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 [m].

I hope you can help me with it.

Best regards, and thank you in advance,

Erik (Dirk's trainee)

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 [m].

I hope you can help me with it.

Best regards, and thank you in advance,

Erik (Dirk's trainee)

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.