpolate over this missing point I'll get 0 for the three values between the two 0s, and by the suggestion, I'll estimate my error a 1 at my known point. But that's meaningless as I see it –  Llaves Sep 1 '13 at 4:30
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@Llaves, If a given point has undue influence, to the degree that you are implying, then the assumption of stationarity is not being met. Bootstrap/Jackknife approaches are common and well represented in the literature. A Jackknife holds back a single observation from your model but iterates through all or n-percent of the observations thus, requires n models. You cannot hold all of your data because, even with inexact interpolators, your smoothest error will be around your points. This will provide a bias in the error distribution. –  Jeffrey Evans Dec 5 '13 at 19:28
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2 Answers

Please keep in mind that the topo to raster tool is an implementation of the Hutchinson ANUDEM model. This is a conditional spline model and as such, enforces certain conditions in relation to sinks, drainage, etc... It is also a best approximation based on an iterative multi-scale spline fit. Because of this, estimated elevation may deviate from the observed data and, according to the model, not be an error per se. I am not sure that an error assessment such as RMSE is appropriate in this regard. You could plausibly receive a RMSE that does not represent the quality DEM.

The authors of ANUDEM recommended some qualitative assessment of correctness but there is nothing akin to a variance surface like what is produced in a Kriging model.

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Ordinary kriging provides a standard error map that shows the uncertainty related to the predicted values. Steps:

Right-click the geostatistical layer in the ArcMap table of contents that was created using ordinary kriging and click Change output to Prediction Standard Error.

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Thank you for the attempt, but I am not using kriging and not working with geostatistical layers. Topo to Raster is a completely different method. –  nadya Jul 2 '13 at 20:39
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