topic Re: some kriging issues in ArcGIS GeoStatistical Analyst Questions

some kriging issues

DirkOostwoud — Fri, 04 Nov 2011 12:09:17 GMT

Hello all,

I'm currently using the Geostatistical Analyst to perform some kriging interpolations, and interpret the results. However, I unfortunately stumbled up some questions, which I hope you have the answers for:
First of all, when assigning weighting values to the points, I noticed that some points are assigned negative values. I understand how they come there (inverse of a matrix), but: what does that mean. How can points account negatively to an unknown point?

Second question gets more clear in the example: I have a point file of monitoring wells measuring phreatic groundwater levels. I want to say something about the maximum distance between these wells in order to have a maximum uncertainty in an area (for instance a village, where houses can be damaged due to high or low water tables). So I set a level: I don't want my standard error to be larger than 20 centimeters, a value that does occur on the prediction error map. I thought that I should take the square of 20 cm, 4cm^2 as semivariance input to the model and that the x-value was then my maximum distance of the wells (which could be easily turned into a preferred well density). However, in the table of the exported semivariogram, this value of 0.04 doesn't exist, in fact, only the non-squared values of the map are in that table. So I wonder: how can it be that the values of the semivariance - which is given in [m^2] - are the same as the values of the prediction error map - given in .

I hope you can help me with it.

Best regards, and thank you in advance,

Erik (Dirk's trainee)

Re: some kriging issues

EricKrause — Fri, 04 Nov 2011 14:04:56 GMT

Good questions.

For your first question, the simplest explanation is that these weights are what the kriging equations indicate is the best linear unbiased predictor for the new location, but I realize that isn't very helpful conceptually. Probably the best way to think about this phenomenon is that a point that receives a negative weight does not have useful or unique information. In other words, the information that the point provides is already contained in other other neighboring points.

For your second question, I think the problem is that you're treating semivariances and standard errors as the same thing (ie, one is a square of the other), but they're actually very different. Semivariances are just squared differences between pairs of measured values that are binned together and averaged by distance. The prediction standard errors come from the kriging equations, which require a semivariogram in order to calculate. So the semivariances and the prediction standard errors are related, but the relationship is complicated and indirect. If your goal is to get all the prediction standard errors under 20cm, adjusting the range (the x-axis of the semivariogram) and other semivariogram parameters generally is not going to work. To reduce standard errors, you need to take more samples in the areas of high standard errors.

If you're seeing the semivariances take on roughly the same values as the prediction standard errors of the output, it's probably just a coincidence. There's no mathematical reason that they would be the same.

Hope that helps. Feel free to ask more questions if that wasn't clear.

Re: some kriging issues

DirkOostwoud — Fri, 04 Nov 2011 14:31:40 GMT

Thank you, Eric, for your quick and helpful reply!
Reading your answer on my second question I think I haven't made my second question sufficiently clear, though, so please give me a second chance:
I have a network of monitoring wells, and I want to optimize it: I want to say on what locations the construction of extra monitoring wells would sufficienty lower the standard error. I thought that it was possible to calculate a 'wanted' semivariance value out of a 'wanted' maximum standard error. Then I could read that 'wanted' semivariance on the Y-axis of the semivariogram and would I get an X-value which forms then the 'wanted maximum distance between monitoring wells'.
I thought it was possible to do so, and to get the semivariance out of the wanted standard error by taking the square of the latter.
But if I'm wrong, is there a different way to do so?

Thank you! 🙂

Re: some kriging issues

EricKrause — Fri, 04 Nov 2011 16:04:58 GMT

We have a tool to do exactly what you need. It's called Densify Sampling Network, and it's in the Geostatistical Analyst toolbox, under Sampling Network Design toolset.

You will use your kriging layer as input, then specify the number of new locations for lowering the overall prediction standard errors. It will create a point feature class that determines the best new locations for monitoring sites. However, this technique attempts to minimize the overall standard errors; it won't give preferences for particular locations (like cities).

If you're only interested in low standard errors near cities of interest, there's another technique you can try. The trick with this technique is that the standard errors only depend on the locations of the data points, not the data values themselves (unless you applied a transformation). In other words, if you add a new point and give it a value of 1, the standard error surface will be the same as using a value of 1 million (this is obviously not true for the prediction surface). So, you can create artificial new points and test how they will affect the standard error surface. The easiest way to do this is to copy your original point feature class, then append new points near cities that you're interested in (you can give them any data value you want). Then use the Create Geostatistical Layer tool. Give the tool the original kriging layer you created with the original points, then provide the appended point feature class for the input dataset(s). Run the tool, then look at the standard error surface and decide if it's acceptable.

But remember, this last paragraph will only work if you did not apply a transformation when doing the kriging. If you did, then the standard errors actually do depend on the data values, so you can't just make up new data values.

As for your idea, I don't think it will work. At least, I don't see how it would work, but maybe I'm just missing something.

Re: some kriging issues

DirkOostwoud — Mon, 07 Nov 2011 06:04:20 GMT

Hi Eric,

Thank you for your useful reply. I'm confident this will help solving my problem. 🙂

Re: some kriging issues

EricKrause — Mon, 07 Nov 2011 16:23:19 GMT

Good to hear. If anything comes up, feel free to ask more questions.